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diminuem a corre\xe7\xe3o."),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"})))),"Informa\xe7\xe3o")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Valores menores que ",Object(m.b)("span",Object(s.a)({parentName:"p"},{className:"math 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",Object(m.b)("em",{parentName:"p"},"podem")," auxiliar na converg\xeancia, por\xe9m aumentam o n\xfamero de itera\xe7\xf5es e consequentemente o tempo de processamento do m\xe9todo."))),Object(m.b)("p",null,"Essa op\xe7\xe3o \xe9 habilitada somente para o m\xe9todo de ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow#newton-raphson"}),"Newton-Raphson"),"."),Object(m.b)("h4",{id:"toler\xe2ncia-do-gauss"},"Toler\xe2ncia do Gauss"),Object(m.b)("p",null,"Define a toler\xe2ncia do Gauss-Seidel para o m\xe9todo h\xedbrido. 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t=e?l._parseNumbers(e):{};this.facets=t.facets||[],this.disjunctiveFacets=t.disjunctiveFacets||[],this.hierarchicalFacets=t.hierarchicalFacets||[],this.facetsRefinements=t.facetsRefinements||{},this.facetsExcludes=t.facetsExcludes||{},this.disjunctiveFacetsRefinements=t.disjunctiveFacetsRefinements||{},this.numericRefinements=t.numericRefinements||{},this.tagRefinements=t.tagRefinements||[],this.hierarchicalFacetsRefinements=t.hierarchicalFacetsRefinements||{};var i=this;Object.keys(t).forEach((function(e){var n=-1!==l.PARAMETERS.indexOf(e),r=void 0!==t[e];!n&&r&&(i[e]=t[e])}))}l.PARAMETERS=Object.keys(new l),l._parseNumbers=function(e){if(e instanceof l)return e;var t={};if(["aroundPrecision","aroundRadius","getRankingInfo","minWordSizefor2Typos","minWordSizefor1Typo","page","maxValuesPerFacet","distinct","minimumAroundRadius","hitsPerPage","minProximity"].forEach((function(i){var n=e[i];if("string"==typeof n){var 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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},212: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=0||(r[i]=e[i]);return r}},213:function(e,t,i){"use strict";var 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Tal valor \xe9 definido pelo usu\xe1rio e caso seja um curto-circuito franco, um valor n\xe3o nulo, mas suficientemente pr\xf3ximo de zero, \xe9 aplicado, de forma que a tens\xe3o no barramento \xe9 levada a zero durante o dist\xfarbio.")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Chaveamento de ramo"),": Da mesma forma que as faltas, o chaveamento de ramos \xe9 realizado por meio da altera\xe7\xe3o na matriz admit\xe2ncia, removendo ou inserindo os par\xe2metros do elemento a ser chaveado.\nCada ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"elemento de pot\xeancia"),' possui um bot\xe3o de "Chaveamento" ou "Estabilidade", em que pode ser inserido os tempos de remo\xe7\xe3o e/ou inser\xe7\xe3o do componente.')),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Chaveamento de m\xe1quinas"),": A remo\xe7\xe3o de uma m\xe1quina s\xedncrona \xe9 efetivada com a retirada de sua participa\xe7\xe3o no vetor de correntes, al\xe9m da remo\xe7\xe3o de sua admit\xe2ncia fict\xedcia.\nAssim como os ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"elementos de pot\xeancia"),", as ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quinas s\xedncronas"),' possui um bot\xe3o "Chaveamento", em que pode ser inserido os tempos de remo\xe7\xe3o e/ou inser\xe7\xe3o do componente.'),Object(m.b)("div",Object(s.a)({parentName:"li"},{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"},"Mesmo que removida da barra, os par\xe2metros das ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quinas s\xedncronas")," continuam a ser calculados com a corrente do estator nula, podendo fornecer resultados em uma eventual reconex\xe3o."))))),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"},"Eventos nos ",Object(m.b)("strong",{parentName:"p"},"sistemas de controle")," podem ser facilmente introduzidos com o bloco de ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mathExpression"}),"express\xe3o matem\xe1tica"),". Nesse caso, tais eventos ",Object(m.b)("strong",{parentName:"p"},"n\xe3o")," ser\xe3o exibidos na lista de eventos de estabilidade."))),Object(m.b)("h3",{id:"erros-comuns-na-execu\xe7\xe3o-do-estudo-de-estabilidade"},"Erros comuns na execu\xe7\xe3o do estudo de estabilidade"),Object(m.b)("p",null,"A seguir s\xe3o apresentados os erros mais comuns relacionados ao estudo de estabilidade."),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-n\xe3o-foi-poss\xedvel-construir-a-matriz-admit\xe2ncia"},'A seguinte mensagem de erro \xe9 exibida: "N\xe3o foi poss\xedvel construir a matriz admit\xe2ncia"'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel construir a matriz admit\xe2ncia de barras. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum barramento est\xe1 isolado"),". Esse erro \xe9 bastante comum e pode ocorrer ao inserir um barramento sem conect\xe1-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solu\xe7\xe3o \xe9 eliminar essa barra do diagrama."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis.")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-erro-ao-inicializar-os-valores-de-satura\xe7\xe3o-do"},'A seguinte mensagem de erro \xe9 exibida: "Erro ao inicializar os valores de satura\xe7\xe3o do..."'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel calcular os fatores de satura\xe7\xe3o da ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quina s\xedncrona"),". As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O fator de satura\xe7\xe3o \xe9 menor que 1,2"),". Esse valor deve ser maior que 1,2, ou ir\xe1 gerar erros na simula\xe7\xe3o. Caso n\xe3o seja informado, a satura\xe7\xe3o da m\xe1quina n\xe3o \xe9 considerada nos c\xe1lculos."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros da m\xe1quina s\xedncrona est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o das m\xe1quinas s\xedncronas sejam inseridos, o c\xe1lculo dos fatores de satura\xe7\xe3o pode divergir. Verifique se os dados foram inseridos corretamente.")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-erro-ao-inicializar-o-avr--regulador-de-velocidade"},'A seguinte mensagem de erro \xe9 exibida: "Erro ao inicializar o AVR / regulador de velocidade..."'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor#inicializa%C3%A7%C3%A3o-do-sistema-de-controle"}),"inicializar o sistema de controle")," de uma ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quina s\xedncrona"),". As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O sistema de controle est\xe1 vazio"),". Caso esteja habilitado o AVR e/ou o regulador de velocidade e o controle n\xe3o foi inserido, esse erro pode ser acionado. Insira o controle da m\xe1quina ou desmarque a op\xe7\xe3o de utiliza\xe7\xe3o do AVR e/ou regulador de velocidade."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O sistema de controle n\xe3o possui ao menos uma entrada e uma sa\xedda"),". O sistema de controle deve ter ao menos uma ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"io"}),"entrada e uma sa\xedda"),", caso contr\xe1rio apresentar\xe1 erro de execu\xe7\xe3o."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O passo de integra\xe7\xe3o est\xe1 muito pequeno"),". Caso o passo de integra\xe7\xe3o esteja muito pequeno, os c\xe1lculos gerar\xe3o erros e ir\xe3o divergir. Reduza o passo de integra\xe7\xe3o nas ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),".")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-imposs\xedvel-resolver-as-m\xe1quinas-do-sistema"},'A seguinte mensagem de erro \xe9 exibida: "Imposs\xedvel resolver as m\xe1quinas do sistema"'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel resolver as EADs das m\xe1quinas s\xedncronas inseridas no sistemas. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros da m\xe1quina s\xedncrona est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o das m\xe1quinas s\xedncronas sejam inseridos, o c\xe1lculo das EADs pode se tornar imposs\xedvel. Verifique se os dados foram inseridos corretamente."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O passo de integra\xe7\xe3o est\xe1 muito pequeno"),". Caso o passo de integra\xe7\xe3o esteja muito pequeno, os c\xe1lculos gerar\xe3o erros e ir\xe3o divergir. Reduza o passo de integra\xe7\xe3o nas ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),"."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum barramento est\xe1 isolado"),". Esse erro \xe9 bastante comum e pode ocorrer ao inserir um barramento sem conect\xe1-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solu\xe7\xe3o \xe9 eliminar essa barra do diagrama."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis.")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-erro-ao-inicializar-o-escorregamento-do-motor"},'A seguinte mensagem de erro \xe9 exibida: "Erro ao inicializar o escorregamento do motor..."'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel calcular o valor de escorregamento inicial do motor de indu\xe7\xe3o. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros de estabilidade do motor est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o dos motores de indu\xe7\xe3o sejam inseridos, o c\xe1lculo do escorregamento pode se tornar imposs\xedvel. Verifique se os dados foram inseridos corretamente.")),Object(m.b)("h2",{id:"estrutura-da-ferramenta-de-estabilidade"},"Estrutura da ferramenta de estabilidade"),Object(m.b)("p",null,"A estabilidade de um SEP \xe9 um problema din\xe2mico e necessita de modelos mais elaborados de elementos de pot\xeancia comparados \xe0queles apresentados nos outros estudos. Esses modelos s\xe3o descritos individualmente, com destaque \xe0s ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator#gerador-s%C3%ADncrono-no-estudo-de-estabilidade"}),"m\xe1quinas s\xedncronas"),", ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"load#carga-no-estudo-de-estabilidade"}),"cargas ZIP")," e ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-estudo-de-estabilidade"}),"motores de indu\xe7\xe3o"),"."),Object(m.b)("p",null,"A representa\xe7\xe3o dos demais componentes do sistema el\xe9trico: ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"line"}),"linhas de transmiss\xe3o"),", ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"transformer"}),"transformadores")," e elementos ",Object(m.b)("em",{parentName:"p"},"shunt")," (com exce\xe7\xe3o de cargas ZIP), que formam a rede de transmiss\xe3o ou distribui\xe7\xe3o balanceada, \xe9 realizada utilizando os mesmos modelos do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow"}),"fluxo de carga"),"."),Object(m.b)("p",null,"Os modelos din\xe2micos para a an\xe1lise no dom\xednio do tempo s\xe3o na forma de um sistema de equa\xe7\xf5es alg\xe9brico-diferenciais (EADs), descritas a seguir:"),Object(m.b)("div",{className:"math 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Os m\xe9todos expl\xedcitos, devido \xe0 sua formula\xe7\xe3o, calculam diretamente o estado do sistema em um instante de tempo posterior, enquanto m\xe9todos impl\xedcitos envolvem estados atuais e posteriores em suas equa\xe7\xf5es, exigindo, portanto, um processo iterativo."),Object(m.b)("p",null,"As constantes de tempo presentes no estudo de estabilidade t\xeam uma grande varia\xe7\xe3o em seu valor (podem variar de ",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)("mn",{parentName:"mrow"},"1"),Object(m.b)("msup",{parentName:"mrow"},Object(m.b)("mn",{parentName:"msup"},"0"),Object(m.b)("mrow",{parentName:"msup"},Object(m.b)("mo",{parentName:"mrow"},"\u2212"),Object(m.b)("mn",{parentName:"mrow"},"3"))),Object(m.b)("mtext",{parentName:"mrow"},"\xa0"),Object(m.b)("mi",{parentName:"mrow"},"s")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"10^{-3}~s")))),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:"0.8141079999999999em",verticalAlign:"0em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"1"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"msupsub"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-t"}),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:"0.8141079999999999em"}}),Object(m.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3.063em",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 mtight"}),"\u2212"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mtight"}),"3"))))))))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mspace nobreak"}),"\xa0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"s")))))," a ",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)("mn",{parentName:"mrow"},"10"),Object(m.b)("mtext",{parentName:"mrow"},"\xa0"),Object(m.b)("mi",{parentName:"mrow"},"s")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"10~s")))),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:"0.64444em",verticalAlign:"0em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"1"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mspace nobreak"}),"\xa0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"s"))))),"). Isso torna o sistema de equa\xe7\xf5es diferenciais da m\xe1quina s\xedncrona como um sistema r\xedgido (",Object(m.b)("em",{parentName:"p"},Object(m.b)("a",Object(s.a)({parentName:"em"},{href:"https://en.wikipedia.org/wiki/Stiff_equation"}),"stiff equation")),"). Caso a an\xe1lise da estabilidade num\xe9rica tanto das equa\xe7\xf5es diferenciais r\xedgidas quanto do m\xe9todo de integra\xe7\xe3o obtenham o mesmo comportamento, o m\xe9todo \xe9 chamado de absolutamente est\xe1vel, ou A-est\xe1vel."),Object(m.b)("p",null,"M\xe9todos de integra\xe7\xe3o num\xe9rica expl\xedcitos, como por exemplo o ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods"}),"Runge-Kutta")," de quarta ordem, n\xe3o podem ser A-est\xe1veis e, portanto, normalmente possuem comportamento ruim em problemas com equa\xe7\xf5es diferenciais r\xedgidas. Por outro lado, m\xe9todos impl\xedcitos podem ser A-est\xe1veis. Um m\xe9todo impl\xedcito adequado para solu\xe7\xe3o do comportamento din\xe2mico de sistemas el\xe9tricos \xe9 o ",Object(m.b)("strong",{parentName:"p"},"Trapezoidal Impl\xedcito"),", por possuir as seguintes vantagens:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},"\xc9 numericamente est\xe1vel (A-est\xe1vel);"),Object(m.b)("li",{parentName:"ul"},"\xc9 bastante r\xe1pida;"),Object(m.b)("li",{parentName:"ul"},"Possui boa precis\xe3o (dependendo somente do passo de integra\xe7\xe3o utilizado).")),Object(m.b)("p",null,"Tal m\xe9todo foi implementado no PSP-UFU tanto para solu\xe7\xe3o das equa\xe7\xf5es diferenciais da m\xe1quina s\xedncrona quanto nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"transferFunction"}),"fun\xe7\xf5es transfer\xeancia")," do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"sistema de controle"),". 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O valor retornado varia de ",Object(b.b)("span",Object(n.a)({parentName:"td"},{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)("mo",{parentName:"mrow"},"\u2212"),Object(b.b)("mi",{parentName:"mrow"},"\u03c0")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"-\\pi")))),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:"0.66666em",verticalAlign:"-0.08333em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"\u2212"),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.03588em"}}),"\u03c0")))))," a ",Object(b.b)("span",Object(n.a)({parentName:"td"},{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"},"\u03c0")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"\\pi")))),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:"0.43056em",verticalAlign:"0em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.03588em"}}),"\u03c0"))))),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"atanh(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Mesmo que ",Object(b.b)("inlineCode",{parentName:"td"},"atan()"),", mas para tangente hiperb\xf3lica.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"cbrt(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Raiz c\xfabica 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"},"conj(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Conjugado complexo 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"},"ceil(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Teto de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Arredonda para o pr\xf3ximo maior inteiro.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"cos(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Cosseno de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". 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"},"cosh(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Mesmo que ",Object(b.b)("inlineCode",{parentName:"td"},"cos()"),", mas para cosseno 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"},"cot(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Cotangente de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". 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"},"csc(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Cossecante de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". 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"},"exp(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Exponencial de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Retorna o valor de e elevado a pot\xeancia A.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"exp2(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Exponencial de ",Object(b.b)("inlineCode",{parentName:"td"},"A")," na base ",Object(b.b)("span",Object(n.a)({parentName:"td"},{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)("mn",{parentName:"mrow"},"2")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"2")))),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:"0.64444em",verticalAlign:"0em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"2"))))),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"floor(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Piso de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Arredonda para o pr\xf3ximo menor inteiro.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"hypot(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Fun\xe7\xe3o de dist\xe2ncia Euclidiana.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"if(A,B,C)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"int(A)")," \xe9 diferente de ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math 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",Object(b.b)("inlineCode",{parentName:"td"},"C"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"imag(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Retorna a parte imagin\xe1ria do n\xfamero complexo ",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"},"int(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Arredonda ",Object(b.b)("inlineCode",{parentName:"td"},"A")," para o inteiro mais pr\xf3ximo.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"log(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Logaritmo natural (base ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math 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",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"},"log10(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Logaritmo na base ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math 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A.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"max(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"A>B"),", o resultado \xe9 ",Object(b.b)("inlineCode",{parentName:"td"},"A"),", sen\xe3o \xe9 ",Object(b.b)("inlineCode",{parentName:"td"},"B"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"min(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"A := ; \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. 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Arredonda para o pr\xf3ximo maior inteiro.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"cos(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Cosseno de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". 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"},"cosh(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Mesmo que ",Object(b.b)("inlineCode",{parentName:"td"},"cos()"),", mas para cosseno 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"},"cot(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Cotangente de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". 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"},"csc(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Cossecante de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". 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"},"exp(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Exponencial de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Retorna o valor de e elevado a pot\xeancia A.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"exp2(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Exponencial de ",Object(b.b)("inlineCode",{parentName:"td"},"A")," na base ",Object(b.b)("span",Object(n.a)({parentName:"td"},{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)("mn",{parentName:"mrow"},"2")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"2")))),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:"0.64444em",verticalAlign:"0em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"2"))))),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"floor(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Piso de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Arredonda para o pr\xf3ximo menor inteiro.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"hypot(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Fun\xe7\xe3o de dist\xe2ncia Euclidiana.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"if(A,B,C)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"int(A)")," \xe9 diferente de ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math 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",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"},"log10(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Logaritmo na base ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math 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A.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"max(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"A>B"),", o resultado \xe9 ",Object(b.b)("inlineCode",{parentName:"td"},"A"),", sen\xe3o \xe9 ",Object(b.b)("inlineCode",{parentName:"td"},"B"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"min(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"A := ; \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. 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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,n){var i=c(n);if(this.isNumericRefined(e,t,i))return this;var a=r({},this.numericRefinements);return a[e]=r({},a[e]),a[e][t]?(a[e][t]=a[e][t].slice(),a[e][t].push(i)):a[e][t]=[i],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,n){return void 0!==n?this.isNumericRefined(e,t,n)?this.setQueryParameters({numericRefinements:this._clearNumericRefinements((function(r,i){return i===e&&r.op===t&&h(r.val,c(n))}))}):this:void 0!==t?this.isNumericRefined(e,t)?this.setQueryParameters({numericRefinements:this._clearNumericRefinements((function(n,r){return r===e&&n.op===t}))}):this:this.isNumericRefined(e)?this.setQueryParameters({numericRefinements:this._clearNumericRefinements((function(t,n){return n===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,n=this.numericRefinements,r=Object.keys(n).reduce((function(r,i){var a=n[i],s={};return a=a||{},Object.keys(a).forEach((function(n){var r=a[n]||[],c=[];r.forEach((function(t){e({val:t,op:n},i,"numeric")||c.push(t)})),c.length!==r.length&&(t=!0),s[n]=c})),r[i]=s,r}),{});return t?r: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 f.isRefined(this.facetsRefinements,e,t)?this:this.setQueryParameters({facetsRefinements:f.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 f.isRefined(this.facetsExcludes,e,t)?this:this.setQueryParameters({facetsExcludes:f.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 f.isRefined(this.disjunctiveFacetsRefinements,e,t)?this:this.setQueryParameters({disjunctiveFacetsRefinements:f.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 f.isRefined(this.facetsRefinements,e,t)?this.setQueryParameters({facetsRefinements:f.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 f.isRefined(this.facetsExcludes,e,t)?this.setQueryParameters({facetsExcludes:f.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 f.isRefined(this.disjunctiveFacetsRefinements,e,t)?this.setQueryParameters({disjunctiveFacetsRefinements:f.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:f.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:f.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:f.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 n=this._getHierarchicalFacetSeparator(this.getHierarchicalFacetByName(e)),r={};return void 0!==this.hierarchicalFacetsRefinements[e]&&this.hierarchicalFacetsRefinements[e].length>0&&(this.hierarchicalFacetsRefinements[e][0]===t||0===this.hierarchicalFacetsRefinements[e][0].indexOf(t+n))?-1===t.indexOf(n)?r[e]=[]:r[e]=[t.slice(0,t.lastIndexOf(n))]:r[e]=[t],this.setQueryParameters({hierarchicalFacetsRefinements:i({},r,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 n={};return n[e]=[t],this.setQueryParameters({hierarchicalFacetsRefinements:i({},n,this.hierarchicalFacetsRefinements)})},removeHierarchicalFacetRefinement:function(e){if(!this.isHierarchicalFacetRefined(e))return this;var t={};return t[e]=[],this.setQueryParameters({hierarchicalFacetsRefinements:i({},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)&&f.isRefined(this.facetsRefinements,e,t)},isExcludeRefined:function(e,t){return!!this.isConjunctiveFacet(e)&&f.isRefined(this.facetsExcludes,e,t)},isDisjunctiveFacetRefined:function(e,t){return!!this.isDisjunctiveFacet(e)&&f.isRefined(this.disjunctiveFacetsRefinements,e,t)},isHierarchicalFacetRefined:function(e,t){if(!this.isHierarchicalFacet(e))return!1;var n=this.getHierarchicalRefinement(e);return t?-1!==n.indexOf(t):n.length>0},isNumericRefined:function(e,t,n){if(void 0===n&&void 0===t)return!!this.numericRefinements[e];var r=this.numericRefinements[e]&&void 0!==this.numericRefinements[e][t];if(void 0===n||!r)return r;var i,a,u=c(n),o=void 0!==(i=this.numericRefinements[e][t],a=u,s(i,(function(e){return h(e,a)})));return r&&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={},n=this;return Object.keys(this).forEach((function(r){var i=n[r];-1===e.indexOf(r)&&void 0!==i&&(t[r]=i)})),t},setQueryParameter:function(e,t){if(this[e]===t)return this;var n={};return n[e]=t,this.setQueryParameters(n)},setQueryParameters:function(e){if(!e)return this;var t=l.validate(this,e);if(t)throw t;var n=this,r=l._parseNumbers(e),i=Object.keys(this).reduce((function(e,t){return e[t]=n[t],e}),{}),a=Object.keys(r).reduce((function(e,t){var n=void 0!==e[t],i=void 0!==r[t];return n&&!i?u(e,[t]):(i&&(e[t]=r[t]),e)}),i);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 n=this._getHierarchicalFacetSeparator(this.getHierarchicalFacetByName(e));return t.split(n).map((function(e){return e.trim()}))},toString:function(){return JSON.stringify(this,null,2)}},e.exports=l},154:function(e,t,n){"use strict";e.exports=function(e,t){if(null===e)return{};var n,r,i={},a=Object.keys(e);for(r=0;r=0||(i[n]=e[n]);return i}},155:function(e,t,n){"use strict";var r=n(138),i=n(139),a=n(156),s=n(176),c=n(135),u=n(177),o=n(157),f=n(178);function h(e){var t={};return e.forEach((function(e,n){t[e]=n})),t}function l(e,t,n){t&&t[n]&&(e.stats=t[n])}function m(e,t){var n=t[0];this._rawResults=t;var a=this;Object.keys(n).forEach((function(e){a[e]=n[e]})),this.processingTimeMS=t.reduce((function(e,t){return void 0===t.processingTimeMS?e:e+t.processingTimeMS}),0),this.disjunctiveFacets=[],this.hierarchicalFacets=e.hierarchicalFacets.map((function(){return[]})),this.facets=[];var o=e.getRefinedDisjunctiveFacets(),m=h(e.facets),d=h(e.disjunctiveFacets),v=1,p=n.facets||{};Object.keys(p).forEach((function(t){var r,i,s=p[t],o=(r=e.hierarchicalFacets,i=t,c(r,(function(e){return(e.attributes||[]).indexOf(i)>-1})));if(o){var f=o.attributes.indexOf(t),h=u(e.hierarchicalFacets,(function(e){return e.name===o.name}));a.hierarchicalFacets[h][f]={attribute:t,data:s,exhaustive:n.exhaustiveFacetsCount}}else{var v,g=-1!==e.disjunctiveFacets.indexOf(t),y=-1!==e.facets.indexOf(t);g&&(v=d[t],a.disjunctiveFacets[v]={name:t,data:s,exhaustive:n.exhaustiveFacetsCount},l(a.disjunctiveFacets[v],n.facets_stats,t)),y&&(v=m[t],a.facets[v]={name:t,data:s,exhaustive:n.exhaustiveFacetsCount},l(a.facets[v],n.facets_stats,t))}})),this.hierarchicalFacets=s(this.hierarchicalFacets),o.forEach((function(s){var c=t[v],o=c&&c.facets?c.facets:{},f=e.getHierarchicalFacetByName(s);Object.keys(o).forEach((function(t){var s,h=o[t];if(f){s=u(e.hierarchicalFacets,(function(e){return e.name===f.name}));var m=u(a.hierarchicalFacets[s],(function(e){return e.attribute===t}));if(-1===m)return;a.hierarchicalFacets[s][m].data=r({},a.hierarchicalFacets[s][m].data,h)}else{s=d[t];var v=n.facets&&n.facets[t]||{};a.disjunctiveFacets[s]={name:t,data:i({},h,v),exhaustive:c.exhaustiveFacetsCount},l(a.disjunctiveFacets[s],c.facets_stats,t),e.disjunctiveFacetsRefinements[t]&&e.disjunctiveFacetsRefinements[t].forEach((function(n){!a.disjunctiveFacets[s].data[n]&&e.disjunctiveFacetsRefinements[t].indexOf(n)>-1&&(a.disjunctiveFacets[s].data[n]=0)}))}})),v++})),e.getRefinedHierarchicalFacets().forEach((function(n){var r=e.getHierarchicalFacetByName(n),s=e._getHierarchicalFacetSeparator(r),c=e.getHierarchicalRefinement(n);if(!(0===c.length||c[0].split(s).length<2)){var o=t[v],f=o&&o.facets?o.facets:{};Object.keys(f).forEach((function(t){var n=f[t],o=u(e.hierarchicalFacets,(function(e){return e.name===r.name})),h=u(a.hierarchicalFacets[o],(function(e){return e.attribute===t}));if(-1!==h){var l={};if(c.length>0){var m=c[0].split(s)[0];l[m]=a.hierarchicalFacets[o][h].data[m]}a.hierarchicalFacets[o][h].data=i(l,n,a.hierarchicalFacets[o][h].data)}})),v++}})),Object.keys(e.facetsExcludes).forEach((function(t){var r=e.facetsExcludes[t],i=m[t];a.facets[i]={name:t,data:n.facets[t],exhaustive:n.exhaustiveFacetsCount},r.forEach((function(e){a.facets[i]=a.facets[i]||{name:t},a.facets[i].data=a.facets[i].data||{},a.facets[i].data[e]=0}))})),this.hierarchicalFacets=this.hierarchicalFacets.map(f(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 n=t.data.map((function(t){return d(e,t)})),i=e(n);return r({},t,{data:i})}function v(e,t){var n=c(e,(function(e){return e.name===t}));return n&&n.stats}function p(e,t,n,r,i){var a=c(i,(function(e){return e.name===n})),s=a&&a.data&&a.data[r]?a.data[r]:0,u=a&&a.exhaustive||!1;return{type:t,attributeName:n,name:r,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 n=function(e,t){function n(e){return e.name===t}if(e._state.isConjunctiveFacet(t)){var r=c(e.facets,n);return r?Object.keys(r.data).map((function(n){return{name:n,count:r.data[n],isRefined:e._state.isFacetRefined(t,n),isExcluded:e._state.isExcludeRefined(t,n)}})):[]}if(e._state.isDisjunctiveFacet(t)){var i=c(e.disjunctiveFacets,n);return i?Object.keys(i.data).map((function(n){return{name:n,count:i.data[n],isRefined:e._state.isDisjunctiveFacetRefined(t,n)}})):[]}if(e._state.isHierarchicalFacet(t))return c(e.hierarchicalFacets,n)}(this,e);if(n){var r=i({},t,{sortBy:m.DEFAULT_SORT});if(Array.isArray(r.sortBy)){var s=o(r.sortBy,m.DEFAULT_SORT);return Array.isArray(n)?a(n,s[0],s[1]):d((function(e){return a(e,s[0],s[1])}),n)}if("function"==typeof r.sortBy)return Array.isArray(n)?n.sort(r.sortBy):d((function(e){return function(e,t){return t.sort(e)}(r.sortBy,e)}),n);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,n=[];return 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t=this.$input[0].getBoundingClientRect();this.autoWidth&&this.$node.css("width",t.width+"px");var e=this.$node[0].getBoundingClientRect(),n=t.bottom-e.top;this.$node.css("top",n+"px");var i=t.left-e.left;this.$node.css("left",i+"px"),this.eventBus.trigger("redrawn")},_onShown:function(){this.eventBus.trigger("shown"),this.autoselect&&this.dropdown.cursorTopSuggestion()},_onClosed:function(){this.input.clearHint(),this.input.removeActiveDescendant(),this.input.collapse(),this.eventBus.trigger("closed")},_onFocused:function(){if(this.isActivated=!0,this.openOnFocus){var t=this.input.getQuery();t.length>=this.minLength?this.dropdown.update(t):this.dropdown.empty(),this.dropdown.open()}},_onBlurred:function(){var t,e;t=this.dropdown.getDatumForCursor(),e=this.dropdown.getDatumForTopSuggestion();var n={selectionMethod:"blur"};this.debug||(this.autoselectOnBlur&&t?this._select(t,n):this.autoselectOnBlur&&e?this._select(e,n):(this.isActivated=!1,this.dropdown.empty(),this.dropdown.close()))},_onEnterKeyed:function(t,e){var n,i;n=this.dropdown.getDatumForCursor(),i=this.dropdown.getDatumForTopSuggestion();var s={selectionMethod:"enterKey"};n?(this._select(n,s),e.preventDefault()):this.autoselect&&i&&(this._select(i,s),e.preventDefault())},_onTabKeyed:function(t,e){if(this.tabAutocomplete){var n;(n=this.dropdown.getDatumForCursor())?(this._select(n,{selectionMethod:"tabKey"}),e.preventDefault()):this._autocomplete(!0)}else this.dropdown.close()},_onEscKeyed:function(){this.dropdown.close(),this.input.resetInputValue()},_onUpKeyed:function(){var t=this.input.getQuery();this.dropdown.isEmpty&&t.length>=this.minLength?this.dropdown.update(t):this.dropdown.moveCursorUp(),this.dropdown.open()},_onDownKeyed:function(){var t=this.input.getQuery();this.dropdown.isEmpty&&t.length>=this.minLength?this.dropdown.update(t):this.dropdown.moveCursorDown(),this.dropdown.open()},_onLeftKeyed:function(){"rtl"===this.dir&&this._autocomplete()},_onRightKeyed:function(){"ltr"===this.dir&&this._autocomplete()},_onQueryChanged:function(t,e){this.input.clearHintIfInvalid(),e.length>=this.minLength?this.dropdown.update(e):this.dropdown.empty(),this.dropdown.open(),this._setLanguageDirection()},_onWhitespaceChanged:function(){this._updateHint(),this.dropdown.open()},_setLanguageDirection:function(){var t=this.input.getLanguageDirection();this.dir!==t&&(this.dir=t,this.$node.css("direction",t),this.dropdown.setLanguageDirection(t))},_updateHint:function(){var t,e,n,s,r;(t=this.dropdown.getDatumForTopSuggestion())&&this.dropdown.isVisible()&&!this.input.hasOverflow()?(e=this.input.getInputValue(),n=a.normalizeQuery(e),s=i.escapeRegExChars(n),(r=new RegExp("^(?:"+s+")(.+$)","i").exec(t.value))?this.input.setHint(e+r[1]):this.input.clearHint()):this.input.clearHint()},_autocomplete:function(t){var e,n,i,s;e=this.input.getHint(),n=this.input.getQuery(),i=t||this.input.isCursorAtEnd(),e&&n!==e&&i&&((s=this.dropdown.getDatumForTopSuggestion())&&this.input.setInputValue(s.value),this.eventBus.trigger("autocompleted",s.raw,s.datasetName))},_select:function(t,e){void 0!==t.value&&this.input.setQuery(t.value),this.clearOnSelected?this.setVal(""):this.input.setInputValue(t.value,!0),this._setLanguageDirection(),!1===this.eventBus.trigger("selected",t.raw,t.datasetName,e).isDefaultPrevented()&&(this.dropdown.close(),i.defer(i.bind(this.dropdown.empty,this.dropdown)))},open:function(){if(!this.isActivated){var t=this.input.getInputValue();t.length>=this.minLength?this.dropdown.update(t):this.dropdown.empty()}this.dropdown.open()},close:function(){this.dropdown.close()},setVal:function(t){t=i.toStr(t),this.isActivated?this.input.setInputValue(t):(this.input.setQuery(t),this.input.setInputValue(t,!0)),this._setLanguageDirection()},getVal:function(){return this.input.getQuery()},destroy:function(){this.input.destroy(),this.dropdown.destroy(),function(t,e){var n=t.find(i.className(e.prefix,e.input));i.each(n.data("aaAttrs"),(function(t,e){void 0===t?n.removeAttr(e):n.attr(e,t)})),n.detach().removeClass(i.className(e.prefix,e.input,!0)).insertAfter(t),n.removeData&&n.removeData("aaAttrs");t.remove()}(this.$node,this.cssClasses),this.$node=null},getWrapper:function(){return this.dropdown.$container[0]}}),l.Dropdown=o,l.Input=a,l.sources=n(284),t.exports=l},274:function(t,e,n){"use strict";var i;i={9:"tab",27:"esc",37:"left",39:"right",13:"enter",38:"up",40:"down"};var s=n(175),r=n(177),a=n(195);function o(t){var e,n,a,o,u,c=this;(t=t||{}).input||s.error("input is missing"),e=s.bind(this._onBlur,this),n=s.bind(this._onFocus,this),a=s.bind(this._onKeydown,this),o=s.bind(this._onInput,this),this.$hint=r.element(t.hint),this.$input=r.element(t.input).on("blur.aa",e).on("focus.aa",n).on("keydown.aa",a),0===this.$hint.length&&(this.setHint=this.getHint=this.clearHint=this.clearHintIfInvalid=s.noop),s.isMsie()?this.$input.on("keydown.aa keypress.aa cut.aa paste.aa",(function(t){i[t.which||t.keyCode]||s.defer(s.bind(c._onInput,c,t))})):this.$input.on("input.aa",o),this.query=this.$input.val(),this.$overflowHelper=(u=this.$input,r.element('').css({position:"absolute",visibility:"hidden",whiteSpace:"pre",fontFamily:u.css("font-family"),fontSize:u.css("font-size"),fontStyle:u.css("font-style"),fontVariant:u.css("font-variant"),fontWeight:u.css("font-weight"),wordSpacing:u.css("word-spacing"),letterSpacing:u.css("letter-spacing"),textIndent:u.css("text-indent"),textRendering:u.css("text-rendering"),textTransform:u.css("text-transform")}).insertAfter(u))}function u(t){return t.altKey||t.ctrlKey||t.metaKey||t.shiftKey}o.normalizeQuery=function(t){return(t||"").replace(/^\s*/g,"").replace(/\s{2,}/g," ")},s.mixin(o.prototype,a,{_onBlur:function(){this.resetInputValue(),this.$input.removeAttr("aria-activedescendant"),this.trigger("blurred")},_onFocus:function(){this.trigger("focused")},_onKeydown:function(t){var e=i[t.which||t.keyCode];this._managePreventDefault(e,t),e&&this._shouldTrigger(e,t)&&this.trigger(e+"Keyed",t)},_onInput:function(){this._checkInputValue()},_managePreventDefault:function(t,e){var n,i,s;switch(t){case"tab":i=this.getHint(),s=this.getInputValue(),n=i&&i!==s&&!u(e);break;case"up":case"down":n=!u(e);break;default:n=!1}n&&e.preventDefault()},_shouldTrigger:function(t,e){var n;switch(t){case"tab":n=!u(e);break;default:n=!0}return n},_checkInputValue:function(){var t,e,n,i,s;t=this.getInputValue(),i=t,s=this.query,n=!(!(e=o.normalizeQuery(i)===o.normalizeQuery(s))||!this.query)&&this.query.length!==t.length,this.query=t,e?n&&this.trigger("whitespaceChanged",this.query):this.trigger("queryChanged",this.query)},focus:function(){this.$input.focus()},blur:function(){this.$input.blur()},getQuery:function(){return this.query},setQuery:function(t){this.query=t},getInputValue:function(){return this.$input.val()},setInputValue:function(t,e){void 0===t&&(t=this.query),this.$input.val(t),e?this.clearHint():this._checkInputValue()},expand:function(){this.$input.attr("aria-expanded","true")},collapse:function(){this.$input.attr("aria-expanded","false")},setActiveDescendant:function(t){this.$input.attr("aria-activedescendant",t)},removeActiveDescendant:function(){this.$input.removeAttr("aria-activedescendant")},resetInputValue:function(){this.setInputValue(this.query,!0)},getHint:function(){return this.$hint.val()},setHint:function(t){this.$hint.val(t)},clearHint:function(){this.setHint("")},clearHintIfInvalid:function(){var t,e,n;n=(t=this.getInputValue())!==(e=this.getHint())&&0===e.indexOf(t),""!==t&&n&&!this.hasOverflow()||this.clearHint()},getLanguageDirection:function(){return(this.$input.css("direction")||"ltr").toLowerCase()},hasOverflow:function(){var t=this.$input.width()-2;return this.$overflowHelper.text(this.getInputValue()),this.$overflowHelper.width()>=t},isCursorAtEnd:function(){var t,e,n;return t=this.$input.val().length,e=this.$input[0].selectionStart,s.isNumber(e)?e===t:!document.selection||((n=document.selection.createRange()).moveStart("character",-t),t===n.text.length)},destroy:function(){this.$hint.off(".aa"),this.$input.off(".aa"),this.$hint=this.$input=this.$overflowHelper=null}}),t.exports=o},275:function(t,e,n){"use strict";var i,s,r,a=[n(276),n(277),n(278),n(279),n(280),n(281)],o=-1,u=[],c=!1;function l(){i&&s&&(i=!1,s.length?u=s.concat(u):o=-1,u.length&&h())}function h(){if(!i){c=!1,i=!0;for(var t=u.length,e=setTimeout(l);t;){for(s=u,u=[];s&&++o1)for(var n=1;n'),this.$menu.append(this.$empty),this.$empty.hide()),this.datasets=i.map(t.datasets,(function(e){return function(t,e,n){return new u.Dataset(i.mixin({$menu:t,cssClasses:n},e))}(a.$menu,e,t.cssClasses)})),i.each(this.datasets,(function(t){var e=t.getRoot();e&&0===e.parent().length&&a.$menu.append(e),t.onSync("rendered",a._onRendered,a)})),t.templates&&t.templates.footer&&(this.templates.footer=i.templatify(t.templates.footer),this.$menu.append(this.templates.footer()));var l=this;s.element(window).resize((function(){l._redraw()}))}i.mixin(u.prototype,r,{_onSuggestionClick:function(t){this.trigger("suggestionClicked",s.element(t.currentTarget))},_onSuggestionMouseEnter:function(t){var e=s.element(t.currentTarget);if(!e.hasClass(i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0))){this._removeCursor();var n=this;setTimeout((function(){n._setCursor(e,!1)}),0)}},_onSuggestionMouseLeave:function(t){if(t.relatedTarget&&s.element(t.relatedTarget).closest("."+i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0)).length>0)return;this._removeCursor(),this.trigger("cursorRemoved")},_onRendered:function(t,e){if(this.isEmpty=i.every(this.datasets,(function(t){return t.isEmpty()})),this.isEmpty)if(e.length>=this.minLength&&this.trigger("empty"),this.$empty)if(e.length=this.minLength?this._show():this._hide());this.trigger("datasetRendered")},_hide:function(){this.$container.hide()},_show:function(){this.$container.css("display","block"),this._redraw(),this.trigger("shown")},_redraw:function(){this.isOpen&&this.appendTo&&this.trigger("redrawn")},_getSuggestions:function(){return this.$menu.find(i.className(this.cssClasses.prefix,this.cssClasses.suggestion))},_getCursor:function(){return this.$menu.find(i.className(this.cssClasses.prefix,this.cssClasses.cursor)).first()},_setCursor:function(t,e){t.first().addClass(i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0)).attr("aria-selected","true"),this.trigger("cursorMoved",e)},_removeCursor:function(){this._getCursor().removeClass(i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0)).removeAttr("aria-selected")},_moveCursor:function(t){var e,n,i,s;this.isOpen&&(n=this._getCursor(),e=this._getSuggestions(),this._removeCursor(),-1!==(i=((i=e.index(n)+t)+1)%(e.length+1)-1)?(i<-1&&(i=e.length-1),this._setCursor(s=e.eq(i),!0),this._ensureVisible(s)):this.trigger("cursorRemoved"))},_ensureVisible:function(t){var e,n,i,s;n=(e=t.position().top)+t.height()+parseInt(t.css("margin-top"),10)+parseInt(t.css("margin-bottom"),10),i=this.$menu.scrollTop(),s=this.$menu.height()+parseInt(this.$menu.css("padding-top"),10)+parseInt(this.$menu.css("padding-bottom"),10),e<0?this.$menu.scrollTop(i+e):s"+u(t)+"

