Documentation update

184 files changed, 1668 insertions, 1015 deletions

diff --git a/docs/01a85c17.d61de859.js b/docs/01a85c17.f9936b95.js
index 8a433c6..7f541ce 100644
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diff --git a/docs/08185850.26b2b5f8.js b/docs/08185850.26b2b5f8.js
new file mode 100644
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diff --git a/docs/0b24b4d1.5746dd20.js b/docs/0b24b4d1.0b43c69d.js
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",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Desenho_assistido_por_computador"}),"Wikipedia"))),Object(n.b)("h2",{id:"ferramentas-do-menu"},"Ferramentas do menu"),Object(n.b)("p",null,"Todos os objetos criados cont\xeam v\xe1rios atributos gr\xe1ficos, como: posi\xe7\xe3o, orienta\xe7\xe3o, cor, tamanho, etc. Para modific\xe1-los foram inseridas algumas ferramentas intuitivas e de f\xe1cil utiliza\xe7\xe3o, as quais s\xe3o: ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#selecionar"}),Object(n.b)("strong",{parentName:"a"},"selecionar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#mover"}),Object(n.b)("strong",{parentName:"a"},"mover")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#girar"}),Object(n.b)("strong",{parentName:"a"},"girar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#arrastar"}),Object(n.b)("strong",{parentName:"a"},"arrastar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#zoom"}),Object(n.b)("strong",{parentName:"a"},"zoom")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#encaixar"}),Object(n.b)("strong",{parentName:"a"},"encaixar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#copiar-e-colar"}),Object(n.b)("strong",{parentName:"a"},"copiar, colar"))," e ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#excluir"}),Object(n.b)("strong",{parentName:"a"},"excluir")),"."),Object(n.b)("p",null,"Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu Ferramentas"),"."),Object(n.b)("p",null,"Tais ferramentas permitem a ",Object(n.b)("strong",{parentName:"p"},"personaliza\xe7\xe3o"),", ",Object(n.b)("strong",{parentName:"p"},"navega\xe7\xe3o")," e auxiliam a ",Object(n.b)("strong",{parentName:"p"},"cria\xe7\xe3o")," de redes el\xe9tricas de pot\xeancia, assim como diagramas de controle na plataforma."),Object(n.b)("h3",{id:"selecionar"},"Selecionar"),Object(n.b)("p",null,"A sele\xe7\xe3o de um \xfanico objeto \xe9 realizada clicando com o bot\xe3o esquerdo do mouse sobre o elemento, que ser\xe1 identificado pelo contorno em ",Object(n.b)(d,{color:"#80bfff",mdxType:"Highlight"},"azul")," do objeto."),Object(n.b)("p",null,"Para a sele\xe7\xe3o de v\xe1rios objetos simultaneamente \xe9 necess\xe1rio clicar com o bot\xe3o esquerdo do mouse em um local vazio da tela e arrast\xe1-lo, criando assim um ",Object(n.b)("strong",{parentName:"p"},"ret\xe2ngulo de sele\xe7\xe3o")," que ir\xe1 acompanhar o ponteiro do mouse enquanto o bot\xe3o esquerdo estiver pressionado. Ao solt\xe1-lo todos os objetos que intercederem o ret\xe2ngulo ser\xe3o selecionados."),Object(n.b)("p",null,"Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter sele\xe7\xf5es anteriores enquanto novos elementos s\xe3o selecionados."),Object(n.b)("p",null,"Para desmarcar todos os objetos basta clicar em uma \xe1rea sem objetos."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/select.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/select.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"mover"},"Mover"),Object(n.b)("p",null,"Um elemento poder\xe1 ser movido para qualquer local por meio da a\xe7\xe3o ",Object(n.b)("em",{parentName:"p"},"drag-and-drop")," (clicando e arrastando) ou pela ferramenta mover."),Object(n.b)("p",null,"Ao habilitar o \u201cmodo mover\u201d, movendo todos os componentes selecionados \xe0 medida que a posi\xe7\xe3o do mouse \xe9 alterada. Para desabilitar esse modo basta pressionar a tecla Escape do teclado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/move.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/move.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"girar"},"Girar"),Object(n.b)("p",null,"Alguns objetos poder\xe3o ser rotacionados atrav\xe9s da ferramenta girar, acessado pela tecla de atalho \u201cR\u201d, girando o objeto no sentido hor\xe1rio, ou \u201cShift + R\u201d, para o sentido anti-hor\xe1rio (essa op\xe7\xe3o ir\xe1 afetar todos os objetos selecionados). O elemento tamb\xe9m pode ser rotacionado pelo ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu Ferramentas")," ou ao acessar o menu de contexto clicando com o bot\xe3o direito sobre o elemento."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O menu de contexto somente ser\xe1 exibido se o elemento estiver selecionado."))),Object(n.b)("p",null,"Ao utilizar essa ferramenta os objetos ir\xe3o girar 45\xba a partir do seu ponto de origem. Para atingir a angula\xe7\xe3o pretendida basta repetir o processo de rota\xe7\xe3o."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/rotate.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/rotate.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"arrastar"},"Arrastar"),Object(n.b)("p",null,"Tr\xeas ferramentas muito \xfateis na navega\xe7\xe3o do circuito, principalmente em grandes redes, s\xe3o: arrastar, zoom e encaixar."),Object(n.b)("p",null,"A ferramenta arrastar possibilita mover todo o circuito ",Object(n.b)("strong",{parentName:"p"},"preservando as posi\xe7\xf5es relativas entre os elementos"),". Esta ferramenta pode ser acessada pelo submenu \u201cFerramentas\u201d ou ",Object(n.b)("strong",{parentName:"p"},"mantendo pressionada o ",Object(n.b)("em",{parentName:"strong"},"scroll")," do mouse"),", ativando assim o \u201cmodo arrastar\u201d. Ao ativ\xe1-lo todo o circuito ser\xe1 movido clicando e arrastando na dire\xe7\xe3o desejada."),Object(n.b)("p",null,"Para sair do \u201cmodo arrastar\u201d basta pressionar a tecla Escape do teclado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/drag.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/drag.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"zoom"},"Zoom"),Object(n.b)("p",null,"O zoom ser\xe1 aplicado ao utilizar o ",Object(n.b)("strong",{parentName:"p"},"scroll do mouse")," para mais ou menos zoom. A ferramenta zoom ir\xe1 aproximar ou distanciar o circuito a partir da posi\xe7\xe3o do ponteiro do mouse na tela para encontrar objetos ou destaca-los."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/zoom.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/zoom.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"encaixar"},"Encaixar"),Object(n.b)("p",null,"A ferramenta encaixar ir\xe1 mover o circuito e aplicar o zoom necess\xe1rio para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada atrav\xe9s do submenu \u201cFerramentas\u201d ou pela combina\xe7\xe3o de teclas \u201cShift + F\u201d."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/fit.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/fit.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"copiar-e-colar"},"Copiar e Colar"),Object(n.b)("p",null,"Duas ferramentas importantes durante o processo de cria\xe7\xe3o da rede el\xe9trica de pot\xeancia no ",Object(n.b)("em",{parentName:"p"},"software")," s\xe3o copiar e colar. Qualquer circuito criado no PSP-UFU poder\xe1 ser duplicado completamente ou parcialmente no mesmo projeto ou em m\xfaltiplos atrav\xe9s dessas ferramentas."),Object(n.b)("p",null,"Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu \u201cFerramentas\u201d ou pressionando a combina\xe7\xe3o das teclas \u201cCtrl + C\u201d, ent\xe3o os dados do circuito ser\xe3o copiados para a \xe1rea de transfer\xeancia. Ao copiar um circuito ele poder\xe1 ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combina\xe7\xe3o das teclas \u201cCtrl + V\u201d."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/copyPaste.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/copyPaste.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"excluir"},"Excluir"),Object(n.b)("p",null,"Qualquer objeto poder\xe1 ser exclu\xeddo do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o bot\xe3o direito sobre o elemento selecionado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/delete.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/delete.webm"),type:"video/webm"})),Object(n.b)("h2",{id:"personaliza\xe7\xe3o-gr\xe1fica-os-elementos"},"Personaliza\xe7\xe3o gr\xe1fica os elementos"),Object(n.b)("p",null,"Alguns elementos permitem sua personaliza\xe7\xe3o gr\xe1fica, como as barras e linhas."),Object(n.b)("h3",{id:"barra"},"Barra"),Object(n.b)("p",null,"No caso dos barramentos, pode-se alterar o ",Object(n.b)("strong",{parentName:"p"},"comprimento da barra")," clicando e arrastando no ",Object(n.b)("em",{parentName:"p"},"pickbox")," exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado."),Object(n.b)("h3",{id:"linha"},"Linha"),Object(n.b)("p",null,"As linhas podem ser inseridas com ",Object(n.b)("strong",{parentName:"p"},'"n\xf3s" (pontos de ancoragem)'),", personalizando a disposi\xe7\xe3o das linhas no diagrama unifilar. Esses n\xf3s s\xe3o inseridos durante o processo de cria\xe7\xe3o do elemento, anteriormente \xe0 sele\xe7\xe3o da segunda barra."),Object(n.b)("p",null,"Ap\xf3s a sua inser\xe7\xe3o, novos n\xf3s podem ser anexados pelo menu de contexto acessado ao clicar com o bot\xe3o direito sobre a linha selecionada. Sua remo\xe7\xe3o tamb\xe9m \xe9 alcan\xe7ada por uma op\xe7\xe3o do menu de contexto."),Object(n.b)("p",null,"Assim como nos barramentos, a altera\xe7\xe3o da posi\xe7\xe3o dos n\xf3s \xe9 obtida clicando e arrastando o ",Object(n.b)("em",{parentName:"p"},"pickbox")," exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/graphicPropsChange.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/graphicPropsChange.webm"),type:"video/webm"})),Object(n.b)("h2",{id:"conex\xe3o-e-desconex\xe3o-de-elemetos-na-barra"},"Conex\xe3o e desconex\xe3o de elemetos na barra"),Object(n.b)("p",null,"Os elementos podem ser desconectados e reconectados \xe0s barras ap\xf3s sua inser\xe7\xe3o somente pela ferramenta ",Object(n.b)("em",{parentName:"p"},"drag-and-drop"),". Para isso, o elemento deve ser selecionado e o seu n\xf3 de conex\xe3o deve ser arrastado para o local requerido."),Object(n.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O elemento a ser desconectado/reconectado ",Object(n.b)("strong",{parentName:"p"},"deve ser previamente selecionado")," para efetuar a opera\xe7\xe3o. Caso contr\xe1rio a barra ser\xe1 movida ou nenhuma opera\xe7\xe3o ser\xe1 realizada."))),Object(n.b)("p",null,"No caso de desconex\xe3o, o elemento ser\xe1 automaticamente removido da simula\xe7\xe3o, sendo indicado pela sua cor (o elemento passa a ter cor ",Object(n.b)(d,{color:"#7f7f7f",mdxType:"Highlight"},"cinza"),")."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Ao reconectar o elemento ao circuito, deve-se ",Object(n.b)("strong",{parentName:"p"},'atentar para estado do seu "disjuntor"'),", indicado por um quadrado pr\xf3ximo ao seu n\xf3 de conex\xe3o. 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No caso do ",Object(n.b)("em",{parentName:"p"},"design"),", este pode estar ligado especificamente a todas as suas vertentes (produtos como vestu\xe1rio, eletroeletr\xf4nicos, automobil\xedsticos, etc.), de modo que os jarg\xf5es de cada especialidade s\xe3o incorporados na interface de cada programa. ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Desenho_assistido_por_computador"}),"Wikipedia"))),Object(n.b)("h2",{id:"ferramentas-do-menu"},"Ferramentas do menu"),Object(n.b)("p",null,"Todos os objetos criados cont\xeam v\xe1rios atributos gr\xe1ficos, como: posi\xe7\xe3o, orienta\xe7\xe3o, cor, tamanho, etc. Para modific\xe1-los foram inseridas algumas ferramentas intuitivas e de f\xe1cil utiliza\xe7\xe3o, as quais s\xe3o: ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#selecionar"}),Object(n.b)("strong",{parentName:"a"},"selecionar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#mover"}),Object(n.b)("strong",{parentName:"a"},"mover")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#girar"}),Object(n.b)("strong",{parentName:"a"},"girar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#arrastar"}),Object(n.b)("strong",{parentName:"a"},"arrastar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#zoom"}),Object(n.b)("strong",{parentName:"a"},"zoom")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#encaixar"}),Object(n.b)("strong",{parentName:"a"},"encaixar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#copiar-e-colar"}),Object(n.b)("strong",{parentName:"a"},"copiar, colar"))," e ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#excluir"}),Object(n.b)("strong",{parentName:"a"},"excluir")),"."),Object(n.b)("p",null,"Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu Ferramentas"),"."),Object(n.b)("p",null,"Tais ferramentas permitem a ",Object(n.b)("strong",{parentName:"p"},"personaliza\xe7\xe3o"),", ",Object(n.b)("strong",{parentName:"p"},"navega\xe7\xe3o")," e auxiliam a ",Object(n.b)("strong",{parentName:"p"},"cria\xe7\xe3o")," de redes el\xe9tricas de pot\xeancia, assim como diagramas de controle na plataforma."),Object(n.b)("h3",{id:"selecionar"},"Selecionar"),Object(n.b)("p",null,"A sele\xe7\xe3o de um \xfanico objeto \xe9 realizada clicando com o bot\xe3o esquerdo do mouse sobre o elemento, que ser\xe1 identificado pelo contorno em ",Object(n.b)(d,{color:"#80bfff",mdxType:"Highlight"},"azul")," do objeto."),Object(n.b)("p",null,"Para a sele\xe7\xe3o de v\xe1rios objetos simultaneamente \xe9 necess\xe1rio clicar com o bot\xe3o esquerdo do mouse em um local vazio da tela e arrast\xe1-lo, criando assim um ",Object(n.b)("strong",{parentName:"p"},"ret\xe2ngulo de sele\xe7\xe3o")," que ir\xe1 acompanhar o ponteiro do mouse enquanto o bot\xe3o esquerdo estiver pressionado. Ao solt\xe1-lo todos os objetos que intercederem o ret\xe2ngulo ser\xe3o selecionados."),Object(n.b)("p",null,"Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter sele\xe7\xf5es anteriores enquanto novos elementos s\xe3o selecionados."),Object(n.b)("p",null,"Para desmarcar todos os objetos basta clicar em uma \xe1rea sem objetos."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/select.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/select.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"mover"},"Mover"),Object(n.b)("p",null,"Um elemento poder\xe1 ser movido para qualquer local por meio da a\xe7\xe3o ",Object(n.b)("em",{parentName:"p"},"drag-and-drop")," (clicando e arrastando) ou pela ferramenta mover."),Object(n.b)("p",null,"Ao habilitar o \u201cmodo mover\u201d, movendo todos os componentes selecionados \xe0 medida que a posi\xe7\xe3o do mouse \xe9 alterada. Para desabilitar esse modo basta pressionar a tecla Escape do teclado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/move.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/move.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"girar"},"Girar"),Object(n.b)("p",null,"Alguns objetos poder\xe3o ser rotacionados atrav\xe9s da ferramenta girar, acessado pela tecla de atalho \u201cR\u201d, girando o objeto no sentido hor\xe1rio, ou \u201cShift + R\u201d, para o sentido anti-hor\xe1rio (essa op\xe7\xe3o ir\xe1 afetar todos os objetos selecionados). O elemento tamb\xe9m pode ser rotacionado pelo ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu Ferramentas")," ou ao acessar o menu de contexto clicando com o bot\xe3o direito sobre o elemento."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O menu de contexto somente ser\xe1 exibido se o elemento estiver selecionado."))),Object(n.b)("p",null,"Ao utilizar essa ferramenta os objetos ir\xe3o girar 45\xba a partir do seu ponto de origem. Para atingir a angula\xe7\xe3o pretendida basta repetir o processo de rota\xe7\xe3o."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/rotate.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/rotate.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"arrastar"},"Arrastar"),Object(n.b)("p",null,"Tr\xeas ferramentas muito \xfateis na navega\xe7\xe3o do circuito, principalmente em grandes redes, s\xe3o: arrastar, zoom e encaixar."),Object(n.b)("p",null,"A ferramenta arrastar possibilita mover todo o circuito ",Object(n.b)("strong",{parentName:"p"},"preservando as posi\xe7\xf5es relativas entre os elementos"),". Esta ferramenta pode ser acessada pelo submenu \u201cFerramentas\u201d ou ",Object(n.b)("strong",{parentName:"p"},"mantendo pressionada o ",Object(n.b)("em",{parentName:"strong"},"scroll")," do mouse"),", ativando assim o \u201cmodo arrastar\u201d. Ao ativ\xe1-lo todo o circuito ser\xe1 movido clicando e arrastando na dire\xe7\xe3o desejada."),Object(n.b)("p",null,"Para sair do \u201cmodo arrastar\u201d basta pressionar a tecla Escape do teclado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/drag.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/drag.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"zoom"},"Zoom"),Object(n.b)("p",null,"O zoom ser\xe1 aplicado ao utilizar o ",Object(n.b)("strong",{parentName:"p"},"scroll do mouse")," para mais ou menos zoom. A ferramenta zoom ir\xe1 aproximar ou distanciar o circuito a partir da posi\xe7\xe3o do ponteiro do mouse na tela para encontrar objetos ou destaca-los."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/zoom.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/zoom.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"encaixar"},"Encaixar"),Object(n.b)("p",null,"A ferramenta encaixar ir\xe1 mover o circuito e aplicar o zoom necess\xe1rio para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada atrav\xe9s do submenu \u201cFerramentas\u201d ou pela combina\xe7\xe3o de teclas \u201cShift + F\u201d."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/fit.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/fit.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"copiar-e-colar"},"Copiar e Colar"),Object(n.b)("p",null,"Duas ferramentas importantes durante o processo de cria\xe7\xe3o da rede el\xe9trica de pot\xeancia no ",Object(n.b)("em",{parentName:"p"},"software")," s\xe3o copiar e colar. Qualquer circuito criado no PSP-UFU poder\xe1 ser duplicado completamente ou parcialmente no mesmo projeto ou em m\xfaltiplos atrav\xe9s dessas ferramentas."),Object(n.b)("p",null,"Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu \u201cFerramentas\u201d ou pressionando a combina\xe7\xe3o das teclas \u201cCtrl + C\u201d, ent\xe3o os dados do circuito ser\xe3o copiados para a \xe1rea de transfer\xeancia. Ao copiar um circuito ele poder\xe1 ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combina\xe7\xe3o das teclas \u201cCtrl + V\u201d."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/copyPaste.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/copyPaste.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"excluir"},"Excluir"),Object(n.b)("p",null,"Qualquer objeto poder\xe1 ser exclu\xeddo do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o bot\xe3o direito sobre o elemento selecionado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/delete.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/delete.webm"),type:"video/webm"})),Object(n.b)("h2",{id:"personaliza\xe7\xe3o-gr\xe1fica-os-elementos"},"Personaliza\xe7\xe3o gr\xe1fica os elementos"),Object(n.b)("p",null,"Alguns elementos permitem sua personaliza\xe7\xe3o gr\xe1fica, como as barras e linhas."),Object(n.b)("h3",{id:"barra"},"Barra"),Object(n.b)("p",null,"No caso dos barramentos, pode-se alterar o ",Object(n.b)("strong",{parentName:"p"},"comprimento da barra")," clicando e arrastando no ",Object(n.b)("em",{parentName:"p"},"pickbox")," exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado."),Object(n.b)("h3",{id:"linha"},"Linha"),Object(n.b)("p",null,"As linhas podem ser inseridas com ",Object(n.b)("strong",{parentName:"p"},'"n\xf3s" (pontos de ancoragem)'),", personalizando a disposi\xe7\xe3o das linhas no diagrama unifilar. Esses n\xf3s s\xe3o inseridos durante o processo de cria\xe7\xe3o do elemento, anteriormente \xe0 sele\xe7\xe3o da segunda barra."),Object(n.b)("p",null,"Ap\xf3s a sua inser\xe7\xe3o, novos n\xf3s podem ser anexados pelo menu de contexto acessado ao clicar com o bot\xe3o direito sobre a linha selecionada. Sua remo\xe7\xe3o tamb\xe9m \xe9 alcan\xe7ada por uma op\xe7\xe3o do menu de contexto."),Object(n.b)("p",null,"Assim como nos barramentos, a altera\xe7\xe3o da posi\xe7\xe3o dos n\xf3s \xe9 obtida clicando e arrastando o ",Object(n.b)("em",{parentName:"p"},"pickbox")," exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/graphicPropsChange.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/graphicPropsChange.webm"),type:"video/webm"})),Object(n.b)("h2",{id:"conex\xe3o-e-desconex\xe3o-de-elemetos-na-barra"},"Conex\xe3o e desconex\xe3o de elemetos na barra"),Object(n.b)("p",null,"Os elementos podem ser desconectados e reconectados \xe0s barras ap\xf3s sua inser\xe7\xe3o somente pela ferramenta ",Object(n.b)("em",{parentName:"p"},"drag-and-drop"),". Para isso, o elemento deve ser selecionado e o seu n\xf3 de conex\xe3o deve ser arrastado para o local requerido."),Object(n.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O elemento a ser desconectado/reconectado ",Object(n.b)("strong",{parentName:"p"},"deve ser previamente selecionado")," para efetuar a opera\xe7\xe3o. Caso contr\xe1rio a barra ser\xe1 movida ou nenhuma opera\xe7\xe3o ser\xe1 realizada."))),Object(n.b)("p",null,"No caso de desconex\xe3o, o elemento ser\xe1 automaticamente removido da simula\xe7\xe3o, sendo indicado pela sua cor (o elemento passa a ter cor ",Object(n.b)(d,{color:"#7f7f7f",mdxType:"Highlight"},"cinza"),")."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Ao reconectar o elemento ao circuito, deve-se ",Object(n.b)("strong",{parentName:"p"},'atentar para estado do seu "disjuntor"'),", indicado por um quadrado pr\xf3ximo ao seu n\xf3 de conex\xe3o. Um elemento reconectado volta ao circuito com seu disjuntor aberto (",Object(n.b)(d,{color:"#ff1919",mdxType:"Highlight"},"vermelho"),"), sendo necess\xe1rio clicar sobre o mesmo a fim de inserir o elemento no circuito."))),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/disconnect.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/disconnect.webm"),type:"video/webm"})))}m.isMDXComponent=!0},165:function(e,o,a){"use strict";var t=a(0),r=a(35);o.a=function(){return Object(t.useContext)(r.a)}},166:function(e,o,a){"use strict";a.d(o,"a",(function(){return l})),a.d(o,"b",(function(){return u}));var t=a(0),r=a.n(t);function n(e,o,a){return o in e?Object.defineProperty(e,o,{value:a,enumerable:!0,configurable:!0,writable:!0}):e[o]=a,e}function s(e,o){var a=Object.keys(e);if(Object.getOwnPropertySymbols){var t=Object.getOwnPropertySymbols(e);o&&(t=t.filter((function(o){return Object.getOwnPropertyDescriptor(e,o).enumerable}))),a.push.apply(a,t)}return a}function c(e){for(var o=1;o<arguments.length;o++){var a=null!=arguments[o]?arguments[o]:{};o%2?s(Object(a),!0).forEach((function(o){n(e,o,a[o])})):Object.getOwnPropertyDescriptors?Object.defineProperties(e,Object.getOwnPropertyDescriptors(a)):s(Object(a)).forEach((function(o){Object.defineProperty(e,o,Object.getOwnPropertyDescriptor(a,o))}))}return e}function i(e,o){if(null==e)return{};var a,t,r=function(e,o){if(null==e)return{};var a,t,r={},n=Object.keys(e);for(t=0;t<n.length;t++)a=n[t],o.indexOf(a)>=0||(r[a]=e[a]);return r}(e,o);if(Object.getOwnPropertySymbols){var n=Object.getOwnPropertySymbols(e);for(t=0;t<n.length;t++)a=n[t],o.indexOf(a)>=0||Object.prototype.propertyIsEnumerable.call(e,a)&&(r[a]=e[a])}return r}var d=r.a.createContext({}),b=function(e){var o=r.a.useContext(d),a=o;return e&&(a="function"==typeof e?e(o):c(c({},o),e)),a},l=function(e){var o=b(e.components);return r.a.createElement(d.Provider,{value:o},e.children)},m={inlineCode:"code",wrapper:function(e){var o=e.children;return r.a.createElement(r.a.Fragment,{},o)}},p=r.a.forwardRef((function(e,o){var a=e.components,t=e.mdxType,n=e.originalType,s=e.parentName,d=i(e,["components","mdxType","originalType","parentName"]),l=b(a),p=t,u=l["".concat(s,".").concat(p)]||l[p]||m[p]||n;return a?r.a.createElement(u,c(c({ref:o},d),{},{components:a})):r.a.createElement(u,c({ref:o},d))}));function u(e,o){var a=arguments,t=o&&o.mdxType;if("string"==typeof e||t){var n=a.length,s=new Array(n);s[0]=p;var c={};for(var i in o)hasOwnProperty.call(o,i)&&(c[i]=o[i]);c.originalType=e,c.mdxType="string"==typeof e?e:t,s[1]=c;for(var d=2;d<n;d++)s[d]=a[d];return r.a.createElement.apply(null,s)}return r.a.createElement.apply(null,a)}p.displayName="MDXCreateElement"},167:function(e,o,a){"use strict";a.d(o,"a",(function(){return n}));var t=a(165),r=a(168);function n(e,{forcePrependBaseUrl:o=!1,absolute:a=!1}={}){const{siteConfig:{baseUrl:n="/",url:s}={}}=Object(t.a)();if(!e)return e;if(o)return n+e;if(!Object(r.a)(e))return e;const c=n+e.replace(/^\//,"");return a?s+c:c}},168:function(e,o,a){"use strict";function t(e){return!1===/^(https?:|\/\/|mailto:|tel:)/.test(e)}a.d(o,"a",(function(){return t}))}}]);
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diff --git a/docs/0bf0c192.f4c281f5.js b/docs/0bf0c192.0c12431b.js
index 1e42899..754e443 100644
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+++ b/docs/0bf0c192.0c12431b.js
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0===this.tagFilters&&0===this.tagRefinements.length?this:this.setQueryParameters({tagFilters:void 0,tagRefinements:[]})},setIndex:function(e){return e===this.index?this:this.setQueryParameters({index:e})},setQuery:function(e){return e===this.query?this:this.setQueryParameters({query:e})},setPage:function(e){return e===this.page?this:this.setQueryParameters({page:e})},setFacets:function(e){return this.setQueryParameters({facets:e})},setDisjunctiveFacets:function(e){return this.setQueryParameters({disjunctiveFacets:e})},setHitsPerPage:function(e){return this.hitsPerPage===e?this:this.setQueryParameters({hitsPerPage:e})},setTypoTolerance:function(e){return this.typoTolerance===e?this:this.setQueryParameters({typoTolerance:e})},addNumericRefinement:function(e,t,i){var r=c(i);if(this.isNumericRefined(e,t,r))return this;var a=n({},this.numericRefinements);return a[e]=n({},a[e]),a[e][t]?(a[e][t]=a[e][t].slice(),a[e][t].push(r)):a[e][t]=[r],this.setQueryParameters({numericRefinements:a})},getConjunctiveRefinements:function(e){return this.isConjunctiveFacet(e)&&this.facetsRefinements[e]||[]},getDisjunctiveRefinements:function(e){return this.isDisjunctiveFacet(e)&&this.disjunctiveFacetsRefinements[e]||[]},getHierarchicalRefinement:function(e){return this.hierarchicalFacetsRefinements[e]||[]},getExcludeRefinements:function(e){return this.isConjunctiveFacet(e)&&this.facetsExcludes[e]||[]},removeNumericRefinement:function(e,t,i){return void 0!==i?this.isNumericRefined(e,t,i)?this.setQueryParameters({numericRefinements:this._clearNumericRefinements((function(n,r){return r===e&&n.op===t&&f(n.val,c(i))}))}):this:void 0!==t?this.isNumericRefined(e,t)?this.setQueryParameters({numericRefinements:this._clearNumericRefinements((function(i,n){return n===e&&i.op===t}))}):this:this.isNumericRefined(e)?this.setQueryParameters({numericRefinements:this._clearNumericRefinements((function(t,i){return i===e}))}):this},getNumericRefinements:function(e){return this.numericRefinements[e]||{}},getNumericRefinement:function(e,t){return this.numericRefinements[e]&&this.numericRefinements[e][t]},_clearNumericRefinements:function(e){if(void 0===e)return o(this.numericRefinements)?{}:this.numericRefinements;if("string"==typeof e)return o(this.numericRefinements[e])?u(this.numericRefinements,[e]):this.numericRefinements;if("function"==typeof e){var t=!1,i=this.numericRefinements,n=Object.keys(i).reduce((function(n,r){var a=i[r],s={};return a=a||{},Object.keys(a).forEach((function(i){var n=a[i]||[],c=[];n.forEach((function(t){e({val:t,op:i},r,"numeric")||c.push(t)})),c.length!==n.length&&(t=!0),s[i]=c})),n[r]=s,n}),{});return t?n:this.numericRefinements}},addFacet:function(e){return this.isConjunctiveFacet(e)?this:this.setQueryParameters({facets:this.facets.concat([e])})},addDisjunctiveFacet:function(e){return this.isDisjunctiveFacet(e)?this:this.setQueryParameters({disjunctiveFacets:this.disjunctiveFacets.concat([e])})},addHierarchicalFacet:function(e){if(this.isHierarchicalFacet(e.name))throw new Error("Cannot declare two hierarchical facets with the same name: `"+e.name+"`");return this.setQueryParameters({hierarchicalFacets:this.hierarchicalFacets.concat([e])})},addFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return h.isRefined(this.facetsRefinements,e,t)?this:this.setQueryParameters({facetsRefinements:h.addRefinement(this.facetsRefinements,e,t)})},addExcludeRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return h.isRefined(this.facetsExcludes,e,t)?this:this.setQueryParameters({facetsExcludes:h.addRefinement(this.facetsExcludes,e,t)})},addDisjunctiveFacetRefinement:function(e,t){if(!this.isDisjunctiveFacet(e))throw new Error(e+" is not defined in the disjunctiveFacets attribute of the helper configuration");return h.isRefined(this.disjunctiveFacetsRefinements,e,t)?this:this.setQueryParameters({disjunctiveFacetsRefinements:h.addRefinement(this.disjunctiveFacetsRefinements,e,t)})},addTagRefinement:function(e){if(this.isTagRefined(e))return this;var t={tagRefinements:this.tagRefinements.concat(e)};return this.setQueryParameters(t)},removeFacet:function(e){return this.isConjunctiveFacet(e)?this.clearRefinements(e).setQueryParameters({facets:this.facets.filter((function(t){return t!==e}))}):this},removeDisjunctiveFacet:function(e){return this.isDisjunctiveFacet(e)?this.clearRefinements(e).setQueryParameters({disjunctiveFacets:this.disjunctiveFacets.filter((function(t){return t!==e}))}):this},removeHierarchicalFacet:function(e){return this.isHierarchicalFacet(e)?this.clearRefinements(e).setQueryParameters({hierarchicalFacets:this.hierarchicalFacets.filter((function(t){return t.name!==e}))}):this},removeFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return h.isRefined(this.facetsRefinements,e,t)?this.setQueryParameters({facetsRefinements:h.removeRefinement(this.facetsRefinements,e,t)}):this},removeExcludeRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return h.isRefined(this.facetsExcludes,e,t)?this.setQueryParameters({facetsExcludes:h.removeRefinement(this.facetsExcludes,e,t)}):this},removeDisjunctiveFacetRefinement:function(e,t){if(!this.isDisjunctiveFacet(e))throw new Error(e+" is not defined in the disjunctiveFacets attribute of the helper configuration");return h.isRefined(this.disjunctiveFacetsRefinements,e,t)?this.setQueryParameters({disjunctiveFacetsRefinements:h.removeRefinement(this.disjunctiveFacetsRefinements,e,t)}):this},removeTagRefinement:function(e){if(!this.isTagRefined(e))return this;var t={tagRefinements:this.tagRefinements.filter((function(t){return t!==e}))};return this.setQueryParameters(t)},toggleRefinement:function(e,t){return this.toggleFacetRefinement(e,t)},toggleFacetRefinement:function(e,t){if(this.isHierarchicalFacet(e))return this.toggleHierarchicalFacetRefinement(e,t);if(this.isConjunctiveFacet(e))return this.toggleConjunctiveFacetRefinement(e,t);if(this.isDisjunctiveFacet(e))return this.toggleDisjunctiveFacetRefinement(e,t);throw new Error("Cannot refine the undeclared facet "+e+"; it should be added to the helper options facets, disjunctiveFacets or hierarchicalFacets")},toggleConjunctiveFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return this.setQueryParameters({facetsRefinements:h.toggleRefinement(this.facetsRefinements,e,t)})},toggleExcludeFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return this.setQueryParameters({facetsExcludes:h.toggleRefinement(this.facetsExcludes,e,t)})},toggleDisjunctiveFacetRefinement:function(e,t){if(!this.isDisjunctiveFacet(e))throw new Error(e+" is not defined in the disjunctiveFacets attribute of the helper configuration");return this.setQueryParameters({disjunctiveFacetsRefinements:h.toggleRefinement(this.disjunctiveFacetsRefinements,e,t)})},toggleHierarchicalFacetRefinement:function(e,t){if(!this.isHierarchicalFacet(e))throw new Error(e+" is not defined in the hierarchicalFacets attribute of the helper configuration");var i=this._getHierarchicalFacetSeparator(this.getHierarchicalFacetByName(e)),n={};return void 0!==this.hierarchicalFacetsRefinements[e]&&this.hierarchicalFacetsRefinements[e].length>0&&(this.hierarchicalFacetsRefinements[e][0]===t||0===this.hierarchicalFacetsRefinements[e][0].indexOf(t+i))?-1===t.indexOf(i)?n[e]=[]:n[e]=[t.slice(0,t.lastIndexOf(i))]:n[e]=[t],this.setQueryParameters({hierarchicalFacetsRefinements:r({},n,this.hierarchicalFacetsRefinements)})},addHierarchicalFacetRefinement:function(e,t){if(this.isHierarchicalFacetRefined(e))throw new Error(e+" is already refined.");if(!this.isHierarchicalFacet(e))throw new Error(e+" is not defined in the hierarchicalFacets attribute of the helper configuration.");var i={};return i[e]=[t],this.setQueryParameters({hierarchicalFacetsRefinements:r({},i,this.hierarchicalFacetsRefinements)})},removeHierarchicalFacetRefinement:function(e){if(!this.isHierarchicalFacetRefined(e))return this;var t={};return t[e]=[],this.setQueryParameters({hierarchicalFacetsRefinements:r({},t,this.hierarchicalFacetsRefinements)})},toggleTagRefinement:function(e){return this.isTagRefined(e)?this.removeTagRefinement(e):this.addTagRefinement(e)},isDisjunctiveFacet:function(e){return this.disjunctiveFacets.indexOf(e)>-1},isHierarchicalFacet:function(e){return void 0!==this.getHierarchicalFacetByName(e)},isConjunctiveFacet:function(e){return this.facets.indexOf(e)>-1},isFacetRefined:function(e,t){return!!this.isConjunctiveFacet(e)&&h.isRefined(this.facetsRefinements,e,t)},isExcludeRefined:function(e,t){return!!this.isConjunctiveFacet(e)&&h.isRefined(this.facetsExcludes,e,t)},isDisjunctiveFacetRefined:function(e,t){return!!this.isDisjunctiveFacet(e)&&h.isRefined(this.disjunctiveFacetsRefinements,e,t)},isHierarchicalFacetRefined:function(e,t){if(!this.isHierarchicalFacet(e))return!1;var i=this.getHierarchicalRefinement(e);return t?-1!==i.indexOf(t):i.length>0},isNumericRefined:function(e,t,i){if(void 0===i&&void 0===t)return!!this.numericRefinements[e];var n=this.numericRefinements[e]&&void 0!==this.numericRefinements[e][t];if(void 0===i||!n)return n;var r,a,u=c(i),o=void 0!==(r=this.numericRefinements[e][t],a=u,s(r,(function(e){return f(e,a)})));return n&&o},isTagRefined:function(e){return-1!==this.tagRefinements.indexOf(e)},getRefinedDisjunctiveFacets:function(){var e=this,t=a(Object.keys(this.numericRefinements).filter((function(t){return Object.keys(e.numericRefinements[t]).length>0})),this.disjunctiveFacets);return Object.keys(this.disjunctiveFacetsRefinements).filter((function(t){return e.disjunctiveFacetsRefinements[t].length>0})).concat(t).concat(this.getRefinedHierarchicalFacets())},getRefinedHierarchicalFacets:function(){var e=this;return a(this.hierarchicalFacets.map((function(e){return e.name})),Object.keys(this.hierarchicalFacetsRefinements).filter((function(t){return e.hierarchicalFacetsRefinements[t].length>0})))},getUnrefinedDisjunctiveFacets:function(){var e=this.getRefinedDisjunctiveFacets();return this.disjunctiveFacets.filter((function(t){return-1===e.indexOf(t)}))},managedParameters:["index","facets","disjunctiveFacets","facetsRefinements","facetsExcludes","disjunctiveFacetsRefinements","numericRefinements","tagRefinements","hierarchicalFacets","hierarchicalFacetsRefinements"],getQueryParams:function(){var e=this.managedParameters,t={},i=this;return Object.keys(this).forEach((function(n){var r=i[n];-1===e.indexOf(n)&&void 0!==r&&(t[n]=r)})),t},setQueryParameter:function(e,t){if(this[e]===t)return this;var i={};return i[e]=t,this.setQueryParameters(i)},setQueryParameters:function(e){if(!e)return this;var t=l.validate(this,e);if(t)throw t;var i=this,n=l._parseNumbers(e),r=Object.keys(this).reduce((function(e,t){return e[t]=i[t],e}),{}),a=Object.keys(n).reduce((function(e,t){var i=void 0!==e[t],r=void 0!==n[t];return i&&!r?u(e,[t]):(r&&(e[t]=n[t]),e)}),r);return new this.constructor(a)},resetPage:function(){return void 0===this.page?this:this.setPage(0)},_getHierarchicalFacetSortBy:function(e){return e.sortBy||["isRefined:desc","name:asc"]},_getHierarchicalFacetSeparator:function(e){return e.separator||" > "},_getHierarchicalRootPath:function(e){return e.rootPath||null},_getHierarchicalShowParentLevel:function(e){return"boolean"!=typeof e.showParentLevel||e.showParentLevel},getHierarchicalFacetByName:function(e){return s(this.hierarchicalFacets,(function(t){return t.name===e}))},getHierarchicalFacetBreadcrumb:function(e){if(!this.isHierarchicalFacet(e))return[];var t=this.getHierarchicalRefinement(e)[0];if(!t)return[];var i=this._getHierarchicalFacetSeparator(this.getHierarchicalFacetByName(e));return t.split(i).map((function(e){return e.trim()}))},toString:function(){return JSON.stringify(this,null,2)}},e.exports=l},205:function(e,t,i){"use strict";e.exports=function(e,t){if(null===e)return{};var i,n,r={},a=Object.keys(e);for(n=0;n<a.length;n++)i=a[n],t.indexOf(i)>=0||(r[i]=e[i]);return r}},206:function(e,t,i){"use strict";var n=i(180),r=i(181),a=i(207),s=i(252),c=i(177),u=i(253),o=i(208),h=i(254);function f(e){var t={};return e.forEach((function(e,i){t[e]=i})),t}function l(e,t,i){t&&t[i]&&(e.stats=t[i])}function m(e,t){var i=t[0];this._rawResults=t,this.query=i.query,this.parsedQuery=i.parsedQuery,this.hits=i.hits,this.index=i.index,this.hitsPerPage=i.hitsPerPage,this.nbHits=i.nbHits,this.nbPages=i.nbPages,this.page=i.page,this.processingTimeMS=t.reduce((function(e,t){return void 0===t.processingTimeMS?e:e+t.processingTimeMS}),0),this.aroundLatLng=i.aroundLatLng,this.automaticRadius=i.automaticRadius,this.serverUsed=i.serverUsed,this.timeoutCounts=i.timeoutCounts,this.timeoutHits=i.timeoutHits,this.exhaustiveFacetsCount=i.exhaustiveFacetsCount,this.exhaustiveNbHits=i.exhaustiveNbHits,this.userData=i.userData,this.queryID=i.queryID,this.disjunctiveFacets=[],this.hierarchicalFacets=e.hierarchicalFacets.map((function(){return[]})),this.facets=[];var a=e.getRefinedDisjunctiveFacets(),o=f(e.facets),m=f(e.disjunctiveFacets),d=1,v=this,g=i.facets||{};Object.keys(g).forEach((function(t){var n,r,a=g[t],s=(n=e.hierarchicalFacets,r=t,c(n,(function(e){return(e.attributes||[]).indexOf(r)>-1})));if(s){var h=s.attributes.indexOf(t),f=u(e.hierarchicalFacets,(function(e){return e.name===s.name}));v.hierarchicalFacets[f][h]={attribute:t,data:a,exhaustive:i.exhaustiveFacetsCount}}else{var d,p=-1!==e.disjunctiveFacets.indexOf(t),y=-1!==e.facets.indexOf(t);p&&(d=m[t],v.disjunctiveFacets[d]={name:t,data:a,exhaustive:i.exhaustiveFacetsCount},l(v.disjunctiveFacets[d],i.facets_stats,t)),y&&(d=o[t],v.facets[d]={name:t,data:a,exhaustive:i.exhaustiveFacetsCount},l(v.facets[d],i.facets_stats,t))}})),this.hierarchicalFacets=s(this.hierarchicalFacets),a.forEach((function(a){var s=t[d],c=s&&s.facets?s.facets:{},o=e.getHierarchicalFacetByName(a);Object.keys(c).forEach((function(t){var a,h=c[t];if(o){a=u(e.hierarchicalFacets,(function(e){return e.name===o.name}));var f=u(v.hierarchicalFacets[a],(function(e){return e.attribute===t}));if(-1===f)return;v.hierarchicalFacets[a][f].data=n({},v.hierarchicalFacets[a][f].data,h)}else{a=m[t];var d=i.facets&&i.facets[t]||{};v.disjunctiveFacets[a]={name:t,data:r({},h,d),exhaustive:s.exhaustiveFacetsCount},l(v.disjunctiveFacets[a],s.facets_stats,t),e.disjunctiveFacetsRefinements[t]&&e.disjunctiveFacetsRefinements[t].forEach((function(i){!v.disjunctiveFacets[a].data[i]&&e.disjunctiveFacetsRefinements[t].indexOf(i)>-1&&(v.disjunctiveFacets[a].data[i]=0)}))}})),d++})),e.getRefinedHierarchicalFacets().forEach((function(i){var n=e.getHierarchicalFacetByName(i),a=e._getHierarchicalFacetSeparator(n),s=e.getHierarchicalRefinement(i);if(!(0===s.length||s[0].split(a).length<2)){var c=t[d],o=c&&c.facets?c.facets:{};Object.keys(o).forEach((function(t){var i=o[t],c=u(e.hierarchicalFacets,(function(e){return e.name===n.name})),h=u(v.hierarchicalFacets[c],(function(e){return e.attribute===t}));if(-1!==h){var f={};if(s.length>0){var l=s[0].split(a)[0];f[l]=v.hierarchicalFacets[c][h].data[l]}v.hierarchicalFacets[c][h].data=r(f,i,v.hierarchicalFacets[c][h].data)}})),d++}})),Object.keys(e.facetsExcludes).forEach((function(t){var n=e.facetsExcludes[t],r=o[t];v.facets[r]={name:t,data:i.facets[t],exhaustive:i.exhaustiveFacetsCount},n.forEach((function(e){v.facets[r]=v.facets[r]||{name:t},v.facets[r].data=v.facets[r].data||{},v.facets[r].data[e]=0}))})),this.hierarchicalFacets=this.hierarchicalFacets.map(h(e)),this.facets=s(this.facets),this.disjunctiveFacets=s(this.disjunctiveFacets),this._state=e}function d(e,t){if(!t.data||0===t.data.length)return t;var i=t.data.map((function(t){return d(e,t)})),r=e(i);return n({},t,{data:r})}function v(e,t){var i=c(e,(function(e){return e.name===t}));return i&&i.stats}function g(e,t,i,n,r){var a=c(r,(function(e){return e.name===i})),s=a&&a.data&&a.data[n]?a.data[n]:0,u=a&&a.exhaustive||!1;return{type:t,attributeName:i,name:n,count:s,exhaustive:u}}m.prototype.getFacetByName=function(e){function t(t){return t.name===e}return c(this.facets,t)||c(this.disjunctiveFacets,t)||c(this.hierarchicalFacets,t)},m.DEFAULT_SORT=["isRefined:desc","count:desc","name:asc"],m.prototype.getFacetValues=function(e,t){var i=function(e,t){function i(e){return e.name===t}if(e._state.isConjunctiveFacet(t)){var n=c(e.facets,i);return n?Object.keys(n.data).map((function(i){return{name:i,count:n.data[i],isRefined:e._state.isFacetRefined(t,i),isExcluded:e._state.isExcludeRefined(t,i)}})):[]}if(e._state.isDisjunctiveFacet(t)){var r=c(e.disjunctiveFacets,i);return r?Object.keys(r.data).map((function(i){return{name:i,count:r.data[i],isRefined:e._state.isDisjunctiveFacetRefined(t,i)}})):[]}if(e._state.isHierarchicalFacet(t))return c(e.hierarchicalFacets,i)}(this,e);if(i){var n=r({},t,{sortBy:m.DEFAULT_SORT});if(Array.isArray(n.sortBy)){var s=o(n.sortBy,m.DEFAULT_SORT);return Array.isArray(i)?a(i,s[0],s[1]):d((function(e){return a(e,s[0],s[1])}),i)}if("function"==typeof n.sortBy)return Array.isArray(i)?i.sort(n.sortBy):d((function(e){return function(e,t){return t.sort(e)}(n.sortBy,e)}),i);throw new Error("options.sortBy is optional but if defined it must be either an array of string (predicates) or a sorting function")}},m.prototype.getFacetStats=function(e){return this._state.isConjunctiveFacet(e)?v(this.facets,e):this._state.isDisjunctiveFacet(e)?v(this.disjunctiveFacets,e):void 0},m.prototype.getRefinements=function(){var e=this._state,t=this,i=[];return Object.keys(e.facetsRefinements).forEach((function(n){e.facetsRefinements[n].forEach((function(r){i.push(g(e,"facet",n,r,t.facets))}))})),Object.keys(e.facetsExcludes).forEach((function(n){e.facetsExcludes[n].forEach((function(r){i.push(g(e,"exclude",n,r,t.facets))}))})),Object.keys(e.disjunctiveFacetsRefinements).forEach((function(n){e.disjunctiveFacetsRefinements[n].forEach((function(r){i.push(g(e,"disjunctive",n,r,t.disjunctiveFacets))}))})),Object.keys(e.hierarchicalFacetsRefinements).forEach((function(n){e.hierarchicalFacetsRefinements[n].forEach((function(r){i.push(function(e,t,i,n){var r=e.getHierarchicalFacetByName(t),a=e._getHierarchicalFacetSeparator(r),s=i.split(a),u=c(n,(function(e){return e.name===t})),o=s.reduce((function(e,t){var i=e&&c(e.data,(function(e){return e.name===t}));return void 0!==i?i:e}),u),h=o&&o.count||0,f=o&&o.exhaustive||!1,l=o&&o.path||"";return{type:"hierarchical",attributeName:t,name:l,count:h,exhaustive:f}}(e,n,r,t.hierarchicalFacets))}))})),Object.keys(e.numericRefinements).forEach((function(t){var n=e.numericRefinements[t];Object.keys(n).forEach((function(e){n[e].forEach((function(n){i.push({type:"numeric",attributeName:t,name:n,numericValue:n,operator:e})}))}))})),e.tagRefinements.forEach((function(e){i.push({type:"tag",attributeName:"_tags",name:e})})),i},e.exports=m},207:function(e,t,i){"use strict";function n(e,t){if(e!==t){var i=void 0!==e,n=null===e,r=void 0!==t,a=null===t;if(!a&&e>t||n&&r||!i)return 1;if(!n&&e<t||a&&i||!r)return-1}return 0}e.exports=function(e,t,i){if(!Array.isArray(e))return[];Array.isArray(i)||(i=[]);var r=e.map((function(e,i){return{criteria:t.map((function(t){return e[t]})),index:i,value:e}}));return r.sort((function(e,t){for(var r=-1;++r<e.criteria.length;){var a=n(e.criteria[r],t.criteria[r]);if(a)return 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t!==e}))}):this},removeHierarchicalFacet:function(e){return this.isHierarchicalFacet(e)?this.clearRefinements(e).setQueryParameters({hierarchicalFacets:this.hierarchicalFacets.filter((function(t){return t.name!==e}))}):this},removeFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return h.isRefined(this.facetsRefinements,e,t)?this.setQueryParameters({facetsRefinements:h.removeRefinement(this.facetsRefinements,e,t)}):this},removeExcludeRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return h.isRefined(this.facetsExcludes,e,t)?this.setQueryParameters({facetsExcludes:h.removeRefinement(this.facetsExcludes,e,t)}):this},removeDisjunctiveFacetRefinement:function(e,t){if(!this.isDisjunctiveFacet(e))throw new Error(e+" is not defined in the disjunctiveFacets attribute of the helper 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this.emit("searchForFacetValues",{state:a,facet:e,query:t}),(r?this.client.searchForFacetValues([{indexName:a.index,params:u}]):this.client.initIndex(a.index).searchForFacetValues(u)).then((function(t){return o._currentNbQueries--,0===o._currentNbQueries&&o.emit("searchQueueEmpty"),(t=Array.isArray(t)?t[0]:t).facetHits.forEach((function(t){t.isRefined=c?a.isDisjunctiveFacetRefined(e,t.value):a.isFacetRefined(e,t.value)})),t}),(function(e){throw o._currentNbQueries--,0===o._currentNbQueries&&o.emit("searchQueueEmpty"),e}))},f.prototype.setQuery=function(e){return this._change({state:this.state.resetPage().setQuery(e),isPageReset:!0}),this},f.prototype.clearRefinements=function(e){return this._change({state:this.state.resetPage().clearRefinements(e),isPageReset:!0}),this},f.prototype.clearTags=function(){return this._change({state:this.state.resetPage().clearTags(),isPageReset:!0}),this},f.prototype.addDisjunctiveFacetRefinement=function(e,t){return this._change({state:this.state.resetPage().addDisjunctiveFacetRefinement(e,t),isPageReset:!0}),this},f.prototype.addDisjunctiveRefine=function(){return this.addDisjunctiveFacetRefinement.apply(this,arguments)},f.prototype.addHierarchicalFacetRefinement=function(e,t){return this._change({state:this.state.resetPage().addHierarchicalFacetRefinement(e,t),isPageReset:!0}),this},f.prototype.addNumericRefinement=function(e,t,i){return this._change({state:this.state.resetPage().addNumericRefinement(e,t,i),isPageReset:!0}),this},f.prototype.addFacetRefinement=function(e,t){return this._change({state:this.state.resetPage().addFacetRefinement(e,t),isPageReset:!0}),this},f.prototype.addRefine=function(){return this.addFacetRefinement.apply(this,arguments)},f.prototype.addFacetExclusion=function(e,t){return this._change({state:this.state.resetPage().addExcludeRefinement(e,t),isPageReset:!0}),this},f.prototype.addExclude=function(){return 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this.removeFacetRefinement.apply(this,arguments)},f.prototype.removeFacetExclusion=function(e,t){return this._change({state:this.state.resetPage().removeExcludeRefinement(e,t),isPageReset:!0}),this},f.prototype.removeExclude=function(){return this.removeFacetExclusion.apply(this,arguments)},f.prototype.removeTag=function(e){return this._change({state:this.state.resetPage().removeTagRefinement(e),isPageReset:!0}),this},f.prototype.toggleFacetExclusion=function(e,t){return this._change({state:this.state.resetPage().toggleExcludeFacetRefinement(e,t),isPageReset:!0}),this},f.prototype.toggleExclude=function(){return this.toggleFacetExclusion.apply(this,arguments)},f.prototype.toggleRefinement=function(e,t){return this.toggleFacetRefinement(e,t)},f.prototype.toggleFacetRefinement=function(e,t){return this._change({state:this.state.resetPage().toggleFacetRefinement(e,t),isPageReset:!0}),this},f.prototype.toggleRefine=function(){return 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t=[];if(this.state.isConjunctiveFacet(e))this.state.getConjunctiveRefinements(e).forEach((function(e){t.push({value:e,type:"conjunctive"})})),this.state.getExcludeRefinements(e).forEach((function(e){t.push({value:e,type:"exclude"})}));else if(this.state.isDisjunctiveFacet(e)){this.state.getDisjunctiveRefinements(e).forEach((function(e){t.push({value:e,type:"disjunctive"})}))}var i=this.state.getNumericRefinements(e);return Object.keys(i).forEach((function(e){var n=i[e];t.push({value:n,operator:e,type:"numeric"})})),t},f.prototype.getNumericRefinement=function(e,t){return this.state.getNumericRefinement(e,t)},f.prototype.getHierarchicalFacetBreadcrumb=function(e){return this.state.getHierarchicalFacetBreadcrumb(e)},f.prototype._search=function(e){var t=this.state,i=[],n=[];e.onlyWithDerivedHelpers||(n=s._getQueries(t.index,t),i.push({state:t,queriesCount:n.length,helper:this}),this.emit("search",{state:t,results:this.lastResults}));var r=this.derivedHelpers.map((function(e){var n=e.getModifiedState(t),r=s._getQueries(n.index,n);return i.push({state:n,queriesCount:r.length,helper:e}),e.emit("search",{state:n,results:e.lastResults}),r})),a=Array.prototype.concat.apply(n,r),c=this._queryId++;this._currentNbQueries++;try{this.client.search(a).then(this._dispatchAlgoliaResponse.bind(this,i,c)).catch(this._dispatchAlgoliaError.bind(this,c))}catch(u){this.emit("error",{error:u})}},f.prototype._dispatchAlgoliaResponse=function(e,t,i){if(!(t<this._lastQueryIdReceived)){this._currentNbQueries-=t-this._lastQueryIdReceived,this._lastQueryIdReceived=t,0===this._currentNbQueries&&this.emit("searchQueueEmpty");var n=i.results.slice();e.forEach((function(e){var t=e.state,i=e.queriesCount,a=e.helper,s=n.splice(0,i),c=a.lastResults=new r(t,s);a.emit("result",{results:c,state:t})}))}},f.prototype._dispatchAlgoliaError=function(e,t){e<this._lastQueryIdReceived||(this._currentNbQueries-=e-this._lastQueryIdReceived,this._lastQueryIdReceived=e,this.emit("error",{error:t}),0===this._currentNbQueries&&this.emit("searchQueueEmpty"))},f.prototype.containsRefinement=function(e,t,i,n){return e||0!==t.length||0!==i.length||0!==n.length},f.prototype._hasDisjunctiveRefinements=function(e){return this.state.disjunctiveRefinements[e]&&this.state.disjunctiveRefinements[e].length>0},f.prototype._change=function(e){var t=e.state,i=e.isPageReset;t!==this.state&&(this.state=t,this.emit("change",{state:this.state,results:this.lastResults,isPageReset:i}))},f.prototype.clearCache=function(){return this.client.clearCache&&this.client.clearCache(),this},f.prototype.setClient=function(e){return this.client===e||("function"==typeof e.addAlgoliaAgent&&e.addAlgoliaAgent("JS Helper ("+h+")"),this.client=e),this},f.prototype.getClient=function(){return this.client},f.prototype.derive=function(e){var t=new a(this,e);return this.derivedHelpers.push(t),t},f.prototype.detachDerivedHelper=function(e){var t=this.derivedHelpers.indexOf(e);if(-1===t)throw new Error("Derived helper already detached");this.derivedHelpers.splice(t,1)},f.prototype.hasPendingRequests=function(){return this._currentNbQueries>0},e.exports=f},256:function(e,t,i){"use strict";e.exports=function(e,t){return e.filter((function(i,n){return t.indexOf(i)>-1&&e.indexOf(i)===n}))}},257:function(e,t,i){"use strict";e.exports=function e(t){if("number"==typeof t)return t;if("string"==typeof t)return parseFloat(t);if(Array.isArray(t))return t.map(e);throw new Error("The value should be a number, a parsable string or an array of those.")}},258:function(e,t,i){"use strict";var n=i(190),r=i(212),a=i(191),s={addRefinement:function(e,t,i){if(s.isRefined(e,t,i))return e;var r=""+i,a=e[t]?e[t].concat(r):[r],c={};return c[t]=a,n({},c,e)},removeRefinement:function(e,t,i){if(void 0===i)return s.clearRefinement(e,(function(e,i){return t===i}));var n=""+i;return s.clearRefinement(e,(function(e,i){return t===i&&n===e}))},toggleRefinement:function(e,t,i){if(void 0===i)throw new Error("toggleRefinement should be used with a value");return s.isRefined(e,t,i)?s.removeRefinement(e,t,i):s.addRefinement(e,t,i)},clearRefinement:function(e,t,i){if(void 0===t)return a(e)?{}:e;if("string"==typeof t)return r(e,[t]);if("function"==typeof t){var n=!1,s=Object.keys(e).reduce((function(r,a){var s=e[a]||[],c=s.filter((function(e){return!t(e,a,i)}));return c.length!==s.length&&(n=!0),r[a]=c,r}),{});return n?s:e}},isRefined:function(e,t,i){var n=!!e[t]&&e[t].length>0;if(void 0===i||!n)return n;var r=""+i;return-1!==e[t].indexOf(r)}};e.exports=s},259:function(e,t,i){"use strict";e.exports=function(e){return Array.isArray(e)?e.filter(Boolean):[]}},260:function(e,t,i){"use 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function(e,t,i,n,r,a){if(r&&(0!==e.indexOf(r)||r===e))return!1;return!r&&-1===e.indexOf(n)||r&&e.split(n).length-r.split(n).length==1||-1===e.indexOf(n)&&-1===i.indexOf(n)||0===i.indexOf(e)||0===e.indexOf(t+n)&&(a||0===e.indexOf(i))}(e[0],h.path||i,s,t,i,a)}));h.data=n(m.map((function(e){var i=e[0];return function(e,t,i,n,r){var a=t.split(i);return{name:a[a.length-1].trim(),path:t,count:e,isRefined:n===t||0===n.indexOf(t+i),exhaustive:r,data:null}}(e[1],i,t,s,u.exhaustive)})),e[0],e[1])}return c}}(f,u,o,h,c),d=t;return o&&(d=t.slice(o.split(u).length)),d.reduce(m,{name:e.hierarchicalFacets[i].name,count:null,isRefined:!0,path:null,exhaustive:l,data:null})}};var n=i(214),r=i(186),a=i(215)},262:function(e,t,i){"use strict";var n=i(216);function r(e,t){this.main=e,this.fn=t,this.lastResults=null}i(217)(r,n.EventEmitter),r.prototype.detach=function(){this.removeAllListeners(),this.main.detachDerivedHelper(this)},r.prototype.getModifiedState=function(e){return this.fn(e)},e.exports=r},263:function(e,t,i){"use strict";var n=i(189),r={_getQueries:function(e,t){var i=[];return i.push({indexName:e,params:r._getHitsSearchParams(t)}),t.getRefinedDisjunctiveFacets().forEach((function(n){i.push({indexName:e,params:r._getDisjunctiveFacetSearchParams(t,n)})})),t.getRefinedHierarchicalFacets().forEach((function(n){var a=t.getHierarchicalFacetByName(n),s=t.getHierarchicalRefinement(n),c=t._getHierarchicalFacetSeparator(a);s.length>0&&s[0].split(c).length>1&&i.push({indexName:e,params:r._getDisjunctiveFacetSearchParams(t,n,!0)})})),i},_getHitsSearchParams:function(e){var t=e.facets.concat(e.disjunctiveFacets).concat(r._getHitsHierarchicalFacetsAttributes(e)),i=r._getFacetFilters(e),a=r._getNumericFilters(e),s={facets:t,tagFilters:r._getTagFilters(e)};return i.length>0&&(s.facetFilters=i),a.length>0&&(s.numericFilters=a),n({},e.getQueryParams(),s)},_getDisjunctiveFacetSearchParams:function(e,t,i){var a=r._getFacetFilters(e,t,i),s=r._getNumericFilters(e,t),c={hitsPerPage:1,page:0,attributesToRetrieve:[],attributesToHighlight:[],attributesToSnippet:[],tagFilters:r._getTagFilters(e),analytics:!1,clickAnalytics:!1},u=e.getHierarchicalFacetByName(t);return c.facets=u?r._getDisjunctiveHierarchicalFacetAttribute(e,u,i):t,s.length>0&&(c.numericFilters=s),a.length>0&&(c.facetFilters=a),n({},e.getQueryParams(),c)},_getNumericFilters:function(e,t){if(e.numericFilters)return e.numericFilters;var i=[];return Object.keys(e.numericRefinements).forEach((function(n){var r=e.numericRefinements[n]||{};Object.keys(r).forEach((function(e){var a=r[e]||[];t!==n&&a.forEach((function(t){if(Array.isArray(t)){var r=t.map((function(t){return n+e+t}));i.push(r)}else i.push(n+e+t)}))}))})),i},_getTagFilters:function(e){return e.tagFilters?e.tagFilters:e.tagRefinements.join(",")},_getFacetFilters:function(e,t,i){var n=[],r=e.facetsRefinements||{};Object.keys(r).forEach((function(e){(r[e]||[]).forEach((function(t){n.push(e+":"+t)}))}));var a=e.facetsExcludes||{};Object.keys(a).forEach((function(e){(a[e]||[]).forEach((function(t){n.push(e+":-"+t)}))}));var s=e.disjunctiveFacetsRefinements||{};Object.keys(s).forEach((function(e){var i=s[e]||[];if(e!==t&&i&&0!==i.length){var r=[];i.forEach((function(t){r.push(e+":"+t)})),n.push(r)}}));var c=e.hierarchicalFacetsRefinements||{};return Object.keys(c).forEach((function(r){var a=(c[r]||[])[0];if(void 0!==a){var s,u,o=e.getHierarchicalFacetByName(r),h=e._getHierarchicalFacetSeparator(o),f=e._getHierarchicalRootPath(o);if(t===r){if(-1===a.indexOf(h)||!f&&!0===i||f&&f.split(h).length===a.split(h).length)return;f?(u=f.split(h).length-1,a=f):(u=a.split(h).length-2,a=a.slice(0,a.lastIndexOf(h))),s=o.attributes[u]}else u=a.split(h).length-1,s=o.attributes[u];s&&n.push([s+":"+a])}})),n},_getHitsHierarchicalFacetsAttributes:function(e){return e.hierarchicalFacets.reduce((function(t,i){var n=e.getHierarchicalRefinement(i.name)[0];if(!n)return t.push(i.attributes[0]),t;var r=e._getHierarchicalFacetSeparator(i),a=n.split(r).length,s=i.attributes.slice(0,a+1);return t.concat(s)}),[])},_getDisjunctiveHierarchicalFacetAttribute:function(e,t,i){var n=e._getHierarchicalFacetSeparator(t);if(!0===i){var r=e._getHierarchicalRootPath(t),a=0;return r&&(a=r.split(n).length),[t.attributes[a]]}var s=(e.getHierarchicalRefinement(t.name)[0]||"").split(n).length-1;return t.attributes.slice(0,s+1)},getSearchForFacetQuery:function(e,t,i,a){var s=a.isDisjunctiveFacet(e)?a.clearRefinements(e):a,c={facetQuery:t,facetName:e};return"number"==typeof i&&(c.maxFacetHits=i),n({},r._getHitsSearchParams(s),c)}};e.exports=r},264:function(e,t,i){"use strict";Object.defineProperty(t,"__esModule",{value:!0});let n=[];try{n=i(!function(){var e=new Error("Cannot find module '@site/versions.json'");throw e.code="MODULE_NOT_FOUND",e}())}catch(r){}t.default=function(){return{versioningEnabled:n.length>0,versions:n,latestVersion:n[0]}}}}]);
\ No newline at end of file
diff --git a/docs/1.27fbcdaa.js b/docs/1.837a9375.js
index 1833d11..1c1494c 100644
--- a/docs/1.27fbcdaa.js
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Esse formul\xe1rio, comum a v\xe1rios outros elementos, permite a inser\xe7\xe3o e/ou remo\xe7\xe3o da linha durante o estudo de ',Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(c.a)("images/lineSw.png"),alt:"Formul\xe1rio de chaveamento da linha",title:"Formul\xe1rio de chaveamento da linha"}))),Object(m.b)(b.a,{groupId:"line-tabs",defaultValue:"general",values:[{label:"Geral",value:"general"},{label:"Falta",value:"fault"},{label:"Bot\xe3o Estabilidade",value:"stability"}],mdxType:"Tabs"},Object(m.b)(p.a,{value:"general",mdxType:"TabItem"},Object(m.b)("h4",{id:"nome"},"Nome"),Object(m.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(m.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(m.b)("h4",{id:"tens\xe3o-nominal"},"Tens\xe3o nominal"),Object(m.b)("p",null,"Campo de informa\xe7\xe3o ",Object(m.b)("em",{parentName:"p"},"n\xe3o edit\xe1vel")," que apresenta a tens\xe3o nominal da linha. 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Esse formul\xe1rio, comum a v\xe1rios outros elementos, permite a inser\xe7\xe3o e/ou remo\xe7\xe3o da linha durante o estudo de ',Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(b.a)("images/lineSw.png"),alt:"Formul\xe1rio de chaveamento da linha",title:"Formul\xe1rio de chaveamento da linha"}))),Object(m.b)("hr",null),Object(m.b)("h3",{id:"geral"},"Geral"),Object(m.b)("h4",{id:"nome"},"Nome"),Object(m.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(m.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(m.b)("h4",{id:"tens\xe3o-nominal"},"Tens\xe3o nominal"),Object(m.b)("p",null,"Campo de informa\xe7\xe3o ",Object(m.b)("em",{parentName:"p"},"n\xe3o edit\xe1vel")," que apresenta a tens\xe3o nominal da linha. 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o=r(173),n=r(228),s=r(229),a=r(235),i=t.env.RESET_APP_DATA_TIMER&&parseInt(t.env.RESET_APP_DATA_TIMER,10)||12e4;function c(e,t,n){var s=r(176)("algoliasearch"),a=r(170),i=r(174),c=r(175),l="Usage: algoliasearch(applicationID, apiKey, opts)";if(!0!==n._allowEmptyCredentials&&!e)throw new o.AlgoliaSearchError("Please provide an application ID. "+l);if(!0!==n._allowEmptyCredentials&&!t)throw new o.AlgoliaSearchError("Please provide an API key. "+l);this.applicationID=e,this.apiKey=t,this.hosts={read:[],write:[]},n=n||{},this._timeouts=n.timeouts||{connect:1e3,read:2e3,write:3e4},n.timeout&&(this._timeouts.connect=this._timeouts.read=this._timeouts.write=n.timeout);var p=n.protocol||"https:";if(/:$/.test(p)||(p+=":"),"http:"!==p&&"https:"!==p)throw new o.AlgoliaSearchError("protocol must be `http:` or `https:` (was `"+n.protocol+"`)");if(this._checkAppIdData(),n.hosts)i(n.hosts)?(this.hosts.read=a(n.hosts),this.hosts.write=a(n.hosts)):(this.hosts.read=a(n.hosts.read),this.hosts.write=a(n.hosts.write));else{var h=c(this._shuffleResult,(function(t){return e+"-"+t+".algolianet.com"})),f=(!1===n.dsn?"":"-dsn")+".algolia.net";this.hosts.read=[this.applicationID+f].concat(h),this.hosts.write=[this.applicationID+".algolia.net"].concat(h)}this.hosts.read=c(this.hosts.read,u(p)),this.hosts.write=c(this.hosts.write,u(p)),this.extraHeaders={},this.cache=n._cache||{},this._ua=n._ua,this._useCache=!(void 0!==n._useCache&&!n._cache)||n._useCache,this._useRequestCache=this._useCache&&n._useRequestCache,this._useFallback=void 0===n.useFallback||n.useFallback,this._setTimeout=n._setTimeout,s("init done, %j",this)}function u(e){return function(t){return e+"//"+t.toLowerCase()}}function l(e){if(void 0===Array.prototype.toJSON)return JSON.stringify(e);var t=Array.prototype.toJSON;delete Array.prototype.toJSON;var r=JSON.stringify(e);return Array.prototype.toJSON=t,r}function p(e){var t={};for(var r in e){var o;if(Object.prototype.hasOwnProperty.call(e,r))o="x-algolia-api-key"===r||"x-algolia-application-id"===r?"**hidden for security purposes**":e[r],t[r]=o}return t}c.prototype.initIndex=function(e){return new s(this,e)},c.prototype.setExtraHeader=function(e,t){this.extraHeaders[e.toLowerCase()]=t},c.prototype.getExtraHeader=function(e){return this.extraHeaders[e.toLowerCase()]},c.prototype.unsetExtraHeader=function(e){delete this.extraHeaders[e.toLowerCase()]},c.prototype.addAlgoliaAgent=function(e){var t="; "+e;-1===this._ua.indexOf(t)&&(this._ua+=t)},c.prototype._jsonRequest=function(e){this._checkAppIdData();var t,s,a,i=r(176)("algoliasearch:"+e.url),c=e.additionalUA||"",u=e.cache,h=this,f=0,d=!1,y=h._useFallback&&h._request.fallback&&e.fallback;this.apiKey.length>500&&void 0!==e.body&&(void 0!==e.body.params||void 0!==e.body.requests)?(e.body.apiKey=this.apiKey,a=this._computeRequestHeaders({additionalUA:c,withApiKey:!1,headers:e.headers})):a=this._computeRequestHeaders({additionalUA:c,headers:e.headers}),void 0!==e.body&&(t=l(e.body)),i("request start");var m=[];function g(e,t,r){return h._useCache&&e&&t&&void 0!==t[r]}function v(t,r){if(g(h._useRequestCache,u,s)&&t.catch((function(){delete u[s]})),"function"!=typeof e.callback)return t.then(r);t.then((function(t){n((function(){e.callback(null,r(t))}),h._setTimeout||setTimeout)}),(function(t){n((function(){e.callback(t)}),h._setTimeout||setTimeout)}))}if(h._useCache&&h._useRequestCache&&(s=e.url),h._useCache&&h._useRequestCache&&t&&(s+="_body_"+t),g(h._useRequestCache,u,s)){i("serving request from cache");var b=u[s];return v("function"!=typeof b.then?h._promise.resolve({responseText:b}):b,(function(e){return JSON.parse(e.responseText)}))}var w=function r(n,v){h._checkAppIdData();var b=new Date;if(h._useCache&&!h._useRequestCache&&(s=e.url),h._useCache&&!h._useRequestCache&&t&&(s+="_body_"+v.body),g(!h._useRequestCache,u,s)){i("serving response from cache");var w=u[s];return h._promise.resolve({body:JSON.parse(w),responseText:w})}if(f>=h.hosts[e.hostType].length)return!y||d?(i("could not get any response"),h._promise.reject(new o.AlgoliaSearchError("Cannot connect to the AlgoliaSearch API. Send an email to support@algolia.com to report and resolve the issue. Application id was: "+h.applicationID,{debugData:m}))):(i("switching to fallback"),f=0,v.method=e.fallback.method,v.url=e.fallback.url,v.jsonBody=e.fallback.body,v.jsonBody&&(v.body=l(v.jsonBody)),a=h._computeRequestHeaders({additionalUA:c,headers:e.headers}),v.timeouts=h._getTimeoutsForRequest(e.hostType),h._setHostIndexByType(0,e.hostType),d=!0,r(h._request.fallback,v));var _=h._getHostByType(e.hostType),x=_+v.url,T={body:v.body,jsonBody:v.jsonBody,method:v.method,headers:a,timeouts:v.timeouts,debug:i,forceAuthHeaders:v.forceAuthHeaders};return i("method: %s, url: %s, headers: %j, timeouts: %d",T.method,x,T.headers,T.timeouts),n===h._request.fallback&&i("using fallback"),n.call(h,x,T).then((function(e){var r=e&&e.body&&e.body.message&&e.body.status||e.statusCode||e&&e.body&&200;i("received response: statusCode: %s, computed statusCode: %d, headers: %j",e.statusCode,r,e.headers);var n=2===Math.floor(r/100),c=new Date;if(m.push({currentHost:_,headers:p(a),content:t||null,contentLength:void 0!==t?t.length:null,method:v.method,timeouts:v.timeouts,url:v.url,startTime:b,endTime:c,duration:c-b,statusCode:r}),n)return h._useCache&&!h._useRequestCache&&u&&(u[s]=e.responseText),{responseText:e.responseText,body:e.body};if(4!==Math.floor(r/100))return f+=1,S();i("unrecoverable error");var l=new o.AlgoliaSearchError(e.body&&e.body.message,{debugData:m,statusCode:r});return h._promise.reject(l)}),(function(s){i("error: %s, stack: %s",s.message,s.stack);var c=new Date;m.push({currentHost:_,headers:p(a),content:t||null,contentLength:void 0!==t?t.length:null,method:v.method,timeouts:v.timeouts,url:v.url,startTime:b,endTime:c,duration:c-b}),s instanceof o.AlgoliaSearchError||(s=new o.Unknown(s&&s.message,s));if(f+=1,s instanceof o.Unknown||s instanceof o.UnparsableJSON||f>=h.hosts[e.hostType].length&&(d||!y))return s.debugData=m,h._promise.reject(s);if(s instanceof o.RequestTimeout)return i("retrying request with higher timeout"),h._incrementHostIndex(e.hostType),h._incrementTimeoutMultipler(),v.timeouts=h._getTimeoutsForRequest(e.hostType),r(n,v);return S()}));function S(){return i("retrying request"),h._incrementHostIndex(e.hostType),r(n,v)}}(h._request,{url:e.url,method:e.method,body:t,jsonBody:e.body,timeouts:h._getTimeoutsForRequest(e.hostType),forceAuthHeaders:e.forceAuthHeaders});return h._useCache&&h._useRequestCache&&u&&(u[s]=w),v(w,(function(e){return e.body}))},c.prototype._getSearchParams=function(e,t){if(null==e)return t;for(var r in e)null!==r&&void 0!==e[r]&&e.hasOwnProperty(r)&&(t+=""===t?"":"&",t+=r+"="+encodeURIComponent("[object Array]"===Object.prototype.toString.call(e[r])?l(e[r]):e[r]));return t},c.prototype._computeRequestHeaders=function(e){var t=r(169),o={"x-algolia-agent":e.additionalUA?this._ua+"; "+e.additionalUA:this._ua,"x-algolia-application-id":this.applicationID};return!1!==e.withApiKey&&(o["x-algolia-api-key"]=this.apiKey),this.userToken&&(o["x-algolia-usertoken"]=this.userToken),this.securityTags&&(o["x-algolia-tagfilters"]=this.securityTags),t(this.extraHeaders,(function(e,t){o[t]=e})),e.headers&&t(e.headers,(function(e,t){o[t]=e})),o},c.prototype.search=function(e,t,o){var n=r(174),s=r(175);if(!n(e))throw new Error("Usage: client.search(arrayOfQueries[, callback])");"function"==typeof t?(o=t,t={}):void 0===t&&(t={});var a=this,i={requests:s(e,(function(e){var t="";return void 0!==e.query&&(t+="query="+encodeURIComponent(e.query)),{indexName:e.indexName,params:a._getSearchParams(e.params,t)}}))},c=s(i.requests,(function(e,t){return t+"="+encodeURIComponent("/1/indexes/"+encodeURIComponent(e.indexName)+"?"+e.params)})).join("&");return void 0!==t.strategy&&(i.strategy=t.strategy),this._jsonRequest({cache:this.cache,method:"POST",url:"/1/indexes/*/queries",body:i,hostType:"read",fallback:{method:"GET",url:"/1/indexes/*",body:{params:c}},callback:o})},c.prototype.searchForFacetValues=function(e){var t=r(174),o=r(175),n="Usage: client.searchForFacetValues([{indexName, params: {facetName, facetQuery, ...params}}, ...queries])";if(!t(e))throw new Error(n);var s=this;return s._promise.all(o(e,(function(e){if(!e||void 0===e.indexName||void 0===e.params.facetName||void 0===e.params.facetQuery)throw new Error(n);var t=r(170),o=r(201),a=e.indexName,i=e.params,c=i.facetName,u=o(t(i),(function(e){return"facetName"===e})),l=s._getSearchParams(u,"");return s._jsonRequest({cache:s.cache,method:"POST",url:"/1/indexes/"+encodeURIComponent(a)+"/facets/"+encodeURIComponent(c)+"/query",hostType:"read",body:{params:l}})})))},c.prototype.setSecurityTags=function(e){if("[object Array]"===Object.prototype.toString.call(e)){for(var t=[],r=0;r<e.length;++r)if("[object Array]"===Object.prototype.toString.call(e[r])){for(var o=[],n=0;n<e[r].length;++n)o.push(e[r][n]);t.push("("+o.join(",")+")")}else t.push(e[r]);e=t.join(",")}this.securityTags=e},c.prototype.setUserToken=function(e){this.userToken=e},c.prototype.clearCache=function(){this.cache={}},c.prototype.setRequestTimeout=function(e){e&&(this._timeouts.connect=this._timeouts.read=this._timeouts.write=e)},c.prototype.setTimeouts=function(e){this._timeouts=e},c.prototype.getTimeouts=function(){return this._timeouts},c.prototype._getAppIdData=function(){var e=a.get(this.applicationID);return null!==e&&this._cacheAppIdData(e),e},c.prototype._setAppIdData=function(e){return e.lastChange=(new Date).getTime(),this._cacheAppIdData(e),a.set(this.applicationID,e)},c.prototype._checkAppIdData=function(){var e=this._getAppIdData(),t=(new Date).getTime();return null===e||t-e.lastChange>i?this._resetInitialAppIdData(e):e},c.prototype._resetInitialAppIdData=function(e){var t=e||{};return t.hostIndexes={read:0,write:0},t.timeoutMultiplier=1,t.shuffleResult=t.shuffleResult||function(e){var t,r,o=e.length;for(;0!==o;)r=Math.floor(Math.random()*o),t=e[o-=1],e[o]=e[r],e[r]=t;return e}([1,2,3]),this._setAppIdData(t)},c.prototype._cacheAppIdData=function(e){this._hostIndexes=e.hostIndexes,this._timeoutMultiplier=e.timeoutMultiplier,this._shuffleResult=e.shuffleResult},c.prototype._partialAppIdDataUpdate=function(e){var t=r(169),o=this._getAppIdData();return t(e,(function(e,t){o[t]=e})),this._setAppIdData(o)},c.prototype._getHostByType=function(e){return this.hosts[e][this._getHostIndexByType(e)]},c.prototype._getTimeoutMultiplier=function(){return this._timeoutMultiplier},c.prototype._getHostIndexByType=function(e){return this._hostIndexes[e]},c.prototype._setHostIndexByType=function(e,t){var o=r(170)(this._hostIndexes);return o[t]=e,this._partialAppIdDataUpdate({hostIndexes:o}),e},c.prototype._incrementHostIndex=function(e){return this._setHostIndexByType((this._getHostIndexByType(e)+1)%this.hosts[e].length,e)},c.prototype._incrementTimeoutMultipler=function(){var e=Math.max(this._timeoutMultiplier+1,4);return this._partialAppIdDataUpdate({timeoutMultiplier:e})},c.prototype._getTimeoutsForRequest=function(e){return{connect:this._timeouts.connect*this._timeoutMultiplier,complete:this._timeouts[e]*this._timeoutMultiplier}}}).call(this,r(179))},228:function(e,t){e.exports=function(e,t){t(e,0)}},229:function(e,t,r){var o=r(200),n=r(230),s=r(231);function a(e,t){this.indexName=t,this.as=e,this.typeAheadArgs=null,this.typeAheadValueOption=null,this.cache={}}e.exports=a,a.prototype.clearCache=function(){this.cache={}},a.prototype.search=o("query"),a.prototype.similarSearch=n(o("similarQuery"),s("index.similarSearch(query[, callback])","index.search({ similarQuery: query }[, callback])")),a.prototype.browse=function(e,t,o){var n,s,a=r(232),i=this;0===arguments.length||1===arguments.length&&"function"==typeof arguments[0]?(n=0,o=arguments[0],e=void 0):"number"==typeof arguments[0]?(n=arguments[0],"number"==typeof arguments[1]?s=arguments[1]:"function"==typeof arguments[1]&&(o=arguments[1],s=void 0),e=void 0,t=void 0):"object"==typeof arguments[0]?("function"==typeof arguments[1]&&(o=arguments[1]),t=arguments[0],e=void 0):"string"==typeof arguments[0]&&"function"==typeof arguments[1]&&(o=arguments[1],t=void 0),t=a({},t||{},{page:n,hitsPerPage:s,query:e});var c=this.as._getSearchParams(t,"");return this.as._jsonRequest({method:"POST",url:"/1/indexes/"+encodeURIComponent(i.indexName)+"/browse",body:{params:c},hostType:"read",callback:o})},a.prototype.browseFrom=function(e,t){return this.as._jsonRequest({method:"POST",url:"/1/indexes/"+encodeURIComponent(this.indexName)+"/browse",body:{cursor:e},hostType:"read",callback:t})},a.prototype.searchForFacetValues=function(e,t){var o=r(170),n=r(201);if(void 0===e.facetName||void 0===e.facetQuery)throw new Error("Usage: index.searchForFacetValues({facetName, facetQuery, ...params}[, callback])");var s=e.facetName,a=n(o(e),(function(e){return"facetName"===e})),i=this.as._getSearchParams(a,"");return this.as._jsonRequest({method:"POST",url:"/1/indexes/"+encodeURIComponent(this.indexName)+"/facets/"+encodeURIComponent(s)+"/query",hostType:"read",body:{params:i},callback:t})},a.prototype.searchFacet=n((function(e,t){return this.searchForFacetValues(e,t)}),s("index.searchFacet(params[, callback])","index.searchForFacetValues(params[, callback])")),a.prototype._search=function(e,t,r,o){return this.as._jsonRequest({cache:this.cache,method:"POST",url:t||"/1/indexes/"+encodeURIComponent(this.indexName)+"/query",body:{params:e},hostType:"read",fallback:{method:"GET",url:"/1/indexes/"+encodeURIComponent(this.indexName),body:{params:e}},callback:r,additionalUA:o})},a.prototype.getObject=function(e,t,r){var o=this;1!==arguments.length&&"function"!=typeof t||(r=t,t=void 0);var n="";if(void 0!==t){n="?attributes=";for(var s=0;s<t.length;++s)0!==s&&(n+=","),n+=t[s]}return this.as._jsonRequest({method:"GET",url:"/1/indexes/"+encodeURIComponent(o.indexName)+"/"+encodeURIComponent(e)+n,hostType:"read",callback:r})},a.prototype.getObjects=function(e,t,o){var n=r(174),s=r(175),a="Usage: index.getObjects(arrayOfObjectIDs[, callback])";if(!n(e))throw new Error(a);var i=this;1!==arguments.length&&"function"!=typeof t||(o=t,t=void 0);var c={requests:s(e,(function(e){var r={indexName:i.indexName,objectID:e};return t&&(r.attributesToRetrieve=t.join(",")),r}))};return this.as._jsonRequest({method:"POST",url:"/1/indexes/*/objects",hostType:"read",body:c,callback:o})},a.prototype.as=null,a.prototype.indexName=null,a.prototype.typeAheadArgs=null,a.prototype.typeAheadValueOption=null},230:function(e,t){e.exports=function(e,t){var r=!1;return function(){return r||(console.warn(t),r=!0),e.apply(this,arguments)}}},231:function(e,t){e.exports=function(e,t){var r=e.toLowerCase().replace(/[\.\(\)]/g,"");return"algoliasearch: `"+e+"` was replaced by `"+t+"`. 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Date;if(m.push({currentHost:_,headers:p(a),content:t||null,contentLength:void 0!==t?t.length:null,method:v.method,timeouts:v.timeouts,url:v.url,startTime:b,endTime:c,duration:c-b,statusCode:r}),n)return h._useCache&&!h._useRequestCache&&u&&(u[s]=e.responseText),{responseText:e.responseText,body:e.body};if(4!==Math.floor(r/100))return f+=1,S();i("unrecoverable error");var l=new o.AlgoliaSearchError(e.body&&e.body.message,{debugData:m,statusCode:r});return h._promise.reject(l)}),(function(s){i("error: %s, stack: %s",s.message,s.stack);var c=new Date;m.push({currentHost:_,headers:p(a),content:t||null,contentLength:void 0!==t?t.length:null,method:v.method,timeouts:v.timeouts,url:v.url,startTime:b,endTime:c,duration:c-b}),s instanceof o.AlgoliaSearchError||(s=new o.Unknown(s&&s.message,s));if(f+=1,s instanceof o.Unknown||s instanceof o.UnparsableJSON||f>=h.hosts[e.hostType].length&&(d||!y))return s.debugData=m,h._promise.reject(s);if(s instanceof o.RequestTimeout)return i("retrying request 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0!==t.strategy&&(i.strategy=t.strategy),this._jsonRequest({cache:this.cache,method:"POST",url:"/1/indexes/*/queries",body:i,hostType:"read",fallback:{method:"GET",url:"/1/indexes/*",body:{params:c}},callback:o})},c.prototype.searchForFacetValues=function(e){var t=r(183),o=r(184),n="Usage: client.searchForFacetValues([{indexName, params: {facetName, facetQuery, ...params}}, ...queries])";if(!t(e))throw new Error(n);var s=this;return s._promise.all(o(e,(function(e){if(!e||void 0===e.indexName||void 0===e.params.facetName||void 0===e.params.facetQuery)throw new Error(n);var t=r(179),o=r(208),a=e.indexName,i=e.params,c=i.facetName,u=o(t(i),(function(e){return"facetName"===e})),l=s._getSearchParams(u,"");return s._jsonRequest({cache:s.cache,method:"POST",url:"/1/indexes/"+encodeURIComponent(a)+"/facets/"+encodeURIComponent(c)+"/query",hostType:"read",body:{params:l}})})))},c.prototype.setSecurityTags=function(e){if("[object Array]"===Object.prototype.toString.call(e)){for(var t=[],r=0;r<e.length;++r)if("[object Array]"===Object.prototype.toString.call(e[r])){for(var o=[],n=0;n<e[r].length;++n)o.push(e[r][n]);t.push("("+o.join(",")+")")}else t.push(e[r]);e=t.join(",")}this.securityTags=e},c.prototype.setUserToken=function(e){this.userToken=e},c.prototype.clearCache=function(){this.cache={}},c.prototype.setRequestTimeout=function(e){e&&(this._timeouts.connect=this._timeouts.read=this._timeouts.write=e)},c.prototype.setTimeouts=function(e){this._timeouts=e},c.prototype.getTimeouts=function(){return this._timeouts},c.prototype._getAppIdData=function(){var e=a.get(this.applicationID);return null!==e&&this._cacheAppIdData(e),e},c.prototype._setAppIdData=function(e){return e.lastChange=(new Date).getTime(),this._cacheAppIdData(e),a.set(this.applicationID,e)},c.prototype._checkAppIdData=function(){var e=this._getAppIdData(),t=(new Date).getTime();return null===e||t-e.lastChange>i?this._resetInitialAppIdData(e):e},c.prototype._resetInitialAppIdData=function(e){var t=e||{};return t.hostIndexes={read:0,write:0},t.timeoutMultiplier=1,t.shuffleResult=t.shuffleResult||function(e){var t,r,o=e.length;for(;0!==o;)r=Math.floor(Math.random()*o),t=e[o-=1],e[o]=e[r],e[r]=t;return e}([1,2,3]),this._setAppIdData(t)},c.prototype._cacheAppIdData=function(e){this._hostIndexes=e.hostIndexes,this._timeoutMultiplier=e.timeoutMultiplier,this._shuffleResult=e.shuffleResult},c.prototype._partialAppIdDataUpdate=function(e){var t=r(178),o=this._getAppIdData();return t(e,(function(e,t){o[t]=e})),this._setAppIdData(o)},c.prototype._getHostByType=function(e){return this.hosts[e][this._getHostIndexByType(e)]},c.prototype._getTimeoutMultiplier=function(){return this._timeoutMultiplier},c.prototype._getHostIndexByType=function(e){return this._hostIndexes[e]},c.prototype._setHostIndexByType=function(e,t){var o=r(179)(this._hostIndexes);return o[t]=e,this._partialAppIdDataUpdate({hostIndexes:o}),e},c.prototype._incrementHostIndex=function(e){return this._setHostIndexByType((this._getHostIndexByType(e)+1)%this.hosts[e].length,e)},c.prototype._incrementTimeoutMultipler=function(){var e=Math.max(this._timeoutMultiplier+1,4);return this._partialAppIdDataUpdate({timeoutMultiplier:e})},c.prototype._getTimeoutsForRequest=function(e){return{connect:this._timeouts.connect*this._timeoutMultiplier,complete:this._timeouts[e]*this._timeoutMultiplier}}}).call(this,r(188))},235:function(e,t){e.exports=function(e,t){t(e,0)}},236:function(e,t,r){var o=r(207),n=r(237),s=r(238);function a(e,t){this.indexName=t,this.as=e,this.typeAheadArgs=null,this.typeAheadValueOption=null,this.cache={}}e.exports=a,a.prototype.clearCache=function(){this.cache={}},a.prototype.search=o("query"),a.prototype.similarSearch=n(o("similarQuery"),s("index.similarSearch(query[, callback])","index.search({ similarQuery: query }[, callback])")),a.prototype.browse=function(e,t,o){var n,s,a=r(239),i=this;0===arguments.length||1===arguments.length&&"function"==typeof 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Retorna o \xe2ngulo em radianos.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"sinh(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Mesmo que ",Object(b.b)("inlineCode",{parentName:"td"},"sin()"),", mas para seno hiperb\xf3lico.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"sqrt(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Raiz quadrada de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"tan(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Tangente de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". 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Retorna o n\xfamero inteiro de ",Object(b.b)("inlineCode",{parentName:"td"},"A")," sem a parcela fracionada.")))),Object(b.b)("p",null,"\xc9 poss\xedvel atribuir novas vari\xe1veis utilizando a seguinte sintaxe: "),Object(b.b)("pre",null,Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"<nome da vari\xe1vel> := <express\xe3o>; <fun\xe7\xe3o>\n")),Object(b.b)("p",null,"Por exemplo:"),Object(b.b)("pre",null,Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"comprimento := sqrt(x*x+y*y); 2*comprimento*sin(comprimento)\n")),Object(b.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"O caractere de espa\xe7o e de nova linha s\xe3o ignorados na interpreta\xe7\xe3o da express\xe3o, portanto para maior organiza\xe7\xe3o, o c\xf3digo anterior pode ser escrito da seguinte forma:"),Object(b.b)("pre",{parentName:"div"},Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"comprimento := sqrt(x*x+y*y);\n2*comprimento*sin(comprimento)\n")))),Object(b.