"}}),this.css=i.mixin({},a,t.appendTo?a.appendTo:{}),this.cssClasses=t.cssClasses=i.mixin({},a.defaultClasses,t.cssClasses||{}),this.cssClasses.prefix=t.cssClasses.formattedPrefix||i.formatPrefix(this.cssClasses.prefix,this.cssClasses.noPrefix);var c=i.className(this.cssClasses.prefix,this.cssClasses.dataset);this.$el=t.$menu&&t.$menu.find(c+"-"+this.name).length>0?s.element(t.$menu.find(c+"-"+this.name)[0]):s.element(r.dataset.replace("%CLASS%",this.name).replace("%PREFIX%",this.cssClasses.prefix).replace("%DATASET%",this.cssClasses.dataset)),this.$menu=t.$menu,this.clearCachedSuggestions()}u.extractDatasetName=function(t){return s.element(t).data("aaDataset")},u.extractValue=function(t){return s.element(t).data("aaValue")},u.extractDatum=function(t){var e=s.element(t).data("aaDatum");return"string"==typeof e&&(e=JSON.parse(e)),e},i.mixin(u.prototype,o,{_render:function(t,e){if(this.$el){var n,a=this,o=[].slice.call(arguments,2);if(this.$el.empty(),n=e&&e.length,this._isEmpty=!n,!n&&this.templates.empty)this.$el.html(u.apply(this,o)).prepend(a.templates.header?l.apply(this,o):null).append(a.templates.footer?h.apply(this,o):null);else if(n)this.$el.html(c.apply(this,o)).prepend(a.templates.header?l.apply(this,o):null).append(a.templates.footer?h.apply(this,o):null);else if(e&&!Array.isArray(e))throw new TypeError("suggestions must be an array");this.$menu&&this.$menu.addClass(this.cssClasses.prefix+(n?"with":"without")+"-"+this.name).removeClass(this.cssClasses.prefix+(n?"without":"with")+"-"+this.name),this.trigger("rendered",t)}function u(){var e=[].slice.call(arguments,0);return e=[{query:t,isEmpty:!0}].concat(e),a.templates.empty.apply(this,e)}function c(){var t,n,o=[].slice.call(arguments,0),u=this,c=r.suggestions.replace("%PREFIX%",this.cssClasses.prefix).replace("%SUGGESTIONS%",this.cssClasses.suggestions);return t=s.element(c).css(this.css.suggestions),n=i.map(e,l),t.append.apply(t,n),t;function l(t){var e,n=r.suggestion.replace("%PREFIX%",u.cssClasses.prefix).replace("%SUGGESTION%",u.cssClasses.suggestion);return(e=s.element(n).attr({role:"option",id:["option",Math.floor(1e8*Math.random())].join("-")}).append(a.templates.suggestion.apply(this,[t].concat(o)))).data("aaDataset",a.name),e.data("aaValue",a.displayFn(t)||void 0),e.data("aaDatum",JSON.stringify(t)),e.children().each((function(){s.element(this).css(u.css.suggestionChild)})),e}}function l(){var e=[].slice.call(arguments,0);return e=[{query:t,isEmpty:!n}].concat(e),a.templates.header.apply(this,e)}function h(){var e=[].slice.call(arguments,0);return e=[{query:t,isEmpty:!n}].concat(e),a.templates.footer.apply(this,e)}},getRoot:function(){return this.$el},update:function(t){function e(e){if(!this.canceled&&t===this.query){var n=[].slice.call(arguments,1);this.cacheSuggestions(t,e,n),this._render.apply(this,[t,e].concat(n))}}if(this.query=t,this.canceled=!1,this.shouldFetchFromCache(t))e.apply(this,[this.cachedSuggestions].concat(this.cachedRenderExtraArgs));else{var n=this,i=function(){n.canceled||n.source(t,e.bind(n))};if(this.debounce){clearTimeout(this.debounceTimeout),this.debounceTimeout=setTimeout((function(){n.debounceTimeout=null,i()}),this.debounce)}else i()}},cacheSuggestions:function(t,e,n){this.cachedQuery=t,this.cachedSuggestions=e,this.cachedRenderExtraArgs=n},shouldFetchFromCache:function(t){return this.cache&&this.cachedQuery===t&&this.cachedSuggestions&&this.cachedSuggestions.length},clearCachedSuggestions:function(){delete this.cachedQuery,delete this.cachedSuggestions,delete this.cachedRenderExtraArgs},cancel:function(){this.canceled=!0},clear:function(){this.cancel(),this.$el.empty(),this.trigger("rendered","")},isEmpty:function(){return this._isEmpty},destroy:function(){this.clearCachedSuggestions(),this.$el=null}}),t.exports=u},284:function(t,e,n){"use strict";t.exports={hits:n(285),popularIn:n(286)}},285:function(t,e,n){"use strict";var i=n(175),s=n(222),r=n(223);t.exports=function(t,e){var n=r(t.as._ua);return n&&n[0]>=3&&n[1]>20&&((e=e||{}).additionalUA="autocomplete.js "+s),function(n,s){t.search(n,e,(function(t,e){t?i.error(t.message):s(e.hits,e)}))}}},286:function(t,e,n){"use strict";var i=n(175),s=n(222),r=n(223);t.exports=function(t,e,n,a){var o=r(t.as._ua);if(o&&o[0]>=3&&o[1]>20&&((e=e||{}).additionalUA="autocomplete.js "+s),!n.source)return i.error("Missing 'source' key");var u=i.isFunction(n.source)?n.source:function(t){return t[n.source]};if(!n.index)return i.error("Missing 'index' key");var c=n.index;return a=a||{},function(o,l){t.search(o,e,(function(t,o){if(t)i.error(t.message);else{if(o.hits.length>0){var h=o.hits[0],p=i.mixin({hitsPerPage:0},n);delete p.source,delete p.index;var f=r(c.as._ua);return f&&f[0]>=3&&f[1]>20&&(e.additionalUA="autocomplete.js "+s),void c.search(u(h),p,(function(t,e){if(t)i.error(t.message);else{var n=[];if(a.includeAll){var s=a.allTitle||"All departments";n.push(i.mixin({facet:{value:s,count:e.nbHits}},i.cloneDeep(h)))}i.each(e.facets,(function(t,e){i.each(t,(function(t,s){n.push(i.mixin({facet:{facet:e,value:s,count:t}},i.cloneDeep(h)))}))}));for(var r=1;r\n
\n {{{category}}}\n
\n
\n
\n {{{subcategory}}}\n
\n {{#isTextOrSubcategoryNonEmpty}}\n
\n
{{{subcategory}}}
\n
{{{title}}}
\n {{#text}}
{{{text}}}
{{/text}}\n
\n {{/isTextOrSubcategoryNonEmpty}}\n
\n \n ',suggestionSimple:'\n
\n
\n {{^isLvl0}}\n {{{category}}}\n {{^isLvl1}}\n {{^isLvl1EmptyOrDuplicate}}\n \n {{{subcategory}}}\n \n {{/isLvl1EmptyOrDuplicate}}\n {{/isLvl1}}\n {{/isLvl0}}\n
\n {{#isLvl2}}\n {{{title}}}\n {{/isLvl2}}\n {{#isLvl1}}\n {{{subcategory}}}\n {{/isLvl1}}\n {{#isLvl0}}\n {{{category}}}\n {{/isLvl0}}\n
\n
\n
\n {{#text}}\n
\n
{{{text}}}
\n
\n {{/text}}\n
\n
\n ',footer:'\n
\n Search by \n
\n ',empty:'\n
\n
\n
\n
\n
\n No results found for query "{{query}}"\n
\n
\n
\n
\n
\n ',searchBox:'\n
\n \n
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e=a.components,t=Object(s.a)(a,["components"]);return Object(r.b)("wrapper",Object(n.a)({},l,t,{components:e,mdxType:"MDXLayout"}),Object(r.b)("link",{rel:"stylesheet",href:Object(m.a)("katex/katex.min.css")}),Object(r.b)("blockquote",null,Object(r.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. ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=151-12-30"}),Object(r.b)("em",{parentName:"a"},"tradu\xe7\xe3o livre")," - IEC 60050"),".")),Object(r.b)("h2",{id:"barramento-no-psp-ufu"},"Barramento no PSP-UFU"),Object(r.b)("p",null,"O elemento ",Object(r.b)("strong",{parentName:"p"},"barramento"),", ou simplesmente ",Object(r.b)("strong",{parentName:"p"},"barra"),", \xe9 um conector ou n\xf3 do diagrama unifilar do PSP-UFU. Essa barra pode representar um PAC (Ponto de Acoplamento Comum), um poste de distribui\xe7\xe3o, uma subesta\xe7\xe3o, um barramento da subesta\xe7\xe3o, entre in\xfameros outros tipos pontos de an\xe1lise e conex\xe3o entre elementos."),Object(r.b)("h2",{id:"formul\xe1rio-de-edi\xe7\xe3o-dos-barramentos"},"Formul\xe1rio de edi\xe7\xe3o dos barramentos"),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"},"O barramento deve ser o ",Object(r.b)("strong",{parentName:"p"},"primeiro elemento el\xe9trico a ser inserido no diagrama de pot\xeancia"),", uma vez que os demais componentes de pot\xeancia s\xe3o conectados nele."))),Object(r.b)("p",null,"A imagem abaixo apresenta o formul\xe1rio de inser\xe7\xe3o/altera\xe7\xe3o de dados das barras:"),Object(r.b)("div",null,Object(r.b)("center",null,Object(r.b)("img",{src:Object(m.a)("images/busForm.png"),alt:"Formul\xe1rio dos barramentos no PSP-UFU",title:"Formul\xe1rio dos barramentos no PSP-UFU"}))),Object(r.b)("p",null,"Esse formul\xe1rio \xe9 subdividido em quatro contextos distintos:"),Object(r.b)("ul",null,Object(r.b)("li",{parentName:"ul"},Object(r.b)("strong",{parentName:"li"},"Geral"),": no qual s\xe3o inseridas informa\xe7\xf5es gerais da barra e informa\xe7\xf5es do fluxo de carga;"),Object(r.b)("li",{parentName:"ul"},Object(r.b)("strong",{parentName:"li"},"Falta"),": local onde o curto-circuito ",Object(r.b)("em",{parentName:"li"},"shunt")," deve ser inserido;"),Object(r.b)("li",{parentName:"ul"},Object(r.b)("strong",{parentName:"li"},"Estabilidade"),": contendo op\xe7\xf5es de visualiza\xe7\xe3o de dados da barra em gr\xe1ficos no tempo e inser\xe7\xe3o de faltas trif\xe1sicas no c\xe1lculo de estabilidade transit\xf3ria;"),Object(r.b)("li",{parentName:"ul"},Object(r.b)("strong",{parentName:"li"},"Qualidade de energia"),": cont\xe9m a op\xe7\xe3o de de visualiza\xe7\xe3o da imped\xe2ncia harm\xf4nica vista pela barra.")),Object(r.b)("hr",null),Object(r.b)(c.a,{groupId:"bus-tabs",defaultValue:"general",values:[{label:"Geral",value:"general"},{label:"Falta",value:"fault"},{label:"Estabilidade",value:"stability"},{label:"Qualidade de energia",value:"powerQuality"}],mdxType:"Tabs"},Object(r.b)(b.a,{value:"general",mdxType:"TabItem"},Object(r.b)("h4",{id:"nome"},"Nome"),Object(r.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(r.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(r.b)("h4",{id:"tens\xe3o-nominal"},"Tens\xe3o nominal"),Object(r.b)("p",null,"Utilizado para c\xe1lculo da imped\xe2ncia base de alguns elementos conectados, al\xe9m do c\xe1lculo da rela\xe7\xe3o de transforma\xe7\xe3o dos transformadores conectados entre barras. Sua unidade pode ser selecionada, sendo expressa em V ou em kV."),Object(r.b)("p",null,"A modifica\xe7\xe3o desse par\xe2metro ir\xe1 alterar toda a tens\xe3o do trecho conectado por linhas el\xe9tricas, sendo emitido um alerta ao usu\xe1rio."),Object(r.b)("h4",{id:"tens\xe3o-controlada"},"Tens\xe3o controlada"),Object(r.b)("p",null,"Caracteriza o barramento como ",Object(r.b)("strong",{parentName:"p"},"barra de tens\xe3o controlada (",Object(r.b)("a",Object(n.a)({parentName:"strong"},{href:"powerFlow"}),"Barra PV"),")"),","),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"},"Essa op\xe7\xe3o \xe9 somente v\xe1lida caso alguma m\xe1quina s\xedncrona esteja conectado, caso contr\xe1rio esse valor ser\xe1 ignorado. Caso o limite de pot\xeancia reativa da m\xe1quina s\xedncrona conectada seja ultrapassado esse valor tamb\xe9m \xe9 ignorado."))),Object(r.b)("p",null,"O valor poder\xe1 ser inserido em p.u. ou em volts (ou kV caso a tens\xe3o nominal esteja nesta unidade)."),Object(r.b)("h4",{id:"barra-de-refer\xeancia"},"Barra de refer\xeancia"),Object(r.b)("p",null,"Caracteriza o barramento como ",Object(r.b)("strong",{parentName:"p"},"barra de refer\xeancia (",Object(r.b)("a",Object(n.a)({parentName:"strong"},{href:"powerFlow"}),"Barra de oscila\xe7\xe3o"),")"),". Essa op\xe7\xe3o \xe9 somente v\xe1lida caso esteja conectado um gerador s\xedncrono, caso contr\xe1rio uma mensagem de erro ser\xe1 exibida ao usu\xe1rio ao realizar algum dos c\xe1lculos do programa.")),Object(r.b)(b.a,{value:"fault",mdxType:"TabItem"},Object(r.b)("h4",{id:"inserir-falta"},"Inserir falta"),Object(r.b)("p",null,"Indica se existe um curto-circuito na barra nos estudos de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"fault"}),"curto-circuito"),"."),Object(r.b)("div",{className:"admonition admonition-warning alert alert--danger"},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:"12",height:"16",viewBox:"0 0 12 16"}),Object(r.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(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Nota-se que essa op\xe7\xe3o ir\xe1 inserir uma falta no c\xe1lculo de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"fault"}),"curto-circuito")," e ",Object(r.b)("strong",{parentName:"p"},"n\xe3o ser\xe1 considerado no estudo de estabilidade"),"."))),Object(r.b)("h4",{id:"tipo-de-falta"},"Tipo de falta"),Object(r.b)("p",null,"Seleciona o tipo de falha shunt da barra:"),Object(r.b)("ul",null,Object(r.b)("li",{parentName:"ul"},"trif\xe1sico para a terra"),Object(r.b)("li",{parentName:"ul"},"fase-fase"),Object(r.b)("li",{parentName:"ul"},"fase-fase-terra"),Object(r.b)("li",{parentName:"ul"},"fase-terra")),Object(r.b)("h4",{id:"local-da-falta"},"Local da falta"),Object(r.b)("p",null,"Seleciona a fase em que se situa a falta (ou combina\xe7\xe3o delas no caso de falha entre duas fases), sendo essa op\xe7\xe3o desabilitada para o tipo de falta trif\xe1sica."),Object(r.b)("h4",{id:"resist\xeancia-e-reat\xe2ncia-de-falta"},"Resist\xeancia e reat\xe2ncia de falta"),Object(r.b)("p",null,"Representam a imped\xe2ncia da falta. 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Essa op\xe7\xe3o \xe9 somente v\xe1lida caso esteja conectado um gerador s\xedncrono, caso contr\xe1rio uma mensagem de erro ser\xe1 exibida ao usu\xe1rio ao realizar algum dos c\xe1lculos do programa.")),Object(r.b)(b.a,{value:"fault",mdxType:"TabItem"},Object(r.b)("h4",{id:"inserir-falta"},"Inserir falta"),Object(r.b)("p",null,"Indica se existe um curto-circuito na barra nos estudos de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"fault"}),"curto-circuito"),"."),Object(r.b)("div",{className:"admonition admonition-warning alert alert--danger"},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:"12",height:"16",viewBox:"0 0 12 16"}),Object(r.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(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Nota-se que essa op\xe7\xe3o ir\xe1 inserir uma falta no c\xe1lculo de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"fault"}),"curto-circuito")," e ",Object(r.b)("strong",{parentName:"p"},"n\xe3o ser\xe1 considerado no estudo de estabilidade"),"."))),Object(r.b)("h4",{id:"tipo-de-falta"},"Tipo de falta"),Object(r.b)("p",null,"Seleciona o tipo de falha shunt da barra:"),Object(r.b)("ul",null,Object(r.b)("li",{parentName:"ul"},"trif\xe1sico para a terra"),Object(r.b)("li",{parentName:"ul"},"fase-fase"),Object(r.b)("li",{parentName:"ul"},"fase-fase-terra"),Object(r.b)("li",{parentName:"ul"},"fase-terra")),Object(r.b)("h4",{id:"local-da-falta"},"Local da falta"),Object(r.b)("p",null,"Seleciona a fase em que se situa a falta (ou combina\xe7\xe3o delas no caso de falha entre duas fases), sendo essa op\xe7\xe3o desabilitada para o tipo de falta trif\xe1sica."),Object(r.b)("h4",{id:"resist\xeancia-e-reat\xe2ncia-de-falta"},"Resist\xeancia e reat\xe2ncia de falta"),Object(r.b)("p",null,"Representam a imped\xe2ncia da falta. 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Os seguintes dados s\xe3o exibidos:"),Object(r.b)("ul",null,Object(r.b)("li",{parentName:"ul"},"m\xf3dulo da tens\xe3o do barramento"),Object(r.b)("li",{parentName:"ul"},"\xe2ngulo da tens\xe3o do barramento.")),Object(r.b)("h4",{id:"inserir-falta-1"},"Inserir falta"),Object(r.b)("p",null,"Insere uma falta trif\xe1sica na barra no c\xe1lculo de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(r.b)("div",{className:"admonition admonition-warning alert alert--danger"},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:"12",height:"16",viewBox:"0 0 12 16"}),Object(r.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(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Nota-se que essa op\xe7\xe3o ir\xe1 inserir uma falta no c\xe1lculo de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"stability"}),"estabilidade")," e ",Object(r.b)("strong",{parentName:"p"},"n\xe3o ser\xe1 considerado no estudo de ",Object(r.b)("a",Object(n.a)({parentName:"strong"},{href:"fault"}),"curto-circuito")),"."))),Object(r.b)("h4",{id:"tempo"},"Tempo"),Object(r.b)("p",null,"Instante no tempo (",Object(r.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(r.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(r.b)("semantics",{parentName:"math"},Object(r.b)("mrow",{parentName:"semantics"},Object(r.b)("msub",{parentName:"mrow"},Object(r.b)("mi",{parentName:"msub"},"t"),Object(r.b)("mrow",{parentName:"msub"},Object(r.b)("mi",{parentName:"mrow"},"f"),Object(r.b)("mi",{parentName:"mrow"},"a"),Object(r.b)("mi",{parentName:"mrow"},"l"),Object(r.b)("mi",{parentName:"mrow"},"t"),Object(r.b)("mi",{parentName:"mrow"},"a")))),Object(r.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"t_{falta}")))),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.9011879999999999em",verticalAlign:"-0.286108em"}})),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"t"),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"msupsub"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-t vlist-t2"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-r"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist",style:{height:"0.3361079999999999em"}}),Object(r.b)("span",Object(n.a)({parentName:"span"},{style:{top:"-2.5500000000000003em",marginLeft:"0em",marginRight:"0.05em"}}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mtight"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.10764em"}}),"f"),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"a"),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.01968em"}}),"l"),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"t"),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"a"))))),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-r"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist",style:{height:"0.286108em"}}),Object(r.b)("span",{parentName:"span"})))))))))),") em que ocorre a falta durante os estudos de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"stability"}),"estabilidade"),". 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Cada tipo de entrada e sa\xedda est\xe1 relacionada a um regulador da m\xe1quina: ",Object(m.b)("strong",{parentName:"p"},"Regulador de Tens\xe3o (AVR, do ingl\xeas ",Object(m.b)("em",{parentName:"strong"},"Automatic Voltage Regulator"),")")," e ",Object(m.b)("strong",{parentName:"p"},"Regulador de Velocidade (RV)"),"."),Object(m.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(m.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(m.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(m.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"O sistema de controle deve ter ",Object(m.b)("strong",{parentName:"p"},"ao menos uma entrada e uma sa\xedda"),"."))),Object(m.b)("p",null,"As entradas e sa\xeddas do sistema de controle s\xe3o definidas por esses blocos, os quais s\xe3o distintos para cada tipo de escopo. 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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 no c\xe1lculo do erro de velocidade nos reguladores de velocidade, al\xe9m de entrada do PSS em AVRs;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Pot\xeancia ativa e reativa")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR"),"): Pot\xeancia ativa fornecida pela m\xe1quina s\xedncrona, 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"}),"."))))),", vari\xe1vel no tempo. 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 (",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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",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"https://wiki.wxwidgets.org/Compiling_and_getting_started#Running_wxWidgets_projects"}),"diret\xf3rio das bibliotecas do wxWidgets")," nas vari\xe1veis de ambiente.\nPara isso, siga ",Object(r.b)("strong",{parentName:"p"},"UM")," dos m\xe9todos apresentados abaixo:"),Object(r.b)("h4",{id:"m\xe9todo-i-recomendado"},Object(r.b)("em",{parentName:"h4"},"M\xe9todo I (recomendado)")),Object(r.b)("p",null,"Insira o seguinte comando no arquivo ",Object(r.b)("strong",{parentName:"p"},"~/.bashrc"),":"),Object(r.b)("pre",null,Object(r.b)("code",Object(n.a)({parentName:"pre"},{className:"language-shell"}),'echo "export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib" >> ~/.bashrc\n')),Object(r.b)("h4",{id:"m\xe9todo-ii-n\xe3o-recomendado"},Object(r.b)("em",{parentName:"h4"},"M\xe9todo II (n\xe3o recomendado)")),Object(r.b)("div",{className:"admonition admonition-warning alert alert--danger"},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:"12",height:"16",viewBox:"0 0 12 16"}),Object(r.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(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Utilizando esse m\xe9todo os passos abaixo devem ser executados 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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 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Essa barra \xe9 necessariamente geradora, uma vez que ela \xe9 respons\xe1vel pelo equil\xedbrio do balan\xe7o de pot\xeancia do sistema."))),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"},"O tipo de barra deve ser definido no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"bus"}),"elemento barramento"),"."),Object(n.b)("p",{parentName:"div"},"Note que ",Object(n.b)("strong",{parentName:"p"},"o sistema deve possuir somente uma barra de refer\xeancia"),"."))),Object(n.b)("p",null,"Como mencionado anteriormente, as equa\xe7\xf5es s\xe3o n\xe3o-lineares e a solu\xe7\xe3o anal\xedtica n\xe3o \xe9 pr\xe1tica. As solu\xe7\xf5es dessas equa\xe7\xf5es seguem ",Object(n.b)("strong",{parentName:"p"},Object(n.b)("a",Object(s.a)({parentName:"strong"},{href:"https://en.wikipedia.org/wiki/Iterative_method"}),"processos iterativos")),", em que s\xe3o atribu\xeddos valores estimados (ou iniciais) para as barras com tens\xf5es desconhecidas e, baseado na pot\xeancia ativa e reativa e m\xf3dulo da tens\xe3o especificados, calcula-se por meio das equa\xe7\xf5es previamente apresentadas as novas tens\xf5es complexas em cada n\xf3 do sistema."),Object(n.b)("p",null,"Na sequ\xeancia, esse conjunto de valores para as tens\xf5es em cada barra \xe9 utilizado para novamente calcular outro grupo de tens\xf5es. Cada c\xe1lculo de um novo conjunto de tens\xf5es \xe9 chamado itera\xe7\xe3o. O processo iterativo \xe9 repetido at\xe9 que as mudan\xe7as em todas as barras sejam menores do que um valor pr\xe9-estipulado, obtendo assim a converg\xeancia."),Object(n.b)("h2",{id:"execu\xe7\xe3o-do-fluxo-de-carga-no-psp-ufu"},"Execu\xe7\xe3o do fluxo de carga no PSP-UFU"),Object(n.b)("p",null,"Ap\xf3s a constru\xe7\xe3o do diagrama unifilar no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia"),", a execu\xe7\xe3o do fluxo de carga \xe9 realizada no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," clicando no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Fluxo de carga"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/menuSimulationPF.svg"),alt:"Menu Simula\xe7\xe3o",title:"Menu Simula\xe7\xe3o"}))),Object(n.b)("div",{className:"admonition admonition-tip alert alert--success"},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:"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(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Caso o fluxo de carga tenha sido executado com sucesso, as setas de pot\xeancia ser\xe3o exibidas, a barra de status indicar\xe1 sucesso na opera\xe7\xe3o e os ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto")," ser\xe3o atualizados."))),Object(n.b)("p",null,Object(n.b)("strong",{parentName:"p"},"Outra possibilidade")," \xe9 a execu\xe7\xe3o por meio do c\xe1lculo cont\xednuo, tamb\xe9m presente no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," e seu acionamento \xe9 realizado co clicar no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Habilitar solu\xe7\xe3o"),". Com essa op\xe7\xe3o, os c\xe1lculos est\xe1ticos selecionados nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," s\xe3o automaticamente realizados ao modificar quaisquer par\xe2metros da rede, como dados el\xe9tricos e acionamento dos disjuntores dos elementos (remo\xe7\xe3o ou inser\xe7\xe3o)."),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"},"Evite construir o circuito com o c\xe1lculo cont\xednuo habilitado, uma vez que configura\xe7\xf5es tempor\xe1rias podem levar a erros de execu\xe7\xe3o da simula\xe7\xe3o."),Object(n.b)("p",{parentName:"div"},"Para desabilitar o c\xe1lculo cont\xednuo clique no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Desabilitar solu\xe7\xe3o"),"."))),Object(n.b)("p",null,"Os resultados do fluxo de carga s\xe3o exibidos nos ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto vinculado"),", ao posicionar o mouse sobre os elementos e em ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"tabularReport"}),"relat\xf3rios tabulares"),"."),Object(n.b)("h3",{id:"erros-comuns-na-execu\xe7\xe3o-do-fluxo-de-carga"},"Erros comuns na execu\xe7\xe3o do fluxo de carga"),Object(n.b)("p",null,"A seguir s\xe3o apresentados os erros mais comuns relacionados ao fluxo de carga."),Object(n.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-o-n\xfamero-m\xe1ximo-de-itera\xe7\xf5es-foi-alcan\xe7ado"},'A seguinte mensagem de erro \xe9 exibida: "O n\xfamero m\xe1ximo de itera\xe7\xf5es foi alcan\xe7ado"'),Object(n.b)("p",null,"Essa mensagem de erro \xe9 exibida quando o m\xe9todo de solu\xe7\xe3o num\xe9rica selecionado nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," atinge o n\xfamero m\xe1ximo de itera\xe7\xf5es inserido. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"O n\xfamero m\xe1ximo de itera\xe7\xf5es est\xe1 muito baixo"),". Alguns circuitos exigem um n\xfamero maior de itera\xe7\xf5es, portanto altere o valor do m\xe1ximo de itera\xe7\xf5es nas ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),". Tamb\xe9m tente alternar entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros de simula\xe7\xe3o est\xe3o inadequados"),". Caso um par\xe2metro do m\xe9todo de solu\xe7\xe3o esteja inadequado, como fator de acelera\xe7\xe3o ou toler\xe2ncia, o c\xe1lculo pode n\xe3o alcan\xe7ar a converg\xeancia. Altere esses par\xe2metros nas ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),".")),Object(n.b)("h4",{id:"os-dados-de-sa\xedda-s\xe3o-exibidos-como-nan-ou-nan"},'Os dados de sa\xedda s\xe3o exibidos como "NaN" ou "nan"'),Object(n.b)("p",null,'Isso ocorre devido a erros de opera\xe7\xf5es matem\xe1ticas nos c\xe1lculos de fluxo de carga. "NaN" significa ',Object(n.b)("em",{parentName:"p"},"Not a Number"),"."),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum barramento est\xe1 isolado"),". Esse erro \xe9 bastante comum e pode ocorrer ao inserir um barramento sem conect\xe1-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solu\xe7\xe3o \xe9 eliminar essa barra do diagrama."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis.")),Object(n.b)("h2",{id:"m\xe9todos-de-solu\xe7\xe3o-num\xe9rica-do-fluxo-de-carga-no-psp-ufu"},"M\xe9todos de solu\xe7\xe3o num\xe9rica do fluxo de carga no PSP-UFU"),Object(n.b)("p",null,"Os m\xe9todos implementados no programa para solu\xe7\xe3o do problema de fluxo de carga no PSP-UFU s\xe3o ",Object(n.b)("strong",{parentName:"p"},"Gauss-Seidel (GS)")," e ",Object(n.b)("strong",{parentName:"p"},"Newton-Raphson (NR)"),". Al\xe9m desses m\xe9todos cl\xe1ssicos, um m\xe9todo h\xedbrido pode ser utilizado (definido nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),"), em que \xe9 utilizado inicialmente o GS e na sequ\xeancia o NR, aumentando a chance de converg\xeancia do NR."),Object(n.b)("h3",{id:"gauss-seidel"},"Gauss-Seidel"),Object(n.b)("p",null,"O m\xe9todo de Gauss-Seidel tem sido bastante utilizado nas \xfaltimas d\xe9cadas para solu\xe7\xe3o do problema de fluxo de carga, uma vez que n\xe3o h\xe1 a necessidade de fatorar a matrizes, reduzindo o esfor\xe7o computacional. 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tens\xe3o deixa de ser controlada partir de ent\xe3o."),Object(n.b)("p",null,"A verifica\xe7\xe3o de viola\xe7\xe3o e troca de tipo de barra pode ser realizada a cada itera\xe7\xe3o ou ao final da converg\xeancia do c\xe1lculo. No PSP-UFU foi implementada a \xfaltima estrat\xe9gia, uma vez que separa os conceitos de c\xe1lculo e de verifica\xe7\xe3o de limites, tornando mais f\xe1cil o desenvolvimento de novos m\xe9todos num\xe9ricos e limites. Nessa abordagem, ao ajustar o sistema para a nova situa\xe7\xe3o n\xe3o violadora o c\xe1lculo iterativo deve ser retomado at\xe9 que obtenha novamente a converg\xeancia."),Object(n.b)("h2",{id:"refer\xeancias"},"Refer\xeancias"),Object(n.b)("ol",null,Object(n.b)("li",{parentName:"ol"},"MONTICELLI, A. J. Fluxo de Carga em Redes de Energia El\xe9trica. S\xe3o Paulo: Edgar Bl\xfccher, 1983."),Object(n.b)("li",{parentName:"ol"},"STEVENSON JR.; WILLIAN, D. Elementos de An\xe1lise de Sistemas de Pot\xeancia. 2\xaa ed. S\xe3o Paulo: McGraw-Hill, 1986."),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"},"TINNEY, W. F.; HART, C. E. Power Flow Solution by Newton\u2019s Method. IEEE Transaction on Power Apparatus and Systems, v. PAS-86, n. 11, nov. 1967. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/TPAS.1967.291823"}),"https://doi.org/10.1109/TPAS.1967.291823"))))}j.isMDXComponent=!0}}]); \ No newline at end of file diff --git a/docs/9949b94b.f16f6673.js b/docs/9949b94b.f16f6673.js deleted file mode 100644 index 98fca27..0000000 --- a/docs/9949b94b.f16f6673.js +++ /dev/null @@ -1 +0,0 @@ -(window.webpackJsonp=window.webpackJsonp||[]).push([[34],{136:function(a,e,t){"use strict";t.r(e),t.d(e,"frontMatter",(function(){return p})),t.d(e,"metadata",(function(){return c})),t.d(e,"rightToc",(function(){return r})),t.d(e,"default",(function(){return j}));var s=t(2),m=t(6),n=(t(0),t(166)),b=t(167),p=(t(172),t(173),{id:"powerFlow",title:"Fluxo de Pot\xeancia",sidebar_label:"Fluxo de Pot\xeancia"}),c={id:"powerFlow",isDocsHomePage:!1,title:"Fluxo de Pot\xeancia",description:"Um estudo fundamental no planejamento da expans\xe3o e opera\xe7\xe3o de um sistema el\xe9trico \xe9 o fluxo de pot\xeancia (ou fluxo de carga) uma vez que a opera\xe7\xe3o satisfat\xf3ria desse sistema depende do conhecimento dos efeitos da interliga\xe7\xe3o, de novas cargas, de novas centrais geradoras e de novas linhas antes que elas sejam instaladas. 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mtight"}),"i")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.15em"}}),Object(n.b)("span",{parentName:"span"}))))))))))," s\xe3o calculados.")),Object(n.b)("div",{className:"admonition admonition-info alert alert--info"},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:"14",height:"16",viewBox:"0 0 14 16"}),Object(n.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"})))),"Informa\xe7\xe3o")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"As ",Object(n.b)("strong",{parentName:"p"},"barras PQ")," geralmente s\xe3o representadas pelos barramentos de carga, os quais n\xe3o h\xe1 gera\xe7\xe3o e controle de tens\xe3o."),Object(n.b)("p",{parentName:"div"},"As ",Object(n.b)("strong",{parentName:"p"},"barras PV")," se caracterizam pelo controle de tens\xe3o mediante a inje\xe7\xe3o ou absor\xe7\xe3o de pot\xeancia reativa por meio do controle da excita\xe7\xe3o de uma m\xe1quina s\xedncrona."),Object(n.b)("p",{parentName:"div"},"A ",Object(n.b)("strong",{parentName:"p"},"barra de Refer\xeancia")," (ou de folga, de oscila\xe7\xe3o) tem como fun\xe7\xe3o, assim como o pr\xf3prio nome diz, servir de refer\xeancia de tens\xe3o e \xe2ngulo do sistema. Essa barra \xe9 necessariamente geradora, uma vez que ela \xe9 respons\xe1vel pelo equil\xedbrio do balan\xe7o de pot\xeancia do sistema."))),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"},"O tipo de barra deve ser definido no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"bus"}),"elemento barramento"),"."),Object(n.b)("p",{parentName:"div"},"Note que ",Object(n.b)("strong",{parentName:"p"},"o sistema deve possuir somente uma barra de refer\xeancia"),"."))),Object(n.b)("p",null,"Como mencionado anteriormente, as equa\xe7\xf5es s\xe3o n\xe3o-lineares e a solu\xe7\xe3o anal\xedtica n\xe3o \xe9 pr\xe1tica. As solu\xe7\xf5es dessas equa\xe7\xf5es seguem ",Object(n.b)("strong",{parentName:"p"},Object(n.b)("a",Object(s.a)({parentName:"strong"},{href:"https://en.wikipedia.org/wiki/Iterative_method"}),"processos iterativos")),", em que s\xe3o atribu\xeddos valores estimados (ou iniciais) para as barras com tens\xf5es desconhecidas e, baseado na pot\xeancia ativa e reativa e m\xf3dulo da tens\xe3o especificados, calcula-se por meio das equa\xe7\xf5es previamente apresentadas as novas tens\xf5es complexas em cada n\xf3 do sistema."),Object(n.b)("p",null,"Na sequ\xeancia, esse conjunto de valores para as tens\xf5es em cada barra \xe9 utilizado para novamente calcular outro grupo de tens\xf5es. Cada c\xe1lculo de um novo conjunto de tens\xf5es \xe9 chamado itera\xe7\xe3o. O processo iterativo \xe9 repetido at\xe9 que as mudan\xe7as em todas as barras sejam menores do que um valor pr\xe9-estipulado, obtendo assim a converg\xeancia."),Object(n.b)("h2",{id:"execu\xe7\xe3o-do-fluxo-de-carga-no-psp-ufu"},"Execu\xe7\xe3o do fluxo de carga no PSP-UFU"),Object(n.b)("p",null,"Ap\xf3s a constru\xe7\xe3o do diagrama unifilar no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia"),", a execu\xe7\xe3o do fluxo de carga \xe9 realizada no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," clicando no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Fluxo de carga"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/menuSimulationPF.svg"),alt:"Menu Simula\xe7\xe3o",title:"Menu Simula\xe7\xe3o"}))),Object(n.b)("div",{className:"admonition admonition-tip alert alert--success"},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:"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(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Caso o fluxo de carga tenha sido executado com sucesso, as setas de pot\xeancia ser\xe3o exibidas, a barra de status indicar\xe1 sucesso na opera\xe7\xe3o e os ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto")," ser\xe3o atualizados."))),Object(n.b)("p",null,Object(n.b)("strong",{parentName:"p"},"Outra possibilidade")," \xe9 a execu\xe7\xe3o por meio do c\xe1lculo cont\xednuo, tamb\xe9m presente no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," e seu acionamento \xe9 realizado co clicar no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Habilitar solu\xe7\xe3o"),". Com essa op\xe7\xe3o, os c\xe1lculos est\xe1ticos selecionados nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," s\xe3o automaticamente realizados ao modificar quaisquer par\xe2metros da rede, como dados el\xe9tricos e acionamento dos disjuntores dos elementos (remo\xe7\xe3o ou inser\xe7\xe3o)."),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"},"Evite construir o circuito com o c\xe1lculo cont\xednuo habilitado, uma vez que configura\xe7\xf5es tempor\xe1rias podem levar a erros de execu\xe7\xe3o da simula\xe7\xe3o."),Object(n.b)("p",{parentName:"div"},"Para desabilitar o c\xe1lculo cont\xednuo clique no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Desabilitar solu\xe7\xe3o"),"."))),Object(n.b)("p",null,"Os resultados do fluxo de carga s\xe3o exibidos nos ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto vinculado"),", ao posicionar o mouse sobre os elementos e em ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"tabularReport"}),"relat\xf3rios tabulares"),"."),Object(n.b)("h3",{id:"erros-comuns-na-execu\xe7\xe3o-do-fluxo-de-carga"},"Erros comuns na execu\xe7\xe3o do fluxo de carga"),Object(n.b)("p",null,"A seguir s\xe3o apresentados os erros mais comuns relacionados ao fluxo de carga."),Object(n.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-o-n\xfamero-m\xe1ximo-de-itera\xe7\xf5es-foi-alcan\xe7ado"},'A seguinte mensagem de erro \xe9 exibida: "O n\xfamero m\xe1ximo de itera\xe7\xf5es foi alcan\xe7ado"'),Object(n.b)("p",null,"Essa mensagem de erro \xe9 exibida quando o m\xe9todo de solu\xe7\xe3o num\xe9rica selecionado nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," atinge o n\xfamero m\xe1ximo de itera\xe7\xf5es inserido. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"O n\xfamero m\xe1ximo de itera\xe7\xf5es est\xe1 muito baixo"),". Alguns circuitos exigem um n\xfamero maior de itera\xe7\xf5es, portanto altere o valor do m\xe1ximo de itera\xe7\xf5es nas ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),". Tamb\xe9m tente alternar entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros de simula\xe7\xe3o est\xe3o inadequados"),". Caso um par\xe2metro do m\xe9todo de solu\xe7\xe3o esteja inadequado, como fator de acelera\xe7\xe3o ou toler\xe2ncia, o c\xe1lculo pode n\xe3o alcan\xe7ar a converg\xeancia. Altere esses par\xe2metros nas ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),".")),Object(n.b)("h4",{id:"os-dados-de-sa\xedda-s\xe3o-exibidos-como-nan-ou-nan"},'Os dados de sa\xedda s\xe3o exibidos como "NaN" ou "nan"'),Object(n.b)("p",null,'Isso ocorre devido a erros de opera\xe7\xf5es matem\xe1ticas nos c\xe1lculos de fluxo de carga. "NaN" significa ',Object(n.b)("em",{parentName:"p"},"Not a Number"),"."),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum barramento est\xe1 isolado"),". Esse erro \xe9 bastante comum e pode ocorrer ao inserir um barramento sem conect\xe1-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solu\xe7\xe3o \xe9 eliminar essa barra do diagrama."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis.")),Object(n.b)("h2",{id:"m\xe9todos-de-solu\xe7\xe3o-num\xe9rica-do-fluxo-de-carga-no-psp-ufu"},"M\xe9todos de solu\xe7\xe3o num\xe9rica do fluxo de carga no PSP-UFU"),Object(n.b)("p",null,"Os m\xe9todos implementados no programa para solu\xe7\xe3o do problema de fluxo de carga no PSP-UFU s\xe3o ",Object(n.b)("strong",{parentName:"p"},"Gauss-Seidel (GS)")," e ",Object(n.b)("strong",{parentName:"p"},"Newton-Raphson (NR)"),". Al\xe9m desses m\xe9todos cl\xe1ssicos, um m\xe9todo h\xedbrido pode ser utilizado (definido nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),"), em que \xe9 utilizado inicialmente o GS e na sequ\xeancia o NR, aumentando a chance de converg\xeancia do NR."),Object(n.b)("h3",{id:"gauss-seidel"},"Gauss-Seidel"),Object(n.b)("p",null,"O m\xe9todo de Gauss-Seidel tem sido bastante utilizado nas \xfaltimas d\xe9cadas para solu\xe7\xe3o do problema de fluxo de carga, uma vez que n\xe3o h\xe1 a necessidade de fatorar a matrizes, reduzindo o esfor\xe7o computacional. Atualmente, restri\xe7\xf5es computacionais s\xe3o menos problem\xe1ticas e outros m\xe9todos s\xe3o normalmente escolhidos, por\xe9m o Gauss-Seidel ainda possui valor did\xe1tico e, visto que o PSP-UFU tamb\xe9m possui fins educacionais, optou-se pela implementa\xe7\xe3o desse m\xe9todo."),Object(n.b)("p",null,"Para iniciar as itera\xe7\xf5es do m\xe9todo s\xe3o necess\xe1rios valores iniciais para as tens\xf5es (",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)("msubsup",{parentName:"mrow"},Object(n.b)("mover",Object(s.a)({parentName:"msubsup"},{accent:"true"}),Object(n.b)("mi",{parentName:"mover"},"V"),Object(n.b)("mo",{parentName:"mover"},"\u02d9")),Object(n.b)("mi",{parentName:"msubsup"},"i"),Object(n.b)("mn",{parentName:"msubsup"},"0"))),Object(n.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"\\dot{V}_i^0")))),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:"1.178854em",verticalAlign:"-0.258664em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord accent"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-t"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.9201900000000001em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"3em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.22222em"}}),"V"))),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3.25233em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"3em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"accent-body",style:{left:"-0.13889em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"\u02d9"))))))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"msupsub"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-t vlist-t2"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.8141079999999999em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-2.441336em",marginRight:"0.05em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"i"))),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3.063em",marginRight:"0.05em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mtight"}),"0")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.258664em"}}),Object(n.b)("span",{parentName:"span"})))))))))),") que devem ser calculadas. 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tens\xe3o deixa de ser controlada partir de ent\xe3o."),Object(n.b)("p",null,"A verifica\xe7\xe3o de viola\xe7\xe3o e troca de tipo de barra pode ser realizada a cada itera\xe7\xe3o ou ao final da converg\xeancia do c\xe1lculo. No PSP-UFU foi implementada a \xfaltima estrat\xe9gia, uma vez que separa os conceitos de c\xe1lculo e de verifica\xe7\xe3o de limites, tornando mais f\xe1cil o desenvolvimento de novos m\xe9todos num\xe9ricos e limites. Nessa abordagem, ao ajustar o sistema para a nova situa\xe7\xe3o n\xe3o violadora o c\xe1lculo iterativo deve ser retomado at\xe9 que obtenha novamente a converg\xeancia."),Object(n.b)("h2",{id:"refer\xeancias"},"Refer\xeancias"),Object(n.b)("ol",null,Object(n.b)("li",{parentName:"ol"},"MONTICELLI, A. J. Fluxo de Carga em Redes de Energia El\xe9trica. S\xe3o Paulo: Edgar Bl\xfccher, 1983."),Object(n.b)("li",{parentName:"ol"},"STEVENSON JR.; WILLIAN, D. Elementos de An\xe1lise de Sistemas de Pot\xeancia. 2\xaa ed. S\xe3o Paulo: McGraw-Hill, 1986."),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"},"TINNEY, W. F.; HART, C. E. Power Flow Solution by Newton\u2019s Method. IEEE Transaction on Power Apparatus and Systems, v. 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Nesse tipo de c\xe1lculo \xe9 poss\xedvel calcular faltas ",Object(m.b)("em",{parentName:"li"},"shunt")," nos ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"bus"}),"barramentos")," balanceadas e desbalanceadas."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"N\xedvel de curto-circuito"),": Calcula o n\xedvel de curto-circuito (falta trif\xe1sica) em todos ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"bus"}),"barramentos")," do sistema.")),Object(m.b)("p",null,"Ap\xf3s a constru\xe7\xe3o do diagrama unifilar no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia"),", a execu\xe7\xe3o do c\xe1lculo de curto-circuito \xe9 realizada no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," clicando no bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"Falta"),". Para calcular o n\xedvel de curto-circuito (falta trif\xe1sica) em todos ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"bus"}),"barramentos")," do sistema, basta clicar no bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"N\xedvel de curto-circuito"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(b.a)("images/menuSimulationFaulta.svg"),alt:"Execu\xe7\xe3o dos c\xe1lculos de curto-circuito",title:"Execu\xe7\xe3o dos c\xe1lculos de curto-circuito"}))),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"},"\xc9 poss\xedvel calcular as faltas sem a execu\xe7\xe3o do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow"}),"fluxo de carga"),", por\xe9m ",Object(m.b)("strong",{parentName:"p"},"n\xe3o \xe9 recomend\xe1vel"),", visto que os valores das correntes de falta s\xe3o significativamente alteradas."))),Object(m.b)("p",null,Object(m.b)("strong",{parentName:"p"},"Outra possibilidade")," \xe9 a execu\xe7\xe3o por meio do c\xe1lculo cont\xednuo, tamb\xe9m presente no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," e seu acionamento \xe9 realizado co clicar no bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"Habilitar solu\xe7\xe3o"),". Com essa op\xe7\xe3o, os c\xe1lculos est\xe1ticos selecionados nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," s\xe3o automaticamente realizados ao modificar quaisquer par\xe2metros da rede, como dados el\xe9tricos e acionamento dos disjuntores dos elementos (remo\xe7\xe3o ou inser\xe7\xe3o)."),Object(m.b)("div",{className:"admonition admonition-warning alert alert--danger"},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:"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(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Os c\xe1lculos de curtos-circuitos n\xe3o s\xe3o habilitados por padr\xe3o no c\xe1lculo cont\xednuo e devem ser inseridos nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),"."))),Object(m.b)("p",null,"Os resultados do c\xe1lculo de curto-circuito s\xe3o exibidos nos ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto vinculado"),", ao posicionar o mouse sobre os barramentos e em ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"tabularReport"}),"relat\xf3rios tabulares"),"."),Object(m.b)("h3",{id:"erros-comuns-na-execu\xe7\xe3o-do-c\xe1lculo-de-curto-circuito"},"Erros comuns na execu\xe7\xe3o do c\xe1lculo de curto-circuito"),Object(m.b)("p",null,"A seguir s\xe3o apresentados os erros mais comuns relacionados ao calculo de curto-circuito."),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-falha-ao-inverter-a-matriz-admit\xe2ncia-de-sequ\xeancia-zero"},'A seguinte mensagem de erro \xe9 exibida: "Falha ao inverter a matriz admit\xe2ncia de sequ\xeancia zero"'),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Impossibilidade de circula\xe7\xe3o da corrente de sequ\xeancia zero"),". Caso o gerador n\xe3o seja aterrado, n\xe3o circular\xe1 corrente de sequ\xeancia zero por ele. Nesse caso, dependendo da conex\xe3o do transformador pr\xf3ximo ao gerador sem aterramento, a matriz admit\xe2ncia de sequ\xeancia zero \xe9 singular. Para contornar esse problema escolha uma das duas solu\xe7\xf5es abaixo:",Object(m.b)("ul",{parentName:"li"},Object(m.b)("li",{parentName:"ul"},'Marque a op\xe7\xe3o "Neutro aterrado" e insira um alto valor de reat\xe2ncia de aterramento (',Object(m.b)("span",Object(s.a)({parentName:"li"},{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"},"j"),Object(m.b)("mn",{parentName:"mrow"},"9999"),Object(m.b)("mtext",{parentName:"mrow"},"\xa0"),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"}),"j9999~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:"0.85396em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.05724em"}}),"j"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mspace nobreak"}),"\xa0"),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"}),"."))))),", por exemplo);"),Object(m.b)("li",{parentName:"ul"},"Ou, na barra do gerador, insira um reator de baixo valor de pot\xeancia reativa (",Object(m.b)("span",Object(s.a)({parentName:"li"},{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)("mn",{parentName:"mrow"},"1"),Object(m.b)("mo",Object(s.a)({parentName:"mrow"},{separator:"true",lspace:"0em",rspace:"0em"}),","),Object(m.b)("mn",{parentName:"mrow"},"0"),Object(m.b)("mtext",{parentName:"mrow"},"\xa0"),Object(m.b)("mi",{parentName:"mrow"},"v"),Object(m.b)("mi",{parentName:"mrow"},"a"),Object(m.b)("mi",{parentName:"mrow"},"r")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"1{,}0~var")))),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:"0.8388800000000001em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"1"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mpunct"}),",")),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mspace nobreak"}),"\xa0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.03588em"}}),"v"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"a"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.02778em"}}),"r"))))),", por exemplo).")))),Object(m.b)("h2",{id:"o-c\xe1lculo-de-curto-circuito"},"O c\xe1lculo de curto-circuito"),Object(m.b)("p",null,"Como j\xe1 foi apresentado anteriormente, as faltas que ocorrem com maior frequ\xeancia em sistemas de pot\xeancia s\xe3o assim\xe9tricas. Como qualquer falta assim\xe9trica provoca fluxo de corrente desequilibrada \xe9 necess\xe1rio empregar o m\xe9todo das componentes sim\xe9tricas. Esse m\xe9todo permite o estudo de sistemas balanceados com cargas desbalanceadas."),Object(m.b)("h3",{id:"m\xe9todo-das-componentes-sim\xe9tricas"},"M\xe9todo das componentes sim\xe9tricas"),Object(m.b)("p",null,"Esse m\xe9todo proposto por C. L. Fortescue, permite definir um sistema de n fasores desbalanceados em n \u2013 1 sistemas de n fases balanceados e um sistema de fase zero. O sistema de fase zero \xe9 definido por todas as fases de mesmo m\xf3dulo e \xe2ngulo.\nPara um sistema trif\xe1sico pode-se definir tr\xeas componentes de sequ\xeancia:"),Object(m.b)("ol",null,Object(m.b)("li",{parentName:"ol"},"Componentes de sequ\xeancia positiva, constituindo em tr\xeas fasores iguais em m\xf3dulo, 120\xba defasados entre si, e tendo a mesma sequ\xeancia de fase que os fasores originais;"),Object(m.b)("li",{parentName:"ol"},"Componentes de sequ\xeancia negativa, constituindo em tr\xeas fasores iguais em m\xf3dulo, 120\xba defasados entre si, e tendo a sequ\xeancia de fase oposta \xe0 dos fasores originais."),Object(m.b)("li",{parentName:"ol"},"Componentes de sequ\xeancia zero, constituindo em tr\xeas fasores iguais em m\xf3dulo e com defasagem nula entre si.")),Object(m.b)("p",null,"Com isso pode-se decompor as tens\xf5es de fase em componentes sim\xe9tricas pelas seguintes equa\xe7\xf5es:"),Object(m.b)("div",{className:"math 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Essas configura\xe7\xf5es s\xe3o aplicadas para todos os projetos e permanecem gravadas no disco."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(i.a)("images/generalSettings.png"),alt:"Configura\xe7\xf5es gerais",title:"Configura\xe7\xf5es gerais"}))),Object(n.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(o.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(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Algumas configura\xe7\xf5es de seguran\xe7a do seu computador (principalmente em sistemas Windows) podem gerar uma mensagem de erro ao confirmar as altera\xe7\xf5es das configura\xe7\xf5es gerais."),Object(n.b)("p",{parentName:"div"},"Para resolver esse problema basta ",Object(n.b)("strong",{parentName:"p"},"executar o PSP-UFU como administrador")," (clicar com bot\xe3o direito no atalho do programa e posteriormente em executar como administrador). 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Essa a\xe7\xe3o cria um sistema em branco na \xe1rea de trabalho, local onde \xe9 poss\xedvel inserir os elementos el\xe9tricos por meio do ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu ",Object(n.b)("strong",{parentName:"a"},"Ferramentas"))," ou pelas ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"powerEditor#teclas-de-atalho"}),"teclas de atalho"),"."),Object(n.b)("p",null,"Esse sistema em branco pode ser ciado utilizando o ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"powerEditor"}),"Editor de Pot\xeancia"),"."),Object(n.b)("h3",{id:"salvar-e-salvar-como"},"Salvar e Salvar como..."),Object(n.b)("p",null,'A op\xe7\xe3o "Salvar" sobrep\xf5e as altera\xe7\xf5es realizadas no projeto aberto e grava no disco. 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Esses arquivos nada mais s\xe3o que arquivos de texto utilizando a ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"https://en.wikipedia.org/wiki/Markup_language"}),"linguagem de marca\xe7\xe3o")," XML (",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"https://en.wikipedia.org/wiki/XML"}),"eXtensible Markup Language"),"), que define uma s\xe9rie de regras de formata\xe7\xe3o dos dados de forma que eles s\xe3o tanto leg\xedveis por humanos quanto por m\xe1quinas."),Object(n.b)("p",{parentName:"div"},"Portanto, os dados el\xe9tricos contidos neles podem ser facilmente identificados e alterados, caso necess\xe1rio."))),Object(n.b)("h3",{id:"abrir-projeto"},"Abrir projeto"),Object(n.b)("p",null,"Essa op\xe7\xe3o abre os projetos gravados no disco por meio com o aux\xedlio de uma janela de sele\xe7\xe3o de arquivos. 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De acordo com a teoria dos grafos, o sistema \xe9 modelado como v\xe9rtices e arestas. Nesse contexto, os barramentos s\xe3o os v\xe9rtices e os ramos do sistema (linhas e transformadores) s\xe3o as arestas. As localiza\xe7\xf5es de elementos de deriva\xe7\xe3o, assim como os n\xf3s dos elementos, s\xe3o automaticamente controladas pelo PSP-UFU."),Object(n.b)("p",null,"A ferramenta de ",Object(n.b)("em",{parentName:"p"},"layout")," autom\xe1tico \xe9 composta por um processo iterativo e os resultados s\xe3o mais refinados com um n\xfamero maior de itera\xe7\xf5es. 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limitador de taxa no PSP-UFU"}))),Object(m.b)("p",null,"Esse bloco \xe9 definido pelo ",Object(m.b)("strong",{parentName:"p"},"limite superior (taxa de crescimento m\xe1xima) e inferior (taxa de decrescimento m\xe1xima)"),", inseridos pelo usu\xe1rio."),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 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-