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"Note que a express\xe3o que determina o valor de sa\xedda do bloco ",Object(b.b)("strong",{parentName:"p"},"n\xe3o possui")," o caractere ",Object(b.b)("inlineCode",{parentName:"p"},";")," em seu final."))),Object(b.b)("h2",{id:"formul\xe1rio-de-edi\xe7\xe3o-de-dados-do-bloco-de-express\xe3o-matem\xe1tica"},"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de Express\xe3o Matem\xe1tica"),Object(b.b)("p",null,"O formul\xe1rio de inser\xe7\xe3o e edi\xe7\xe3o das entradas do bloco e da express\xe3o matem\xe1tica gen\xe9rica, assim como ferramentas de aux\xedlio de sua constru\xe7\xe3o \xe9 apresentado na figura abaixo."),Object(b.b)("div",null,Object(b.b)("center",null,Object(b.b)("img",{src:Object(m.a)("images/mathExpressionForm.png"),alt:"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de express\xe3o matem\xe1tica no PSP-UFU",title:"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de express\xe3o matem\xe1tica no PSP-UFU"}))),Object(b.b)("p",null,"No campo de \u201cVari\xe1veis de entrada\u201d \xe9 inserida uma lista com os nomes das entradas separados por espa\xe7os. Um n\xfamero qualquer de entrada pode ser definido nessa lista esses nomes s\xe3o apresentados no \xedcone gr\xe1fico presente no editor de controle, al\xe9m de serem destacados na express\xe3o inserida pelo usu\xe1rio. O n\xfamero de entradas e sa\xeddas se comporta de forma semelhante aos ",Object(b.b)("a",Object(n.a)({parentName:"p"},{href:"sum"}),"blocos somadores"),"."),Object(b.b)("p",null,"Abaixo do campo das vari\xe1veis de entrada est\xe1 presente o local para inser\xe7\xe3o da express\xe3o matem\xe1tica. A sintaxe da express\xe3o inserida pelo usu\xe1rio possui realce (por meio de diferentes formas e cores da fonte) para n\xfameros, operadores, vari\xe1veis de entrada, fun\xe7\xf5es e constantes, facilitando a cria\xe7\xe3o, manipula\xe7\xe3o e identifica\xe7\xe3o de erros de digita\xe7\xe3o e l\xf3gica."),Object(b.b)("div",{className:"admonition admonition-info alert alert--info"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"Como ferramenta de aux\xedlio ao usu\xe1rio foi desenvolvida uma verifica\xe7\xe3o da express\xe3o inserida."))),Object(b.b)("p",null,"Tal ferramenta ir\xe1 encontrar erros e indicar\xe1 ao usu\xe1rio qual o tipo do erro, al\xe9m da sua localiza\xe7\xe3o, destacando-o. A figura anterior exemplifica a identifica\xe7\xe3o autom\xe1tica do erro pelo PSP-UFU, assim como sua posi\xe7\xe3o na express\xe3o inserida."),Object(b.b)("h2",{id:"exemplo-de-express\xe3o-matem\xe1tica"},"Exemplo de Express\xe3o Matem\xe1tica"),Object(b.b)("p",null,"A corrente de campo em ",Object(b.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(b.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(b.b)("semantics",{parentName:"math"},Object(b.b)("mrow",{parentName:"semantics"},Object(b.b)("mi",{parentName:"mrow"},"p"),Object(b.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(b.b)("mi",{parentName:"mrow"},"u"),Object(b.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),".")))))," pode ser estimada de forma aproximada utilizando as pot\xeancias ativa (",Object(b.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(b.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(b.b)("semantics",{parentName:"math"},Object(b.b)("mrow",{parentName:"semantics"},Object(b.b)("mi",{parentName:"mrow"},"P")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"P")))),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.68333em",verticalAlign:"0em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.13889em"}}),"P"))))),") e reativa (",Object(b.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(b.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(b.b)("semantics",{parentName:"math"},Object(b.b)("mrow",{parentName:"semantics"},Object(b.b)("mi",{parentName:"mrow"},"Q")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"Q")))),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.8777699999999999em",verticalAlign:"-0.19444em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"Q"))))),"), assim como as reat\xe2ncias transit\xf3rias de eixo direto 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t=this.input.getInputValue();t.length>=this.minLength?this.dropdown.update(t):this.dropdown.empty()}this.dropdown.open()},close:function(){this.dropdown.close()},setVal:function(t){t=i.toStr(t),this.isActivated?this.input.setInputValue(t):(this.input.setQuery(t),this.input.setInputValue(t,!0)),this._setLanguageDirection()},getVal:function(){return this.input.getQuery()},destroy:function(){this.input.destroy(),this.dropdown.destroy(),function(t,e){var n=t.find(i.className(e.prefix,e.input));i.each(n.data("aaAttrs"),(function(t,e){void 0===t?n.removeAttr(e):n.attr(e,t)})),n.detach().removeClass(i.className(e.prefix,e.input,!0)).insertAfter(t),n.removeData&&n.removeData("aaAttrs");t.remove()}(this.$node,this.cssClasses),this.$node=null},getWrapper:function(){return this.dropdown.$container[0]}}),l.Dropdown=o,l.Input=a,l.sources=n(277),t.exports=l},267:function(t,e,n){"use strict";var i;i={9:"tab",27:"esc",37:"left",39:"right",13:"enter",38:"up",40:"down"};var 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e=new Array(arguments.length-1);if(arguments.length>1)for(var n=1;n<arguments.length;n++)e[n-1]=arguments[n];u.push(new d(t,e)),c||i||(c=!0,r())}},270:function(t,e,n){"use strict";(function(t){e.test=function(){return"function"==typeof t.queueMicrotask},e.install=function(e){return function(){t.queueMicrotask(e)}}}).call(this,n(52))},271:function(t,e,n){"use strict";(function(t){var n=t.MutationObserver||t.WebKitMutationObserver;e.test=function(){return n},e.install=function(e){var i=0,s=new n(e),r=t.document.createTextNode("");return s.observe(r,{characterData:!0}),function(){r.data=i=++i%2}}}).call(this,n(52))},272:function(t,e,n){"use strict";(function(t){e.test=function(){return!t.setImmediate&&void 0!==t.MessageChannel},e.install=function(e){var n=new t.MessageChannel;return n.port1.onmessage=e,function(){n.port2.postMessage(0)}}}).call(this,n(52))},273:function(t,e,n){"use strict";(function(t){e.test=function(){return"document"in t&&"onreadystatechange"in 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-(window.webpackJsonp=window.webpackJsonp||[]).push([[21],{121:function(a,e,t){"use strict";t.r(e),t.d(e,"frontMatter",(function(){return b})),t.d(e,"metadata",(function(){return c})),t.d(e,"rightToc",(function(){return p})),t.d(e,"default",(function(){return o}));var n=t(2),s=t(6),m=(t(0),t(161)),r=t(162),b={id:"bus",title:"Barramento",sidebar_label:"Barramento"},c={id:"bus",isDocsHomePage:!1,title:"Barramento",description:"Condutor de baixa imped\xe2ncia ao qual v\xe1rios circuitos el\xe9tricos podem ser conectados em pontos separados.",source:"@site/docs\\bus.md",permalink:"/PSP/docs/bus",editUrl:"https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/bus.md",sidebar_label:"Barramento",sidebar:"docs",previous:{title:"Editor de Pot\xeancia",permalink:"/PSP/docs/powerEditor"},next:{title:"Linha",permalink:"/PSP/docs/line"}},p=[{value:"Barramento no PSP-UFU",id:"barramento-no-psp-ufu",children:[]},{value:"Formul\xe1rio de edi\xe7\xe3o dos barramentos",id:"formul\xe1rio-de-edi\xe7\xe3o-dos-barramentos",children:[{value:"Geral",id:"geral",children:[]},{value:"Falta",id:"falta",children:[]},{value:"Estabilidade",id:"estabilidade",children:[]},{value:"Qualidade de energia",id:"qualidade-de-energia",children:[]}]}],i={rightToc:p};function o(a){var e=a.components,t=Object(s.a)(a,["components"]);return Object(m.b)("wrapper",Object(n.a)({},i,t,{components:e,mdxType:"MDXLayout"}),Object(m.b)("link",{rel:"stylesheet",href:Object(r.a)("katex/katex.min.css")}),Object(m.b)("blockquote",null,Object(m.b)("p",{parentName:"blockquote"},"Condutor de baixa imped\xe2ncia ao qual v\xe1rios circuitos el\xe9tricos podem ser conectados em pontos separados.\nNota - Em muitos casos, o barramento consiste em uma barra. 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Essa vari\xe1vel \xe9 normalmente utilizada no c\xe1lculo do erro da tens\xe3o de refer\xeancia do AVR;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Velocidade")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR e RV"),"): Velocidade da m\xe1quina s\xedncrona, em rad/s, vari\xe1vel no tempo. 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Normalmente utilizada como entrada do PSS (pot\xeancia ativa) e controle de sub e sobrecorrente de excita\xe7\xe3o nos AVRs;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Tens\xe3o terminal inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR"),"): M\xf3dulo da tens\xe3o no barramento da m\xe1quina s\xedncrona pr\xe9via ao estudo din\xe2mico originado do fluxo de carga, em ",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."))))),", fixo no tempo. Essa vari\xe1vel est\xe1 normalmente associada \xe0 refer\xeancia de tens\xe3o do AVR;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Velocidade inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR e RV"),"): Velocidade do sistema (2\u03c0f_ref), definida nas op\xe7\xf5es de simula\xe7\xe3o, em rad/s, fixa no tempo. Normalmente utiliza-se essa vari\xe1vel como refer\xeancia de velocidade em RVs e normaliza\xe7\xe3o da velocidade;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Pot\xeancia mec\xe2nica inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: RV"),"): Pot\xeancia mec\xe2nica inicial, calculada ap\xf3s a inicializa\xe7\xe3o das m\xe1quinas s\xedncronas com os dados originados do fluxo de carga, em ",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."))))),", fixa no tempo. Normalmente \xe9 utilizada como refer\xeancia de pot\xeancia mec\xe2nica nos reguladores de velocidade;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Varia\xe7\xe3o de velocidade e pot\xeancia ativa")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR"),"): C\xe1lculo da varia\xe7\xe3o dessas entradas entre os passos de integra\xe7\xe3o normalizada pelo passo de integra\xe7\xe3o, conforme a equa\xe7\xe3o:"),Object(m.b)("div",Object(n.a)({parentName:"li"},{className:"math 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Essa vari\xe1vel est\xe1 normalmente associada \xe0 refer\xeancia de tens\xe3o do AVR;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Velocidade inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR e RV"),"): Velocidade do sistema (",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mn",{parentName:"mrow"},"2"),Object(m.b)("mi",{parentName:"mrow"},"\u03c0"),Object(m.b)("msub",{parentName:"mrow"},Object(m.b)("mi",{parentName:"msub"},"f"),Object(m.b)("mrow",{parentName:"msub"},Object(m.b)("mi",{parentName:"mrow"},"r"),Object(m.b)("mi",{parentName:"mrow"},"e"),Object(m.b)("mi",{parentName:"mrow"},"f")))),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"2 \\pi f_{ref}")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.980548em",verticalAlign:"-0.286108em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"2"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.03588em"}}),"\u03c0"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.10764em"}}),"f"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"msupsub"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-t vlist-t2"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist",style:{height:"0.3361079999999999em"}}),Object(m.b)("span",Object(n.a)({parentName:"span"},{style:{top:"-2.5500000000000003em",marginLeft:"-0.10764em",marginRight:"0.05em"}}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mtight"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.02778em"}}),"r"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"e"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.10764em"}}),"f"))))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist",style:{height:"0.286108em"}}),Object(m.b)("span",{parentName:"span"})))))))))),"), definida nas ",Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"simulationConfig"}),"op\xe7\xf5es de simula\xe7\xe3o"),", em rad/s, fixa no tempo. Normalmente utiliza-se essa vari\xe1vel como refer\xeancia de velocidade em RVs e normaliza\xe7\xe3o da velocidade;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Pot\xeancia mec\xe2nica inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: RV"),"): Pot\xeancia mec\xe2nica inicial, calculada ap\xf3s a inicializa\xe7\xe3o das m\xe1quinas s\xedncronas com os dados originados do fluxo de carga, em ",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."))))),", fixa no tempo. Normalmente \xe9 utilizada como refer\xeancia de pot\xeancia mec\xe2nica nos reguladores de velocidade;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Varia\xe7\xe3o de velocidade e pot\xeancia ativa")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR"),"): C\xe1lculo da varia\xe7\xe3o dessas entradas entre os passos de integra\xe7\xe3o normalizada pelo passo de integra\xe7\xe3o, conforme a equa\xe7\xe3o:"),Object(m.b)("div",Object(n.a)({parentName:"li"},{className:"math 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Tamb\xe9m s\xe3o apresentadas as solu\xe7\xf5es para os erros mais recorrentes."),Object(r.b)("h2",{id:"windows"},"Windows"),Object(r.b)("p",null,"Ap\xf3s baixar o arquivo ",Object(r.b)("em",{parentName:"p"},".exe")," avance em cada passo do instalador. O execut\xe1vel ir\xe1 solicitar automaticamente a instala\xe7\xe3o do ",Object(r.b)("strong",{parentName:"p"},"Microsoft Visual C++ Redistribu\xedvel")," e, caso n\xe3o esteja instalado no seu computador, realize os procedimentos do programa."),Object(r.b)("p",null,"Caso o execut\xe1vel falhe em abrir, baixe o arquivo ",Object(r.b)("em",{parentName:"p"},".zip")," e descompacte em alguma pasta do seu sistema. 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O execut\xe1vel est\xe1 presente na pasta "',Object(r.b)("em",{parentName:"p"},"<local de instala\xe7\xe3o>/PSP-UFU/bin/PSP-UFU.exe"),'".'),Object(r.b)("h3",{id:"problemas-recorrentes-no-windows"},"Problemas recorrentes no Windows"),Object(r.b)("ul",null,Object(r.b)("li",{parentName:"ul"},"Ao baixar o navegador pode ",Object(r.b)("strong",{parentName:"li"},"falsamente"),' sinalizar que \xe9 um arquivo perigoso, basta clicar em "Manter arquivo";'),Object(r.b)("li",{parentName:"ul"},'Ao abrir o instalador, novamente o Windows sinaliza que o arquivo \xe9 perigoso, basta clicar em "Executar assim mesmo";'),Object(r.b)("li",{parentName:"ul"},"Ao abrir o programa e alterar o seu idioma, uma mensagem de erro \xe9 exibida. Para resolver esse problema basta executar o PSP-UFU como administrador (clicar com bot\xe3o direito no atalho do programa e posteriormente em executar como administrador). Altere novamente o idioma e reinicie o programa;"),Object(r.b)("li",{parentName:"ul"},'Ao criar um novo projeto a tela de trabalho n\xe3o \xe9 exibida ou \xe9 exibida uma tela preta. V\xe1 nas op\xe7\xf5es gerais e altere o renderizador para "Device Context". Caso apare\xe7a uma mensagem de erro, execute o programa como administrador e repita o processo. Reinicie o programa.')),Object(r.b)("h2",{id:"linux"},"Linux"),Object(r.b)("p",null,"A instala\xe7\xe3o no sistema Linux \xe9 facilmente realizado pelo pacote de instala\xe7\xe3o autom\xe1tico ",Object(r.b)("em",{parentName:"p"},".deb"),"."),Object(r.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 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terminal:")),Object(r.b)("pre",null,Object(r.b)("code",Object(n.a)({parentName:"pre"},{className:"language-shell"}),"./PSP-UFU\n")),Object(r.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Verifique se o computador possui as unidades de v\xeddeo instaladas corretamente, caso contr\xe1rio, o programa n\xe3o exibir\xe1 a \xe1rea de trabalho para criar e editar diagramas de linha \xfanica ou diagramas de blocos de controle."))))}m.isMDXComponent=!0},160:function(e,a,t){"use strict";var n=t(0),o=t(35);a.a=function(){return Object(n.useContext)(o.a)}},161:function(e,a,t){"use strict";t.d(a,"a",(function(){return m})),t.d(a,"b",(function(){return u}));var n=t(0),o=t.n(n);function r(e,a,t){return a in e?Object.defineProperty(e,a,{value:t,enumerable:!0,configurable:!0,writable:!0}):e[a]=t,e}function i(e,a){var t=Object.keys(e);if(Object.getOwnPropertySymbols){var n=Object.getOwnPropertySymbols(e);a&&(n=n.filter((function(a){return 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Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(m.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(m.b)("h4",{id:"tens\xe3o-nominal"},"Tens\xe3o nominal"),Object(m.b)("p",null,"Campo de informa\xe7\xe3o ",Object(m.b)("em",{parentName:"p"},"n\xe3o edit\xe1vel")," que apresenta a tens\xe3o prim\xe1ria e secund\xe1ria do transformador. 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href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Minor changes to 32bit MSW version for compatibility;</li><li>Travis CI (Continuous Integration) implemented (Linux).</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><div><a href="https://github.com/Thales1330/PSP/tree/master/docs/blog/2019-11-01-2019w44a-beta.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" 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some machines can&#x27;t use it properly);</li><li>Added Visual Studio solution to the GitHub project;</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><div><a href="https://github.com/Thales1330/PSP/tree/master/docs/blog/2020-06-13-2020w24a-beta.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="margin-vert--xl"><nav class="pagination-nav" aria-label="Blog post page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/blog/2020w28a-beta"><div class="pagination-nav__sublabel">Previous Post</div><div class="pagination-nav__label">« 2020w28a-beta</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/blog/2019w44a-beta"><div class="pagination-nav__sublabel">Next Post</div><div class="pagination-nav__label">22019w44a-beta »</div></a></div></nav></div></div></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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Code</a><div class="react-toggle react-toggle--disabled displayOnlyInLargeViewport_1gtM"><div class="react-toggle-track"><div class="react-toggle-track-check"><span class="toggle_keGJ moon_1gwN"></span></div><div class="react-toggle-track-x"><span class="toggle_keGJ sun_3CPA"></span></div></div><div class="react-toggle-thumb"></div><input type="checkbox" disabled="" aria-label="Dark mode toggle" class="react-toggle-screenreader-only"></div><div class="navbar__search"><div class="searchWrapper_-F3-"><span aria-label="expand searchbar" role="button" class="searchIconButton_1Dnz" tabindex="0"></span><input type="search" id="search_input_react" placeholder="Search" aria-label="Search" class="navbar__search-input searchInput_2eto"></div></div></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link navbar__link--active" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><div class="container margin-vert--lg"><div class="row"><div class="col col--8 col--offset-2"><article><header><h1 class="margin-bottom--sm blogPostTitle_2RZH">2020w28a-beta</h1><div class="margin-vert--md"><time datetime="2020-07-09T00:00:00.000Z" class="blogPostDate_3tRe">July 9, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Voltage heatmap implemented (OpenGL enabled);</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><div><a href="https://github.com/Thales1330/PSP/tree/master/docs/blog/2020-07-09-2020w28a-beta.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="margin-vert--xl"><nav class="pagination-nav" aria-label="Blog post page navigation"><div class="pagination-nav__item"></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/blog/2020w24a-beta"><div class="pagination-nav__sublabel">Next Post</div><div class="pagination-nav__label">2020w24a-beta »</div></a></div></nav></div></div></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" 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 <nav class="navbar navbar--light navbar--fixed-top"><div class="navbar__inner"><div class="navbar__items"><div aria-label="Navigation bar toggle" class="navbar__toggle" role="button" tabindex="0"><svg xmlns="http://www.w3.org/2000/svg" width="30" height="30" viewBox="0 0 30 30" role="img" focusable="false"><title>Menu</title><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></div><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a><a class="navbar__item navbar__link" href="/PSP/docs/">User Guide</a><a aria-current="page" class="navbar__item navbar__link navbar__link--active" href="/PSP/blog">Changelog</a></div><div class="navbar__items navbar__items--right"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="navbar__item navbar__link">PSP-UFU Source Code</a><div class="react-toggle react-toggle--disabled displayOnlyInLargeViewport_1gtM"><div class="react-toggle-track"><div class="react-toggle-track-check"><span class="toggle_keGJ moon_1gwN"></span></div><div class="react-toggle-track-x"><span class="toggle_keGJ sun_3CPA"></span></div></div><div class="react-toggle-thumb"></div><input type="checkbox" disabled="" aria-label="Dark mode toggle" class="react-toggle-screenreader-only"></div><div class="navbar__search"><div class="searchWrapper_-F3-"><span aria-label="expand searchbar" role="button" class="searchIconButton_1Dnz" tabindex="0"></span><input type="search" id="search_input_react" placeholder="Search" aria-label="Search" class="navbar__search-input searchInput_2eto"></div></div></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link navbar__link--active" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><div class="container margin-vert--lg"><div class="row"><main class="col col--8 col--offset-2"><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_2RZH"><a href="/PSP/blog/2020w28a-beta">2020w28a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-07-09T00:00:00.000Z" class="blogPostDate_3tRe">July 9, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Voltage heatmap implemented (OpenGL enabled);</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_2RZH"><a href="/PSP/blog/2020w24a-beta">2020w24a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-06-13T00:00:00.000Z" class="blogPostDate_3tRe">June 13, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Device context render implemented (to avoid use OpenGL - some machines can&#x27;t use it properly);</li><li>Added Visual Studio solution to the GitHub project;</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_2RZH"><a href="/PSP/blog/2019w44a-beta">22019w44a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-11-01T00:00:00.000Z" class="blogPostDate_3tRe">November 1, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Minor changes to 32bit MSW version for compatibility;</li><li>Travis CI (Continuous Integration) implemented (Linux).</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_2RZH"><a href="/PSP/blog/2019w42a-beta">2019w42a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-10-13T00:00:00.000Z" class="blogPostDate_3tRe">October 13, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Harmonic study implemented;</li><li>Autolayout from importation implemented;</li><li>Importation of Matpower files;</li><li>Several minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"></div><div class="pagination-nav__item pagination-nav__item--next"></div></nav></main></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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 <nav class="navbar navbar--light navbar--fixed-top"><div class="navbar__inner"><div class="navbar__items"><div aria-label="Navigation bar toggle" class="navbar__toggle" role="button" tabindex="0"><svg xmlns="http://www.w3.org/2000/svg" width="30" height="30" viewBox="0 0 30 30" role="img" focusable="false"><title>Menu</title><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></div><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a><a class="navbar__item navbar__link" href="/PSP/docs/">User Guide</a><a aria-current="page" class="navbar__item navbar__link navbar__link--active" href="/PSP/blog">Changelog</a></div><div class="navbar__items navbar__items--right"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="navbar__item navbar__link">PSP-UFU Source Code</a><div class="react-toggle react-toggle--disabled displayOnlyInLargeViewport_1gtM"><div class="react-toggle-track"><div class="react-toggle-track-check"><span class="toggle_keGJ moon_1gwN"></span></div><div class="react-toggle-track-x"><span class="toggle_keGJ sun_3CPA"></span></div></div><div class="react-toggle-thumb"></div><input type="checkbox" disabled="" aria-label="Dark mode toggle" class="react-toggle-screenreader-only"></div><div class="navbar__search"><div class="searchWrapper_-F3-"><span aria-label="expand searchbar" role="button" class="searchIconButton_1Dnz" tabindex="0"></span><input type="search" id="search_input_react" placeholder="Search" aria-label="Search" class="navbar__search-input searchInput_2eto"></div></div></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link navbar__link--active" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><div class="container margin-vert--lg"><div class="row"><main class="col col--8 col--offset-2"><h1>4 posts tagged with &quot;psp-ufu&quot;</h1><a href="/PSP/blog/tags">View All Tags</a><div class="margin-vert--xl"><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_2RZH"><a href="/PSP/blog/2020w28a-beta">2020w28a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-07-09T00:00:00.000Z" class="blogPostDate_3tRe">July 9, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Voltage heatmap implemented (OpenGL enabled);</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 2020w28a-beta" href="/PSP/blog/2020w28a-beta"><strong>Read More</strong></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_2RZH"><a href="/PSP/blog/2020w24a-beta">2020w24a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-06-13T00:00:00.000Z" class="blogPostDate_3tRe">June 13, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Device context render implemented (to avoid use OpenGL - some machines can&#x27;t use it properly);</li><li>Added Visual Studio solution to the GitHub project;</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 2020w24a-beta" href="/PSP/blog/2020w24a-beta"><strong>Read More</strong></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_2RZH"><a href="/PSP/blog/2019w44a-beta">22019w44a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-11-01T00:00:00.000Z" class="blogPostDate_3tRe">November 1, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Minor changes to 32bit MSW version for compatibility;</li><li>Travis CI (Continuous Integration) implemented (Linux).</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 22019w44a-beta" href="/PSP/blog/2019w44a-beta"><strong>Read More</strong></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_2RZH"><a href="/PSP/blog/2019w42a-beta">2019w42a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-10-13T00:00:00.000Z" class="blogPostDate_3tRe">October 13, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Harmonic study implemented;</li><li>Autolayout from importation implemented;</li><li>Importation of Matpower files;</li><li>Several minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 2019w42a-beta" href="/PSP/blog/2019w42a-beta"><strong>Read More</strong></a></div></footer></article></div></main></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. Built with Docusaurus.</div></div></div></footer></div>
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Os elementos s\xe3o ent\xe3o conectados por \u201clinhas de conex\xe3o\u201d inseridas ao clicar nos n\xf3s dos componentes previamente adicionados, permitindo a constru\xe7\xe3o da rede de controle gen\xe9rica."),Object(m.b)("p",null,"As ferramentas de manipula\xe7\xe3o e navega\xe7\xe3o, como arrastar, mover e excluir s\xe3o ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"cadTools"}),"herdadas")," do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de elementos de pot\xeancia"),", possuindo comportamento id\xeantico. 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Tal procedimento \xe9 realizado por meio da solu\xe7\xe3o de toda rede de controle at\xe9 que se obtenha sua converg\xeancia, ou seja, a diferen\xe7a absoluta entre as mesmas sa\xeddas de uma solu\xe7\xe3o anterior e uma atual deve ser nula ou muito pr\xf3xima de zero."),Object(m.b)("div",{className:"admonition admonition-info alert alert--info"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"info")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"O processo de ",Object(m.b)("strong",{parentName:"p"},"inicializa\xe7\xe3o \xe9 realizada automaticamente")," pelo PSP-UFU."),Object(m.b)("p",{parentName:"div"},"Uma vez que a inicializa\xe7\xe3o \xe9 imposta pelas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"io"}),"entradas")," do controle, erros de converg\xeancia podem ocorrer devido \xe0 m\xe1 parametriza\xe7\xe3o dos elementos dos sistemas de ",Object(m.b)("strong",{parentName:"p"},"pot\xeancia e controle"),"."))),Object(m.b)("p",null,"Para otimizar e melhorar a estabilidade do processo de inicializa\xe7\xe3o utilizou-se um passo de integra\xe7\xe3o vari\xe1vel dentro de limites, de forma que o passo aumenta em condi\xe7\xf5es de diferen\xe7as menores entre as solu\xe7\xf5es do sistema de controle e diminui caso essa diferen\xe7a se torne elevada. 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+(window.webpackJsonp=window.webpackJsonp||[]).push([[48],{147:function(e,a,t){"use strict";t.r(a),t.d(a,"frontMatter",(function(){return b})),t.d(a,"metadata",(function(){return p})),t.d(a,"rightToc",(function(){return r})),t.d(a,"default",(function(){return i}));var s=t(2),n=t(6),m=(t(0),t(166)),c=t(167),b={id:"controlEditor",title:"Editor de Controle",sidebar_label:"Editor de Controle"},p={id:"controlEditor",isDocsHomePage:!1,title:"Editor de Controle",description:"Os controles das m\xe1quinas s\xedncronas s\xe3o criados, modificados, importados e exportados em um editor distinto dos elementos de pot\xeancia, apresentado na figura abaixo.",source:"@site/docs\\controlEditor.md",permalink:"/PSP/docs/controlEditor",editUrl:"https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/controlEditor.md",sidebar_label:"Editor de Controle",sidebar:"docs",previous:{title:"Motor de Indu\xe7\xe3o",permalink:"/PSP/docs/indMotor"},next:{title:"Entrada / Sa\xedda",permalink:"/PSP/docs/io"}},r=[{value:"Elementos de Controle",id:"elementos-de-controle",children:[]},{value:"Inicializa\xe7\xe3o do sistema de controle",id:"inicializa\xe7\xe3o-do-sistema-de-controle",children:[]},{value:"Teste do diagrama de controle",id:"teste-do-diagrama-de-controle",children:[]}],l={rightToc:r};function i(e){var a=e.components,t=Object(n.a)(e,["components"]);return Object(m.b)("wrapper",Object(s.a)({},l,t,{components:a,mdxType:"MDXLayout"}),Object(m.b)("link",{rel:"stylesheet",href:Object(c.a)("katex/katex.min.css")}),Object(m.b)("p",null,"Os controles das ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quinas s\xedncronas")," s\xe3o criados, modificados, importados e exportados em um editor distinto dos elementos de pot\xeancia, apresentado na figura abaixo."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(c.a)("images/controlEditor.png"),alt:"Editor de elementos de controle do PSP-UFU",title:"Editor de elementos de controle do PSP-UFU"}))),Object(m.b)("p",null,"O acesso ao editor \xe9 realizado por meio de dois bot\xf5es presentes no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator#formul%C3%A1rio-de-edi%C3%A7%C3%A3o-dos-geradores-s%C3%ADncronos"}),"formul\xe1rio de edi\xe7\xe3o dos dados de estabilidade dos geradores s\xedncronos"),":"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"syncGenerator#utilizar-avr-e-regulador-de-velocidade"}),"Editar AVR")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"syncGenerator#utilizar-avr-e-regulador-de-velocidade"}),"Editar regulador de velocidade"))),Object(m.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"No PSP-UFU a op\xe7\xe3o de editar o ",Object(m.b)("strong",{parentName:"p"},"AVR")," engloba mais que somente o controle de tens\xe3o da m\xe1quina. 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Nessa op\xe7\xe3o ",Object(m.b)("strong",{parentName:"p"},"deve")," ser inserida ao menos a malha de controle da regula\xe7\xe3o prim\xe1ria de velocidade, assim como o ",Object(m.b)("strong",{parentName:"p"},"modelo da turbina"),". Estrat\xe9gias opcionais de controle da velocidade tamb\xe9m s\xe3o inseridas nessa op\xe7\xe3o."))),Object(m.b)("h2",{id:"elementos-de-controle"},"Elementos de Controle"),Object(m.b)("p",null,"O acesso aos elementos de controle \xe9 realizado em uma janela (remov\xedvel e encaix\xe1vel) por meio de \xedcones relacionados."),Object(m.b)("p",null,"Uma vez que o usu\xe1rio clicar no \xedcone desejado, o elemento de controle acompanhar\xe1 o ponteiro do mouse at\xe9 ser efetivamente inserido na posi\xe7\xe3o desejada ao clicar novamente na \xe1rea de trabalho. Os elementos s\xe3o ent\xe3o conectados por \u201clinhas de conex\xe3o\u201d inseridas ao clicar nos n\xf3s dos componentes previamente adicionados, permitindo a constru\xe7\xe3o da rede de controle gen\xe9rica."),Object(m.b)("p",null,"As ferramentas de manipula\xe7\xe3o e navega\xe7\xe3o, como arrastar, mover e excluir s\xe3o ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"cadTools"}),"herdadas")," do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de elementos de pot\xeancia"),", possuindo comportamento id\xeantico. 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Nele \xe9 poss\xedvel tamb\xe9m acessar aos controles das m\xe1quinas s\xedncronas manipulados pelo ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"editor de controle"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/syncGeneratorStabForm.png"),alt:"Formul\xe1rio de estabilidade dos geradores s\xedncronos no PSP-UFU",title:"Formul\xe1rio de estabilidade dos geradores s\xedncronos no PSP-UFU"}))),Object(n.b)("p",null,'No formul\xe1rio de estabilidade pode ser observado o bot\xe3o "Chaveamento" na parte inferior esquerda do formul\xe1rio. 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Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(n.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(n.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(n.b)("p",null,"Pot\xeancia nominal do gerador, inserida em MVA, kVA ou VA."),Object(n.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(n.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(n.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador."),Object(n.b)("p",null,"Caso a barra conectada seja PV o valor de pot\xeancia reativa ser\xe1 ignorado e caso seja de refer\xeancia ambos os valores inseridos ser\xe3o desprezados."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Caso mais de um gerador esteja conectado na mesma barra, os valores de pot\xeancia reativa (nas barras de refer\xeancia e PV) e ativa (nas barras de refer\xeancia) s\xe3o igualmente distribu\xeddas, respeitando os limites individuais de pot\xeancia reativa."))),Object(n.b)("h4",{id:"pot\xeancias-reativas-m\xe1xima-e-m\xednima"},"Pot\xeancias reativas m\xe1xima e m\xednima"),Object(n.b)("p",null,"Limites de pot\xeancia reativa m\xe1xima e m\xednima do gerador para controle de tens\xe3o em barras PV. 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IEEE, New York, nov. 2003. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/IEEESTD.2003.94408"}),"https://doi.org/10.1109/IEEESTD.2003.94408")),Object(n.b)("li",{parentName:"ol"},"KIMBARK, E. W. Power System Stability: Volume III \u2013 Synchronous Machine. New York: Wiley-IEEE Press, 1995.")))}l.isMDXComponent=!0},165:function(a,e,t){"use strict";var s=t(0),m=t(35);e.a=function(){return Object(s.useContext)(m.a)}},166:function(a,e,t){"use strict";t.d(e,"a",(function(){return j})),t.d(e,"b",(function(){return i}));var s=t(0),m=t.n(s);function n(a,e,t){return e in a?Object.defineProperty(a,e,{value:t,enumerable:!0,configurable:!0,writable:!0}):a[e]=t,a}function b(a,e){var t=Object.keys(a);if(Object.getOwnPropertySymbols){var s=Object.getOwnPropertySymbols(a);e&&(s=s.filter((function(e){return Object.getOwnPropertyDescriptor(a,e).enumerable}))),t.push.apply(t,s)}return t}function p(a){for(var e=1;e<arguments.length;e++){var t=null!=arguments[e]?arguments[e]:{};e%2?b(Object(t),!0).forEach((function(e){n(a,e,t[e])})):Object.getOwnPropertyDescriptors?Object.defineProperties(a,Object.getOwnPropertyDescriptors(t)):b(Object(t)).forEach((function(e){Object.defineProperty(a,e,Object.getOwnPropertyDescriptor(t,e))}))}return a}function c(a,e){if(null==a)return{};var t,s,m=function(a,e){if(null==a)return{};var t,s,m={},n=Object.keys(a);for(s=0;s<n.length;s++)t=n[s],e.indexOf(t)>=0||(m[t]=a[t]);return m}(a,e);if(Object.getOwnPropertySymbols){var n=Object.getOwnPropertySymbols(a);for(s=0;s<n.length;s++)t=n[s],e.indexOf(t)>=0||Object.prototype.propertyIsEnumerable.call(a,t)&&(m[t]=a[t])}return m}var r=m.a.createContext({}),O=function(a){var e=m.a.useContext(r),t=e;return a&&(t="function"==typeof a?a(e):p(p({},e),a)),t},j=function(a){var e=O(a.components);return m.a.createElement(r.Provider,{value:e},a.children)},N={inlineCode:"code",wrapper:function(a){var e=a.children;return m.a.createElement(m.a.Fragment,{},e)}},l=m.a.forwardRef((function(a,e){var t=a.components,s=a.mdxType,n=a.originalType,b=a.parentName,r=c(a,["components","mdxType","originalType","parentName"]),j=O(t),l=s,i=j["".concat(b,".").concat(l)]||j[l]||N[l]||n;return t?m.a.createElement(i,p(p({ref:e},r),{},{components:t})):m.a.createElement(i,p({ref:e},r))}));function i(a,e){var t=arguments,s=e&&e.mdxType;if("string"==typeof a||s){var n=t.length,b=new Array(n);b[0]=l;var p={};for(var c in e)hasOwnProperty.call(e,c)&&(p[c]=e[c]);p.originalType=a,p.mdxType="string"==typeof a?a:s,b[1]=p;for(var r=2;r<n;r++)b[r]=t[r];return m.a.createElement.apply(null,b)}return m.a.createElement.apply(null,t)}l.displayName="MDXCreateElement"},167:function(a,e,t){"use strict";t.d(e,"a",(function(){return n}));var s=t(165),m=t(168);function n(a,{forcePrependBaseUrl:e=!1,absolute:t=!1}={}){const{siteConfig:{baseUrl:n="/",url:b}={}}=Object(s.a)();if(!a)return a;if(e)return n+a;if(!Object(m.a)(a))return a;const p=n+a.replace(/^\//,"");return t?b+p:p}},168:function(a,e,t){"use strict";function s(a){return!1===/^(https?:|\/\/|mailto:|tel:)/.test(a)}t.d(e,"a",(function(){return s}))},169:function(a,e,t){"use strict";function s(a){var e,t,m="";if("string"==typeof a||"number"==typeof a)m+=a;else if("object"==typeof a)if(Array.isArray(a))for(e=0;e<a.length;e++)a[e]&&(t=s(a[e]))&&(m&&(m+=" "),m+=t);else for(e in a)a[e]&&(m&&(m+=" "),m+=e);return m}e.a=function(){for(var a,e,t=0,m="";t<arguments.length;)(a=arguments[t++])&&(e=s(a))&&(m&&(m+=" "),m+=e);return m}},170:function(a,e,t){"use strict";var s=t(0);const m=Object(s.createContext)({tabGroupChoices:{},setTabGroupChoices:()=>{},isAnnouncementBarClosed:!1,closeAnnouncementBar:()=>{}});e.a=m},171:function(a,e,t){"use strict";var s=t(0),m=t(170);e.a=function(){return Object(s.useContext)(m.a)}},172:function(a,e,t){"use strict";var s=t(0),m=t.n(s),n=t(171),b=t(169),p=t(92),c=t.n(p);const r=37,O=39;e.a=function(a){const{block:e,children:t,defaultValue:p,values:j,groupId:N}=a,{tabGroupChoices:l,setTabGroupChoices:i}=Object(n.a)(),[o,h]=Object(s.useState)(p);if(null!=N){const a=l[N];null!=a&&a!==o&&j.some(e=>e.value===a)&&h(a)}const d=a=>{h(a),null!=N&&i(N,a)},g=[];return m.a.createElement("div",null,m.a.createElement("ul",{role:"tablist","aria-orientation":"horizontal",className:Object(b.a)("tabs",{"tabs--block":e})},j.map(({value:a,label:e})=>m.a.createElement("li",{role:"tab",tabIndex:"0","aria-selected":o===a,className:Object(b.a)("tabs__item",c.a.tabItem,{"tabs__item--active":o===a}),key:a,ref:a=>g.push(a),onKeyDown:a=>((a,e,t)=>{switch(t.keyCode){case O:((a,e)=>{const t=a.indexOf(e)+1;a[t]?a[t].focus():a[0].focus()})(a,e);break;case r:((a,e)=>{const t=a.indexOf(e)-1;a[t]?a[t].focus():a[a.length-1].focus()})(a,e)}})(g,a.target,a),onFocus:()=>d(a),onClick:()=>d(a)},e))),m.a.createElement("div",{role:"tabpanel",className:"margin-vert--md"},s.Children.toArray(t).filter(a=>a.props.value===o)[0]))}},173:function(a,e,t){"use strict";var s=t(0),m=t.n(s);e.a=function(a){return m.a.createElement("div",null,a.children)}}}]);
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Nele \xe9 poss\xedvel tamb\xe9m acessar aos controles das m\xe1quinas s\xedncronas manipulados pelo ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"editor de controle"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/syncGeneratorStabForm.png"),alt:"Formul\xe1rio de estabilidade dos geradores s\xedncronos no PSP-UFU",title:"Formul\xe1rio de estabilidade dos geradores s\xedncronos no PSP-UFU"}))),Object(n.b)("p",null,'No formul\xe1rio de estabilidade pode ser observado o bot\xe3o "Chaveamento" na parte inferior esquerda do formul\xe1rio. Esse formul\xe1rio, comum a v\xe1rios outros elementos, permite a inser\xe7\xe3o e/ou remo\xe7\xe3o do gerador durante o estudo de ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/syncGeneratorSw.png"),alt:"Formul\xe1rio de chaveamento do gerador s\xedncrono",title:"Formul\xe1rio de chaveamento do gerador s\xedncrono"}))),Object(n.b)("hr",null),Object(n.b)("h3",{id:"geral"},"Geral"),Object(n.b)("h4",{id:"nome"},"Nome"),Object(n.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(n.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(n.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(n.b)("p",null,"Pot\xeancia nominal do gerador, inserida em MVA, kVA ou VA."),Object(n.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(n.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(n.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador."),Object(n.b)("p",null,"Caso a barra conectada seja PV o valor de pot\xeancia reativa ser\xe1 ignorado e caso seja de refer\xeancia ambos os valores inseridos ser\xe3o desprezados."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Caso mais de um gerador esteja conectado na mesma barra, os valores de pot\xeancia reativa (nas barras de refer\xeancia e PV) e ativa (nas barras de refer\xeancia) s\xe3o igualmente distribu\xeddas, respeitando os limites individuais de pot\xeancia reativa."))),Object(n.b)("h4",{id:"pot\xeancias-reativas-m\xe1xima-e-m\xednima"},"Pot\xeancias reativas m\xe1xima e m\xednima"),Object(n.b)("p",null,"Limites de pot\xeancia reativa m\xe1xima e m\xednima do gerador para controle de tens\xe3o em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade ser\xe1 limitado ao valor inserido e a barra conectada ser\xe1 transformada em PQ, n\xe3o controlando a tens\xe3o estabelecida."),Object(n.b)("h4",{id:"utilizar-pot\xeancia-nominal-como-base"},"Utilizar pot\xeancia nominal como base"),Object(n.b)("p",null,"Caso essa op\xe7\xe3o seja marcada, o programa ir\xe1 utilizar a pot\xeancia nominal do gerador como base para a convers\xe3o das unidades, inclusive aqueles no formul\xe1rio de estabilidade, caso contr\xe1rio ser\xe1 usada a ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"pot\xeancia base do sistema"),"."),Object(n.b)("hr",null),Object(n.b)("h3",{id:"falta"},"Falta"),Object(n.b)("h4",{id:"imped\xe2ncias-de-sequ\xeancia"},"Imped\xe2ncias de sequ\xeancia"),Object(n.b)("p",null,"Valores de resist\xeancia e reat\xe2ncia para c\xe1lculo das correntes de falta. S\xe3o inseridos dados de sequ\xeancia positiva, negativa e zero."),Object(n.b)("h4",{id:"imped\xe2ncia-de-aterramento"},"Imped\xe2ncia de aterramento"),Object(n.b)("p",null,"Valores utilizados para o c\xe1lculo das correntes de falta do tipo fase-terra e fase-fase-terra. Caso o neutro do gerador n\xe3o seja aterrado, o valor inserido nesse campo \xe9 ignorado."),Object(n.b)("h4",{id:"neutro-aterrado"},"Neutro aterrado"),Object(n.b)("p",null,"Indica se o neutro do gerador \xe9 aterrado."),Object(n.b)("hr",null),Object(n.b)("h3",{id:"bot\xe3o-estabilidade"},"Bot\xe3o Estabilidade"),Object(n.b)("h4",{id:"imprimir-dados-da-m\xe1quina-s\xedncrona"},"Imprimir dados da m\xe1quina s\xedncrona"),Object(n.b)("p",null,"Exibe os dados do gerador s\xedncrono nos gr\xe1ficos no tempo. Os seguintes dados s\xe3o exibidos:"),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},"tens\xe3o terminal"),Object(n.b)("li",{parentName:"ul"},"pot\xeancias ativa e reativas"),Object(n.b)("li",{parentName:"ul"},"pot\xeancia mec\xe2nica"),Object(n.b)("li",{parentName:"ul"},"frequ\xeancia"),Object(n.b)("li",{parentName:"ul"},"tens\xe3o de campo"),Object(n.b)("li",{parentName:"ul"},"\xe2ngulo ",Object(n.b)("span",Object(s.a)({parentName:"li"},{className:"math 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math-inline"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(n.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(n.b)("semantics",{parentName:"math"},Object(n.b)("mrow",{parentName:"semantics"},Object(n.b)("mi",{parentName:"mrow"},"p"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(n.b)("mi",{parentName:"mrow"},"u"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(n.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."))))),") de corrente de campo necess\xe1ria para atingir 1,2 p.u. de tens\xe3o terminal."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 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Os valores de eixo direto e em quadratura devem ser iguais ou muito pr\xf3ximos para representa\xe7\xe3o de uma m\xe1quina de polos lisos, enquanto para polos salientes esses valores s\xe3o distintos."),Object(n.b)("h4",{id:"reat\xe2ncias-e-constantes-de-tempo-transit\xf3rias"},"Reat\xe2ncias e constantes de tempo transit\xf3rias"),Object(n.b)("p",null,"Par\xe2metros transit\xf3rios da m\xe1quina s\xedncrona em ",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(n.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(n.b)("semantics",{parentName:"math"},Object(n.b)("mrow",{parentName:"semantics"},Object(n.b)("mi",{parentName:"mrow"},"p"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(n.b)("mi",{parentName:"mrow"},"u"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(n.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),".")))))," ou segundos."),Object(n.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O valor da reat\xe2ncia transit\xf3ria de eixo direto deve ser diferente de zero ou levar\xe1 o programa a erro."))),Object(n.b)("p",null,"De acordo com a quantidade de par\xe2metros inseridos \xe9 definido internamente pelo programa qual o modelo a ser utilizado."),Object(n.b)("h4",{id:"reat\xe2ncias-e-constantes-de-tempo-subtransit\xf3rias"},"Reat\xe2ncias e constantes de tempo subtransit\xf3rias"),Object(n.b)("p",null,"Par\xe2metros subtransit\xf3rios da m\xe1quina s\xedncrona em ",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(n.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(n.b)("semantics",{parentName:"math"},Object(n.b)("mrow",{parentName:"semantics"},Object(n.b)("mi",{parentName:"mrow"},"p"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(n.b)("mi",{parentName:"mrow"},"u"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(n.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),".")))))," ou segundos, representando em detalhes a presen\xe7a de enrolamentos amortecedores. Assim como os dados transit\xf3rios, esses par\xe2metros definem o modelo da m\xe1quina."),Object(n.b)("hr",null),Object(n.b)("h3",{id:"bot\xe3o-chaveamento"},"Bot\xe3o Chaveamento"),Object(n.b)("p",null,'O bot\xe3o "Chaveamento" ir\xe1 abrir um formul\xe1rio, comum a v\xe1rios outros elementos, que permite a inser\xe7\xe3o e/ou remo\xe7\xe3o do gerador durante o estudo de ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(n.b)("p",null,'Nesse formul\xe1rio pode ser criada uma lista gen\xe9rica de inser\xe7\xf5es e remo\xe7\xf5es da linha no tempo, personalizada por um contexto de propriedades de chaveamento que s\xe3o editados o tipo de chaveamento (inser\xe7\xe3o ou remo\xe7\xe3o) e o instante (em segundos) do evento. Essas propriedades s\xe3o atribu\xeddas e retiradas da lista gen\xe9rica por meio dos bot\xf5es "Adicionar" e "Remover", respectivamente.'),Object(n.b)("h2",{id:"refer\xeancias"},"Refer\xeancias"),Object(n.b)("ol",null,Object(n.b)("li",{parentName:"ol"},"MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1007/978-3-642-13669-6"}),"https://doi.org/10.1007/978-3-642-13669-6")),Object(n.b)("li",{parentName:"ol"},"ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1002/9781118878286"}),"https://doi.org/10.1002/9781118878286")),Object(n.b)("li",{parentName:"ol"},"KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994."),Object(n.b)("li",{parentName:"ol"},"DOMMEL, H. W.; SATO, N. Fast Transient Stability Solutions. IEEE Transactions on Power Aparatus and Systems, v. PAS-91, n. 4, jul 1972, p. 1643-1650. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/TPAS.1972.293341"}),"https://doi.org/10.1109/TPAS.1972.293341")),Object(n.b)("li",{parentName:"ol"},"IEEE Std 1110-2002 IEEE Guide for Synchronous Generator Modeling Practices and Applications in Power System Stability Analyses. IEEE, New York, nov. 2003. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/IEEESTD.2003.94408"}),"https://doi.org/10.1109/IEEESTD.2003.94408")),Object(n.b)("li",{parentName:"ol"},"KIMBARK, E. W. Power System Stability: Volume III \u2013 Synchronous Machine. New York: Wiley-IEEE Press, 1995.")))}j.isMDXComponent=!0},160:function(a,e,t){"use strict";var s=t(0),m=t(35);e.a=function(){return Object(s.useContext)(m.a)}},161:function(a,e,t){"use strict";t.d(e,"a",(function(){return j})),t.d(e,"b",(function(){return i}));var s=t(0),m=t.n(s);function n(a,e,t){return e in a?Object.defineProperty(a,e,{value:t,enumerable:!0,configurable:!0,writable:!0}):a[e]=t,a}function b(a,e){var t=Object.keys(a);if(Object.getOwnPropertySymbols){var s=Object.getOwnPropertySymbols(a);e&&(s=s.filter((function(e){return Object.getOwnPropertyDescriptor(a,e).enumerable}))),t.push.apply(t,s)}return t}function p(a){for(var e=1;e<arguments.length;e++){var t=null!=arguments[e]?arguments[e]:{};e%2?b(Object(t),!0).forEach((function(e){n(a,e,t[e])})):Object.getOwnPropertyDescriptors?Object.defineProperties(a,Object.getOwnPropertyDescriptors(t)):b(Object(t)).forEach((function(e){Object.defineProperty(a,e,Object.getOwnPropertyDescriptor(t,e))}))}return a}function c(a,e){if(null==a)return{};var t,s,m=function(a,e){if(null==a)return{};var t,s,m={},n=Object.keys(a);for(s=0;s<n.length;s++)t=n[s],e.indexOf(t)>=0||(m[t]=a[t]);return m}(a,e);if(Object.getOwnPropertySymbols){var n=Object.getOwnPropertySymbols(a);for(s=0;s<n.length;s++)t=n[s],e.indexOf(t)>=0||Object.prototype.propertyIsEnumerable.call(a,t)&&(m[t]=a[t])}return m}var r=m.a.createContext({}),O=function(a){var e=m.a.useContext(r),t=e;return a&&(t="function"==typeof a?a(e):p(p({},e),a)),t},j=function(a){var e=O(a.components);return m.a.createElement(r.Provider,{value:e},a.children)},N={inlineCode:"code",wrapper:function(a){var e=a.children;return m.a.createElement(m.a.Fragment,{},e)}},l=m.a.forwardRef((function(a,e){var t=a.components,s=a.mdxType,n=a.originalType,b=a.parentName,r=c(a,["components","mdxType","originalType","parentName"]),j=O(t),l=s,i=j["".concat(b,".").concat(l)]||j[l]||N[l]||n;return t?m.a.createElement(i,p(p({ref:e},r),{},{components:t})):m.a.createElement(i,p({ref:e},r))}));function i(a,e){var t=arguments,s=e&&e.mdxType;if("string"==typeof a||s){var n=t.length,b=new Array(n);b[0]=l;var p={};for(var c in e)hasOwnProperty.call(e,c)&&(p[c]=e[c]);p.originalType=a,p.mdxType="string"==typeof a?a:s,b[1]=p;for(var r=2;r<n;r++)b[r]=t[r];return m.a.createElement.apply(null,b)}return m.a.createElement.apply(null,t)}l.displayName="MDXCreateElement"},162:function(a,e,t){"use strict";t.d(e,"a",(function(){return n}));var s=t(160),m=t(163);function n(a,{forcePrependBaseUrl:e=!1,absolute:t=!1}={}){const{siteConfig:{baseUrl:n="/",url:b}={}}=Object(s.a)();if(!a)return a;if(e)return n+a;if(!Object(m.a)(a))return a;const p=n+a.replace(/^\//,"");return t?b+p:p}},163:function(a,e,t){"use strict";function s(a){return!1===/^(https?:|\/\/|mailto:|tel:)/.test(a)}t.d(e,"a",(function(){return s}))}}]);
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href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Barramento</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Condutor de baixa impedância ao qual vários circuitos elétricos podem ser conectados em pontos separados.
-Nota - Em muitos casos, o barramento consiste em uma barra. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=151-12-30" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="barramento-no-psp-ufu"></a>Barramento no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barramento-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento <strong>barramento</strong>, ou simplesmente <strong>barra</strong>, é um conector ou nó do diagrama unifilar do PSP-UFU. Essa barra pode representar um PAC (Ponto de Acoplamento Comum), um poste de distribuição, uma subestação, um barramento da subestação, entre inúmeros outros tipos pontos de análise e conexão entre elementos.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-barramentos"></a>Formulário de edição dos barramentos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-barramentos" title="Direct link to heading">#</a></h2><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O barramento deve ser o <strong>primeiro elemento elétrico a ser inserido no diagrama de potência</strong>, uma vez que os demais componentes de potência são conectados nele.</p></div></div><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das barras:</p><div><center><img src="/PSP/images/busForm.png" alt="Formulário dos barramentos no PSP-UFU" title="Formulário dos barramentos no PSP-UFU"></center></div><p>Esse formulário é subdividido em quatro contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais da barra e informações do fluxo de carga;</li><li><strong>Falta</strong>: local onde o curto-circuito <em>shunt</em> deve ser inserido;</li><li><strong>Estabilidade</strong>: contendo opções de visualização de dados da barra em gráficos no tempo e inserção de faltas trifásicas no cálculo de estabilidade transitória;</li><li><strong>Qualidade de energia</strong>: contém a opção de de visualização da impedância harmônica vista pela barra.</li></ul><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="geral"></a>Geral<a aria-hidden="true" tabindex="-1" class="hash-link" href="#geral" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Utilizado para cálculo da impedância base de alguns elementos conectados, além do cálculo da relação de transformação dos transformadores conectados entre barras. Sua unidade pode ser selecionada, sendo expressa em V ou em kV.</p><p>A modificação desse parâmetro irá alterar toda a tensão do trecho conectado por linhas elétricas, sendo emitido um alerta ao usuário.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tensão-controlada"></a>Tensão controlada<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-controlada" title="Direct link to heading">#</a></h4><p>Caracteriza o barramento como <strong>barra de tensão controlada (<a href="/PSP/docs/powerFlow">Barra PV</a>)</strong>,</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Essa opção é somente válida caso alguma máquina síncrona esteja conectado, caso contrário esse valor será ignorado. Caso o limite de potência reativa da máquina síncrona conectada seja ultrapassado esse valor também é ignorado.</p></div></div><p>O valor poderá ser inserido em p.u. ou em volts (ou kV caso a tensão nominal esteja nesta unidade).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="barra-de-referência"></a>Barra de referência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barra-de-referência" title="Direct link to heading">#</a></h4><p>Caracteriza o barramento como <strong>barra de referência (<a href="/PSP/docs/powerFlow">Barra de oscilação</a>)</strong>. Essa opção é somente válida caso esteja conectado um gerador síncrono, caso contrário uma mensagem de erro será exibida ao usuário ao realizar algum dos cálculos do programa.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="falta"></a>Falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#falta" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="inserir-falta"></a>Inserir falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inserir-falta" title="Direct link to heading">#</a></h4><p>Indica se existe um curto-circuito na barra nos estudos de <a href="/PSP/docs/fault">curto-circuito</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Nota-se que essa opção irá inserir uma falta no cálculo de <a href="/PSP/docs/fault">curto-circuito</a> e <strong>não será considerado no estudo de estabilidade</strong>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tipo-de-falta"></a>Tipo de falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tipo-de-falta" title="Direct link to heading">#</a></h4><p>Seleciona o tipo de falha shunt da barra:</p><ul><li>trifásico para a terra</li><li>fase-fase</li><li>fase-fase-terra</li><li>fase-terra</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="local-da-falta"></a>Local da falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#local-da-falta" title="Direct link to heading">#</a></h4><p>Seleciona a fase em que se situa a falta (ou combinação delas no caso de falha entre duas fases), sendo essa opção desabilitada para o tipo de falta trifásica.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="resistência-e-reatância-de-falta"></a>Resistência e reatância de falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#resistência-e-reatância-de-falta" title="Direct link to heading">#</a></h4><p>Representam a impedância da falta. Curtos-circuitos francos (sem impedância de falta) são representados inserindo valor zero em ambos os campos.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="estabilidade"></a>Estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#estabilidade" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="imprimir-dados"></a>Imprimir dados<a aria-hidden="true" tabindex="-1" class="hash-link" href="#imprimir-dados" title="Direct link to heading">#</a></h4><p>Mostra os dados da barra editada no gráfico gerado pelo estudo de estabilidade transitória. Os seguintes dados são exibidos:</p><ul><li>módulo da tensão do barramento</li><li>ângulo da tensão do barramento.</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="inserir-falta-1"></a>Inserir falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inserir-falta-1" title="Direct link to heading">#</a></h4><p>Insere uma falta trifásica na barra no cálculo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Nota-se que essa opção irá inserir uma falta no cálculo de <a href="/PSP/docs/stability">estabilidade</a> e <strong>não será considerado no estudo de <a href="/PSP/docs/fault">curto-circuito</a></strong>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tempo"></a>Tempo<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tempo" title="Direct link to heading">#</a></h4><p>Instante no tempo (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mrow><mi>f</mi><mi>a</mi><mi>l</mi><mi>t</mi><mi>a</mi></mrow></msub></mrow><annotation encoding="application/x-tex">t_{falta}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9011879999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>) em que ocorre a falta durante os estudos de <a href="/PSP/docs/stability">estabilidade</a>. Esse campo e os próximos são somente acessados caso seja inserida uma falta no estudo de estabilidade.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="duração-da-falta"></a>Duração da falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#duração-da-falta" title="Direct link to heading">#</a></h4><p>Duração da falta inserida (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>t</mi><mrow><mi>f</mi><mi>a</mi><mi>l</mi><mi>t</mi><mi>a</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\Delta t_{falta}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>) no estudo de estabilidade. A falta irá iniciar no instante <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mrow><mi>f</mi><mi>a</mi><mi>l</mi><mi>t</mi><mi>a</mi></mrow></msub></mrow><annotation encoding="application/x-tex">t_{falta}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9011879999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> e será interrompida em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mrow><mi>f</mi><mi>a</mi><mi>l</mi><mi>t</mi><mi>a</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">Δ</mi><msub><mi>t</mi><mrow><mi>f</mi><mi>a</mi><mi>l</mi><mi>t</mi><mi>a</mi></mrow></msub></mrow><annotation encoding="application/x-tex">t_{falta}+\Delta t_{falta}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9011879999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="resistência-e-reatância-de-falta-1"></a>Resistência e reatância de falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#resistência-e-reatância-de-falta-1" title="Direct link to heading">#</a></h4><p>Impedância de falta nos estudos de estabilidade. Uma falta franca é representada pela inserção de um valor de impedância shunt de valor muito baixo (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mn>1</mn><msup><mn>0</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">j10^{-5} p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.008548em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">5</span></span></span></span></span></span></span></span></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>).</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="qualidade-de-energia"></a>Qualidade de energia<a aria-hidden="true" tabindex="-1" class="hash-link" href="#qualidade-de-energia" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="imprimir-impedância-harmônica-da-barra"></a>Imprimir impedância harmônica da barra<a aria-hidden="true" tabindex="-1" class="hash-link" href="#imprimir-impedância-harmônica-da-barra" title="Direct link to heading">#</a></h4><p>Imprime a impedância harmônica vista por essa barra referente ao estudo de <a href="/PSP/docs/harmonics">Resposta na Frequência</a>.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/bus.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/powerEditor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Editor de Potência</div></a></div><div class="pagination-nav__item 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conectados em pontos separados.
+Nota - Em muitos casos, o barramento consiste em uma barra. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=151-12-30" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="barramento-no-psp-ufu"></a>Barramento no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barramento-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento <strong>barramento</strong>, ou simplesmente <strong>barra</strong>, é um conector ou nó do diagrama unifilar do PSP-UFU. Essa barra pode representar um PAC (Ponto de Acoplamento Comum), um poste de distribuição, uma subestação, um barramento da subestação, entre inúmeros outros tipos pontos de análise e conexão entre elementos.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-barramentos"></a>Formulário de edição dos barramentos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-barramentos" title="Direct link to heading">#</a></h2><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O barramento deve ser o <strong>primeiro elemento elétrico a ser inserido no diagrama de potência</strong>, uma vez que os demais componentes de potência são conectados nele.</p></div></div><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das barras:</p><div><center><img src="/PSP/images/busForm.png" alt="Formulário dos barramentos no PSP-UFU" title="Formulário dos barramentos no PSP-UFU"></center></div><p>Esse formulário é subdividido em quatro contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais da barra e informações do fluxo de carga;</li><li><strong>Falta</strong>: local onde o curto-circuito <em>shunt</em> deve ser inserido;</li><li><strong>Estabilidade</strong>: contendo opções de visualização de dados da barra em gráficos no tempo e inserção de faltas trifásicas no cálculo de estabilidade transitória;</li><li><strong>Qualidade de energia</strong>: contém a opção de de visualização da impedância harmônica vista pela barra.</li></ul><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_3zTA tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Falta</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Qualidade de energia</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Utilizado para cálculo da impedância base de alguns elementos conectados, além do cálculo da relação de transformação dos transformadores conectados entre barras. Sua unidade pode ser selecionada, sendo expressa em V ou em kV.</p><p>A modificação desse parâmetro irá alterar toda a tensão do trecho conectado por linhas elétricas, sendo emitido um alerta ao usuário.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tensão-controlada"></a>Tensão controlada<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-controlada" title="Direct link to heading">#</a></h4><p>Caracteriza o barramento como <strong>barra de tensão controlada (<a href="/PSP/docs/powerFlow">Barra PV</a>)</strong>,</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Essa opção é somente válida caso alguma máquina síncrona esteja conectado, caso contrário esse valor será ignorado. Caso o limite de potência reativa da máquina síncrona conectada seja ultrapassado esse valor também é ignorado.</p></div></div><p>O valor poderá ser inserido em p.u. ou em volts (ou kV caso a tensão nominal esteja nesta unidade).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="barra-de-referência"></a>Barra de referência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barra-de-referência" title="Direct link to heading">#</a></h4><p>Caracteriza o barramento como <strong>barra de referência (<a href="/PSP/docs/powerFlow">Barra de oscilação</a>)</strong>. Essa opção é somente válida caso esteja conectado um gerador síncrono, caso contrário uma mensagem de erro será exibida ao usuário ao realizar algum dos cálculos do programa.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/bus.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/powerEditor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Editor de Potência</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/line"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Linha »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#barramento-no-psp-ufu" class="table-of-contents__link">Barramento no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-barramentos" class="table-of-contents__link">Formulário de edição dos barramentos</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Ferramentas CAD</h1></header><div class="markdown"><blockquote><p>Desenho assistido por computador (DAC; em inglês: <em>computer aided design</em> - CAD) é o nome genérico de sistemas computacionais (<em>software</em>) utilizados pela engenharia, geologia, geografia, arquitetura e design para facilitar o projeto e desenho técnicos. No caso do <em>design</em>, este pode estar ligado especificamente a todas as suas vertentes (produtos como vestuário, eletroeletrônicos, automobilísticos, etc.), de modo que os jargões de cada especialidade são incorporados na interface de cada programa. <a href="https://pt.wikipedia.org/wiki/Desenho_assistido_por_computador" target="_blank" rel="noopener noreferrer">Wikipedia</a></p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="ferramentas-do-menu"></a>Ferramentas do menu<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ferramentas-do-menu" title="Direct link to heading">#</a></h2><p>Todos os objetos criados contêm vários atributos gráficos, como: posição, orientação, cor, tamanho, etc. Para modificá-los foram inseridas algumas ferramentas intuitivas e de fácil utilização, as quais são: <a href="/PSP/docs/cadTools#selecionar"><strong>selecionar</strong></a>, <a href="/PSP/docs/cadTools#mover"><strong>mover</strong></a>, <a href="/PSP/docs/cadTools#girar"><strong>girar</strong></a>, <a href="/PSP/docs/cadTools#arrastar"><strong>arrastar</strong></a>, <a href="/PSP/docs/cadTools#zoom"><strong>zoom</strong></a>, <a href="/PSP/docs/cadTools#encaixar"><strong>encaixar</strong></a>, <a href="/PSP/docs/cadTools#copiar-e-colar"><strong>copiar, colar</strong></a> e <a href="/PSP/docs/cadTools#excluir"><strong>excluir</strong></a>.</p><p>Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ferramentas</a>.</p><p>Tais ferramentas permitem a <strong>personalização</strong>, <strong>navegação</strong> e auxiliam a <strong>criação</strong> de redes elétricas de potência, assim como diagramas de controle na plataforma.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="selecionar"></a>Selecionar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#selecionar" title="Direct link to heading">#</a></h3><p>A seleção de um único objeto é realizada clicando com o botão esquerdo do mouse sobre o elemento, que será identificado pelo contorno em <span style="background-color:#80bfff;border-radius:2px;color:#000;padding:0.2rem">azul</span> do objeto.</p><p>Para a seleção de vários objetos simultaneamente é necessário clicar com o botão esquerdo do mouse em um local vazio da tela e arrastá-lo, criando assim um <strong>retângulo de seleção</strong> que irá acompanhar o ponteiro do mouse enquanto o botão esquerdo estiver pressionado. Ao soltá-lo todos os objetos que intercederem o retângulo serão selecionados.</p><p>Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter seleções anteriores enquanto novos elementos são selecionados.</p><p>Para desmarcar todos os objetos basta clicar em uma área sem objetos.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/select.mp4" type="video/mp4"><source src="/PSP/videos/select.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="mover"></a>Mover<a aria-hidden="true" tabindex="-1" class="hash-link" href="#mover" title="Direct link to heading">#</a></h3><p>Um elemento poderá ser movido para qualquer local por meio da ação <em>drag-and-drop</em> (clicando e arrastando) ou pela ferramenta mover.</p><p>Ao habilitar o “modo mover”, movendo todos os componentes selecionados à medida que a posição do mouse é alterada. Para desabilitar esse modo basta pressionar a tecla Escape do teclado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/move.mp4" type="video/mp4"><source src="/PSP/videos/move.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="girar"></a>Girar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#girar" title="Direct link to heading">#</a></h3><p>Alguns objetos poderão ser rotacionados através da ferramenta girar, acessado pela tecla de atalho “R”, girando o objeto no sentido horário, ou “Shift + R”, para o sentido anti-horário (essa opção irá afetar todos os objetos selecionados). O elemento também pode ser rotacionado pelo <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ferramentas</a> ou ao acessar o menu de contexto clicando com o botão direito sobre o elemento.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O menu de contexto somente será exibido se o elemento estiver selecionado.</p></div></div><p>Ao utilizar essa ferramenta os objetos irão girar 45º a partir do seu ponto de origem. Para atingir a angulação pretendida basta repetir o processo de rotação.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/rotate.mp4" type="video/mp4"><source src="/PSP/videos/rotate.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="arrastar"></a>Arrastar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#arrastar" title="Direct link to heading">#</a></h3><p>Três ferramentas muito úteis na navegação do circuito, principalmente em grandes redes, são: arrastar, zoom e encaixar.</p><p>A ferramenta arrastar possibilita mover todo o circuito <strong>preservando as posições relativas entre os elementos</strong>. Esta ferramenta pode ser acessada pelo submenu “Ferramentas” ou <strong>mantendo pressionada o <em>scroll</em> do mouse</strong>, ativando assim o “modo arrastar”. Ao ativá-lo todo o circuito será movido clicando e arrastando na direção desejada.</p><p>Para sair do “modo arrastar” basta pressionar a tecla Escape do teclado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/drag.mp4" type="video/mp4"><source src="/PSP/videos/drag.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="zoom"></a>Zoom<a aria-hidden="true" tabindex="-1" class="hash-link" href="#zoom" title="Direct link to heading">#</a></h3><p>O zoom será aplicado ao utilizar o <strong>scroll do mouse</strong> para mais ou menos zoom. A ferramenta zoom irá aproximar ou distanciar o circuito a partir da posição do ponteiro do mouse na tela para encontrar objetos ou destaca-los.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/zoom.mp4" type="video/mp4"><source src="/PSP/videos/zoom.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="encaixar"></a>Encaixar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#encaixar" title="Direct link to heading">#</a></h3><p>A ferramenta encaixar irá mover o circuito e aplicar o zoom necessário para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada através do submenu “Ferramentas” ou pela combinação de teclas “Shift + F”.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/fit.mp4" type="video/mp4"><source src="/PSP/videos/fit.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="copiar-e-colar"></a>Copiar e Colar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#copiar-e-colar" title="Direct link to heading">#</a></h3><p>Duas ferramentas importantes durante o processo de criação da rede elétrica de potência no <em>software</em> são copiar e colar. Qualquer circuito criado no PSP-UFU poderá ser duplicado completamente ou parcialmente no mesmo projeto ou em múltiplos através dessas ferramentas.</p><p>Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu “Ferramentas” ou pressionando a combinação das teclas “Ctrl + C”, então os dados do circuito serão copiados para a área de transferência. Ao copiar um circuito ele poderá ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combinação das teclas “Ctrl + V”.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/copyPaste.mp4" type="video/mp4"><source src="/PSP/videos/copyPaste.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="excluir"></a>Excluir<a aria-hidden="true" tabindex="-1" class="hash-link" href="#excluir" title="Direct link to heading">#</a></h3><p>Qualquer objeto poderá ser excluído do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o botão direito sobre o elemento selecionado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/delete.mp4" type="video/mp4"><source src="/PSP/videos/delete.webm" type="video/webm"></video><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="personalização-gráfica-os-elementos"></a>Personalização gráfica os elementos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#personalização-gráfica-os-elementos" title="Direct link to heading">#</a></h2><p>Alguns elementos permitem sua personalização gráfica, como as barras e linhas.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="barra"></a>Barra<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barra" title="Direct link to heading">#</a></h3><p>No caso dos barramentos, pode-se alterar o <strong>comprimento da barra</strong> clicando e arrastando no <em>pickbox</em> exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="linha"></a>Linha<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linha" title="Direct link to heading">#</a></h3><p>As linhas podem ser inseridas com <strong>&quot;nós&quot; (pontos de ancoragem)</strong>, personalizando a disposição das linhas no diagrama unifilar. Esses nós são inseridos durante o processo de criação do elemento, anteriormente à seleção da segunda barra.</p><p>Após a sua inserção, novos nós podem ser anexados pelo menu de contexto acessado ao clicar com o botão direito sobre a linha selecionada. Sua remoção também é alcançada por uma opção do menu de contexto.</p><p>Assim como nos barramentos, a alteração da posição dos nós é obtida clicando e arrastando o <em>pickbox</em> exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/graphicPropsChange.mp4" type="video/mp4"><source src="/PSP/videos/graphicPropsChange.webm" type="video/webm"></video><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="conexão-e-desconexão-de-elemetos-na-barra"></a>Conexão e desconexão de elemetos na barra<a aria-hidden="true" tabindex="-1" class="hash-link" href="#conexão-e-desconexão-de-elemetos-na-barra" title="Direct link to heading">#</a></h2><p>Os elementos podem ser desconectados e reconectados às barras após sua inserção somente pela ferramenta <em>drag-and-drop</em>. Para isso, o elemento deve ser selecionado e o seu nó de conexão deve ser arrastado para o local requerido.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O elemento a ser desconectado/reconectado <strong>deve ser previamente selecionado</strong> para efetuar a operação. Caso contrário a barra será movida ou nenhuma operação será realizada.</p></div></div><p>No caso de desconexão, o elemento será automaticamente removido da simulação, sendo indicado pela sua cor (o elemento passa a ter cor <span style="background-color:#7f7f7f;border-radius:2px;color:#000;padding:0.2rem">cinza</span>).</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Ao reconectar o elemento ao circuito, deve-se <strong>atentar para estado do seu &quot;disjuntor&quot;</strong>, indicado por um quadrado próximo ao seu nó de conexão. Um elemento reconectado volta ao circuito com seu disjuntor aberto (<span style="background-color:#ff1919;border-radius:2px;color:#000;padding:0.2rem">vermelho</span>), sendo necessário clicar sobre o mesmo a fim de inserir o elemento no circuito.</p></div></div><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/disconnect.mp4" type="video/mp4"><source src="/PSP/videos/disconnect.webm" type="video/webm"></video></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/cadTools.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/mainScreen"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Tela Principal</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/powerEditor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Editor de Potência »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#ferramentas-do-menu" class="table-of-contents__link">Ferramentas do menu</a><ul><li><a href="#selecionar" class="table-of-contents__link">Selecionar</a></li><li><a href="#mover" class="table-of-contents__link">Mover</a></li><li><a href="#girar" class="table-of-contents__link">Girar</a></li><li><a href="#arrastar" class="table-of-contents__link">Arrastar</a></li><li><a href="#zoom" class="table-of-contents__link">Zoom</a></li><li><a href="#encaixar" class="table-of-contents__link">Encaixar</a></li><li><a href="#copiar-e-colar" class="table-of-contents__link">Copiar e Colar</a></li><li><a href="#excluir" class="table-of-contents__link">Excluir</a></li></ul></li><li><a href="#personalização-gráfica-os-elementos" class="table-of-contents__link">Personalização gráfica os elementos</a><ul><li><a href="#barra" class="table-of-contents__link">Barra</a></li><li><a href="#linha" class="table-of-contents__link">Linha</a></li></ul></li><li><a href="#conexão-e-desconexão-de-elemetos-na-barra" class="table-of-contents__link">Conexão e desconexão de elemetos na barra</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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focusable="false"><title>Menu</title><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></button><ul class="menu__list"><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#!">Introdução</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/">PSP-UFU</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/installation">Instalação</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/mainScreen">Tela Principal</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link menu__link--active active" tabindex="0" href="/PSP/docs/cadTools">Ferramentas CAD</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Editor de Elementos de Potência</a><ul class="menu__list"><li 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href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Ferramentas CAD</h1></header><div class="markdown"><blockquote><p>Desenho assistido por computador (DAC; em inglês: <em>computer aided design</em> - CAD) é o nome genérico de sistemas computacionais (<em>software</em>) utilizados pela engenharia, geologia, geografia, arquitetura e design para facilitar o projeto e desenho técnicos. No caso do <em>design</em>, este pode estar ligado especificamente a todas as suas vertentes (produtos como vestuário, eletroeletrônicos, automobilísticos, etc.), de modo que os jargões de cada especialidade são incorporados na interface de cada programa. <a href="https://pt.wikipedia.org/wiki/Desenho_assistido_por_computador" target="_blank" rel="noopener noreferrer">Wikipedia</a></p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="ferramentas-do-menu"></a>Ferramentas do menu<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ferramentas-do-menu" title="Direct link to heading">#</a></h2><p>Todos os objetos criados contêm vários atributos gráficos, como: posição, orientação, cor, tamanho, etc. Para modificá-los foram inseridas algumas ferramentas intuitivas e de fácil utilização, as quais são: <a href="/PSP/docs/cadTools#selecionar"><strong>selecionar</strong></a>, <a href="/PSP/docs/cadTools#mover"><strong>mover</strong></a>, <a href="/PSP/docs/cadTools#girar"><strong>girar</strong></a>, <a href="/PSP/docs/cadTools#arrastar"><strong>arrastar</strong></a>, <a href="/PSP/docs/cadTools#zoom"><strong>zoom</strong></a>, <a href="/PSP/docs/cadTools#encaixar"><strong>encaixar</strong></a>, <a href="/PSP/docs/cadTools#copiar-e-colar"><strong>copiar, colar</strong></a> e <a href="/PSP/docs/cadTools#excluir"><strong>excluir</strong></a>.