2019w42a-beta

Thales

Thales

PhD
  • Harmonic study implemented;
  • Autolayout from importation implemented;
  • Importation of Matpower files;
  • Several minor bugfixes.
- - - - - - - - +
+

2019w42a-beta

Thales

Thales

PhD
  • Harmonic study implemented;
  • Autolayout from importation implemented;
  • Importation of Matpower files;
  • Several minor bugfixes.
+ + + + + + + + \ No newline at end of file diff --git a/docs/blog/2019w44a-beta/index.html b/docs/blog/2019w44a-beta/index.html index 709c3b6..11c2653 100644 --- a/docs/blog/2019w44a-beta/index.html +++ b/docs/blog/2019w44a-beta/index.html @@ -3,27 +3,27 @@ - -22019w44a-beta | PSP-UFU - - - - - - - - + +22019w44a-beta | PSP-UFU + + + + + + + + -
-

22019w44a-beta

Thales

Thales

PhD
  • Minor changes to 32bit MSW version for compatibility;
  • Travis CI (Continuous Integration) implemented (Linux).
- - - - - - - - +
+

22019w44a-beta

Thales

Thales

PhD
  • Minor changes to 32bit MSW version for compatibility;
  • Travis CI (Continuous Integration) implemented (Linux).
+ + + + + + + + \ No newline at end of file diff --git a/docs/blog/2020w24a-beta/index.html b/docs/blog/2020w24a-beta/index.html index d9f285e..0448c74 100644 --- a/docs/blog/2020w24a-beta/index.html +++ b/docs/blog/2020w24a-beta/index.html @@ -3,27 +3,27 @@ - -2020w24a-beta | PSP-UFU - - - - - - - - + +2020w24a-beta | PSP-UFU + + + + + + + + -
-

2020w24a-beta

Thales

Thales

PhD
  • Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
  • Added Visual Studio solution to the GitHub project;
  • Several major and minor bugfixes.
- - - - - - - - +
+

2020w24a-beta

Thales

Thales

PhD
  • Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
  • Added Visual Studio solution to the GitHub project;
  • Several major and minor bugfixes.
+ + + + + + + + \ No newline at end of file diff --git a/docs/blog/2020w28a-beta/index.html b/docs/blog/2020w28a-beta/index.html index ffe5fb6..80324ba 100644 --- a/docs/blog/2020w28a-beta/index.html +++ b/docs/blog/2020w28a-beta/index.html @@ -3,27 +3,27 @@ - -2020w28a-beta | PSP-UFU - - - - - - - - + +2020w28a-beta | PSP-UFU + + + + + + + + -
-

2020w28a-beta

Thales

Thales

PhD
  • Voltage heatmap implemented (OpenGL enabled);
  • Several major and minor bugfixes.
- - - - - - - - +
+

2020w28a-beta

Thales

Thales

PhD
  • Voltage heatmap implemented (OpenGL enabled);
  • Several major and minor bugfixes.
+ + + + + + + + \ No newline at end of file diff --git a/docs/blog/index.html b/docs/blog/index.html index 3377d4b..c99e325 100644 --- a/docs/blog/index.html +++ b/docs/blog/index.html @@ -3,35 +3,35 @@ - -Blog | PSP-UFU - - - - - - - - - - - - + +Blog | PSP-UFU + + + + + + + + + + + + -
-

2020w28a-beta

Thales

Thales

PhD
  • Voltage heatmap implemented (OpenGL enabled);
  • Several major and minor bugfixes.

2020w24a-beta

Thales

Thales

PhD
  • Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
  • Added Visual Studio solution to the GitHub project;
  • Several major and minor bugfixes.

22019w44a-beta

Thales

Thales

PhD
  • Minor changes to 32bit MSW version for compatibility;
  • Travis CI (Continuous Integration) implemented (Linux).

2019w42a-beta

Thales

Thales

PhD
  • Harmonic study implemented;
  • Autolayout from importation implemented;
  • Importation of Matpower files;
  • Several minor bugfixes.
- - - - - - - - - - - - +
+

2020w28a-beta

Thales

Thales

PhD
  • Voltage heatmap implemented (OpenGL enabled);
  • Several major and minor bugfixes.

2020w24a-beta

Thales

Thales

PhD
  • Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
  • Added Visual Studio solution to the GitHub project;
  • Several major and minor bugfixes.

22019w44a-beta

Thales

Thales

PhD
  • Minor changes to 32bit MSW version for compatibility;
  • Travis CI (Continuous Integration) implemented (Linux).

2019w42a-beta

Thales

Thales

PhD
  • Harmonic study implemented;
  • Autolayout from importation implemented;
  • Importation of Matpower files;
  • Several minor bugfixes.
+ + + + + + + + + + + + \ No newline at end of file diff --git a/docs/blog/tags/index.html b/docs/blog/tags/index.html index e8e4e66..a5e3b70 100644 --- a/docs/blog/tags/index.html +++ b/docs/blog/tags/index.html @@ -3,25 +3,25 @@ - -Tags | PSP-UFU - - - - - - - + +Tags | PSP-UFU + + + + + + + -
-

Tags

- - - - - - - +
+

Tags

+ + + + + + + \ No newline at end of file diff --git a/docs/blog/tags/psp-ufu/index.html b/docs/blog/tags/psp-ufu/index.html index 392a088..5fdb5ef 100644 --- a/docs/blog/tags/psp-ufu/index.html +++ b/docs/blog/tags/psp-ufu/index.html @@ -3,35 +3,35 @@ - -Posts tagged "psp-ufu" | PSP-UFU - - - - - - - - - - - - + +Posts tagged "psp-ufu" | PSP-UFU + + + + + + + + + + + + -
-

4 posts tagged with "psp-ufu"

View All Tags

2020w24a-beta

Thales

Thales

PhD
  • Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
  • Added Visual Studio solution to the GitHub project;
  • Several major and minor bugfixes.

22019w44a-beta

Thales

Thales

PhD
  • Minor changes to 32bit MSW version for compatibility;
  • Travis CI (Continuous Integration) implemented (Linux).

2019w42a-beta

Thales

Thales

PhD
  • Harmonic study implemented;
  • Autolayout from importation implemented;
  • Importation of Matpower files;
  • Several minor bugfixes.
- - - - - - - - - - - - +
+

4 posts tagged with "psp-ufu"

View All Tags

2020w24a-beta

Thales

Thales

PhD
  • Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
  • Added Visual Studio solution to the GitHub project;
  • Several major and minor bugfixes.

22019w44a-beta

Thales

Thales

PhD
  • Minor changes to 32bit MSW version for compatibility;
  • Travis CI (Continuous Integration) implemented (Linux).

2019w42a-beta

Thales

Thales

PhD
  • Harmonic study implemented;
  • Autolayout from importation implemented;
  • Importation of Matpower files;
  • Several minor bugfixes.
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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. A ",Object(m.b)("strong",{parentName:"p"},"edi\xe7\xe3o dos dados")," dos componentes inseridos tamb\xe9m \xe9 realizada com ",Object(m.b)("strong",{parentName:"p"},"duplo clique")," sobre o elemento inserido, exibindo um formul\xe1rio de edi\xe7\xe3o de dados."),Object(m.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(m.b)("source",{src:"/PSP/videos/timelapseControlEditor.mp4",type:"video/mp4"}),Object(m.b)("source",{src:"/PSP/videos/timelapseControlEditor.webm",type:"video/webm"})),Object(m.b)("p",null,"Os seguintes blocos de controle est\xe3o presentes no PSP-UFU:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"io"}),"Entrada e Sa\xedda")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"transferFunction"}),"Fun\xe7\xe3o Transfer\xeancia")),Object(m.b)("li",{parentName:"ul"},"Matem\xe1tica",Object(m.b)("ul",{parentName:"li"},Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"sum"}),"Somador")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"multiplier"}),"Multiplicador")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"divider"}),"Divisor")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"exponential"}),"Exponencial")))),Object(m.b)("li",{parentName:"ul"},"Limitadores",Object(m.b)("ul",{parentName:"li"},Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"limiter"}),"Limitador absoluto")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"rateLimiter"}),"Limitador de taxa")))),Object(m.b)("li",{parentName:"ul"},"Constantes",Object(m.b)("ul",{parentName:"li"},Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"const"}),"Constante")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"gain"}),"Ganho")))),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"mathExpression"}),"Express\xe3o Matem\xe1tica"))),Object(m.b)("h2",{id:"inicializa\xe7\xe3o-do-sistema-de-controle"},"Inicializa\xe7\xe3o do sistema de controle"),Object(m.b)("p",null,"Caso as entradas do sistema de controle apresentem valores diferentes de zero ou a primeira opera\xe7\xe3o entre elas n\xe3o resulte em uma sa\xedda nula, o sistema necessita de inicializa\xe7\xe3o, de forma a adequar os valores de entradas e sa\xedda dos blocos elementares e dos vetores de estado das ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"transferFunction"}),"fun\xe7\xf5es transfer\xeancias")," presentes. 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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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. A ",Object(m.b)("strong",{parentName:"p"},"edi\xe7\xe3o dos dados")," dos componentes inseridos tamb\xe9m \xe9 realizada com ",Object(m.b)("strong",{parentName:"p"},"duplo clique")," sobre o elemento inserido, exibindo um formul\xe1rio de edi\xe7\xe3o de dados."),Object(m.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(m.b)("source",{src:"/PSP/videos/timelapseControlEditor.mp4",type:"video/mp4"}),Object(m.b)("source",{src:"/PSP/videos/timelapseControlEditor.webm",type:"video/webm"})),Object(m.b)("p",null,"Os seguintes blocos de controle est\xe3o presentes no PSP-UFU:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"io"}),"Entrada e Sa\xedda")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"transferFunction"}),"Fun\xe7\xe3o Transfer\xeancia")),Object(m.b)("li",{parentName:"ul"},"Matem\xe1tica",Object(m.b)("ul",{parentName:"li"},Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"sum"}),"Somador")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"multiplier"}),"Multiplicador")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"divider"}),"Divisor")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"exponential"}),"Exponencial")))),Object(m.b)("li",{parentName:"ul"},"Limitadores",Object(m.b)("ul",{parentName:"li"},Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"limiter"}),"Limitador absoluto")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"rateLimiter"}),"Limitador de taxa")))),Object(m.b)("li",{parentName:"ul"},"Constantes",Object(m.b)("ul",{parentName:"li"},Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"const"}),"Constante")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"gain"}),"Ganho")))),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"mathExpression"}),"Express\xe3o Matem\xe1tica"))),Object(m.b)("h2",{id:"inicializa\xe7\xe3o-do-sistema-de-controle"},"Inicializa\xe7\xe3o do sistema de controle"),Object(m.b)("p",null,"Caso as entradas do sistema de controle apresentem valores diferentes de zero ou a primeira opera\xe7\xe3o entre elas n\xe3o resulte em uma sa\xedda nula, o sistema necessita de inicializa\xe7\xe3o, de forma a adequar os valores de entradas e sa\xedda dos blocos elementares e dos vetores de estado das ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"transferFunction"}),"fun\xe7\xf5es transfer\xeancias")," presentes. 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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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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Caso n\xe3o seja informado, a satura\xe7\xe3o da m\xe1quina n\xe3o \xe9 considerada nos c\xe1lculos."))),Object(n.b)("h4",{id:"frequ\xeancia-de-circuito-aberto"},"Frequ\xeancia de circuito aberto"),Object(n.b)("p",null,"Indica a velocidade da m\xe1quina no caso de in\xedcio da simula\xe7\xe3o desconectada da rede."),Object(n.b)("div",{className:"admonition admonition-info alert alert--info"},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:"14",height:"16",viewBox:"0 0 14 16"}),Object(n.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"})))),"Informa\xe7\xe3o")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Essa informa\xe7\xe3o \xe9 particularmente \xfatil na an\xe1lise de conex\xe3o de geradores dessincronizados na rede."))),Object(n.b)("h4",{id:"reat\xe2ncias-s\xedncronas"},"Reat\xe2ncias s\xedncronas"),Object(n.b)("p",null,"Valores de reat\xe2ncia s\xedncrona (regime permanente) da m\xe1quina. 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)(c.a,{value:"switching",mdxType:"TabItem"},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:"acesso-aos-controles-da-m\xe1quina-s\xedncrona"},"Acesso aos controles da m\xe1quina s\xedncrona"),Object(n.b)("p",null,"Como j\xe1 ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator#utilizar-avr-e-regulador-de-velocidade"}),"mencionado anteriormente"),', os reguladores de velocidade e tens\xe3o da m\xe1quina s\xedncrona podem ser acionados ou inibidos por meio das caixas de sele\xe7\xe3o "',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator#utilizar-avr-e-regulador-de-velocidade"}),"Utilizar AVR e regulador de velocidade"),'". Ambas as op\xe7\xf5es ir\xe3o acessar o ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"editor de controles"),"."),Object(n.b)("p",null,"O acesso aos controles do ",Object(n.b)("strong",{parentName:"p"},"AVR"),' poder\xe3o ent\xe3o ser criados e manipulados ao clicar no bot\xe3o "Editar AVR", assim como o ',Object(n.b)("strong",{parentName:"p"},"Regulador de Velocidade"),' \xe9 acessado no bot\xe3o "Editar regulador de velocidade".'),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"},"No PSP-UFU a op\xe7\xe3o de editar o ",Object(n.b)("strong",{parentName:"p"},"AVR")," engloba mais que somente o controle de tens\xe3o da m\xe1quina. Nele ",Object(n.b)("strong",{parentName:"p"},"deve")," ser inserida a malha de controle da m\xe1quina assim como a ",Object(n.b)("strong",{parentName:"p"},"excitatriz da m\xe1quina s\xedncrona"),". Outras estrat\xe9gias de controle (opcionais), como PSS (",Object(n.b)("em",{parentName:"p"},"Power System Stabilizer"),") e/ou controles de sobre e sub excita\xe7\xe3o, s\xe3o tamb\xe9m implementadas em conjunto."))),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"},"Assim como no AVR, o ",Object(n.b)("strong",{parentName:"p"},"Regulador de Velocidade")," engloba mais que a regula\xe7\xe3o prim\xe1ria da m\xe1quina. Nessa op\xe7\xe3o ",Object(n.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(n.b)("strong",{parentName:"p"},"modelo da turbina"),". Estrat\xe9gias opcionais de controle da velocidade tamb\xe9m s\xe3o inseridas nessa op\xe7\xe3o."))),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.")))}l.isMDXComponent=!0},121:function(a,e,t){"use strict";var s=t(0),m=t(19);e.a=function(){const a=Object(s.useContext)(m.a);if(null===a)throw new Error("Docusaurus context not provided");return a}},122: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=0||(m[t]=a[t]);return m}(a,e);if(Object.getOwnPropertySymbols){var n=Object.getOwnPropertySymbols(a);for(s=0;s=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;rfunction(a,e,t,{forcePrependBaseUrl:s=!1,absolute:n=!1}={}){if(!t)return t;if(t.startsWith("#"))return t;if(Object(m.b)(t))return t;if(s)return e+t;const b=!t.startsWith(e)?e+t.replace(/^\//,""):t;return n?a+b:b}(e,a,t,s)}}function b(a,e={}){const{withBaseUrl:t}=n();return t(a,e)}},124:function(a,e,t){"use strict";function s(a){return!0===/^(\w*:|\/\/)/.test(a)}function m(a){return void 0!==a&&!s(a)}t.d(e,"b",(function(){return s})),t.d(e,"a",(function(){return m}))},125: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;ee.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]))}},129: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)}}}]); \ No newline at end of file diff --git a/docs/docs/bus/index.html b/docs/docs/bus/index.html index 9ea0407..af1f10d 100644 --- a/docs/docs/bus/index.html +++ b/docs/docs/bus/index.html @@ -3,32 +3,32 @@ - -Barramento | PSP-UFU - - - - - - - - - - + +Barramento | PSP-UFU + + + + + + + + + + -
-

Barramento

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.

Barramento no PSP-UFU

O elemento barramento, ou simplesmente barra, 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.

Formulário de edição dos barramentos

Atenção!

O barramento deve ser o primeiro elemento elétrico a ser inserido no diagrama de potência, uma vez que os demais componentes de potência são conectados nele.

A imagem abaixo apresenta o formulário de inserção/alteração de dados das barras:

Formulário dos barramentos no PSP-UFU

Esse formulário é subdividido em quatro contextos distintos:

  • Geral: no qual são inseridas informações gerais da barra e informações do fluxo de carga;
  • Falta: local onde o curto-circuito shunt deve ser inserido;
  • 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.

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

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.

A modificação desse parâmetro irá alterar toda a tensão do trecho conectado por linhas elétricas, sendo emitido um alerta ao usuário.

Tensão controlada

Caracteriza o barramento como barra de tensão controlada (Barra PV),

Atenção!

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.

O valor poderá ser inserido em p.u. ou em volts (ou kV caso a tensão nominal esteja nesta unidade).

Barra de referência

Caracteriza o barramento como barra de referência (Barra de oscilação). 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.

Dica

Resumo de como definir o tipo de barra:

  • Para definir o barramento como sendo uma Barra PQ, as opções "Barra de referência" e "Tensão controlada" devem estar desmarcadas;
  • Para definir o barramento como sendo uma Barra PV, deve-se marcar somente a opção "Tensão controlada", mantendo a opção "Barra de referência" desmarcada;
  • Para definir o barramento como sendo uma Barra de Referência, deve-se marcar a opção "Barra de referência". Caso a opção "Tensão controlada" esteja desmarcada será admitido um valor de tensão controlada de 1,0 p.u.1{,}0~p.u.
Cuidado!

O sistema deve possuir somente uma barra de referência.

Edit this page
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+

Barramento

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.

Barramento no PSP-UFU

O elemento barramento, ou simplesmente barra, 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.

Formulário de edição dos barramentos

Atenção!

O barramento deve ser o primeiro elemento elétrico a ser inserido no diagrama de potência, uma vez que os demais componentes de potência são conectados nele.

A imagem abaixo apresenta o formulário de inserção/alteração de dados das barras:

Formulário dos barramentos no PSP-UFU

Esse formulário é subdividido em quatro contextos distintos:

  • Geral: no qual são inseridas informações gerais da barra e informações do fluxo de carga;
  • Falta: local onde o curto-circuito shunt deve ser inserido;
  • 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.

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

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.

A modificação desse parâmetro irá alterar toda a tensão do trecho conectado por linhas elétricas, sendo emitido um alerta ao usuário.

Tensão controlada

Caracteriza o barramento como barra de tensão controlada (Barra PV),

Atenção!

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.

O valor poderá ser inserido em p.u. ou em volts (ou kV caso a tensão nominal esteja nesta unidade).

Barra de referência

Caracteriza o barramento como barra de referência (Barra de oscilação). 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.

Dica

Resumo de como definir o tipo de barra:

  • Para definir o barramento como sendo uma Barra PQ, as opções "Barra de referência" e "Tensão controlada" devem estar desmarcadas;
  • Para definir o barramento como sendo uma Barra PV, deve-se marcar somente a opção "Tensão controlada", mantendo a opção "Barra de referência" desmarcada;
  • Para definir o barramento como sendo uma Barra de Referência, deve-se marcar a opção "Barra de referência". Caso a opção "Tensão controlada" esteja desmarcada será admitido um valor de tensão controlada de 1,0 p.u.1{,}0~p.u.
Cuidado!

O sistema deve possuir somente uma barra de referência.

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Ferramentas CAD

Desenho assistido por computador (DAC; em inglês: computer aided design - CAD) é o nome genérico de sistemas computacionais (software) utilizados pela engenharia, geologia, geografia, arquitetura e design para facilitar o projeto e desenho técnicos. No caso do design, 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. Wikipedia

Ferramentas do menu

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: selecionar, mover, girar, arrastar, zoom, encaixar, copiar, colar e excluir.

Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo submenu Ferramentas.

Tais ferramentas permitem a personalização, navegação e auxiliam a criação de redes elétricas de potência, assim como diagramas de controle na plataforma.

Selecionar

A seleção de um único objeto é realizada clicando com o botão esquerdo do mouse sobre o elemento, que será identificado pelo contorno em azul do objeto.

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 retângulo de seleção 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.

Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter seleções anteriores enquanto novos elementos são selecionados.

Para desmarcar todos os objetos basta clicar em uma área sem objetos.

Mover

Um elemento poderá ser movido para qualquer local por meio da ação drag-and-drop (clicando e arrastando) ou pela ferramenta mover.

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.

Girar

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 submenu Ferramentas ou ao acessar o menu de contexto clicando com o botão direito sobre o elemento.

Atenção!

O menu de contexto somente será exibido se o elemento estiver selecionado.

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.

Arrastar

Três ferramentas muito úteis na navegação do circuito, principalmente em grandes redes, são: arrastar, zoom e encaixar.