</p><p>Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ferramentas</a>.</p><p>Tais ferramentas permitem a <strong>personalização</strong>, <strong>navegação</strong> e auxiliam a <strong>criação</strong> de redes elétricas de potência, assim como diagramas de controle na plataforma.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="selecionar"></a>Selecionar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#selecionar" title="Direct link to heading">#</a></h3><p>A seleção de um único objeto é realizada clicando com o botão esquerdo do mouse sobre o elemento, que será identificado pelo contorno em <span style="background-color:#80bfff;border-radius:2px;color:#000;padding:0.2rem">azul</span> do objeto.</p><p>Para a seleção de vários objetos simultaneamente é necessário clicar com o botão esquerdo do mouse em um local vazio da tela e arrastá-lo, criando assim um <strong>retângulo de seleção</strong> que irá acompanhar o ponteiro do mouse enquanto o botão esquerdo estiver pressionado. Ao soltá-lo todos os objetos que intercederem o retângulo serão selecionados.</p><p>Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter seleções anteriores enquanto novos elementos são selecionados.</p><p>Para desmarcar todos os objetos basta clicar em uma área sem objetos.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/select.mp4" type="video/mp4"><source src="/PSP/videos/select.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="mover"></a>Mover<a aria-hidden="true" tabindex="-1" class="hash-link" href="#mover" title="Direct link to heading">#</a></h3><p>Um elemento poderá ser movido para qualquer local por meio da ação <em>drag-and-drop</em> (clicando e arrastando) ou pela ferramenta mover.</p><p>Ao habilitar o “modo mover”, movendo todos os componentes selecionados à medida que a posição do mouse é alterada. Para desabilitar esse modo basta pressionar a tecla Escape do teclado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/move.mp4" type="video/mp4"><source src="/PSP/videos/move.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="girar"></a>Girar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#girar" title="Direct link to heading">#</a></h3><p>Alguns objetos poderão ser rotacionados através da ferramenta girar, acessado pela tecla de atalho “R”, girando o objeto no sentido horário, ou “Shift + R”, para o sentido anti-horário (essa opção irá afetar todos os objetos selecionados). O elemento também pode ser rotacionado pelo <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ferramentas</a> ou ao acessar o menu de contexto clicando com o botão direito sobre o elemento.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O menu de contexto somente será exibido se o elemento estiver selecionado.</p></div></div><p>Ao utilizar essa ferramenta os objetos irão girar 45º a partir do seu ponto de origem. Para atingir a angulação pretendida basta repetir o processo de rotação.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/rotate.mp4" type="video/mp4"><source src="/PSP/videos/rotate.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="arrastar"></a>Arrastar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#arrastar" title="Direct link to heading">#</a></h3><p>Três ferramentas muito úteis na navegação do circuito, principalmente em grandes redes, são: arrastar, zoom e encaixar.</p><p>A ferramenta arrastar possibilita mover todo o circuito <strong>preservando as posições relativas entre os elementos</strong>. Esta ferramenta pode ser acessada pelo submenu “Ferramentas” ou <strong>mantendo pressionada o <em>scroll</em> do mouse</strong>, ativando assim o “modo arrastar”. Ao ativá-lo todo o circuito será movido clicando e arrastando na direção desejada.</p><p>Para sair do “modo arrastar” basta pressionar a tecla Escape do teclado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/drag.mp4" type="video/mp4"><source src="/PSP/videos/drag.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="zoom"></a>Zoom<a aria-hidden="true" tabindex="-1" class="hash-link" href="#zoom" title="Direct link to heading">#</a></h3><p>O zoom será aplicado ao utilizar o <strong>scroll do mouse</strong> para mais ou menos zoom. A ferramenta zoom irá aproximar ou distanciar o circuito a partir da posição do ponteiro do mouse na tela para encontrar objetos ou destaca-los.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/zoom.mp4" type="video/mp4"><source src="/PSP/videos/zoom.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="encaixar"></a>Encaixar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#encaixar" title="Direct link to heading">#</a></h3><p>A ferramenta encaixar irá mover o circuito e aplicar o zoom necessário para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada através do submenu “Ferramentas” ou pela combinação de teclas “Shift + F”.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/fit.mp4" type="video/mp4"><source src="/PSP/videos/fit.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="copiar-e-colar"></a>Copiar e Colar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#copiar-e-colar" title="Direct link to heading">#</a></h3><p>Duas ferramentas importantes durante o processo de criação da rede elétrica de potência no <em>software</em> são copiar e colar. Qualquer circuito criado no PSP-UFU poderá ser duplicado completamente ou parcialmente no mesmo projeto ou em múltiplos através dessas ferramentas.</p><p>Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu “Ferramentas” ou pressionando a combinação das teclas “Ctrl + C”, então os dados do circuito serão copiados para a área de transferência. Ao copiar um circuito ele poderá ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combinação das teclas “Ctrl + V”.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/copyPaste.mp4" type="video/mp4"><source src="/PSP/videos/copyPaste.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="excluir"></a>Excluir<a aria-hidden="true" tabindex="-1" class="hash-link" href="#excluir" title="Direct link to heading">#</a></h3><p>Qualquer objeto poderá ser excluído do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o botão direito sobre o elemento selecionado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/delete.mp4" type="video/mp4"><source src="/PSP/videos/delete.webm" type="video/webm"></video><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="personalização-gráfica-os-elementos"></a>Personalização gráfica os elementos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#personalização-gráfica-os-elementos" title="Direct link to heading">#</a></h2><p>Alguns elementos permitem sua personalização gráfica, como as barras e linhas.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="barra"></a>Barra<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barra" title="Direct link to heading">#</a></h3><p>No caso dos barramentos, pode-se alterar o <strong>comprimento da barra</strong> clicando e arrastando no <em>pickbox</em> exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="linha"></a>Linha<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linha" title="Direct link to heading">#</a></h3><p>As linhas podem ser inseridas com <strong>&quot;nós&quot; (pontos de ancoragem)</strong>, personalizando a disposição das linhas no diagrama unifilar. Esses nós são inseridos durante o processo de criação do elemento, anteriormente à seleção da segunda barra.</p><p>Após a sua inserção, novos nós podem ser anexados pelo menu de contexto acessado ao clicar com o botão direito sobre a linha selecionada. Sua remoção também é alcançada por uma opção do menu de contexto.</p><p>Assim como nos barramentos, a alteração da posição dos nós é obtida clicando e arrastando o <em>pickbox</em> exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/graphicPropsChange.mp4" type="video/mp4"><source src="/PSP/videos/graphicPropsChange.webm" type="video/webm"></video><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="conexão-e-desconexão-de-elemetos-na-barra"></a>Conexão e desconexão de elemetos na barra<a aria-hidden="true" tabindex="-1" class="hash-link" href="#conexão-e-desconexão-de-elemetos-na-barra" title="Direct link to heading">#</a></h2><p>Os elementos podem ser desconectados e reconectados às barras após sua inserção somente pela ferramenta <em>drag-and-drop</em>. Para isso, o elemento deve ser selecionado e o seu nó de conexão deve ser arrastado para o local requerido.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O elemento a ser desconectado/reconectado <strong>deve ser previamente selecionado</strong> para efetuar a operação. Caso contrário a barra será movida ou nenhuma operação será realizada.</p></div></div><p>No caso de desconexão, o elemento será automaticamente removido da simulação, sendo indicado pela sua cor (o elemento passa a ter cor <span style="background-color:#7f7f7f;border-radius:2px;color:#000;padding:0.2rem">cinza</span>).</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Ao reconectar o elemento ao circuito, deve-se <strong>atentar para estado do seu &quot;disjuntor&quot;</strong>, indicado por um quadrado próximo ao seu nó de conexão. Um elemento reconectado volta ao circuito com seu disjuntor aberto (<span style="background-color:#ff1919;border-radius:2px;color:#000;padding:0.2rem">vermelho</span>), sendo necessário clicar sobre o mesmo a fim de inserir o elemento no circuito.</p></div></div><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/disconnect.mp4" type="video/mp4"><source src="/PSP/videos/disconnect.webm" type="video/webm"></video></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/cadTools.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/mainScreen"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Tela Principal</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/powerEditor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Editor de Potência »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#ferramentas-do-menu" class="table-of-contents__link">Ferramentas do menu</a><ul><li><a href="#selecionar" class="table-of-contents__link">Selecionar</a></li><li><a href="#mover" class="table-of-contents__link">Mover</a></li><li><a href="#girar" class="table-of-contents__link">Girar</a></li><li><a href="#arrastar" class="table-of-contents__link">Arrastar</a></li><li><a href="#zoom" class="table-of-contents__link">Zoom</a></li><li><a href="#encaixar" class="table-of-contents__link">Encaixar</a></li><li><a href="#copiar-e-colar" class="table-of-contents__link">Copiar e Colar</a></li><li><a href="#excluir" class="table-of-contents__link">Excluir</a></li></ul></li><li><a href="#personalização-gráfica-os-elementos" class="table-of-contents__link">Personalização gráfica os elementos</a><ul><li><a href="#barra" class="table-of-contents__link">Barra</a></li><li><a href="#linha" class="table-of-contents__link">Linha</a></li></ul></li><li><a href="#conexão-e-desconexão-de-elemetos-na-barra" class="table-of-contents__link">Conexão e desconexão de elemetos na barra</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Capacitor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um dispositivo constituído essencialmente por dois eletrodos separados por um dielétrico. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=436-01-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="capacitor-no-psp-ufu"></a>Capacitor no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#capacitor-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento capacitor representa, geralmente, um banco de capacitores <em>shunt</em> no circuito do PSP-UFU.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Um arranjo série de uma <a href="/PSP/docs/line">linha</a> sem as susceptâncias <em>shunt</em>, um <a href="/PSP/docs/bus">barramento</a> e um <a href="/PSP/docs/capacitor">capacitor</a> pode ser utilizado para fabricar um filtro passivo nos <a href="/PSP/docs/harmonics">estudos harmônicos</a>. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.</p></div></div><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-capacitores"></a>Formulário de edição dos capacitores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-capacitores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos capacitores:</p><div><center><img src="/PSP/images/capacitorForm.png" alt="Formulário dos capacitores no PSP-UFU" title="Formulário dos capacitores no PSP-UFU"></center></div><p>Além do único contexto geral, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do capacitor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/swCapacitor.png" alt="Formulário de chaveamento do capacitor" title="Formulário de chaveamento do capacitor"></center></div><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="geral"></a>Geral<a aria-hidden="true" tabindex="-1" class="hash-link" href="#geral" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base de potência do sistema). </p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="botão-estabilidade"></a>Botão Estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#botão-estabilidade" title="Direct link to heading">#</a></h3><p>O botão &quot;Estabilidade&quot; irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do transformador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><p>Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões &quot;Adicionar&quot; e &quot;Remover&quot;, respectivamente.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/capacitor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/load"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Carga</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/inductor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Indutor »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#capacitor-no-psp-ufu" class="table-of-contents__link">Capacitor no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-capacitores" class="table-of-contents__link">Formulário de edição dos capacitores</a><ul><li><a href="#geral" class="table-of-contents__link">Geral</a></li><li><a href="#botão-estabilidade" class="table-of-contents__link">Botão Estabilidade</a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Capacitor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um dispositivo constituído essencialmente por dois eletrodos separados por um dielétrico. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=436-01-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="capacitor-no-psp-ufu"></a>Capacitor no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#capacitor-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento capacitor representa, geralmente, um banco de capacitores <em>shunt</em> no circuito do PSP-UFU.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Um arranjo série de uma <a href="/PSP/docs/line">linha</a> sem as susceptâncias <em>shunt</em>, um <a href="/PSP/docs/bus">barramento</a> e um <a href="/PSP/docs/capacitor">capacitor</a> pode ser utilizado para fabricar um filtro passivo nos <a href="/PSP/docs/harmonics">estudos harmônicos</a>. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.</p></div></div><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-capacitores"></a>Formulário de edição dos capacitores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-capacitores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos capacitores:</p><div><center><img src="/PSP/images/capacitorForm.png" alt="Formulário dos capacitores no PSP-UFU" title="Formulário dos capacitores no PSP-UFU"></center></div><p>Além do único contexto geral, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do capacitor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/swCapacitor.png" alt="Formulário de chaveamento do capacitor" title="Formulário de chaveamento do capacitor"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_3zTA tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base de potência do sistema). </p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/capacitor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/load"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Carga</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/inductor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Indutor »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#capacitor-no-psp-ufu" class="table-of-contents__link">Capacitor no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-capacitores" class="table-of-contents__link">Formulário de edição dos capacitores</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Constante</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>As constantes são valores numéricos reais que permanecem inalteradas em todo o período de simulação. Esses elementos possuem somente um nó de saída, o qual poderá ser conectado a qualquer outro nó de entrada dos elementos de controle.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Esse elemento pode, por exemplo, ser utilizado para definir valores alvos ou deslocamentos de sinal.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/const.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/rateLimiter"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Limitador de taxa</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/gain"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Ganho »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="menu__link" tabindex="-1" href="/PSP/docs/powerEditor">Editor de Potência</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="-1">Elementos de Potência</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/bus">Barramento</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/line">Linha</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/transformer">Transformador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/load">Carga</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/capacitor">Capacitor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/inductor">Indutor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul></li><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#!">Editor de Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a aria-current="page" class="menu__link menu__link--active active" tabindex="0" href="/PSP/docs/controlEditor">Editor de Controle</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="0">Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/io">Entrada / Saída</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/transferFunction">Função Transferência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/sum">Somador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/multiplier">Multiplicador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/divider">Divisor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/exponential">Exponencial</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/limiter">Limitador absoluto</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/rateLimiter">Limitador de taxa</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/const">Constante</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Editor de Controle</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Os controles das <a href="/PSP/docs/syncGenerator">máquinas síncronas</a> são criados, modificados, importados e exportados em um editor distinto dos elementos de potência, apresentado na figura abaixo.</p><div><center><img src="/PSP/images/controlEditor.png" alt="Editor de elementos de controle do PSP-UFU" title="Editor de elementos de controle do PSP-UFU"></center></div><p>O acesso ao editor é realizado por meio de dois botões presentes no <a href="/PSP/docs/syncGenerator#formul%C3%A1rio-de-edi%C3%A7%C3%A3o-dos-geradores-s%C3%ADncronos">formulário de edição dos dados de estabilidade dos geradores síncronos</a>:</p><ul><li><a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">Editar AVR</a></li><li><a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">Editar regulador de velocidade</a></li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="elementos-de-controle"></a>Elementos de Controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#elementos-de-controle" title="Direct link to heading">#</a></h2><p>O acesso aos elementos de controle é realizado em uma janela (removível e encaixável) por meio de ícones relacionados.</p><p>Uma vez que o usuário clicar no ícone desejado, o elemento de controle acompanhará o ponteiro do mouse até ser efetivamente inserido na posição desejada ao clicar novamente na área de trabalho. Os elementos são então conectados por “linhas de conexão” inseridas ao clicar nos nós dos componentes previamente adicionados, permitindo a construção da rede de controle genérica.</p><p>As ferramentas de manipulação e navegação, como arrastar, mover e excluir são <a href="/PSP/docs/cadTools">herdadas</a> do <a href="/PSP/docs/powerEditor">editor de elementos de potência</a>, possuindo comportamento idêntico. A <strong>edição dos dados</strong> dos componentes inseridos também é realizada com <strong>duplo clique</strong> sobre o elemento inserido, exibindo um formulário de edição de dados.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/timelapseControlEditor.mp4" type="video/mp4"><source src="/PSP/videos/timelapseControlEditor.webm" type="video/webm"></video><p>Os seguintes blocos de controle estão presentes no PSP-UFU:</p><ul><li><a href="/PSP/docs/io">Entrada e Saída</a></li><li><a href="/PSP/docs/transferFunction">Função Transferência</a></li><li>Matemática<ul><li><a href="/PSP/docs/sum">Somador</a></li><li><a href="/PSP/docs/multiplier">Multiplicador</a></li><li><a href="/PSP/docs/divider">Divisor</a></li><li><a href="/PSP/docs/exponential">Exponencial</a></li></ul></li><li>Limitadores<ul><li><a href="/PSP/docs/limiter">Limitador absoluto</a></li><li><a href="/PSP/docs/rateLimiter">Limitador de taxa</a></li></ul></li><li>Constantes<ul><li><a href="/PSP/docs/const">Constante</a></li><li><a href="/PSP/docs/gain">Ganho</a></li></ul></li><li><a href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="inicialização-do-sistema-de-controle"></a>Inicialização do sistema de controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inicialização-do-sistema-de-controle" title="Direct link to heading">#</a></h2><p>Caso as entradas do sistema de controle apresentem valores diferentes de zero ou a primeira operação entre elas não resulte em uma saída nula, o sistema necessita de inicialização, de forma a adequar os valores de entradas e saída dos blocos elementares e dos vetores de estado das <a href="/PSP/docs/transferFunction">funções transferências</a> presentes. Tal procedimento é realizado por meio da solução de toda rede de controle até que se obtenha sua convergência, ou seja, a diferença absoluta entre as mesmas saídas de uma solução anterior e uma atual deve ser nula ou muito próxima de zero.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>info</h5></div><div class="admonition-content"><p>O processo de <strong>inicialização é realizada automaticamente</strong> pelo PSP-UFU.</p><p>Uma vez que a inicialização é imposta pelas <a href="/PSP/docs/io">entradas</a> do controle, erros de convergência podem ocorrer devido à má parametrização dos elementos dos sistemas de <strong>potência e controle</strong>.</p></div></div><p>Para otimizar e melhorar a estabilidade do processo de inicialização utilizou-se um passo de integração variável dentro de limites, de forma que o passo aumenta em condições de diferenças menores entre as soluções do sistema de controle e diminui caso essa diferença se torne elevada. A implementação dessa abordagem reduziu significativamente o encerramento do processo com erro causado pela instabilidade numérica, além de acelerar a inicialização.</p><p>O fluxograma abaixo evidencia o processo de inicialização implementado no PSP-UFU:</p><div><center><img src="/PSP/images/controlInit.png" alt="Estrutura da inicialização do sistema de controle" title="Estrutura da inicialização do sistema de controle"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="teste-do-diagrama-de-controle"></a>Teste do diagrama de controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#teste-do-diagrama-de-controle" title="Direct link to heading">#</a></h2><p>Na parte inferior esquerda do Editor de Controle está presente o botão &quot;<strong>Testar Sistema...</strong>&quot;. O botão acessa o formulário de teste de controles, como é indicado na figura abaixo:</p><div><center><img src="/PSP/images/testControl.png" alt="Formulário de teste de controles" title="Formulário de teste de controles"></center></div><p>Nesse formulário é possível inserir o comportamento de <strong>todas as entradas do diagrama</strong>:</p><ul><li><strong>Tipo de entrada</strong>: Define um dos tipos de entradas possíveis no PSP-UFU: &quot;Passo (<em>Step</em>)&quot;, Rampa (<em>Ramp</em>) ou Quadrática (<em>Quadratic</em>);</li><li><strong>Tempo de início (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">t_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76508em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>)</strong>: Define o tempo de início na simulação da entrada definida. As entradas iniciais são sempre definidas como zero e assumem valores diferentes após o tempo de início;</li><li><strong>Inclinação (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span></span></span></span></span>)</strong>: Valor relacionado ao tipo de entrada:<ul><li>Para entrada do tipo &quot;Passo&quot; - O valor da inclinação define o valor final do passo:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li><li>Para entrada do tipo &quot;Rampa&quot; - define o coeficiente de inclinação da reta:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi><mo>×</mo><mi>t</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li><li>Para entrada do tipo &quot;Quadrática&quot; - define o coeficiente de crescimento da curva:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi><mo>×</mo><msup><mi>t</mi><mn>2</mn></msup></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t^2 \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li></ul></li><li><strong>Passo de integração (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>)</strong>: Passo do método de integração Trapezoidal Implícito;</li><li><strong>Tempo de simulação (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>f</mi></msub></mrow><annotation encoding="application/x-tex">t_f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9011879999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>)</strong>: Tempo total de simulação.</li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A mesma parametrização de entrada é aplicada em todos os blocos de <a href="/PSP/docs/io">entrada</a> do sistema.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>É possível aplicar <strong>várias entradas distintas</strong> (inclusive com condicionais!) utilizando o bloco de <a href="/PSP/docs/mathExpression">expressão matemática</a>.</p></div></div><p>Utilizando o bloco de <a href="/PSP/docs/mathExpression">expressão matemática</a> é possível inserir entradas complexas, como por exemplo testar o diagrama de blocos (AVR DC1C + PSS1A - <a href="https://doi.org/10.1109/IEEESTD.2016.7553421">IEEE Std. 421.5-2016</a>) da figura abaixo:</p><div><center><img src="/PSP/images/exControl.svg" alt="Sistema de controle sob teste" title="Sistema de controle sob teste"></center></div><div><center><img src="/PSP/images/compControl.svg" alt="Comparação do sistema de 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Corrente Harmônica</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul></li><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#!">Editor de Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a aria-current="page" class="menu__link menu__link--active active" tabindex="0" href="/PSP/docs/controlEditor">Editor de Controle</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="0">Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/io">Entrada / 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href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Editor de Controle</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Os controles das <a href="/PSP/docs/syncGenerator">máquinas síncronas</a> são criados, modificados, importados e exportados em um editor distinto dos elementos de potência, apresentado na figura abaixo.</p><div><center><img src="/PSP/images/controlEditor.png" alt="Editor de elementos de controle do PSP-UFU" title="Editor de elementos de controle do PSP-UFU"></center></div><p>O acesso ao editor é realizado por meio de dois botões presentes no <a href="/PSP/docs/syncGenerator#formul%C3%A1rio-de-edi%C3%A7%C3%A3o-dos-geradores-s%C3%ADncronos">formulário de edição dos dados de estabilidade dos geradores síncronos</a>:</p><ul><li><a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">Editar AVR</a></li><li><a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">Editar regulador de velocidade</a></li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>No PSP-UFU a opção de editar o <strong>AVR</strong> engloba mais que somente o controle de tensão da máquina. Nele <strong>deve</strong> ser inserida a malha de controle da máquina assim como a <strong>excitatriz da máquina síncrona</strong>. Outras estratégias de controle (opcionais), como PSS (<em>Power System Stabilizer</em>) e/ou controles de sobre e sub excitação, são também implementadas em conjunto (como apresentado na figura anterior).</p></div></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Assim como no AVR, o <strong>Regulador de Velocidade</strong> engloba mais que a regulação primária da máquina. Nessa opção <strong>deve</strong> ser inserida ao menos a malha de controle da regulação primária de velocidade, assim como o <strong>modelo da turbina</strong>. Estratégias opcionais de controle da velocidade também são inseridas nessa opção.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="elementos-de-controle"></a>Elementos de Controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#elementos-de-controle" title="Direct link to heading">#</a></h2><p>O acesso aos elementos de controle é realizado em uma janela (removível e encaixável) por meio de ícones relacionados.</p><p>Uma vez que o usuário clicar no ícone desejado, o elemento de controle acompanhará o ponteiro do mouse até ser efetivamente inserido na posição desejada ao clicar novamente na área de trabalho. Os elementos são então conectados por “linhas de conexão” inseridas ao clicar nos nós dos componentes previamente adicionados, permitindo a construção da rede de controle genérica.</p><p>As ferramentas de manipulação e navegação, como arrastar, mover e excluir são <a href="/PSP/docs/cadTools">herdadas</a> do <a href="/PSP/docs/powerEditor">editor de elementos de potência</a>, possuindo comportamento idêntico. A <strong>edição dos dados</strong> dos componentes inseridos também é realizada com <strong>duplo clique</strong> sobre o elemento inserido, exibindo um formulário de edição de dados.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/timelapseControlEditor.mp4" type="video/mp4"><source src="/PSP/videos/timelapseControlEditor.webm" type="video/webm"></video><p>Os seguintes blocos de controle estão presentes no PSP-UFU:</p><ul><li><a href="/PSP/docs/io">Entrada e Saída</a></li><li><a href="/PSP/docs/transferFunction">Função Transferência</a></li><li>Matemática<ul><li><a href="/PSP/docs/sum">Somador</a></li><li><a href="/PSP/docs/multiplier">Multiplicador</a></li><li><a href="/PSP/docs/divider">Divisor</a></li><li><a href="/PSP/docs/exponential">Exponencial</a></li></ul></li><li>Limitadores<ul><li><a href="/PSP/docs/limiter">Limitador absoluto</a></li><li><a href="/PSP/docs/rateLimiter">Limitador de taxa</a></li></ul></li><li>Constantes<ul><li><a href="/PSP/docs/const">Constante</a></li><li><a href="/PSP/docs/gain">Ganho</a></li></ul></li><li><a href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="inicialização-do-sistema-de-controle"></a>Inicialização do sistema de controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inicialização-do-sistema-de-controle" title="Direct link to heading">#</a></h2><p>Caso as entradas do sistema de controle apresentem valores diferentes de zero ou a primeira operação entre elas não resulte em uma saída nula, o sistema necessita de inicialização, de forma a adequar os valores de entradas e saída dos blocos elementares e dos vetores de estado das <a href="/PSP/docs/transferFunction">funções transferências</a> presentes. Tal procedimento é realizado por meio da solução de toda rede de controle até que se obtenha sua convergência, ou seja, a diferença absoluta entre as mesmas saídas de uma solução anterior e uma atual deve ser nula ou muito próxima de zero.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>info</h5></div><div class="admonition-content"><p>O processo de <strong>inicialização é realizada automaticamente</strong> pelo PSP-UFU.</p><p>Uma vez que a inicialização é imposta pelas <a href="/PSP/docs/io">entradas</a> do controle, erros de convergência podem ocorrer devido à má parametrização dos elementos dos sistemas de <strong>potência e controle</strong>.</p></div></div><p>Para otimizar e melhorar a estabilidade do processo de inicialização utilizou-se um passo de integração variável dentro de limites, de forma que o passo aumenta em condições de diferenças menores entre as soluções do sistema de controle e diminui caso essa diferença se torne elevada. A implementação dessa abordagem reduziu significativamente o encerramento do processo com erro causado pela instabilidade numérica, além de acelerar a inicialização.</p><p>O fluxograma abaixo evidencia o processo de inicialização implementado no PSP-UFU:</p><div><center><img src="/PSP/images/controlInit.png" alt="Estrutura da inicialização do sistema de controle" title="Estrutura da inicialização do sistema de controle"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="teste-do-diagrama-de-controle"></a>Teste do diagrama de controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#teste-do-diagrama-de-controle" title="Direct link to heading">#</a></h2><p>Na parte inferior esquerda do Editor de Controle está presente o botão &quot;<strong>Testar Sistema...</strong>&quot;. O botão acessa o formulário de teste de controles, como é indicado na figura abaixo:</p><div><center><img src="/PSP/images/testControl.png" alt="Formulário de teste de controles" title="Formulário de teste de controles"></center></div><p>Nesse formulário é possível inserir o comportamento de <strong>todas as entradas do diagrama</strong>:</p><ul><li><strong>Tipo de entrada</strong>: Define um dos tipos de entradas possíveis no PSP-UFU: &quot;Passo (<em>Step</em>)&quot;, Rampa (<em>Ramp</em>) ou Quadrática (<em>Quadratic</em>);</li><li><strong>Tempo de início (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">t_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76508em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>)</strong>: Define o tempo de início na simulação da entrada definida. As entradas iniciais são sempre definidas como zero e assumem valores diferentes após o tempo de início;</li><li><strong>Inclinação (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span></span></span></span></span>)</strong>: Valor relacionado ao tipo de entrada:<ul><li>Para entrada do tipo &quot;Passo&quot; - O valor da inclinação define o valor final do passo:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li><li>Para entrada do tipo &quot;Rampa&quot; - define o coeficiente de inclinação da reta:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi><mo>×</mo><mi>t</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li><li>Para entrada do tipo &quot;Quadrática&quot; - define o coeficiente de crescimento da curva:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi><mo>×</mo><msup><mi>t</mi><mn>2</mn></msup></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t^2 \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li></ul></li><li><strong>Passo de integração (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>)</strong>: Passo do método de integração Trapezoidal Implícito;</li><li><strong>Tempo de simulação (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>f</mi></msub></mrow><annotation encoding="application/x-tex">t_f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9011879999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>)</strong>: Tempo total de simulação.</li></ul><p>Após a simulação os resultados são exibidos no <a href="/PSP/docs/graphViewer">visualizador de gráficos</a>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A mesma parametrização de entrada é aplicada em todos os blocos de <a href="/PSP/docs/io">entrada</a> do sistema.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>É possível aplicar <strong>várias entradas distintas</strong> (inclusive com condicionais!) utilizando o bloco de <a href="/PSP/docs/mathExpression">expressão matemática</a>.</p></div></div><p>Utilizando o bloco de <a href="/PSP/docs/mathExpression">expressão matemática</a> é possível inserir entradas complexas, como por exemplo testar o diagrama de blocos (AVR DC1C + PSS1A - <a href="https://doi.org/10.1109/IEEESTD.2016.7553421">IEEE Std. 421.5-2016</a>) da figura abaixo:</p><div><center><img src="/PSP/images/exControl.svg" alt="Sistema de controle sob teste" title="Sistema de controle sob teste"></center></div><div><center><img src="/PSP/images/compControl.svg" alt="Comparação do sistema de controle sob teste" title="Comparação do sistema de controle sob teste"></center></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/controlEditor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/indMotor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« 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class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Divisor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Esse elemento é bastante simples e cumpre com a função matemáticas de seu nome.</p><p>Possui duas entradas de valores reais e sua saída é computada na sequência do nó superior pelo inferior, ou seja, a saída será o valor presente no nó 1 dividido pelo nó 2.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Nós não conectados no divisor são considerados como valor nulo. Caso a divisão possua numerador zero, o valor da saída é definida como sendo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>15</mn></msup></mrow><annotation encoding="application/x-tex">10^{15}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">5</span></span></span></span></span></span></span></span></span></span></span></span></span>.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/divider.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/multiplier"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Multiplicador</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/exponential"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Exponencial »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Exponencial</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>A função exponencial dos elementos de controle realiza essa operação com uma entrada real, obedecendo a expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub><mo>=</mo><mi mathvariant="bold">A</mi><msup><mi>e</mi><mrow><mi mathvariant="bold">B</mi><msub><mi>u</mi><mi>n</mi></msub></mrow></msup></mrow><annotation encoding="application/x-tex">y_n = \bold{A} e^{\bold{B} u_n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8932769999999999em;vertical-align:0em"></span><span class="mord"><span class="mord mathbf">A</span></span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8932769999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathbf mtight">B</span></span><span class="mord mtight"><span class="mord mathdefault mtight">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é a entrada e a saída do bloco exponencial, respectivamente;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">A</mi></mrow><annotation encoding="application/x-tex">\bold{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68611em;vertical-align:0em"></span><span class="mord"><span class="mord mathbf">A</span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">B</mi></mrow><annotation encoding="application/x-tex">\bold{B}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68611em;vertical-align:0em"></span><span class="mord"><span class="mord mathbf">B</span></span></span></span></span></span>	são constantes definidas pelo usuário.</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-de-dados-do-bloco-exponencial"></a>Formulário de edição de dados do bloco Exponencial<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-bloco-exponencial" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados do bloco exponencial.</p><div><center><img src="/PSP/images/expForm.png" alt="Formulário de edição de dados do bloco exponencial no PSP-UFU" title="Formulário de edição de dados do bloco exponencial no PSP-UFU"></center></div><p>Esse bloco não linear é definido pelas constantes A e B, inseridas pelo usuário.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Tais blocos são úteis na representação de não linearidades, como, por exemplo, modelagem da saturação de máquinas de corrente contínuas presentes em alguns reguladores automáticos de tensão.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/exponential.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Fonte de Corrente Harmônica</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>(<strong>Fonte de perturbação harmônica</strong>) Parte do sistema elétrico de potência ou das instalações a ele conectadas, que causa distorção harmônica da forma de onda da corrente e / ou tensão. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=614-01-16" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="fonte-de-corrente-harmônica-no-psp-ufu"></a>Fonte de corrente harmônica no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#fonte-de-corrente-harmônica-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As fontes de corrente harmônica são responsáveis pela injeção de correntes harmônicas e são utilizadas pela ferramenta de cálculo de <a href="/PSP/docs/harmonics">distorções harmônicas</a>. Uma lista de correntes harmônicas pode ser inserida em um mesmo elemento, conforme é exibido na o formulário de edição de dados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A presença da fonte de corrente harmônica <strong>não é considerada</strong> nos estudos de <a href="/PSP/docs/powerFlow">fluxo de carga</a>, <a href="/PSP/docs/fault">curto-circuito</a> e <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-das-fontes-de-corrente-harmônica"></a>Formulário de edição das fontes de corrente harmônica<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-fontes-de-corrente-harmônica" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados da fonte de corrente harmônica:</p><div><center><img src="/PSP/images/harmSourceForm.png" alt="Formulário dos indutores no PSP-UFU" title="Formulário dos indutores no PSP-UFU"></center></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="ordem"></a>Ordem<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ordem" title="Direct link to heading">#</a></h4><p>Especifica a ordem harmônica a ser inserida na lista de correntes harmônicas do elemento. Caso a ordem harmônica já exista na lista, ela será substituída pelos novos parâmetros.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="corrente"></a>Corrente<a aria-hidden="true" tabindex="-1" class="hash-link" href="#corrente" title="Direct link to heading">#</a></h4><p>Módulo da corrente harmônica.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="unidade"></a>Unidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#unidade" title="Direct link to heading">#</a></h4><p>Unidade do módulo de corrente harmônica, em A ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="ângulo"></a>Ângulo<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ângulo" title="Direct link to heading">#</a></h4><p>Ângulo da corrente harmônica, em graus.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="adicionar--remover"></a>Adicionar / Remover<a aria-hidden="true" tabindex="-1" class="hash-link" href="#adicionar--remover" title="Direct link to heading">#</a></h4><p>Insere ou modifica a nova ordem harmônica ao clicar em “Adicionar”. Retira a ordem harmônica selecionada da lista ao clicar em “Remover”.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/harmSource.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/inductor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Indutor</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/syncGenerator"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Gerador Síncrono »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#fonte-de-corrente-harmônica-no-psp-ufu" class="table-of-contents__link">Fonte de corrente harmônica no PSP-UFU</a></li><li><a href="#formulário-de-edição-das-fontes-de-corrente-harmônica" class="table-of-contents__link">Formulário de edição das fontes de corrente harmônica</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Fonte de Corrente Harmônica</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>(<strong>Fonte de perturbação harmônica</strong>) Parte do sistema elétrico de potência ou das instalações a ele conectadas, que causa distorção harmônica da forma de onda da corrente e / ou tensão. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=614-01-16" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="fonte-de-corrente-harmônica-no-psp-ufu"></a>Fonte de corrente harmônica no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#fonte-de-corrente-harmônica-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As fontes de corrente harmônica são responsáveis pela injeção de correntes harmônicas e são utilizadas pela ferramenta de cálculo de <a href="/PSP/docs/harmonics">distorções harmônicas</a>. Uma lista de correntes harmônicas pode ser inserida em um mesmo elemento, conforme é exibido na o formulário de edição de dados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A presença da fonte de corrente harmônica <strong>não é considerada</strong> nos estudos de <a href="/PSP/docs/powerFlow">fluxo de carga</a>, <a href="/PSP/docs/fault">curto-circuito</a> e <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-das-fontes-de-corrente-harmônica"></a>Formulário de edição das fontes de corrente harmônica<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-fontes-de-corrente-harmônica" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados da fonte de corrente harmônica:</p><div><center><img src="/PSP/images/harmSourceForm.png" alt="Formulário dos indutores no PSP-UFU" title="Formulário dos indutores no PSP-UFU"></center></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="ordem"></a>Ordem<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ordem" title="Direct link to heading">#</a></h4><p>Especifica a ordem harmônica a ser inserida na lista de correntes harmônicas do elemento. Caso a ordem harmônica já exista na lista, ela será substituída pelos novos parâmetros.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="corrente"></a>Corrente<a aria-hidden="true" tabindex="-1" class="hash-link" href="#corrente" title="Direct link to heading">#</a></h4><p>Módulo da corrente harmônica.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="unidade"></a>Unidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#unidade" title="Direct link to heading">#</a></h4><p>Unidade do módulo de corrente harmônica, em A ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="ângulo"></a>Ângulo<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ângulo" title="Direct link to heading">#</a></h4><p>Ângulo da corrente harmônica, em graus.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="adicionar--remover"></a>Adicionar / Remover<a aria-hidden="true" tabindex="-1" class="hash-link" href="#adicionar--remover" title="Direct link to heading">#</a></h4><p>Insere ou modifica a nova ordem harmônica ao clicar em “Adicionar”. Retira a ordem harmônica selecionada da lista ao clicar em “Remover”.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/harmSource.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/inductor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Indutor</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/syncGenerator"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Gerador Síncrono »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#fonte-de-corrente-harmônica-no-psp-ufu" class="table-of-contents__link">Fonte de corrente harmônica no PSP-UFU</a></li><li><a href="#formulário-de-edição-das-fontes-de-corrente-harmônica" class="table-of-contents__link">Formulário de edição das fontes de corrente harmônica</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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Corrente Harmônica</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Editor de Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/controlEditor">Editor de Controle</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="-1">Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/io">Entrada / Saída</a></li><li class="menu__list-item"><a 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Motor de Indução</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina assíncrona da qual apenas um enrolamento é energizado. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-31-10" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="motor-de-indução-trifásico-no-psp-ufu"></a>Motor de indução trifásico no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-psp-ufu" title="Direct link to heading">#</a></h2><p>No PSP-UFU, os motores de indução são contemplados nos estudos de <a href="/PSP/docs/powerFLow">fluxo de carga</a> e no estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Os dados de estabilidade da máquina de indução são utilizados em conjunto com o fluxo de carga, <strong>calculando de forma correta a potência reativa das máquinas</strong> e consequentemente a tensão no barramento conectado.</p></div></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Ao marcar a opção &quot;Calcular a potência reativa no fluxo de carga&quot;, devem ser inseridos os dados corretos na aba &quot;Estabilidade&quot;, caso contrário, será atribuída uma potência reativa incorreta no motor.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga"></a>Motor de indução trifásico no cálculo do fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga" title="Direct link to heading">#</a></h3><p>A figura abaixo apresenta o modelo do motor de indução trifásico (MIT) de gaiola simples.</p><div><center><img src="/PSP/images/indMotorModel.svg" alt="Circuito equivalente do motor de indução" title="Circuito equivalente do motor de indução"></center></div><p>As potências ativa e reativa podem ser calculadas em relação às variáveis e parâmetros do motor em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> como:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo>=</mo><mfrac><mrow><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">{</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mo>+</mo><msub><mi>K</mi><mn>1</mn></msub><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mo fence="true">}</mo></mrow></mrow><mrow><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup></mrow></mfrac><mspace linebreak="newline"></mspace><mi>Q</mi><mo>=</mo><mfrac><mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">{</mo><msub><mi>K</mi><mn>1</mn></msub><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mo>−</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mo fence="true">}</mo></mrow></mrow><mrow><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup></mrow></mfrac><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>1</mn></msub><mo>=</mo><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">P = \frac{V^2 \left\{ \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]+K_1 \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ Q = \frac{-V^2 \left\{ K_1 \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]- \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ ~\\ K_1=x_2+x_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.884028em;vertical-align:-1.2940180000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.59001em"><span style="top:-2.11em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.284008em"><span class="pstrut" style="height:3.054008em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.7940180000000003em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">{</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2940180000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.884028em;vertical-align:-1.2940180000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.59001em"><span style="top:-2.11em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.284008em"><span class="pstrut" style="height:3.054008em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.7940180000000003em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">{</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2940180000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Como pode ser observado nas equações acima, existem quatro variáveis e somente duas equações. Na prática, as variáveis podem ser reduzidas a três, uma vez que o módulo da tensão (V) é obtido nos resultados do <a href="/PSP/docs/powerFlow">fluxo de potência</a>. Para resolver as equações é necessário definir uma variável adicional. A variável escolhida como fixa no PSP-UFU é a potência ativa (P), por fornecer resultados numericamente corretos e adequados para motores em situações de estabilidade.</p><p>Portanto, nesse modelo estático, a potência ativa é mantida constante durante o cálculo do fluxo de carga e o escorregamento (s) é atualizado em cada iteração. A equação da potência ativa pode ser reescrita em relação ao escorregamento:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mi>A</mi><mo>+</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mi>B</mi><mo>+</mo><mi>C</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)^2 A + \left(\frac{r_2}{s} \right) B + C = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.040008em;vertical-align:-0.686em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">s</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.3540079999999999em"><span style="top:-3.6029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.8359999999999999em;vertical-align:-0.686em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">s</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span></div><p>Em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mi>P</mi><mrow><mo fence="true">(</mo><msubsup><mi>r</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>K</mi><mn>3</mn><mn>2</mn></msubsup><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><msub><mi>r</mi><mn>1</mn></msub><mspace linebreak="newline"></mspace><mi>B</mi><mo>=</mo><mn>2</mn><mi>P</mi><mo stretchy="false">(</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>2</mn></msub><mo>+</mo><msub><mi>K</mi><mn>3</mn></msub><msub><mi>K</mi><mn>4</mn></msub><mo stretchy="false">)</mo><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">(</mo><msub><mi>K</mi><mn>2</mn></msub><mo>+</mo><msub><mi>K</mi><mn>1</mn></msub><msub><mi>K</mi><mn>3</mn></msub><mo fence="true">)</mo></mrow><mspace linebreak="newline"></mspace><mi>C</mi><mo>=</mo><mi>P</mi><mrow><mo fence="true">(</mo><msubsup><mi>K</mi><mn>2</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>K</mi><mn>4</mn><mn>2</mn></msubsup><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><msub><mi>K</mi><mn>1</mn></msub><msub><mi>K</mi><mn>4</mn></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>2</mn></msub><mo>=</mo><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>3</mn></msub><mo>=</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>4</mn></msub><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">A = P \left( r_1^2 + K_3^2 \right) - V^2 r_1\\ B = 2P(r_1 K_2 + K_3 K_4) - V^2 \left(K_2 + K_1 K_3 \right)\\ C = P \left( K_2^2 + K_4^2 \right) - V^2 K_1 K_4\\ K_2 = -x_1 K_1 -x_2 x_m\\ K_3 = x_m + x_1\\ K_4 = r_1 K_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.2141179999999998em;vertical-align:-0.35001em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.0141079999999998em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.1141079999999999em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.2141179999999998em;vertical-align:-0.35001em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.0141079999999998em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord">−</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Esse modelo pode ser inserido na solução do <a href="/PSP/docs/powerFlow">fluxo de carga</a> seguindo os seguintes passos:</p><ol><li>As constantes <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>K</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">K_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> a <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>K</mi><mn>4</mn></msub></mrow><annotation encoding="application/x-tex">K_4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são inicialmente calculadas . Esses valores são mantidos constantes durante toda a solução;</li><li>Em cada iteração são calculados os coeficientes <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span></span></span></span></span> utilizando o valor atualizado de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span></span></span>;</li><li>A equação quadrática é resolvida e dois valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span></span></span></span></span> são obtidos, em que o maior deles é escolhido por estar na região estável da característica toque-escorregamento do motor;</li><li>Utilizando o novo valor de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span></span></span></span></span>, a potência reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span></span></span></span></span>) é obtida. O vetor de potências é então atualizado e os procedimentos convencionais de solução do fluxo de potência são realizados.</li></ol><p>Os passos de 2 a 4 são repetidos até que se obtenha a convergência.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>No PSP-UFU, os motores de indução não são considerados no cálculo de curto-circuito.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="motor-de-indução-trifásico-no-estudo-de-estabilidade"></a>Motor de indução trifásico no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>Uma importante carga dinâmica são os motores de indução, uma vez que correspondem a uma parcela significativa das cargas presentes no sistema elétrico. O <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">modelo da máquina de indução apresentado anteriormente</a>, a qual pode ser utilizada tanto como motor quanto como gerador, é bem estabelecida na literatura.</p><p>Como descrito na <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">seção anterior</a>, a inicialização dessa máquina é realizada em conjunto com o fluxo de potência, visto que a potência reativa exigida pela máquina de indução é dependente dos parâmetros do motor, assim como a tensão do seu barramento. Essa abordagem é necessária, pois métodos convencionais conduzem a resultados errôneos em sistemas altamente carregados.</p><p>É necessário expressar a equação de movimento da máquina de indução em termos de torque e não potência, como é realizado com as máquinas síncronas. A simetria do rotor também faz com que a posição angular não seja importante e o escorregamento (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi></mrow><annotation encoding="application/x-tex">s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">s</span></span></span></span></span>) é utilizado no lugar da velocidade (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">\omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span></span></span></span>), em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mo>=</mo><mi>f</mi><mi>r</mi><mi>a</mi><mi>c</mi><mrow><msub><mi mathvariant="normal">Ω</mi><mn>0</mn></msub><mo>−</mo><mi>ω</mi></mrow><msub><mi mathvariant="normal">Ω</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">s = frac{\Omega_0 - \omega}{\Omega_0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">s</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mord mathdefault">a</span><span class="mord mathdefault">c</span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span></div><p>Desprezando as perdas por atrito e ventilação e a potência no eixo suave, as equações mecânicas do motor são expressas da seguinte forma:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>=</mo><mi>A</mi><mo>−</mo><mi>B</mi><mi>s</mi><mo>+</mo><mi>C</mi><msup><mi>s</mi><mn>2</mn></msup><mspace linebreak="newline"></mspace><msub><mi>T</mi><mi>e</mi></msub><mo>=</mo><mfrac><mrow><mi>R</mi><mi>e</mi><mrow><mo fence="true">{</mo><mover accent="true"><mi>E</mi><mo>˙</mo></mover><msup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mo>∗</mo></msup><mo fence="true">}</mo></mrow></mrow><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>s</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo fence="true">(</mo><msub><mi>T</mi><mi>m</mi></msub><mo>−</mo><msub><mi>T</mi><mi>e</mi></msub><mo fence="true">)</mo></mrow><mrow><mn>2</mn><mi>H</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">T_m = A -Bs + Cs^2\\ T_e = \frac{Re\left\{ \dot{E}\dot{I}^* \right\}}{\Omega_b}\\ \frac{ds}{dt} = \frac{\left( T_m - T_e \right)}{2H}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mord mathdefault">s</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8641079999999999em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:3.02602em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.19002em"><span style="top:-2.464em"><span class="pstrut" style="height:3.15em"></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.38em"><span class="pstrut" style="height:3.15em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-4.1900200000000005em"><span class="pstrut" style="height:3.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">{</span></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.688696em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.113em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">T_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é o torque mecânico;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>e</mi></msub></mrow><annotation encoding="application/x-tex">T_e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é o torque elétrico;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>H</mi></mrow><annotation encoding="application/x-tex">H</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span></span></span> é a inércia do conjunto motor - carga mecânica</li></ul><p>Os termos <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span></span></span></span></span> são termos que definem o comportamento do torque mecânico da carga de acordo com o escorregamento. O torque mecânico normalmente varia com a <strong>velocidade</strong>, podendo ser expressa proporcionalmente com a seguinte equação quadrática:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>∝</mo><mi>a</mi><mo>+</mo><mi>b</mi><mi>ω</mi><mo>+</mo><mi>c</mi><msup><mi>ω</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">T_m \propto a + b\omega + c\omega^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em"></span><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em"></span><span class="mord mathdefault">b</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8641079999999999em;vertical-align:0em"></span><span class="mord mathdefault">c</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>A</mi><mo>∝</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>B</mi><mo>∝</mo><mi>b</mi><mo>+</mo><mn>2</mn><mi>c</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>C</mi><mo>∝</mo><mi>c</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} A \propto a + b + c \\ B \propto b + 2c \\ C \propto c \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">b</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">c</span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">b</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">2</span><span class="mord mathdefault">c</span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>As equações elétricas do motor de indução de gaiola simples são baseadas no circuito equivalente da <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">figura anterior</a>. De forma semelhante ao modelo transitório da máquina síncrona, o motor de indução pode ser modelado pelo circuito equivalente de Thevenin de tensão transitória <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>E</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">E&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span> atrás de uma resistência do estator <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">r_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e uma reatância transitória <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">x&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>. A reatância transitória aparente de rotor bloqueado é dada por:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><mfrac><mrow><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub></mrow><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x&#x27; = x_1 + \frac{x_2 x_m}{x_2 + x_m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.801892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.94356em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>A constante de tempo de circuito aberto do rotor (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">T_0&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.24810799999999997em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4518920000000004em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24810799999999997em"><span></span></span></span></span></span></span></span></span></span></span>) é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><mrow><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><msub><mi>r</mi><mn>2</mn></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">T_0&#x27; = \frac{x_2 + x_m}{\Omega_b r_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.09633em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2603300000000002em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>E a reatância de circuito aberto é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">x_0 = x_1 + x_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Uma vez que as reatâncias não são afetadas pela posição do rotor, as EADs do motor de indução podem ser expressar diretamente por componentes reais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>) e imaginárias (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">m</span></span></span></span></span>). Portanto, a descrição completa desse modelo é representada pelo seguinte sistema de equações algébrico-diferenciais:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>r</mi></msub><mo>−</mo><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>I</mi><mi>r</mi></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msub><mi>I</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><msub><mi>V</mi><mi>m</mi></msub><mo>−</mo><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>I</mi><mi>m</mi></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msub><mi>I</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mi>s</mi><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><mfrac><mrow><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>m</mi></msub></mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mi>s</mi><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><mfrac><mrow><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>i</mi><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>r</mi></msub></mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac></mrow><annotation encoding="application/x-tex">V_r - E_r&#x27; = r_1 I_r - x&#x27; I_m\\ V_m - E_m&#x27; = r_1 I_m - x&#x27; I_m\\ \frac{dE_r&#x27;}{dt} = \Omega_b s E_m&#x27; - \frac{E_r&#x27; + \left( x_0 - x&#x27; \right) I_m}{T_0&#x27;}\\ \frac{dE_m&#x27;}{dt} = \Omega_b s E_r&#x27; - \frac{E_m&#x27; i \left( x_0 - x&#x27; \right) I_r}{T_0&#x27;}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.9518920000000001em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.9518920000000001em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.3811999999999998em;vertical-align:-0.9523079999999999em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.433692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9523079999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.3811999999999998em;vertical-align:-0.9523079999999999em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.433692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9523079999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-geradores-síncronos"></a>Formulário de edição dos geradores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-geradores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos motores de indução:</p><div><center><img src="/PSP/images/indMotorForm.png" alt="Formulário dos motores de indução no PSP-UFU" title="Formulário dos motores de indução no PSP-UFU"></center></div><p>No formulário pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do motor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/indMotorSw.png" alt="Formulário de chaveamento do motores de indução" title="Formulário de chaveamento do motores de indução"></center></div><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="geral"></a>Geral<a aria-hidden="true" tabindex="-1" class="hash-link" href="#geral" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do gerador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) e reativa (inserida em var, kvar, Mvar ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) do motor.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso a opção “Calcular a potência reativa no fluxo de carga” esteja ativada, o campo de potência reativa é desativado para edição.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="calcular-a-potência-reativa-no-fluxo-de-carga"></a>Calcular a potência reativa no fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#calcular-a-potência-reativa-no-fluxo-de-carga" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar os dados fornecidos no formulário de estabilidade para calcular a potência reativa do motor durante o processo iterativo do fluxo de carga.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Caso essa opção não seja utilizada o motor será considerado uma <a href="/PSP/docs/load">carga de potência constante</a> no estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>.</p><p>A não utilização dessa opção poderá gerar erros de regime permamente no estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><p>Utilizar potência nominal como base
-Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="estabilidade"></a>Estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#estabilidade" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="imprimir-dados-da-máquina-de-indução"></a>Imprimir dados da máquina de indução<a aria-hidden="true" tabindex="-1" class="hash-link" href="#imprimir-dados-da-máquina-de-indução" title="Direct link to heading">#</a></h4><p>Exibe os dados do gerador síncrono nos gráficos no tempo. Os seguintes dados são exibidos:</p><ul><li>tensão terminal</li><li>potências ativa e reativas</li><li>corrente, torque elétrico</li><li>torque mecânico</li><li>velocidade</li><li>escorregamento</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="inércia"></a>Inércia<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inércia" title="Direct link to heading">#</a></h4><p>Inércia do conjunto motor-carga, em s.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="resistência-e-reatância-do-estator"></a>Resistência e reatância do estator<a aria-hidden="true" tabindex="-1" class="hash-link" href="#resistência-e-reatância-do-estator" title="Direct link to heading">#</a></h4><p>Resistência e reatância do estator do motor de indução, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="resistência-e-reatância-do-rotor"></a>Resistência e reatância do rotor<a aria-hidden="true" tabindex="-1" class="hash-link" href="#resistência-e-reatância-do-rotor" title="Direct link to heading">#</a></h4><p>Resistência e reatância do rotor do motor de indução, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="reatância-de-magnetização"></a>Reatância de magnetização<a aria-hidden="true" tabindex="-1" class="hash-link" href="#reatância-de-magnetização" title="Direct link to heading">#</a></h4><p>Reatância do ramo de magnetização do motor de indução, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-fator-de-gaiola"></a>Utilizar fator de gaiola<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-fator-de-gaiola" title="Direct link to heading">#</a></h4><p>Permite a inserção de um fator de gaiola (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>K</mi><mi>g</mi></msub></mrow><annotation encoding="application/x-tex">K_g</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">g</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>) no motor de indução. Tal fator eleva o valor da resistência do rotor em condições de grande escorregamento, como ocorre em motores de gaiola dupla ou gaiola profunda. A resistência do rotor segue a seguinte equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mn>2</mn></msub><mo>=</mo><msub><mi>r</mi><msub><mn>2</mn><mn>0</mn></msub></msub><mrow><mo fence="true">(</mo><mn>1</mn><mo>+</mo><msub><mi>K</mi><mi>g</mi></msub><mi>s</mi><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">r_2 = r_{2_0} \left( 1+K_g s \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">g</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord mathdefault">s</span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><msub><mn>2</mn><mn>0</mn></msub></msub></mrow><annotation encoding="application/x-tex">r_{2_0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68066em;vertical-align:-0.2501em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em"><span></span></span></span></span></span></span></span></span></span></span> é a resistência do rotor inserida no formulário.</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="característica-da-carga"></a>Característica da carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#característica-da-carga" title="Direct link to heading">#</a></h4><p>Descreve a característica do torque da carga mecânica no eixo do motor seguindo a equação do torque mecânico.</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>∝</mo><mi mathvariant="bold">a</mi><mo>+</mo><mi mathvariant="bold">b</mi><mi>ω</mi><mo>+</mo><mi mathvariant="bold">c</mi><msup><mi>ω</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">T_m \propto \bold{a} + \bold{b}\omega + \bold{c}\omega^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em"></span><span class="mord"><span class="mord mathbf">a</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em"></span><span class="mord"><span class="mord mathbf">b</span></span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8641079999999999em;vertical-align:0em"></span><span class="mord"><span class="mord mathbf">c</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>A soma dos coeficientes (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow><annotation encoding="application/x-tex">a + b + c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em"></span><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em"></span><span class="mord mathdefault">b</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">c</span></span></span></span></span>) deve ser unitária.</p></div></div><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="botão-chaveamento"></a>Botão Chaveamento<a aria-hidden="true" tabindex="-1" class="hash-link" href="#botão-chaveamento" title="Direct link to heading">#</a></h3><p>O botão &quot;Chaveamento&quot; irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do gerador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><p>Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões &quot;Adicionar&quot; e &quot;Remover&quot;, respectivamente.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>SÁNCHEZ, J. C.; OLIVARES, T. I. A.; ORTIZ, G. R.; VEGA, D. R. Induction Motor Static Models for Power Flow and Voltage Stability Studies. In: IEEE Power and Energy Society General Meeting, 2012, San Diego. doi: <a href="https://doi.org/10.1109/PESGM.2012.6345618">https://doi.org/10.1109/PESGM.2012.6345618</a></li><li>IEEE Std 399-1997. IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (Brown Book). IEEE, New York, ago. 1998. doi: <a href="https://doi.org/10.1109/IEEESTD.1998.88568">https://doi.org/10.1109/IEEESTD.1998.88568</a></li><li>MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: <a href="https://doi.org/10.1007/978-3-642-13669-6" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/978-3-642-13669-6</a></li><li>ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley &amp; Sons, New York, 2001. doi: <a href="https://doi.org/10.1002/9781118878286" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/9781118878286</a></li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/indMotor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/syncMotor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Compensador Síncrono</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/controlEditor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Editor de Controle »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#motor-de-indução-trifásico-no-psp-ufu" class="table-of-contents__link">Motor de indução trifásico no PSP-UFU</a><ul><li><a href="#motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga" class="table-of-contents__link">Motor de indução trifásico no cálculo do fluxo de carga</a></li><li><a href="#motor-de-indução-trifásico-no-estudo-de-estabilidade" class="table-of-contents__link">Motor de indução trifásico no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-dos-geradores-síncronos" class="table-of-contents__link">Formulário de edição dos geradores síncronos</a><ul><li><a href="#geral" class="table-of-contents__link">Geral</a></li><li><a href="#estabilidade" class="table-of-contents__link">Estabilidade</a></li><li><a href="#botão-chaveamento" class="table-of-contents__link">Botão Chaveamento</a></li></ul></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Motor de Indução</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina assíncrona da qual apenas um enrolamento é energizado. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-31-10" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="motor-de-indução-trifásico-no-psp-ufu"></a>Motor de indução trifásico no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-psp-ufu" title="Direct link to heading">#</a></h2><p>No PSP-UFU, os motores de indução são contemplados nos estudos de <a href="/PSP/docs/powerFLow">fluxo de carga</a> e no estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Os dados de estabilidade da máquina de indução são utilizados em conjunto com o fluxo de carga, <strong>calculando de forma correta a potência reativa das máquinas</strong> e consequentemente a tensão no barramento conectado.</p></div></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Ao marcar a opção &quot;Calcular a potência reativa no fluxo de carga&quot;, devem ser inseridos os dados corretos na aba &quot;Estabilidade&quot;, caso contrário, será atribuída uma potência reativa incorreta no motor.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga"></a>Motor de indução trifásico no cálculo do fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga" title="Direct link to heading">#</a></h3><p>A figura abaixo apresenta o modelo do motor de indução trifásico (MIT) de gaiola simples.</p><div><center><img src="/PSP/images/indMotorModel.svg" alt="Circuito equivalente do motor de indução" title="Circuito equivalente do motor de indução"></center></div><p>As potências ativa e reativa podem ser calculadas em relação às variáveis e parâmetros do motor em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> como:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo>=</mo><mfrac><mrow><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">{</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mo>+</mo><msub><mi>K</mi><mn>1</mn></msub><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mo fence="true">}</mo></mrow></mrow><mrow><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup></mrow></mfrac><mspace linebreak="newline"></mspace><mi>Q</mi><mo>=</mo><mfrac><mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">{</mo><msub><mi>K</mi><mn>1</mn></msub><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mo>−</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mo fence="true">}</mo></mrow></mrow><mrow><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup></mrow></mfrac><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>1</mn></msub><mo>=</mo><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">P = \frac{V^2 \left\{ \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]+K_1 \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ Q = \frac{-V^2 \left\{ K_1 \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]- \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ ~\\ K_1=x_2+x_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.884028em;vertical-align:-1.2940180000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.59001em"><span style="top:-2.11em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.284008em"><span class="pstrut" style="height:3.054008em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.7940180000000003em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">{</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2940180000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.884028em;vertical-align:-1.2940180000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.59001em"><span style="top:-2.11em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.284008em"><span class="pstrut" style="height:3.054008em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.7940180000000003em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">{</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2940180000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Como pode ser observado nas equações acima, existem quatro variáveis e somente duas equações. Na prática, as variáveis podem ser reduzidas a três, uma vez que o módulo da tensão (V) é obtido nos resultados do <a href="/PSP/docs/powerFlow">fluxo de potência</a>. Para resolver as equações é necessário definir uma variável adicional. A variável escolhida como fixa no PSP-UFU é a potência ativa (P), por fornecer resultados numericamente corretos e adequados para motores em situações de estabilidade.</p><p>Portanto, nesse modelo estático, a potência ativa é mantida constante durante o cálculo do fluxo de carga e o escorregamento (s) é atualizado em cada iteração. A equação da potência ativa pode ser reescrita em relação ao escorregamento:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mi>A</mi><mo>+</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mi>B</mi><mo>+</mo><mi>C</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)^2 A + \left(\frac{r_2}{s} \right) B + C = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.040008em;vertical-align:-0.686em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">s</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.3540079999999999em"><span style="top:-3.6029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.8359999999999999em;vertical-align:-0.686em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">s</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span></div><p>Em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mi>P</mi><mrow><mo fence="true">(</mo><msubsup><mi>r</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>K</mi><mn>3</mn><mn>2</mn></msubsup><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><msub><mi>r</mi><mn>1</mn></msub><mspace linebreak="newline"></mspace><mi>B</mi><mo>=</mo><mn>2</mn><mi>P</mi><mo stretchy="false">(</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>2</mn></msub><mo>+</mo><msub><mi>K</mi><mn>3</mn></msub><msub><mi>K</mi><mn>4</mn></msub><mo stretchy="false">)</mo><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">(</mo><msub><mi>K</mi><mn>2</mn></msub><mo>+</mo><msub><mi>K</mi><mn>1</mn></msub><msub><mi>K</mi><mn>3</mn></msub><mo fence="true">)</mo></mrow><mspace linebreak="newline"></mspace><mi>C</mi><mo>=</mo><mi>P</mi><mrow><mo fence="true">(</mo><msubsup><mi>K</mi><mn>2</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>K</mi><mn>4</mn><mn>2</mn></msubsup><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><msub><mi>K</mi><mn>1</mn></msub><msub><mi>K</mi><mn>4</mn></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>2</mn></msub><mo>=</mo><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>3</mn></msub><mo>=</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>4</mn></msub><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">A = P \left( r_1^2 + K_3^2 \right) - V^2 r_1\\ B = 2P(r_1 K_2 + K_3 K_4) - V^2 \left(K_2 + K_1 K_3 \right)\\ C = P \left( K_2^2 + K_4^2 \right) - V^2 K_1 K_4\\ K_2 = -x_1 K_1 -x_2 x_m\\ K_3 = x_m + x_1\\ K_4 = r_1 K_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.2141179999999998em;vertical-align:-0.35001em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.0141079999999998em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.1141079999999999em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.2141179999999998em;vertical-align:-0.35001em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.0141079999999998em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord">−</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Esse modelo pode ser inserido na solução do <a href="/PSP/docs/powerFlow">fluxo de carga</a> seguindo os seguintes passos:</p><ol><li>As constantes <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>K</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">K_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> a <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>K</mi><mn>4</mn></msub></mrow><annotation encoding="application/x-tex">K_4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são inicialmente calculadas . Esses valores são mantidos constantes durante toda a solução;</li><li>Em cada iteração são calculados os coeficientes <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span></span></span></span></span> utilizando o valor atualizado de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span></span></span>;</li><li>A equação quadrática é resolvida e dois valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span></span></span></span></span> são obtidos, em que o maior deles é escolhido por estar na região estável da característica toque-escorregamento do motor;</li><li>Utilizando o novo valor de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span></span></span></span></span>, a potência reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span></span></span></span></span>) é obtida. O vetor de potências é então atualizado e os procedimentos convencionais de solução do fluxo de potência são realizados.</li></ol><p>Os passos de 2 a 4 são repetidos até que se obtenha a convergência.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>No PSP-UFU, os motores de indução não são considerados no cálculo de curto-circuito.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="motor-de-indução-trifásico-no-estudo-de-estabilidade"></a>Motor de indução trifásico no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>Uma importante carga dinâmica são os motores de indução, uma vez que correspondem a uma parcela significativa das cargas presentes no sistema elétrico. O <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">modelo da máquina de indução apresentado anteriormente</a>, a qual pode ser utilizada tanto como motor quanto como gerador, é bem estabelecida na literatura.</p><p>Como descrito na <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">seção anterior</a>, a inicialização dessa máquina é realizada em conjunto com o fluxo de potência, visto que a potência reativa exigida pela máquina de indução é dependente dos parâmetros do motor, assim como a tensão do seu barramento. Essa abordagem é necessária, pois métodos convencionais conduzem a resultados errôneos em sistemas altamente carregados.</p><p>É necessário expressar a equação de movimento da máquina de indução em termos de torque e não potência, como é realizado com as máquinas síncronas. A simetria do rotor também faz com que a posição angular não seja importante e o escorregamento (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi></mrow><annotation encoding="application/x-tex">s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">s</span></span></span></span></span>) é utilizado no lugar da velocidade (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">\omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span></span></span></span>), em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mo>=</mo><mi>f</mi><mi>r</mi><mi>a</mi><mi>c</mi><mrow><msub><mi mathvariant="normal">Ω</mi><mn>0</mn></msub><mo>−</mo><mi>ω</mi></mrow><msub><mi mathvariant="normal">Ω</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">s = frac{\Omega_0 - \omega}{\Omega_0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">s</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mord mathdefault">a</span><span class="mord mathdefault">c</span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span></div><p>Desprezando as perdas por atrito e ventilação e a potência no eixo suave, as equações mecânicas do motor são expressas da seguinte forma:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>=</mo><mi>A</mi><mo>−</mo><mi>B</mi><mi>s</mi><mo>+</mo><mi>C</mi><msup><mi>s</mi><mn>2</mn></msup><mspace linebreak="newline"></mspace><msub><mi>T</mi><mi>e</mi></msub><mo>=</mo><mfrac><mrow><mi>R</mi><mi>e</mi><mrow><mo fence="true">{</mo><mover accent="true"><mi>E</mi><mo>˙</mo></mover><msup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mo>∗</mo></msup><mo fence="true">}</mo></mrow></mrow><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>s</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo fence="true">(</mo><msub><mi>T</mi><mi>m</mi></msub><mo>−</mo><msub><mi>T</mi><mi>e</mi></msub><mo fence="true">)</mo></mrow><mrow><mn>2</mn><mi>H</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">T_m = A -Bs + Cs^2\\ T_e = \frac{Re\left\{ \dot{E}\dot{I}^* \right\}}{\Omega_b}\\ \frac{ds}{dt} = \frac{\left( T_m - T_e \right)}{2H}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mord mathdefault">s</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8641079999999999em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:3.02602em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.19002em"><span style="top:-2.464em"><span class="pstrut" style="height:3.15em"></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.38em"><span class="pstrut" style="height:3.15em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-4.1900200000000005em"><span class="pstrut" style="height:3.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">{</span></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.688696em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.113em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">T_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é o torque mecânico;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>e</mi></msub></mrow><annotation encoding="application/x-tex">T_e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é o torque elétrico;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>H</mi></mrow><annotation encoding="application/x-tex">H</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span></span></span> é a inércia do conjunto motor - carga mecânica</li></ul><p>Os termos <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span></span></span></span></span> são termos que definem o comportamento do torque mecânico da carga de acordo com o escorregamento. O torque mecânico normalmente varia com a <strong>velocidade</strong>, podendo ser expressa proporcionalmente com a seguinte equação quadrática:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>∝</mo><mi>a</mi><mo>+</mo><mi>b</mi><mi>ω</mi><mo>+</mo><mi>c</mi><msup><mi>ω</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">T_m \propto a + b\omega + c\omega^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em"></span><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em"></span><span class="mord mathdefault">b</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8641079999999999em;vertical-align:0em"></span><span class="mord mathdefault">c</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>A</mi><mo>∝</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>B</mi><mo>∝</mo><mi>b</mi><mo>+</mo><mn>2</mn><mi>c</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>C</mi><mo>∝</mo><mi>c</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} A \propto a + b + c \\ B \propto b + 2c \\ C \propto c \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">b</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">c</span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">b</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">2</span><span class="mord mathdefault">c</span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>As equações elétricas do motor de indução de gaiola simples são baseadas no circuito equivalente da <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">figura anterior</a>. De forma semelhante ao modelo transitório da máquina síncrona, o motor de indução pode ser modelado pelo circuito equivalente de Thevenin de tensão transitória <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>E</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">E&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span> atrás de uma resistência do estator <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">r_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e uma reatância transitória <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">x&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>. A reatância transitória aparente de rotor bloqueado é dada por:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><mfrac><mrow><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub></mrow><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x&#x27; = x_1 + \frac{x_2 x_m}{x_2 + x_m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.801892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.94356em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>A constante de tempo de circuito aberto do rotor (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">T_0&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.24810799999999997em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4518920000000004em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24810799999999997em"><span></span></span></span></span></span></span></span></span></span></span>) é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><mrow><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><msub><mi>r</mi><mn>2</mn></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">T_0&#x27; = \frac{x_2 + x_m}{\Omega_b r_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.09633em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2603300000000002em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>E a reatância de circuito aberto é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">x_0 = x_1 + x_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Uma vez que as reatâncias não são afetadas pela posição do rotor, as EADs do motor de indução podem ser expressar diretamente por componentes reais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>) e imaginárias (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">m</span></span></span></span></span>). Portanto, a descrição completa desse modelo é representada pelo seguinte sistema de equações algébrico-diferenciais:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>r</mi></msub><mo>−</mo><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>I</mi><mi>r</mi></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msub><mi>I</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><msub><mi>V</mi><mi>m</mi></msub><mo>−</mo><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>I</mi><mi>m</mi></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msub><mi>I</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mi>s</mi><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><mfrac><mrow><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>m</mi></msub></mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mi>s</mi><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><mfrac><mrow><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>i</mi><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>r</mi></msub></mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac></mrow><annotation encoding="application/x-tex">V_r - E_r&#x27; = r_1 I_r - x&#x27; I_m\\ V_m - E_m&#x27; = r_1 I_m - x&#x27; I_m\\ \frac{dE_r&#x27;}{dt} = \Omega_b s E_m&#x27; - \frac{E_r&#x27; + \left( x_0 - x&#x27; \right) I_m}{T_0&#x27;}\\ \frac{dE_m&#x27;}{dt} = \Omega_b s E_r&#x27; - \frac{E_m&#x27; i \left( x_0 - x&#x27; \right) I_r}{T_0&#x27;}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.9518920000000001em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.9518920000000001em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.3811999999999998em;vertical-align:-0.9523079999999999em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.433692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span 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style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9523079999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.3811999999999998em;vertical-align:-0.9523079999999999em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.433692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9523079999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-geradores-síncronos"></a>Formulário de edição dos geradores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-geradores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos motores de indução:</p><div><center><img src="/PSP/images/indMotorForm.png" alt="Formulário dos motores de indução no PSP-UFU" title="Formulário dos motores de indução no PSP-UFU"></center></div><p>No formulário pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do motor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/indMotorSw.png" alt="Formulário de chaveamento do motores de indução" title="Formulário de chaveamento do motores de indução"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_3zTA tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Botão Chaveamento</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do gerador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) e reativa (inserida em var, kvar, Mvar ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) do motor.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso a opção “Calcular a potência reativa no fluxo de carga” esteja ativada, o campo de potência reativa é desativado para edição.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="calcular-a-potência-reativa-no-fluxo-de-carga"></a>Calcular a potência reativa no fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#calcular-a-potência-reativa-no-fluxo-de-carga" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar os dados fornecidos no formulário de estabilidade para calcular a potência reativa do motor durante o processo iterativo do fluxo de carga.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Caso essa opção não seja utilizada o motor será considerado uma <a href="/PSP/docs/load">carga de potência constante</a> no estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>.</p><p>A não utilização dessa opção poderá gerar erros de regime permamente no estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.</p></div></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>SÁNCHEZ, J. C.; OLIVARES, T. I. A.; ORTIZ, G. R.; VEGA, D. R. Induction Motor Static Models for Power Flow and Voltage Stability Studies. In: IEEE Power and Energy Society General Meeting, 2012, San Diego. doi: <a href="https://doi.org/10.1109/PESGM.2012.6345618">https://doi.org/10.1109/PESGM.2012.6345618</a></li><li>IEEE Std 399-1997. IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (Brown Book). IEEE, New York, ago. 1998. doi: <a href="https://doi.org/10.1109/IEEESTD.1998.88568">https://doi.org/10.1109/IEEESTD.1998.88568</a></li><li>MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: <a href="https://doi.org/10.1007/978-3-642-13669-6" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/978-3-642-13669-6</a></li><li>ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley &amp; Sons, New York, 2001. doi: <a href="https://doi.org/10.1002/9781118878286" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/9781118878286</a></li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/indMotor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/syncMotor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Compensador Síncrono</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/controlEditor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Editor de Controle »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#motor-de-indução-trifásico-no-psp-ufu" class="table-of-contents__link">Motor de indução trifásico no PSP-UFU</a><ul><li><a href="#motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga" class="table-of-contents__link">Motor de indução trifásico no cálculo do fluxo de carga</a></li><li><a href="#motor-de-indução-trifásico-no-estudo-de-estabilidade" class="table-of-contents__link">Motor de indução trifásico no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-dos-geradores-síncronos" class="table-of-contents__link">Formulário de edição dos geradores síncronos</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">PSP-UFU</h1></header><div class="markdown"><div class="admonition admonition-important alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>important</h5></div><div class="admonition-content"><p>This user guide was written in Brazilian Portuguese. If you want to help me translate this guide, contact-me on <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> or <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="sobre-o-psp-ufu"></a>Sobre o PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#sobre-o-psp-ufu" title="Direct link to heading">#</a></h2><p>O PSP-UFU (Plataforma de Sistemas de Potência da Universidade Federal de Uberlândia) é um software <strong>multi-plataforma</strong>, <strong>multilíngue</strong>, <strong>livre e de código aberto (FOSS)</strong> com <strong>recursos avançados de GUI (<em>Graphical User Interface</em>)</strong> e <strong>ferramentas CAD (<em>Computer Aided Design</em>)</strong> para estudos de sistemas elétricos de potência.</p><p>O software permite a construção de qualquer rede de transmissão elétrica e sistemas de controle através da inserção de elementos visuais. Para a visualização dos resultados, o programa oferece <strong>elementos de texto vinculados</strong> na tela principal e também <strong>editores de tabelas e gráficos</strong>.</p><p>O PSP-UFU tem como objetivo fornecer ferramentas eficientes de simulação para fins de <strong>pesquisa</strong> e <strong>educação</strong>, além de <strong>aplicações industriais</strong> em sistemas elétricos de potência.</p><p>Resumidamente, o <em>software</em> pode executar os seguintes estudos:</p><ul><li>Fluxo de potência</li><li>Cálculo de curto-circuito</li><li>Harmônicos</li><li>Estabilidade transitória e dinâmica</li></ul><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="publicações"></a>Publicações<a aria-hidden="true" tabindex="-1" class="hash-link" href="#publicações" title="Direct link to heading">#</a></h3><p>Os artigos abaixo possuem maiores detalhes a respeito do PSP-UFU:</p><blockquote><p>Oliveira, T. L., Guimarães, G. C., &amp; Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. <em>International Transactions on Electrical Energy Systems</em>, e12185. doi: <a href="https://doi.org/10.1002/2050-7038.12185">10.1002/2050-7038.12185</a></p></blockquote><blockquote><p>Oliveira, T. L., Guimarães, G. C., Silva, L. R., &amp; Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. <em>The International Journal of Electrical Engineering &amp; Education</em>, 0020720919879058. doi: <a href="https://doi.org/10.1177/0020720919879058" target="_blank" rel="noopener noreferrer">10.1177/0020720919879058</a></p></blockquote><p>A Tese de Doutorado abaixo detalha em profundidade os cálculos envolvidos, arquitetura de software e ferramentas implementadas no PSP-UFU:</p><blockquote><p>Oliveira, T. L. (2019). Desenvolvimento de um programa computacional livre, gráfico, e multiplataforma para analisar sistemas elétricos de potência em regime permanente e dinâmico. doi: <a href="https://dx.doi.org/10.14393/ufu.te.2019.2444">10.14393/ufu.te.2019.2444</a></p></blockquote><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="contribuindo-com-o-projeto"></a>Contribuindo com o projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#contribuindo-com-o-projeto" title="Direct link to heading">#</a></h3><p>Se você está interessado em contribuir com o PSP-UFU de alguma forma (desenvolvimento, críticas, sugestões, etc.), entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="desenvolvedores"></a>Desenvolvedor<del>es</del><a aria-hidden="true" tabindex="-1" class="hash-link" href="#desenvolvedores" title="Direct link to heading">#</a></h3><p><a href="https://github.com/Thales1330" target="_blank" rel="noopener noreferrer">Thales Lima Oliveira</a></p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/aboutPSP.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/installation"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Instalação »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#sobre-o-psp-ufu" class="table-of-contents__link">Sobre o PSP-UFU</a><ul><li><a href="#publicações" class="table-of-contents__link">Publicações</a></li><li><a href="#contribuindo-com-o-projeto" class="table-of-contents__link">Contribuindo com o projeto</a></li><li><a href="#desenvolvedores" class="table-of-contents__link">Desenvolvedor<del>es</del></a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">PSP-UFU</h1></header><div class="markdown"><div class="admonition admonition-important alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>important</h5></div><div class="admonition-content"><p>This user guide was written in Brazilian Portuguese. If you want to help me translate this guide, contact-me on <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> or <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="sobre-o-psp-ufu"></a>Sobre o PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#sobre-o-psp-ufu" title="Direct link to heading">#</a></h2><p>O PSP-UFU (Plataforma de Sistemas de Potência da Universidade Federal de Uberlândia) é um software <strong>multi-plataforma</strong>, <strong>multilíngue</strong>, <strong>livre e de código aberto (FOSS)</strong> com <strong>recursos avançados de GUI (<em>Graphical User Interface</em>)</strong> e <strong>ferramentas CAD (<em>Computer Aided Design</em>)</strong> para estudos de sistemas elétricos de potência.</p><p>O software permite a construção de qualquer rede de transmissão elétrica e sistemas de controle através da inserção de elementos visuais. Para a visualização dos resultados, o programa oferece <strong>elementos de texto vinculados</strong> na tela principal e também <strong>editores de tabelas e gráficos</strong>.</p><p>O PSP-UFU tem como objetivo fornecer ferramentas eficientes de simulação para fins de <strong>pesquisa</strong> e <strong>educação</strong>, além de <strong>aplicações industriais</strong> em sistemas elétricos de potência.</p><p>Resumidamente, o <em>software</em> pode executar os seguintes estudos:</p><ul><li>Fluxo de potência</li><li>Cálculo de curto-circuito</li><li>Harmônicos</li><li>Estabilidade transitória e dinâmica</li></ul><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="publicações"></a>Publicações<a aria-hidden="true" tabindex="-1" class="hash-link" href="#publicações" title="Direct link to heading">#</a></h3><p>Os artigos abaixo possuem maiores detalhes a respeito do PSP-UFU:</p><blockquote><p>Oliveira, T. L., Guimarães, G. C., &amp; Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. <em>International Transactions on Electrical Energy Systems</em>, e12185. doi: <a href="https://doi.org/10.1002/2050-7038.12185">10.1002/2050-7038.12185</a></p></blockquote><blockquote><p>Oliveira, T. L., Guimarães, G. C., Silva, L. R., &amp; Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. <em>The International Journal of Electrical Engineering &amp; Education</em>, 0020720919879058. doi: <a href="https://doi.org/10.1177/0020720919879058" target="_blank" rel="noopener noreferrer">10.1177/0020720919879058</a></p></blockquote><p>A Tese de Doutorado abaixo detalha em profundidade os cálculos envolvidos, arquitetura de software e ferramentas implementadas no PSP-UFU:</p><blockquote><p>Oliveira, T. L. (2019). Desenvolvimento de um programa computacional livre, gráfico, e multiplataforma para analisar sistemas elétricos de potência em regime permanente e dinâmico. doi: <a href="https://dx.doi.org/10.14393/ufu.te.2019.2444">10.14393/ufu.te.2019.2444</a></p></blockquote><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="contribuindo-com-o-projeto"></a>Contribuindo com o projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#contribuindo-com-o-projeto" title="Direct link to heading">#</a></h3><p>Se você está interessado em contribuir com o PSP-UFU de alguma forma (desenvolvimento, críticas, sugestões, etc.), entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="desenvolvedores"></a>Desenvolvedor<del>es</del><a aria-hidden="true" tabindex="-1" class="hash-link" href="#desenvolvedores" title="Direct link to heading">#</a></h3><p><a href="https://github.com/Thales1330" target="_blank" rel="noopener noreferrer">Thales Lima Oliveira</a></p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/aboutPSP.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/installation"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Instalação »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#sobre-o-psp-ufu" class="table-of-contents__link">Sobre o PSP-UFU</a><ul><li><a href="#publicações" class="table-of-contents__link">Publicações</a></li><li><a href="#contribuindo-com-o-projeto" class="table-of-contents__link">Contribuindo com o projeto</a></li><li><a href="#desenvolvedores" class="table-of-contents__link">Desenvolvedor<del>es</del></a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Indutor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um reator destinado à conexão de derivação em uma rede para compensar a corrente capacitiva. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=421-01-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="indutor-no-psp-ufu"></a>Indutor no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#indutor-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento indutor (ou reator) representa, geralmente, reator <em>shunt</em> no circuito do PSP-UFU.</p><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-indutores"></a>Formulário de edição dos indutores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-indutores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos indutores:</p><div><center><img src="/PSP/images/indForm.png" alt="Formulário dos indutores no PSP-UFU" title="Formulário dos indutores no PSP-UFU"></center></div><p>Além do único contexto geral, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do indutor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/indSw.png" alt="Formulário de chaveamento do indutor" title="Formulário de chaveamento do indutor"></center></div><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="geral"></a>Geral<a aria-hidden="true" tabindex="-1" class="hash-link" href="#geral" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base de potência do sistema). </p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="botão-estabilidade"></a>Botão Estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#botão-estabilidade" title="Direct link to heading">#</a></h3><p>O botão &quot;Estabilidade&quot; irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do indutor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><p>Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões &quot;Adicionar&quot; e &quot;Remover&quot;, respectivamente.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/inductor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/capacitor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Capacitor</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/harmSource"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Fonte de Corrente Harmônica »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#indutor-no-psp-ufu" class="table-of-contents__link">Indutor no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-indutores" class="table-of-contents__link">Formulário de edição dos indutores</a><ul><li><a href="#geral" class="table-of-contents__link">Geral</a></li><li><a href="#botão-estabilidade" class="table-of-contents__link">Botão Estabilidade</a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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Saída</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/transferFunction">Função Transferência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/sum">Somador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/multiplier">Multiplicador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/divider">Divisor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/exponential">Exponencial</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/limiter">Limitador absoluto</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/rateLimiter">Limitador de taxa</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/const">Constante</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Indutor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um reator destinado à conexão de derivação em uma rede para compensar a corrente capacitiva. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=421-01-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="indutor-no-psp-ufu"></a>Indutor no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#indutor-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento indutor (ou reator) representa, geralmente, reator <em>shunt</em> no circuito do PSP-UFU.</p><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-indutores"></a>Formulário de edição dos indutores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-indutores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos indutores:</p><div><center><img src="/PSP/images/indForm.png" alt="Formulário dos indutores no PSP-UFU" title="Formulário dos indutores no PSP-UFU"></center></div><p>Além do único contexto geral, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do indutor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/indSw.png" alt="Formulário de chaveamento do indutor" title="Formulário de chaveamento do indutor"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_3zTA tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base de potência do sistema). </p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/inductor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/capacitor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Capacitor</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/harmSource"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Fonte de Corrente Harmônica »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#indutor-no-psp-ufu" class="table-of-contents__link">Indutor no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-indutores" class="table-of-contents__link">Formulário de edição dos indutores</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Instalação</h1></header><div class="markdown"><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="download"></a>Download<a aria-hidden="true" tabindex="-1" class="hash-link" href="#download" title="Direct link to heading">#</a></h2><p>O download do PSP-UFU pode ser realizado pelo <a href="https://github.com/Thales1330/PSP/releases/latest" target="_blank" rel="noopener noreferrer">&quot;<em>last release</em>&quot; do repositório do PSP-UFU no GitHub</a>.</p><p>Ao acessar ao link, role a página até encontrar os <em>Assets</em>:</p><div><center><img src="/PSP/images/download.png" alt="Assets download" title="Informações da Figura"></center></div><p>Como o PSP-UFU é um <em>software</em> multiplataforma, você deve baixar o arquivo correto:</p><ul><li>Para o sistema operacional <a href="/PSP/docs/installation#windows">Windows</a> baixe os arquivos <em>.exe</em> (recomendado) ou <em>.zip</em>.</li><li>Para os sistemas <a href="/PSP/docs/installation#linux">Linux</a> baseados no Debian (por exemplo, Ubuntu, Mint) <em>64 bits</em> baixe o pacote de instalação <em>.deb</em>.</li></ul><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Se você está interessado em contribuir com o PSP-UFU construindo-o para outros sistemas operacionais (principalmente macOS!) entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><p>Na sequência são apresentados o passo-a-passo para instalação dos SOs <a href="/PSP/docs/installation#windows">Windows</a> e <a href="/PSP/docs/installation#linux">Linux</a>. Também são apresentadas as soluções para os erros mais recorrentes.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="windows"></a>Windows<a aria-hidden="true" tabindex="-1" class="hash-link" href="#windows" title="Direct link to heading">#</a></h2><p>Após baixar o arquivo <em>.exe</em> avance em cada passo do instalador. O executável irá solicitar automaticamente a instalação do <strong>Microsoft Visual C++ Redistribuível</strong> e, caso não esteja instalado no seu computador, realize os procedimentos do programa.</p><p>Caso o executável falhe em abrir, baixe o arquivo <em>.zip</em> e descompacte em alguma pasta do seu sistema. Nesse caso é necessário baixar e instalar manualmente o <a href="https://aka.ms/vs/16/release/vc_redist.x86.exe"><strong>Microsoft Visual C++ Redistribuível 32 bits</strong></a>.</p><p>Após a conclusão da instalação abra o PSP-UFU para verificar a correta instalação. O executável está presente na pasta &quot;<em>&lt;local de instalação&gt;/PSP-UFU/bin/PSP-UFU.exe</em>&quot;.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="problemas-recorrentes-no-windows"></a>Problemas recorrentes no Windows<a aria-hidden="true" tabindex="-1" class="hash-link" href="#problemas-recorrentes-no-windows" title="Direct link to heading">#</a></h3><ul><li>Ao baixar o navegador pode <strong>falsamente</strong> sinalizar que é um arquivo perigoso, basta clicar em &quot;Manter arquivo&quot;;</li><li>Ao abrir o instalador, novamente o Windows sinaliza que o arquivo é perigoso, basta clicar em &quot;Executar assim mesmo&quot;;</li><li>Ao abrir o programa e alterar o seu idioma, uma mensagem de erro é exibida. Para resolver esse problema basta executar o PSP-UFU como administrador (clicar com botão direito no atalho do programa e posteriormente em executar como administrador). Altere novamente o idioma e reinicie o programa;</li><li>Ao criar um novo projeto a tela de trabalho não é exibida ou é exibida uma tela preta. Vá nas opções gerais e altere o renderizador para &quot;Device Context&quot;. Caso apareça uma mensagem de erro, execute o programa como administrador e repita o processo. Reinicie o programa.</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="linux"></a>Linux<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linux" title="Direct link to heading">#</a></h2><p>A instalação no sistema Linux é facilmente realizado pelo pacote de instalação automático <em>.deb</em>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Note que essa versão para Linux está defasada e algumas funcionalidades do programa podem não estar presentes.</p><p>Caso queira contribuir com o projeto e construir a versão atual no sistema Linux baseado em Debian ou em outras distribuições entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="problemas-recorrentes-no-linux"></a>Problemas recorrentes no Linux<a aria-hidden="true" tabindex="-1" class="hash-link" href="#problemas-recorrentes-no-linux" title="Direct link to heading">#</a></h3><p>Pode ser necessário adicionar o <a href="https://wiki.wxwidgets.org/Compiling_and_getting_started#Running_wxWidgets_projects" target="_blank" rel="noopener noreferrer">diretório das bibliotecas do wxWidgets</a> nas variáveis de ambiente.
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class="hash-link" href="#download" title="Direct link to heading">#</a></h2><p>O download do PSP-UFU pode ser realizado pelo <a href="https://github.com/Thales1330/PSP/releases/latest" target="_blank" rel="noopener noreferrer">&quot;<em>last release</em>&quot; do repositório do PSP-UFU no GitHub</a>.</p><p>Ao acessar ao link, role a página até encontrar os <em>Assets</em>:</p><div><center><img src="/PSP/images/download.png" alt="Assets download" title="Informações da Figura"></center></div><p>Como o PSP-UFU é um <em>software</em> multiplataforma, você deve baixar o arquivo correto:</p><ul><li>Para o sistema operacional <a href="/PSP/docs/installation#windows">Windows</a> baixe os arquivos <em>.exe</em> (recomendado) ou <em>.zip</em>.</li><li>Para os sistemas <a href="/PSP/docs/installation#linux">Linux</a> baseados no Debian (por exemplo, Ubuntu, Mint) <em>64 bits</em> baixe o pacote de instalação <em>.deb</em>.</li></ul><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Se você está interessado em contribuir com o PSP-UFU construindo-o para outros sistemas operacionais (principalmente macOS!) entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><p>Na sequência são apresentados o passo-a-passo para instalação dos SOs <a href="/PSP/docs/installation#windows">Windows</a> e <a href="/PSP/docs/installation#linux">Linux</a>. Também são apresentadas as soluções para os erros mais recorrentes.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="windows"></a>Windows<a aria-hidden="true" tabindex="-1" class="hash-link" href="#windows" title="Direct link to heading">#</a></h2><p>Após baixar o arquivo <em>.exe</em> avance em cada passo do instalador. O executável irá solicitar automaticamente a instalação do <strong>Microsoft Visual C++ Redistribuível</strong> e, caso não esteja instalado no seu computador, realize os procedimentos do programa.</p><p>Caso o executável falhe em abrir, baixe o arquivo <em>.zip</em> e descompacte em alguma pasta do seu sistema. Nesse caso é necessário baixar e instalar manualmente o <a href="https://aka.ms/vs/16/release/vc_redist.x86.exe"><strong>Microsoft Visual C++ Redistribuível 32 bits</strong></a>.</p><p>Após a conclusão da instalação abra o PSP-UFU para verificar a correta instalação. O executável está presente na pasta &quot;<em>&lt;local de instalação&gt;/PSP-UFU/bin/PSP-UFU.exe</em>&quot;.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="problemas-recorrentes-no-windows"></a>Problemas recorrentes no Windows<a aria-hidden="true" tabindex="-1" class="hash-link" href="#problemas-recorrentes-no-windows" title="Direct link to heading">#</a></h3><ul><li>Ao baixar o navegador pode <strong>falsamente</strong> sinalizar que é um arquivo perigoso, basta clicar em &quot;Manter arquivo&quot;;</li><li>Ao abrir o instalador, novamente o Windows sinaliza que o arquivo é perigoso, basta clicar em &quot;Executar assim mesmo&quot;;</li><li>Ao abrir o programa e alterar o seu idioma, uma mensagem de erro é exibida. Para resolver esse problema basta executar o PSP-UFU como administrador (clicar com botão direito no atalho do programa e posteriormente em executar como administrador). Altere novamente o idioma e reinicie o programa;</li><li>Ao criar um novo projeto a tela de trabalho não é exibida ou é exibida uma tela preta. Vá nas opções gerais e altere o renderizador para &quot;Device Context&quot;. Caso apareça uma mensagem de erro, execute o programa como administrador e repita o processo. Reinicie o programa.</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="linux"></a>Linux<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linux" title="Direct link to heading">#</a></h2><p>A instalação no sistema Linux é facilmente realizado pelo pacote de instalação automático <em>.deb</em>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Note que essa versão para Linux está defasada e algumas funcionalidades do programa podem não estar presentes.</p><p>Caso queira contribuir com o projeto e construir a versão atual no sistema Linux baseado em Debian ou em outras distribuições entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="problemas-recorrentes-no-linux"></a>Problemas recorrentes no Linux<a aria-hidden="true" tabindex="-1" class="hash-link" href="#problemas-recorrentes-no-linux" title="Direct link to heading">#</a></h3><p>Pode ser necessário adicionar o <a href="https://wiki.wxwidgets.org/Compiling_and_getting_started#Running_wxWidgets_projects" target="_blank" rel="noopener noreferrer">diretório das bibliotecas do wxWidgets</a> nas variáveis de ambiente.
 Para isso, siga <strong>UM</strong> dos métodos apresentados abaixo:</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="método-i-recomendado"></a><em>Método I (recomendado)</em><a aria-hidden="true" tabindex="-1" class="hash-link" href="#método-i-recomendado" title="Direct link to heading">#</a></h4><p>Insira o seguinte comando no arquivo <strong>~/.bashrc</strong>:</p><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-shell codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token builtin class-name" style="color:rgb(255, 203, 107)">echo</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;export LD_LIBRARY_PATH=</span><span class="token string variable" style="color:rgb(191, 199, 213)">$LD_LIBRARY_PATH</span><span class="token string" style="color:rgb(195, 232, 141)">:/usr/local/lib&quot;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;&gt;</span><span class="token plain"> ~/.bashrc</span></div></div></div></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="método-ii-não-recomendado"></a><em>Método II (não recomendado)</em><a aria-hidden="true" tabindex="-1" class="hash-link" href="#método-ii-não-recomendado" title="Direct link to heading">#</a></h4><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Utilizando esse método os passos abaixo devem ser executados <strong>todas as vezes</strong> que você quiser abrir o PSP-UFU.</p></div></div><ol><li>Abra o terminal e acesse o diretório onde está instalado o PSP-UFU:</li></ol><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-shell codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token builtin class-name" style="color:rgb(255, 203, 107)">cd</span><span class="token plain"> /usr/local/bin</span></div></div></div></div></div><ol start="2"><li>Insira as bibliotecas compartilhadas do wxWidgets nas variáveis de ambiente:</li></ol><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-shell codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token builtin class-name" style="color:rgb(255, 203, 107)">export</span><span class="token plain"> </span><span class="token assign-left variable" style="color:rgb(191, 199, 213)">LD_LIBRARY_PATH</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token variable" style="color:rgb(191, 199, 213)">$LD_LIBRARY_PATH</span><span class="token plain">:/usr/local/lib</span></div></div></div></div></div><ol start="3"><li>Então, execute o PSP-UFU na <strong>mesma seção</strong> do terminal:</li></ol><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-shell codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">./PSP-UFU</span></div></div></div></div></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Verifique se o computador possui as unidades de vídeo instaladas corretamente, caso contrário, o programa não exibirá a área de trabalho para criar e editar diagramas de linha única ou diagramas de blocos de controle.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/installation.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav 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class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Entrada / Saída</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>As entradas e saída são variáveis relacionadas às máquinas síncronas. Cada tipo de entrada e saída está relacionada a um regulador da máquina: <strong>Regulador de Tensão (AVR, do inglês <em>Automatic Voltage Regulator</em>)</strong> e <strong>Regulador de Velocidade (RV)</strong>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O sistema de controle deve ter <strong>ao menos uma entrada e uma saída</strong>.</p></div></div><p>As entradas e saídas do sistema de controle são definidas por esses blocos, os quais são distintos para cada tipo de escopo. A figura abaixo apresenta um exemplo de um formulário de edição das entradas e saídas de um AVR:</p><div><center><img src="/PSP/images/ioForm.png" alt="Formulário de edição de entradas e saídas de sistemas de controle de um AVR" title="Formulário de edição de entradas e saídas de sistemas de controle de um AVR"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="variáveis-de-entrada-e-saída"></a>Variáveis de entrada e saída<a aria-hidden="true" tabindex="-1" class="hash-link" href="#variáveis-de-entrada-e-saída" title="Direct link to heading">#</a></h2><p>O usuário deve sinalizar o tipo de bloco entre entrada e saída e, então, selecionar em uma lista a variável desejada. As seguintes variáveis de controle estão atualmente disponíveis no programa:</p><ul><li><p><strong>Tensão terminal</strong> (<em>entrada: AVR</em>): Módulo da tensão no barramento da máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, variável no tempo. Essa variável é normalmente utilizada no cálculo do erro da tensão de referência do AVR;</p></li><li><p><strong>Velocidade</strong> (<em>entrada: AVR e RV</em>): Velocidade da máquina síncrona, em rad/s, variável no tempo. Normalmente utilizada no cálculo do erro de velocidade nos reguladores de velocidade, além de entrada do PSS em AVRs;</p></li><li><p><strong>Potência ativa e reativa</strong> (<em>entrada: AVR</em>): Potência ativa fornecida pela máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, variável no tempo. Normalmente utilizada como entrada do PSS (potência ativa) e controle de sub e sobrecorrente de excitação nos AVRs;</p></li><li><p><strong>Tensão terminal inicial</strong> (<em>entrada: AVR</em>): Módulo da tensão no barramento da máquina síncrona prévia ao estudo dinâmico originado do fluxo de carga, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, fixo no tempo. Essa variável está normalmente associada à referência de tensão do AVR;</p></li><li><p><strong>Velocidade inicial</strong> (<em>entrada: AVR e RV</em>): Velocidade do sistema (2πf_ref), definida nas opções de simulação, em rad/s, fixa no tempo. Normalmente utiliza-se essa variável como referência de velocidade em RVs e normalização da velocidade;</p></li><li><p><strong>Potência mecânica inicial</strong> (<em>entrada: RV</em>): Potência mecânica inicial, calculada após a inicialização das máquinas síncronas com os dados originados do fluxo de carga, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, fixa no tempo. Normalmente é utilizada como referência de potência mecânica nos reguladores de velocidade;</p></li><li><p><strong>Variação de velocidade e potência ativa</strong> (<em>entrada: AVR</em>): Cálculo da variação dessas entradas entre os passos de integração normalizada pelo passo de integração, conforme a equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>n</mi></msub><mo>−</mo><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><mi>h</mi></mfrac></mrow><annotation encoding="application/x-tex">\Delta x = \frac{x_n-x_{n-1}}{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault">x</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.9463300000000001em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">h</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\Delta x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault">x</span></span></span></span></span>	é a variação da entrada (velocidade ou potência ativa);</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">x_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">x_{n-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span></span>	é a variável no passo atual e anterior, respectivamente;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>	é o passo de integração.</li></ul><div class="admonition admonition-note alert alert--secondary"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M6.3 5.69a.942.942 0 0 1-.28-.7c0-.28.09-.52.28-.7.19-.18.42-.28.7-.28.28 0 .52.09.7.28.18.19.28.42.28.7 0 .28-.09.52-.28.7a1 1 0 0 1-.7.3c-.28 0-.52-.11-.7-.3zM8 7.99c-.02-.25-.11-.48-.31-.69-.2-.19-.42-.3-.69-.31H6c-.27.02-.48.13-.69.31-.2.2-.3.44-.31.69h1v3c.02.27.11.5.31.69.2.2.42.31.69.31h1c.27 0 .48-.11.69-.31.2-.19.3-.42.31-.69H8V7.98v.01zM7 2.3c-3.14 0-5.7 2.54-5.7 5.68 0 3.14 2.56 5.7 5.7 5.7s5.7-2.55 5.7-5.7c0-3.15-2.56-5.69-5.7-5.69v.01zM7 .98c3.86 0 7 3.14 7 7s-3.14 7-7 7-7-3.12-7-7 3.14-7 7-7z"></path></svg></span>Nota</h5></div><div class="admonition-content"><p>A normalização é necessária para a correta utilização da razão de passo de controle, definida nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</p></div></div></li><li><p><strong>Tensão de campo</strong> (<em>saída: AVR</em>): Define a tensão aplicada ao campo na máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> Utilizada como saída dos AVRs, controlando principalmente tensão no barramento conectado e/ou fator de potência da máquina;</p></li><li><p><strong>Potência mecânica</strong> (<em>saída: RV</em>): Define qual a potência mecânica aplicada no eixo da máquina síncrona. Utilizada como saída dos reguladores de velocidade, controlando principalmente a potência ativa injetada pela máquina e sua frequência.</p></li></ul></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/io.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/controlEditor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Editor de Controle</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/transferFunction"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Função Transferência »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#variáveis-de-entrada-e-saída" class="table-of-contents__link">Variáveis de entrada e saída</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Entrada / Saída</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>As entradas e saída são variáveis relacionadas às máquinas síncronas. Cada tipo de entrada e saída está relacionada a um regulador da máquina: <strong>Regulador de Tensão (AVR, do inglês <em>Automatic Voltage Regulator</em>)</strong> e <strong>Regulador de Velocidade (RV)</strong>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O sistema de controle deve ter <strong>ao menos uma entrada e uma saída</strong>.</p></div></div><p>As entradas e saídas do sistema de controle são definidas por esses blocos, os quais são distintos para cada tipo de escopo. A figura abaixo apresenta um exemplo de um formulário de edição das entradas e saídas de um AVR:</p><div><center><img src="/PSP/images/ioForm.png" alt="Formulário de edição de entradas e saídas de sistemas de controle de um AVR" title="Formulário de edição de entradas e saídas de sistemas de controle de um AVR"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="variáveis-de-entrada-e-saída"></a>Variáveis de entrada e saída<a aria-hidden="true" tabindex="-1" class="hash-link" href="#variáveis-de-entrada-e-saída" title="Direct link to heading">#</a></h2><p>O usuário deve sinalizar o tipo de bloco entre entrada e saída e, então, selecionar em uma lista a variável desejada. As seguintes variáveis de controle estão atualmente disponíveis no programa:</p><ul><li><p><strong>Tensão terminal</strong> (<em>entrada: AVR</em>): Módulo da tensão no barramento da máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, variável no tempo. Essa variável é normalmente utilizada no cálculo do erro da tensão de referência do AVR;</p></li><li><p><strong>Velocidade</strong> (<em>entrada: AVR e RV</em>): Velocidade da máquina síncrona, em rad/s, variável no tempo. Normalmente utilizada no cálculo do erro de velocidade nos reguladores de velocidade, além de entrada do PSS em AVRs;</p></li><li><p><strong>Potência ativa e reativa</strong> (<em>entrada: AVR</em>): Potência ativa fornecida pela máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, variável no tempo. Normalmente utilizada como entrada do PSS (potência ativa) e controle de sub e sobrecorrente de excitação nos AVRs;</p></li><li><p><strong>Tensão terminal inicial</strong> (<em>entrada: AVR</em>): Módulo da tensão no barramento da máquina síncrona prévia ao estudo dinâmico originado do fluxo de carga, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, fixo no tempo. Essa variável está normalmente associada à referência de tensão do AVR;</p></li><li><p><strong>Velocidade inicial</strong> (<em>entrada: AVR e RV</em>): Velocidade do sistema (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi>π</mi><msub><mi>f</mi><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msub></mrow><annotation encoding="application/x-tex">2 \pi f_{ref}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.03588em">π</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>), definida nas <a href="/PSP/docs/simulationConfig">opções de simulação</a>, em rad/s, fixa no tempo. Normalmente utiliza-se essa variável como referência de velocidade em RVs e normalização da velocidade;</p></li><li><p><strong>Potência mecânica inicial</strong> (<em>entrada: RV</em>): Potência mecânica inicial, calculada após a inicialização das máquinas síncronas com os dados originados do fluxo de carga, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, fixa no tempo. Normalmente é utilizada como referência de potência mecânica nos reguladores de velocidade;</p></li><li><p><strong>Variação de velocidade e potência ativa</strong> (<em>entrada: AVR</em>): Cálculo da variação dessas entradas entre os passos de integração normalizada pelo passo de integração, conforme a equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>n</mi></msub><mo>−</mo><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><mi>h</mi></mfrac></mrow><annotation encoding="application/x-tex">\Delta x = \frac{x_n-x_{n-1}}{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault">x</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.9463300000000001em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">h</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\Delta x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault">x</span></span></span></span></span>	é a variação da entrada (velocidade ou potência ativa);</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">x_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">x_{n-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span></span>	é a variável no passo atual e anterior, respectivamente;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>	é o passo de integração.</li></ul><div class="admonition admonition-note alert alert--secondary"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M6.3 5.69a.942.942 0 0 1-.28-.7c0-.28.09-.52.28-.7.19-.18.42-.28.7-.28.28 0 .52.09.7.28.18.19.28.42.28.7 0 .28-.09.52-.28.7a1 1 0 0 1-.7.3c-.28 0-.52-.11-.7-.3zM8 7.99c-.02-.25-.11-.48-.31-.69-.2-.19-.42-.3-.69-.31H6c-.27.02-.48.13-.69.31-.2.2-.3.44-.31.69h1v3c.02.27.11.5.31.69.2.2.42.31.69.31h1c.27 0 .48-.11.69-.31.2-.19.3-.42.31-.69H8V7.98v.01zM7 2.3c-3.14 0-5.7 2.54-5.7 5.68 0 3.14 2.56 5.7 5.7 5.7s5.7-2.55 5.7-5.7c0-3.15-2.56-5.69-5.7-5.69v.01zM7 .98c3.86 0 7 3.14 7 7s-3.14 7-7 7-7-3.12-7-7 3.14-7 7-7z"></path></svg></span>Nota</h5></div><div class="admonition-content"><p>A normalização é necessária para a correta utilização da razão de passo de controle, definida nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</p></div></div></li><li><p><strong>Tensão de campo</strong> (<em>saída: AVR</em>): Define a tensão aplicada ao campo na máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> Utilizada como saída dos AVRs, controlando principalmente tensão no barramento conectado e/ou fator de potência da máquina;</p></li><li><p><strong>Potência mecânica</strong> (<em>saída: RV</em>): Define qual a potência mecânica aplicada no eixo da máquina síncrona. Utilizada como saída dos reguladores de velocidade, controlando principalmente a potência ativa injetada pela máquina e sua frequência.</p></li></ul></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/io.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/controlEditor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Editor de Controle</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/transferFunction"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Função Transferência »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#variáveis-de-entrada-e-saída" class="table-of-contents__link">Variáveis de entrada e saída</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Limitador absoluto</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Os blocos de limite absoluto cumprem a função de restringir os valores de entrada de acordo com os limites máximos e mínimos inseridos pelo usuário. Caso a entrada ultrapasse algum dos limites impostos, a saída será igual a esse valor limite até que a entrada retorne para a faixa permitida.</p><p>As restrições máximas e mínimas de valores dos sistemas de controle são modeladas utilizando um Limitador, cuja implementação é bastante simples e segue a seguinte expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>u</mi><mi>n</mi></msub><mo>&gt;</mo><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>u</mi><mi>n</mi></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub><mo>≤</mo><msub><mi>u</mi><mi>n</mi></msub><mo>≤</mo><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>u</mi><mi>n</mi></msub><mo>&lt;</mo><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">y_n = \begin{cases} L_{sup}{,} &amp; \text{se } u_n &gt; L_{sup} \\ u_n{,} &amp; \text{se } L_{inf} \le u_n \le L_{sup}\\ L_{inf}{,} &amp; \text{se } u_n &lt; L_{inf} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	Éé o valor de saída atual do bloco</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub></mrow><annotation encoding="application/x-tex">L_{sup}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub></mrow><annotation encoding="application/x-tex">L_{inf}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>	são os limites superior e inferior, respectivamente</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é o valor de entrada atual do bloco</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-do-bloco-limitador"></a>Formulário de edição do bloco Limitador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-do-bloco-limitador" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados do bloco limitador.</p><div><center><img src="/PSP/images/limiterForm.png" alt="Formulário de edição de dados do bloco limitador no PSP-UFU" title="Formulário de edição de dados do bloco limitador no PSP-UFU"></center></div><p>Esse bloco não linear é definido pelo <strong>limite superior e inferior</strong>, inseridos pelo usuário.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Tais blocos são bastante encontrados nos sistemas de controle para limitar a atuação do controlador, além de representar limites físicos de modelos implementados, como, por exemplo, valores máximos de corrente de excitação ou potência mecânica fornecida pelas turbinas.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/limiter.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/exponential"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Exponencial</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/rateLimiter"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Limitador de taxa »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#formulário-de-edição-do-bloco-limitador" class="table-of-contents__link">Formulário de edição do bloco Limitador</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Linha</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um meio de transmissão fabricado usado para transmitir energia eletromagnética entre dois pontos com um mínimo de radiação. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=704-02-02" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="linha-no-psp-ufu"></a>Linha no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linha-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As linhas no PSP-UFU são modelos <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> equilibradas. Podem ser utilizadas como linhas de transmissão e distribuição de sistemas elétricos de potência.</p><p>A figura abaixo mostra o modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> implementado no PSP-UFU:</p><div><center><img src="/PSP/images/lineModel.svg" alt="Modelo PI da linha" title="Modelo PI da linha"></center></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">r</mi><mi mathvariant="bold">L</mi></msub></mrow><annotation encoding="application/x-tex">\bold{r_L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a resistência da linha;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">x</mi><mi mathvariant="bold">L</mi></msub></mrow><annotation encoding="application/x-tex">\bold{x_L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a reatância indutiva da linha;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi mathvariant="bold">b</mi><mi mathvariant="bold">L</mi><mi mathvariant="bold">d</mi></msubsup></mrow><annotation encoding="application/x-tex">\bold{b_{L}^{d}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.126385em;vertical-align:-0.277277em"></span><span class="mord"><span class="mord"><span class="mord mathbf">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.4227230000000004em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathbf mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathbf mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.277277em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a susceptância capacitiva <em>shunt</em> da linha.</li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O modelo utilizado no PSP-UFU é <strong>equilibrado</strong> e <strong>não possui impedâncias mútuas</strong> entre as fases.</p></div></div><p>A linha pode ser inseridas com pontos de ancoragem, ou &quot;nós&quot;, para maior personalização gráfica do elemento, como apresentado nas <a href="/PSP/docs/cadTools#linha">Ferramentas CAD</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>A linha deve ser inserida entre duas barras de <strong>mesma tensão nominal</strong>. Caso você tente inseri-la entre barras de tensão diferentes, uma mensagem de erro será exibida.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Um arranjo série de uma <a href="/PSP/docs/line">linha</a> sem as susceptâncias <em>shunt</em>, um <a href="/PSP/docs/bus">barramento</a> e um <a href="/PSP/docs/capacitor">capacitor</a> pode ser utilizado para fabricar um filtro passivo nos <a href="/PSP/docs/harmonics">estudos harmônicos</a>. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-das-linhas"></a>Formulário de edição das linhas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-linhas" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das linhas de transmissão:</p><div><center><img src="/PSP/images/lineForm.png" alt="Formulário das linhas no PSP-UFU" title="Formulário das linhas no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais da linha e informações do fluxo de carga;</li><li><strong>Falta</strong>: local onde as impedâncias de sequência zero são inseridas.</li></ul><div class="admonition admonition-note alert alert--secondary"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M6.3 5.69a.942.942 0 0 1-.28-.7c0-.28.09-.52.28-.7.19-.18.42-.28.7-.28.28 0 .52.09.7.28.18.19.28.42.28.7 0 .28-.09.52-.28.7a1 1 0 0 1-.7.3c-.28 0-.52-.11-.7-.3zM8 7.99c-.02-.25-.11-.48-.31-.69-.2-.19-.42-.3-.69-.31H6c-.27.02-.48.13-.69.31-.2.2-.3.44-.31.69h1v3c.02.27.11.5.31.69.2.2.42.31.69.31h1c.27 0 .48-.11.69-.31.2-.19.3-.42.31-.69H8V7.98v.01zM7 2.3c-3.14 0-5.7 2.54-5.7 5.68 0 3.14 2.56 5.7 5.7 5.7s5.7-2.55 5.7-5.7c0-3.15-2.56-5.69-5.7-5.69v.01zM7 .98c3.86 0 7 3.14 7 7s-3.14 7-7 7-7-3.12-7-7 3.14-7 7-7z"></path></svg></span>Nota</h5></div><div class="admonition-content"><p>Os parâmetros necessários para construção da linha segundo seu modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> são inseridos na aba Geral, utilizados para construção da matriz admitância de sequência positiva e negativa.</p><p>Dados adicionais de impedâncias de sequência zero necessário para o cálculo de curtos-circuitos desbalanceados são editados na aba Falta, utilizados na construção da matriz admitância de sequência zero.</p></div></div><p>Além desses dois contextos, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da linha durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/lineSw.png" alt="Formulário de chaveamento da linha" title="Formulário de chaveamento da linha"></center></div><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="geral"></a>Geral<a aria-hidden="true" tabindex="-1" class="hash-link" href="#geral" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Campo de informação <em>não editável</em> que apresenta a tensão nominal da linha. Para alterar esse campo é necessário editar o campo correspondente do <a href="/PSP/docs/bus#geral">barramento</a> conectado.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal da linha, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="parâmetros-do-modelo-pi"></a>Parâmetros do modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span><a aria-hidden="true" tabindex="-1" class="hash-link" href="#parâmetros-do-modelo-pi" title="Direct link to heading">#</a></h4><p>Resistência (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">r_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), Reatância indutiva (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">x_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) série e Susceptância capacitiva shunt <strong>total</strong> (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><msubsup><mi>b</mi><mi>L</mi><mi>d</mi></msubsup></mrow><annotation encoding="application/x-tex">2b_{L}^{d}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.124439em;vertical-align:-0.275331em"></span><span class="mord">2</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.424669em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.275331em"><span></span></span></span></span></span></span></span></span></span></span>) presentes no modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> da linha.</p><p>Esses parâmetros são inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">\Omega/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">Ω</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">S/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>b</mi><mi>L</mi><mi>d</mi></msubsup></mrow><annotation encoding="application/x-tex">b_{L}^{d}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.124439em;vertical-align:-0.275331em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.424669em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.275331em"><span></span></span></span></span></span></span></span></span></span></span>).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="comprimento-da-linha"></a>Comprimento da linha<a aria-hidden="true" tabindex="-1" class="hash-link" href="#comprimento-da-linha" title="Direct link to heading">#</a></h4><p>Utilizado para calcular o valor dos parâmetros da linha inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">\Omega/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">Ω</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> (ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">S/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span>).</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>O comprimento da linha é ignorado caso não sejam utilizadas as unidades por quilometro.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal da linha como base para a conversão das unidades, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="falta"></a>Falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#falta" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="parâmetros-do-modelo-pi-de-sequência-zero"></a>Parâmetros do modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> de sequência zero<a aria-hidden="true" tabindex="-1" class="hash-link" href="#parâmetros-do-modelo-pi-de-sequência-zero" title="Direct link to heading">#</a></h4><p>Esses parâmetros são necessários para o correto cálculo das correntes de <a href="/PSP/docs/fault">falta desbalanceadas</a> (fase-fase, fase-fase-terra e fase-terra) e devem ser inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>A não inserção desses dados acarretarão em resultados incorretos para <a href="/PSP/docs/fault">faltas desbalanceadas</a>.</p></div></div><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="botão-estabilidade"></a>Botão Estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#botão-estabilidade" title="Direct link to heading">#</a></h3><p>O botão &quot;Estabilidade&quot; irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção da linha durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><p>Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões &quot;Adicionar&quot; e &quot;Remover&quot;, respectivamente.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/line.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/bus"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Barramento</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/transformer"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Transformador »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#linha-no-psp-ufu" class="table-of-contents__link">Linha no PSP-UFU</a></li><li><a href="#formulário-de-edição-das-linhas" class="table-of-contents__link">Formulário de edição das linhas</a><ul><li><a href="#geral" class="table-of-contents__link">Geral</a></li><li><a href="#falta" class="table-of-contents__link">Falta</a></li><li><a href="#botão-estabilidade" class="table-of-contents__link">Botão Estabilidade</a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Linha</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um meio de transmissão fabricado usado para transmitir energia eletromagnética entre dois pontos com um mínimo de radiação. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=704-02-02" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="linha-no-psp-ufu"></a>Linha no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linha-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As linhas no PSP-UFU são modelos <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> equilibradas. Podem ser utilizadas como linhas de transmissão e distribuição de sistemas elétricos de potência.</p><p>A figura abaixo mostra o modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> implementado no PSP-UFU:</p><div><center><img src="/PSP/images/lineModel.svg" alt="Modelo PI da linha" title="Modelo PI da linha"></center></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">r</mi><mi mathvariant="bold">L</mi></msub></mrow><annotation encoding="application/x-tex">\bold{r_L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a resistência da linha;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">x</mi><mi mathvariant="bold">L</mi></msub></mrow><annotation encoding="application/x-tex">\bold{x_L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a reatância indutiva da linha;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi mathvariant="bold">b</mi><mi mathvariant="bold">L</mi><mi mathvariant="bold">d</mi></msubsup></mrow><annotation encoding="application/x-tex">\bold{b_{L}^{d}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.126385em;vertical-align:-0.277277em"></span><span class="mord"><span class="mord"><span class="mord mathbf">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.4227230000000004em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathbf mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathbf mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.277277em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a susceptância capacitiva <em>shunt</em> da linha.</li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O modelo utilizado no PSP-UFU é <strong>equilibrado</strong> e <strong>não possui impedâncias mútuas</strong> entre as fases.</p></div></div><p>A linha pode ser inseridas com pontos de ancoragem, ou &quot;nós&quot;, para maior personalização gráfica do elemento, como apresentado nas <a href="/PSP/docs/cadTools#linha">Ferramentas CAD</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>A linha deve ser inserida entre duas barras de <strong>mesma tensão nominal</strong>. Caso você tente inseri-la entre barras de tensão diferentes, uma mensagem de erro será exibida.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Um arranjo série de uma <a href="/PSP/docs/line">linha</a> sem as susceptâncias <em>shunt</em>, um <a href="/PSP/docs/bus">barramento</a> e um <a href="/PSP/docs/capacitor">capacitor</a> pode ser utilizado para fabricar um filtro passivo nos <a href="/PSP/docs/harmonics">estudos harmônicos</a>. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-das-linhas"></a>Formulário de edição das linhas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-linhas" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das linhas de transmissão:</p><div><center><img src="/PSP/images/lineForm.png" alt="Formulário das linhas no PSP-UFU" title="Formulário das linhas no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais da linha e informações do fluxo de carga;</li><li><strong>Falta</strong>: local onde as impedâncias de sequência zero são inseridas.</li></ul><div class="admonition admonition-note alert alert--secondary"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M6.3 5.69a.942.942 0 0 1-.28-.7c0-.28.09-.52.28-.7.19-.18.42-.28.7-.28.28 0 .52.09.7.28.18.19.28.42.28.7 0 .28-.09.52-.28.7a1 1 0 0 1-.7.3c-.28 0-.52-.11-.7-.3zM8 7.99c-.02-.25-.11-.48-.31-.69-.2-.19-.42-.3-.69-.31H6c-.27.02-.48.13-.69.31-.2.2-.3.44-.31.69h1v3c.02.27.11.5.31.69.2.2.42.31.69.31h1c.27 0 .48-.11.69-.31.2-.19.3-.42.31-.69H8V7.98v.01zM7 2.3c-3.14 0-5.7 2.54-5.7 5.68 0 3.14 2.56 5.7 5.7 5.7s5.7-2.55 5.7-5.7c0-3.15-2.56-5.69-5.7-5.69v.01zM7 .98c3.86 0 7 3.14 7 7s-3.14 7-7 7-7-3.12-7-7 3.14-7 7-7z"></path></svg></span>Nota</h5></div><div class="admonition-content"><p>Os parâmetros necessários para construção da linha segundo seu modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> são inseridos na aba Geral, utilizados para construção da matriz admitância de sequência positiva e negativa.</p><p>Dados adicionais de impedâncias de sequência zero necessário para o cálculo de curtos-circuitos desbalanceados são editados na aba Falta, utilizados na construção da matriz admitância de sequência zero.</p></div></div><p>Além desses dois contextos, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da linha durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/lineSw.png" alt="Formulário de chaveamento da linha" title="Formulário de chaveamento da linha"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_3zTA tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Falta</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Campo de informação <em>não editável</em> que apresenta a tensão nominal da linha. Para alterar esse campo é necessário editar o campo correspondente do <a href="/PSP/docs/bus#geral">barramento</a> conectado.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal da linha, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="parâmetros-do-modelo-pi"></a>Parâmetros do modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span><a aria-hidden="true" tabindex="-1" class="hash-link" href="#parâmetros-do-modelo-pi" title="Direct link to heading">#</a></h4><p>Resistência (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">r_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), Reatância indutiva (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">x_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) série e Susceptância capacitiva shunt <strong>total</strong> (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><msubsup><mi>b</mi><mi>L</mi><mi>d</mi></msubsup></mrow><annotation encoding="application/x-tex">2b_{L}^{d}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.124439em;vertical-align:-0.275331em"></span><span class="mord">2</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.424669em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.275331em"><span></span></span></span></span></span></span></span></span></span></span>) presentes no modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> da linha.</p><p>Esses parâmetros são inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">\Omega/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">Ω</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">S/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>b</mi><mi>L</mi><mi>d</mi></msubsup></mrow><annotation encoding="application/x-tex">b_{L}^{d}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.124439em;vertical-align:-0.275331em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.424669em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.275331em"><span></span></span></span></span></span></span></span></span></span></span>).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="comprimento-da-linha"></a>Comprimento da linha<a aria-hidden="true" tabindex="-1" class="hash-link" href="#comprimento-da-linha" title="Direct link to heading">#</a></h4><p>Utilizado para calcular o valor dos parâmetros da linha inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">\Omega/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">Ω</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> (ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">S/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span>).</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>O comprimento da linha é ignorado caso não sejam utilizadas as unidades por quilometro.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal da linha como base para a conversão das unidades, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/line.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Carga</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><ol><li>a potência ativa, reativa ou aparente gerada, transmitida ou distribuída dentro de um sistema;</li><li>a potência demandada por um grupo de consumidores classificados de acordo com suas particularidades e características, por exemplo, carga de aquecimento, carga reativa diurna, etc. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=601-01-15" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</li></ol></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="carga-no-psp-ufu"></a>Carga no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#carga-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As cargas são os elementos de potência consumidores de potência genéricos. Nos estudos de fluxo de carga é possível modelar a carga como <strong>potência ou impedância constante</strong> e em estabilidade pode-se compor a carga na proporção desejada em três tipos (<strong>carga ZIP</strong>): potência constante, impedância constante e corrente constante.</p><p>As cargas de potência constante nos estudos de fluxo de carga são inseridos no vetor de potências e permanecem fixos durante toda a simulação.</p><p>Os elementos shunt, como reatores, banco de capacitores e cargas de impedância constante, são representados simplesmente por suas admitâncias em derivação. Como os parâmetros de entrada geralmente se constituem de suas potências ativa (P) e reativa (Q) nominais (no caso de reatores e capacitores, P=0), deve-se, portanto, encontrar sua admitância com a equação abaixo para inseri-la na matriz admitância:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mfrac><mrow><mi>P</mi><mo>−</mo><mi>j</mi><mi>Q</mi></mrow><msup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\overline{y} = \frac{P-jQ}{\dot{V}^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.825em;vertical-align:-0.19444em"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.17052em;vertical-align:-0.8101900000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603299999999998em"><span style="top:-2.18981em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord mathdefault">Q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8101900000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Para os estudos de <strong>curto-circuito</strong> e <strong>harmônicos</strong> as cargas são modeladas como impedância constante, independentemente da sinalização indicada em seu formulário de edição de dados.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="carga-no-estudo-de-estabilidade"></a>Carga no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#carga-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>A modelagem das cargas do sistema de forma exata se torna impraticável em um problemas de estabilidade, visto à grande quantidade e variedade dos componentes envolvidos, além de apresentar modificações em suas composições causado por vários fatores, como tempo, condições climáticas e economia. Portanto várias aproximações devem ser utilizadas na formulação de um modelo de carga nos estudos aqui postos.</p><p>Uma forma interessante de se representar cargas dependentes da tensão são as cargas ZIP, as quais são funções quadráticas, possuindo três parcelas: impedância constante (Z), corrente constante (I) e potência constante (P). As potências ativa e reativa são obtidas pelas seguintes equações:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>L</mi></msub><mo>=</mo><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><mrow><msub><mi>V</mi><mi>i</mi></msub><mn>0</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_L=P_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+P_{I0} \left(\frac{V_i}{V_i0} \right)+P_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.604038em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.6540080000000001em"><span style="top:-3.9029000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>L</mi></msub><mo>=</mo><msub><mi>Q</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msub><mi>Q</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><mrow><msub><mi>V</mi><mi>i</mi></msub><mn>0</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>Q</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_L=Q_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+Q_{I0} \left(\frac{V_i}{V_i0} \right)+Q_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.604038em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.6540080000000001em"><span style="top:-3.9029000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">P_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">Q_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	são as potências ativa e reativa da carga ZIP, respectivamente, conectadas em uma barra genérica i;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">V_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão atual de uma barra genérica i;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">V_{i0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão inicial de uma barra genérica i, obtida do estudo de fluxo de carga;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{Z0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{Z0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de impedância constante para potências ativa e reativa, respectivamente;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{I0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{I0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de corrente constante para potências ativa e reativa, respectivamente;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de potência constante para potências ativa e reativa, respectivamente.</p><p>Os valores das parcelas de potência da carga ZIP são obtidos utilizando as potências da carga após a convergência do cálculo do fluxo de carga (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{L0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, para a potência ativa e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{L0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, para a potência reativa), utilizando as seguintes expressões:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>Z</mi></mrow></msub><mn>100</mn></mfrac><mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub><msubsup><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow><mn>2</mn></msubsup></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>I</mi></mrow></msub><mn>100</mn></mfrac><mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>P</mi></mrow></msub><mn>100</mn></mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mstyle></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} P_{Z0}=\displaystyle \frac{k_{PZ}}{100} \frac{P_{L0}}{V_{i0}^2}\\ P_{I0}=\displaystyle \frac{k_{PI}}{100} \frac{P_{L0}}{V_{i0}}\\ P_{P0}=\displaystyle \frac{k_{PP}}{100} P_{L0} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.60004em;vertical-align:-3.05002em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5500200000000004em"><span style="top:-0.9999899999999999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-0.99499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.2899900000000002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.5849900000000003em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.8799900000000005em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.1749900000000006em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.2049900000000004em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.1500100000000004em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.29501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.59001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.885010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.180010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.475010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.50501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.80002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.05002em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5495919999999996em"><span style="top:-5.549592em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7959080000000001em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9628639999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.215288em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-1.007848em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.0495919999999996em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Os valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>Z</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PZ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>I</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>P</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> representam a composição em impedância, corrente e potência constantes, respectivamente, da parcela ativa da carga, os quais são inseridos pelo usuário na forma de porcentagem, sendo a soma desses três valores necessariamente igual a 100%. Os parâmetros <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>Z</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QZ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>I</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>P</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> podem ser interpretados de forma análoga, porém compõe a parcela reativa da carga.</p><p>O comportamento das potências, retiradas de simulações no PSP-UFU, de cada parcela que compõe a carga ZIP são evidenciadas na figura abaixo.</p><div><center><img src="/PSP/images/loadModel.svg" alt="Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente" title="Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente"></center></div><p>Cargas de corrente e potência constantes possuem problemas em tensões muito baixas. À medida que a tensão diminui as correntes dessas cargas não reduz, como pode ser observado na figura acima, resultando em perda de precisão e problemas na convergência de processos iterativos. Para contornar esse problema utiliza-se uma tensão pré-definida pelo usuário (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>l</mi><mi>o</mi><mi>w</mi></mrow></msub></mrow><annotation encoding="application/x-tex">V_{low}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight" style="margin-right:0.02691em">w</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), a qual as cargas (ou parcelas) de corrente e potência constantes são modeladas como impedância constante, resultando no comportamento de potência e corrente apresentados na figura acima.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-das-cargas"></a>Formulário de edição das cargas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-cargas" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das cargas:</p><div><center><img src="/PSP/images/loadForm.png" alt="Formulário das cargas no PSP-UFU" title="Formulário das cargas no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais das cargas, informações e o tipo de carga no fluxo de carga;</li><li><strong>Estabilidade</strong>: contendo opções de visualização de dados da carga em gráficos no tempo e opções de parametrização da carga ZIP.</li></ul><p>Além desses dois contextos, pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da carga durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/loadSw.png" alt="Formulário de chaveamento da carga" title="Formulário de chaveamento da carga"></center></div><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="geral"></a>Geral<a aria-hidden="true" tabindex="-1" class="hash-link" href="#geral" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-ativa"></a>Potência ativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-ativa" title="Direct link to heading">#</a></h4><p>Parcela de potência ativa da carga. Pode ser inserido em MW, kW W ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base do sistema).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Parcela de potência reativa da carga. Pode ser inserido em Mvar, kvar var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base do sistema).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tipo-de-carga-fluxo-de-carga"></a>Tipo de carga (fluxo de carga)<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tipo-de-carga-fluxo-de-carga" title="Direct link to heading">#</a></h4><p>Tipo da carga para o estudo de fluxo de carga, podendo ser selecionado dois tipos: Potência constante e Impedância constante. As cargas de potência constantes são inseridas nos vetores de potência e permanecem invariantes no cálculo, enquanto que para as cargas de impedância constante determina-se o valor da impedância utilizando a potência e tensão nominal, a qual é inserida na matriz admitância.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="estabilidade"></a>Estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#estabilidade" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="imprimir-dados"></a>Imprimir dados<a aria-hidden="true" tabindex="-1" class="hash-link" href="#imprimir-dados" title="Direct link to heading">#</a></h4><p>Exibe os dados da carga nos gráficos no tempo.
-Os seguintes dados são exibidos:</p><ul><li>módulo da tensão</li><li>corrente</li><li>potências ativa e reativa.</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-composição-de-carga-zip"></a>Utilizar composição de carga ZIP<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-composição-de-carga-zip" title="Direct link to heading">#</a></h4><p>Permite compor a carga ZIP para estudos de estabilidade. Caso essa opção não esteja selecionada é usada a composição global definida nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>Por padrão, todas as cargas no PSP-UFU são definidas como impedância constante no estudo de estabilidade.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Caso todas as barras possuírem o mesmo comportamento de carga ZIP, a parametrização poderá ser realizada nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a> para todas as cargas, sem a necessidade de parametrização individual.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="composição-de-potência-ativa-e-reativa"></a>Composição de potência ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#composição-de-potência-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Valores da composição da carga ZIP, inseridas para potência ativa e reativa separadamente, em porcentagem. A soma da composição deve ser igual a 100%, caso contrário será exibida uma mensagem de erro ao usuário.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="botão-chaveamento"></a>Botão Chaveamento<a aria-hidden="true" tabindex="-1" class="hash-link" href="#botão-chaveamento" title="Direct link to heading">#</a></h3><p>O botão &quot;Chaveamento&quot; irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do transformador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><p>Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões &quot;Adicionar&quot; e &quot;Remover&quot;, respectivamente.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/load.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/transformer"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Transformador</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/capacitor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Capacitor »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#carga-no-psp-ufu" class="table-of-contents__link">Carga no PSP-UFU</a><ul><li><a href="#carga-no-estudo-de-estabilidade" class="table-of-contents__link">Carga no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-das-cargas" class="table-of-contents__link">Formulário de edição das cargas</a><ul><li><a href="#geral" class="table-of-contents__link">Geral</a></li><li><a href="#estabilidade" class="table-of-contents__link">Estabilidade</a></li><li><a href="#botão-chaveamento" class="table-of-contents__link">Botão Chaveamento</a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Carga</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><ol><li>a potência ativa, reativa ou aparente gerada, transmitida ou distribuída dentro de um sistema;</li><li>a potência demandada por um grupo de consumidores classificados de acordo com suas particularidades e características, por exemplo, carga de aquecimento, carga reativa diurna, etc. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=601-01-15" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</li></ol></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="carga-no-psp-ufu"></a>Carga no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#carga-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As cargas são os elementos de potência consumidores de potência genéricos. Nos estudos de fluxo de carga é possível modelar a carga como <strong>potência ou impedância constante</strong> e em estabilidade pode-se compor a carga na proporção desejada em três tipos (<strong>carga ZIP</strong>): potência constante, impedância constante e corrente constante.</p><p>As cargas de potência constante nos estudos de fluxo de carga são inseridos no vetor de potências e permanecem fixos durante toda a simulação.</p><p>Os elementos shunt, como reatores, banco de capacitores e cargas de impedância constante, são representados simplesmente por suas admitâncias em derivação. Como os parâmetros de entrada geralmente se constituem de suas potências ativa (P) e reativa (Q) nominais (no caso de reatores e capacitores, P=0), deve-se, portanto, encontrar sua admitância com a equação abaixo para inseri-la na matriz admitância:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mfrac><mrow><mi>P</mi><mo>−</mo><mi>j</mi><mi>Q</mi></mrow><msup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\overline{y} = \frac{P-jQ}{\dot{V}^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.825em;vertical-align:-0.19444em"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.17052em;vertical-align:-0.8101900000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603299999999998em"><span style="top:-2.18981em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord mathdefault">Q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8101900000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Para os estudos de <strong>curto-circuito</strong> e <strong>harmônicos</strong> as cargas são modeladas como impedância constante, independentemente da sinalização indicada em seu formulário de edição de dados.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="carga-no-estudo-de-estabilidade"></a>Carga no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#carga-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>A modelagem das cargas do sistema de forma exata se torna impraticável em um problemas de estabilidade, visto à grande quantidade e variedade dos componentes envolvidos, além de apresentar modificações em suas composições causado por vários fatores, como tempo, condições climáticas e economia. Portanto várias aproximações devem ser utilizadas na formulação de um modelo de carga nos estudos aqui postos.</p><p>Uma forma interessante de se representar cargas dependentes da tensão são as cargas ZIP, as quais são funções quadráticas, possuindo três parcelas: impedância constante (Z), corrente constante (I) e potência constante (P). As potências ativa e reativa são obtidas pelas seguintes equações:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>L</mi></msub><mo>=</mo><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><mrow><msub><mi>V</mi><mi>i</mi></msub><mn>0</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_L=P_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+P_{I0} \left(\frac{V_i}{V_i0} \right)+P_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.604038em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.6540080000000001em"><span style="top:-3.9029000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>L</mi></msub><mo>=</mo><msub><mi>Q</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msub><mi>Q</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><mrow><msub><mi>V</mi><mi>i</mi></msub><mn>0</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>Q</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_L=Q_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+Q_{I0} \left(\frac{V_i}{V_i0} \right)+Q_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.604038em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.6540080000000001em"><span style="top:-3.9029000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">P_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">Q_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	são as potências ativa e reativa da carga ZIP, respectivamente, conectadas em uma barra genérica i;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">V_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão atual de uma barra genérica i;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">V_{i0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão inicial de uma barra genérica i, obtida do estudo de fluxo de carga;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{Z0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{Z0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de impedância constante para potências ativa e reativa, respectivamente;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{I0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{I0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de corrente constante para potências ativa e reativa, respectivamente;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de potência constante para potências ativa e reativa, respectivamente.</p><p>Os valores das parcelas de potência da carga ZIP são obtidos utilizando as potências da carga após a convergência do cálculo do fluxo de carga (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{L0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, para a potência ativa e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{L0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, para a potência reativa), utilizando as seguintes expressões:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>Z</mi></mrow></msub><mn>100</mn></mfrac><mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub><msubsup><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow><mn>2</mn></msubsup></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>I</mi></mrow></msub><mn>100</mn></mfrac><mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>P</mi></mrow></msub><mn>100</mn></mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mstyle></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} P_{Z0}=\displaystyle \frac{k_{PZ}}{100} \frac{P_{L0}}{V_{i0}^2}\\ P_{I0}=\displaystyle \frac{k_{PI}}{100} \frac{P_{L0}}{V_{i0}}\\ P_{P0}=\displaystyle \frac{k_{PP}}{100} P_{L0} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.60004em;vertical-align:-3.05002em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5500200000000004em"><span style="top:-0.9999899999999999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-0.99499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.2899900000000002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.5849900000000003em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.8799900000000005em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.1749900000000006em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.2049900000000004em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.1500100000000004em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.29501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.59001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.885010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.180010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.475010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.50501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.80002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.05002em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5495919999999996em"><span style="top:-5.549592em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7959080000000001em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9628639999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.215288em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-1.007848em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.0495919999999996em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Os valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>Z</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PZ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>I</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>P</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> representam a composição em impedância, corrente e potência constantes, respectivamente, da parcela ativa da carga, os quais são inseridos pelo usuário na forma de porcentagem, sendo a soma desses três valores necessariamente igual a 100%. Os parâmetros <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>Z</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QZ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>I</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>P</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> podem ser interpretados de forma análoga, porém compõe a parcela reativa da carga.</p><p>O comportamento das potências, retiradas de simulações no PSP-UFU, de cada parcela que compõe a carga ZIP são evidenciadas na figura abaixo.</p><div><center><img src="/PSP/images/loadModel.svg" alt="Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente" title="Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente"></center></div><p>Cargas de corrente e potência constantes possuem problemas em tensões muito baixas. À medida que a tensão diminui as correntes dessas cargas não reduz, como pode ser observado na figura acima, resultando em perda de precisão e problemas na convergência de processos iterativos. Para contornar esse problema utiliza-se uma tensão pré-definida pelo usuário (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>l</mi><mi>o</mi><mi>w</mi></mrow></msub></mrow><annotation encoding="application/x-tex">V_{low}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight" style="margin-right:0.02691em">w</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), a qual as cargas (ou parcelas) de corrente e potência constantes são modeladas como impedância constante, resultando no comportamento de potência e corrente apresentados na figura acima.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-das-cargas"></a>Formulário de edição das cargas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-cargas" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das cargas:</p><div><center><img src="/PSP/images/loadForm.png" alt="Formulário das cargas no PSP-UFU" title="Formulário das cargas no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais das cargas, informações e o tipo de carga no fluxo de carga;</li><li><strong>Estabilidade</strong>: contendo opções de visualização de dados da carga em gráficos no tempo e opções de parametrização da carga ZIP.</li></ul><p>Além desses dois contextos, pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da carga durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/loadSw.png" alt="Formulário de chaveamento da carga" title="Formulário de chaveamento da carga"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_3zTA tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Botão Chaveamento</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-ativa"></a>Potência ativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-ativa" title="Direct link to heading">#</a></h4><p>Parcela de potência ativa da carga. Pode ser inserido em MW, kW W ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base do sistema).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Parcela de potência reativa da carga. Pode ser inserido em Mvar, kvar var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base do sistema).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tipo-de-carga-fluxo-de-carga"></a>Tipo de carga (fluxo de carga)<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tipo-de-carga-fluxo-de-carga" title="Direct link to heading">#</a></h4><p>Tipo da carga para o estudo de fluxo de carga, podendo ser selecionado dois tipos: Potência constante e Impedância constante. As cargas de potência constantes são inseridas nos vetores de potência e permanecem invariantes no cálculo, enquanto que para as cargas de impedância constante determina-se o valor da impedância utilizando a potência e tensão nominal, a qual é inserida na matriz admitância.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/load.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/transformer"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Transformador</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/capacitor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Capacitor »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#carga-no-psp-ufu" class="table-of-contents__link">Carga no PSP-UFU</a><ul><li><a href="#carga-no-estudo-de-estabilidade" class="table-of-contents__link">Carga no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-das-cargas" class="table-of-contents__link">Formulário de edição das cargas</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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focusable="false"><title>Menu</title><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></button><ul class="menu__list"><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#!">Introdução</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/">PSP-UFU</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/installation">Instalação</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link menu__link--active active" tabindex="0" href="/PSP/docs/mainScreen">Tela Principal</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/cadTools">Ferramentas CAD</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Editor de Elementos de Potência</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerEditor">Editor de Potência</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="-1">Elementos de Potência</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/bus">Barramento</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/line">Linha</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/transformer">Transformador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/load">Carga</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/capacitor">Capacitor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/inductor">Indutor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Editor de Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/controlEditor">Editor de Controle</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="-1">Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/io">Entrada / Saída</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/transferFunction">Função Transferência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/sum">Somador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/multiplier">Multiplicador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/divider">Divisor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/exponential">Exponencial</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/limiter">Limitador absoluto</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/rateLimiter">Limitador de taxa</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/const">Constante</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Tela Principal</h1></header><div class="markdown"><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="organização-da-tela-principal"></a>Organização da tela principal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#organização-da-tela-principal" title="Direct link to heading">#</a></h2><p>A tela principal do PSP-UFU é dividida em três seções: <em><a href="/PSP/docs/mainScreen#menu-ribbon">Menu &quot;Ribbon&quot;</a></em>, <em><a href="/PSP/docs/mainScreen#%C3%A1rea-de-trabalho">Área de Trabalho</a></em> e <em><a href="/PSP/docs/mainScreen#barra-de-status">Barra de Status</a></em>.</p><div><center><img src="/PSP/images/mainScreen.svg" alt="Tela principal" title="Tela principal do PSP-UFU no Windows"></center></div><p>Resumidamente, no <strong>Menu Ribbon</strong> são acessadas as ferramentas do PSP-UFU; na <strong>Área de Trabalho</strong> são criados os diagramas unifilares de potência; e na <strong>Barra de Status</strong> são exibidas importantes informações acerca do estado da Área de Trabalho.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="menu-ribbon"></a>Menu Ribbon<a aria-hidden="true" tabindex="-1" class="hash-link" href="#menu-ribbon" title="Direct link to heading">#</a></h3><blockquote><p>Em informática o ribbon (faixa, em inglês) é um formato de apresentação de interface baseada na GUI onde a barra de ferramentas é mostrada através de uma barra mais larga com icones maiores possibilitando o uso dos aplicativos por dispositivos <em>touch screen</em>.
+<nav class="navbar navbar--light navbar--fixed-top"><div class="navbar__inner"><div class="navbar__items"><div aria-label="Navigation bar toggle" class="navbar__toggle" role="button" tabindex="0"><svg xmlns="http://www.w3.org/2000/svg" width="30" height="30" viewBox="0 0 30 30" role="img" focusable="false"><title>Menu</title><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></div><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a><a aria-current="page" class="navbar__item navbar__link navbar__link--active" href="/PSP/docs/">User Guide</a><a class="navbar__item navbar__link" href="/PSP/blog">Changelog</a></div><div class="navbar__items navbar__items--right"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="navbar__item navbar__link">PSP-UFU Source Code</a><div class="react-toggle react-toggle--disabled displayOnlyInLargeViewport_1gtM"><div class="react-toggle-track"><div class="react-toggle-track-check"><span class="toggle_keGJ moon_1gwN"></span></div><div class="react-toggle-track-x"><span class="toggle_keGJ sun_3CPA"></span></div></div><div class="react-toggle-thumb"></div><input type="checkbox" disabled="" aria-label="Dark mode toggle" class="react-toggle-screenreader-only"></div><div class="navbar__search"><div class="searchWrapper_-F3-"><span aria-label="expand searchbar" role="button" class="searchIconButton_1Dnz" tabindex="0"></span><input type="search" id="search_input_react" placeholder="Search" aria-label="Search" class="navbar__search-input searchInput_2eto"></div></div></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a aria-current="page" class="menu__link navbar__link--active" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a class="menu__link" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><div class="docPage_1kjD"><div class="docSidebarContainer_1cYp" role="complementary"><div class="sidebar_1kLs"><div class="menu menu--responsive menu_w2sC"><button aria-label="Open Menu" aria-haspopup="true" class="button button--secondary button--sm menu__button" type="button"><svg aria-label="Menu" class="sidebarMenuIcon_2vk4" xmlns="http://www.w3.org/2000/svg" height="24" width="24" viewBox="0 0 32 32" role="img" focusable="false"><title>Menu</title><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></button><ul class="menu__list"><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#!">Introdução</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/">PSP-UFU</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/installation">Instalação</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link menu__link--active active" tabindex="0" href="/PSP/docs/mainScreen">Tela Principal</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/cadTools">Ferramentas CAD</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Editor de Elementos de Potência</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerEditor">Editor de Potência</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="-1">Elementos de Potência</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/bus">Barramento</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/line">Linha</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/transformer">Transformador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/load">Carga</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/capacitor">Capacitor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/inductor">Indutor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Editor de Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/controlEditor">Editor de Controle</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="-1">Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/io">Entrada / Saída</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/transferFunction">Função Transferência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/sum">Somador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/multiplier">Multiplicador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/divider">Divisor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/exponential">Exponencial</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/limiter">Limitador absoluto</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/rateLimiter">Limitador de taxa</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/const">Constante</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Tela Principal</h1></header><div class="markdown"><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="organização-da-tela-principal"></a>Organização da tela principal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#organização-da-tela-principal" title="Direct link to heading">#</a></h2><p>A tela principal do PSP-UFU é dividida em três seções: <em><a href="/PSP/docs/mainScreen#menu-ribbon">Menu &quot;Ribbon&quot;</a></em>, <em><a href="/PSP/docs/mainScreen#%C3%A1rea-de-trabalho">Área de Trabalho</a></em> e <em><a href="/PSP/docs/mainScreen#barra-de-status">Barra de Status</a></em>.</p><div><center><img src="/PSP/images/mainScreen.svg" alt="Tela principal" title="Tela principal do PSP-UFU no Windows"></center></div><p>Resumidamente, no <strong>Menu Ribbon</strong> são acessadas as ferramentas do PSP-UFU; na <strong>Área de Trabalho</strong> são criados os diagramas unifilares de potência; e na <strong>Barra de Status</strong> são exibidas importantes informações acerca do estado da Área de Trabalho.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="menu-ribbon"></a>Menu Ribbon<a aria-hidden="true" tabindex="-1" class="hash-link" href="#menu-ribbon" title="Direct link to heading">#</a></h3><blockquote><p>Em informática o ribbon (faixa, em inglês) é um formato de apresentação de interface baseada na GUI onde a barra de ferramentas é mostrada através de uma barra mais larga com icones maiores possibilitando o uso dos aplicativos por dispositivos <em>touch screen</em>.
 <a href="https://pt.wikipedia.org/wiki/Ribbon_(inform%C3%A1tica)" target="_blank" rel="noopener noreferrer">Wikipedia</a></p></blockquote><p>O menu Ribbon é composto de três submenus: “Arquivo”, “Ferramentas” e “Simulação”.</p><div><center><img src="/PSP/images/menuFile.png" alt="Menu Arquivo" title="Menu Arquivo"></center></div><p>Em <strong>Arquivo</strong> estão as ferramentas gerais do programa, as quais permitem ao usuário criar e salvar novos projetos, além daquelas que possibilitam carregar os projetos já existentes e importar arquivos de outros programas. Esse submenu também possui opções gerais do programa e acesso a informações sobre o programa.</p><div><center><img src="/PSP/images/menuTools.png" alt="Menu Ferramentas" title="Menu Ferramentas"></center></div><p>Em <strong>Ferramentas</strong> estão presentes os itens específicos, os quais estão relacionados à criação e manipulação da rede elétrica de potência, relatórios tabulares de saída de dados e acesso ao formulário de criação de gráficos no tempo. Algumas configurações específicas do projeto ativo são acessadas por esse menu.</p><div><center><img src="/PSP/images/menuSimulation.png" alt="Menu Simulação" title="Menu Simulação"></center></div><p>Finalmente, o submenu <strong>Simulação</strong> proporciona o acesso do usuário aos cálculos realizados pelo <em>software</em> e suas configurações, além da ferramenta de “solução contínua”, a qual resolve os cálculos estáticos (fluxo de potência, curto-circuito e harmônicos) após quaisquer mudanças na rede de potência, como remoção de componente ou alteração de seus dados. Todas as configurações de simulação do projeto ativo são acessadas por esse menu.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="área-de-trabalho"></a>Área de Trabalho<a aria-hidden="true" tabindex="-1" class="hash-link" href="#área-de-trabalho" title="Direct link to heading">#</a></h3><p>Na área de trabalho estão presentes os projetos em execução, os quais são divididos por abas identificadas pelo nome do projeto (caso já esteja gravado no disco). É nessa área que são inseridos e excluídos os elementos elétricos, cujas ferramentas são acessadas por meio do <a href="/PSP/docs/mainScreen#menu-ribbon">Menu Ribbon</a>.</p><p>As edições gráficas dos elementos, como posição, conexão e tamanho dos barramentos, são realizadas por meio da ação <em>drag-and-drop</em> (arrastar e soltar) com a utilização do mouse. A edição dos dados elétricos é feita por meio de formulários de dados acessados clicando duas vezes sobre os elementos.</p><div><center><img src="/PSP/images/workspace.png" alt="Área de Trabalho" title="Área de Trabalho"></center></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="barra-de-status"></a>Barra de Status<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barra-de-status" title="Direct link to heading">#</a></h3><p>A barra de status é responsável por informações interessantes sobre as circunstâncias atuais do programa: modo de operação do mouse (editar, mover, arrastar), zoom aplicado e posição do mouse na área de trabalho, além de dados sobre as ações dos usuários, como: inserção de elementos, informação sobre copiar e colar, etc.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p><strong>Sempre fique atendo à barra de status</strong>, pois são fornecidas informações importantes acerca da operação do programa. 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class="menu__link menu__link--active active" tabindex="0" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Expressão Matemática</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O bloco de expressão matemática utiliza a biblioteca externa <a href="http://warp.povusers.org/FunctionParser/" target="_blank" rel="noopener noreferrer">fparser</a> e permite ao usuário inserir expressões matemáticas genéricas de qualquer complexidade combinadas a estruturas condicionais em um diagrama de controle, aumentando significativamente a capacidade de generalização do programa.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="sintaxe-das-expressões-matemáticas"></a>Sintaxe das expressões matemáticas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#sintaxe-das-expressões-matemáticas" title="Direct link to heading">#</a></h2><p>As sintaxes das operações (para expressões <code>A</code> e <code>B</code>) são apresentadas na tabela abaixo:</p><table><thead><tr><th>Operador</th><th>Expressão</th></tr></thead><tbody><tr><td><code>( )</code></td><td>Expressão em parênteses primeiro</td></tr><tr><td><code>A unit</code></td><td>Um multiplicador de unidade (se um estiver sido adicionado)</td></tr><tr><td><code>A^B</code></td><td>Exponenciação (<code>A</code> elevado à potência <code>B</code>)</td></tr><tr><td><code>-A</code></td><td>Operação unária de oposto</td></tr><tr><td><code>!A</code></td><td>Operação lógica unária de negação (resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> se <code>int(A)</code> é <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, senão <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>)</td></tr><tr><td><code>A*B</code> <code>A/B</code> <code>A%B</code></td><td>Multiplicação, divisão e módulo</td></tr><tr><td><code>A+B</code> <code>A-B</code></td><td>Adição e subtração</td></tr><tr><td><code>A=B</code> <code>A&lt;B</code> <code>A&lt;=B</code> <code>A!=B</code> <code>A&gt;B</code> <code>A&gt;=B</code></td><td>Comparação entre <code>A</code> e <code>B</code> (resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>)</td></tr><tr><td><code>A&amp;B</code></td><td>Resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> se <code>int(A)</code> e <code>int(B)</code> forem diferentes de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, senão <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span></td></tr><tr><td><code>A</code>|<code>B</code></td><td>Resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> se <code>int(A)</code> ou <code>int(B)</code> forem diferentes de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, senão <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span></td></tr></tbody></table><p>As <strong>funções matemáticas</strong> suportadas pela biblioteca, as quais podem ser utilizadas na construção de diagrama de blocos, são descritas na tabela abaixo:</p><table><thead><tr><th>Expressão</th><th>Descrição</th></tr></thead><tbody><tr><td><code>abs(A)</code></td><td>Valor absoluto de <code>A</code>. Para números reais, se <code>A</code> é negativo, retorna <code>–A</code>, senão retorna <code>A</code>. Para números complexos a expressão é equivalente a <code>hypot(real(x),imag(x))</code>.</td></tr><tr><td><code>acos(A)</code></td><td>Arco cosseno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>acosh(A)</code></td><td>O mesmo que <code>acos()</code> mas para cosseno hiperbólico</td></tr><tr><td><code>arg(A)</code></td><td>Ângulo de fase de um número complexo <code>A</code>.</td></tr><tr><td><code>asin(A)</code></td><td>Arco seno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>asinh(A)</code></td><td>Mesmo que <code>asin()</code>, mas para seno hiperbólico</td></tr><tr><td><code>atan(A)</code></td><td>Arco tangente de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>atan2(A,B)</code></td><td>Arco tangente de <code>A/B</code>, a qual os sinais dos dois argumentos para determinar o quadrante do resultado. Retorna a solução de do seguinte sistema: <code>hypot(A,B)*sin(x)=A, hypot(A,B)*cos(x)=B</code>. O valor retornado varia de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mi>π</mi></mrow><annotation encoding="application/x-tex">-\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em"></span><span class="mord">−</span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> a <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span>.</td></tr><tr><td><code>atanh(A)</code></td><td>Mesmo que <code>atan()</code>, mas para tangente hiperbólica.</td></tr><tr><td><code>cbrt(A)</code></td><td>Raiz cúbica de <code>A</code>.</td></tr><tr><td><code>conj(A)</code></td><td>Conjugado complexo de <code>A</code>.</td></tr><tr><td><code>ceil(A)</code></td><td>Teto de <code>A</code>. Arredonda para o próximo maior inteiro.</td></tr><tr><td><code>cos(A)</code></td><td>Cosseno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>cosh(A)</code></td><td>Mesmo que <code>cos()</code>, mas para cosseno hiperbólico</td></tr><tr><td><code>cot(A)</code></td><td>Cotangente de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>csc(A)</code></td><td>Cossecante de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>exp(A)</code></td><td>Exponencial de <code>A</code>. Retorna o valor de e elevado a potência A.</td></tr><tr><td><code>exp2(A)</code></td><td>Exponencial de <code>A</code> na base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">2</span></span></span></span></span>.</td></tr><tr><td><code>floor(A)</code></td><td>Piso de <code>A</code>. Arredonda para o próximo menor inteiro.</td></tr><tr><td><code>hypot(A,B)</code></td><td>Função de distância Euclidiana.</td></tr><tr><td><code>if(A,B,C)</code></td><td>Se <code>int(A)</code> é diferente de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, retorna o valor de <code>B</code>, senão retorna <code>C</code>.</td></tr><tr><td><code>imag(A)</code></td><td>Retorna a parte imaginária do número complexo <code>A</code>.</td></tr><tr><td><code>int(A)</code></td><td>Arredonda <code>A</code> para o inteiro mais próximo.</td></tr><tr><td><code>log(A)</code></td><td>Logaritmo natural (base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>e</mi></mrow><annotation encoding="application/x-tex">e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">e</span></span></span></span></span>) de <code>A</code>.</td></tr><tr><td><code>log2(A)</code></td><td>Logaritmo na base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">2</span></span></span></span></span> de <code>A</code>.</td></tr><tr><td><code>log10(A)</code></td><td>Logaritmo na base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn></mrow><annotation encoding="application/x-tex">10</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span><span class="mord">0</span></span></span></span></span> de A.</td></tr><tr><td><code>max(A,B)</code></td><td>Se <code>A&gt;B</code>, o resultado é <code>A</code>, senão é <code>B</code>.</td></tr><tr><td><code>min(A,B)</code></td><td>Se <code>A&lt;B</code>, o resultado é <code>A</code>, senão é <code>B</code>.</td></tr><tr><td><code>polar(A,B)</code></td><td>Retorna o número complexo de magnitude <code>A</code> e ângulo de fase <code>B</code> (em radianos).</td></tr><tr><td><code>pow(A,B)</code></td><td>Exponenciação (<code>A</code> elevado à potência <code>B</code>)</td></tr><tr><td><code>real(A,B)</code></td><td>Retorna a parte real do número complexo <code>A</code>.</td></tr><tr><td><code>sec(A)</code></td><td>Secante de <code>A</code>.</td></tr><tr><td><code>sin(A)</code></td><td>Seno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>sinh(A)</code></td><td>Mesmo que <code>sin()</code>, mas para seno hiperbólico.</td></tr><tr><td><code>sqrt(A)</code></td><td>Raiz quadrada de <code>A</code>.</td></tr><tr><td><code>tan(A)</code></td><td>Tangente de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>tanh(A)</code></td><td>Mesmo que <code>tan()</code>, mas para tangente hiperbólica.</td></tr><tr><td><code>trunc(A)</code></td><td>Valor truncado de <code>A</code>. Retorna o número inteiro de <code>A</code> sem a parcela fracionada.</td></tr></tbody></table><p>É possível atribuir novas variáveis utilizando a seguinte sintaxe: </p><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token operator" style="color:rgb(137, 221, 255)">&lt;</span><span class="token plain">nome da variável</span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">&lt;</span><span class="token plain">expressão</span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">&lt;</span><span class="token plain">função</span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;</span></div></div></div></div></div><p>Por exemplo:</p><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">comprimento </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain">y</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">y</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">comprimento</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token function" style="color:rgb(130, 170, 255)">sin</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">comprimento</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span></div></div></div></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>O caractere de espaço e de nova linha são ignorados na interpretação da expressão, portanto para maior organização, o código anterior pode ser escrito da seguinte forma:</p><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">comprimento </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain">y</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">y</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain"></span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">comprimento</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token function" style="color:rgb(130, 170, 255)">sin</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">comprimento</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span></div></div></div></div></div></div></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Note que a expressão que determina o valor de saída do bloco <strong>não possui</strong> o caractere <code>;</code> em seu final.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-de-dados-do-bloco-de-expressão-matemática"></a>Formulário de edição de dados do bloco de Expressão Matemática<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-bloco-de-expressão-matemática" title="Direct link to heading">#</a></h2><p>O formulário de inserção e edição das entradas do bloco e da expressão matemática genérica, assim como ferramentas de auxílio de sua construção é apresentado na figura abaixo.</p><div><center><img src="/PSP/images/mathExpressionForm.png" alt="Formulário de edição de dados do bloco de expressão matemática no PSP-UFU" title="Formulário de edição de dados do bloco de expressão matemática no PSP-UFU"></center></div><p>No campo de “Variáveis de entrada” é inserida uma lista com os nomes das entradas separados por espaços. Um número qualquer de entrada pode ser definido nessa lista esses nomes são apresentados no ícone gráfico presente no editor de controle, além de serem destacados na expressão inserida pelo usuário. O número de entradas e saídas se comporta de forma semelhante aos <a href="/PSP/docs/sum">blocos somadores</a>.</p><p>Abaixo do campo das variáveis de entrada está presente o local para inserção da expressão matemática. A sintaxe da expressão inserida pelo usuário possui realce (por meio de diferentes formas e cores da fonte) para números, operadores, variáveis de entrada, funções e constantes, facilitando a criação, manipulação e identificação de erros de digitação e lógica.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Como ferramenta de auxílio ao usuário foi desenvolvida uma verificação da expressão inserida.</p></div></div><p>Tal ferramenta irá encontrar erros e indicará ao usuário qual o tipo do erro, além da sua localização, destacando-o. A figura anterior exemplifica a identificação automática do erro pelo PSP-UFU, assim como sua posição na expressão inserida.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="exemplo-de-expressão-matemática"></a>Exemplo de Expressão Matemática<a aria-hidden="true" tabindex="-1" class="hash-link" href="#exemplo-de-expressão-matemática" title="Direct link to heading">#</a></h2><p>A corrente de campo em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> pode ser estimada de forma aproximada utilizando as potências ativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span></span></span></span></span>) e reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span></span></span></span></span>), assim como as reatâncias transitórias de eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>d</mi></msub></mrow><annotation encoding="application/x-tex">x_d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) e em quadratura (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>q</mi></msub></mrow><annotation encoding="application/x-tex">x_q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>) e o módulo da tensão terminal (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span></span></span>) da máquina:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>i</mi><mi>f</mi></msub><mo>≈</mo><msqrt><mrow><msup><mrow><mo fence="true">(</mo><mi>V</mi><mo>+</mo><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>P</mi><mn>2</mn></msup></mrow></msqrt><mo>+</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>x</mi><mi>d</mi></msub><msub><mi>x</mi><mi>q</mi></msub></mfrac><mo>+</mo><mn>1</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mo fence="true">)</mo></mrow><mo>×</mo><mfrac><mrow><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mrow><mo fence="true">(</mo><mi>V</mi><mo>+</mo><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><mo>+</mo><msup><msup><mi>P</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mn>2</mn></msup></mrow><msqrt><mrow><msup><mrow><mo fence="true">(</mo><mi>V</mi><mo>+</mo><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>P</mi><mn>2</mn></msup></mrow></msqrt></mfrac></mrow><annotation encoding="application/x-tex">i_f \approx \sqrt{ \left( V + Q&#x27; \right)^2 + P^2} + \left(\frac{x_d}{x_q} +1{,}0 \right) \times \frac{Q&#x27; \left( V + Q&#x27; \right) + {P&#x27;}^2}{\sqrt{\left( V + Q&#x27;\right)^2 + P^2}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9456279999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">i</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.84em;vertical-align:-0.454121em"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.385879em"><span class="svg-align" style="top:-3.8em"><span class="pstrut" style="height:3.8em"></span><span class="mord" style="padding-left:1em"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6778919999999999em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954008em"><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.345879em"><span class="pstrut" style="height:3.8em"></span><span class="hide-tail" style="min-width:1.02em;height:1.8800000000000001em"><svg width="400em" height="1.8800000000000001em" viewBox="0 0 400000 1944" preserveAspectRatio="xMinYMin slice"><path d="M983 90
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vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.972108em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:3.3629em;vertical-align:-1.73em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6329em"><span style="top:-2.1100000000000003em"><span class="pstrut" style="height:3.3370040000000003em"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.337004em"><span class="svg-align" style="top:-3.8em"><span class="pstrut" style="height:3.8em"></span><span class="mord" style="padding-left:1em"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6778919999999999em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954008em"><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.297004em"><span class="pstrut" style="height:3.8em"></span><span class="hide-tail" style="min-width:1.02em;height:1.8800000000000001em"><svg width="400em" height="1.8800000000000001em" viewBox="0 0 400000 1944" preserveAspectRatio="xMinYMin slice"><path d="M983 90
+l0 -0
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+M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.502996em"><span></span></span></span></span></span></span></span><span style="top:-3.5670040000000003em"><span class="pstrut" style="height:3.3370040000000003em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-4.014004em"><span class="pstrut" style="height:3.3370040000000003em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9559em"><span style="top:-3.2047920000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.73em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>P</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>=</mo><msub><mi>x</mi><mi>q</mi></msub><mo>×</mo><mfrac><mi>P</mi><mi>V</mi></mfrac></mrow><annotation encoding="application/x-tex">P&#x27; = x_q \times \frac{P}{V}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8694379999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.217331em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.872331em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>=</mo><msub><mi>x</mi><mi>q</mi></msub><mo>×</mo><mfrac><mi>Q</mi><mi>V</mi></mfrac></mrow><annotation encoding="application/x-tex">Q&#x27; = x_q \times \frac{Q}{V}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.946332em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8694379999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.269439em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.924439em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.446108em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></li></ul><p>Primeiramente, deve-se inserir no campo &quot;variáveis de entrada&quot; as grandezas fornecidas pelo PSP-UFU. Nesse caso, como pode ser observado no bloco de <a href="/PSP/docs/io">entrada / saída</a>, todas as variáveis necessárias são fornecidas: <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span></span></span>. Essas variáveis devem ser inseridas separadas por espaço: <code>p q v</code>.</p><p>Utilizando três blocos de <a href="/PSP/docs/io">entrada / saída</a> pode-se fornecer tais dados ao conectá-los ao bloco de expressão matemática.</p><p>As reatâncias transitórias de eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>d</mi></msub></mrow><annotation encoding="application/x-tex">x_d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) e em quadratura (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>q</mi></msub></mrow><annotation encoding="application/x-tex">x_q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>) podem ser definidas diretamente na expressão matemática:</p><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">xd </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">0.146</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">xq </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">0.0969</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span></div></div></div></div></div><p>Os valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>P</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">P&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">Q&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.946332em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span> podem ser também calculados:</p><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">yp </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> p </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> v</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">yq </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> q </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> v</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span></div></div></div></div></div><p>Com todos os dados necessários pode-se calcular a corrente de campo:</p><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">i_f </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> p</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">xd </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">1.0</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">       </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">yq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yp</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> p</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span></div></div></div></div></div><p>Finalmente, pode-se definir a saída do bloco (não inserindo <code>;</code>):</p><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">i_f</span></div></div></div></div></div><p>Portanto, para as entradas definidas como <code>p q v</code>, a expressão matemática total para cálculo da corrente de campo será:</p><div class="mdxCodeBlock_iHAB"><div class="codeBlockContent_32p_"><button type="button" aria-label="Copy code to clipboard" class="copyButton_1BYj">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_19pQ"><div class="codeBlockLines_2n9r" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">xd </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">0.146</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">xq </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">0.0969</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">yp </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> p </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> v</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">yq </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> q </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> v</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">i_f </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> p</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">xd </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">1.0</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">       </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">yq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yp</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> p</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">i_f</span></div></div></div></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ul><li>NIEMINEN, J.; YLILUOMA, J. Function Parser for C++ v4.5.2. Disponível em: <a href="http://warp.povusers.org/FunctionParser/" target="_blank" rel="noopener noreferrer">http://warp.povusers.org/FunctionParser/</a>. </li></ul></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/mathExpression.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/gain"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Ganho</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/powerFlow"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Fluxo de Potência »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#sintaxe-das-expressões-matemáticas" class="table-of-contents__link">Sintaxe das expressões matemáticas</a></li><li><a href="#formulário-de-edição-de-dados-do-bloco-de-expressão-matemática" class="table-of-contents__link">Formulário de edição de dados do bloco de Expressão Matemática</a></li><li><a href="#exemplo-de-expressão-matemática" class="table-of-contents__link">Exemplo de Expressão Matemática</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Multiplicador</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Esse elemento é bastante simples e cumpre com a função matemáticas de seu nome.</p><p>Possui duas entradas de valores reais e sua saída é computada na sequência do nó superior pelo inferior, ou seja, a saída será o valor presente no nó 1 multiplicado pelo nó 2.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Nós não conectados no multiplicador são assumidos com o valor unitário e para o divisor é considerado valor nulo.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/multiplier.md" 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Editor de Potência</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O Editor de Elementos de Potência no PSP-UFU permite a inserção, manipulação e edição de elementos elétricos de potência por meio de um diagrama unifilar.</p><blockquote><p>(<strong>Diagrama unifilar</strong>) Um diagrama do sistema no qual as linhas polifásicas são representados por sua única linha equivalente. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=601-02-04" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Todos os elementos inseridos pode ser manipulados e editados utilizando as <a href="/PSP/docs/cadTools">Ferramentas CAD</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="novo-projeto"></a>Novo projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#novo-projeto" title="Direct link to heading">#</a></h2><p>A criação de um novo projeto é realizada clicando no item <strong>Novo projeto</strong> no <a href="/PSP/docs/mainScreen#menu-ribbon">submenu <strong>Arquivo</strong></a>. Essa ação cria um sistema em branco na área de trabalho, local onde é possível inserir os elementos elétricos por meio do <a href="/PSP/docs/mainScreen#menu-ribbon">submenu <strong>Ferramentas</strong></a> ou pelas <a href="/PSP/docs/powerEditor#teclas-de-atalho">teclas de atalho</a>.</p><p>Abaixo são apresentados os elementos elétricos de potência que podem ser inseridos no PSP-UFU:</p><ul><li><a href="/PSP/docs/bus">Barramento</a></li><li>Elementos de ramo<ul><li><a href="/PSP/docs/line">Linha</a></li><li><a href="/PSP/docs/transformer">Transformador</a></li></ul></li><li>Elementos Shunt<ul><li><a href="/PSP/docs/load">Carga</a></li><li><a href="/PSP/docs/capacitor">Capacitor</a></li><li><a href="/PSP/docs/inductor">Indutor</a></li><li><a href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a></li></ul></li><li>Máquinas<ul><li><a href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li><a href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li><a href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul><div><center><img src="/PSP/images/powerElements.svg" alt="Elementos de potência" title="Elementos de potência"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="inserindo-elementos"></a>Inserindo elementos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inserindo-elementos" title="Direct link to heading">#</a></h2><p>Por meio do submenu <strong>Ferramentas</strong> pode-se inserir os elementos de potência, como é apresentado na imagem abaixo.</p><div><center><img src="/PSP/images/addPowerElements.png" alt="Adicionar elementos de potência" title="Adicionar elementos de potência"></center></div><p>No caso de inserção de um barramento, o usuário deve apenas clicar na posição desejada, já para os outros componentes será solicitado que o usuário selecione em uma ou duas barras, o qual o novo componente será conectado.</p><p>Sempre que são inseridos novos elementos, um formulário de dados é exibido e pode-se editar os dados elétricos e acessar formulários adicionais, como dados de estabilidade.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O primeiro elemento que a ser inserido no projeto <strong>deve</strong> ser um barramento. Os demais elementos elétricos devem ser conectados em uma ou mais barras.</p></div></div><p>Além dos elementos de potência pode-se inserir os elementos de <em>texto vinculado</em>, os quais estão associados a uma grandeza que se deseja vizualizar diretamente na <a href="/PSP/docs/mainScreen#%C3%A1rea-de-trabalho">Área de Trabalho</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Ao inserir um barramento, a mesma irá acompanhar o ponteiro do mouse até que você clique na posição desejada. Para os demais elementos <strong>deve-se clicar em uma mais barras</strong> para exibir o elemento inserido.</p><p><strong>Sempre fique atento às instruções da <a href="/PSP/docs/mainScreen#barra-de-status">Barra de Status</a>.</strong></p></div></div><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/timelapseBuild.mp4" type="video/mp4"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="teclas-de-atalho"></a>Teclas de atalho<a aria-hidden="true" tabindex="-1" class="hash-link" href="#teclas-de-atalho" title="Direct link to heading">#</a></h3><p>É possível inserir todos os elementos de potência por meio de teclas de atalho, facilitando e agilizando a criação dos diagramas unifilares no PSP-UFU. A tabela abaixo apresenta tais atalhos:</p><table><thead><tr><th>Elemento</th><th align="center">Atalho</th><th>Elemento</th><th align="center">Atalho</th></tr></thead><tbody><tr><td>Barramento</td><td align="center">B</td><td>Carga</td><td align="center">Shift + L</td></tr><tr><td>Linha</td><td align="center">L</td><td>Capacitor</td><td align="center">Shift + C</td></tr><tr><td>Transformador</td><td align="center">T</td><td>Indutor</td><td align="center">Shift + I</td></tr><tr><td>Gerador</td><td align="center">G</td><td>Corrente harmônica</td><td align="center">Shift + H</td></tr><tr><td>Motor de indução</td><td align="center">I</td><td>Texto</td><td align="center">A</td></tr><tr><td>Compensador síncrono</td><td align="center">K</td><td></td><td align="center"></td></tr></tbody></table><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="editando-dados-elétricos"></a>Editando dados elétricos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#editando-dados-elétricos" title="Direct link to heading">#</a></h2><p>Ao inserir um elemento, seu respectivo formulário de edição é exibido para inserção dos dados elétricos d elemento. Todos os dados podem ser <strong>alterados</strong> ao <strong>clicar duas vezes sobre o elemento</strong> ou por opção do <strong>menu de contexto</strong> exibido ao clicar com o botão direito sobre o elemento.</p><p>Cada formulário de edição de dados elétricos dos elementos possuem suas particularidades e são descritos em documentação específica: <a href="/PSP/docs/bus">Barramento</a>, <a href="/PSP/docs/line">Linha</a>, <a href="/PSP/docs/transformer">Transformador</a>, <a href="/PSP/docs/load">Carga</a>, <a href="/PSP/docs/capacitor">Capacitor</a>, <a href="/PSP/docs/inductor">Indutor</a>, <a href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a>, <a href="/PSP/docs/syncGenerator">Gerador Síncrono</a>, <a href="/PSP/docs/syncMotor">Compensador Síncrono</a>, <a href="/PSP/docs/indMotor">Motor de Indução</a>.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/powerEditor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/cadTools"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Ferramentas CAD</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/bus"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Barramento »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#novo-projeto" class="table-of-contents__link">Novo projeto</a></li><li><a href="#inserindo-elementos" class="table-of-contents__link">Inserindo elementos</a><ul><li><a href="#teclas-de-atalho" class="table-of-contents__link">Teclas de atalho</a></li></ul></li><li><a href="#editando-dados-elétricos" class="table-of-contents__link">Editando dados elétricos</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Editor de Potência</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O Editor de Elementos de Potência no PSP-UFU permite a inserção, manipulação e edição de elementos elétricos de potência por meio de um diagrama unifilar.</p><blockquote><p>(<strong>Diagrama unifilar</strong>) Um diagrama do sistema no qual as linhas polifásicas são representados por sua única linha equivalente. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=601-02-04" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Todos os elementos inseridos pode ser manipulados e editados utilizando as <a href="/PSP/docs/cadTools">Ferramentas CAD</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="novo-projeto"></a>Novo projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#novo-projeto" title="Direct link to heading">#</a></h2><p>A criação de um novo projeto é realizada clicando no item <strong>Novo projeto</strong> no <a href="/PSP/docs/mainScreen#menu-ribbon">submenu <strong>Arquivo</strong></a>. Essa ação cria um sistema em branco na área de trabalho, local onde é possível inserir os elementos elétricos por meio do <a href="/PSP/docs/mainScreen#menu-ribbon">submenu <strong>Ferramentas</strong></a> ou pelas <a href="/PSP/docs/powerEditor#teclas-de-atalho">teclas de atalho</a>.</p><p>Abaixo são apresentados os elementos elétricos de potência que podem ser inseridos no PSP-UFU:</p><ul><li><a href="/PSP/docs/bus">Barramento</a></li><li>Elementos de ramo<ul><li><a href="/PSP/docs/line">Linha</a></li><li><a href="/PSP/docs/transformer">Transformador</a></li></ul></li><li>Elementos Shunt<ul><li><a href="/PSP/docs/load">Carga</a></li><li><a href="/PSP/docs/capacitor">Capacitor</a></li><li><a href="/PSP/docs/inductor">Indutor</a></li><li><a href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a></li></ul></li><li>Máquinas<ul><li><a href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li><a href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li><a href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul><div><center><img src="/PSP/images/powerElements.svg" alt="Elementos de potência" title="Elementos de potência"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="inserindo-elementos"></a>Inserindo elementos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inserindo-elementos" title="Direct link to heading">#</a></h2><p>Por meio do submenu <strong>Ferramentas</strong> pode-se inserir os elementos de potência, como é apresentado na imagem abaixo.</p><div><center><img src="/PSP/images/addPowerElements.png" alt="Adicionar elementos de potência" title="Adicionar elementos de potência"></center></div><p>No caso de inserção de um barramento, o usuário deve apenas clicar na posição desejada, já para os outros componentes será solicitado que o usuário selecione em uma ou duas barras, o qual o novo componente será conectado.</p><p>Sempre que são inseridos novos elementos, um formulário de dados é exibido e pode-se editar os dados elétricos e acessar formulários adicionais, como dados de estabilidade.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O primeiro elemento que a ser inserido no projeto <strong>deve</strong> ser um barramento. Os demais elementos elétricos devem ser conectados em uma ou mais barras.</p></div></div><p>Além dos elementos de potência pode-se inserir os elementos de <em>texto vinculado</em>, os quais estão associados a uma grandeza que se deseja vizualizar diretamente na <a href="/PSP/docs/mainScreen#%C3%A1rea-de-trabalho">Área de Trabalho</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Ao inserir um barramento, a mesma irá acompanhar o ponteiro do mouse até que você clique na posição desejada. Para os demais elementos <strong>deve-se clicar em uma mais barras</strong> para exibir o elemento inserido.</p><p><strong>Sempre fique atento às instruções da <a href="/PSP/docs/mainScreen#barra-de-status">Barra de Status</a>.