A ferramenta arrastar possibilita mover todo o circuito preservando as posições relativas entre os elementos. Esta ferramenta pode ser acessada pelo submenu “Ferramentas” ou mantendo pressionada o scroll do mouse, ativando assim o “modo arrastar”. Ao ativá-lo todo o circuito será movido clicando e arrastando na direção desejada.

Para sair do “modo arrastar” basta pressionar a tecla Escape do teclado.

Zoom

O zoom será aplicado ao utilizar o scroll do mouse 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.

Encaixar

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”.

Copiar e Colar

Duas ferramentas importantes durante o processo de criação da rede elétrica de potência no software 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.

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”.

Excluir

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.

Personalização gráfica os elementos

Alguns elementos permitem sua personalização gráfica, como as barras e linhas.

Barra

No caso dos barramentos, pode-se alterar o comprimento da barra clicando e arrastando no pickbox exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.

Linha

As linhas podem ser inseridas com "nós" (pontos de ancoragem), 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.

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.

Assim como nos barramentos, a alteração da posição dos nós é obtida clicando e arrastando o pickbox exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.

Conexão e desconexão de elemetos na barra

Os elementos podem ser desconectados e reconectados às barras após sua inserção somente pela ferramenta drag-and-drop. Para isso, o elemento deve ser selecionado e o seu nó de conexão deve ser arrastado para o local requerido.

Cuidado!

O elemento a ser desconectado/reconectado deve ser previamente selecionado para efetuar a operação. Caso contrário a barra será movida ou nenhuma operação será realizada.

No caso de desconexão, o elemento será automaticamente removido da simulação, sendo indicado pela sua cor (o elemento passa a ter cor cinza).

Atenção!

Ao reconectar o elemento ao circuito, deve-se atentar para estado do seu "disjuntor", indicado por um quadrado próximo ao seu nó de conexão. Um elemento reconectado volta ao circuito com seu disjuntor aberto (vermelho), sendo necessário clicar sobre o mesmo a fim de inserir o elemento no circuito.

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Ferramentas CAD

Desenho assistido por computador (DAC; em inglês: computer aided design - CAD) é o nome genérico de sistemas computacionais (software) utilizados pela engenharia, geologia, geografia, arquitetura e design para facilitar o projeto e desenho técnicos. No caso do design, 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. Wikipedia

Ferramentas do menu

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: selecionar, mover, girar, arrastar, zoom, encaixar, copiar, colar e excluir.

Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo submenu Ferramentas.

Tais ferramentas permitem a personalização, navegação e auxiliam a criação de redes elétricas de potência, assim como diagramas de controle na plataforma.

Selecionar

A seleção de um único objeto é realizada clicando com o botão esquerdo do mouse sobre o elemento, que será identificado pelo contorno em azul do objeto.

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 retângulo de seleção 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.

Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter seleções anteriores enquanto novos elementos são selecionados.

Para desmarcar todos os objetos basta clicar em uma área sem objetos.

Mover

Um elemento poderá ser movido para qualquer local por meio da ação drag-and-drop (clicando e arrastando) ou pela ferramenta mover.

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.

Girar

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 submenu Ferramentas ou ao acessar o menu de contexto clicando com o botão direito sobre o elemento.

Atenção!

O menu de contexto somente será exibido se o elemento estiver selecionado.

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.

Arrastar

Três ferramentas muito úteis na navegação do circuito, principalmente em grandes redes, são: arrastar, zoom e encaixar.

A ferramenta arrastar possibilita mover todo o circuito preservando as posições relativas entre os elementos. Esta ferramenta pode ser acessada pelo submenu “Ferramentas” ou mantendo pressionada o scroll do mouse, ativando assim o “modo arrastar”. Ao ativá-lo todo o circuito será movido clicando e arrastando na direção desejada.

Para sair do “modo arrastar” basta pressionar a tecla Escape do teclado.

Zoom

O zoom será aplicado ao utilizar o scroll do mouse 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.

Encaixar

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”.

Copiar e Colar

Duas ferramentas importantes durante o processo de criação da rede elétrica de potência no software 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.

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”.

Excluir

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.

Personalização gráfica os elementos

Alguns elementos permitem sua personalização gráfica, como as barras e linhas.

Barra

No caso dos barramentos, pode-se alterar o comprimento da barra clicando e arrastando no pickbox exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.

Linha

As linhas podem ser inseridas com "nós" (pontos de ancoragem), 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.

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.

Assim como nos barramentos, a alteração da posição dos nós é obtida clicando e arrastando o pickbox exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.

Conexão e desconexão de elemetos na barra

Os elementos podem ser desconectados e reconectados às barras após sua inserção somente pela ferramenta drag-and-drop. Para isso, o elemento deve ser selecionado e o seu nó de conexão deve ser arrastado para o local requerido.

Cuidado!

O elemento a ser desconectado/reconectado deve ser previamente selecionado para efetuar a operação. Caso contrário a barra será movida ou nenhuma operação será realizada.

No caso de desconexão, o elemento será automaticamente removido da simulação, sendo indicado pela sua cor (o elemento passa a ter cor cinza).

Atenção!

Ao reconectar o elemento ao circuito, deve-se atentar para estado do seu "disjuntor", indicado por um quadrado próximo ao seu nó de conexão. Um elemento reconectado volta ao circuito com seu disjuntor aberto (vermelho), sendo necessário clicar sobre o mesmo a fim de inserir o elemento no circuito.

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Capacitor

Um dispositivo constituído essencialmente por dois eletrodos separados por um dielétrico. tradução livre - IEC 60050.

Capacitor no PSP-UFU

O elemento capacitor representa, geralmente, um banco de capacitores shunt no circuito do PSP-UFU.

Dica

Um arranjo série de uma linha sem as susceptâncias shunt, um barramento e um capacitor pode ser utilizado para fabricar um filtro passivo nos estudos harmônicos. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.

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.

Formulário de edição dos capacitores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos capacitores:

Formulário dos capacitores no PSP-UFU

Além do único contexto geral, pode ser observado o botão "Estabilidade" 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 estabilidade.

Formulário de chaveamento do capacitor

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

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.p.u. (na base de potência do sistema).

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Capacitor

Um dispositivo constituído essencialmente por dois eletrodos separados por um dielétrico. tradução livre - IEC 60050.

Capacitor no PSP-UFU

O elemento capacitor representa, geralmente, um banco de capacitores shunt no circuito do PSP-UFU.

Dica

Um arranjo série de uma linha sem as susceptâncias shunt, um barramento e um capacitor pode ser utilizado para fabricar um filtro passivo nos estudos harmônicos. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.

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.

Formulário de edição dos capacitores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos capacitores:

Formulário dos capacitores no PSP-UFU

Além do único contexto geral, pode ser observado o botão "Estabilidade" 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 estabilidade.

Formulário de chaveamento do capacitor

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

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.p.u. (na base de potência do sistema).

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Constante

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.

Informação

Esse elemento pode, por exemplo, ser utilizado para definir valores alvos ou deslocamentos de sinal.

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Constante

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.

Informação

Esse elemento pode, por exemplo, ser utilizado para definir valores alvos ou deslocamentos de sinal.

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Editor de Controle

Os controles das máquinas síncronas são criados, modificados, importados e exportados em um editor distinto dos elementos de potência, apresentado na figura abaixo.

Editor de elementos de controle do PSP-UFU

O acesso ao editor é realizado por meio de dois botões presentes no formulário de edição dos dados de estabilidade dos geradores síncronos:

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).

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.

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.

As ferramentas de manipulação e navegação, como arrastar, mover e excluir são herdadas do editor de elementos de potência, possuindo comportamento idêntico. A edição dos dados dos componentes inseridos também é realizada com duplo clique sobre o elemento inserido, exibindo um formulário de edição de dados.

Os seguintes blocos de controle estão presentes no PSP-UFU:

Inicialização do sistema de controle

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 funções transferências 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.

info

O processo de inicialização é realizada automaticamente pelo PSP-UFU.

Uma vez que a inicialização é imposta pelas entradas do controle, erros de convergência podem ocorrer devido à má parametrização dos elementos dos sistemas de potência e controle.

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.

O fluxograma abaixo evidencia o processo de inicialização implementado no PSP-UFU:

Estrutura da inicialização do sistema de controle

Teste do diagrama de controle

Na parte inferior esquerda do Editor de Controle está presente o botão "Testar Sistema...". O botão acessa o formulário de teste de controles, como é indicado na figura abaixo:

Formulário de teste de controles

Nesse formulário é possível inserir o comportamento de todas as entradas do diagrama:

  • Tipo de entrada: Define um dos tipos de entradas possíveis no PSP-UFU: "Passo (Step)", Rampa (Ramp) ou Quadrática (Quadratic);
  • Tempo de início (tit_i): 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;
  • Inclinação (α\alpha): Valor relacionado ao tipo de entrada:
    • Para entrada do tipo "Passo" - O valor da inclinação define o valor final do passo:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \end{cases}
    • Para entrada do tipo "Rampa" - define o coeficiente de inclinação da reta:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α×t\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t \end{cases}
    • Para entrada do tipo "Quadrática" - define o coeficiente de crescimento da curva:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α×t2\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t^2 \end{cases}
  • Passo de integração (hh): Passo do método de integração Trapezoidal Implícito;
  • Tempo de simulação (tft_f): Tempo total de simulação.

Após a simulação os resultados são exibidos no visualizador de gráficos.

Atenção!

A mesma parametrização de entrada é aplicada em todos os blocos de entrada do sistema.

Dica

É possível aplicar várias entradas distintas (inclusive com condicionais!) utilizando o bloco de expressão matemática.

Utilizando o bloco de expressão matemática é possível inserir entradas complexas, como por exemplo testar o diagrama de blocos (AVR DC1C + PSS1A - IEEE Std. 421.5-2016) da figura abaixo:

Sistema de controle sob teste
Comparação do sistema de controle sob teste
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Editor de Controle

Os controles das máquinas síncronas são criados, modificados, importados e exportados em um editor distinto dos elementos de potência, apresentado na figura abaixo.

Editor de elementos de controle do PSP-UFU

O acesso ao editor é realizado por meio de dois botões presentes no formulário de edição dos dados de estabilidade dos geradores síncronos:

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).

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.

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.

As ferramentas de manipulação e navegação, como arrastar, mover e excluir são herdadas do editor de elementos de potência, possuindo comportamento idêntico. A edição dos dados dos componentes inseridos também é realizada com duplo clique sobre o elemento inserido, exibindo um formulário de edição de dados.

Os seguintes blocos de controle estão presentes no PSP-UFU:

Inicialização do sistema de controle

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 funções transferências 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.

info

O processo de inicialização é realizada automaticamente pelo PSP-UFU.

Uma vez que a inicialização é imposta pelas entradas do controle, erros de convergência podem ocorrer devido à má parametrização dos elementos dos sistemas de potência e controle.

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.

O fluxograma abaixo evidencia o processo de inicialização implementado no PSP-UFU:

Estrutura da inicialização do sistema de controle

Teste do diagrama de controle

Na parte inferior esquerda do Editor de Controle está presente o botão "Testar Sistema...". O botão acessa o formulário de teste de controles, como é indicado na figura abaixo:

Formulário de teste de controles

Nesse formulário é possível inserir o comportamento de todas as entradas do diagrama:

  • Tipo de entrada: Define um dos tipos de entradas possíveis no PSP-UFU: "Passo (Step)", Rampa (Ramp) ou Quadrática (Quadratic);
  • Tempo de início (tit_i): 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;
  • Inclinação (α\alpha): Valor relacionado ao tipo de entrada:
    • Para entrada do tipo "Passo" - O valor da inclinação define o valor final do passo:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \end{cases}
    • Para entrada do tipo "Rampa" - define o coeficiente de inclinação da reta:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α×t\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t \end{cases}
    • Para entrada do tipo "Quadrática" - define o coeficiente de crescimento da curva:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α×t2\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t^2 \end{cases}
  • Passo de integração (hh): Passo do método de integração Trapezoidal Implícito;
  • Tempo de simulação (tft_f): Tempo total de simulação.

Após a simulação os resultados são exibidos no visualizador de gráficos.

Atenção!

A mesma parametrização de entrada é aplicada em todos os blocos de entrada do sistema.

Dica

É possível aplicar várias entradas distintas (inclusive com condicionais!) utilizando o bloco de expressão matemática.

Utilizando o bloco de expressão matemática é possível inserir entradas complexas, como por exemplo testar o diagrama de blocos (AVR DC1C + PSS1A - IEEE Std. 421.5-2016) da figura abaixo:

Sistema de controle sob teste
Comparação do sistema de controle sob teste
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Divisor

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.

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 101510^{15}.

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Divisor

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.

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 101510^{15}.

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Exponencial

A função exponencial dos elementos de controle realiza essa operação com uma entrada real, obedecendo a expressão:

yn=AeBuny_n = \bold{A} e^{\bold{B} u_n}

Em que:

  • unu_n e yny_n é a entrada e a saída do bloco exponencial, respectivamente;
  • A\bold{A} e B\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.

Formulário de edição de dados do bloco exponencial no PSP-UFU

Esse bloco não linear é definido pelas constantes A e B, inseridas pelo usuário.

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.

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Exponencial

A função exponencial dos elementos de controle realiza essa operação com uma entrada real, obedecendo a expressão:

yn=AeBuny_n = \bold{A} e^{\bold{B} u_n}

Em que:

  • unu_n e yny_n é a entrada e a saída do bloco exponencial, respectivamente;
  • A\bold{A} e B\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.

Formulário de edição de dados do bloco exponencial no PSP-UFU

Esse bloco não linear é definido pelas constantes A e B, inseridas pelo usuário.

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.

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Curto-Circuito

O principal objetivo da análise de curto-circuito é o cálculo das correntes e tensões de falta para especificação de disjuntores, transformadores de corrente e a parametrização de relés de proteção. De 70 a 80% das faltas em linhas de transmissão são entre uma fase e terra, as quais ocorrem devido ao centelhamento de apenas uma fase da linha para a torre e então para a terra.O menor número de faltas, cerca de 5%, envolve todas as três fases, chamadas de faltas trifásicas. Os outros tipos de faltas envolvem duas fases e duas fases e a terra.

Todas essas falhas, exceto a trifásica, são assimétricas e causam desequilíbrio entre as fases.

Cálculo de Curto-Circuito no PSP-UFU

O primeiro estágio do cálculo de curto-circuito é a determinação das tensões pré-falta, das potências de geração e cargas do sistema. Esses dados são obtidos por meio do estudo de fluxo de carga.

Informação

Atualmente, o PSP-UFU fornece resultado para os seguintes tipos de falta:

  • Falta Trifásica (3F-T);
  • Falta Fase-Terra (F-T);
  • Falta Fase-Fase (F-F);
  • Falta Fase-Fase-Terra (F-F-T).

Os modelos dos elementos elétricos que constituem um sistema de potência para o estudo de curto-circuito são semelhantes aos do fluxo de carga, apresentando algumas divergências para as faltas desbalanceadas (F-T, F-F e F-F-T).

As faltas que ocorrem com maior frequência em sistemas de potência são assimétricas. Como qualquer falta assimétrica provoca fluxo de corrente desequilibrada é necessário empregar o método das componentes simétricas. Esse método permite o estudo de sistemas balanceados em conjunto cargas desbalanceadas.

Execução do cálculo de curto-circuito no PSP-UFU

Existem duas formas de se calcular o curto-circuito no PSP-UFU:

  • Falta: Calcula a falta inserida nas barras. Nesse tipo de cálculo é possível calcular faltas shunt nos barramentos balanceadas e desbalanceadas.
  • Nível de curto-circuito: Calcula o nível de curto-circuito (falta trifásica) em todos barramentos do sistema.

Após a construção do diagrama unifilar no editor de potência, a execução do cálculo de curto-circuito é realizada no menu Simulação clicando no botão Falta. Para calcular o nível de curto-circuito (falta trifásica) em todos barramentos do sistema, basta clicar no botão Nível de curto-circuito.

Execução dos cálculos de curto-circuito
Atenção

É possível calcular as faltas sem a execução do fluxo de carga, porém não é recomendável, visto que os valores das correntes de falta são significativamente alteradas.

Outra possibilidade é a execução por meio do cálculo contínuo, também presente no menu Simulação e seu acionamento é realizado co clicar no botão Habilitar solução. Com essa opção, os cálculos estáticos selecionados nas configurações de simulação são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).

Cuidado!

Os cálculos de curtos-circuitos não são habilitados por padrão no cálculo contínuo e devem ser inseridos nas configurações de simulação.

Os resultados do cálculo de curto-circuito são exibidos nos elementos de texto vinculado, ao posicionar o mouse sobre os barramentos e em relatórios tabulares.

Erros comuns na execução do cálculo de curto-circuito

A seguir são apresentados os erros mais comuns relacionados ao calculo de curto-circuito.

A seguinte mensagem de erro é exibida: "Falha ao inverter a matriz admitância de sequência zero"

  • Impossibilidade de circulação da corrente de sequência zero. 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 matriz admitância de sequência zero é singular. Para contornar esse problema escolha uma das duas soluções abaixo:
    • Marque a opção "Neutro aterrado" e insira um alto valor de reatância de aterramento (j9999 p.u.j9999~p.u., por exemplo);
    • Ou, na barra do gerador, insira um reator de baixo valor de potência reativa (1,0 var1{,}0~var, por exemplo).

O cálculo de curto-circuito

Como já foi apresentado anteriormente, as faltas que ocorrem com maior frequência em sistemas de potência são assimétricas. Como qualquer falta assimétrica provoca fluxo de corrente desequilibrada é necessário empregar o método das componentes simétricas. Esse método permite o estudo de sistemas balanceados com cargas desbalanceadas.

Método das componentes simétricas

Esse método proposto por C. L. Fortescue, permite definir um sistema de n fasores desbalanceados em n – 1 sistemas de n fases balanceados e um sistema de fase zero. O sistema de fase zero é definido por todas as fases de mesmo módulo e ângulo. +

+

Curto-Circuito

O principal objetivo da análise de curto-circuito é o cálculo das correntes e tensões de falta para especificação de disjuntores, transformadores de corrente e a parametrização de relés de proteção. De 70 a 80% das faltas em linhas de transmissão são entre uma fase e terra, as quais ocorrem devido ao centelhamento de apenas uma fase da linha para a torre e então para a terra.O menor número de faltas, cerca de 5%, envolve todas as três fases, chamadas de faltas trifásicas. Os outros tipos de faltas envolvem duas fases e duas fases e a terra.

Todas essas falhas, exceto a trifásica, são assimétricas e causam desequilíbrio entre as fases.

Cálculo de Curto-Circuito no PSP-UFU

O primeiro estágio do cálculo de curto-circuito é a determinação das tensões pré-falta, das potências de geração e cargas do sistema. Esses dados são obtidos por meio do estudo de fluxo de carga.

Informação

Atualmente, o PSP-UFU fornece resultado para os seguintes tipos de falta:

  • Falta Trifásica (3F-T);
  • Falta Fase-Terra (F-T);
  • Falta Fase-Fase (F-F);
  • Falta Fase-Fase-Terra (F-F-T).

Os modelos dos elementos elétricos que constituem um sistema de potência para o estudo de curto-circuito são semelhantes aos do fluxo de carga, apresentando algumas divergências para as faltas desbalanceadas (F-T, F-F e F-F-T).

As faltas que ocorrem com maior frequência em sistemas de potência são assimétricas. Como qualquer falta assimétrica provoca fluxo de corrente desequilibrada é necessário empregar o método das componentes simétricas. Esse método permite o estudo de sistemas balanceados em conjunto cargas desbalanceadas.

Execução do cálculo de curto-circuito no PSP-UFU

Existem duas formas de se calcular o curto-circuito no PSP-UFU:

  • Falta: Calcula a falta inserida nas barras. Nesse tipo de cálculo é possível calcular faltas shunt nos barramentos balanceadas e desbalanceadas.
  • Nível de curto-circuito: Calcula o nível de curto-circuito (falta trifásica) em todos barramentos do sistema.

Após a construção do diagrama unifilar no editor de potência, a execução do cálculo de curto-circuito é realizada no menu Simulação clicando no botão Falta. Para calcular o nível de curto-circuito (falta trifásica) em todos barramentos do sistema, basta clicar no botão Nível de curto-circuito.

Execução dos cálculos de curto-circuito
Atenção

É possível calcular as faltas sem a execução do fluxo de carga, porém não é recomendável, visto que os valores das correntes de falta são significativamente alteradas.

Outra possibilidade é a execução por meio do cálculo contínuo, também presente no menu Simulação e seu acionamento é realizado co clicar no botão Habilitar solução. Com essa opção, os cálculos estáticos selecionados nas configurações de simulação são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).

Cuidado!

Os cálculos de curtos-circuitos não são habilitados por padrão no cálculo contínuo e devem ser inseridos nas configurações de simulação.

Os resultados do cálculo de curto-circuito são exibidos nos elementos de texto vinculado, ao posicionar o mouse sobre os barramentos e em relatórios tabulares.

Erros comuns na execução do cálculo de curto-circuito

A seguir são apresentados os erros mais comuns relacionados ao calculo de curto-circuito.

A seguinte mensagem de erro é exibida: "Falha ao inverter a matriz admitância de sequência zero"

  • Impossibilidade de circulação da corrente de sequência zero. 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 matriz admitância de sequência zero é singular. Para contornar esse problema escolha uma das duas soluções abaixo:
    • Marque a opção "Neutro aterrado" e insira um alto valor de reatância de aterramento (j9999 p.u.j9999~p.u., por exemplo);
    • Ou, na barra do gerador, insira um reator de baixo valor de potência reativa (1,0 var1{,}0~var, por exemplo).

O cálculo de curto-circuito

Como já foi apresentado anteriormente, as faltas que ocorrem com maior frequência em sistemas de potência são assimétricas. Como qualquer falta assimétrica provoca fluxo de corrente desequilibrada é necessário empregar o método das componentes simétricas. Esse método permite o estudo de sistemas balanceados com cargas desbalanceadas.

Método das componentes simétricas

Esse método proposto por C. L. Fortescue, permite definir um sistema de n fasores desbalanceados em n – 1 sistemas de n fases balanceados e um sistema de fase zero. O sistema de fase zero é definido por todas as fases de mesmo módulo e ângulo. Para um sistema trifásico pode-se definir três componentes de sequência:

  1. Componentes de sequência positiva, constituindo em três fasores iguais em módulo, 120º defasados entre si, e tendo a mesma sequência de fase que os fasores originais;
  2. Componentes de sequência negativa, constituindo em três fasores iguais em módulo, 120º defasados entre si, e tendo a sequência de fase oposta à dos fasores originais.
  3. Componentes de sequência zero, constituindo em três fasores iguais em módulo e com defasagem nula entre si.

Com isso pode-se decompor as tensões de fase em componentes simétricas pelas seguintes equações:

{V˙a=V˙a1+V˙a2+V˙a0V˙b=V˙b1+V˙b2+V˙b0V˙c=V˙c1+V˙c2+V˙c0\begin{cases} \dot{V}_a = \dot{V}_{a1} + \dot{V}_{a2} + \dot{V}_{a0}\\ \dot{V}_b = \dot{V}_{b1} + \dot{V}_{b2} + \dot{V}_{b0}\\ \dot{V}_c = \dot{V}_{c1} + \dot{V}_{c2} + \dot{V}_{c0} \end{cases}

A figura abaixo apresenta um exemplo de componentes simétricas e sua soma para obter os fasores desequilibrados.

Exemplo de componentes simétricas e sua soma para obter os fasores desequilibrados

Para simplificar os cálculos adota-se um operador “a‾\overline{a}”, com o intuito de indicar a rotação de um fasor. Tal operador é um número complexo de módulo unitário e ângulo de 120º:

a‾=1∠120∘=1ej2π/3=−0,5+j0,866\overline{a} = 1 \angle 120^{\circ} = 1 e^{j2\pi/3} = -0{,}5 + j0{,}866

Com isso pode-se utilizar as equações (de tensão apresentadas em conjunto com o operador “a‾\overline{a}” para construir a seguinte equação matricial:

[V˙aV˙bV˙c]=[1111a‾2a‾1a‾a‾2]⏞[A][V˙a0V˙a1V˙a2]\begin{bmatrix} \dot{V}_a\\ \dot{V}_b\\ \dot{V}_c \end{bmatrix} = \overbrace{ \begin{bmatrix} 1 & 1 & 1\\ 1 & \overline{a}^2 & \overline{a}\\ 1 & \overline{a} & \overline{a}^2 \end{bmatrix} }^{\left[ \bold{A} \right]} \begin{bmatrix} \dot{V}_{a0}\\ \dot{V}_{a1}\\ \dot{V}_{a2} \end{bmatrix}

Considerando a matriz quadrada da equação anterior sendo [A]\left[ \bold{A} \right], pode-se encontrar as componentes simétricas pré-multiplicando ambos os lados dessa mesma equação por [A]−1\left[ \bold{A} \right]^{-1}.

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 faltas assimétricas (F-T, F-F e F-F-T) é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.

Nota

As informações a respeito das particularidades dos modelos para o estudo de curto-circuito são apresentados individualmente nos elementos de potência.

Equações do curto-circuito

Primeiramente será tratado o equacionamento para faltas balanceadas e então os estudos serão estendidos para as faltas desbalanceadas por meio da utilização do método das componentes simétricas.

Faltas balanceadas

Utiliza-se da matriz impedância de barras para o cálculo de curto-circuito, definida pela seguinte equação matricial:

[V˙]=[Zbus][I˙][\dot{V}] = [Z_{bus}][\dot{I}]

Em que:

  • [Zbus][Z_{bus}] é a inversa da matriz admitância de barras, chamada de matriz impedância de barras.

Por meio da expansão da equação anterior é possível calcular a corrente de falta trifásica na barra genérica ii:

I˙f=E˙iz‾ii+z‾f\dot{I}_f = \frac{\dot{E}_i}{\overline{z}_{ii}+\overline{z}_{f}}

Em que:

  • I˙f\dot{I}_f é a corrente de falta trifásica na barra ii
  • E˙i\dot{E}_i é a tensão pré-falta na barra ii
  • z‾ii\overline{z}_{ii} é a impedância equivalente de Thevenin vista pela barra ii, retirada da matriz impedância
  • z‾f\overline{z}_{f} é a impedância de falta

Faltas desbalanceadas

O desenvolvimento das equações do cálculo de curto-circuito para faltas desbalanceadas é realizado seguindo o seguinte procedimento:

  1. Definir os diagramas no ponto da falta, mostrando as conexões de todas fases para a falta. Assume-se que apenas impedâncias balanceadas estão presentes em ambos os lados do ponto da falta e o equivalente Thevenin até esse ponto é conhecido;
  2. Escrever as condições de contorno relacionando as tensões e corrente conhecidas para o tipo de falta estudada;
  3. Transformar as correntes e tensões do item 2 de a-b-c para o sistema de coordenadas 0-1-2;
  4. Encontrar a corrente do curto-circuito em estudo baseado no seguinte sistema de equações (para a fase A):
    {V˙a1=E˙a−I˙a1z‾1V˙a2=−I˙a2z‾2V˙a0=−I˙a0z‾0\begin{cases} \dot{V}_{a1} = \dot{E}_a - \dot{I}_{a1} \overline{z}_1\\ \dot{V}_{a2} = - \dot{I}_{a2} \overline{z}_2\\ \dot{V}_{a0} = - \dot{I}_{a0} \overline{z}_0 \end{cases}

A tabela abaixo apresenta as equações para as faltas desbalanceadas após a execução do procedimento apresenteado:

FaltaSeq. Positiva (I˙f1\dot{I}_{f}^{1})Seq. Negativa (I˙f2\dot{I}_{f}^{2})Seq. Zero (I˙f0\dot{I}_{f}^{0})
F-TE˙iz‾ii1+z‾ii2+z‾ii0+3z‾f\dfrac{\dot{E}_i}{\overline{z}_{ii}^{1} + \overline{z}_{ii}^{2} + \overline{z}_{ii}^{0} + 3 \overline{z}_{f}}I˙f1\dot{I}_{f}^{1}I˙f1\dot{I}_{f}^{1}
F-FE˙iz‾ii1+z‾ii2+z‾f\dfrac{\dot{E}_i}{\overline{z}_{ii}^{1} + \overline{z}_{ii}^{2} + \overline{z}_{f}}−I˙f1- \dot{I}_{f}^{1}0,00{,}0
F-F-TE˙i(z‾ii2+z‾ii0+3z‾f)z‾ii1z‾ii2+3z‾ii2z‾f+z‾ii2z‾ii0+3z‾ii1z‾f+z‾ii1z‾ii0\dfrac{\dot{E}_i \left( \overline{z}_{ii}^{2} + \overline{z}_{ii}^{0} + 3 \overline{z}_{f} \right)}{\overline{z}_{ii}^{1} \overline{z}_{ii}^{2} + 3 \overline{z}_{ii}^{2} \overline{z}_{f} + \overline{z}_{ii}^{2} \overline{z}_{ii}^{0} + 3 \overline{z}_{ii}^{1} \overline{z}_{f} + \overline{z}_{ii}^{1} \overline{z}_{ii}^{0} }−E˙i−z‾ii1I˙f1z‾ii2- \dfrac{\dot{E}_i - \overline{z}_{ii}^{1} \dot{I}_{f}^{1}}{\overline{z}_{ii}^{2}}−E˙i−z‾ii1I˙f1z‾ii0+3z‾f- \dfrac{\dot{E}_i - \overline{z}_{ii}^{1} \dot{I}_{f}^{1}}{\overline{z}_{ii}^{0} + 3 \overline{z}_{f}}

Para obter os valores em a-b-c é usada a equação matricial apresentada anteriormente, encerrando o cálculo de curto-circuito.

Referências

  1. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
  2. STEVENSON JR.; WILLIAN, D. Elementos de Análise de Sistemas de Potência. 2ª ed. São Paulo: McGraw-Hill, 1986.
  3. ANDERSON, P. M.; FOUAD, A. A. Power System Control and Stability. Wiley-IEEE Press, New York, 2002. doi: https://doi.org/10.1109/9780470545577
  4. FORTESCUE, C. L. Method of Symmetrical Coordinates Applied to the Solution of Polyphase Networks. Trans. AIEE, v. 37, p.1027-1140, 1918. doi: https://doi.org/10.1109/T-AIEE.1918.4765570
  5. ANDERSON, P. M. Analysis of faulted power systems. New York: IEEE Press, 1995.
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- - - - - - - - - - +c124.7 8 235 61.7 331 161 31.3 33.3 59.7 72.7 85 118l7 13v35z">​[A]​⎣⎢⎡​V˙a0​V˙a1​V˙a2​​⎦⎥⎤​

Considerando a matriz quadrada da equação anterior sendo [A]\left[ \bold{A} \right], pode-se encontrar as componentes simétricas pré-multiplicando ambos os lados dessa mesma equação por [A]−1\left[ \bold{A} \right]^{-1}.

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 faltas assimétricas (F-T, F-F e F-F-T) é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.

Informação

As informações a respeito das particularidades dos modelos para o estudo de curto-circuito são apresentados individualmente nos elementos de potência.

Equações do curto-circuito

Primeiramente será tratado o equacionamento para faltas balanceadas e então os estudos serão estendidos para as faltas desbalanceadas por meio da utilização do método das componentes simétricas.

Faltas balanceadas

Utiliza-se da matriz impedância de barras para o cálculo de curto-circuito, definida pela seguinte equação matricial:

[V˙]=[Zbus][I˙][\dot{V}] = [Z_{bus}][\dot{I}]

Em que:

  • [Zbus][Z_{bus}] é a inversa da matriz admitância de barras, chamada de matriz impedância de barras.

Por meio da expansão da equação anterior é possível calcular a corrente de falta trifásica na barra genérica ii:

I˙f=E˙iz‾ii+z‾f\dot{I}_f = \frac{\dot{E}_i}{\overline{z}_{ii}+\overline{z}_{f}}

Em que:

  • I˙f\dot{I}_f é a corrente de falta trifásica na barra ii
  • E˙i\dot{E}_i é a tensão pré-falta na barra ii
  • z‾ii\overline{z}_{ii} é a impedância equivalente de Thevenin vista pela barra ii, retirada da matriz impedância
  • z‾f\overline{z}_{f} é a impedância de falta

Faltas desbalanceadas

O desenvolvimento das equações do cálculo de curto-circuito para faltas desbalanceadas é realizado seguindo o seguinte procedimento:

  1. Definir os diagramas no ponto da falta, mostrando as conexões de todas fases para a falta. Assume-se que apenas impedâncias balanceadas estão presentes em ambos os lados do ponto da falta e o equivalente Thevenin até esse ponto é conhecido;
  2. Escrever as condições de contorno relacionando as tensões e corrente conhecidas para o tipo de falta estudada;
  3. Transformar as correntes e tensões do item 2 de a-b-c para o sistema de coordenadas 0-1-2;
  4. Encontrar a corrente do curto-circuito em estudo baseado no seguinte sistema de equações (para a fase A):
    {V˙a1=E˙a−I˙a1z‾1V˙a2=−I˙a2z‾2V˙a0=−I˙a0z‾0\begin{cases} \dot{V}_{a1} = \dot{E}_a - \dot{I}_{a1} \overline{z}_1\\ \dot{V}_{a2} = - \dot{I}_{a2} \overline{z}_2\\ \dot{V}_{a0} = - \dot{I}_{a0} \overline{z}_0 \end{cases}

A tabela abaixo apresenta as equações para as faltas desbalanceadas após a execução do procedimento apresenteado:

FaltaSeq. Positiva (I˙f1\dot{I}_{f}^{1})Seq. Negativa (I˙f2\dot{I}_{f}^{2})Seq. Zero (I˙f0\dot{I}_{f}^{0})
F-TE˙iz‾ii1+z‾ii2+z‾ii0+3z‾f\dfrac{\dot{E}_i}{\overline{z}_{ii}^{1} + \overline{z}_{ii}^{2} + \overline{z}_{ii}^{0} + 3 \overline{z}_{f}}I˙f1\dot{I}_{f}^{1}I˙f1\dot{I}_{f}^{1}
F-FE˙iz‾ii1+z‾ii2+z‾f\dfrac{\dot{E}_i}{\overline{z}_{ii}^{1} + \overline{z}_{ii}^{2} + \overline{z}_{f}}−I˙f1- \dot{I}_{f}^{1}0,00{,}0
F-F-TE˙i(z‾ii2+z‾ii0+3z‾f)z‾ii1z‾ii2+3z‾ii2z‾f+z‾ii2z‾ii0+3z‾ii1z‾f+z‾ii1z‾ii0\dfrac{\dot{E}_i \left( \overline{z}_{ii}^{2} + \overline{z}_{ii}^{0} + 3 \overline{z}_{f} \right)}{\overline{z}_{ii}^{1} \overline{z}_{ii}^{2} + 3 \overline{z}_{ii}^{2} \overline{z}_{f} + \overline{z}_{ii}^{2} \overline{z}_{ii}^{0} + 3 \overline{z}_{ii}^{1} \overline{z}_{f} + \overline{z}_{ii}^{1} \overline{z}_{ii}^{0} }−E˙i−z‾ii1I˙f1z‾ii2- \dfrac{\dot{E}_i - \overline{z}_{ii}^{1} \dot{I}_{f}^{1}}{\overline{z}_{ii}^{2}}−E˙i−z‾ii1I˙f1z‾ii0+3z‾f- \dfrac{\dot{E}_i - \overline{z}_{ii}^{1} \dot{I}_{f}^{1}}{\overline{z}_{ii}^{0} + 3 \overline{z}_{f}}

Para obter os valores em a-b-c é usada a equação matricial apresentada anteriormente, encerrando o cálculo de curto-circuito.

Referências

  1. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
  2. STEVENSON JR.; WILLIAN, D. Elementos de Análise de Sistemas de Potência. 2ª ed. São Paulo: McGraw-Hill, 1986.
  3. ANDERSON, P. M.; FOUAD, A. A. Power System Control and Stability. Wiley-IEEE Press, New York, 2002. doi: https://doi.org/10.1109/9780470545577
  4. FORTESCUE, C. L. Method of Symmetrical Coordinates Applied to the Solution of Polyphase Networks. Trans. AIEE, v. 37, p.1027-1140, 1918. doi: https://doi.org/10.1109/T-AIEE.1918.4765570
  5. ANDERSON, P. M. Analysis of faulted power systems. New York: IEEE Press, 1995.
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Ganho

O bloco de ganho multiplica o valor de entrada por uma constante definida pelo usuário, possuindo comportamento idêntico à combinação de uma constante e um bloco multiplicador.

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.

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Ganho

O bloco de ganho multiplica o valor de entrada por uma constante definida pelo usuário, possuindo comportamento idêntico à combinação de uma constante e um bloco multiplicador.

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.

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Visualizador de Gráficos

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Visualizador de Gráficos

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Fonte de Corrente Harmônica

(Fonte de perturbação harmônica) 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. tradução livre - IEC 60050.

Fonte de corrente harmônica no PSP-UFU

As fontes de corrente harmônica são responsáveis pela injeção de correntes harmônicas e são utilizadas pela ferramenta de cálculo de distorções harmônicas. Uma lista de correntes harmônicas pode ser inserida em um mesmo elemento, conforme é exibido na o formulário de edição de dados.

Atenção!

A presença da fonte de corrente harmônica não é considerada nos estudos de fluxo de carga, curto-circuito e estabilidade.

Formulário de edição das fontes de corrente harmônica

A imagem abaixo apresenta o formulário de inserção/alteração de dados da fonte de corrente harmônica:

Formulário dos indutores no PSP-UFU

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Ordem

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.

Corrente

Módulo da corrente harmônica.

Unidade

Unidade do módulo de corrente harmônica, em A ou p.u.p.u.

Ângulo

Ângulo da corrente harmônica, em graus.

Adicionar / Remover

Insere ou modifica a nova ordem harmônica ao clicar em “Adicionar”. Retira a ordem harmônica selecionada da lista ao clicar em “Remover”.

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Fonte de Corrente Harmônica

(Fonte de perturbação harmônica) 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. tradução livre - IEC 60050.

Fonte de corrente harmônica no PSP-UFU

As fontes de corrente harmônica são responsáveis pela injeção de correntes harmônicas e são utilizadas pela ferramenta de cálculo de distorções harmônicas. Uma lista de correntes harmônicas pode ser inserida em um mesmo elemento, conforme é exibido na o formulário de edição de dados.

Atenção!

A presença da fonte de corrente harmônica não é considerada nos estudos de fluxo de carga, curto-circuito e estabilidade.

Formulário de edição das fontes de corrente harmônica

A imagem abaixo apresenta o formulário de inserção/alteração de dados da fonte de corrente harmônica:

Formulário dos indutores no PSP-UFU

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Ordem

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.

Corrente

Módulo da corrente harmônica.

Unidade

Unidade do módulo de corrente harmônica, em A ou p.u.p.u.

Ângulo

Ângulo da corrente harmônica, em graus.

Adicionar / Remover

Insere ou modifica a nova ordem harmônica ao clicar em “Adicionar”. Retira a ordem harmônica selecionada da lista ao clicar em “Remover”.

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Harmônicos

Duas ferramentas relacionadas a harmônicos foram desenvolvidas no PSP-UFU:

  • Distorção Harmônica Total de Tensão (THD, do inglês Total Harmonic Distortion);
  • Resposta na Frequência.

A ferramenta de Distorção Harmônica Total calcula as tensões harmônicas causadas por fontes de corrente harmônicas, assim como o THD de todos os barramentos do sistema.

A ferramenta de Resposta na Frequência (ou análise de varredura de frequência) envolve a variação da impedância da rede em um espectro de frequências observado a partir de um certo barramento.

Informação

A análise de varredura de frequência é amplamente usada no projeto de filtros harmônicos.

Dica

Um arranjo série de uma linha sem as susceptâncias shunt, um barramento e um capacitor pode ser utilizado para fabricar um filtro passivo nos estudos harmônicos. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.

Atenção!

Na versão atual do programa não são consideradas as alterações das resistências do sistema causado pelo efeito pelicular. Versões futuras irão contemplar tal característica.

Execução do cálculo de harmônicos no PSP-UFU

Após a construção do diagrama unifilar no editor de potência, a execução do cálculo das distorções harmônicas é realizada no menu Simulação clicando no botão Distorções Harmônicas. Para acessar a ferramenta de de varredura de frequência, basta clicar no botão Resposta na Frequência.

Acesso às ferramentas de estudo harmônico

Distorções Harmônicas

Ao clicar sobre o botão "Distorções Harmônicas" as distorções causadas pelas fontes de corrente harmônica são calculadas em todos os barramentos do sistema.

Atenção!

Caso não forem inseridas fontes de corrente harmônica no sistema de potência, a distorção de tensão de todas as barras será 0,0 %0{,}0~\%.

Outra possibilidade é a execução por meio do cálculo contínuo, também presente no menu Simulação e seu acionamento é realizado co clicar no botão Habilitar solução. Com essa opção, os cálculos estáticos selecionados nas configurações de simulação são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).

Cuidado!

Os cálculos dos níveis de THD não são habilitados por padrão no cálculo contínuo e devem ser inseridos nas configurações de simulação.

Os resultados das distorções harmônicas são exibidos nos elementos de texto vinculados e ao posicionar o mouse sobre um barramento.

Resposta na Frequência

Ao clicar sobre o botão "Resposta na Frequência" será exibido um formulário para inserção dos parâmetros da ferramenta:

Acesso à ferramentas resposta na frequência

Frequência inicial

Define a frequência inicial da varredura.

Frequência final

Define a frequência final da varredura.

Passo de frequência

Define o passo de incremento da frequência. Passos menores irão gerar gráficos mais precisos, porém podem aumentar muito o tempo de execução.

Corrente injetada

Define o barramento o qual será injetada a corrente harmônica para análise.

Dica

Esse campo pode ser entendido como: "A resposta das impedâncias harmônicas vistas pelos barramentos do sistema caso tenha uma fonte de corrente harmônica na barra selecionada".

Botão Executar

Ao clicar no botão executar a varredura será executada e os resultados exibidos no vizualizador de gráficos, como mostra a imagem abaixo.

Exemplo de resposta na frequência
Cuidado!

Para visualizar a varredura da impedância harmônica de um barramento, essa opção deve ser habilitada em seu formulário de edição de dados.

Cálculos das ferramentas harmônicas

Ambos cálculos são realizados a partir da seguinte equação matricial:

[I˙]h=[Ybus]h[V˙]h[\dot{I}]^h= [Y_{bus}]^h [\dot{V}]^h

Em que:

  • [I˙]h[\dot{I}]^h Vetor das correntes harmônicas injetadas nas barras
  • [Ybus]h[Y_{bus}]^h Matriz admitância harmônica de barras
  • [V˙]h[\dot{V}]^h Vetor das tensões harmônicas nas barras
  • hh Ordem harmônica

O vetor das correntes harmônicas injetadas é definido no programa utilizando um elemento de potência, chamado “fonte de corrente harmônica”, em que o usuário pode criar uma lista de correntes injetadas (em A e/ou p.u.p.u.) em um barramento.

O programa define automaticamente as ordens harmônicas na simulação analisando todas as listas de fontes de corrente harmônicas previamente aos cálculos. Com isso são calculadas as admitâncias harmônicas necessárias de cada elemento pela multiplicação das reatâncias indutivas (xl1x_{l}^1) e susceptâncias capacitivas (bc1b_{c}^1) fundamentais de cada elemento pelas ordens harmônicas:

xlh=h×xl1bch=h×bc1x_{l}^h=h×x_l^1\\ b_{c}^h=h×b_c^1

Uma vez calculadas as admitâncias harmônicas, são utilizados os mesmos modelos e algoritmos convencionais para construção da YbushY_{bus}^h.

A equação matricial é resolvida usando o método de eliminação gaussiana para evitar a inversão de cada matriz de admitância harmônica. Este procedimento torna o cálculo das tensões harmônicas computacionalmente eficiente.

Uma vez calculadas as tensões harmônicas, a THD em uma barra genérica ii pode ser definida por:

THDi=∑h=2nVihVi1\text{THD}_i=\dfrac{\sum_{h=2}^{n} V_{i}^h}{V_i^1}

Na ferramenta de Resposta na Frequência uma corrente senoidal é injetada na barra em uma faixa de frequências e o conjunto de equações matriciais é usado para calcular a resposta da tensão. Este cálculo é repetido em etapas discretas cobrindo o espectro de frequência especificado.

O programa usa a matriz admitância de sequência positiva e uma corrente injetada de 1,0p.u.1{,}0 p.u. também de sequência positiva na equação matricial para calcular diretamente as impedâncias em p.u.

Referências

  1. ARRILLAGA, J.; WATSON, N. R. Power System Harmonics. John Wiley & Sons; Chichester, 2003. doi: https://doi.org/10.1002/0470871229
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Harmônicos

Duas ferramentas relacionadas a harmônicos foram desenvolvidas no PSP-UFU:

  • Distorção Harmônica Total de Tensão (THD, do inglês Total Harmonic Distortion);
  • Resposta na Frequência.

A ferramenta de Distorção Harmônica Total calcula as tensões harmônicas causadas por fontes de corrente harmônicas, assim como o THD de todos os barramentos do sistema.

A ferramenta de Resposta na Frequência (ou análise de varredura de frequência) envolve a variação da impedância da rede em um espectro de frequências observado a partir de um certo barramento.

Informação

A análise de varredura de frequência é amplamente usada no projeto de filtros harmônicos.

Dica

Um arranjo série de uma linha sem as susceptâncias shunt, um barramento e um capacitor pode ser utilizado para fabricar um filtro passivo nos estudos harmônicos. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.

Atenção!

Na versão atual do programa não são consideradas as alterações das resistências do sistema causado pelo efeito pelicular. Versões futuras irão contemplar tal característica.

Execução do cálculo de harmônicos no PSP-UFU

Após a construção do diagrama unifilar no editor de potência, a execução do cálculo das distorções harmônicas é realizada no menu Simulação clicando no botão Distorções Harmônicas. Para acessar a ferramenta de de varredura de frequência, basta clicar no botão Resposta na Frequência.

Acesso às ferramentas de estudo harmônico

Distorções Harmônicas

Ao clicar sobre o botão "Distorções Harmônicas" as distorções causadas pelas fontes de corrente harmônica são calculadas em todos os barramentos do sistema.

Atenção!

Caso não forem inseridas fontes de corrente harmônica no sistema de potência, a distorção de tensão de todas as barras será 0,0 %0{,}0~\%.

Outra possibilidade é a execução por meio do cálculo contínuo, também presente no menu Simulação e seu acionamento é realizado co clicar no botão Habilitar solução. Com essa opção, os cálculos estáticos selecionados nas configurações de simulação são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).

Cuidado!

Os cálculos dos níveis de THD não são habilitados por padrão no cálculo contínuo e devem ser inseridos nas configurações de simulação.

Os resultados das distorções harmônicas são exibidos nos elementos de texto vinculados e ao posicionar o mouse sobre um barramento.

Resposta na Frequência

Ao clicar sobre o botão "Resposta na Frequência" será exibido um formulário para inserção dos parâmetros da ferramenta:

Acesso à ferramentas resposta na frequência

Frequência inicial

Define a frequência inicial da varredura.

Frequência final

Define a frequência final da varredura.

Passo de frequência

Define o passo de incremento da frequência. Passos menores irão gerar gráficos mais precisos, porém podem aumentar muito o tempo de execução.

Corrente injetada

Define o barramento o qual será injetada a corrente harmônica para análise.

Dica

Esse campo pode ser entendido como: "A resposta das impedâncias harmônicas vistas pelos barramentos do sistema caso tenha uma fonte de corrente harmônica na barra selecionada".

Botão Executar

Ao clicar no botão executar a varredura será executada e os resultados exibidos no vizualizador de gráficos, como mostra a imagem abaixo.

Exemplo de resposta na frequência
Cuidado!

Para visualizar a varredura da impedância harmônica de um barramento, essa opção deve ser habilitada em seu formulário de edição de dados.

Cálculos das ferramentas harmônicas

Ambos cálculos são realizados a partir da seguinte equação matricial:

[I˙]h=[Ybus]h[V˙]h[\dot{I}]^h= [Y_{bus}]^h [\dot{V}]^h

Em que:

  • [I˙]h[\dot{I}]^h Vetor das correntes harmônicas injetadas nas barras
  • [Ybus]h[Y_{bus}]^h Matriz admitância harmônica de barras
  • [V˙]h[\dot{V}]^h Vetor das tensões harmônicas nas barras
  • hh Ordem harmônica

O vetor das correntes harmônicas injetadas é definido no programa utilizando um elemento de potência, chamado “fonte de corrente harmônica”, em que o usuário pode criar uma lista de correntes injetadas (em A e/ou p.u.p.u.) em um barramento.

O programa define automaticamente as ordens harmônicas na simulação analisando todas as listas de fontes de corrente harmônicas previamente aos cálculos. Com isso são calculadas as admitâncias harmônicas necessárias de cada elemento pela multiplicação das reatâncias indutivas (xl1x_{l}^1) e susceptâncias capacitivas (bc1b_{c}^1) fundamentais de cada elemento pelas ordens harmônicas:

xlh=h×xl1bch=h×bc1x_{l}^h=h×x_l^1\\ b_{c}^h=h×b_c^1

Uma vez calculadas as admitâncias harmônicas, são utilizados os mesmos modelos e algoritmos convencionais para construção da YbushY_{bus}^h.

A equação matricial é resolvida usando o método de eliminação gaussiana para evitar a inversão de cada matriz de admitância harmônica. Este procedimento torna o cálculo das tensões harmônicas computacionalmente eficiente.

Uma vez calculadas as tensões harmônicas, a THD em uma barra genérica ii pode ser definida por:

THDi=∑h=2nVihVi1\text{THD}_i=\dfrac{\sum_{h=2}^{n} V_{i}^h}{V_i^1}

Na ferramenta de Resposta na Frequência uma corrente senoidal é injetada na barra em uma faixa de frequências e o conjunto de equações matriciais é usado para calcular a resposta da tensão. Este cálculo é repetido em etapas discretas cobrindo o espectro de frequência especificado.

O programa usa a matriz admitância de sequência positiva e uma corrente injetada de 1,0p.u.1{,}0 p.u. também de sequência positiva na equação matricial para calcular diretamente as impedâncias em p.u.

Referências

  1. ARRILLAGA, J.; WATSON, N. R. Power System Harmonics. John Wiley & Sons; Chichester, 2003. doi: https://doi.org/10.1002/0470871229
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Mapa de Tensão

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Mapa de Tensão

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Motor de Indução

Uma máquina assíncrona da qual apenas um enrolamento é energizado. tradução livre - IEC 60050.

Motor de indução trifásico no PSP-UFU

No PSP-UFU, os motores de indução são contemplados nos estudos de fluxo de carga e no estudo de estabilidade.

Informação

Os dados de estabilidade da máquina de indução são utilizados em conjunto com o fluxo de carga, calculando de forma correta a potência reativa das máquinas e consequentemente a tensão no barramento conectado.

Cuidado!

Ao marcar a opção "Calcular a potência reativa no fluxo de carga", devem ser inseridos os dados corretos na aba "Estabilidade", caso contrário, será atribuída uma potência reativa incorreta no motor.

Motor de indução trifásico no cálculo do fluxo de carga

A figura abaixo apresenta o modelo do motor de indução trifásico (MIT) de gaiola simples.

Circuito equivalente do motor de indução

As potências ativa e reativa podem ser calculadas em relação às variáveis e parâmetros do motor em p.u.p.u. como:

P=V2{(r2s)[(r2s)r1−x1K1−x2xm]+K1[(r2s)(xm+x1)+r1K1]}[(r2s)r1−x1K1−x2xm]2+[(r2s)(xm+x1)+r1K1]2Q=−V2{K1[(r2s)r1−x1K1−x2xm]−(r2s)[(r2s)(xm+x1)+r1K1]}[(r2s)r1−x1K1−x2xm]2+[(r2s)(xm+x1)+r1K1]2 K1=x2+xmP = \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

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 fluxo de potência. 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.

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:

(r2s)2A+(r2s)B+C=0\left(\frac{r_2}{s} \right)^2 A + \left(\frac{r_2}{s} \right) B + C = 0

Em que:

A=P(r12+K32)−V2r1B=2P(r1K2+K3K4)−V2(K2+K1K3)C=P(K22+K42)−V2K1K4K2=−x1K1−x2xmK3=xm+x1K4=r1K1A = 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

Esse modelo pode ser inserido na solução do fluxo de carga seguindo os seguintes passos:

  1. As constantes K1K_1 a K4K_4 são inicialmente calculadas . Esses valores são mantidos constantes durante toda a solução;
  2. Em cada iteração são calculados os coeficientes AA, BB e CC utilizando o valor atualizado de VV;
  3. A equação quadrática é resolvida e dois valores de (r2s)\left(\frac{r_2}{s} \right) são obtidos, em que o maior deles é escolhido por estar na região estável da característica toque-escorregamento do motor;
  4. Utilizando o novo valor de (r2s)\left(\frac{r_2}{s} \right), a potência reativa (QQ) é obtida. O vetor de potências é então atualizado e os procedimentos convencionais de solução do fluxo de potência são realizados.

Os passos de 2 a 4 são repetidos até que se obtenha a convergência.

Atenção!

No PSP-UFU, os motores de indução não são considerados no cálculo de curto-circuito.

Motor de indução trifásico no estudo de estabilidade

Uma importante carga dinâmica são os motores de indução, uma vez que correspondem a uma parcela significativa das cargas presentes no sistema elétrico. O modelo da máquina de indução apresentado anteriormente, a qual pode ser utilizada tanto como motor quanto como gerador, é bem estabelecida na literatura.

Como descrito na seção anterior, 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.

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 (ss) é utilizado no lugar da velocidade (ω\omega), em que:

s=fracΩ0−ωΩ0s = frac{\Omega_0 - \omega}{\Omega_0}

Desprezando as perdas por atrito e ventilação e a potência no eixo suave, as equações mecânicas do motor são expressas da seguinte forma:

Tm=A−Bs+Cs2Te=Re{E˙I˙∗}Ωbdsdt=(Tm−Te)2HT_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}

Em que:

  • TmT_m é o torque mecânico;
  • TeT_e é o torque elétrico;
  • HH é a inércia do conjunto motor - carga mecânica

Os termos AA, BB e CC são termos que definem o comportamento do torque mecânico da carga de acordo com o escorregamento. O torque mecânico normalmente varia com a velocidade, podendo ser expressa proporcionalmente com a seguinte equação quadrática:

Tm∝a+bω+cω2T_m \propto a + b\omega + c\omega^2

Em que:

{A∝a+b+cB∝b+2cC∝c\begin{cases} A \propto a + b + c \\ B \propto b + 2c \\ C \propto c \end{cases}

As equações elétricas do motor de indução de gaiola simples são baseadas no circuito equivalente da figura anterior. De forma semelhante ao modelo transitório da máquina síncrona, o motor de indução pode ser modelado pelo circuito equivalente de Thevenin de tensão transitória E′E' atrás de uma resistência do estator r1r_1 e uma reatância transitória x′x'. A reatância transitória aparente de rotor bloqueado é dada por:

x′=x1+x2xmx2+xmx' = x_1 + \frac{x_2 x_m}{x_2 + x_m}

A constante de tempo de circuito aberto do rotor (T0′T_0') é:

T0′=x2+xmΩbr2T_0' = \frac{x_2 + x_m}{\Omega_b r_2}

E a reatância de circuito aberto é:

x0=x1+xmx_0 = x_1 + x_m

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 (rr) e imaginárias (mm). Portanto, a descrição completa desse modelo é representada pelo seguinte sistema de equações algébrico-diferenciais:

Vr−Er′=r1Ir−x′ImVm−Em′=r1Im−x′ImdEr′dt=ΩbsEm′−Er′+(x0−x′)ImT0′dEm′dt=ΩbsEr′−Em′i(x0−x′)IrT0′V_r - E_r' = r_1 I_r - x' I_m\\ V_m - E_m' = r_1 I_m - x' I_m\\ \frac{dE_r'}{dt} = \Omega_b s E_m' - \frac{E_r' + \left( x_0 - x' \right) I_m}{T_0'}\\ \frac{dE_m'}{dt} = \Omega_b s E_r' - \frac{E_m' i \left( x_0 - x' \right) I_r}{T_0'}

Formulário de edição dos geradores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos motores de indução:

Formulário dos motores de indução no PSP-UFU

No formulário pode ser observado o botão "Chaveamento" 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 estabilidade.

Formulário de chaveamento do motores de indução

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do gerador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.p.u.) do motor.

Atenção!

Caso a opção “Calcular a potência reativa no fluxo de carga” esteja ativada, o campo de potência reativa é desativado para edição.

Calcular a potência reativa no fluxo de carga

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.

Cuidado!

Caso essa opção não seja utilizada o motor será considerado uma carga de potência constante no estudo de fluxo de carga.

A não utilização dessa opção poderá gerar erros de regime permamente no estudo de estabilidade.

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.

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
  3. MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: https://doi.org/10.1007/978-3-642-13669-6
  4. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
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Motor de Indução

Uma máquina assíncrona da qual apenas um enrolamento é energizado. tradução livre - IEC 60050.

Motor de indução trifásico no PSP-UFU

No PSP-UFU, os motores de indução são contemplados nos estudos de fluxo de carga e no estudo de estabilidade.

Informação

Os dados de estabilidade da máquina de indução são utilizados em conjunto com o fluxo de carga, calculando de forma correta a potência reativa das máquinas e consequentemente a tensão no barramento conectado.

Cuidado!

Ao marcar a opção "Calcular a potência reativa no fluxo de carga", devem ser inseridos os dados corretos na aba "Estabilidade", caso contrário, será atribuída uma potência reativa incorreta no motor.

Motor de indução trifásico no cálculo do fluxo de carga

A figura abaixo apresenta o modelo do motor de indução trifásico (MIT) de gaiola simples.

Circuito equivalente do motor de indução

As potências ativa e reativa podem ser calculadas em relação às variáveis e parâmetros do motor em p.u.p.u. como:

P=V2{(r2s)[(r2s)r1−x1K1−x2xm]+K1[(r2s)(xm+x1)+r1K1]}[(r2s)r1−x1K1−x2xm]2+[(r2s)(xm+x1)+r1K1]2Q=−V2{K1[(r2s)r1−x1K1−x2xm]−(r2s)[(r2s)(xm+x1)+r1K1]}[(r2s)r1−x1K1−x2xm]2+[(r2s)(xm+x1)+r1K1]2 K1=x2+xmP = \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

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 fluxo de potência. 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.