</strong></p></div></div><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/timelapseBuild.mp4" type="video/mp4"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="teclas-de-atalho"></a>Teclas de atalho<a aria-hidden="true" tabindex="-1" class="hash-link" href="#teclas-de-atalho" title="Direct link to heading">#</a></h3><p>É possível inserir todos os elementos de potência por meio de teclas de atalho, facilitando e agilizando a criação dos diagramas unifilares no PSP-UFU. A tabela abaixo apresenta tais atalhos:</p><table><thead><tr><th>Elemento</th><th align="center">Atalho</th><th>Elemento</th><th align="center">Atalho</th></tr></thead><tbody><tr><td>Barramento</td><td align="center">B</td><td>Carga</td><td align="center">Shift + L</td></tr><tr><td>Linha</td><td align="center">L</td><td>Capacitor</td><td align="center">Shift + C</td></tr><tr><td>Transformador</td><td align="center">T</td><td>Indutor</td><td align="center">Shift + I</td></tr><tr><td>Gerador</td><td align="center">G</td><td>Corrente harmônica</td><td align="center">Shift + H</td></tr><tr><td>Motor de indução</td><td align="center">I</td><td>Texto</td><td align="center">A</td></tr><tr><td>Compensador síncrono</td><td align="center">K</td><td></td><td align="center"></td></tr></tbody></table><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="editando-dados-elétricos"></a>Editando dados elétricos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#editando-dados-elétricos" title="Direct link to heading">#</a></h2><p>Ao inserir um elemento, seu respectivo formulário de edição é exibido para inserção dos dados elétricos d elemento. Todos os dados podem ser <strong>alterados</strong> ao <strong>clicar duas vezes sobre o elemento</strong> ou por opção do <strong>menu de contexto</strong> exibido ao clicar com o botão direito sobre o elemento.</p><p>Cada formulário de edição de dados elétricos dos elementos possuem suas particularidades e são descritos em documentação específica: <a href="/PSP/docs/bus">Barramento</a>, <a href="/PSP/docs/line">Linha</a>, <a href="/PSP/docs/transformer">Transformador</a>, <a href="/PSP/docs/load">Carga</a>, <a href="/PSP/docs/capacitor">Capacitor</a>, <a href="/PSP/docs/inductor">Indutor</a>, <a href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a>, <a href="/PSP/docs/syncGenerator">Gerador Síncrono</a>, <a href="/PSP/docs/syncMotor">Compensador Síncrono</a>, <a href="/PSP/docs/indMotor">Motor de Indução</a>.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/powerEditor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/cadTools"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Ferramentas CAD</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/bus"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Barramento »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#novo-projeto" class="table-of-contents__link">Novo projeto</a></li><li><a href="#inserindo-elementos" class="table-of-contents__link">Inserindo elementos</a><ul><li><a href="#teclas-de-atalho" class="table-of-contents__link">Teclas de atalho</a></li></ul></li><li><a href="#editando-dados-elétricos" class="table-of-contents__link">Editando dados elétricos</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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pelo usuário. A taxa de variação é calculada a partir dos valores de entrada atual e passado e, caso seja violada, será definida uma saída que respeite essas taxas (de crescimento ou decrescimento).</p><p>A taxa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>) é calculada de acordo com a equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mo>=</mo><mfrac><mrow><msub><mi>u</mi><mi>n</mi></msub><mo>−</mo><msub><mi>y</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><mi>h</mi></mfrac></mrow><annotation encoding="application/x-tex">r = \frac{u_n - y_{n-1}}{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.9463300000000001em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">h</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é a entrada atual do bloco</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">y_{n-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span></span>	é o valor de saída anterior do bloco</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>	é o passo de integração</li></ul><p>Obtida a taxa, o bloco irá resultar em um valor calculado pelas seguintes condições:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>h</mi><mo>×</mo><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><mi>r</mi><mo>&gt;</mo><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>u</mi><mi>n</mi></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub><mo>≤</mo><mi>r</mi><mo>≤</mo><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>h</mi><mo>×</mo><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><mi>r</mi><mo>&lt;</mo><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} h \times R_{cre}{,} &amp; \text{se } r &gt; R_{cre} \\ u_n{,} &amp; \text{se } R_{dec} \le r \le R_{cre}\\ h \times R_{dec}{,} &amp; \text{se } r &lt; R_{dec} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub></mrow><annotation encoding="application/x-tex">R_{cre}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub></mrow><annotation encoding="application/x-tex">R_{dec}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	são as taxas de crescimento e decaimento, respectivamente</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-de-dados-do-limitador-de-taxa"></a>Formulário de edição de dados do Limitador de taxa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-limitador-de-taxa" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados do bloco limitador de taxa.</p><div><center><img src="/PSP/images/rateLimitForm.png" alt="Formulário de edição de dados do bloco limitador de taxa no PSP-UFU" title="Formulário de edição de dados do bloco limitador de taxa no PSP-UFU"></center></div><p>Esse bloco é definido pelo <strong>limite superior (taxa de crescimento máxima) e inferior (taxa de decrescimento máxima)</strong>, inseridos pelo usuário.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Esses blocos são úteis para limitar variações bruscas na entrada que possam comprometer o controle ou limites físicos de modelos de turbina, por exemplo.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div 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href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Configurações da Simulação</h1></header><div class="markdown"></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a 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Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Somador</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Como o próprio nome sugere, os somadores são elementos de controle capazes de somar qualquer quantidade de valores reais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-de-dados-do-somador"></a>Formulário de edição de dados do somador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-somador" title="Direct link to heading">#</a></h2><p>A quantidade de entradas, assim como seus sinais são definidas pelo usuário, como mostra a figura abaixo.</p><div><center><img src="/PSP/images/sumForm.png" alt="Formulário de edição de dados do somador no PSP-UFU" title="Formulário de edição de dados do somador no PSP-UFU"></center></div><p>No seu único campo “<strong>Sinais</strong>” é inserida uma lista de sinais <strong>separados por espaços</strong> contendo os símbolos “+” para uma entrada positiva e “-” para negativa.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Gerador Síncrono</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina de corrente alternada na qual a frequência das tensões geradas e a velocidade da máquina estão em uma proporção constante. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-31-08" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="gerador-síncrono-no-psp-ufu"></a>Gerador Síncrono no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Os geradores síncronos são a fonte de potência para o cálculo do fluxo de carga e estabilidade, além de serem um dos principais contribuintes para as correntes de falta.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Somente barramentos que possuem esse elemento conectado podem ser considerados <a href="/PSP/docs/powerFlow">barras de referência</a>. <a href="/PSP/docs/powerFlow">Barras do tipo PV</a> devem conter um gerador síncrono ou um <a href="/PSP/docs/syncMotor">motor síncrono (compensador síncrono)</a>.</p></div></div><p>O formulário de dados é dividido em dois, sendo o primeiro responsável pelos dados gerais, de <a href="/PSP/docs/powerFlow">fluxo de carga</a> e de <a href="/PSP/docs/fault">falta</a> e um segundo pelos dados de <a href="/PSP/docs/stability">estabilidade</a> . Esse último também permite o acesso aos controles das máquinas síncronas manipulados pelo editor de controle.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Os dados referentes às <strong>impedâncias de sequência positiva do gerador síncrono</strong> inseridas no <a href="/PSP/docs/syncGenerator#falta">contexto (aba) &quot;Falta&quot;</a> são utilizados <strong>tanto para os estudos de <a href="/PSP/docs/fault">curto-circuito</a> quanto para os estudos de <a href="/PSP/docs/harmonics">harmônicos</a></strong>.</p><p>Esses dados são ignorados nos estudos de <a href="/PSP/docs/powerFlow">fluxo de carga</a> (<em>não são utilizado nesse estudo</em>) e <a href="/PSP/docs/stability">estabilidade</a> (<em>são utilizados dados inseridos em formulário específico</em>).</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="gerador-síncrono-no-fluxo-de-carga"></a>Gerador Síncrono no fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-fluxo-de-carga" title="Direct link to heading">#</a></h3><p>O gerador síncrono é a fonte de potência do PSP-UFU no estudo de fluxo de carga. Seu comportamento difere de acordo com o tipo de barra conectada:</p><ul><li><a href="/PSP/docs/powerFlow">Barra de referência</a>: Os dados de potência ativa e reativa inseridos são desprezados, uma vez que esse elemento será utilizado para completar o balanço de potência do estudo de fluxo d carga;</li><li><a href="/PSP/docs/powerFlow">Barra PV</a>: O dado de potência ativa é considerado, porém o dados de potência reativa são desprezados. O valor da potência reativa é utilizado para manter o módulo da tensão constante no barramento conectado;</li><li><a href="/PSP/docs/powerFlow">Barra PQ</a>: Para os geradores conectados a essa barra tanto a potência ativa quanto reativa inseridas são consideradas.</li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>Caso o limite de potência reativa seja excedido, o programa automaticamente transforma a <a href="/PSP/docs/powerFlow">Barra PV</a> conectada em uma <a href="/PSP/docs/powerFlow">Barra PQ</a>, utilizando o valor limite de potência reativa que seria ultrapassado.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="gerador-síncrono-no-estudo-de-curto-circuito"></a>Gerador Síncrono no estudo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-estudo-de-curto-circuito" title="Direct link to heading">#</a></h3><p>Enquanto os geradores no estudo de fluxo de carga são modelados somente por correntes injetadas nas barras, para o curto-circuito utiliza-se uma tensão atrás de uma impedância. A figura abaixo mostra o caminho da corrente e o circuito equivalente de cada sequência nos geradores.</p><div><center><img src="/PSP/images/sycGeneratorSeq.svg" alt="Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero" title="Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero"></center></div><p>As tensões geradas são somente de sequência positiva, uma vez que o gerador fornece sempre tensões trifásicas equilibradas. Portanto a rede de sequência positiva é composta de uma tensão pré-falta atrás de uma impedância de sequência positiva. As redes de sequência negativa e zero não contêm forças eletromotrizes, porém incluem as impedâncias do gerador de sequência negativa e zero.</p><p>A corrente que circula na impedância <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> entre o neutro e a terra é <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">3\dot{I}_{a0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>. Pela figura acima (c), observa-se que a queda de tensão de sequência zero do ponto a para terra (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\dot{V}_{a0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><mo>=</mo><mo>−</mo><mn>3</mn><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub><mo>−</mo><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>g</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\dot{V}_{a0} = -3\dot{I}_{a0}\overline{z}_n - \dot{I}_{a0}\overline{z}_{g0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord">−</span><span class="mord">3</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.206298em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">g</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span></div><p>A rede de sequência zero, que é um circuito monofásico pelo qual se supõe que circule apenas corrente de sequência zero e deve, portanto, ter uma impedância definida pela seguinte equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mn>0</mn></msub><mo>=</mo><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub><mo>+</mo><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>g</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\overline{z}_{0} = 3\overline{z}_n + \overline{z}_{g0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.79444em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.916668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">g</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Caso o gerador não seja aterrado, não circulará corrente de sequência zero por ele. Nesse caso, dependendo da conexão do transformador próximo ao gerador sem aterramento, a seguinte mensagem de erro pode ser exibida:</p><p><center>&quot;<i>Falha ao inverter a matriz admitância de sequência zero</i>&quot;</center></p><p>Isso ocorre porque a matriz admitância de sequência zero é singular. Para contornar esse problema escolha <strong>uma</strong> das duas soluções abaixo:</p><ol><li>Marque a opção &quot;Neutro aterrado&quot; e insira um alto valor de reatância de aterramento (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mn>9999</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">j9999~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, por exemplo);</li><li><strong>Ou</strong>, na barra do gerador, insira um <a href="/PSP/docs/inductor">reator</a> de baixo valor de potência reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>0</mn><mtext> </mtext><mi>v</mi><mi>a</mi><mi>r</mi></mrow><annotation encoding="application/x-tex">1,0~var</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault" style="margin-right:0.03588em">v</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>, por exemplo).</li></ol></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="gerador-síncrono-no-estudo-de-estabilidade"></a>Gerador Síncrono no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>A relação de valores observados em testes adequados (definidos na <a href="https://doi.org/10.1109/IEEESTD.2020.9050934">IEEE Std. 115-2019</a>), denominados parâmetros padrões, são utilizados para modelar a máquina síncrona no estudo de estabilidade do PSP-UFU.</p><p>Os parâmetros da máquina síncrona que influenciam rapidamente no decaimento de valores são chamados <strong>subtransitórios</strong> (indicados por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup></mrow><annotation encoding="application/x-tex">&#x27;&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>), aqueles que influenciam mais lentamente são chamados <strong>transitórios</strong> (indicados por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>) e, finalmente, aqueles que influenciam continuamente são chamados de parâmetros <strong>síncronos</strong> (sem indicação de sobrescrito).</p><p>Um conjunto de equações algébrico-diferenciais determinam o comportamento da máquina síncrona no estudo de estabilidade:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msub><mi>V</mi><mi>q</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>I</mi><mi>d</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msub><mi>V</mi><mi>d</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>I</mi><mi>q</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo>−</mo><msub><mi>V</mi><mi>q</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mi>I</mi><mi>d</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo>−</mo><msub><mi>V</mi><mi>d</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mi>I</mi><mi>q</mi><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>V</mi><mrow><mi>f</mi><mi>d</mi></mrow></msub><mo>+</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>d</mi><mn>0</mn></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msub><mi>s</mi><mi>q</mi></msub><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>q</mi><mn>0</mn></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msubsup><mi>x</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>d</mi><mn>0</mn></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msubsup><mi>x</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>q</mi><mn>0</mn></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mfrac><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>ω</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><msub><mi>ω</mi><mi>r</mi></msub><mrow><mn>2</mn><mi>H</mi></mrow></mfrac><mrow><mo fence="true">[</mo><msub><mi>P</mi><mi>m</mi></msub><mo>−</mo><msub><mi>P</mi><mi>e</mi></msub><mo>−</mo><msub><mi>D</mi><mi>a</mi></msub><mrow><mo fence="true">(</mo><mi>ω</mi><mo>−</mo><msub><mi>ω</mi><mi>r</mi></msub><mo fence="true">)</mo></mrow><mo fence="true">]</mo></mrow><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>δ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mrow><mo fence="true">(</mo><mi>ω</mi><mo>−</mo><msub><mi>ω</mi><mi>r</mi></msub><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">E_{q}&#x27; - V_q = r_aI_q - x_{ds}&#x27;Id\\ E_{d}&#x27; - V_d = r_aI_d - x_{qs}&#x27;Iq\\ E_{q}&#x27;&#x27; - V_q = r_aI_q - x_{ds}&#x27;&#x27;Id\\ E_{d}&#x27;&#x27; - V_d = r_aI_d - x_{qs}&#x27;&#x27;Iq\\ ~\\ \frac{dE_{q}&#x27;}{dt} = \frac{V_{fd} + \left( x_d - x_{d}&#x27; \right)I_d - s_d E_{q}&#x27;}{T_{d0}&#x27;}\\ \frac{dE_{d}&#x27;}{dt} = \frac{- \left( x_q - x_{q}&#x27; \right)I_q - s_q E_{d}&#x27;}{T_{q0}&#x27;}\\ \frac{dE_{q}&#x27;&#x27;}{dt} = \frac{s_dE_{q}&#x27; + \left( x_{d}&#x27; - x_{d}&#x27;&#x27; \right)I_d - s_d E_{q}&#x27;&#x27;}{T_{d0}&#x27;&#x27;}\\ \frac{dE_{d}&#x27;&#x27;}{dt} = \frac{s_dE_{d}&#x27; + \left( x_{q}&#x27; - x_{q}&#x27;&#x27; \right)I_q - s_d E_{d}&#x27;&#x27;}{T_{q0}&#x27;&#x27;}\\ ~\\ \frac{d\omega}{dt} = \frac{\omega_r}{2H} \left[ P_m - P_e - D_a \left( \omega - \omega_r \right) \right]\\ \frac{d\delta}{dt} = \Omega_b\left( \omega - \omega_r \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault">d</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault" style="margin-right:0.03588em">q</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault">d</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault" style="margin-right:0.03588em">q</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.211em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.512308em;vertical-align:-0.9873080000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.398692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30130799999999996em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9873080000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.7115240000000003em;vertical-align:-1.088416em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231080000000002em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.4336920000000006em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4024159999999999em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">−</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.088416em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.211em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.512308em;vertical-align:-0.9873080000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.398692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30130799999999996em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9873080000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.7115240000000003em;vertical-align:-1.088416em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231080000000002em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.4336920000000006em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4024159999999999em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.088416em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.7935599999999998em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">[</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mclose delimcenter" style="top:0em">]</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault" style="margin-right:0.03785em">δ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span></span></div><p>As duas últimas equações diferenciais são as equações mecânicas da máquina; e as demais são equações elétricas (consulte essa <a href="https://dx.doi.org/10.14393/ufu.te.2019.2444">tese</a> para maiores detalhes acerca dos parâmetros dessas equações).</p><p>Utilizando as equações transitórias e subtransitórias podem-se definir cinco modelos de distintas complexidades.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O modelo da máquina síncrona é <strong>selecionado automaticamente</strong> de acordo com os dados fornecidos ao programa.</p></div></div><p>Na sequência são apresentados tais modelos, incluídos os efeitos da saturação magnética, em conjunto com seus diagramas de blocos:</p><ul><li><strong>Modelo 1</strong>: Corresponde a uma tensão constante atrás de uma reatância transitória de eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">x_{d}&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.035em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span>), não exigindo equações diferenciais;</li><li><strong>Modelo 2</strong>: São representados os efeitos transitórios de eixo direto, sendo necessária a solução de uma equação diferencial (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model2SyncGenerator.svg" alt="Diagrama de blocos do Modelo 2 das máquinas síncronas" title="Diagrama de blocos do Modelo 2 das máquinas síncronas"></center></div><ul><li><strong>Modelo 3</strong>: São representados os efeitos transitórios de eixo direto e em quadratura, exigindo duas equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model3SyncGenerator.svg" alt="Diagrama de blocos do Modelo 3 das máquinas síncronas" title="Diagrama de blocos do Modelo 3 das máquinas síncronas"></center></div><ul><li><strong>Modelo 4</strong>: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de três equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model4SyncGenerator.svg" alt="Diagrama de blocos do Modelo 4 das máquinas síncronas" title="Diagrama de blocos do Modelo 4 das máquinas síncronas"></center></div><ul><li><strong>Modelo 5</strong>: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de quatro equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model5SyncGenerator.svg" alt="Diagrama de blocos do Modelo 4 das máquinas síncronas" title="Diagrama de blocos do Modelo 4 das máquinas síncronas"></center></div><div class="admonition admonition-note alert alert--secondary"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M6.3 5.69a.942.942 0 0 1-.28-.7c0-.28.09-.52.28-.7.19-.18.42-.28.7-.28.28 0 .52.09.7.28.18.19.28.42.28.7 0 .28-.09.52-.28.7a1 1 0 0 1-.7.3c-.28 0-.52-.11-.7-.3zM8 7.99c-.02-.25-.11-.48-.31-.69-.2-.19-.42-.3-.69-.31H6c-.27.02-.48.13-.69.31-.2.2-.3.44-.31.69h1v3c.02.27.11.5.31.69.2.2.42.31.69.31h1c.27 0 .48-.11.69-.31.2-.19.3-.42.31-.69H8V7.98v.01zM7 2.3c-3.14 0-5.7 2.54-5.7 5.68 0 3.14 2.56 5.7 5.7 5.7s5.7-2.55 5.7-5.7c0-3.15-2.56-5.69-5.7-5.69v.01zM7 .98c3.86 0 7 3.14 7 7s-3.14 7-7 7-7-3.12-7-7 3.14-7 7-7z"></path></svg></span>Nota</h5></div><div class="admonition-content"><p>Em todos os modelos as equações diferenciais mecânicas são solucionadas.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="barramento-infinito"></a>Barramento infinito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barramento-infinito" title="Direct link to heading">#</a></h4><p>Algumas referências incluem um modelo sem equações diferenciais, em que a máquina é somente representada por uma tensão constante atrás de uma reatância transitória de eixo direto. Tal é utilizado na representação de um <strong>barramento infinito</strong>, o qual é normalmente constituído de um subsistema muito maior àquele simulado.</p><p>No PSP-UFU a <strong>representação de um barramento infinito</strong> pode ser obtido por meio da utilização de uma máquina representada pelo Modelo 1 cujo valor da constante de inércia (H) é infinito ou muito grande (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9999</mn><mtext> </mtext><mi>s</mi></mrow><annotation encoding="application/x-tex">9999~s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord mathdefault">s</span></span></span></span></span>, por exemplo) em relação às demais máquinas do sistema, e o valor de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">x_{d}&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.035em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span> deve ser um valor muito pequeno (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">10^{-3}~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.008548em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">3</span></span></span></span></span></span></span></span></span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, por exemplo).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="centro-de-inércia"></a>Centro de inércia<a aria-hidden="true" tabindex="-1" class="hash-link" href="#centro-de-inércia" title="Direct link to heading">#</a></h4><p>Normalmente utiliza-se a velocidade de referência como sendo a síncrona e portanto, nesse caso, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ω</mi><mi>r</mi></msub><mo>=</mo><msub><mi>ω</mi><mi>b</mi></msub><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>0</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">\omega_r = \omega_b = 1,0~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> Essa abordagem, adotada por vários livros de estabilidade, considera como referência uma máquina fictícia girando sempre na velocidade síncrona independente das perturbações aplicadas no sistema. No PSP-UFU foi implementado o conceito de centro de inércia (COI, do inglês, <em>Center of Inertia</em>), que constitui uma soma ponderada das velocidades das máquinas presentes no sistema:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ω</mi><mi>r</mi></msub><mo>=</mo><mfrac><mrow><mo fence="true">(</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>H</mi><mi>i</mi></msub><msub><mi>ω</mi><mi>i</mi></msub><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>H</mi><mi>i</mi></msub><mo fence="true">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\omega_r=\frac{\left( \sum_{i=1}^{n} H_i \omega_i \right)}{\left( \sum_{i=1}^{n} H_i \right)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.488004em;vertical-align:-0.994002em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.494002em"><span style="top:-2.305708em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6897100000000003em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994002em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:
-<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">n</span></span></span></span></span>	é o número de máquinas síncronas <strong>conectadas</strong> no sistema.</p><p>A aplicação do COI resulta em dados de saída, como o ângulo do rotor, mais fáceis de serem analisados. Na implementação realizada no programa a utilização ou não desse recurso é opcional e pode ser <a href="/PSP/docs/simulationConfig">definida pelo usuário</a>.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-geradores-síncronos"></a>Formulário de edição dos geradores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-geradores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos geradores síncronos:</p><div><center><img src="/PSP/images/syncGeneratorForm.png" alt="Formulário dos geradores síncronos no PSP-UFU" title="Formulário dos geradores síncronos no PSP-UFU"></center></div><p>Um segundo pelos dados de estabilidade, como mostra a figura abaixo, acessado ao clicar no botão &quot;Estabilidade&quot; do formulário principal. Nele é possível também acessar aos controles das máquinas síncronas manipulados pelo <a href="/PSP/docs/controlEditor">editor de controle</a>.</p><div><center><img src="/PSP/images/syncGeneratorStabForm.png" alt="Formulário de estabilidade dos geradores síncronos no PSP-UFU" title="Formulário de estabilidade dos geradores síncronos no PSP-UFU"></center></div><p>No formulário de estabilidade pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do gerador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/syncGeneratorSw.png" alt="Formulário de chaveamento do gerador síncrono" title="Formulário de chaveamento do gerador síncrono"></center></div><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="geral"></a>Geral<a aria-hidden="true" tabindex="-1" class="hash-link" href="#geral" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do gerador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador.</p><p>Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso mais de um gerador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potências-reativas-máxima-e-mínima"></a>Potências reativas máxima e mínima<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-reativas-máxima-e-mínima" title="Direct link to heading">#</a></h4><p>Limites de potência reativa máxima e mínima do gerador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="falta"></a>Falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#falta" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="impedâncias-de-sequência"></a>Impedâncias de sequência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#impedâncias-de-sequência" title="Direct link to heading">#</a></h4><p>Valores de resistência e reatância para cálculo das correntes de falta. São inseridos dados de sequência positiva, negativa e zero.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="impedância-de-aterramento"></a>Impedância de aterramento<a aria-hidden="true" tabindex="-1" class="hash-link" href="#impedância-de-aterramento" title="Direct link to heading">#</a></h4><p>Valores utilizados para o cálculo das correntes de falta do tipo fase-terra e fase-fase-terra. Caso o neutro do gerador não seja aterrado, o valor inserido nesse campo é ignorado.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="neutro-aterrado"></a>Neutro aterrado<a aria-hidden="true" tabindex="-1" class="hash-link" href="#neutro-aterrado" title="Direct link to heading">#</a></h4><p>Indica se o neutro do gerador é aterrado.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="botão-estabilidade"></a>Botão Estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#botão-estabilidade" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="imprimir-dados-da-máquina-síncrona"></a>Imprimir dados da máquina síncrona<a aria-hidden="true" tabindex="-1" class="hash-link" href="#imprimir-dados-da-máquina-síncrona" title="Direct link to heading">#</a></h4><p>Exibe os dados do gerador síncrono nos gráficos no tempo. Os seguintes dados são exibidos:</p><ul><li>tensão terminal</li><li>potências ativa e reativas</li><li>potência mecânica</li><li>frequência</li><li>tensão de campo</li><li>ângulo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>δ</mi></mrow><annotation encoding="application/x-tex">\delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03785em">δ</span></span></span></span></span>.</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-avr-e-regulador-de-velocidade"></a>Utilizar AVR e regulador de velocidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-avr-e-regulador-de-velocidade" title="Direct link to heading">#</a></h4><p>Esses campos acionam ou inibem os controles da máquina síncrona, assim como modelos de turbina e excitatrizes.</p><p>Caso selecionadas os controles podem ser inseridos e modificados pelos botões “Editar AVR” e “Editar regulador de velocidade”, os quais acessam o <a href="/PSP/docs/controlEditor">editor de controle do PSP-UFU</a>.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="resistência-de-armadura"></a>Resistência de armadura<a aria-hidden="true" tabindex="-1" class="hash-link" href="#resistência-de-armadura" title="Direct link to heading">#</a></h4><p>Resistência de armadura da máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="reatância-de-potier"></a>Reatância de Potier<a aria-hidden="true" tabindex="-1" class="hash-link" href="#reatância-de-potier" title="Direct link to heading">#</a></h4><p>Reatância de Potier para cálculo da saturação da máquina, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="fator-de-saturação"></a>Fator de saturação<a aria-hidden="true" tabindex="-1" class="hash-link" href="#fator-de-saturação" title="Direct link to heading">#</a></h4><p>Valor utilizado no cálculo da curva de saturação.</p><p>Representa o valor (em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) de corrente de campo necessária para atingir 1,2 p.u. de tensão terminal.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Esse valor deve ser <strong>maior que 1,2</strong>, ou irá gerar erros na simulação. Caso não seja informado, a saturação da máquina não é considerada nos cálculos.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="reatâncias-síncronas"></a>Reatâncias síncronas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#reatâncias-síncronas" title="Direct link to heading">#</a></h4><p>Valores de reatância síncrona (regime permanente) da máquina. Os valores de eixo direto e em quadratura devem ser iguais ou muito próximos para representação de uma máquina de polos lisos, enquanto para polos salientes esses valores são distintos.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="reatâncias-e-constantes-de-tempo-transitórias"></a>Reatâncias e constantes de tempo transitórias<a aria-hidden="true" tabindex="-1" class="hash-link" href="#reatâncias-e-constantes-de-tempo-transitórias" title="Direct link to heading">#</a></h4><p>Parâmetros transitórios da máquina síncrona em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> ou segundos.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O valor da reatância transitória de eixo direto deve ser diferente de zero ou levará o programa a erro.</p></div></div><p>De acordo com a quantidade de parâmetros inseridos é definido internamente pelo programa qual o modelo a ser utilizado.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="reatâncias-e-constantes-de-tempo-subtransitórias"></a>Reatâncias e constantes de tempo subtransitórias<a aria-hidden="true" tabindex="-1" class="hash-link" href="#reatâncias-e-constantes-de-tempo-subtransitórias" title="Direct link to heading">#</a></h4><p>Parâmetros subtransitórios da máquina síncrona em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> ou segundos, representando em detalhes a presença de enrolamentos amortecedores. Assim como os dados transitórios, esses parâmetros definem o modelo da máquina.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="botão-chaveamento"></a>Botão Chaveamento<a aria-hidden="true" tabindex="-1" class="hash-link" href="#botão-chaveamento" title="Direct link to heading">#</a></h3><p>O botão &quot;Chaveamento&quot; irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do gerador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><p>Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões &quot;Adicionar&quot; e &quot;Remover&quot;, respectivamente.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: <a href="https://doi.org/10.1007/978-3-642-13669-6" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/978-3-642-13669-6</a></li><li>ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley &amp; Sons, New York, 2001. doi: <a href="https://doi.org/10.1002/9781118878286" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/9781118878286</a></li><li>KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994.</li><li>DOMMEL, H. W.; SATO, N. Fast Transient Stability Solutions. IEEE Transactions on Power Aparatus and Systems, v. PAS-91, n. 4, jul 1972, p. 1643-1650. doi: <a href="https://doi.org/10.1109/TPAS.1972.293341">https://doi.org/10.1109/TPAS.1972.293341</a></li><li>IEEE Std 1110-2002 IEEE Guide for Synchronous Generator Modeling Practices and Applications in Power System Stability Analyses. IEEE, New York, nov. 2003. doi: <a href="https://doi.org/10.1109/IEEESTD.2003.94408">https://doi.org/10.1109/IEEESTD.2003.94408</a></li><li>KIMBARK, E. W. Power System Stability: Volume III – Synchronous Machine. New York: Wiley-IEEE Press, 1995.</li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/syncGenerator.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/harmSource"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Fonte de Corrente Harmônica</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/syncMotor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Compensador Síncrono »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#gerador-síncrono-no-psp-ufu" class="table-of-contents__link">Gerador Síncrono no PSP-UFU</a><ul><li><a href="#gerador-síncrono-no-fluxo-de-carga" class="table-of-contents__link">Gerador Síncrono no fluxo de carga</a></li><li><a href="#gerador-síncrono-no-estudo-de-curto-circuito" class="table-of-contents__link">Gerador Síncrono no estudo de curto-circuito</a></li><li><a href="#gerador-síncrono-no-estudo-de-estabilidade" class="table-of-contents__link">Gerador Síncrono no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-dos-geradores-síncronos" class="table-of-contents__link">Formulário de edição dos geradores síncronos</a><ul><li><a href="#geral" class="table-of-contents__link">Geral</a></li><li><a href="#falta" class="table-of-contents__link">Falta</a></li><li><a href="#botão-estabilidade" class="table-of-contents__link">Botão Estabilidade</a></li><li><a href="#botão-chaveamento" class="table-of-contents__link">Botão Chaveamento</a></li></ul></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Gerador Síncrono</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina de corrente alternada na qual a frequência das tensões geradas e a velocidade da máquina estão em uma proporção constante. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-31-08" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="gerador-síncrono-no-psp-ufu"></a>Gerador Síncrono no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Os geradores síncronos são a fonte de potência para o cálculo do fluxo de carga e estabilidade, além de serem um dos principais contribuintes para as correntes de falta.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Somente barramentos que possuem esse elemento conectado podem ser considerados <a href="/PSP/docs/powerFlow">barras de referência</a>. <a href="/PSP/docs/powerFlow">Barras do tipo PV</a> devem conter um gerador síncrono ou um <a href="/PSP/docs/syncMotor">motor síncrono (compensador síncrono)</a>.</p></div></div><p>O formulário de dados é dividido em dois, sendo o primeiro responsável pelos dados gerais, de <a href="/PSP/docs/powerFlow">fluxo de carga</a> e de <a href="/PSP/docs/fault">falta</a> e um segundo pelos dados de <a href="/PSP/docs/stability">estabilidade</a> . Esse último também permite o acesso aos controles das máquinas síncronas manipulados pelo editor de controle.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Os dados referentes às <strong>impedâncias de sequência positiva do gerador síncrono</strong> inseridas no <a href="/PSP/docs/syncGenerator#falta">contexto (aba) &quot;Falta&quot;</a> são utilizados <strong>tanto para os estudos de <a href="/PSP/docs/fault">curto-circuito</a> quanto para os estudos de <a href="/PSP/docs/harmonics">harmônicos</a></strong>.</p><p>Esses dados são ignorados nos estudos de <a href="/PSP/docs/powerFlow">fluxo de carga</a> (<em>não são utilizado nesse estudo</em>) e <a href="/PSP/docs/stability">estabilidade</a> (<em>são utilizados dados inseridos em formulário específico</em>).</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="gerador-síncrono-no-fluxo-de-carga"></a>Gerador Síncrono no fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-fluxo-de-carga" title="Direct link to heading">#</a></h3><p>O gerador síncrono é a fonte de potência do PSP-UFU no estudo de fluxo de carga. Seu comportamento difere de acordo com o tipo de barra conectada:</p><ul><li><a href="/PSP/docs/powerFlow">Barra de referência</a>: Os dados de potência ativa e reativa inseridos são desprezados, uma vez que esse elemento será utilizado para completar o balanço de potência do estudo de fluxo d carga;</li><li><a href="/PSP/docs/powerFlow">Barra PV</a>: O dado de potência ativa é considerado, porém o dados de potência reativa são desprezados. O valor da potência reativa é utilizado para manter o módulo da tensão constante no barramento conectado;</li><li><a href="/PSP/docs/powerFlow">Barra PQ</a>: Para os geradores conectados a essa barra tanto a potência ativa quanto reativa inseridas são consideradas.</li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>Caso o limite de potência reativa seja excedido, o programa automaticamente transforma a <a href="/PSP/docs/powerFlow">Barra PV</a> conectada em uma <a href="/PSP/docs/powerFlow">Barra PQ</a>, utilizando o valor limite de potência reativa que seria ultrapassado.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="gerador-síncrono-no-estudo-de-curto-circuito"></a>Gerador Síncrono no estudo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-estudo-de-curto-circuito" title="Direct link to heading">#</a></h3><p>Enquanto os geradores no estudo de fluxo de carga são modelados somente por correntes injetadas nas barras, para o curto-circuito utiliza-se uma tensão atrás de uma impedância. A figura abaixo mostra o caminho da corrente e o circuito equivalente de cada sequência nos geradores.</p><div><center><img src="/PSP/images/sycGeneratorSeq.svg" alt="Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero" title="Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero"></center></div><p>As tensões geradas são somente de sequência positiva, uma vez que o gerador fornece sempre tensões trifásicas equilibradas. Portanto a rede de sequência positiva é composta de uma tensão pré-falta atrás de uma impedância de sequência positiva. As redes de sequência negativa e zero não contêm forças eletromotrizes, porém incluem as impedâncias do gerador de sequência negativa e zero.</p><p>A corrente que circula na impedância <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> entre o neutro e a terra é <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">3\dot{I}_{a0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>. Pela figura acima (c), observa-se que a queda de tensão de sequência zero do ponto a para terra (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\dot{V}_{a0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><mo>=</mo><mo>−</mo><mn>3</mn><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub><mo>−</mo><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>g</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\dot{V}_{a0} = -3\dot{I}_{a0}\overline{z}_n - \dot{I}_{a0}\overline{z}_{g0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord">−</span><span class="mord">3</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.206298em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">g</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span></div><p>A rede de sequência zero, que é um circuito monofásico pelo qual se supõe que circule apenas corrente de sequência zero e deve, portanto, ter uma impedância definida pela seguinte equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mn>0</mn></msub><mo>=</mo><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub><mo>+</mo><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>g</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\overline{z}_{0} = 3\overline{z}_n + \overline{z}_{g0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.79444em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.916668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">g</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Caso o gerador não seja aterrado, não circulará corrente de sequência zero por ele. Nesse caso, dependendo da conexão do transformador próximo ao gerador sem aterramento, a seguinte mensagem de erro pode ser exibida:</p><p><center>&quot;<i>Falha ao inverter a matriz admitância de sequência zero</i>&quot;</center></p><p>Isso ocorre porque a matriz admitância de sequência zero é singular. Para contornar esse problema escolha <strong>uma</strong> das duas soluções abaixo:</p><ol><li>Marque a opção &quot;Neutro aterrado&quot; e insira um alto valor de reatância de aterramento (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mn>9999</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">j9999~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, por exemplo);</li><li><strong>Ou</strong>, na barra do gerador, insira um <a href="/PSP/docs/inductor">reator</a> de baixo valor de potência reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>0</mn><mtext> </mtext><mi>v</mi><mi>a</mi><mi>r</mi></mrow><annotation encoding="application/x-tex">1,0~var</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault" style="margin-right:0.03588em">v</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>, por exemplo).</li></ol></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="gerador-síncrono-no-estudo-de-estabilidade"></a>Gerador Síncrono no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>A relação de valores observados em testes adequados (definidos na <a href="https://doi.org/10.1109/IEEESTD.2020.9050934">IEEE Std. 115-2019</a>), denominados parâmetros padrões, são utilizados para modelar a máquina síncrona no estudo de estabilidade do PSP-UFU.</p><p>Os parâmetros da máquina síncrona que influenciam rapidamente no decaimento de valores são chamados <strong>subtransitórios</strong> (indicados por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup></mrow><annotation encoding="application/x-tex">&#x27;&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>), aqueles que influenciam mais lentamente são chamados <strong>transitórios</strong> (indicados por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>) e, finalmente, aqueles que influenciam continuamente são chamados de parâmetros <strong>síncronos</strong> (sem indicação de sobrescrito).</p><p>Um conjunto de equações algébrico-diferenciais determinam o comportamento da máquina síncrona no estudo de estabilidade:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msub><mi>V</mi><mi>q</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>I</mi><mi>d</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msub><mi>V</mi><mi>d</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>I</mi><mi>q</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo>−</mo><msub><mi>V</mi><mi>q</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mi>I</mi><mi>d</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo>−</mo><msub><mi>V</mi><mi>d</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mi>I</mi><mi>q</mi><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>V</mi><mrow><mi>f</mi><mi>d</mi></mrow></msub><mo>+</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>d</mi><mn>0</mn></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msub><mi>s</mi><mi>q</mi></msub><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>q</mi><mn>0</mn></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msubsup><mi>x</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>d</mi><mn>0</mn></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msubsup><mi>x</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>q</mi><mn>0</mn></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mfrac><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>ω</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><msub><mi>ω</mi><mi>r</mi></msub><mrow><mn>2</mn><mi>H</mi></mrow></mfrac><mrow><mo fence="true">[</mo><msub><mi>P</mi><mi>m</mi></msub><mo>−</mo><msub><mi>P</mi><mi>e</mi></msub><mo>−</mo><msub><mi>D</mi><mi>a</mi></msub><mrow><mo fence="true">(</mo><mi>ω</mi><mo>−</mo><msub><mi>ω</mi><mi>r</mi></msub><mo fence="true">)</mo></mrow><mo fence="true">]</mo></mrow><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>δ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mrow><mo fence="true">(</mo><mi>ω</mi><mo>−</mo><msub><mi>ω</mi><mi>r</mi></msub><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">E_{q}&#x27; - V_q = r_aI_q - x_{ds}&#x27;Id\\ E_{d}&#x27; - V_d = r_aI_d - x_{qs}&#x27;Iq\\ E_{q}&#x27;&#x27; - V_q = r_aI_q - x_{ds}&#x27;&#x27;Id\\ E_{d}&#x27;&#x27; - V_d = r_aI_d - x_{qs}&#x27;&#x27;Iq\\ ~\\ \frac{dE_{q}&#x27;}{dt} = \frac{V_{fd} + \left( x_d - x_{d}&#x27; \right)I_d - s_d E_{q}&#x27;}{T_{d0}&#x27;}\\ \frac{dE_{d}&#x27;}{dt} = \frac{- \left( x_q - x_{q}&#x27; \right)I_q - s_q E_{d}&#x27;}{T_{q0}&#x27;}\\ \frac{dE_{q}&#x27;&#x27;}{dt} = \frac{s_dE_{q}&#x27; + \left( x_{d}&#x27; - x_{d}&#x27;&#x27; \right)I_d - s_d E_{q}&#x27;&#x27;}{T_{d0}&#x27;&#x27;}\\ \frac{dE_{d}&#x27;&#x27;}{dt} = \frac{s_dE_{d}&#x27; + \left( x_{q}&#x27; - x_{q}&#x27;&#x27; \right)I_q - s_d E_{d}&#x27;&#x27;}{T_{q0}&#x27;&#x27;}\\ ~\\ \frac{d\omega}{dt} = \frac{\omega_r}{2H} \left[ P_m - P_e - D_a \left( \omega - \omega_r \right) \right]\\ \frac{d\delta}{dt} = \Omega_b\left( \omega - \omega_r \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault">d</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault" style="margin-right:0.03588em">q</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault">d</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault" style="margin-right:0.03588em">q</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.211em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.512308em;vertical-align:-0.9873080000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.398692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30130799999999996em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9873080000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.7115240000000003em;vertical-align:-1.088416em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231080000000002em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.4336920000000006em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4024159999999999em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">−</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.088416em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.211em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.512308em;vertical-align:-0.9873080000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.398692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30130799999999996em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9873080000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.7115240000000003em;vertical-align:-1.088416em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231080000000002em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.4336920000000006em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4024159999999999em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.088416em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.7935599999999998em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">[</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mclose delimcenter" style="top:0em">]</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault" style="margin-right:0.03785em">δ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span></span></div><p>As duas últimas equações diferenciais são as equações mecânicas da máquina; e as demais são equações elétricas (consulte essa <a href="https://dx.doi.org/10.14393/ufu.te.2019.2444">tese</a> para maiores detalhes acerca dos parâmetros dessas equações).</p><p>Utilizando as equações transitórias e subtransitórias podem-se definir cinco modelos de distintas complexidades.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O modelo da máquina síncrona é <strong>selecionado automaticamente</strong> de acordo com os dados fornecidos ao programa.</p></div></div><p>Na sequência são apresentados tais modelos, incluídos os efeitos da saturação magnética, em conjunto com seus diagramas de blocos:</p><ul><li><strong>Modelo 1</strong>: Corresponde a uma tensão constante atrás de uma reatância transitória de eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">x_{d}&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.035em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span>), não exigindo equações diferenciais;</li><li><strong>Modelo 2</strong>: São representados os efeitos transitórios de eixo direto, sendo necessária a solução de uma equação diferencial (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model2SyncGenerator.svg" alt="Diagrama de blocos do Modelo 2 das máquinas síncronas" title="Diagrama de blocos do Modelo 2 das máquinas síncronas"></center></div><ul><li><strong>Modelo 3</strong>: São representados os efeitos transitórios de eixo direto e em quadratura, exigindo duas equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model3SyncGenerator.svg" alt="Diagrama de blocos do Modelo 3 das máquinas síncronas" title="Diagrama de blocos do Modelo 3 das máquinas síncronas"></center></div><ul><li><strong>Modelo 4</strong>: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de três equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model4SyncGenerator.svg" alt="Diagrama de blocos do Modelo 4 das máquinas síncronas" title="Diagrama de blocos do Modelo 4 das máquinas síncronas"></center></div><ul><li><strong>Modelo 5</strong>: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de quatro equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model5SyncGenerator.svg" alt="Diagrama de blocos do Modelo 4 das máquinas síncronas" title="Diagrama de blocos do Modelo 4 das máquinas síncronas"></center></div><div class="admonition admonition-note alert alert--secondary"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M6.3 5.69a.942.942 0 0 1-.28-.7c0-.28.09-.52.28-.7.19-.18.42-.28.7-.28.28 0 .52.09.7.28.18.19.28.42.28.7 0 .28-.09.52-.28.7a1 1 0 0 1-.7.3c-.28 0-.52-.11-.7-.3zM8 7.99c-.02-.25-.11-.48-.31-.69-.2-.19-.42-.3-.69-.31H6c-.27.02-.48.13-.69.31-.2.2-.3.44-.31.69h1v3c.02.27.11.5.31.69.2.2.42.31.69.31h1c.27 0 .48-.11.69-.31.2-.19.3-.42.31-.69H8V7.98v.01zM7 2.3c-3.14 0-5.7 2.54-5.7 5.68 0 3.14 2.56 5.7 5.7 5.7s5.7-2.55 5.7-5.7c0-3.15-2.56-5.69-5.7-5.69v.01zM7 .98c3.86 0 7 3.14 7 7s-3.14 7-7 7-7-3.12-7-7 3.14-7 7-7z"></path></svg></span>Nota</h5></div><div class="admonition-content"><p>Em todos os modelos as equações diferenciais mecânicas são solucionadas.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="saturação"></a>Saturação<a aria-hidden="true" tabindex="-1" class="hash-link" href="#saturação" title="Direct link to heading">#</a></h4><p>Para representar matematicamente o efeito da saturação nas equações das máquinas síncronas são introduzidos “fatores de saturação” que modificam as impedâncias do circuito equivalente, os quais dependem de uma reatância de dispersão efetiva, chamada de reatância de Potier (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">x_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>).</p><p>Tal reatância pode ser obtida por meio de ensaios (utilizando curvas de saturação de circuito aberto e carga de fator de potência zero) ou estimadas de forma aproximada por outros parâmetros da máquina. A reatância de dispersão (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>l</mi></msub></mrow><annotation encoding="application/x-tex">x_l</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), aqui substituída de forma aproximada por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">x_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>, representa a parcela da reatância da máquina originados do fluxo magnético que percorrem o ar na maioria de seu caminho e, portanto, é independente da saturação.</p><p>O método implementado no programa permite reproduzir a saturação em ambos os eixos (direto e em quadratura), diferindo entre si devido à divergência no tamanho do entreferro. É assumido que a soma vetorial das duas componentes do fluxo magnético saturado está em fase com a f.m.m. e proporcional à Tensão de Potier (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>E</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">E_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>, a qual é a tensão atrás da reatância de Potier).</p><p>Para isso, são utilizados internamente dois fatores de saturação, sendo um no eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>s</mi><mi>d</mi></msub></mrow><annotation encoding="application/x-tex">s_d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) e outro no eixo em quadratura (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>s</mi><mi>q</mi></msub></mrow><annotation encoding="application/x-tex">s_q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>). Esses fatores de saturação são <strong>automaticamente calculados</strong> a cada passo de integração e dependem da curva de saturação da máquina definida pelo <a href="/PSP/docs/syncGenerator#fator-de-satura%C3%A7%C3%A3o">fator de saturação inserido no formulário de edição de dados</a>.</p><p>Portanto as reatâncias saturadas, que devem ser inseridas nas equações algébricas da máquina, são definidas pelas seguintes equações:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>d</mi></msub><mo>−</mo><msub><mi>x</mi><mi>p</mi></msub></mrow><mrow><msub><mi>s</mi><mi>d</mi></msub><mo>+</mo><msub><mi>x</mi><mi>p</mi></msub></mrow></mfrac><mspace linebreak="newline"></mspace><msub><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>q</mi></msub><mo>−</mo><msub><mi>x</mi><mi>p</mi></msub></mrow><mrow><msub><mi>s</mi><mi>q</mi></msub><mo>+</mo><msub><mi>x</mi><mi>p</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_{ds}=\frac{x_d-x_p}{s_d +x_p}\\ x_{qs}=\frac{x_q-x_p}{s_q +x_p}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.232438em;vertical-align:-0.972108em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.972108em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.232438em;vertical-align:-0.972108em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.972108em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Essas equações também são utilizadas para as reatâncias transitórias e subtransitórias, visto que o valor da reatância de Potier (ou de dispersão) não é alterada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="barramento-infinito"></a>Barramento infinito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barramento-infinito" title="Direct link to heading">#</a></h4><p>Algumas referências incluem um modelo sem equações diferenciais, em que a máquina é somente representada por uma tensão constante atrás de uma reatância transitória de eixo direto. Tal é utilizado na representação de um <strong>barramento infinito</strong>, o qual é normalmente constituído de um subsistema muito maior àquele simulado.</p><p>No PSP-UFU a <strong>representação de um barramento infinito</strong> pode ser obtido por meio da utilização de uma máquina representada pelo Modelo 1 cujo valor da constante de inércia (H) é infinito ou muito grande (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9999</mn><mtext> </mtext><mi>s</mi></mrow><annotation encoding="application/x-tex">9999~s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord mathdefault">s</span></span></span></span></span>, por exemplo) em relação às demais máquinas do sistema, e o valor de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">x_{d}&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.035em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span> deve ser um valor muito pequeno (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">10^{-3}~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.008548em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">3</span></span></span></span></span></span></span></span></span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, por exemplo).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="centro-de-inércia"></a>Centro de inércia<a aria-hidden="true" tabindex="-1" class="hash-link" href="#centro-de-inércia" title="Direct link to heading">#</a></h4><p>Normalmente utiliza-se a velocidade de referência como sendo a síncrona e portanto, nesse caso, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ω</mi><mi>r</mi></msub><mo>=</mo><msub><mi>ω</mi><mi>b</mi></msub><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>0</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">\omega_r = \omega_b = 1,0~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> Essa abordagem, adotada por vários livros de estabilidade, considera como referência uma máquina fictícia girando sempre na velocidade síncrona independente das perturbações aplicadas no sistema. No PSP-UFU foi implementado o conceito de centro de inércia (COI, do inglês, <em>Center of Inertia</em>), que constitui uma soma ponderada das velocidades das máquinas presentes no sistema:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ω</mi><mi>r</mi></msub><mo>=</mo><mfrac><mrow><mo fence="true">(</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>H</mi><mi>i</mi></msub><msub><mi>ω</mi><mi>i</mi></msub><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>H</mi><mi>i</mi></msub><mo fence="true">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\omega_r=\frac{\left( \sum_{i=1}^{n} H_i \omega_i \right)}{\left( \sum_{i=1}^{n} H_i \right)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.488004em;vertical-align:-0.994002em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.494002em"><span style="top:-2.305708em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6897100000000003em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994002em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:
+<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">n</span></span></span></span></span>	é o número de máquinas síncronas <strong>conectadas</strong> no sistema.</p><p>A aplicação do COI resulta em dados de saída, como o ângulo do rotor, mais fáceis de serem analisados. Na implementação realizada no programa a utilização ou não desse recurso é opcional e pode ser <a href="/PSP/docs/simulationConfig">definida pelo usuário</a>.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-geradores-síncronos"></a>Formulário de edição dos geradores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-geradores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos geradores síncronos:</p><div><center><img src="/PSP/images/syncGeneratorForm.png" alt="Formulário dos geradores síncronos no PSP-UFU" title="Formulário dos geradores síncronos no PSP-UFU"></center></div><p>Um segundo pelos dados de estabilidade, como mostra a figura abaixo, acessado ao clicar no botão &quot;Estabilidade&quot; do formulário principal. Nele é possível também acessar aos controles das máquinas síncronas manipulados pelo <a href="/PSP/docs/controlEditor">editor de controle</a>.</p><div><center><img src="/PSP/images/syncGeneratorStabForm.png" alt="Formulário de estabilidade dos geradores síncronos no PSP-UFU" title="Formulário de estabilidade dos geradores síncronos no PSP-UFU"></center></div><p>No formulário de estabilidade pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do gerador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/syncGeneratorSw.png" alt="Formulário de chaveamento do gerador síncrono" title="Formulário de chaveamento do gerador síncrono"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_3zTA tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Falta</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Botão Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Botão Chaveamento</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do gerador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador.</p><p>Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso mais de um gerador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potências-reativas-máxima-e-mínima"></a>Potências reativas máxima e mínima<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-reativas-máxima-e-mínima" title="Direct link to heading">#</a></h4><p>Limites de potência reativa máxima e mínima do gerador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="acesso-aos-controles-da-máquina-síncrona"></a>Acesso aos controles da máquina síncrona<a aria-hidden="true" tabindex="-1" class="hash-link" href="#acesso-aos-controles-da-máquina-síncrona" title="Direct link to heading">#</a></h2><p>Como já <a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">mencionado anteriormente</a>, os reguladores de velocidade e tensão da máquina síncrona podem ser acionados ou inibidos por meio das caixas de seleção &quot;<a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">Utilizar AVR e regulador de velocidade</a>&quot;. Ambas as opções irão acessar o <a href="/PSP/docs/controlEditor">editor de controles</a>.</p><p>O acesso aos controles do <strong>AVR</strong> poderão então ser criados e manipulados ao clicar no botão &quot;Editar AVR&quot;, assim como o <strong>Regulador de Velocidade</strong> é acessado no botão &quot;Editar regulador de velocidade&quot;.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>No PSP-UFU a opção de editar o <strong>AVR</strong> engloba mais que somente o controle de tensão da máquina. Nele <strong>deve</strong> ser inserida a malha de controle da máquina assim como a <strong>excitatriz da máquina síncrona</strong>. Outras estratégias de controle (opcionais), como PSS (<em>Power System Stabilizer</em>) e/ou controles de sobre e sub excitação, são também implementadas em conjunto.</p></div></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Assim como no AVR, o <strong>Regulador de Velocidade</strong> engloba mais que a regulação primária da máquina. Nessa opção <strong>deve</strong> ser inserida ao menos a malha de controle da regulação primária de velocidade, assim como o <strong>modelo da turbina</strong>. Estratégias opcionais de controle da velocidade também são inseridas nessa opção.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: <a href="https://doi.org/10.1007/978-3-642-13669-6" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/978-3-642-13669-6</a></li><li>ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley &amp; Sons, New York, 2001. doi: <a href="https://doi.org/10.1002/9781118878286" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/9781118878286</a></li><li>KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994.</li><li>DOMMEL, H. W.; SATO, N. Fast Transient Stability Solutions. IEEE Transactions on Power Aparatus and Systems, v. PAS-91, n. 4, jul 1972, p. 1643-1650. doi: <a href="https://doi.org/10.1109/TPAS.1972.293341">https://doi.org/10.1109/TPAS.1972.293341</a></li><li>IEEE Std 1110-2002 IEEE Guide for Synchronous Generator Modeling Practices and Applications in Power System Stability Analyses. IEEE, New York, nov. 2003. doi: <a href="https://doi.org/10.1109/IEEESTD.2003.94408">https://doi.org/10.1109/IEEESTD.2003.94408</a></li><li>KIMBARK, E. W. Power System Stability: Volume III – Synchronous Machine. New York: Wiley-IEEE Press, 1995.</li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/syncGenerator.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/harmSource"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Fonte de Corrente Harmônica</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/syncMotor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Compensador Síncrono »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#gerador-síncrono-no-psp-ufu" class="table-of-contents__link">Gerador Síncrono no PSP-UFU</a><ul><li><a href="#gerador-síncrono-no-fluxo-de-carga" class="table-of-contents__link">Gerador Síncrono no fluxo de carga</a></li><li><a href="#gerador-síncrono-no-estudo-de-curto-circuito" class="table-of-contents__link">Gerador Síncrono no estudo de curto-circuito</a></li><li><a href="#gerador-síncrono-no-estudo-de-estabilidade" class="table-of-contents__link">Gerador Síncrono no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-dos-geradores-síncronos" class="table-of-contents__link">Formulário de edição dos geradores síncronos</a></li><li><a href="#acesso-aos-controles-da-máquina-síncrona" class="table-of-contents__link">Acesso aos controles da máquina síncrona</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Compensador Síncrono</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina síncrona operando sem carga mecânica e fornecendo ou absorvendo energia reativa. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-34-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="compensador-síncrono-no-psp-ufu"></a>Compensador Síncrono no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#compensador-síncrono-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O compensador síncrono nada mais é que um motor síncrono operando sem carga em seu eixo com o intuito de fornecer ou absorver potência reativa na rede. Em relação ao <a href="/PSP/docs/powerFlow">fluxo de carga</a>, no PSP-UFU esse elemento tem comportamento idêntico ao <a href="/PSP/docs/syncGenerator">gerador síncrono</a>, porém a sua potência ativa é inserida nos algoritmos de solução com sinal negativo.</p><p>Sua parametrização para o estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>, <a href="/PSP/docs/fault">falta</a> e <a href="/PSP/docs/harmonics">harmônicos</a> é idêntica ao <a href="/PSP/docs/syncGenerator">gerador síncrono</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O compensador síncrono <strong>não foi implementado no estudo de <a href="/PSP/docs/stability">estabilidade</a></strong> e sua presença no circuito pode causar erros durante os cálculos.</p><p>Não inclua esse elemento para os estudos de <a href="/PSP/docs/stability">estabilidade</a>. Versões futuras do PSP-UFU irão contemplar esse elemento para esse estudo.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>É possível utilizar um <a href="/PSP/docs/syncGenerator">gerador síncrono</a> com potência ativa <em>nula</em> ou <em>negativa</em> para representar o compensador síncrono nos estudos de <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-compensadores-síncronos"></a>Formulário de edição dos compensadores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-compensadores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos compensadores síncronos:</p><div><center><img src="/PSP/images/syncMotorForm.png" alt="Formulário dos compensadores síncronos no PSP-UFU" title="Formulário dos compensadores síncronos no PSP-UFU"></center></div><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="geral"></a>Geral<a aria-hidden="true" tabindex="-1" class="hash-link" href="#geral" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do compensador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do compensador.</p><p>Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso mais de um compensador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potências-reativas-máxima-e-mínima"></a>Potências reativas máxima e mínima<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-reativas-máxima-e-mínima" title="Direct link to heading">#</a></h4><p>Limites de potência reativa máxima e mínima do compensador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do compensador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="falta"></a>Falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#falta" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="impedâncias-de-sequência"></a>Impedâncias de sequência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#impedâncias-de-sequência" title="Direct link to heading">#</a></h4><p>Valores de resistência e reatância para cálculo das correntes de falta. São inseridos dados de sequência positiva, negativa e zero.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="impedância-de-aterramento"></a>Impedância de aterramento<a aria-hidden="true" tabindex="-1" class="hash-link" href="#impedância-de-aterramento" title="Direct link to heading">#</a></h4><p>Valores utilizados para o cálculo das correntes de falta do tipo fase-terra e fase-fase-terra. Caso o neutro do gerador não seja aterrado, o valor inserido nesse campo é ignorado.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="neutro-aterrado"></a>Neutro aterrado<a aria-hidden="true" tabindex="-1" class="hash-link" href="#neutro-aterrado" title="Direct link to heading">#</a></h4><p>Indica se o neutro do gerador é aterrado.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/syncMotor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/syncGenerator"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Gerador Síncrono</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/indMotor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Motor de Indução »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#compensador-síncrono-no-psp-ufu" class="table-of-contents__link">Compensador Síncrono no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-compensadores-síncronos" class="table-of-contents__link">Formulário de edição dos compensadores síncronos</a><ul><li><a href="#geral" class="table-of-contents__link">Geral</a></li><li><a href="#falta" class="table-of-contents__link">Falta</a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Compensador Síncrono</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina síncrona operando sem carga mecânica e fornecendo ou absorvendo energia reativa. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-34-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="compensador-síncrono-no-psp-ufu"></a>Compensador Síncrono no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#compensador-síncrono-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O compensador síncrono nada mais é que um motor síncrono operando sem carga em seu eixo com o intuito de fornecer ou absorver potência reativa na rede. Em relação ao <a href="/PSP/docs/powerFlow">fluxo de carga</a>, no PSP-UFU esse elemento tem comportamento idêntico ao <a href="/PSP/docs/syncGenerator">gerador síncrono</a>, porém a sua potência ativa é inserida nos algoritmos de solução com sinal negativo.</p><p>Sua parametrização para o estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>, <a href="/PSP/docs/fault">falta</a> e <a href="/PSP/docs/harmonics">harmônicos</a> é idêntica ao <a href="/PSP/docs/syncGenerator">gerador síncrono</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O compensador síncrono <strong>não foi implementado no estudo de <a href="/PSP/docs/stability">estabilidade</a></strong> e sua presença no circuito pode causar erros durante os cálculos.</p><p>Não inclua esse elemento para os estudos de <a href="/PSP/docs/stability">estabilidade</a>. Versões futuras do PSP-UFU irão contemplar esse elemento para esse estudo.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>É possível utilizar um <a href="/PSP/docs/syncGenerator">gerador síncrono</a> com potência ativa <em>nula</em> ou <em>negativa</em> para representar o compensador síncrono nos estudos de <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-compensadores-síncronos"></a>Formulário de edição dos compensadores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-compensadores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos compensadores síncronos:</p><div><center><img src="/PSP/images/syncMotorForm.png" alt="Formulário dos compensadores síncronos no PSP-UFU" title="Formulário dos compensadores síncronos no PSP-UFU"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_3zTA tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Falta</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do compensador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do compensador.</p><p>Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso mais de um compensador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potências-reativas-máxima-e-mínima"></a>Potências reativas máxima e mínima<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-reativas-máxima-e-mínima" title="Direct link to heading">#</a></h4><p>Limites de potência reativa máxima e mínima do compensador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do compensador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/syncMotor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/syncGenerator"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Gerador Síncrono</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/indMotor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Motor de Indução »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#compensador-síncrono-no-psp-ufu" class="table-of-contents__link">Compensador Síncrono no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-compensadores-síncronos" class="table-of-contents__link">Formulário de edição dos compensadores síncronos</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Função Transferência</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>A Função Transferência é um importante bloco elementar e essencial em um sistema de controle, visto que esse componente possibilita a representação de sistemas dinâmicos por meio de equações algébricas no domínio da frequência.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Nesses blocos é utilizado a letra “<strong>s</strong>” para representação no domínio da frequência, pois essa é a terminologia mais utilizada em sistemas de controle.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="função-transferência-no-psp-ufu"></a>Função Transferência no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#função-transferência-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Após a inserção da função transferência, o programa a transforma na representação em espaço de estado, visto que sua solução é sistemática tornando-a, assim, mais eficiente computacionalmente.