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:

(r2s)2A+(r2s)B+C=0\left(\frac{r_2}{s} \right)^2 A + \left(\frac{r_2}{s} \right) B + C = 0

Em que:

A=P(r12+K32)−V2r1B=2P(r1K2+K3K4)−V2(K2+K1K3)C=P(K22+K42)−V2K1K4K2=−x1K1−x2xmK3=xm+x1K4=r1K1A = 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

Esse modelo pode ser inserido na solução do fluxo de carga seguindo os seguintes passos:

  1. As constantes K1K_1 a K4K_4 são inicialmente calculadas . Esses valores são mantidos constantes durante toda a solução;
  2. Em cada iteração são calculados os coeficientes AA, BB e CC utilizando o valor atualizado de VV;
  3. A equação quadrática é resolvida e dois valores de (r2s)\left(\frac{r_2}{s} \right) são obtidos, em que o maior deles é escolhido por estar na região estável da característica toque-escorregamento do motor;
  4. Utilizando o novo valor de (r2s)\left(\frac{r_2}{s} \right), a potência reativa (QQ) é obtida. O vetor de potências é então atualizado e os procedimentos convencionais de solução do fluxo de potência são realizados.

Os passos de 2 a 4 são repetidos até que se obtenha a convergência.

Atenção!

No PSP-UFU, os motores de indução não são considerados no cálculo de curto-circuito.

Motor de indução trifásico no estudo de estabilidade

Uma importante carga dinâmica são os motores de indução, uma vez que correspondem a uma parcela significativa das cargas presentes no sistema elétrico. O modelo da máquina de indução apresentado anteriormente, a qual pode ser utilizada tanto como motor quanto como gerador, é bem estabelecida na literatura.

Como descrito na seção anterior, 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.

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 (ss) é utilizado no lugar da velocidade (ω\omega), em que:

s=fracΩ0−ωΩ0s = frac{\Omega_0 - \omega}{\Omega_0}

Desprezando as perdas por atrito e ventilação e a potência no eixo suave, as equações mecânicas do motor são expressas da seguinte forma:

Tm=A−Bs+Cs2Te=Re{E˙I˙∗}Ωbdsdt=(Tm−Te)2HT_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}

Em que:

  • TmT_m é o torque mecânico;
  • TeT_e é o torque elétrico;
  • HH é a inércia do conjunto motor - carga mecânica

Os termos AA, BB e CC são termos que definem o comportamento do torque mecânico da carga de acordo com o escorregamento. O torque mecânico normalmente varia com a velocidade, podendo ser expressa proporcionalmente com a seguinte equação quadrática:

Tm∝a+bω+cω2T_m \propto a + b\omega + c\omega^2

Em que:

{A∝a+b+cB∝b+2cC∝c\begin{cases} A \propto a + b + c \\ B \propto b + 2c \\ C \propto c \end{cases}

As equações elétricas do motor de indução de gaiola simples são baseadas no circuito equivalente da figura anterior. De forma semelhante ao modelo transitório da máquina síncrona, o motor de indução pode ser modelado pelo circuito equivalente de Thevenin de tensão transitória E′E' atrás de uma resistência do estator r1r_1 e uma reatância transitória x′x'. A reatância transitória aparente de rotor bloqueado é dada por:

x′=x1+x2xmx2+xmx' = x_1 + \frac{x_2 x_m}{x_2 + x_m}

A constante de tempo de circuito aberto do rotor (T0′T_0') é:

T0′=x2+xmΩbr2T_0' = \frac{x_2 + x_m}{\Omega_b r_2}

E a reatância de circuito aberto é:

x0=x1+xmx_0 = x_1 + x_m

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 (rr) e imaginárias (mm). Portanto, a descrição completa desse modelo é representada pelo seguinte sistema de equações algébrico-diferenciais:

Vr−Er′=r1Ir−x′ImVm−Em′=r1Im−x′ImdEr′dt=ΩbsEm′−Er′+(x0−x′)ImT0′dEm′dt=ΩbsEr′−Em′i(x0−x′)IrT0′V_r - E_r' = r_1 I_r - x' I_m\\ V_m - E_m' = r_1 I_m - x' I_m\\ \frac{dE_r'}{dt} = \Omega_b s E_m' - \frac{E_r' + \left( x_0 - x' \right) I_m}{T_0'}\\ \frac{dE_m'}{dt} = \Omega_b s E_r' - \frac{E_m' i \left( x_0 - x' \right) I_r}{T_0'}

Formulário de edição dos geradores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos motores de indução:

Formulário dos motores de indução no PSP-UFU

No formulário pode ser observado o botão "Chaveamento" 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 estabilidade.

Formulário de chaveamento do motores de indução

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do gerador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.p.u.) do motor.

Atenção!

Caso a opção “Calcular a potência reativa no fluxo de carga” esteja ativada, o campo de potência reativa é desativado para edição.

Calcular a potência reativa no fluxo de carga

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.

Cuidado!

Caso essa opção não seja utilizada o motor será considerado uma carga de potência constante no estudo de fluxo de carga.

A não utilização dessa opção poderá gerar erros de regime permamente no estudo de estabilidade.

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.

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
  3. MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: https://doi.org/10.1007/978-3-642-13669-6
  4. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
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-

PSP-UFU

important

This user guide was written in Brazilian Portuguese. If you want to help me translate this guide, contact-me on GitHub or Twitter.

Sobre o PSP-UFU

O PSP-UFU (Plataforma de Sistemas de Potência da Universidade Federal de Uberlândia) é um software multi-plataforma, multilíngue, livre e de código aberto (FOSS) com recursos avançados de GUI (Graphical User Interface) e ferramentas CAD (Computer Aided Design) para estudos de sistemas elétricos de potência.

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 elementos de texto vinculados na tela principal e também editores de tabelas e gráficos.

O PSP-UFU tem como objetivo fornecer ferramentas eficientes de simulação para fins de pesquisa e educação, além de aplicações industriais em sistemas elétricos de potência.

Resumidamente, o software pode executar os seguintes estudos:

  • Fluxo de potência
  • Cálculo de curto-circuito
  • Harmônicos
  • Estabilidade transitória e dinâmica

Publicações

Os artigos abaixo possuem maiores detalhes a respeito do PSP-UFU:

Oliveira, T. L., Guimarães, G. C., & Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. International Transactions on Electrical Energy Systems, e12185. doi: 10.1002/2050-7038.12185

Oliveira, T. L., Guimarães, G. C., Silva, L. R., & Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. The International Journal of Electrical Engineering & Education, 0020720919879058. doi: 10.1177/0020720919879058

A Tese de Doutorado abaixo detalha em profundidade os cálculos envolvidos, arquitetura de software e ferramentas implementadas no PSP-UFU:

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: 10.14393/ufu.te.2019.2444

Contribuindo com o projeto

Se você está interessado em contribuir com o PSP-UFU de alguma forma (desenvolvimento, críticas, sugestões, etc.), entre em contato pelo GitHub ou Twitter.

Desenvolvedores

Thales Lima Oliveira

Edit this page
- - - - - - - - - - +
+

PSP-UFU

important

This user guide was written in Brazilian Portuguese. If you want to help me translate this guide, contact-me on GitHub or Twitter.

Sobre o PSP-UFU

O PSP-UFU (Plataforma de Sistemas de Potência da Universidade Federal de Uberlândia) é um software multi-plataforma, multilíngue, livre e de código aberto (FOSS) com recursos avançados de GUI (Graphical User Interface) e ferramentas CAD (Computer Aided Design) para estudos de sistemas elétricos de potência.

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 elementos de texto vinculados na tela principal e também editores de tabelas e gráficos.

O PSP-UFU tem como objetivo fornecer ferramentas eficientes de simulação para fins de pesquisa e educação, além de aplicações industriais em sistemas elétricos de potência.

Resumidamente, o software pode executar os seguintes estudos:

  • Fluxo de potência
  • Cálculo de curto-circuito
  • Harmônicos
  • Estabilidade transitória e dinâmica

Publicações

Os artigos abaixo possuem maiores detalhes a respeito do PSP-UFU:

Oliveira, T. L., Guimarães, G. C., & Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. International Transactions on Electrical Energy Systems, e12185. doi: 10.1002/2050-7038.12185

Oliveira, T. L., Guimarães, G. C., Silva, L. R., & Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. The International Journal of Electrical Engineering & Education, 0020720919879058. doi: 10.1177/0020720919879058

A Tese de Doutorado abaixo detalha em profundidade os cálculos envolvidos, arquitetura de software e ferramentas implementadas no PSP-UFU:

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: 10.14393/ufu.te.2019.2444

Contribuindo com o projeto

Se você está interessado em contribuir com o PSP-UFU de alguma forma (desenvolvimento, críticas, sugestões, etc.), entre em contato pelo GitHub ou Twitter.

Desenvolvedores

Thales Lima Oliveira

Edit this page
+ + + + + + + + + + \ No newline at end of file diff --git a/docs/docs/inductor/index.html b/docs/docs/inductor/index.html index f3c3892..d77755a 100644 --- a/docs/docs/inductor/index.html +++ b/docs/docs/inductor/index.html @@ -3,31 +3,31 @@ - -Indutor | PSP-UFU - - - - - - - - - - + +Indutor | PSP-UFU + + + + + + + + + + -
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Indutor

Um reator destinado à conexão de derivação em uma rede para compensar a corrente capacitiva. tradução livre - IEC 60050.

Indutor no PSP-UFU

O elemento indutor (ou reator) representa, geralmente, reator shunt no circuito do PSP-UFU.

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.

Formulário de edição dos indutores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos indutores:

Formulário dos indutores no PSP-UFU

Além do único contexto geral, pode ser observado o botão "Estabilidade" 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 estabilidade.

Formulário de chaveamento do indutor

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

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.p.u. (na base de potência do sistema).

Edit this page
- - - - - - - - - - +
+

Indutor

Um reator destinado à conexão de derivação em uma rede para compensar a corrente capacitiva. tradução livre - IEC 60050.

Indutor no PSP-UFU

O elemento indutor (ou reator) representa, geralmente, reator shunt no circuito do PSP-UFU.

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.

Formulário de edição dos indutores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos indutores:

Formulário dos indutores no PSP-UFU

Além do único contexto geral, pode ser observado o botão "Estabilidade" 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 estabilidade.

Formulário de chaveamento do indutor

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

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.p.u. (na base de potência do sistema).

Edit this page
+ + + + + + + + + + \ No newline at end of file diff --git a/docs/docs/installation/index.html b/docs/docs/installation/index.html index d308cd5..27221eb 100644 --- a/docs/docs/installation/index.html +++ b/docs/docs/installation/index.html @@ -3,32 +3,32 @@ - -Instalação | PSP-UFU - - - - - - - - - - + +Instalação | PSP-UFU + + + + + + + + + + -
-

Instalação

Download

O download do PSP-UFU pode ser realizado pelo "last release" do repositório do PSP-UFU no GitHub.

Ao acessar ao link, role a página até encontrar os Assets:

Assets download

Como o PSP-UFU é um software multiplataforma, você deve baixar o arquivo correto:

  • Para o sistema operacional Windows baixe os arquivos .exe (recomendado) ou .zip.
  • Para os sistemas Linux baseados no Debian (por exemplo, Ubuntu, Mint) 64 bits baixe o pacote de instalação .deb.
Dica

Se você está interessado em contribuir com o PSP-UFU construindo-o para outros sistemas operacionais (principalmente macOS!) entre em contato pelo GitHub ou Twitter.

Na sequência são apresentados o passo-a-passo para instalação dos SOs Windows e Linux. Também são apresentadas as soluções para os erros mais recorrentes.

Windows

Após baixar o arquivo .exe avance em cada passo do instalador. O executável irá solicitar automaticamente a instalação do Microsoft Visual C++ Redistribuível e, caso não esteja instalado no seu computador, realize os procedimentos do programa.

Caso o executável falhe em abrir, baixe o arquivo .zip e descompacte em alguma pasta do seu sistema. Nesse caso é necessário baixar e instalar manualmente o Microsoft Visual C++ Redistribuível 32 bits.

Após a conclusão da instalação abra o PSP-UFU para verificar a correta instalação. O executável está presente na pasta "<local de instalação>/PSP-UFU/bin/PSP-UFU.exe".

Problemas recorrentes no Windows

  • Ao baixar o navegador pode falsamente sinalizar que é um arquivo perigoso, basta clicar em "Manter arquivo";
  • Ao abrir o instalador, novamente o Windows sinaliza que o arquivo é perigoso, basta clicar em "Executar assim mesmo";
  • 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;
  • 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 "Device Context". Caso apareça uma mensagem de erro, execute o programa como administrador e repita o processo. Reinicie o programa.

Linux

A instalação no sistema Linux é facilmente realizado pelo pacote de instalação automático .deb.

Atenção!

Note que essa versão para Linux está defasada e algumas funcionalidades do programa podem não estar presentes.

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 GitHub ou Twitter.

Problemas recorrentes no Linux

Pode ser necessário adicionar o diretório das bibliotecas do wxWidgets nas variáveis de ambiente. -Para isso, siga UM dos métodos apresentados abaixo:

Método I (recomendado)

Insira o seguinte comando no arquivo ~/.bashrc:

echo "export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib" >> ~/.bashrc

Método II (não recomendado)

Cuidado!

Utilizando esse método os passos abaixo devem ser executados todas as vezes que você quiser abrir o PSP-UFU.

  1. Abra o terminal e acesse o diretório onde está instalado o PSP-UFU:
cd /usr/local/bin
  1. Insira as bibliotecas compartilhadas do wxWidgets nas variáveis de ambiente:
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib
  1. Então, execute o PSP-UFU na mesma seção do terminal:
./PSP-UFU
Atenção!

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.

Edit this page
- - - - - - - - - - +
+

Instalação

Download

O download do PSP-UFU pode ser realizado pelo "last release" do repositório do PSP-UFU no GitHub.

Ao acessar ao link, role a página até encontrar os Assets:

Assets download

Como o PSP-UFU é um software multiplataforma, você deve baixar o arquivo correto:

  • Para o sistema operacional Windows baixe os arquivos .exe (recomendado) ou .zip.
  • Para os sistemas Linux baseados no Debian (por exemplo, Ubuntu, Mint) 64 bits baixe o pacote de instalação .deb.
Dica

Se você está interessado em contribuir com o PSP-UFU construindo-o para outros sistemas operacionais (principalmente macOS!) entre em contato pelo GitHub ou Twitter.

Na sequência são apresentados o passo-a-passo para instalação dos SOs Windows e Linux. Também são apresentadas as soluções para os erros mais recorrentes.

Windows

Após baixar o arquivo .exe avance em cada passo do instalador. O executável irá solicitar automaticamente a instalação do Microsoft Visual C++ Redistribuível e, caso não esteja instalado no seu computador, realize os procedimentos do programa.

Caso o executável falhe em abrir, baixe o arquivo .zip e descompacte em alguma pasta do seu sistema. Nesse caso é necessário baixar e instalar manualmente o Microsoft Visual C++ Redistribuível 32 bits.

Após a conclusão da instalação abra o PSP-UFU para verificar a correta instalação. O executável está presente na pasta "<local de instalação>/PSP-UFU/bin/PSP-UFU.exe".

Problemas recorrentes no Windows

  • Ao baixar o navegador pode falsamente sinalizar que é um arquivo perigoso, basta clicar em "Manter arquivo";
  • Ao abrir o instalador, novamente o Windows sinaliza que o arquivo é perigoso, basta clicar em "Executar assim mesmo";
  • 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;
  • 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 "Device Context". Caso apareça uma mensagem de erro, execute o programa como administrador e repita o processo. Reinicie o programa.

Linux

A instalação no sistema Linux é facilmente realizado pelo pacote de instalação automático .deb.

Atenção!

Note que essa versão para Linux está defasada e algumas funcionalidades do programa podem não estar presentes.

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 GitHub ou Twitter.

Problemas recorrentes no Linux

Pode ser necessário adicionar o diretório das bibliotecas do wxWidgets nas variáveis de ambiente. +Para isso, siga UM dos métodos apresentados abaixo:

Método I (recomendado)

Insira o seguinte comando no arquivo ~/.bashrc:

echo "export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib" >> ~/.bashrc

Método II (não recomendado)

Cuidado!

Utilizando esse método os passos abaixo devem ser executados todas as vezes que você quiser abrir o PSP-UFU.

  1. Abra o terminal e acesse o diretório onde está instalado o PSP-UFU:
cd /usr/local/bin
  1. Insira as bibliotecas compartilhadas do wxWidgets nas variáveis de ambiente:
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib
  1. Então, execute o PSP-UFU na mesma seção do terminal:
./PSP-UFU
Atenção!

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.

Edit this page
+ + + + + + + + + + \ No newline at end of file diff --git a/docs/docs/io/index.html b/docs/docs/io/index.html index 4f39f5b..ffe6059 100644 --- a/docs/docs/io/index.html +++ b/docs/docs/io/index.html @@ -3,31 +3,31 @@ - -Entrada / Saída | PSP-UFU - - - - - - - - - - + +Entrada / Saída | PSP-UFU + + + + + + + + + + -
-

Entrada / Saída

As entradas e saída são variáveis relacionadas às máquinas síncronas. Cada tipo de entrada e saída está relacionada a um regulador da máquina: Regulador de Tensão (AVR, do inglês Automatic Voltage Regulator) e Regulador de Velocidade (RV).

Cuidado!

O sistema de controle deve ter ao menos uma entrada e uma saída.

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:

Formulário de edição de entradas e saídas de sistemas de controle de um AVR

Variáveis de entrada e saída

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:

  • Tensão terminal (entrada: AVR): Módulo da tensão no barramento da máquina síncrona, em p.u.p.u., variável no tempo. Essa variável é normalmente utilizada no cálculo do erro da tensão de referência do AVR;

  • 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.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.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 (2πfref2 \pi f_{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;

  • 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.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:

    Δx=xn−xn−1h\Delta x = \frac{x_n-x_{n-1}}{h}

    Em que:

    • Δx\Delta x é a variação da entrada (velocidade ou potência ativa);
    • xnx_n e xn−1x_{n-1} é a variável no passo atual e anterior, respectivamente;
    • hh é o passo de integração.
    Nota

    A normalização é necessária para a correta utilização da razão de passo de controle, definida nas configurações de simulação.

  • Tensão de campo (saída: AVR): Define a tensão aplicada ao campo na máquina síncrona, em p.u.p.u. Utilizada como saída dos AVRs, controlando principalmente tensão no barramento conectado e/ou fator de potência da máquina;

  • Potência mecânica (saída: RV): 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.

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Entrada / Saída

As entradas e saída são variáveis relacionadas às máquinas síncronas. Cada tipo de entrada e saída está relacionada a um regulador da máquina: Regulador de Tensão (AVR, do inglês Automatic Voltage Regulator) e Regulador de Velocidade (RV).

Cuidado!

O sistema de controle deve ter ao menos uma entrada e uma saída.

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:

Formulário de edição de entradas e saídas de sistemas de controle de um AVR

Variáveis de entrada e saída

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:

  • Tensão terminal (entrada: AVR): Módulo da tensão no barramento da máquina síncrona, em p.u.p.u., variável no tempo. Essa variável é normalmente utilizada no cálculo do erro da tensão de referência do AVR;

  • 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.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.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 (2πfref2 \pi f_{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;

  • 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.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:

    Δx=xn−xn−1h\Delta x = \frac{x_n-x_{n-1}}{h}

    Em que:

    • Δx\Delta x é a variação da entrada (velocidade ou potência ativa);
    • xnx_n e xn−1x_{n-1} é a variável no passo atual e anterior, respectivamente;
    • hh é o passo de integração.
    Informação

    A normalização é necessária para a correta utilização da razão de passo de controle, definida nas configurações de simulação.

  • Tensão de campo (saída: AVR): Define a tensão aplicada ao campo na máquina síncrona, em p.u.p.u. Utilizada como saída dos AVRs, controlando principalmente tensão no barramento conectado e/ou fator de potência da máquina;

  • Potência mecânica (saída: RV): 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.

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Limitador absoluto

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:

yn={Lsup,se un>Lsupun,se Linf≤un≤LsupLinf,se un<Linfy_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:

  • yny_n Éé o valor de saída atual do bloco
  • LsupL_{sup} e LinfL_{inf} são os limites superior e inferior, respectivamente
  • unu_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.

Formulário de edição de dados do bloco limitador no PSP-UFU

Esse bloco não linear é definido pelo limite superior e inferior, inseridos pelo usuário.

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.

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Limitador absoluto

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:

yn={Lsup,se un>Lsupun,se Linf≤un≤LsupLinf,se un<Linfy_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:

  • yny_n Éé o valor de saída atual do bloco
  • LsupL_{sup} e LinfL_{inf} são os limites superior e inferior, respectivamente
  • unu_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.

Formulário de edição de dados do bloco limitador no PSP-UFU

Esse bloco não linear é definido pelo limite superior e inferior, inseridos pelo usuário.

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.

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Linha

Um meio de transmissão fabricado usado para transmitir energia eletromagnética entre dois pontos com um mínimo de radiação. tradução livre - IEC 60050.

Linha no PSP-UFU

As linhas no PSP-UFU são modelos π\pi equilibradas. Podem ser utilizadas como linhas de transmissão e distribuição de sistemas elétricos de potência.

A figura abaixo mostra o modelo π\pi implementado no PSP-UFU:

Modelo PI da linha

Em que:

  • rL\bold{r_L} é a resistência da linha;
  • xL\bold{x_L} é a reatância indutiva da linha;
  • bLd\bold{b_{L}^{d}} é a susceptância capacitiva shunt da linha.
Atenção

O modelo utilizado no PSP-UFU é equilibrado e não possui impedâncias mútuas entre as fases.

A linha pode ser inseridas com pontos de ancoragem, ou "nós", para maior personalização gráfica do elemento, como apresentado nas Ferramentas CAD.

Cuidado!

A linha deve ser inserida entre duas barras de mesma tensão nominal. Caso você tente inseri-la entre barras de tensão diferentes, uma mensagem de erro será exibida.

Dica

Um arranjo série de uma linha sem as susceptâncias shunt, um barramento e um capacitor pode ser utilizado para fabricar um filtro passivo nos estudos harmônicos. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.

Formulário de edição das linhas

A imagem abaixo apresenta o formulário de inserção/alteração de dados das linhas de transmissão:

Formulário das linhas no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais da linha e informações do fluxo de carga;
  • Falta: local onde as impedâncias de sequência zero são inseridas.
Nota

Os parâmetros necessários para construção da linha segundo seu modelo π\pi são inseridos na aba Geral, utilizados para construção da matriz admitância de sequência positiva e negativa.

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.

Além desses dois contextos, pode ser observado o botão "Estabilidade" 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 estabilidade.

Formulário de chaveamento da linha

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

Campo de informação não editável que apresenta a tensão nominal da linha. Para alterar esse campo é necessário editar o campo correspondente do barramento conectado.

Potência nominal

Potência nominal da linha, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Parâmetros do modelo π\pi

Resistência (rLr_L), Reatância indutiva (xLx_L) série e Susceptância capacitiva shunt total (2bLd2b_{L}^{d}) presentes no modelo π\pi da linha.

Esses parâmetros são inseridos em p.u.p.u., Ω\Omega ou Ω/km\Omega/km (SS ou S/kmS/km para bLdb_{L}^{d}).

Comprimento da linha

Utilizado para calcular o valor dos parâmetros da linha inseridos em Ω/km\Omega/km (ou S/kmS/km).

Informação

O comprimento da linha é ignorado caso não sejam utilizadas as unidades por quilometro.

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.

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Linha

Um meio de transmissão fabricado usado para transmitir energia eletromagnética entre dois pontos com um mínimo de radiação. tradução livre - IEC 60050.

Linha no PSP-UFU

As linhas no PSP-UFU são modelos π\pi equilibradas. Podem ser utilizadas como linhas de transmissão e distribuição de sistemas elétricos de potência.

A figura abaixo mostra o modelo π\pi implementado no PSP-UFU:

Modelo PI da linha

Em que:

  • rL\bold{r_L} é a resistência da linha;
  • xL\bold{x_L} é a reatância indutiva da linha;
  • bLd\bold{b_{L}^{d}} é a susceptância capacitiva shunt da linha.
Atenção

O modelo utilizado no PSP-UFU é equilibrado e não possui impedâncias mútuas entre as fases.

A linha pode ser inseridas com pontos de ancoragem, ou "nós", para maior personalização gráfica do elemento, como apresentado nas Ferramentas CAD.

Cuidado!

A linha deve ser inserida entre duas barras de mesma tensão nominal. Caso você tente inseri-la entre barras de tensão diferentes, uma mensagem de erro será exibida.

Dica

Um arranjo série de uma linha sem as susceptâncias shunt, um barramento e um capacitor pode ser utilizado para fabricar um filtro passivo nos estudos harmônicos. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.

Formulário de edição das linhas

A imagem abaixo apresenta o formulário de inserção/alteração de dados das linhas de transmissão:

Formulário das linhas no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais da linha e informações do fluxo de carga;
  • Falta: local onde as impedâncias de sequência zero são inseridas.
Informação

Os parâmetros necessários para construção da linha segundo seu modelo π\pi são inseridos na aba Geral, utilizados para construção da matriz admitância de sequência positiva e negativa.

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.

Além desses dois contextos, pode ser observado o botão "Estabilidade" 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 estabilidade.

Formulário de chaveamento da linha

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

Campo de informação não editável que apresenta a tensão nominal da linha. Para alterar esse campo é necessário editar o campo correspondente do barramento conectado.

Potência nominal

Potência nominal da linha, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Parâmetros do modelo π\pi

Resistência (rLr_L), Reatância indutiva (xLx_L) série e Susceptância capacitiva shunt total (2bLd2b_{L}^{d}) presentes no modelo π\pi da linha.

Esses parâmetros são inseridos em p.u.p.u., Ω\Omega ou Ω/km\Omega/km (SS ou S/kmS/km para bLdb_{L}^{d}).

Comprimento da linha

Utilizado para calcular o valor dos parâmetros da linha inseridos em Ω/km\Omega/km (ou S/kmS/km).

Informação

O comprimento da linha é ignorado caso não sejam utilizadas as unidades por quilometro.

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.

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Carga

  1. a potência ativa, reativa ou aparente gerada, transmitida ou distribuída dentro de um sistema;
  2. 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.

Carga no PSP-UFU

As cargas são os elementos de potência consumidores de potência genéricos. Nos estudos de fluxo de carga é possível modelar a carga como potência ou impedância constante e em estabilidade pode-se compor a carga na proporção desejada em três tipos (carga ZIP): potência constante, impedância constante e corrente constante.

As cargas de potência constante nos estudos de fluxo de carga são inseridos no vetor de potências e permanecem fixos durante toda a simulação.

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:

y‾=P−jQV˙2\overline{y} = \frac{P-jQ}{\dot{V}^2}
Atenção!

Para os estudos de curto-circuito e harmônicos as cargas são modeladas como impedância constante, independentemente da sinalização indicada em seu formulário de edição de dados.

Carga no estudo de estabilidade

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.

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:

PL=PZ0(ViVi0)2+PI0(ViVi0)+PP0P_L=P_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+P_{I0} \left(\frac{V_i}{V_i0} \right)+P_{P0}
QL=QZ0(ViVi0)2+QI0(ViVi0)+QP0Q_L=Q_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+Q_{I0} \left(\frac{V_i}{V_i0} \right)+Q_{P0}

Em que:

PLP_L e QLQ_L são as potências ativa e reativa da carga ZIP, respectivamente, conectadas em uma barra genérica i;

ViV_i é a tensão atual de uma barra genérica i;

Vi0V_{i0} é a tensão inicial de uma barra genérica i, obtida do estudo de fluxo de carga;

PZ0P_{Z0} e QZ0Q_{Z0} são as parcelas de impedância constante para potências ativa e reativa, respectivamente;

PI0P_{I0} e QI0Q_{I0} são as parcelas de corrente constante para potências ativa e reativa, respectivamente;

PP0P_{P0} e QP0Q_{P0} são as parcelas de potência constante para potências ativa e reativa, respectivamente.

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 (PL0P_{L0}, para a potência ativa e QL0Q_{L0}, para a potência reativa), utilizando as seguintes expressões:

{PZ0=kPZ100PL0Vi02PI0=kPI100PL0Vi0PP0=kPP100PL0\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}

Os valores de kPZk_{PZ}, kPIk_{PI} e kPPk_{PP} 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 kQZk_{QZ}, kQIk_{QI} e kQPk_{QP} podem ser interpretados de forma análoga, porém compõe a parcela reativa da carga.

O comportamento das potências, retiradas de simulações no PSP-UFU, de cada parcela que compõe a carga ZIP são evidenciadas na figura abaixo.

Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente

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 (VlowV_{low}), 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.

Formulário de edição das cargas

A imagem abaixo apresenta o formulário de inserção/alteração de dados das cargas:

Formulário das cargas no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais das cargas, informações e o tipo de carga no fluxo de carga;
  • Estabilidade: contendo opções de visualização de dados da carga em gráficos no tempo e opções de parametrização da carga ZIP.