</p><p>Dada uma função transferência genérica abaixo:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>Y</mi><mo stretchy="false">(</mo><mi mathvariant="bold">s</mi><mo stretchy="false">)</mo></mrow><mrow><mi>U</mi><mo stretchy="false">(</mo><mi mathvariant="bold">s</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>b</mi><mn>0</mn></msub><msup><mi mathvariant="bold">s</mi><mi>k</mi></msup><mo>+</mo><msub><mi>b</mi><mn>1</mn></msub><msup><mi mathvariant="bold">s</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>b</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mi mathvariant="bold">s</mi><mo>+</mo><msub><mi>b</mi><mi>k</mi></msub></mrow><mrow><msup><mi mathvariant="bold">s</mi><mi>k</mi></msup><mo>+</mo><msub><mi>a</mi><mn>1</mn></msub><msup><mi mathvariant="bold">s</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mi mathvariant="bold">s</mi><mo>+</mo><msub><mi>a</mi><mi>k</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{Y(\bold{s})}{U(\bold{s})} = \frac{b_0 \bold{s}^k + b_1 \bold{s}^{k-1} + \cdots + b_{k-1} \bold{s} + b_k}{\bold{s}^k + a_1 \bold{s}^{k-1} + \cdots + a_{k-1} \bold{s} + a_k}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em">U</span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">s</span></span><span class="mclose">)</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">s</span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.420439em;vertical-align:-0.894331em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.526108em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7751079999999999em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7751079999999999em"><span style="top:-2.989em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">s</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">s</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.894331em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>A transformação em espaço de estado na <em>forma canônica controlável</em> ficará da seguinte forma:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mn>1</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mn>2</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mi>k</mi></msub></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋱</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mi>k</mi></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>1</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>2</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mi>k</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>+</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><msub><mi>u</mi><mi>n</mi></msub><mspace linebreak="newline"></mspace><msub><mi>y</mi><mi>n</mi></msub><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mi>n</mi></msub><mo>−</mo><msub><mi>a</mi><mi>n</mi></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>−</mo><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mn>1</mn></msub><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>1</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>2</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mi>k</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>+</mo><msub><mi>b</mi><mn>0</mn></msub><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \bold{s}x_1\\ \bold{s}x_2\\ \vdots\\ \bold{s}x_{k-1}\\ \bold{s}x_k \end{bmatrix} = \begin{bmatrix} 0 &amp; 1 &amp; 0 &amp; \cdots &amp; 0\\ 0 &amp; 0 &amp; 1 &amp; \cdots &amp; 0\\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots\\ 0 &amp; 0 &amp; 0 &amp; \cdots &amp; 1\\ -a_k &amp; -a_{k-1} &amp; -a_{k-2} &amp; \cdots &amp; -a_1 \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_{k-1}\\ x_k \end{bmatrix} + \begin{bmatrix} 0\\ 0\\ \vdots\\ 0\\ 1 \end{bmatrix} u_n\\ y_n = \begin{bmatrix} \left( b_n - a_n b_0 \right) &amp; \left( b_{n-1} - a_{n-1} b_0 \right) &amp; \cdots &amp; \left( b_1 - a_1 b_0 \right) \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_k \end{bmatrix} + b_0 u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.240000000000001em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-5.04em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-3.18em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋱</span></span></span><span style="top:-1.9800000000000009em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-0.7800000000000009em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:5.459999999999999em;vertical-align:-2.4799999999999995em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner">⋯</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.953995em"><span style="top:-1.3499850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-2.4999850000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0959850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6919850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.712975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.953995em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4500349999999997em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.9799999999999995em"><span style="top:-5.8275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-4.6275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.7674999999999996em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-1.5675000000000006em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4799999999999995em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.953995em"><span style="top:-1.3499850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-2.4999850000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0959850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6919850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.712975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.953995em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4500349999999997em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>A equação diferencial matricial é resolvida pelo método <strong>Trapezoidal Implícito</strong>. Um processo iterativo é realizado até que o erro entre os cálculos se torne menor que uma tolerância pré-estipulada e caso as iterações se tornem excessivas, ultrapassando um número máximo definido pelo usuário, o processo é interrompido com erro. Com os valores do vetor de estado (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">x</span></span></span></span></span>) calculados obtém-se o valor da saída do bloco (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>).</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-de-dados-da-função-transferência"></a>Formulário de edição de dados da Função Transferência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-da-função-transferência" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados da função transferência.</p><div><center><img src="/PSP/images/transferFunctionForm.png" alt="Formulário de edição de dados da função transferência no PSP-UFU" title="Formulário de edição de dados da função transferência no PSP-UFU"></center></div><p>A função transferência é definida pelos coeficientes do numerador e denominador, <strong>separados por espaço</strong>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Os elementos não presentes são representados como coeficientes de valor zero.</p><p>Por exemplo, um parâmetro inserido igual a “<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>5</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{matrix} 1 &amp; 0{,}5 &amp; 0 &amp; 2 \end{matrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2000000000000002em;vertical-align:-0.35000000000000003em"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span></span></span></span></span></span></span>” irá gerar: “<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>s</mi><mn>3</mn></msup><mo>+</mo><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>5</mn><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">s^3+0{,}5s^2+2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.008548em;vertical-align:-0.19444em"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">2</span></span></span></span></span>”.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>OGATA, K. Modern Control Engineering. Prentice Hall Inc., New Jersey, 2004.</li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/transferFunction.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/io"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Entrada / Saída</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/sum"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Somador »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#função-transferência-no-psp-ufu" class="table-of-contents__link">Função Transferência no PSP-UFU</a></li><li><a href="#formulário-de-edição-de-dados-da-função-transferência" class="table-of-contents__link">Formulário de edição de dados da Função Transferência</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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Corrente Harmônica</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul></li><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#!">Editor de Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/controlEditor">Editor de Controle</a></li><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#!" tabindex="0">Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/io">Entrada / Saída</a></li><li class="menu__list-item"><a aria-current="page" 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Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Função Transferência</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>A Função Transferência é um importante bloco elementar e essencial em um sistema de controle, visto que esse componente possibilita a representação de sistemas dinâmicos por meio de equações algébricas no domínio da frequência.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Nesses blocos é utilizado a letra “<strong>s</strong>” para representação no domínio da frequência, pois essa é a terminologia mais utilizada em sistemas de controle.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="função-transferência-no-psp-ufu"></a>Função Transferência no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#função-transferência-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Após a inserção da função transferência, o programa a transforma na representação em espaço de estado, visto que sua solução é sistemática tornando-a, assim, mais eficiente computacionalmente.</p><p>Dada uma função transferência genérica abaixo:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>Y</mi><mo stretchy="false">(</mo><mi mathvariant="bold">s</mi><mo stretchy="false">)</mo></mrow><mrow><mi>U</mi><mo stretchy="false">(</mo><mi mathvariant="bold">s</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>b</mi><mn>0</mn></msub><msup><mi mathvariant="bold">s</mi><mi>k</mi></msup><mo>+</mo><msub><mi>b</mi><mn>1</mn></msub><msup><mi mathvariant="bold">s</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>b</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mi mathvariant="bold">s</mi><mo>+</mo><msub><mi>b</mi><mi>k</mi></msub></mrow><mrow><msup><mi mathvariant="bold">s</mi><mi>k</mi></msup><mo>+</mo><msub><mi>a</mi><mn>1</mn></msub><msup><mi mathvariant="bold">s</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mi mathvariant="bold">s</mi><mo>+</mo><msub><mi>a</mi><mi>k</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{Y(\bold{s})}{U(\bold{s})} = \frac{b_0 \bold{s}^k + b_1 \bold{s}^{k-1} + \cdots + b_{k-1} \bold{s} + b_k}{\bold{s}^k + a_1 \bold{s}^{k-1} + \cdots + a_{k-1} \bold{s} + a_k}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em">U</span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">s</span></span><span class="mclose">)</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">s</span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.420439em;vertical-align:-0.894331em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.526108em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7751079999999999em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7751079999999999em"><span style="top:-2.989em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">s</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">s</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.894331em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>A transformação em espaço de estado na <em>forma canônica controlável</em> ficará da seguinte forma:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mn>1</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mn>2</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mi>k</mi></msub></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋱</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mi>k</mi></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>1</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>2</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mi>k</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>+</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><msub><mi>u</mi><mi>n</mi></msub><mspace linebreak="newline"></mspace><msub><mi>y</mi><mi>n</mi></msub><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mi>n</mi></msub><mo>−</mo><msub><mi>a</mi><mi>n</mi></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>−</mo><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mn>1</mn></msub><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>1</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>2</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mi>k</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>+</mo><msub><mi>b</mi><mn>0</mn></msub><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \bold{s}x_1\\ \bold{s}x_2\\ \vdots\\ \bold{s}x_{k-1}\\ \bold{s}x_k \end{bmatrix} = \begin{bmatrix} 0 &amp; 1 &amp; 0 &amp; \cdots &amp; 0\\ 0 &amp; 0 &amp; 1 &amp; \cdots &amp; 0\\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots\\ 0 &amp; 0 &amp; 0 &amp; \cdots &amp; 1\\ -a_k &amp; -a_{k-1} &amp; -a_{k-2} &amp; \cdots &amp; -a_1 \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_{k-1}\\ x_k \end{bmatrix} + \begin{bmatrix} 0\\ 0\\ \vdots\\ 0\\ 1 \end{bmatrix} u_n\\ y_n = \begin{bmatrix} \left( b_n - a_n b_0 \right) &amp; \left( b_{n-1} - a_{n-1} b_0 \right) &amp; \cdots &amp; \left( b_1 - a_1 b_0 \right) \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_k \end{bmatrix} + b_0 u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.240000000000001em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-5.04em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-3.18em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋱</span></span></span><span style="top:-1.9800000000000009em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-0.7800000000000009em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:5.459999999999999em;vertical-align:-2.4799999999999995em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner">⋯</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.953995em"><span style="top:-1.3499850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-2.4999850000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0959850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6919850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.712975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.953995em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4500349999999997em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.9799999999999995em"><span style="top:-5.8275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-4.6275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.7674999999999996em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-1.5675000000000006em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4799999999999995em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.953995em"><span style="top:-1.3499850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-2.4999850000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0959850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6919850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.712975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.953995em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4500349999999997em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>A equação diferencial matricial é resolvida pelo método <strong>Trapezoidal Implícito</strong>. Um processo iterativo é realizado até que o erro entre os cálculos se torne menor que uma tolerância pré-estipulada e caso as iterações se tornem excessivas, ultrapassando um número máximo definido pelo usuário, o processo é interrompido com erro. Com os valores do vetor de estado (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">x</span></span></span></span></span>) calculados obtém-se o valor da saída do bloco (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>).</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-de-dados-da-função-transferência"></a>Formulário de edição de dados da Função Transferência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-da-função-transferência" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados da função transferência.</p><div><center><img src="/PSP/images/transferFunctionForm.png" alt="Formulário de edição de dados da função transferência no PSP-UFU" title="Formulário de edição de dados da função transferência no PSP-UFU"></center></div><p>A função transferência é definida pelos coeficientes do numerador e denominador, <strong>separados por espaço</strong>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Os elementos não presentes são representados como coeficientes de valor zero.</p><p>Por exemplo, um parâmetro inserido igual a “<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>5</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{matrix} 1 &amp; 0{,}5 &amp; 0 &amp; 2 \end{matrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2000000000000002em;vertical-align:-0.35000000000000003em"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span></span></span></span></span></span></span>” irá gerar: “<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>s</mi><mn>3</mn></msup><mo>+</mo><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>5</mn><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">s^3+0{,}5s^2+2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.008548em;vertical-align:-0.19444em"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">2</span></span></span></span></span>”.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>OGATA, K. Modern Control Engineering. Prentice Hall Inc., New Jersey, 2004.</li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/transferFunction.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/io"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Entrada / Saída</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/sum"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Somador »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#função-transferência-no-psp-ufu" class="table-of-contents__link">Função Transferência no PSP-UFU</a></li><li><a href="#formulário-de-edição-de-dados-da-função-transferência" class="table-of-contents__link">Formulário de edição de dados da Função Transferência</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Transformador</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Aparelho estático com dois ou mais enrolamentos que, por indução eletromagnética, transforma um sistema de tensão e corrente alternada em outro sistema de tensão e corrente geralmente de valores diferentes e na mesma frequência com o objetivo de transmitir energia elétrica. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=421-01-01" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="transformador-no-psp-ufu"></a>Transformador no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#transformador-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Transformadores com quaisquer conexões e defasagens entre as tensões primárias e secundárias podem ser inseridos no PSP-UFU. Para isso, os transformadores devem ser modelados representando seu tape (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em"></span><span class="mord mathdefault">t</span></span></span></span></span>) e defasagem (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">ϕ</span></span></span></span></span>), utilizando um transformador ideal de relação de transformação <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>:</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\overline{t}:1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.81508em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> em série com sua impedância (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mo>=</mo><msub><mi>r</mi><mi>T</mi></msub><mo>+</mo><mi>j</mi><msub><mi>x</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">\overline{y}_T = r_T + jx_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8747em;vertical-align:-0.24414em"></span><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), em que <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.81508em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span></span> é um número complexo (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mi mathvariant="normal">∠</mi><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">t\angle\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">t</span><span class="mord">∠</span><span class="mord mathdefault">ϕ</span></span></span></span></span>)</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O modelo utilizado no PSP-UFU <strong>não considera</strong> o ramo magnetizante ou impedâncias mútuas entre as fases.</p></div></div><p>A figura abaixo mostra o modelo do transformador implementado no PSP-UFU:</p><div><center><img src="/PSP/images/transformerModel.svg" alt="Modelo PI da linha" title="Modelo PI da linha"></center></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">r</mi><mi mathvariant="bold">T</mi></msub></mrow><annotation encoding="application/x-tex">\bold{r_T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a resistência total do transformador;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">x</mi><mi mathvariant="bold">T</mi></msub></mrow><annotation encoding="application/x-tex">\bold{x_T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a reatância indutiva total do transformador;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi mathvariant="bold">t</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\bold{\overline{t}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8349200000000001em;vertical-align:0em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8349200000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathbf">t</span></span></span><span style="top:-3.7549200000000003em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span></span></span>	é a o tape complexo do transformador.</li></ul><p>A relação entre as tensões e correntes das barras genéricas <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span></span></span></span></span> é obtida pela equação matricial:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>j</mi><mi>i</mi></mrow></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mi>t</mi><mn>2</mn></msup></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>∗</mo></msup></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mfrac></mstyle></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>×</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>i</mi></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>j</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \dot{I}_{ij}\\ \dot{I}_{ji} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} &amp; -\displaystyle \frac{\overline{y}_T}{\overline{t}^*}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}} &amp; \overline{y}_T \end{bmatrix} \times \begin{bmatrix} \dot{V}_{i}\\ \dot{V}_{j} \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.5603800000000003em;vertical-align:-1.0301900000000004em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.53019em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3298099999999997em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0301900000000004em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.202030000000001em;vertical-align:-1.850025em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000007em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2107020000000004em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.29492em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.70508em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019379999999998em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000007em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.216324em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.893676em"><span style="top:-3.26798em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.783676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2107020000000004em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019379999999998em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.5603800000000003em;vertical-align:-1.0301900000000004em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.53019em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3298099999999997em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0301900000000004em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span></span></span></span></span></div><p>Assim como nas <a href="/PSP/docs/line">linhas</a>, o transformador de dois enrolamentos deve ser inserido entre barras, porém não há a necessidade das tensões nominais desses barramentos serem idênticas.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A primeira barra selecionada será o lado <strong>primário</strong>, o qual é indicado por um círculo. Para alterar o lado primário após a inserção basta desconectar os nós dos transformadores e reconectá-los alternando as barras, utilizando as <a href="/PSP/docs/cadTools#conex%C3%A3o-e-desconex%C3%A3o-de-elemetos-na-barra">ferramentas CAD</a>.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="transformadores-no-estudo-de-curto-circuito"></a>Transformadores no estudo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#transformadores-no-estudo-de-curto-circuito" title="Direct link to heading">#</a></h3><p>Da mesma forma que no estudo de fluxo de carga, a representação dos elementos do sistema para o estudo de curto-circuito é realizada por meio de circuitos equivalentes inseridos na matriz admitância de barras. Nas <a href="/PSP/docs/fault">faltas desbalanceadas</a> é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.</p><p>A matriz admitância de sequência positiva é construída da mesma forma que os estudos de fluxo de carga. Na sequência negativa o ângulo de defasagem entre tensões primária e secundária (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">ϕ</span></span></span></span></span>) deve ser invertido, uma vez que os fasores da sequência negativa <strong>são deslocados na direção oposta</strong>. Com isso, a matriz que representa as admitâncias da equação anterior deve ser substituída pela seguinte expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>j</mi><mi>i</mi></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>j</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mi>t</mi><mn>2</mn></msup></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>∗</mo></msup></mfrac></mstyle></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \overline{Y}_{ii} &amp; \overline{Y}_{ij}\\ \overline{Y}_{ji} &amp; \overline{Y}_{jj} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} &amp; -\displaystyle \frac{\overline{y}_T}{\overline{t}}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}^*} &amp; \overline{y}_T \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4866600000000005em;vertical-align:-0.9933300000000005em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.49333em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3666699999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9933300000000005em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.49333em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3666699999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9933300000000005em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.202030000000001em;vertical-align:-1.850025em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000003em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2892979999999996em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.216324em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.893676em"><span style="top:-3.26798em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.783676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019380000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000003em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.29492em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.70508em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2892979999999996em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019380000000003em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span></span></span></span></span></span></div><p>A impedância de sequência negativa nos transformadores deve ser tratada de maneira específica devido aos diferentes tipos de conexão. Na figura abaixo são mostrados os circuitos equivalentes para cada tipo de conexão de transformadores de dois enrolamentos. As setas indicam os caminhos possíveis para circulação da corrente de sequência zero.</p><div><center><img src="/PSP/images/seqZeroTrafo.svg" alt="Circuitos equivalentes de sequência zero dos transformadores" title="Circuitos equivalentes de sequência zero dos transformadores"></center></div><p>Para os transformadores com conexão estrela aterrado, se a ligação do neutro para a terra apresentar uma impedância <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, o circuito equivalente de sequência zero deve ter impedância de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">3\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.79444em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> em série com a resistência e reatância equivalentes do transformador.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-transformadores"></a>Formulário de edição dos transformadores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-transformadores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos transformadores:</p><div><center><img src="/PSP/images/trafoForm.png" alt="Formulário dos transformadores no PSP-UFU" title="Formulário dos transformadores no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais dos transformadores, informações do fluxo de carga, sua conexão e defasagem;</li><li><strong>Falta</strong>: local onde as impedâncias de sequência zero e impedâncias de aterramento são inseridas.</li></ul><p>Além desses dois contextos, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do transformador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/trafoSw.png" alt="Formulário de chaveamento do transformador" title="Formulário de chaveamento do transformador"></center></div><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="geral"></a>Geral<a aria-hidden="true" tabindex="-1" class="hash-link" href="#geral" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Campo de informação <em>não editável</em> que apresenta a tensão primária e secundária do transformador. Para alterar esse campo é necessário editar o campo correspondente dos <a href="/PSP/docs/bus#geral">barramento</a> conectados.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tensão-base"></a>Tensão base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-base" title="Direct link to heading">#</a></h4><p>Tensão utilizada para converter os parâmetros de impedância inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> As tensões selecionadas por uma caixa de escolha são editadas nos formulários dos <a href="/PSP/docs/bus#geral">barramentos</a> conectados.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>A tensão base é ignorada caso os dados inseridos estejam em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do transformador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="impedância-do-transformador"></a>Impedância do transformador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#impedância-do-transformador" title="Direct link to heading">#</a></h4><p>Impedância série do transformador (resistência e reatância indutiva), inserida em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span>. Caso as impedâncias sejam inseridas em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> será utilizada a tensão base selecionada para conversão para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="conexão"></a>Conexão<a aria-hidden="true" tabindex="-1" class="hash-link" href="#conexão" title="Direct link to heading">#</a></h4><p>Conexão do transformador utilizada para cálculo das correntes de sequência zero nas faltas desbalanceadas com presença de terra (fase-terra e fase-fase-terra).</p><p>As seguintes conexões estão disponíveis:</p><ol><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">Y_{aterrado}-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">Y-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y_{aterrado}-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\Delta-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">\Delta-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">Y_{aterrado}-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">Y-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">\Delta-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li></ol><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tap"></a>TAP<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tap" title="Direct link to heading">#</a></h4><p>Tape do transformador <strong>em relação ao primário</strong>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O tape no PSP-UFU deve ser inserido pela relação entre a tensão primária nominal e a tensão de tape <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mtext>TAP</mtext><mo>=</mo><mfrac><msub><mi>V</mi><mrow><mi>n</mi><mi>o</mi><mi>m</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>l</mi></mrow></msub><msub><mi>V</mi><mrow><mi>t</mi><mi>a</mi><mi>p</mi><mi>e</mi></mrow></msub></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\text{TAP} = \frac{V_{nominal}}{V_{tape}}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord text"><span class="mord">TAP</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.894191em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em"><span style="top:-2.357em;margin-left:-0.22222em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">p</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2818857142857143em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.41586em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em"><span style="top:-2.3487714285714287em;margin-left:-0.22222em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">m</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5423199999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span></span></span></span></span>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="defasagem"></a>Defasagem<a aria-hidden="true" tabindex="-1" class="hash-link" href="#defasagem" title="Direct link to heading">#</a></h4><p>Defasagem do transformador em relação ao primário, em graus. Esse valor independe do tipo de conexão, portanto para conexões diferentes de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span>(aterrado ou não) e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">\Delta-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span>, deve-se inserir o ângulo de defasagem correto.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do transformador como base para a conversão das unidades, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="falta"></a>Falta<a aria-hidden="true" tabindex="-1" class="hash-link" href="#falta" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="impedância-de-sequência-zero-do-transformador"></a>Impedância de sequência zero do transformador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#impedância-de-sequência-zero-do-transformador" title="Direct link to heading">#</a></h4><p>Esses parâmetros são necessários para o correto cálculo das correntes de <a href="/PSP/docs/fault">falta desbalanceadas</a> (fase-fase, fase-fase-terra e fase-terra) e devem ser inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>A não inserção desses dados acarretarão em resultados incorretos para <a href="/PSP/docs/fault">faltas desbalanceadas</a>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="impedâncias-de-aterramento"></a>Impedâncias de aterramento<a aria-hidden="true" tabindex="-1" class="hash-link" href="#impedâncias-de-aterramento" title="Direct link to heading">#</a></h4><p>As impedâncias de aterramento são somente utilizadas para conexão <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e devem ser inseridas em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><hr><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="botão-estabilidade"></a>Botão Estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#botão-estabilidade" title="Direct link to heading">#</a></h3><p>O botão &quot;Estabilidade&quot; irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do transformador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><p>Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões &quot;Adicionar&quot; e &quot;Remover&quot;, respectivamente.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/transformer.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/line"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Linha</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/load"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Carga »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_TbNY"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#transformador-no-psp-ufu" class="table-of-contents__link">Transformador no PSP-UFU</a><ul><li><a href="#transformadores-no-estudo-de-curto-circuito" class="table-of-contents__link">Transformadores no estudo de curto-circuito</a></li></ul></li><li><a href="#formulário-de-edição-dos-transformadores" class="table-of-contents__link">Formulário de edição dos transformadores</a><ul><li><a href="#geral" class="table-of-contents__link">Geral</a></li><li><a href="#falta" class="table-of-contents__link">Falta</a></li><li><a href="#botão-estabilidade" class="table-of-contents__link">Botão Estabilidade</a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_FFX1"><div class="container padding-vert--lg docItemWrapper_1cc7"><div class="row"><div class="col docItemCol_2GOA"><div class="docItemContainer_2cwg"><article><header><h1 class="docTitle_1vWb">Transformador</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Aparelho estático com dois ou mais enrolamentos que, por indução eletromagnética, transforma um sistema de tensão e corrente alternada em outro sistema de tensão e corrente geralmente de valores diferentes e na mesma frequência com o objetivo de transmitir energia elétrica. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=421-01-01" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="transformador-no-psp-ufu"></a>Transformador no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#transformador-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Transformadores com quaisquer conexões e defasagens entre as tensões primárias e secundárias podem ser inseridos no PSP-UFU. Para isso, os transformadores devem ser modelados representando seu tape (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em"></span><span class="mord mathdefault">t</span></span></span></span></span>) e defasagem (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">ϕ</span></span></span></span></span>), utilizando um transformador ideal de relação de transformação <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>:</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\overline{t}:1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.81508em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> em série com sua impedância (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mo>=</mo><msub><mi>r</mi><mi>T</mi></msub><mo>+</mo><mi>j</mi><msub><mi>x</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">\overline{y}_T = r_T + jx_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8747em;vertical-align:-0.24414em"></span><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), em que <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.81508em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span></span> é um número complexo (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mi mathvariant="normal">∠</mi><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">t\angle\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">t</span><span class="mord">∠</span><span class="mord mathdefault">ϕ</span></span></span></span></span>)</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O modelo utilizado no PSP-UFU <strong>não considera</strong> o ramo magnetizante ou impedâncias mútuas entre as fases.</p></div></div><p>A figura abaixo mostra o modelo do transformador implementado no PSP-UFU:</p><div><center><img src="/PSP/images/transformerModel.svg" alt="Modelo PI da linha" title="Modelo PI da linha"></center></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">r</mi><mi mathvariant="bold">T</mi></msub></mrow><annotation encoding="application/x-tex">\bold{r_T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a resistência total do transformador;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">x</mi><mi mathvariant="bold">T</mi></msub></mrow><annotation encoding="application/x-tex">\bold{x_T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a reatância indutiva total do transformador;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi mathvariant="bold">t</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\bold{\overline{t}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8349200000000001em;vertical-align:0em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8349200000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathbf">t</span></span></span><span style="top:-3.7549200000000003em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span></span></span>	é a o tape complexo do transformador.</li></ul><p>A relação entre as tensões e correntes das barras genéricas <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span></span></span></span></span> é obtida pela equação matricial:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>j</mi><mi>i</mi></mrow></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mi>t</mi><mn>2</mn></msup></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>∗</mo></msup></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mfrac></mstyle></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>×</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>i</mi></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>j</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \dot{I}_{ij}\\ \dot{I}_{ji} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} &amp; -\displaystyle \frac{\overline{y}_T}{\overline{t}^*}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}} &amp; \overline{y}_T \end{bmatrix} \times \begin{bmatrix} \dot{V}_{i}\\ \dot{V}_{j} \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.5603800000000003em;vertical-align:-1.0301900000000004em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.53019em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3298099999999997em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0301900000000004em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.202030000000001em;vertical-align:-1.850025em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000007em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2107020000000004em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.29492em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.70508em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019379999999998em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000007em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.216324em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.893676em"><span style="top:-3.26798em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.783676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2107020000000004em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019379999999998em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.5603800000000003em;vertical-align:-1.0301900000000004em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.53019em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3298099999999997em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0301900000000004em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span></span></span></span></span></div><p>Assim como nas <a href="/PSP/docs/line">linhas</a>, o transformador de dois enrolamentos deve ser inserido entre barras, porém não há a necessidade das tensões nominais desses barramentos serem idênticas.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A primeira barra selecionada será o lado <strong>primário</strong>, o qual é indicado por um círculo. Para alterar o lado primário após a inserção basta desconectar os nós dos transformadores e reconectá-los alternando as barras, utilizando as <a href="/PSP/docs/cadTools#conex%C3%A3o-e-desconex%C3%A3o-de-elemetos-na-barra">ferramentas CAD</a>.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="transformadores-no-estudo-de-curto-circuito"></a>Transformadores no estudo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#transformadores-no-estudo-de-curto-circuito" title="Direct link to heading">#</a></h3><p>Da mesma forma que no estudo de fluxo de carga, a representação dos elementos do sistema para o estudo de curto-circuito é realizada por meio de circuitos equivalentes inseridos na matriz admitância de barras. Nas <a href="/PSP/docs/fault">faltas desbalanceadas</a> é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.</p><p>A matriz admitância de sequência positiva é construída da mesma forma que os estudos de fluxo de carga. Na sequência negativa o ângulo de defasagem entre tensões primária e secundária (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">ϕ</span></span></span></span></span>) deve ser invertido, uma vez que os fasores da sequência negativa <strong>são deslocados na direção oposta</strong>. Com isso, a matriz que representa as admitâncias da equação anterior deve ser substituída pela seguinte expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>j</mi><mi>i</mi></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>j</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mi>t</mi><mn>2</mn></msup></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>∗</mo></msup></mfrac></mstyle></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \overline{Y}_{ii} &amp; \overline{Y}_{ij}\\ \overline{Y}_{ji} &amp; \overline{Y}_{jj} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} &amp; -\displaystyle \frac{\overline{y}_T}{\overline{t}}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}^*} &amp; \overline{y}_T \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4866600000000005em;vertical-align:-0.9933300000000005em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.49333em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3666699999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9933300000000005em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.49333em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3666699999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9933300000000005em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.202030000000001em;vertical-align:-1.850025em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000003em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2892979999999996em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.216324em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.893676em"><span style="top:-3.26798em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.783676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019380000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000003em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.29492em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.70508em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2892979999999996em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019380000000003em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span></span></span></span></span></span></div><p>A impedância de sequência negativa nos transformadores deve ser tratada de maneira específica devido aos diferentes tipos de conexão. Na figura abaixo são mostrados os circuitos equivalentes para cada tipo de conexão de transformadores de dois enrolamentos. As setas indicam os caminhos possíveis para circulação da corrente de sequência zero.</p><div><center><img src="/PSP/images/seqZeroTrafo.svg" alt="Circuitos equivalentes de sequência zero dos transformadores" title="Circuitos equivalentes de sequência zero dos transformadores"></center></div><p>Para os transformadores com conexão estrela aterrado, se a ligação do neutro para a terra apresentar uma impedância <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, o circuito equivalente de sequência zero deve ter impedância de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">3\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.79444em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> em série com a resistência e reatância equivalentes do transformador.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="formulário-de-edição-dos-transformadores"></a>Formulário de edição dos transformadores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-transformadores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos transformadores:</p><div><center><img src="/PSP/images/trafoForm.png" alt="Formulário dos transformadores no PSP-UFU" title="Formulário dos transformadores no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais dos transformadores, informações do fluxo de carga, sua conexão e defasagem;</li><li><strong>Falta</strong>: local onde as impedâncias de sequência zero e impedâncias de aterramento são inseridas.</li></ul><p>Além desses dois contextos, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do transformador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/trafoSw.png" alt="Formulário de chaveamento do transformador" title="Formulário de chaveamento do transformador"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_3zTA tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Falta</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_3zTA">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Campo de informação <em>não editável</em> que apresenta a tensão primária e secundária do transformador. Para alterar esse campo é necessário editar o campo correspondente dos <a href="/PSP/docs/bus#geral">barramento</a> conectados.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tensão-base"></a>Tensão base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-base" title="Direct link to heading">#</a></h4><p>Tensão utilizada para converter os parâmetros de impedância inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> As tensões selecionadas por uma caixa de escolha são editadas nos formulários dos <a href="/PSP/docs/bus#geral">barramentos</a> conectados.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>A tensão base é ignorada caso os dados inseridos estejam em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do transformador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="impedância-do-transformador"></a>Impedância do transformador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#impedância-do-transformador" title="Direct link to heading">#</a></h4><p>Impedância série do transformador (resistência e reatância indutiva), inserida em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span>. Caso as impedâncias sejam inseridas em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> será utilizada a tensão base selecionada para conversão para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="conexão"></a>Conexão<a aria-hidden="true" tabindex="-1" class="hash-link" href="#conexão" title="Direct link to heading">#</a></h4><p>Conexão do transformador utilizada para cálculo das correntes de sequência zero nas faltas desbalanceadas com presença de terra (fase-terra e fase-fase-terra).</p><p>As seguintes conexões estão disponíveis:</p><ol><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">Y_{aterrado}-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">Y-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y_{aterrado}-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\Delta-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">\Delta-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">Y_{aterrado}-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">Y-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">\Delta-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li></ol><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="tap"></a>TAP<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tap" title="Direct link to heading">#</a></h4><p>Tape do transformador <strong>em relação ao primário</strong>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O tape no PSP-UFU deve ser inserido pela relação entre a tensão primária nominal e a tensão de tape <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mtext>TAP</mtext><mo>=</mo><mfrac><msub><mi>V</mi><mrow><mi>n</mi><mi>o</mi><mi>m</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>l</mi></mrow></msub><msub><mi>V</mi><mrow><mi>t</mi><mi>a</mi><mi>p</mi><mi>e</mi></mrow></msub></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\text{TAP} = \frac{V_{nominal}}{V_{tape}}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord text"><span class="mord">TAP</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.894191em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em"><span style="top:-2.357em;margin-left:-0.22222em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">p</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2818857142857143em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.41586em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em"><span style="top:-2.3487714285714287em;margin-left:-0.22222em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">m</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5423199999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span></span></span></span></span>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="defasagem"></a>Defasagem<a aria-hidden="true" tabindex="-1" class="hash-link" href="#defasagem" title="Direct link to heading">#</a></h4><p>Defasagem do transformador em relação ao primário, em graus. Esse valor independe do tipo de conexão, portanto para conexões diferentes de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span>(aterrado ou não) e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">\Delta-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span>, deve-se inserir o ângulo de defasagem correto.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_ZqCz" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do transformador como base para a conversão das unidades, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/transformer.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog 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Um processo iterativo \xe9 realizado at\xe9 que o erro entre os c\xe1lculos se torne menor que uma toler\xe2ncia pr\xe9-estipulada e caso as itera\xe7\xf5es se tornem excessivas, ultrapassando um n\xfamero m\xe1ximo definido pelo usu\xe1rio, o processo \xe9 interrompido com erro. 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Corrente"}))),Object(m.b)("p",null,"Cargas de corrente e pot\xeancia constantes possuem problemas em tens\xf5es muito baixas. \xc0 medida que a tens\xe3o diminui as correntes dessas cargas n\xe3o reduz, como pode ser observado na figura acima, resultando em perda de precis\xe3o e problemas na converg\xeancia de processos iterativos. Para contornar esse problema utiliza-se uma tens\xe3o pr\xe9-definida pelo usu\xe1rio (",Object(m.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("msub",{parentName:"mrow"},Object(m.b)("mi",{parentName:"msub"},"V"),Object(m.b)("mrow",{parentName:"msub"},Object(m.b)("mi",{parentName:"mrow"},"l"),Object(m.b)("mi",{parentName:"mrow"},"o"),Object(m.b)("mi",{parentName:"mrow"},"w")))),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"V_{low}")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.83333em",verticalAlign:"-0.15em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.22222em"}}),"V"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"msupsub"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-t vlist-t2"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.33610799999999996em"}}),Object(m.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-2.5500000000000003em",marginLeft:"-0.22222em",marginRight:"0.05em"}}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mtight"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.01968em"}}),"l"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"o"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.02691em"}}),"w"))))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.15em"}}),Object(m.b)("span",{parentName:"span"})))))))))),"), a qual as cargas (ou parcelas) de corrente e pot\xeancia constantes s\xe3o modeladas como imped\xe2ncia constante, resultando no comportamento de pot\xeancia e corrente apresentados na figura acima."),Object(m.b)("h2",{id:"formul\xe1rio-de-edi\xe7\xe3o-das-cargas"},"Formul\xe1rio de edi\xe7\xe3o das cargas"),Object(m.b)("p",null,"A imagem abaixo apresenta o formul\xe1rio de inser\xe7\xe3o/altera\xe7\xe3o de dados das cargas:"),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(b.a)("images/loadForm.png"),alt:"Formul\xe1rio das cargas no PSP-UFU",title:"Formul\xe1rio das cargas no PSP-UFU"}))),Object(m.b)("p",null,"Esse formul\xe1rio \xe9 subdividido em dois contextos distintos:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Geral"),": no qual s\xe3o inseridas informa\xe7\xf5es gerais das cargas, informa\xe7\xf5es e o tipo de carga no fluxo de carga;"),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Estabilidade"),": contendo op\xe7\xf5es de visualiza\xe7\xe3o de dados da carga em gr\xe1ficos no tempo e op\xe7\xf5es de parametriza\xe7\xe3o da carga ZIP.")),Object(m.b)("p",null,'Al\xe9m desses dois contextos, pode ser observado o bot\xe3o "Chaveamento" na parte inferior esquerda do formul\xe1rio. Esse formul\xe1rio, comum a v\xe1rios outros elementos, permite a inser\xe7\xe3o e/ou remo\xe7\xe3o da carga durante o estudo de ',Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(b.a)("images/loadSw.png"),alt:"Formul\xe1rio de chaveamento da carga",title:"Formul\xe1rio de chaveamento da carga"}))),Object(m.b)(p.a,{groupId:"load-tabs",defaultValue:"general",values:[{label:"Geral",value:"general"},{label:"Estabilidade",value:"stability"},{label:"Bot\xe3o Chaveamento",value:"switching"}],mdxType:"Tabs"},Object(m.b)(c.a,{value:"general",mdxType:"TabItem"},Object(m.b)("h4",{id:"nome"},"Nome"),Object(m.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. 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Esse formul\xe1rio, comum a v\xe1rios outros elementos, permite a inser\xe7\xe3o e/ou remo\xe7\xe3o da carga durante o estudo de ',Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(b.a)("images/loadSw.png"),alt:"Formul\xe1rio de chaveamento da carga",title:"Formul\xe1rio de chaveamento da carga"}))),Object(m.b)("hr",null),Object(m.b)("h3",{id:"geral"},"Geral"),Object(m.b)("h4",{id:"nome"},"Nome"),Object(m.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(m.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(m.b)("h4",{id:"pot\xeancia-ativa"},"Pot\xeancia ativa"),Object(m.b)("p",null,"Parcela de pot\xeancia ativa da carga. Pode ser inserido em MW, kW W ou ",Object(m.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),".")))))," (na base do sistema)."),Object(m.b)("h4",{id:"pot\xeancia-reativa"},"Pot\xeancia reativa"),Object(m.b)("p",null,"Parcela de pot\xeancia reativa da carga. Pode ser inserido em Mvar, kvar var ou ",Object(m.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),".")))))," (na base do sistema)."),Object(m.b)("h4",{id:"tipo-de-carga-fluxo-de-carga"},"Tipo de carga (fluxo de carga)"),Object(m.b)("p",null,"Tipo da carga para o estudo de fluxo de carga, podendo ser selecionado dois tipos: Pot\xeancia constante e Imped\xe2ncia constante. As cargas de pot\xeancia constantes s\xe3o inseridas nos vetores de pot\xeancia e permanecem invariantes no c\xe1lculo, enquanto que para as cargas de imped\xe2ncia constante determina-se o valor da imped\xe2ncia utilizando a pot\xeancia e tens\xe3o nominal, a qual \xe9 inserida na matriz admit\xe2ncia."),Object(m.b)("hr",null),Object(m.b)("h3",{id:"estabilidade"},"Estabilidade"),Object(m.b)("h4",{id:"imprimir-dados"},"Imprimir dados"),Object(m.b)("p",null,"Exibe os dados da carga nos gr\xe1ficos no tempo.\nOs seguintes dados s\xe3o exibidos:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},"m\xf3dulo da tens\xe3o"),Object(m.b)("li",{parentName:"ul"},"corrente"),Object(m.b)("li",{parentName:"ul"},"pot\xeancias ativa e reativa.")),Object(m.b)("h4",{id:"utilizar-composi\xe7\xe3o-de-carga-zip"},"Utilizar composi\xe7\xe3o de carga ZIP"),Object(m.b)("p",null,"Permite compor a carga ZIP para estudos de estabilidade. Caso essa op\xe7\xe3o n\xe3o esteja selecionada \xe9 usada a composi\xe7\xe3o global definida nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),"."),Object(m.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Por padr\xe3o, todas as cargas no PSP-UFU s\xe3o definidas como imped\xe2ncia constante no estudo de estabilidade."))),Object(m.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Caso todas as barras possu\xedrem o mesmo comportamento de carga ZIP, a parametriza\xe7\xe3o poder\xe1 ser realizada nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," para todas as cargas, sem a necessidade de parametriza\xe7\xe3o individual."))),Object(m.b)("h4",{id:"composi\xe7\xe3o-de-pot\xeancia-ativa-e-reativa"},"Composi\xe7\xe3o de pot\xeancia ativa e reativa"),Object(m.b)("p",null,"Valores da composi\xe7\xe3o da carga ZIP, inseridas para pot\xeancia ativa e reativa separadamente, em porcentagem. A soma da composi\xe7\xe3o deve ser igual a 100%, caso contr\xe1rio ser\xe1 exibida uma mensagem de erro ao usu\xe1rio."),Object(m.b)("hr",null),Object(m.b)("h3",{id:"bot\xe3o-chaveamento"},"Bot\xe3o Chaveamento"),Object(m.b)("p",null,'O bot\xe3o "Chaveamento" ir\xe1 abrir um formul\xe1rio, comum a v\xe1rios outros elementos, que permite a inser\xe7\xe3o e/ou remo\xe7\xe3o do transformador durante o estudo de ',Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(m.b)("p",null,'Nesse formul\xe1rio pode ser criada uma lista gen\xe9rica de inser\xe7\xf5es e remo\xe7\xf5es da linha no tempo, personalizada por um contexto de propriedades de chaveamento que s\xe3o editados o tipo de chaveamento (inser\xe7\xe3o ou remo\xe7\xe3o) e o instante (em segundos) do evento. 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Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(n.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(n.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(n.b)("p",null,"Pot\xeancia nominal do gerador, inserida em MVA, kVA ou VA."),Object(n.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(n.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(n.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou ",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math 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Tal fator eleva o valor da resist\xeancia do rotor em condi\xe7\xf5es de grande escorregamento, como ocorre em motores de gaiola dupla ou gaiola profunda. 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Esse formul\xe1rio, comum a v\xe1rios outros elementos, permite a inser\xe7\xe3o e/ou remo\xe7\xe3o do motor durante o estudo de ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/indMotorSw.png"),alt:"Formul\xe1rio de chaveamento do motores de indu\xe7\xe3o",title:"Formul\xe1rio de chaveamento do motores de indu\xe7\xe3o"}))),Object(n.b)("hr",null),Object(n.b)("h3",{id:"geral"},"Geral"),Object(n.b)("h4",{id:"nome"},"Nome"),Object(n.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(n.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(n.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(n.b)("p",null,"Pot\xeancia nominal do gerador, inserida em MVA, kVA ou VA."),Object(n.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(n.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(n.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou ",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math 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considerado uma ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"load"}),"carga de pot\xeancia constante")," no estudo de ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow"}),"fluxo de carga"),"."),Object(n.b)("p",{parentName:"div"},"A n\xe3o utiliza\xe7\xe3o dessa op\xe7\xe3o poder\xe1 gerar erros de regime permamente no estudo de ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."))),Object(n.b)("p",null,"Utilizar pot\xeancia nominal como base\nCaso essa op\xe7\xe3o seja marcada, o programa ir\xe1 utilizar a pot\xeancia nominal do gerador como base para a convers\xe3o das unidades, inclusive aqueles no formul\xe1rio de estabilidade, caso contr\xe1rio ser\xe1 usada a pot\xeancia base do sistema."),Object(n.b)("hr",null),Object(n.b)("h3",{id:"estabilidade"},"Estabilidade"),Object(n.b)("h4",{id:"imprimir-dados-da-m\xe1quina-de-indu\xe7\xe3o"},"Imprimir dados da m\xe1quina de indu\xe7\xe3o"),Object(n.b)("p",null,"Exibe os dados do 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Tal fator eleva o valor da resist\xeancia do rotor em condi\xe7\xf5es de grande escorregamento, como ocorre em motores de gaiola dupla ou gaiola profunda. 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 <nav class="navbar navbar--light navbar--fixed-top"><div class="navbar__inner"><div class="navbar__items"><div aria-label="Navigation bar toggle" class="navbar__toggle" role="button" tabindex="0"><svg xmlns="http://www.w3.org/2000/svg" width="30" height="30" viewBox="0 0 30 30" role="img" focusable="false"><title>Menu</title><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></div><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a><a class="navbar__item navbar__link" href="/PSP/docs/">User Guide</a><a class="navbar__item navbar__link" href="/PSP/blog">Changelog</a></div><div class="navbar__items navbar__items--right"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="navbar__item navbar__link">PSP-UFU Source Code</a><div class="react-toggle react-toggle--disabled displayOnlyInLargeViewport_1gtM"><div class="react-toggle-track"><div class="react-toggle-track-check"><span class="toggle_keGJ moon_1gwN"></span></div><div class="react-toggle-track-x"><span class="toggle_keGJ sun_3CPA"></span></div></div><div class="react-toggle-thumb"></div><input type="checkbox" disabled="" aria-label="Dark mode toggle" class="react-toggle-screenreader-only"></div><div class="navbar__search"><div class="searchWrapper_-F3-"><span aria-label="expand searchbar" role="button" class="searchIconButton_1Dnz" tabindex="0"></span><input type="search" id="search_input_react" placeholder="Search" aria-label="Search" class="navbar__search-input searchInput_2eto"></div></div></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a class="menu__link" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><header class="hero hero--primary heroBanner_2Ftp"><div class="container"><h1 class="hero__title">PSP-UFU</h1><p class="hero__subtitle">Power System Platform of Federal University of Uberlândia</p><p><center><iframe src="https://ghbtns.com/github-btn.html?user=thales1330&amp;repo=psp&amp;type=star&amp;count=true&amp;size=large" frameborder="0" scrolling="0" width="130" height="30" title="GitHub"></iframe></center></p><div class="buttons_1Wc3"><a href="https://github.com/Thales1330/PSP/releases/latest" target="_blank" rel="noopener noreferrer" class="button button--outline button--secondary button--lg" to="https://github.com/Thales1330/PSP/releases/latest">Download</a></div><div class="buttons_1Wc3"><a class="button button--outline button--secondary button--lg" href="/PSP/docs/">User Guide</a></div><div class="buttons_1Wc3"><a href="https://minhaskamal.github.io/DownGit/#/home?url=https://github.com/Thales1330/PSP/tree/master/Project/data/samples" target="_blank" rel="noopener noreferrer" class="button button--outline button--secondary button--lg" to="https://minhaskamal.github.io/DownGit/#/home?url=https://github.com/Thales1330/PSP/tree/master/Project/data/samples">Samples</a></div></div></header><main><section class="features_P2SU"><div class="container"><div class="row"><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/complete-platform.svg" alt="[object Object]"></div><h3>Complete Platform</h3><p>PSP-UFU is a <b>cross-platform</b>, <b>multilingual</b>, <b>Free and Open-Source Software (FOSS)</b> with <b>advanced GUI (Graphical User Interface)</b> features and <b>CAD (Computer-Aided Design) tools</b> for electrical power system studies.</p></div><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/advanced-cad.svg" alt="[object Object]"></div><h3>Advanced CAD Features</h3><p>The software allows the construction of any electric <b>transmission network</b> and <b>control systems</b> through the deployment of visual elements.</p></div><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/visualization.svg" alt="[object Object]"></div><h3>Easy Visualization</h3><p>For the visualization of results, the program offers linked text elements in the main screen, voltage heatmap display, and also table and graph editors.</p></div><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/application.svg" alt="[object Object]"></div><h3>Application</h3><p>The PSP-UFU aims to provide efficient computer simulation tools for <b>research</b> and <b>education</b> purposes, in addition to <b>industrial applications</b> in electrical power systems.</p></div></div></div></section><div class="container"><h2>Studies Performed</h2></div><section class="features_P2SU"><div class="container"><div class="row"><div class="col col--4"><h3>Power Flow</h3><ul><li>Newton-Raphson</li><li>Gauss-Seidel</li><li>Hybrid Newton-Gauss</li><li>Three-phase induction motors included</li></ul></div><div class="col col--4"><h3>Short-Circuit calculation</h3><ul><li>Balanced</li><li>Unbalanced</li><li>Short-Circuit power in all system buses</li></ul></div><div class="col col--4"><h3>Harmonics</h3><ul><li>Harmonic voltages and THD (Total Harmonic Distortion) calculation</li><li>Frequency scan</li></ul></div><div class="col col--4"><h3>Transient and Dynamic Stability</h3><ul><li>Several synchronous machine models automatically selected</li><li>Three-phase induction motors</li><li>User-defined machine controls, exciters and prime moves created using block diagrams (Exciters, AVR, PSS, Hydro and Thermal turbines, Speed Governor, etc.)</li></ul></div></div></div></section><div class="container"><h2>Published Papers</h2>Further details can be found in the published papers:<blockquote cite="https://doi.org/10.1002/2050-7038.12185">Oliveira, T. L., Guimarães, G. C., &amp; Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. <i>International Transactions on Electrical Energy Systems</i>, e12185. doi: <a href="https://doi.org/10.1002/2050-7038.12185">10.1002/2050-7038.12185</a></blockquote><blockquote cite="https://doi.org/10.1177/0020720919879058">Oliveira, T. L., Guimarães, G. C., Silva, L. R., &amp; Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. <i>The International Journal of Electrical Engineering &amp; Education</i>, 0020720919879058. doi: <a href="https://doi.org/10.1177/0020720919879058">10.1177/0020720919879058</a></blockquote></div><div class="container"><h2>Code Documentation</h2><p>All detailed descriptions of the source-code can be found at <b><a href="https://thales1330.github.io/PSP/doxygen/html/index.html">Online Documentation</a></b>, generated by <a href="http://www.doxygen.org/">Doxygen</a>.</p></div><div class="container"><h2>Screenshots</h2><center><iframe src="gallery.html" style="position:relative;width:100%;height:56.25vw;display:block;overflow:hidden;border:none">Your browser doesn’t support the this feature.</iframe></center></div></main></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item" to="https://thales1330.github.io/PSP/doxygen/html/index.html">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. Built with Docusaurus.</div></div></div></footer></div>
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t={pattern:/{\$(?:{(?:{[^{}]+}|[^{}]+)}|[^{}])+}|(^|[^\\{])\$+(?:\w+(?:\[.+?]|->\w+)*)/,lookbehind:!0,inside:{rest:e.languages.php}};e.languages.insertBefore("php","string",{"nowdoc-string":{pattern:/<<<'([^']+)'(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\1;/,greedy:!0,alias:"string",inside:{delimiter:{pattern:/^<<<'[^']+'|[a-z_]\w*;$/i,alias:"symbol",inside:{punctuation:/^<<<'?|[';]$/}}}},"heredoc-string":{pattern:/<<<(?:"([^"]+)"(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\1;|([a-z_]\w*)(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\2;)/i,greedy:!0,alias:"string",inside:{delimiter:{pattern:/^<<<(?:"[^"]+"|[a-z_]\w*)|[a-z_]\w*;$/i,alias:"symbol",inside:{punctuation:/^<<<"?|[";]$/}},interpolation:t}},"single-quoted-string":{pattern:/'(?:\\[\s\S]|[^\\'])*'/,greedy:!0,alias:"string"},"double-quoted-string":{pattern:/"(?:\\[\s\S]|[^\\"])*"/,greedy:!0,alias:"string",inside:{interpolation:t}}}),delete 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r=e.pingCache;null!==r&&r.delete(t),xl===e&&Pl===n?_l===Sl||_l===kl&&1073741823===Ol&&Uo()-Ll<500?nu(e,Pl):Il=!0:Nu(e,n)&&(0!==(t=e.lastPingedTime)&&t<n||(e.lastPingedTime=n,Yl(e)))}function wu(e,t){var n=e.stateNode;null!==n&&n.delete(t),0===(t=0)&&(t=Wl(t=Vl(),e,null)),null!==(e=Kl(e,t))&&Yl(e)}gl=function(e,t,n){var r=t.expirationTime;if(null!==e){var o=t.pendingProps;if(e.memoizedProps!==o||po.current)Ri=!0;else{if(r<n){switch(Ri=!1,t.tag){case 3:zi(t),Ci();break;case 5:if(La(t),4&t.mode&&1!==n&&o.hidden)return t.expirationTime=t.childExpirationTime=1,null;break;case 1:go(t.type)&&wo(t);break;case 4:Na(t,t.stateNode.containerInfo);break;case 10:r=t.memoizedProps.value,o=t.type._context,so(Xo,o._currentValue),o._currentValue=r;break;case 13:if(null!==t.memoizedState)return 0!==(r=t.child.childExpirationTime)&&r>=n?qi(e,t,n):(so(ja,1&ja.current),null!==(t=Qi(e,t,n))?t.sibling:null);so(ja,1&ja.current);break;case 19:if(r=t.childExpirationTime>=n,0!=(64&e.effectTag)){if(r)return 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t=e._ctor;t=t(),e._result=t,t.then((function(t){0===e._status&&(t=t.default,e._status=1,e._result=t)}),(function(t){0===e._status&&(e._status=2,e._result=t)}))}}(o),1!==o._status)throw o._result;switch(o=o._result,t.type=o,a=t.tag=function(e){if("function"==typeof e)return Tu(e)?1:0;if(null!=e){if((e=e.$$typeof)===ue)return 11;if(e===fe)return 14}return 2}(o),e=Ko(o,e),a){case 0:t=ji(null,t,o,e,n);break e;case 1:t=Di(null,t,o,e,n);break e;case 11:t=Ni(null,t,o,e,n);break e;case 14:t=Ii(null,t,o,Ko(o.type,e),r,n);break e}throw Error(i(306,o,""))}return t;case 0:return r=t.type,o=t.pendingProps,ji(e,t,r,o=t.elementType===r?o:Ko(r,o),n);case 1:return r=t.type,o=t.pendingProps,Di(e,t,r,o=t.elementType===r?o:Ko(r,o),n);case 3:if(zi(t),r=t.updateQueue,null===e||null===r)throw 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Ai(e,t,t.pendingProps.children,n),t.child;case 10:e:{r=t.type._context,o=t.pendingProps,l=t.memoizedProps,a=o.value;var u=t.type._context;if(so(Xo,u._currentValue),u._currentValue=a,null!==l)if(u=l.value,0===(a=Dr(u,a)?0:0|("function"==typeof r._calculateChangedBits?r._calculateChangedBits(u,a):1073741823))){if(l.children===o.children&&!po.current){t=Qi(e,t,n);break e}}else for(null!==(u=t.child)&&(u.return=t);null!==u;){var s=u.dependencies;if(null!==s){l=u.child;for(var c=s.firstContext;null!==c;){if(c.context===r&&0!=(c.observedBits&a)){1===u.tag&&((c=ua(n,null)).tag=2,sa(u,c)),u.expirationTime<n&&(u.expirationTime=n),null!==(c=u.alternate)&&c.expirationTime<n&&(c.expirationTime=n),na(u.return,n),s.expirationTime<n&&(s.expirationTime=n);break}c=c.next}}else l=10===u.tag&&u.type===t.type?null:u.child;if(null!==l)l.return=u;else for(l=u;null!==l;){if(l===t){l=null;break}if(null!==(u=l.sibling)){u.return=l.return,l=u;break}l=l.return}u=l}Ai(e,t,o.children,n),t=t.child}return t;case 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t={pattern:/{\$(?:{(?:{[^{}]+}|[^{}]+)}|[^{}])+}|(^|[^\\{])\$+(?:\w+(?:\[.+?]|->\w+)*)/,lookbehind:!0,inside:{rest:e.languages.php}};e.languages.insertBefore("php","string",{"nowdoc-string":{pattern:/<<<'([^']+)'(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\1;/,greedy:!0,alias:"string",inside:{delimiter:{pattern:/^<<<'[^']+'|[a-z_]\w*;$/i,alias:"symbol",inside:{punctuation:/^<<<'?|[';]$/}}}},"heredoc-string":{pattern:/<<<(?:"([^"]+)"(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\1;|([a-z_]\w*)(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\2;)/i,greedy:!0,alias:"string",inside:{delimiter:{pattern:/^<<<(?:"[^"]+"|[a-z_]\w*)|[a-z_]\w*;$/i,alias:"symbol",inside:{punctuation:/^<<<"?|[";]$/}},interpolation:t}},"single-quoted-string":{pattern:/'(?:\\[\s\S]|[^\\'])*'/,greedy:!0,alias:"string"},"double-quoted-string":{pattern:/"(?:\\[\s\S]|[^\\"])*"/,greedy:!0,alias:"string",inside:{interpolation:t}}}),delete 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t=/#(?!\{).+/,n={pattern:/#\{[^}]+\}/,alias:"variable"};e.languages.coffeescript=e.languages.extend("javascript",{comment:t,string:[{pattern:/'(?:\\[\s\S]|[^\\'])*'/,greedy:!0},{pattern:/"(?:\\[\s\S]|[^\\"])*"/,greedy:!0,inside:{interpolation:n}}],keyword:/\b(?:and|break|by|catch|class|continue|debugger|delete|do|each|else|extend|extends|false|finally|for|if|in|instanceof|is|isnt|let|loop|namespace|new|no|not|null|of|off|on|or|own|return|super|switch|then|this|throw|true|try|typeof|undefined|unless|until|when|while|window|with|yes|yield)\b/,"class-member":{pattern:/@(?!\d)\w+/,alias:"variable"}}),e.languages.insertBefore("coffeescript","comment",{"multiline-comment":{pattern:/###[\s\S]+?###/,alias:"comment"},"block-regex":{pattern:/\/{3}[\s\S]*?\/{3}/,alias:"regex",inside:{comment:t,interpolation:n}}}),e.languages.insertBefore("coffeescript","string",{"inline-javascript":{pattern:/`(?:\\[\s\S]|[^\\`])*`/,inside:{delimiter:{pattern:/^`|`$/,alias:"punctuation"},rest:e.languages.javascript}},"multiline-string":[{pattern:/'''[\s\S]*?'''/,greedy:!0,alias:"string"},{pattern:/"""[\s\S]*?"""/,greedy:!0,alias:"string",inside:{interpolation:n}}]}),e.languages.insertBefore("coffeescript","keyword",{property:/(?!\d)\w+(?=\s*:(?!:))/}),delete 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img{margin-right:.5rem;height:2rem}.menu_w2sC{flex-grow:1;padding:.5rem}.menu_w2sC::-webkit-scrollbar{width:7px}.menu_w2sC::-webkit-scrollbar-track{background:#f1f1f1;border-radius:10px}.menu_w2sC::-webkit-scrollbar-thumb{background:#888;border-radius:10px}.menu_w2sC::-webkit-scrollbar-thumb:hover{background:#555}.menuLinkText_2sSe{cursor:auto}.menuLinkText_2sSe:hover{background:none}.menuWithAnnouncementBar_2d0G{margin-bottom:var(--docusaurus-announcement-bar-height)}}.sidebarLogo_3ono{display:none}.sidebarMenuIcon_2vk4{vertical-align:middle}.sidebarMenuCloseIcon_1JRa{display:inline-flex;justify-content:center;align-items:center;height:24px;font-size:1.5rem;font-weight:var(--ifm-font-weight-bold);line-height:.9;width:24px}.codeBlockContent_32p_{position:relative}.codeBlockTitle_U1PS{border-top-left-radius:var(--ifm-global-radius);border-top-right-radius:var(--ifm-global-radius);border-bottom:1px solid var(--ifm-color-emphasis-200);font-family:var(--ifm-font-family-monospace);font-weight:700;padding:.75rem var(--ifm-pre-padding);width:100%}.codeBlock_19pQ{overflow:auto;border-radius:var(--ifm-global-radius)}.codeBlockWithTitle_2fj3{border-top-left-radius:0;border-top-right-radius:0}.copyButton_1BYj{background:rgba(0,0,0,.3);border:none;border-radius:var(--ifm-global-radius);color:var(--ifm-color-white);cursor:pointer;opacity:0;outline:none;padding:.4rem .5rem;position:absolute;right:calc(var(--ifm-pre-padding)/2);top:calc(var(--ifm-pre-padding)/2);visibility:hidden;transition:opacity .2s ease-in-out,visibility .2s ease-in-out,bottom .2s ease-in-out}.codeBlockContent_32p_:hover>.copyButton_1BYj,.codeBlockTitle_U1PS:hover+.codeBlockContent_32p_ .copyButton_1BYj{visibility:visible;opacity:1}.codeBlockLines_2n9r{font-family:var(--ifm-font-family-monospace);font-size:inherit;line-height:var(--ifm-pre-line-height);white-space:pre;float:left;min-width:100%;padding:var(--ifm-pre-padding)}.anchor{display:block;position:relative;top:-.5rem;outline:none}.hash-link{opacity:0;padding-left:.5rem}:hover>.hash-link{opacity:1}.enhancedAnchor_ZqCz{top:calc(var(--ifm-navbar-height)*-1)}.mdxCodeBlock_iHAB{position:relative;margin-bottom:var(--ifm-leading);font-size:var(--ifm-code-font-size)}.mdxCodeBlock_iHAB pre{font-size:inherit}.docPage_1kjD{display:flex}.docSidebarContainer_1cYp{border-right:1px solid var(--ifm-toc-border-color);box-sizing:border-box;width:300px;position:relative;margin-top:calc(-1*var(--ifm-navbar-height))}.docMainContainer_FFX1{flex-grow:1}@media (max-width:996px){.docPage_1kjD{display:inherit}.docSidebarContainer_1cYp{margin-top:0}}.blogPostTitle_2RZH{font-size:3rem}.blogPostDate_3tRe{font-size:.9rem}.heroBanner_2Ftp{padding:4rem 0;text-align:center;position:relative;overflow:hidden}@media screen and (max-width:966px){.heroBanner_2Ftp{padding:2rem}}.buttons_1Wc3{display:inline-block;align-items:center;justify-content:center;margin:0 10px}.features_P2SU{display:flex;align-items:center;padding:2rem 0;width:100%}.featureImage_3Xqx{height:200px;width:200px}.docTitle_1vWb{font-size:3rem;margin-bottom:calc(var(--ifm-leading-desktop)*var(--ifm-leading))}.docItemContainer_2cwg{margin:0 auto;padding:0 .5rem}@media only screen and (min-width:997px){.docItemCol_2GOA{max-width:75%!important}}@media (min-width:997px) and (max-width:1320px){.docItemWrapper_1cc7{max-width:calc(var(--ifm-container-width) - 300px - var(--ifm-spacing-horizontal)*2)}}.tableOfContents_TbNY{display:inherit;max-height:calc(100vh - var(--ifm-navbar-height) - 2rem);overflow-y:auto;position:-webkit-sticky;position:sticky;top:calc(var(--ifm-navbar-height) + 2rem)}.tableOfContents_TbNY::-webkit-scrollbar{width:7px}.tableOfContents_TbNY::-webkit-scrollbar-track{background:#f1f1f1;border-radius:10px}.tableOfContents_TbNY::-webkit-scrollbar-thumb{background:#888;border-radius:10px}.tableOfContents_TbNY::-webkit-scrollbar-thumb:hover{background:#555}@media only screen and (max-width:996px){.tableOfContents_TbNY{display:none}.docItemContainer_2cwg{padding:0 .3rem}}.docLastUpdatedAt_1sqk{font-weight:700}.tabItem_3zTA{margin-top:0!important}.tabItem_3zTA:focus{background-color:var(--ifm-hover-overlay)}
\ No newline at end of file
diff --git a/docusaurus/docs/bus.md b/docusaurus/docs/bus.md
index f005c7c..02affa1 100644
--- a/docusaurus/docs/bus.md
+++ b/docusaurus/docs/bus.md
@@ -7,6 +7,9 @@ import useBaseUrl from "@docusaurus/useBaseUrl";
 
 <link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
 
+import Tabs from '@theme/Tabs';
+import TabItem from '@theme/TabItem';
+
 >Condutor de baixa impedância ao qual vários circuitos elétricos podem ser conectados em pontos separados.
 Nota - Em muitos casos, o barramento consiste em uma barra. [*tradução livre* - IEC 60050](
 http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=151-12-30).
@@ -29,8 +32,17 @@ Esse formulário é subdividido em quatro contextos distintos:
 - **Estabilidade**: contendo opções de visualização de dados da barra em gráficos no tempo e inserção de faltas trifásicas no cálculo de estabilidade transitória;
 - **Qualidade de energia**: contém a opção de de visualização da impedância harmônica vista pela barra.
 
----
-### Geral
+<Tabs
+  groupId="bus-tabs"
+  defaultValue="general"
+  values={[
+    {label: 'Geral', value: 'general'},
+    {label: 'Falta', value: 'fault'},
+    {label: 'Estabilidade', value: 'stability'},
+    {label: 'Qualidade de energia', value: 'powerQuality'},
+  ]
+}>
+<TabItem value="general">
 
 #### Nome
 Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão [Unicode](https://pt.wikipedia.org/wiki/Unicode).
@@ -54,8 +66,8 @@ O valor poderá ser inserido em p.u. ou em volts (ou kV caso a tensão nominal e
 #### Barra de referência
 Caracteriza o barramento como **barra de referência ([Barra de oscilação](powerFlow))**. Essa opção é somente válida caso esteja conectado um gerador síncrono, caso contrário uma mensagem de erro será exibida ao usuário ao realizar algum dos cálculos do programa.
 
----
-### Falta
+</TabItem>
+<TabItem value="fault">
 
 #### Inserir falta
 
@@ -78,8 +90,8 @@ Seleciona a fase em que se situa a falta (ou combinação delas no caso de falha
 #### Resistência e reatância de falta
 Representam a impedância da falta. Curtos-circuitos francos (sem impedância de falta) são representados inserindo valor zero em ambos os campos.
 
----
-### Estabilidade
+</TabItem>
+<TabItem value="stability">
 
 #### Imprimir dados
 Mostra os dados da barra editada no gráfico gerado pelo estudo de estabilidade transitória. Os seguintes dados são exibidos:
@@ -101,8 +113,11 @@ Duração da falta inserida ($\Delta t_{falta}$) no estudo de estabilidade. A fa
 #### Resistência e reatância de falta
 Impedância de falta nos estudos de estabilidade. Uma falta franca é representada pela inserção de um valor de impedância shunt de valor muito baixo ($j10^{-5}  p.u.$).
 
----
-### Qualidade de energia
+</TabItem>
+<TabItem value="powerQuality">
 
 #### Imprimir impedância harmônica da barra
 Imprime a impedância harmônica vista por essa barra referente ao estudo de [Resposta na Frequência](harmonics).
+
+</TabItem>
+</Tabs>
\ No newline at end of file
diff --git a/docusaurus/docs/capacitor.md b/docusaurus/docs/capacitor.md
index cd5491f..9c9c0c8 100644
--- a/docusaurus/docs/capacitor.md
+++ b/docusaurus/docs/capacitor.md
@@ -7,6 +7,9 @@ import useBaseUrl from "@docusaurus/useBaseUrl";
 
 <link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
 
+import Tabs from '@theme/Tabs';
+import TabItem from '@theme/TabItem';
+
 >Um dispositivo constituído essencialmente por dois eletrodos separados por um dielétrico. [*tradução livre* - IEC 60050](
 http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=436-01-03).
 
@@ -28,8 +31,15 @@ Além do único contexto geral, pode ser observado o botão "Estabilidade" na pa
 
 <div><center><img src={useBaseUrl("images/swCapacitor.png")} alt="Formulário de chaveamento do capacitor" title="Formulário de chaveamento do capacitor" /></center></div>
 
----
-### Geral
+<Tabs
+  groupId="transformer-tabs"
+  defaultValue="general"
+  values={[
+    {label: 'Geral', value: 'general'},
+    {label: 'Botão Estabilidade', value: 'stability'},
+  ]
+}>
+<TabItem value="general">
 
 #### Nome
 Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão [Unicode](https://pt.wikipedia.org/wiki/Unicode).
@@ -39,8 +49,12 @@ Todos os componentes de potência do PSP-UFU possuem esse campo.
 #### Potência reativa
 Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou $p.u.$ (na base de potência do sistema). 
 
----
-### Botão Estabilidade
+</TabItem>
+<TabItem value="stability">
+
 O botão "Estabilidade" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do transformador durante o estudo de [estabilidade](stability).
 
-Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
\ No newline at end of file
+Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
+
+</TabItem>
+</Tabs>
diff --git a/docusaurus/docs/const.md b/docusaurus/docs/const.md
index 4209d90..bc2eb39 100644
--- a/docusaurus/docs/const.md
+++ b/docusaurus/docs/const.md
@@ -5,4 +5,10 @@ sidebar_label: Constante
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+As constantes são valores numéricos reais que permanecem inalteradas em todo o período de simulação. Esses elementos possuem somente um nó de saída, o qual poderá ser conectado a qualquer outro nó de entrada dos elementos de controle.
+
+:::info Informação
+Esse elemento pode, por exemplo, ser utilizado para definir valores alvos ou deslocamentos de sinal.
+:::
\ No newline at end of file
diff --git a/docusaurus/docs/controlEditor.md b/docusaurus/docs/controlEditor.md
index b9a94f5..c27ac87 100644
--- a/docusaurus/docs/controlEditor.md
+++ b/docusaurus/docs/controlEditor.md
@@ -15,6 +15,14 @@ O acesso ao editor é realizado por meio de dois botões presentes no [formulár
 - [Editar AVR](syncGenerator#utilizar-avr-e-regulador-de-velocidade)
 - [Editar regulador de velocidade](syncGenerator#utilizar-avr-e-regulador-de-velocidade)
 
+:::caution Atenção!
+No PSP-UFU a opção de editar o **AVR** engloba mais que somente o controle de tensão da máquina. Nele **deve** ser inserida a malha de controle da máquina assim como a **excitatriz da máquina síncrona**. Outras estratégias de controle (opcionais), como PSS (*Power System Stabilizer*) e/ou controles de sobre e sub excitação, são também implementadas em conjunto (como apresentado na figura anterior).
+:::
+
+:::caution Atenção!
+Assim como no AVR, o **Regulador de Velocidade** engloba mais que a regulação primária da máquina. Nessa opção **deve** ser inserida ao menos a malha de controle da regulação primária de velocidade, assim como o **modelo da turbina**. Estratégias opcionais de controle da velocidade também são inseridas nessa opção.
+:::
+
 ## Elementos de Controle
 O acesso aos elementos de controle é realizado em uma janela (removível e encaixável) por meio de ícones relacionados.
 
@@ -92,6 +100,8 @@ Nesse formulário é possível inserir o comportamento de **todas as entradas do
 - **Passo de integração ($h$)**: Passo do método de integração Trapezoidal Implícito;
 - **Tempo de simulação ($t_f$)**: Tempo total de simulação.
 
+Após a simulação os resultados são exibidos no [visualizador de gráficos](graphViewer).
+
 :::caution Atenção!
 A mesma parametrização de entrada é aplicada em todos os blocos de [entrada](io) do sistema.
 :::
diff --git a/docusaurus/docs/divider.md b/docusaurus/docs/divider.md
index 2dd7315..af3bcae 100644
--- a/docusaurus/docs/divider.md
+++ b/docusaurus/docs/divider.md
@@ -5,4 +5,12 @@ sidebar_label: Divisor
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+Esse elemento é bastante simples e cumpre com a função matemáticas de seu nome.
+
+Possui duas entradas de valores reais e sua saída é computada na sequência do nó superior pelo inferior, ou seja, a saída será o valor presente no nó 1 dividido pelo nó 2.
+
+:::caution Atenção!
+Nós não conectados no divisor são considerados como valor nulo. Caso a divisão possua numerador zero, o valor da saída é definida como sendo $10^{15}$.
+:::
\ No newline at end of file
diff --git a/docusaurus/docs/exponential.md b/docusaurus/docs/exponential.md
index 351d63b..a327ef8 100644
--- a/docusaurus/docs/exponential.md
+++ b/docusaurus/docs/exponential.md
@@ -5,4 +5,23 @@ sidebar_label: Exponencial
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+A função exponencial dos elementos de controle realiza essa operação com uma entrada real, obedecendo a expressão:
+$$
+y_n = \bold{A} e^{\bold{B} u_n}
+$$
+Em que:
+- $u_n$ e $y_n$	é a entrada e a saída do bloco exponencial, respectivamente;
+- $\bold{A}$ e $\bold{B}$	são constantes definidas pelo usuário.
+
+## Formulário de edição de dados do bloco Exponencial
+A figura abaixo apresenta o formulário de edição de dados do bloco exponencial.
+
+<div><center><img src={useBaseUrl("images/expForm.png")} alt="Formulário de edição de dados do bloco exponencial no PSP-UFU" title="Formulário de edição de dados do bloco exponencial no PSP-UFU" /></center></div>
+
+Esse bloco não linear é definido pelas constantes A e B, inseridas pelo usuário.
+
+:::info Informação
+Tais blocos são úteis na representação de não linearidades, como, por exemplo, modelagem da saturação de máquinas de corrente contínuas presentes em alguns reguladores automáticos de tensão.
+:::
diff --git a/docusaurus/docs/gain.md b/docusaurus/docs/gain.md
index 09e54f9..0e4edf1 100644
--- a/docusaurus/docs/gain.md
+++ b/docusaurus/docs/gain.md
@@ -5,4 +5,8 @@ sidebar_label: Ganho
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+O bloco de ganho multiplica o valor de entrada por uma constante definida pelo usuário, possuindo comportamento idêntico à combinação de uma [constante](const) e um bloco [multiplicador](multiplier).
+
+Esse valor de ganho permanece fixo durante todo o tempo de simulação e é identificado no elemento gráfico exibido no editor de elementos de controle.
\ No newline at end of file
diff --git a/docusaurus/docs/graphViewer.md b/docusaurus/docs/graphViewer.md
new file mode 100644
index 0000000..5498f9a
--- /dev/null
+++ b/docusaurus/docs/graphViewer.md
@@ -0,0 +1,8 @@
+---
+id: graphViewer
+title: Visualizador de Gráficos
+sidebar_label: Visualizador de Gráficos
+---
+import useBaseUrl from "@docusaurus/useBaseUrl";
+
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
diff --git a/docusaurus/docs/heatmap.md b/docusaurus/docs/heatmap.md
new file mode 100644
index 0000000..30ea55f
--- /dev/null
+++ b/docusaurus/docs/heatmap.md
@@ -0,0 +1,8 @@
+---
+id: heatmap
+title: Mapa de Tensão
+sidebar_label: Mapa de Tensão
+---
+import useBaseUrl from "@docusaurus/useBaseUrl";
+
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
diff --git a/docusaurus/docs/indMotor.md b/docusaurus/docs/indMotor.md
index bba7503..6f4a923 100644
--- a/docusaurus/docs/indMotor.md
+++ b/docusaurus/docs/indMotor.md
@@ -7,6 +7,9 @@ import useBaseUrl from "@docusaurus/useBaseUrl";
 
 <link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
 
+import Tabs from '@theme/Tabs';
+import TabItem from '@theme/TabItem';
+
 > Uma máquina assíncrona da qual apenas um enrolamento é energizado. [*tradução livre* - IEC 60050](
 http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=411-31-10).
 
@@ -134,8 +137,16 @@ No formulário pode ser observado o botão "Chaveamento" na parte inferior esque
 
 <div><center><img src={useBaseUrl("images/indMotorSw.png")} alt="Formulário de chaveamento do motores de indução" title="Formulário de chaveamento do motores de indução" /></center></div>
 
----
-### Geral
+<Tabs
+  groupId="indMotor-tabs"
+  defaultValue="general"
+  values={[
+    {label: 'Geral', value: 'general'},
+    {label: 'Estabilidade', value: 'stability'},
+    {label: 'Botão Chaveamento', value: 'switching'},
+  ]
+}>
+<TabItem value="general">
 
 #### Nome
 Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão [Unicode](https://pt.wikipedia.org/wiki/Unicode).
@@ -163,11 +174,11 @@ Caso essa opção não seja utilizada o motor será considerado uma [carga de po
 A não utilização dessa opção poderá gerar erros de regime permamente no estudo de [estabilidade](stability).
 :::
 
-Utilizar potência nominal como base
+#### Utilizar potência nominal como base
 Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.
 
----
-### Estabilidade
+</TabItem>
+<TabItem value="stability">
 
 #### Imprimir dados da máquina de indução
 Exibe os dados do gerador síncrono nos gráficos no tempo. Os seguintes dados são exibidos:
@@ -209,12 +220,16 @@ $$
 A soma dos coeficientes ($a + b + c$) deve ser unitária.
 :::
 
----
-### Botão Chaveamento
+</TabItem>
+<TabItem value="switching">
+
 O botão "Chaveamento" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do gerador durante o estudo de [estabilidade](stability).
 
 Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
 
+</TabItem>
+</Tabs>
+
 ## Referências
 1. SÁNCHEZ, J. C.; OLIVARES, T. I. A.; ORTIZ, G. R.; VEGA, D. R. Induction Motor Static Models for Power Flow and Voltage Stability Studies. In: IEEE Power and Energy Society General Meeting, 2012, San Diego. doi: https://doi.org/10.1109/PESGM.2012.6345618
 2. IEEE Std 399-1997. IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (Brown Book). IEEE, New York, ago. 1998. doi: https://doi.org/10.1109/IEEESTD.1998.88568
diff --git a/docusaurus/docs/inductor.md b/docusaurus/docs/inductor.md
index b126deb..e66e60b 100644
--- a/docusaurus/docs/inductor.md
+++ b/docusaurus/docs/inductor.md
@@ -7,6 +7,9 @@ import useBaseUrl from "@docusaurus/useBaseUrl";
 
 <link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
 
+import Tabs from '@theme/Tabs';
+import TabItem from '@theme/TabItem';
+
 >Um reator destinado à conexão de derivação em uma rede para compensar a corrente capacitiva. [*tradução livre* - IEC 60050](
 http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=421-01-03).
 
@@ -24,8 +27,15 @@ Além do único contexto geral, pode ser observado o botão "Estabilidade" na pa
 
 <div><center><img src={useBaseUrl("images/indSw.png")} alt="Formulário de chaveamento do indutor" title="Formulário de chaveamento do indutor" /></center></div>
 
----
-### Geral
+<Tabs
+  groupId="transformer-tabs"
+  defaultValue="general"
+  values={[
+    {label: 'Geral', value: 'general'},
+    {label: 'Botão Estabilidade', value: 'stability'},
+  ]
+}>
+<TabItem value="general">
 
 #### Nome
 Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão [Unicode](https://pt.wikipedia.org/wiki/Unicode).
@@ -35,8 +45,12 @@ Todos os componentes de potência do PSP-UFU possuem esse campo.
 #### Potência reativa
 Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou $p.u.$ (na base de potência do sistema). 
 
----
-### Botão Estabilidade
-O botão "Estabilidade" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do indutor durante o estudo de [estabilidade](stability).
+</TabItem>
+<TabItem value="stability">
+
+O botão "Estabilidade" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do transformador durante o estudo de [estabilidade](stability).
+
+Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
 
-Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
\ No newline at end of file
+</TabItem>
+</Tabs>
\ No newline at end of file
diff --git a/docusaurus/docs/io.md b/docusaurus/docs/io.md
index 561ab10..2879f6b 100644
--- a/docusaurus/docs/io.md
+++ b/docusaurus/docs/io.md
@@ -25,7 +25,7 @@ O usuário deve sinalizar o tipo de bloco entre entrada e saída e, então, sele
 - **Velocidade** (*entrada: AVR e RV*): Velocidade da máquina síncrona, em rad/s, variável no tempo. Normalmente utilizada no cálculo do erro de velocidade nos reguladores de velocidade, além de entrada do PSS em AVRs;
 - **Potência ativa e reativa** (*entrada: AVR*): Potência ativa fornecida pela máquina síncrona, em $p.u.$, variável no tempo. Normalmente utilizada como entrada do PSS (potência ativa) e controle de sub e sobrecorrente de excitação nos AVRs;
 - **Tensão terminal inicial** (*entrada: AVR*): Módulo da tensão no barramento da máquina síncrona prévia ao estudo dinâmico originado do fluxo de carga, em $p.u.$, fixo no tempo. Essa variável está normalmente associada à referência de tensão do AVR;
-- **Velocidade inicial** (*entrada: AVR e RV*): Velocidade do sistema (2πf_ref), definida nas opções de simulação, em rad/s, fixa no tempo. Normalmente utiliza-se essa variável como referência de velocidade em RVs e normalização da velocidade;
+- **Velocidade inicial** (*entrada: AVR e RV*): Velocidade do sistema ($2 \pi f_{ref}$), definida nas [opções de simulação](simulationConfig), em rad/s, fixa no tempo. Normalmente utiliza-se essa variável como referência de velocidade em RVs e normalização da velocidade;
 - **Potência mecânica inicial** (*entrada: RV*): Potência mecânica inicial, calculada após a inicialização das máquinas síncronas com os dados originados do fluxo de carga, em $p.u.$, fixa no tempo. Normalmente é utilizada como referência de potência mecânica nos reguladores de velocidade;
 - **Variação de velocidade e potência ativa** (*entrada: AVR*): Cálculo da variação dessas entradas entre os passos de integração normalizada pelo passo de integração, conforme a equação:
 	$$
diff --git a/docusaurus/docs/limiter.md b/docusaurus/docs/limiter.md
index 3e829f0..adb4e04 100644
--- a/docusaurus/docs/limiter.md
+++ b/docusaurus/docs/limiter.md
@@ -5,4 +5,31 @@ sidebar_label: Limitador absoluto
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+Os blocos de limite absoluto cumprem a função de restringir os valores de entrada de acordo com os limites máximos e mínimos inseridos pelo usuário. Caso a entrada ultrapasse algum dos limites impostos, a saída será igual a esse valor limite até que a entrada retorne para a faixa permitida.
+
+As restrições máximas e mínimas de valores dos sistemas de controle são modeladas utilizando um Limitador, cuja implementação é bastante simples e segue a seguinte expressão:
+$$
+y_n = 
+\begin{cases}
+L_{sup}{,}	& \text{se } u_n > L_{sup} \\
+u_n{,}		& \text{se } L_{inf} \le u_n \le L_{sup}\\
+L_{inf}{,}	& \text{se } u_n < L_{inf}
+\end{cases}
+$$
+Em que:
+- $y_n$	Éé o valor de saída atual do bloco
+- $L_{sup}$ e $L_{inf}$	são os limites superior e inferior, respectivamente
+- $u_n$	é o valor de entrada atual do bloco
+
+## Formulário de edição do bloco Limitador
+A figura abaixo apresenta o formulário de edição de dados do bloco limitador.
+
+<div><center><img src={useBaseUrl("images/limiterForm.png")} alt="Formulário de edição de dados do bloco limitador no PSP-UFU" title="Formulário de edição de dados do bloco limitador no PSP-UFU" /></center></div>
+
+Esse bloco não linear é definido pelo **limite superior e inferior**, inseridos pelo usuário.
+
+:::info Informação
+Tais blocos são bastante encontrados nos sistemas de controle para limitar a atuação do controlador, além de representar limites físicos de modelos implementados, como, por exemplo, valores máximos de corrente de excitação ou potência mecânica fornecida pelas turbinas.
+:::
\ No newline at end of file
diff --git a/docusaurus/docs/line.md b/docusaurus/docs/line.md
index f7062fa..67e04e7 100644
--- a/docusaurus/docs/line.md
+++ b/docusaurus/docs/line.md
@@ -7,6 +7,9 @@ import useBaseUrl from "@docusaurus/useBaseUrl";
 
 <link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
 
+import Tabs from '@theme/Tabs';
+import TabItem from '@theme/TabItem';
+
 >Um meio de transmissão fabricado usado para transmitir energia eletromagnética entre dois pontos com um mínimo de radiação. [*tradução livre* - IEC 60050](
 http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=704-02-02).
 
@@ -56,8 +59,16 @@ Além desses dois contextos, pode ser observado o botão "Estabilidade" na parte
 
 <div><center><img src={useBaseUrl("images/lineSw.png")} alt="Formulário de chaveamento da linha" title="Formulário de chaveamento da linha" /></center></div>
 
----
-### Geral
+<Tabs
+  groupId="line-tabs"
+  defaultValue="general"
+  values={[
+    {label: 'Geral', value: 'general'},
+    {label: 'Falta', value: 'fault'},
+    {label: 'Botão Estabilidade', value: 'stability'},
+  ]
+}>
+<TabItem value="general">
 
 #### Nome
 Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão [Unicode](https://pt.wikipedia.org/wiki/Unicode).
@@ -88,8 +99,8 @@ O comprimento da linha é ignorado caso não sejam utilizadas as unidades por qu
 #### Utilizar potência nominal como base
 Caso essa opção seja marcada, o programa irá utilizar a potência nominal da linha como base para a conversão das unidades, caso contrário será usada a [potência base do sistema](simulationConfig).
 
----
-### Falta
+</TabItem>
+<TabItem value="fault">
 
 #### Parâmetros do modelo $\pi$ de sequência zero
 Esses parâmetros são necessários para o correto cálculo das correntes de [falta desbalanceadas](fault) (fase-fase, fase-fase-terra e fase-terra) e devem ser inseridos em $p.u.$
@@ -98,8 +109,12 @@ Esses parâmetros são necessários para o correto cálculo das correntes de [fa
 A não inserção desses dados acarretarão em resultados incorretos para [faltas desbalanceadas](fault).
 :::
 
----
-### Botão Estabilidade
+</TabItem>
+<TabItem value="stability">
+
 O botão "Estabilidade" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção da linha durante o estudo de [estabilidade](stability).
 
-Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
\ No newline at end of file
+Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
+
+</TabItem>
+</Tabs>
diff --git a/docusaurus/docs/load.md b/docusaurus/docs/load.md
index 6db0aac..0f2b6f3 100644
--- a/docusaurus/docs/load.md
+++ b/docusaurus/docs/load.md
@@ -7,6 +7,9 @@ import useBaseUrl from "@docusaurus/useBaseUrl";
 
 <link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
 
+import Tabs from '@theme/Tabs';
+import TabItem from '@theme/TabItem';
+
 >1. a potência ativa, reativa ou aparente gerada, transmitida ou distribuída dentro de um sistema;
 1. a potência demandada por um grupo de consumidores classificados de acordo com suas particularidades e características, por exemplo, carga de aquecimento, carga reativa diurna, etc. [*tradução livre* - IEC 60050](
 http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=601-01-15).
@@ -83,8 +86,16 @@ Além desses dois contextos, pode ser observado o botão "Chaveamento" na parte
 
 <div><center><img src={useBaseUrl("images/loadSw.png")} alt="Formulário de chaveamento da carga" title="Formulário de chaveamento da carga" /></center></div>
 
----
-### Geral
+<Tabs
+  groupId="load-tabs"
+  defaultValue="general"
+  values={[
+    {label: 'Geral', value: 'general'},
+    {label: 'Estabilidade', value: 'stability'},
+    {label: 'Botão Chaveamento', value: 'switching'},
+  ]
+}>
+<TabItem value="general">
 
 #### Nome
 Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão [Unicode](https://pt.wikipedia.org/wiki/Unicode).
@@ -100,8 +111,8 @@ Parcela de potência reativa da carga. Pode ser inserido em Mvar, kvar var ou $p
 #### Tipo de carga (fluxo de carga)
 Tipo da carga para o estudo de fluxo de carga, podendo ser selecionado dois tipos: Potência constante e Impedância constante. As cargas de potência constantes são inseridas nos vetores de potência e permanecem invariantes no cálculo, enquanto que para as cargas de impedância constante determina-se o valor da impedância utilizando a potência e tensão nominal, a qual é inserida na matriz admitância.
 
----
-### Estabilidade
+</TabItem>
+<TabItem value="stability">
 
 #### Imprimir dados
 Exibe os dados da carga nos gráficos no tempo.
@@ -124,8 +135,12 @@ Caso todas as barras possuírem o mesmo comportamento de carga ZIP, a parametriz
 #### Composição de potência ativa e reativa
 Valores da composição da carga ZIP, inseridas para potência ativa e reativa separadamente, em porcentagem. A soma da composição deve ser igual a 100%, caso contrário será exibida uma mensagem de erro ao usuário.
 
----
-### Botão Chaveamento
+</TabItem>
+<TabItem value="switching">
+
 O botão "Chaveamento" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do transformador durante o estudo de [estabilidade](stability).
 
 Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
+
+</TabItem>
+</Tabs>
\ No newline at end of file
diff --git a/docusaurus/docs/mathExpression.md b/docusaurus/docs/mathExpression.md
index be330f9..a9f62f4 100644
--- a/docusaurus/docs/mathExpression.md
+++ b/docusaurus/docs/mathExpression.md
@@ -5,4 +5,153 @@ sidebar_label: Expressão Matemática
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+O bloco de expressão matemática utiliza a biblioteca externa [fparser](http://warp.povusers.org/FunctionParser/) e permite ao usuário inserir expressões matemáticas genéricas de qualquer complexidade combinadas a estruturas condicionais em um diagrama de controle, aumentando significativamente a capacidade de generalização do programa.
+
+## Sintaxe das expressões matemáticas
+As sintaxes das operações (para expressões `A` e `B`) são apresentadas na tabela abaixo:
+
+|Operador|Expressão|
+|--------|---------|
+|`( )`	|Expressão em parênteses primeiro
+|`A unit`	|Um multiplicador de unidade (se um estiver sido adicionado)
+|`A^B`	|Exponenciação (`A` elevado à potência `B`)
+|`-A`	|Operação unária de oposto
+|`!A`	|Operação lógica unária de negação (resulta em $1$ se `int(A)` é $0$, senão $0$)
+|`A*B` `A/B` `A%B`	|Multiplicação, divisão e módulo
+|`A+B` `A-B`	|Adição e subtração
+|`A=B` `A<B` `A<=B` `A!=B` `A>B` `A>=B`	|Comparação entre `A` e `B` (resulta em $1$ ou $0$)
+|`A&B`	|Resulta em $1$ se `int(A)` e `int(B)` forem diferentes de $0$, senão $0$
+|`A`\|`B`	|Resulta em $1$ se `int(A)` ou `int(B)` forem diferentes de $0$, senão $0$
+
+As **funções matemáticas** suportadas pela biblioteca, as quais podem ser utilizadas na construção de diagrama de blocos, são descritas na tabela abaixo:
+
+|Expressão|Descrição
+|---------|---------|
+|`abs(A)`|Valor absoluto de `A`. Para números reais, se `A` é negativo, retorna `–A`, senão retorna `A`. Para números complexos a expressão é equivalente a `hypot(real(x),imag(x))`.
+|`acos(A)`|Arco cosseno de `A`. Retorna o ângulo em radianos.
+|`acosh(A)`|O mesmo que `acos()` mas para cosseno hiperbólico
+|`arg(A)`|Ângulo de fase de um número complexo `A`.
+|`asin(A)`|Arco seno de `A`. Retorna o ângulo em radianos.
+|`asinh(A)`|Mesmo que `asin()`, mas para seno hiperbólico
+|`atan(A)`|Arco tangente de `A`. Retorna o ângulo em radianos.
+|`atan2(A,B)`|Arco tangente de `A/B`, a qual os sinais dos dois argumentos para determinar o quadrante do resultado. Retorna a solução de do seguinte sistema: `hypot(A,B)*sin(x)=A, hypot(A,B)*cos(x)=B`. O valor retornado varia de $-\pi$ a $\pi$.
+|`atanh(A)`|Mesmo que `atan()`, mas para tangente hiperbólica.
+|`cbrt(A)`|Raiz cúbica de `A`.
+|`conj(A)`|Conjugado complexo de `A`.
+|`ceil(A)`|Teto de `A`. Arredonda para o próximo maior inteiro.
+|`cos(A)`|Cosseno de `A`. Retorna o ângulo em radianos.
+|`cosh(A)`|Mesmo que `cos()`, mas para cosseno hiperbólico
+|`cot(A)`|Cotangente de `A`. Retorna o ângulo em radianos.
+|`csc(A)`|Cossecante de `A`. Retorna o ângulo em radianos.
+|`exp(A)`|Exponencial de `A`. Retorna o valor de e elevado a potência A.
+|`exp2(A)`|Exponencial de `A` na base $2$.
+|`floor(A)`|Piso de `A`. Arredonda para o próximo menor inteiro.
+|`hypot(A,B)`|Função de distância Euclidiana.
+|`if(A,B,C)`|Se `int(A)` é diferente de $0$, retorna o valor de `B`, senão retorna `C`.
+|`imag(A)`|Retorna a parte imaginária do número complexo `A`.
+|`int(A)`|Arredonda `A` para o inteiro mais próximo.
+|`log(A)`|Logaritmo natural (base $e$) de `A`.
+|`log2(A)`|Logaritmo na base $2$ de `A`.
+|`log10(A)`|Logaritmo na base $10$ de A.
+|`max(A,B)`|Se `A>B`, o resultado é `A`, senão é `B`.
+|`min(A,B)`|Se `A<B`, o resultado é `A`, senão é `B`.
+|`polar(A,B)`|Retorna o número complexo de magnitude `A` e ângulo de fase `B` (em radianos).
+|`pow(A,B)`|Exponenciação (`A` elevado à potência `B`)
+|`real(A,B)`|Retorna a parte real do número complexo `A`.
+|`sec(A)`|Secante de `A`.
+|`sin(A)`|Seno de `A`. Retorna o ângulo em radianos.
+|`sinh(A)`|Mesmo que `sin()`, mas para seno hiperbólico.
+|`sqrt(A)`|Raiz quadrada de `A`.
+|`tan(A)`|Tangente de `A`. Retorna o ângulo em radianos.
+|`tanh(A)`|Mesmo que `tan()`, mas para tangente hiperbólica.
+|`trunc(A)`|Valor truncado de `A`. Retorna o número inteiro de `A` sem a parcela fracionada.
+
+É possível atribuir novas variáveis utilizando a seguinte sintaxe: 
+
+``` cpp
+<nome da variável> := <expressão>; <função>
+```
+
+Por exemplo:
+``` cpp
+comprimento := sqrt(x*x+y*y); 2*comprimento*sin(comprimento)
+```
+
+:::tip Dica
+O caractere de espaço e de nova linha são ignorados na interpretação da expressão, portanto para maior organização, o código anterior pode ser escrito da seguinte forma:
+``` cpp
+comprimento := sqrt(x*x+y*y);
+2*comprimento*sin(comprimento)
+```
+:::
+
+:::warning Cuidado!
+Note que a expressão que determina o valor de saída do bloco **não possui** o caractere `;` em seu final.
+:::
+
+## Formulário de edição de dados do bloco de Expressão Matemática
+O formulário de inserção e edição das entradas do bloco e da expressão matemática genérica, assim como ferramentas de auxílio de sua construção é apresentado na figura abaixo.
+
+<div><center><img src={useBaseUrl("images/mathExpressionForm.png")} alt="Formulário de edição de dados do bloco de expressão matemática no PSP-UFU" title="Formulário de edição de dados do bloco de expressão matemática no PSP-UFU" /></center></div>
+
+No campo de “Variáveis de entrada” é inserida uma lista com os nomes das entradas separados por espaços. Um número qualquer de entrada pode ser definido nessa lista esses nomes são apresentados no ícone gráfico presente no editor de controle, além de serem destacados na expressão inserida pelo usuário. O número de entradas e saídas se comporta de forma semelhante aos [blocos somadores](sum).
+
+Abaixo do campo das variáveis de entrada está presente o local para inserção da expressão matemática. A sintaxe da expressão inserida pelo usuário possui realce (por meio de diferentes formas e cores da fonte) para números, operadores, variáveis de entrada, funções e constantes, facilitando a criação, manipulação e identificação de erros de digitação e lógica.
+
+:::info Informação
+Como ferramenta de auxílio ao usuário foi desenvolvida uma verificação da expressão inserida.
+:::
+
+Tal ferramenta irá encontrar erros e indicará ao usuário qual o tipo do erro, além da sua localização, destacando-o. A figura anterior exemplifica a identificação automática do erro pelo PSP-UFU, assim como sua posição na expressão inserida.
+
+## Exemplo de Expressão Matemática
+A corrente de campo em $p.u.$ pode ser estimada de forma aproximada utilizando as potências ativa ($P$) e reativa ($Q$), assim como as reatâncias transitórias de eixo direto ($x_d$) e em quadratura ($x_q$) e o módulo da tensão terminal ($V$) da máquina:
+$$
+i_f \approx \sqrt{ \left( V + Q' \right)^2 + P^2} + \left(\frac{x_d}{x_q} +1{,}0 \right) \times \frac{Q' \left( V + Q' \right) + {P'}^2}{\sqrt{\left( V + Q'\right)^2 + P^2}}
+$$
+Em que:
+- $P' = x_q \times \frac{P}{V}$
+- $Q' = x_q \times \frac{Q}{V}$
+
+Primeiramente, deve-se inserir no campo "variáveis de entrada" as grandezas fornecidas pelo PSP-UFU. Nesse caso, como pode ser observado no bloco de [entrada / saída](io), todas as variáveis necessárias são fornecidas: $P$, $Q$ e $V$. Essas variáveis devem ser inseridas separadas por espaço: `p q v`.
+
+Utilizando três blocos de [entrada / saída](io) pode-se fornecer tais dados ao conectá-los ao bloco de expressão matemática.
+
+As reatâncias transitórias de eixo direto ($x_d$) e em quadratura ($x_q$) podem ser definidas diretamente na expressão matemática:
+``` cpp
+xd := 0.146;
+xq := 0.0969;
+```
+
+Os valores de $P'$ e $Q'$ podem ser também calculados:
+``` cpp
+yp := xq * p / v;
+yq := xq * q / v;
+```
+
+Com todos os dados necessários pode-se calcular a corrente de campo:
+``` cpp
+i_f := sqrt((v + yq)^2 + p^2) + (xd / xq + 1.0) *
+       ((yq * (v + yq) + yp^2) / sqrt((v + yq)^2 + p^2));
+```
+
+Finalmente, pode-se definir a saída do bloco (não inserindo `;`):
+``` cpp
+i_f
+```
+
+Portanto, para as entradas definidas como `p q v`, a expressão matemática total para cálculo da corrente de campo será:
+``` cpp
+xd := 0.146;
+xq := 0.0969;
+yp := xq * p / v;
+yq := xq * q / v;
+i_f := sqrt((v + yq)^2 + p^2) + (xd / xq + 1.0) *
+       ((yq * (v + yq) + yp^2) / sqrt((v + yq)^2 + p^2));
+i_f
+```
+
+## Referências
+- NIEMINEN, J.; YLILUOMA, J. Function Parser for C++ v4.5.2. Disponível em: <http://warp.povusers.org/FunctionParser/>. 
\ No newline at end of file
diff --git a/docusaurus/docs/multiplier.md b/docusaurus/docs/multiplier.md
index 365f1aa..f21610b 100644
--- a/docusaurus/docs/multiplier.md
+++ b/docusaurus/docs/multiplier.md
@@ -5,4 +5,12 @@ sidebar_label: Multiplicador
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+Esse elemento é bastante simples e cumpre com a função matemáticas de seu nome.
+
+Possui duas entradas de valores reais e sua saída é computada na sequência do nó superior pelo inferior, ou seja, a saída será o valor presente no nó 1 multiplicado pelo nó 2.
+
+:::caution Atenção!
+Nós não conectados no multiplicador são assumidos com o valor unitário e para o divisor é considerado valor nulo.
+:::
\ No newline at end of file
diff --git a/docusaurus/docs/rateLimiter.md b/docusaurus/docs/rateLimiter.md
index 16abcb9..39419ea 100644
--- a/docusaurus/docs/rateLimiter.md
+++ b/docusaurus/docs/rateLimiter.md
@@ -5,4 +5,37 @@ sidebar_label: Limitador de taxa
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+Os blocos de limite de taxa têm como objetivo conter a taxa de crescimento ou decrescimento da sua entrada a valores inseridos pelo usuário. A taxa de variação é calculada a partir dos valores de entrada atual e passado e, caso seja violada, será definida uma saída que respeite essas taxas (de crescimento ou decrescimento).
+
+A taxa ($r$) é calculada de acordo com a equação:
+$$
+r = \frac{u_n - y_{n-1}}{h}
+$$
+Em que:
+- $u_n$	é a entrada atual do bloco
+- $y_{n-1}$	é o valor de saída anterior do bloco
+- $h$	é o passo de integração
+
+Obtida a taxa, o bloco irá resultar em um valor calculado pelas seguintes condições:
+$$
+\begin{cases}
+h \times R_{cre}{,}	& \text{se } r > R_{cre} \\
+u_n{,}		& \text{se } R_{dec} \le r \le R_{cre}\\
+h \times R_{dec}{,}	& \text{se } r < R_{dec}
+\end{cases}
+$$
+Em que:
+- $R_{cre}$ e $R_{dec}$	são as taxas de crescimento e decaimento, respectivamente
+
+## Formulário de edição de dados do Limitador de taxa
+A figura abaixo apresenta o formulário de edição de dados do bloco limitador de taxa.
+
+<div><center><img src={useBaseUrl("images/rateLimitForm.png")} alt="Formulário de edição de dados do bloco limitador de taxa no PSP-UFU" title="Formulário de edição de dados do bloco limitador de taxa no PSP-UFU" /></center></div>
+
+Esse bloco é definido pelo **limite superior (taxa de crescimento máxima) e inferior (taxa de decrescimento máxima)**, inseridos pelo usuário.
+
+:::info Informação
+Esses blocos são úteis para limitar variações bruscas na entrada que possam comprometer o controle ou limites físicos de modelos de turbina, por exemplo.
+:::
\ No newline at end of file
diff --git a/docusaurus/docs/sum.md b/docusaurus/docs/sum.md
index 35afdbc..270b66c 100644
--- a/docusaurus/docs/sum.md
+++ b/docusaurus/docs/sum.md
@@ -5,4 +5,22 @@ sidebar_label: Somador
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+Como o próprio nome sugere, os somadores são elementos de controle capazes de somar qualquer quantidade de valores reais.
+
+## Formulário de edição de dados do somador
+
+A quantidade de entradas, assim como seus sinais são definidas pelo usuário, como mostra a figura abaixo.
+
+<div><center><img src={useBaseUrl("images/sumForm.png")} alt="Formulário de edição de dados do somador no PSP-UFU" title="Formulário de edição de dados do somador no PSP-UFU" /></center></div>
+
+No seu único campo “**Sinais**” é inserida uma lista de sinais **separados por espaços** contendo os símbolos “+” para uma entrada positiva e “-” para negativa.
+
+:::info Informação
+O usuário pode inserir duas ou mais entradas de sinais no bloco.
+:::
+
+Uma vez inseridas novas entradas, nós correspondentes serão incluídos no elemento gráfico do somador, o qual poderá ser conectado por meio das linhas de conexão.
+
+De forma semelhante, o usuário poderá excluir entradas de sinais pré-existentes, as quais serão removidas no ícone gráfico pela remoção do nó e da linha (caso exista alguma conectada).
diff --git a/docusaurus/docs/syncGenerator.md b/docusaurus/docs/syncGenerator.md
index e43a51a..253d8a4 100644
--- a/docusaurus/docs/syncGenerator.md
+++ b/docusaurus/docs/syncGenerator.md
@@ -7,6 +7,9 @@ import useBaseUrl from "@docusaurus/useBaseUrl";
 
 <link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
 
+import Tabs from '@theme/Tabs';
+import TabItem from '@theme/TabItem';
+
 > Uma máquina de corrente alternada na qual a frequência das tensões geradas e a velocidade da máquina estão em uma proporção constante. [*tradução livre* - IEC 60050](
 http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=411-31-08).
 
@@ -118,6 +121,23 @@ Na sequência são apresentados tais modelos, incluídos os efeitos da saturaç�
 Em todos os modelos as equações diferenciais mecânicas são solucionadas.
 :::
 
+#### Saturação
+Para representar matematicamente o efeito da saturação nas equações das máquinas síncronas são introduzidos “fatores de saturação” que modificam as impedâncias do circuito equivalente, os quais dependem de uma reatância de dispersão efetiva, chamada de reatância de Potier ($x_p$).
+
+Tal reatância pode ser obtida por meio de ensaios (utilizando curvas de saturação de circuito aberto e carga de fator de potência zero) ou estimadas de forma aproximada por outros parâmetros da máquina. A reatância de dispersão ($x_l$), aqui substituída de forma aproximada por $x_p$, representa a parcela da reatância da máquina originados do fluxo magnético que percorrem o ar na maioria de seu caminho e, portanto, é independente da saturação.
+
+O método implementado no programa permite reproduzir a saturação em ambos os eixos (direto e em quadratura), diferindo entre si devido à divergência no tamanho do entreferro. É assumido que a soma vetorial das duas componentes do fluxo magnético saturado está em fase com a f.m.m. e proporcional à Tensão de Potier ($E_p$, a qual é a tensão atrás da reatância de Potier).
+
+Para isso, são utilizados internamente dois fatores de saturação, sendo um no eixo direto ($s_d$) e outro no eixo em quadratura ($s_q$). Esses fatores de saturação são **automaticamente calculados** a cada passo de integração e dependem da curva de saturação da máquina definida pelo [fator de saturação inserido no formulário de edição de dados](syncGenerator#fator-de-saturação).
+
+Portanto as reatâncias saturadas, que devem ser inseridas nas equações algébricas da máquina, são definidas pelas seguintes equações:
+$$
+x_{ds}=\frac{x_d-x_p}{s_d +x_p}\\
+x_{qs}=\frac{x_q-x_p}{s_q +x_p}
+$$
+
+Essas equações também são utilizadas para as reatâncias transitórias e subtransitórias, visto que o valor da reatância de Potier (ou de dispersão) não é alterada.
+
 #### Barramento infinito
 Algumas referências incluem um modelo sem equações diferenciais, em que a máquina é somente representada por uma tensão constante atrás de uma reatância transitória de eixo direto. Tal é utilizado na representação de um **barramento infinito**, o qual é normalmente constituído de um subsistema muito maior àquele simulado.
 
@@ -147,8 +167,17 @@ No formulário de estabilidade pode ser observado o botão "Chaveamento" na part
 
 <div><center><img src={useBaseUrl("images/syncGeneratorSw.png")} alt="Formulário de chaveamento do gerador síncrono" title="Formulário de chaveamento do gerador síncrono" /></center></div>
 
----
-### Geral
+<Tabs
+  groupId="syncGenerator-tabs"
+  defaultValue="general"
+  values={[
+    {label: 'Geral', value: 'general'},
+    {label: 'Falta', value: 'fault'},
+    {label: 'Botão Estabilidade', value: 'stability'},
+    {label: 'Botão Chaveamento', value: 'switching'},
+  ]
+}>
+<TabItem value="general">
 
 #### Nome
 Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão [Unicode](https://pt.wikipedia.org/wiki/Unicode).
@@ -175,8 +204,8 @@ Limites de potência reativa máxima e mínima do gerador para controle de tens�
 #### Utilizar potência nominal como base
 Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a [potência base do sistema](simulationConfig).
 
----
-### Falta
+</TabItem>
+<TabItem value="fault">
 
 #### Impedâncias de sequência
 Valores de resistência e reatância para cálculo das correntes de falta. São inseridos dados de sequência positiva, negativa e zero.
@@ -187,8 +216,8 @@ Valores utilizados para o cálculo das correntes de falta do tipo fase-terra e f
 #### Neutro aterrado
 Indica se o neutro do gerador é aterrado.
 
----
-### Botão Estabilidade
+</TabItem>
+<TabItem value="stability">
 
 #### Imprimir dados da máquina síncrona
 Exibe os dados do gerador síncrono nos gráficos no tempo. Os seguintes dados são exibidos:
@@ -219,6 +248,13 @@ Representa o valor (em $p.u.$) de corrente de campo necessária para atingir 1,2
 Esse valor deve ser **maior que 1,2**, ou irá gerar erros na simulação. Caso não seja informado, a saturação da máquina não é considerada nos cálculos.
 :::
 
+#### Frequência de circuito aberto
+Indica a velocidade da máquina no caso de início da simulação desconectada da rede.
+
+:::info Informação
+Essa informação é particularmente útil na análise de conexão de geradores dessincronizados na rede.
+:::
+
 #### Reatâncias síncronas
 Valores de reatância síncrona (regime permanente) da máquina. Os valores de eixo direto e em quadratura devem ser iguais ou muito próximos para representação de uma máquina de polos lisos, enquanto para polos salientes esses valores são distintos.
 
@@ -234,12 +270,29 @@ De acordo com a quantidade de parâmetros inseridos é definido internamente pel
 #### Reatâncias e constantes de tempo subtransitórias
 Parâmetros subtransitórios da máquina síncrona em $p.u.$ ou segundos, representando em detalhes a presença de enrolamentos amortecedores. Assim como os dados transitórios, esses parâmetros definem o modelo da máquina.
 
----
-### Botão Chaveamento
+</TabItem>
+<TabItem value="switching">
+
 O botão "Chaveamento" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do gerador durante o estudo de [estabilidade](stability).
 
 Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
 
+</TabItem>
+</Tabs>
+
+## Acesso aos controles da máquina síncrona
+Como já [mencionado anteriormente](syncGenerator#utilizar-avr-e-regulador-de-velocidade), os reguladores de velocidade e tensão da máquina síncrona podem ser acionados ou inibidos por meio das caixas de seleção "[Utilizar AVR e regulador de velocidade](syncGenerator#utilizar-avr-e-regulador-de-velocidade)". Ambas as opções irão acessar o [editor de controles](controlEditor).
+
+O acesso aos controles do **AVR** poderão então ser criados e manipulados ao clicar no botão "Editar AVR", assim como o **Regulador de Velocidade** é acessado no botão "Editar regulador de velocidade".
+
+:::caution Atenção!
+No PSP-UFU a opção de editar o **AVR** engloba mais que somente o controle de tensão da máquina. Nele **deve** ser inserida a malha de controle da máquina assim como a **excitatriz da máquina síncrona**. Outras estratégias de controle (opcionais), como PSS (*Power System Stabilizer*) e/ou controles de sobre e sub excitação, são também implementadas em conjunto.
+:::
+
+:::caution Atenção!
+Assim como no AVR, o **Regulador de Velocidade** engloba mais que a regulação primária da máquina. Nessa opção **deve** ser inserida ao menos a malha de controle da regulação primária de velocidade, assim como o **modelo da turbina**. Estratégias opcionais de controle da velocidade também são inseridas nessa opção.
+:::
+
 ## Referências
 1. MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: https://doi.org/10.1007/978-3-642-13669-6
 2. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
diff --git a/docusaurus/docs/syncMotor.md b/docusaurus/docs/syncMotor.md
index b1b116c..fb5d005 100644
--- a/docusaurus/docs/syncMotor.md
+++ b/docusaurus/docs/syncMotor.md
@@ -7,6 +7,9 @@ import useBaseUrl from "@docusaurus/useBaseUrl";
 
 <link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
 
+import Tabs from '@theme/Tabs';
+import TabItem from '@theme/TabItem';
+
 > Uma máquina síncrona operando sem carga mecânica e fornecendo ou absorvendo energia reativa. [*tradução livre* - IEC 60050](
 http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=411-34-03).
 
@@ -30,8 +33,16 @@ A imagem abaixo apresenta o formulário de inserção/alteração de dados dos c
 
 <div><center><img src={useBaseUrl("images/syncMotorForm.png")} alt="Formulário dos compensadores síncronos no PSP-UFU" title="Formulário dos compensadores síncronos no PSP-UFU" /></center></div>
 
----
-### Geral
+
+<Tabs
+  groupId="syncMotor-tabs"
+  defaultValue="general"
+  values={[
+    {label: 'Geral', value: 'general'},
+    {label: 'Falta', value: 'fault'},
+  ]
+}>
+<TabItem value="general">
 
 #### Nome
 Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão [Unicode](https://pt.wikipedia.org/wiki/Unicode).
@@ -58,8 +69,8 @@ Limites de potência reativa máxima e mínima do compensador para controle de t
 #### Utilizar potência nominal como base
 Caso essa opção seja marcada, o programa irá utilizar a potência nominal do compensador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a [potência base do sistema](simulationConfig).
 
----
-### Falta
+</TabItem>
+<TabItem value="fault">
 
 #### Impedâncias de sequência
 Valores de resistência e reatância para cálculo das correntes de falta. São inseridos dados de sequência positiva, negativa e zero.
@@ -68,4 +79,7 @@ Valores de resistência e reatância para cálculo das correntes de falta. São
 Valores utilizados para o cálculo das correntes de falta do tipo fase-terra e fase-fase-terra. Caso o neutro do gerador não seja aterrado, o valor inserido nesse campo é ignorado.
 
 #### Neutro aterrado
-Indica se o neutro do gerador é aterrado.
\ No newline at end of file
+Indica se o neutro do gerador é aterrado.
+
+</TabItem>
+</Tabs>
\ No newline at end of file
diff --git a/docusaurus/docs/tabularReport.md b/docusaurus/docs/tabularReport.md
new file mode 100644
index 0000000..b59ad78
--- /dev/null
+++ b/docusaurus/docs/tabularReport.md
@@ -0,0 +1,8 @@
+---
+id: tabularReport
+title: Relatórios Tabulares
+sidebar_label: Relatórios Tabulares
+---
+import useBaseUrl from "@docusaurus/useBaseUrl";
+
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
diff --git a/docusaurus/docs/text.md b/docusaurus/docs/text.md
new file mode 100644
index 0000000..3242c56
--- /dev/null
+++ b/docusaurus/docs/text.md
@@ -0,0 +1,8 @@
+---
+id: text
+title: Texto Vinculado
+sidebar_label: Texto Vinculado
+---
+import useBaseUrl from "@docusaurus/useBaseUrl";
+
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
diff --git a/docusaurus/docs/transformer.md b/docusaurus/docs/transformer.md
index 5fc8c07..ead4e06 100644
--- a/docusaurus/docs/transformer.md
+++ b/docusaurus/docs/transformer.md
@@ -7,6 +7,9 @@ import useBaseUrl from "@docusaurus/useBaseUrl";
 
 <link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
 
+import Tabs from '@theme/Tabs';
+import TabItem from '@theme/TabItem';
+
 >Aparelho estático com dois ou mais enrolamentos que, por indução eletromagnética, transforma um sistema de tensão e corrente alternada em outro sistema de tensão e corrente geralmente de valores diferentes e na mesma frequência com o objetivo de transmitir energia elétrica. [*tradução livre* - IEC 60050](
 http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=421-01-01).
 
@@ -88,8 +91,16 @@ Além desses dois contextos, pode ser observado o botão "Estabilidade" na parte
 
 <div><center><img src={useBaseUrl("images/trafoSw.png")} alt="Formulário de chaveamento do transformador" title="Formulário de chaveamento do transformador" /></center></div>
 
----
-### Geral
+<Tabs
+  groupId="transformer-tabs"
+  defaultValue="general"
+  values={[
+    {label: 'Geral', value: 'general'},
+    {label: 'Falta', value: 'fault'},
+    {label: 'Botão Estabilidade', value: 'stability'},
+  ]
+}>
+<TabItem value="general">
 
 #### Nome
 Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão [Unicode](https://pt.wikipedia.org/wiki/Unicode).
@@ -141,8 +152,8 @@ Defasagem do transformador em relação ao primário, em graus. Esse valor indep
 #### Utilizar potência nominal como base
 Caso essa opção seja marcada, o programa irá utilizar a potência nominal do transformador como base para a conversão das unidades, caso contrário será usada a [potência base do sistema](simulationConfig).
 
----
-### Falta
+</TabItem>
+<TabItem value="fault">
 
 #### Impedância de sequência zero do transformador
 Esses parâmetros são necessários para o correto cálculo das correntes de [falta desbalanceadas](fault) (fase-fase, fase-fase-terra e fase-terra) e devem ser inseridos em $p.u.$
@@ -154,8 +165,12 @@ A não inserção desses dados acarretarão em resultados incorretos para [falta
 #### Impedâncias de aterramento
 As impedâncias de aterramento são somente utilizadas para conexão $Y_{aterrado}$ e devem ser inseridas em $p.u.$
 
----
-### Botão Estabilidade
+</TabItem>
+<TabItem value="stability">
+
 O botão "Estabilidade" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do transformador durante o estudo de [estabilidade](stability).
 
-Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
\ No newline at end of file
+Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.
+
+</TabItem>
+</Tabs>
\ No newline at end of file
diff --git a/docusaurus/sidebars.js b/docusaurus/sidebars.js
index 402bc74..2e0c2c2 100644
--- a/docusaurus/sidebars.js
+++ b/docusaurus/sidebars.js
@@ -28,7 +28,13 @@ module.exports = {
 		'fault',
 		'harmonics',
 		'stability',
-		'simulationConfig'
+		'simulationConfig',
+	],
+	'Visualização dos Dados' : [
+		'text',
+		'tabularReport',
+		'graphViewer',
+		'heatmap'
 	],
   },
 };
diff --git a/docusaurus/src/css/custom.css b/docusaurus/src/css/custom.css
index 08cde97..7ab37bb 100644
--- a/docusaurus/src/css/custom.css
+++ b/docusaurus/src/css/custom.css
@@ -29,3 +29,14 @@ video {
   width: 100%;
   height: 100%;
 }
+
+h4 { 
+  display: block;
+  font-size: 1em;
+  margin-top: 1.33em;
+  margin-bottom: 1.33em;
+  margin-left: 0;
+  margin-right: 0;
+  font-weight: bold;
+  text-decoration: underline;
+}
\ No newline at end of file
diff --git a/docusaurus/static/images/expForm.png b/docusaurus/static/images/expForm.png
new file mode 100644
index 0000000..896ad27
--- /dev/null
+++ b/docusaurus/static/images/expForm.png
diff --git a/docusaurus/static/images/limiterForm.png b/docusaurus/static/images/limiterForm.png
new file mode 100644
index 0000000..3a8f83f
--- /dev/null
+++ b/docusaurus/static/images/limiterForm.png
diff --git a/docusaurus/static/images/mathExpressionForm.png b/docusaurus/static/images/mathExpressionForm.png
new file mode 100644
index 0000000..004901b
--- /dev/null
+++ b/docusaurus/static/images/mathExpressionForm.png
diff --git a/docusaurus/static/images/rateLimitForm.png b/docusaurus/static/images/rateLimitForm.png
new file mode 100644
index 0000000..bbd3d89
--- /dev/null
+++ b/docusaurus/static/images/rateLimitForm.png
diff --git a/docusaurus/static/images/sumForm.png b/docusaurus/static/images/sumForm.png
new file mode 100644
index 0000000..75b8664
--- /dev/null
+++ b/docusaurus/static/images/sumForm.png
diff --git a/docusaurus/static/images/syncGeneratorStabForm.png b/docusaurus/static/images/syncGeneratorStabForm.png
index 2dde53f..64b1695 100644
--- a/docusaurus/static/images/syncGeneratorStabForm.png
+++ b/docusaurus/static/images/syncGeneratorStabForm.png