Além desses dois contextos, pode ser observado o botão "Chaveamento" 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 estabilidade.

Formulário de chaveamento da carga

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência ativa

Parcela de potência ativa da carga. Pode ser inserido em MW, kW W ou p.u.p.u. (na base do sistema).

Potência reativa

Parcela de potência reativa da carga. Pode ser inserido em Mvar, kvar var ou p.u.p.u. (na base do sistema).

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.

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Carga

  1. a potência ativa, reativa ou aparente gerada, transmitida ou distribuída dentro de um sistema;
  2. 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.

Carga no PSP-UFU

As cargas são os elementos de potência consumidores de potência genéricos. Nos estudos de fluxo de carga é possível modelar a carga como potência ou impedância constante e em estabilidade pode-se compor a carga na proporção desejada em três tipos (carga ZIP): potência constante, impedância constante e corrente constante.

As cargas de potência constante nos estudos de fluxo de carga são inseridos no vetor de potências e permanecem fixos durante toda a simulação.

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:

y‾=P−jQV˙2\overline{y} = \frac{P-jQ}{\dot{V}^2}
Atenção!

Para os estudos de curto-circuito e harmônicos as cargas são modeladas como impedância constante, independentemente da sinalização indicada em seu formulário de edição de dados.

Carga no estudo de estabilidade

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.

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:

PL=PZ0(ViVi0)2+PI0(ViVi0)+PP0P_L=P_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+P_{I0} \left(\frac{V_i}{V_i0} \right)+P_{P0}
QL=QZ0(ViVi0)2+QI0(ViVi0)+QP0Q_L=Q_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+Q_{I0} \left(\frac{V_i}{V_i0} \right)+Q_{P0}

Em que:

PLP_L e QLQ_L são as potências ativa e reativa da carga ZIP, respectivamente, conectadas em uma barra genérica i;

ViV_i é a tensão atual de uma barra genérica i;

Vi0V_{i0} é a tensão inicial de uma barra genérica i, obtida do estudo de fluxo de carga;

PZ0P_{Z0} e QZ0Q_{Z0} são as parcelas de impedância constante para potências ativa e reativa, respectivamente;

PI0P_{I0} e QI0Q_{I0} são as parcelas de corrente constante para potências ativa e reativa, respectivamente;

PP0P_{P0} e QP0Q_{P0} são as parcelas de potência constante para potências ativa e reativa, respectivamente.

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 (PL0P_{L0}, para a potência ativa e QL0Q_{L0}, para a potência reativa), utilizando as seguintes expressões:

{PZ0=kPZ100PL0Vi02PI0=kPI100PL0Vi0PP0=kPP100PL0\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}

Os valores de kPZk_{PZ}, kPIk_{PI} e kPPk_{PP} 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 kQZk_{QZ}, kQIk_{QI} e kQPk_{QP} podem ser interpretados de forma análoga, porém compõe a parcela reativa da carga.

O comportamento das potências, retiradas de simulações no PSP-UFU, de cada parcela que compõe a carga ZIP são evidenciadas na figura abaixo.

Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente

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 (VlowV_{low}), 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.

Formulário de edição das cargas

A imagem abaixo apresenta o formulário de inserção/alteração de dados das cargas:

Formulário das cargas no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais das cargas, informações e o tipo de carga no fluxo de carga;
  • Estabilidade: contendo opções de visualização de dados da carga em gráficos no tempo e opções de parametrização da carga ZIP.

Além desses dois contextos, pode ser observado o botão "Chaveamento" 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 estabilidade.

Formulário de chaveamento da carga

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência ativa

Parcela de potência ativa da carga. Pode ser inserido em MW, kW W ou p.u.p.u. (na base do sistema).

Potência reativa

Parcela de potência reativa da carga. Pode ser inserido em Mvar, kvar var ou p.u.p.u. (na base do sistema).

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.

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Tela Principal

Organização da tela principal

A tela principal do PSP-UFU é dividida em três seções: Menu "Ribbon", Área de Trabalho e Barra de Status.

Tela principal

Resumidamente, no Menu Ribbon são acessadas as ferramentas do PSP-UFU; na Área de Trabalho são criados os diagramas unifilares de potência; e na Barra de Status são exibidas importantes informações acerca do estado da Área de Trabalho.

Menu Ribbon

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 touch screen. -Wikipedia

O menu Ribbon é composto de três submenus: “Arquivo”, “Ferramentas” e “Simulação”.

Menu Arquivo

Em Arquivo 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.

Menu Ferramentas

Em Ferramentas 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.

Menu Simulação

Finalmente, o submenu Simulação proporciona o acesso do usuário aos cálculos realizados pelo software 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.

Área de Trabalho

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 Menu Ribbon.

As edições gráficas dos elementos, como posição, conexão e tamanho dos barramentos, são realizadas por meio da ação drag-and-drop (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.

Área de Trabalho

Barra de Status

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.

Dica

Sempre fique atendo à barra de status, pois são fornecidas informações importantes acerca da operação do programa. Caso tenha alguma dúvida siga as instruções apresentadas nesse componente.

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Tela Principal

Organização da tela principal

A tela principal do PSP-UFU é dividida em três seções: Menu "Ribbon", Área de Trabalho e Barra de Status.

Tela principal

Resumidamente, no Menu Ribbon são acessadas as ferramentas do PSP-UFU; na Área de Trabalho são criados os diagramas unifilares de potência; e na Barra de Status são exibidas importantes informações acerca do estado da Área de Trabalho.

Menu Ribbon

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 touch screen. +Wikipedia

O menu Ribbon é composto de três submenus: “Arquivo”, “Ferramentas” e “Simulação”.

Menu Arquivo

Em Arquivo 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.

Menu Ferramentas

Em Ferramentas 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.

Menu Simulação

Finalmente, o submenu Simulação proporciona o acesso do usuário aos cálculos realizados pelo software 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.

Área de Trabalho

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 Menu Ribbon.

As edições gráficas dos elementos, como posição, conexão e tamanho dos barramentos, são realizadas por meio da ação drag-and-drop (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.

Área de Trabalho

Barra de Status

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.

Dica

Sempre fique atendo à barra de status, pois são fornecidas informações importantes acerca da operação do programa. Caso tenha alguma dúvida siga as instruções apresentadas nesse componente.

Configurações gerais

As configurações gerais do programa são acessadas no submenu Ribbon Arquivo. Essas configurações são aplicadas para todos os projetos e permanecem gravadas no disco.

Configurações gerais
Cuidado

Algumas configurações de segurança do seu computador (principalmente em sistemas Windows) podem gerar uma mensagem de erro ao confirmar as alterações das configurações gerais.

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 as configurações e reinicie o programa.

Idioma

Atualmente os seguintes idiomas estão disponíveis no PSP-UFU:

  • Inglês
  • Português
Informação

O programa deve ser reiniciado para surtir efeito da alteração do idioma.

Renderização

Define como os elementos gráficos do editor de potência e do editor de controle são desenhados na tela. Atualmente duas opções estão disponíveis:

Cuidado!

o OpenGL pode não ser suportado pelo seu computador. Nesse caso, ao criar um novo projeto a tela de trabalho não é exibida ou é exibida uma tela preta. A solução é alterar o renderizador para "Device Context".

Caso apareça uma mensagem de erro, execute o programa como administrador e repita o processo.

Informação

O programa deve ser reiniciado para surtir efeito de alteração do renderizador.

Arquivos de projeto do PSP-UFU

As opções de criação, gravação e abertura de projetos no disco, assim como importação de arquivos de outros programas estão presentes no submenu Ribbon Arquivo.

Novo projeto

A criação de um novo projeto é realizada clicando no botão Novo projeto no submenu Arquivo. Essa ação cria um sistema em branco na área de trabalho, local onde é possível inserir os elementos elétricos por meio do submenu Ferramentas ou pelas teclas de atalho.

Esse sistema em branco pode ser ciado utilizando o Editor de Potência.

Salvar e Salvar como...

A opção "Salvar" sobrepõe as alterações realizadas no projeto aberto e grava no disco. A opção "Salvar como..." cria um novo arquivo e grava o projeto no disco com o auxílio de uma janela de seleção de pasta (e definição do nome do arquivo).

Informação

Para projetos que estão sendo gravados pela primeira vez a opção "Salvar" se comporta de forma idêntica à opção "Salvar como...".

Dica

O PSP-UFU grava os arquivos com a extensão .psp. Esses arquivos nada mais são que arquivos de texto utilizando a linguagem de marcação XML (eXtensible Markup Language), que define uma série de regras de formatação dos dados de forma que eles são tanto legíveis por humanos quanto por máquinas.

Portanto, os dados elétricos contidos neles podem ser facilmente identificados e alterados, caso necessário.

Abrir projeto

Essa opção abre os projetos gravados no disco por meio com o auxílio de uma janela de seleção de arquivos.

Importar projeto

O PSP-UFU permite a importação de arquivos dos seguintes programas:

Para importação dos arquivos do ANAREDE são utilizados tanto o arquivo de dados elétricos (.pwf) quanto de dados gráficos dos elementos (.lst).

Uma vez que o arquivo do Matpower (.m) não possui dados gráficos dos elementos elétricos, o diagrama unifilar é automaticamente gerado pelo PSP-UFU ao importá-lo.

Geração automática do layout de diagramas unifilares

Para criar o layout automático, utilizou-se a teoria dos grafos baseada no posicionamento direcionado à força e aplicação de grafos com arestas ponderadas. De acordo com a teoria dos grafos, o sistema é modelado como vértices e arestas. Nesse contexto, os barramentos são os vértices e os ramos do sistema (linhas e transformadores) são as arestas. As localizações de elementos de derivação, assim como os nós dos elementos, são automaticamente controladas pelo PSP-UFU.

A ferramenta de layout automático é composta por um processo iterativo e os resultados são mais refinados com um número maior de iterações. Os melhores resultados são obtidos utilizando o número de iterações igual ou superior a cinco vezes o número de barramentos do sistema.

Atenção!

O layout automático ainda está em desenvolvimento e algumas melhorias podem ser feitas para evitar cruzamentos e sobreposições, porém, em seu estado atual, é totalmente funcional e satisfatório.

Dica

Uma vez que o Matpower pode converter os formatos CDF (Common Data Format) e PSS/E RAW para arquivos .m, estes podem ser importados de forma indireta para o PSP-UFU.

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Expressão Matemática

O bloco de expressão matemática utiliza a biblioteca externa fparser 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:

OperadorExpressão
( )Expressão em parênteses primeiro
A unitUm multiplicador de unidade (se um estiver sido adicionado)
A^BExponenciação (A elevado à potência B)
-AOperação unária de oposto
!AOperação lógica unária de negação (resulta em 11 se int(A) é 00, senão 00)
A*B A/B A%BMultiplicação, divisão e módulo
A+B A-BAdição e subtração
A=B A<B A<=B A!=B A>B A>=BComparação entre A e B (resulta em 11 ou 00)
A&BResulta em 11 se int(A) e int(B) forem diferentes de 00, senão 00
A|BResulta em 11 se int(A) ou int(B) forem diferentes de 00, senão 00

As funções matemáticas suportadas pela biblioteca, as quais podem ser utilizadas na construção de diagrama de blocos, são descritas na tabela abaixo:

ExpressãoDescrição
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 −π-\pi a π\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 22.
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 00, 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 ee) de A.
log2(A)Logaritmo na base 22 de A.
log10(A)Logaritmo na base 1010 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:

<nome da variável> := <expressão>; <função>

Por exemplo:

comprimento := sqrt(x*x+y*y); 2*comprimento*sin(comprimento)
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:

comprimento := sqrt(x*x+y*y);
2*comprimento*sin(comprimento)
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.

Formulário de edição de dados do bloco de expressão matemática no PSP-UFU

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.

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.

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.p.u. pode ser estimada de forma aproximada utilizando as potências ativa (PP) e reativa (QQ), assim como as reatâncias transitórias de eixo direto (xdx_d) e em quadratura (xqx_q) e o módulo da tensão terminal (VV) da máquina:

if≈(V+Q′)2+P2+(xdxq+1,0)×Q′(V+Q′)+P′2(V+Q′)2+P2i_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}}Q′(V+Q′)+P′2​

Em que:

  • P′=xq×PVP' = x_q \times \frac{P}{V}
  • Q′=xq×QVQ' = 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, todas as variáveis necessárias são fornecidas: PP, QQ e VV. Essas variáveis devem ser inseridas separadas por espaço: p q v.

Utilizando três blocos de entrada / saída pode-se fornecer tais dados ao conectá-los ao bloco de expressão matemática.

As reatâncias transitórias de eixo direto (xdx_d) e em quadratura (xqx_q) podem ser definidas diretamente na expressão matemática:

xd := 0.146;
xq := 0.0969;

Os valores de P′P' e Q′Q' podem ser também calculados:

yp := xq * p / v;
yq := xq * q / v;

Com todos os dados necessários pode-se calcular a corrente de campo:

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 ;):

i_f

Portanto, para as entradas definidas como p q v, a expressão matemática total para cálculo da corrente de campo será:

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

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Multiplicador

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.

Atenção!

Nós não conectados no multiplicador são assumidos com o valor unitário e para o divisor é considerado valor nulo.

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Multiplicador

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.

Atenção!

Nós não conectados no multiplicador são assumidos com o valor unitário e para o divisor é considerado valor nulo.

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Editor de Potência

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.

(Diagrama unifilar) Um diagrama do sistema no qual as linhas polifásicas são representados por sua única linha equivalente. tradução livre - IEC 60050.

Informação

Todos os elementos inseridos pode ser manipulados e editados utilizando as Ferramentas CAD.

Novo projeto

A criação de um novo projeto é realizada clicando no item Novo projeto no submenu Arquivo. Essa ação cria um sistema em branco na área de trabalho, local onde é possível inserir os elementos elétricos por meio do submenu Ferramentas ou pelas teclas de atalho.

Abaixo são apresentados os elementos elétricos de potência que podem ser inseridos no PSP-UFU:

Elementos de potência

Inserindo elementos

Por meio do submenu Ferramentas pode-se inserir os elementos de potência, como é apresentado na imagem abaixo.

Adicionar elementos de potência

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.

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.

Atenção

O primeiro elemento que a ser inserido no projeto deve ser um barramento. Os demais elementos elétricos devem ser conectados em uma ou mais barras.

Além dos elementos de potência pode-se inserir os elementos de texto vinculado, os quais estão associados a uma grandeza que se deseja vizualizar diretamente na Área de Trabalho.

Cuidado!

Ao inserir um barramento, a mesma irá acompanhar o ponteiro do mouse até que você clique na posição desejada. Para os demais elementos deve-se clicar em uma mais barras para exibir o elemento inserido.

Sempre fique atento às instruções da Barra de Status.

Teclas de atalho

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:

ElementoAtalhoElementoAtalho
BarramentoBCargaShift + L
LinhaLCapacitorShift + C
TransformadorTIndutorShift + I
GeradorGCorrente harmônicaShift + H
Motor de induçãoITextoA
Compensador síncronoK

Editando dados elétricos

Ao inserir um elemento, seu respectivo formulário de edição é exibido para inserção dos dados elétricos d elemento. Todos os dados podem ser alterados ao clicar duas vezes sobre o elemento ou por opção do menu de contexto exibido ao clicar com o botão direito sobre o elemento.

Cada formulário de edição de dados elétricos dos elementos possuem suas particularidades e são descritos em documentação específica: Barramento, Linha, Transformador, Carga, Capacitor, Indutor, Fonte de Corrente Harmônica, Gerador Síncrono, Compensador Síncrono, Motor de Indução.

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Editor de Potência

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.

(Diagrama unifilar) Um diagrama do sistema no qual as linhas polifásicas são representados por sua única linha equivalente. tradução livre - IEC 60050.

Informação

Todos os elementos inseridos pode ser manipulados e editados utilizando as Ferramentas CAD.

Novo projeto

A criação de um novo projeto é realizada clicando no item Novo projeto no submenu Arquivo. Essa ação cria um sistema em branco na área de trabalho, local onde é possível inserir os elementos elétricos por meio do submenu Ferramentas ou pelas teclas de atalho.

Abaixo são apresentados os elementos elétricos de potência que podem ser inseridos no PSP-UFU:

Elementos de potência

Inserindo elementos

Por meio do submenu Ferramentas pode-se inserir os elementos de potência, como é apresentado na imagem abaixo.

Adicionar elementos de potência

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.

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.

Atenção

O primeiro elemento que a ser inserido no projeto deve ser um barramento. Os demais elementos elétricos devem ser conectados em uma ou mais barras.

Além dos elementos de potência pode-se inserir os elementos de texto vinculado, os quais estão associados a uma grandeza que se deseja vizualizar diretamente na Área de Trabalho.

Cuidado!

Ao inserir um barramento, a mesma irá acompanhar o ponteiro do mouse até que você clique na posição desejada. Para os demais elementos deve-se clicar em uma mais barras para exibir o elemento inserido.

Sempre fique atento às instruções da Barra de Status.

Teclas de atalho

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:

ElementoAtalhoElementoAtalho
BarramentoBCargaShift + L
LinhaLCapacitorShift + C
TransformadorTIndutorShift + I
GeradorGCorrente harmônicaShift + H
Motor de induçãoITextoA
Compensador síncronoK

Editando dados elétricos

Ao inserir um elemento, seu respectivo formulário de edição é exibido para inserção dos dados elétricos d elemento. Todos os dados podem ser alterados ao clicar duas vezes sobre o elemento ou por opção do menu de contexto exibido ao clicar com o botão direito sobre o elemento.

Cada formulário de edição de dados elétricos dos elementos possuem suas particularidades e são descritos em documentação específica: Barramento, Linha, Transformador, Carga, Capacitor, Indutor, Fonte de Corrente Harmônica, Gerador Síncrono, Compensador Síncrono, Motor de Indução.

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Fluxo de Potência

Um estudo fundamental no planejamento da expansão e operação de um sistema elétrico é o fluxo de potência (ou fluxo de carga) uma vez que a operação satisfatória desse sistema depende do conhecimento dos efeitos da interligação, de novas cargas, de novas centrais geradoras e de novas linhas antes que elas sejam instaladas. Esse estudo tem como objetivo encontrar o fluxo de potência nos ramos e as tensões nodais do Sistema Elétrico de Potência (SEP) impostas pela geração e a carga.

As equações formuladas a partir dos modelos dos elementos presentes no estudo de fluxo de carga são não lineares e não possuem solução analítica explícita. Portanto é necessária a utilização de métodos numéricos iterativos para solução do problema de fluxo de carga.

Formulação do problema de fluxo de carga

O problema de fluxo de carga pode ser representado por um sistema de equações e inequações algébricas não-lineares que correspondem às leis de Kirchhoff e a um conjunto de restrições de operação impostos pelos componentes de uma rede elétrica. -Na formulação do problema a cada barra da rede são associadas quatro variáveis, sendo que duas delas surgem como dados e duas como incógnitas (em uma barra de índice ii):

  • ViV_i é a magnitude da tensão na barra ii;
  • θiθ_i é o ângulo da tensão na barra ii;
  • PiP_i é a injeção líquida de potência ativa na barra ii;
  • QiQ_i é a injeção líquida de potência reativa na barra ii.

Relativo às variáveis que são incógnitas e os dados do sistema, podem ser definidos três tipos de barras:

  • Barra PQ: PiP_i e QiQ_i são dados, ViV_i e θiθ_i são calculados;
  • Barra PV: PiP_i e ViV_i são dados, QiQ_i e θiθ_i são calculados;
  • Barra de Referência ViV_i e θiθ_i são dados, PiP_i e QiQ_i são calculados.
Informação

As barras PQ geralmente são representadas pelos barramentos de carga, os quais não há geração e controle de tensão.

As barras PV se caracterizam pelo controle de tensão mediante a injeção ou absorção de potência reativa por meio do controle da excitação de uma máquina síncrona.

A barra de Referência (ou de folga, de oscilação) tem como função, assim como o próprio nome diz, servir de referência de tensão e ângulo do sistema. Essa barra é necessariamente geradora, uma vez que ela é responsável pelo equilíbrio do balanço de potência do sistema.

Atenção!

O tipo de barra deve ser definido no elemento barramento.

Note que o sistema deve possuir somente uma barra de referência.

Como mencionado anteriormente, as equações são não-lineares e a solução analítica não é prática. As soluções dessas equações seguem processos iterativos, em que são atribuídos valores estimados (ou iniciais) para as barras com tensões desconhecidas e, baseado na potência ativa e reativa e módulo da tensão especificados, calcula-se por meio das equações previamente apresentadas as novas tensões complexas em cada nó do sistema.

Na sequência, esse conjunto de valores para as tensões em cada barra é utilizado para novamente calcular outro grupo de tensões. Cada cálculo de um novo conjunto de tensões é chamado iteração. O processo iterativo é repetido até que as mudanças em todas as barras sejam menores do que um valor pré-estipulado, obtendo assim a convergência.

Execução do fluxo de carga no PSP-UFU

Após a construção do diagrama unifilar no editor de potência, a execução do fluxo de carga é realizada no menu Simulação clicando no botão Fluxo de carga.

Menu Simulação
Dica

Caso o fluxo de carga tenha sido executado com sucesso, as setas de potência serão exibidas, a barra de status indicará sucesso na operação e os elementos de texto serão atualizados.

Outra possibilidade é a execução por meio do cálculo contínuo, também presente no menu Simulação e seu acionamento é realizado co clicar no botão Habilitar solução. Com essa opção, os cálculos estáticos selecionados nas configurações de simulação são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).

Atenção!

Evite construir o circuito com o cálculo contínuo habilitado, uma vez que configurações temporárias podem levar a erros de execução da simulação.

Para desabilitar o cálculo contínuo clique no botão Desabilitar solução.

Os resultados do fluxo de carga são exibidos nos elementos de texto vinculado, ao posicionar o mouse sobre os elementos e em relatórios tabulares.

Erros comuns na execução do fluxo de carga

A seguir são apresentados os erros mais comuns relacionados ao fluxo de carga.

A seguinte mensagem de erro é exibida: "O número máximo de iterações foi alcançado"

Essa mensagem de erro é exibida quando o método de solução numérica selecionado nas configurações de simulação atinge o número máximo de iterações inserido. As seguintes situações podem ocasionar esse erro:

  • Os parâmetros do circuito estão incorretos. caso parâmetros muito fora dos valores padrão dos elementos elétricos sejam inseridos, o cálculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente.
  • Algum elemento possui parâmetros discrepantes dos demais. Caso um dos elementos inseridos possua um valor de impedância muito distinto dos demais, como por exemplo uma linha com impedância muito elevada ou uma carga muito pequena, pode levar à divergência do método numérico. Nesse caso, reconsidere a necessidade de representação desses elementos no circuito e alterne entre os métodos numéricos de solução disponíveis.
  • O número máximo de iterações está muito baixo. Alguns circuitos exigem um número maior de iterações, portanto altere o valor do máximo de iterações nas configurações de simulação. Também tente alternar entre os métodos numéricos de solução disponíveis.
  • Os parâmetros de simulação estão inadequados. Caso um parâmetro do método de solução esteja inadequado, como fator de aceleração ou tolerância, o cálculo pode não alcançar a convergência. Altere esses parâmetros nas configurações de simulação.

Os dados de saída são exibidos como "NaN" ou "nan"

Isso ocorre devido a erros de operações matemáticas nos cálculos de fluxo de carga. "NaN" significa Not a Number.

  • Algum barramento está isolado. Esse erro é bastante comum e pode ocorrer ao inserir um barramento sem conectá-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solução é eliminar essa barra do diagrama.
  • Os parâmetros do circuito estão incorretos. caso parâmetros muito fora dos valores padrão dos elementos elétricos sejam inseridos, o cálculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente.
  • Algum elemento possui parâmetros discrepantes dos demais. Caso um dos elementos inseridos possua um valor de impedância muito distinto dos demais, como por exemplo uma linha com impedância muito elevada ou uma carga muito pequena, pode levar à divergência do método numérico. Nesse caso, reconsidere a necessidade de representação desses elementos no circuito e alterne entre os métodos numéricos de solução disponíveis.

Métodos de solução numérica do fluxo de carga no PSP-UFU

Os métodos implementados no programa para solução do problema de fluxo de carga no PSP-UFU são Gauss-Seidel (GS) e Newton-Raphson (NR). Além desses métodos clássicos, um método híbrido pode ser utilizado (definido nas configurações de simulação), em que é utilizado inicialmente o GS e na sequência o NR, aumentando a chance de convergência do NR.

Gauss-Seidel

O método de Gauss-Seidel tem sido bastante utilizado nas últimas décadas para solução do problema de fluxo de carga, uma vez que não há a necessidade de fatorar a matrizes, reduzindo o esforço computacional. Atualmente, restrições computacionais são menos problemáticas e outros métodos são normalmente escolhidos, porém o Gauss-Seidel ainda possui valor didático e, visto que o PSP-UFU também possui fins educacionais, optou-se pela implementação desse método.

Para iniciar as iterações do método são necessários valores iniciais para as tensões (V˙i0\dot{V}_i^0) que devem ser calculadas. Normalmente para barras do tipo PQ tem-se V˙i0=1,0+j0,0 p.u.\dot{V}_i^0=1{,}0+j0{,}0~p.u. e para barras do tipo PV V˙i0=Viesp+j0,0\dot{V}_i^0=V_i^{esp}+j0{,}0 [p.u.], em que ViespV_i^{esp} é o módulo da tensão especificada para a barra PV. A barra de referência tem o módulo e ângulo de tensão fixos e não participam no processo iterativo.

O método de Gauss-Seidel mostra um número excessivo de iterações e, com o intuito reduzi-los, multiplicam-se as correções de tensões por uma constante. Essa operação amplia o valor da correção, trazendo a tensão para mais perto do valor do valor final. Os multiplicadores que realizam essa convergência melhorada são chamados de fatores de aceleração. Para qualquer sistema existem valores ótimos para os fatores de aceleração e uma escolha inadequada pode resultar em uma convergência mais lenta ou torná-la impossível. Normalmente é utilizado um fator de aceleração igual a 1,6, valor definido como padrão no programa. A utilização do fator de aceleração é realizada por meio da equação:

V˙iAC(v+1)=α(V˙i(v+1)−V˙iAC(v))+V˙iAC(v)\dot{V}_{i_{AC}}^{(v + 1)} = \alpha \left( \dot{V}_{i}^{(v + 1)}- \dot{V}_{i_{AC}}^{(v)} \right) + \dot{V}_{i_{AC}}^{(v)}

Em que:

  • V˙iAC(v+1)\dot{V}_{i_{AC}}^{(v + 1)} é a tensão complexa da iteração atual com fator de aceleração aplicado
  • V˙i(v+1)\dot{V}_{i}^{(v + 1)} é a tensão complexa da iteração atual
  • V˙iAC(v)\dot{V}_{i_{AC}}^{(v)} é a tensão complexa da iteração anterior com fator de aceleração aplicado
  • α\alpha é o fator de aceleração

O fluxograma abaixo demonstra como o método de Gauss-Seidel foi implementado no PSP-UFU:

Método numérico de Gauss-Seidel para fluxo de carga

Newton-Raphson

O método de Newton-Raphson (também conhecido como método de Newton ou Newton-Fourier) para solução do fluxo de carga é descrito em vários livros e artigos. Atualmente é o algoritmo mais utilizado para solução do fluxo de carga. Para casos bem condicionados, esse método geralmente converge em 4 a 5 iterações, porém existe a possibilidade da técnica contornar o ponto da solução sem nunca atingi-la, o que também justifica implementação do método de Gauss-Seidel no software.

A expansão da série de Taylor para uma função de duas ou mais variáveis é a base do método de Newton-Raphson para resolver o problema do fluxo de carga. Fazendo a expansão em série de Taylor, para duas equações e duas incógnitas (f1(x1,x2)f_1\left( x_{1}, x_{2} \right) e f2(x1,x2)f_2\left( x_{1}, x_{2} \right)), sem listar as derivadas parciais maiores que 1 na forma matricial, obtêm-se:

[K1−f1(x1(0),x2(0))K2−f2(x1(0),x2(0))]=[∂f1∂x1∂f1∂x2∂f2∂x1∂f2∂x2][Δx1(0)Δx2(0)]\begin{bmatrix} K_1 - f_1\left( x_{1}^{(0)}, x_{2}^{(0)} \right)\\ K_2 - f_2\left( x_{1}^{(0)}, x_{2}^{(0)} \right) \end{bmatrix} = \begin{bmatrix} \displaystyle\frac{\partial f_1}{\partial x_1} & \displaystyle\frac{\partial f_1}{\partial x_2}\\ \displaystyle\frac{\partial f_2}{\partial x_1} & \displaystyle\frac{\partial f_2}{\partial x_2} \end{bmatrix} \begin{bmatrix} \Delta x_{1}^{(0)}\\ \Delta x_{2}^{(0)} \end{bmatrix}

Em que:

  • KK é o resultado da equação f(x1,x2)f\left( x_{1}, x_{2} \right)
  • x(0)x^{(0)} é a estimativa iniciais de xx
  • Δx\Delta x é o valor acrescido de x(0)x^{(0)} que resulta em xx, ou seja: f(x1,x2)=f1(x1(0)+Δx1,x2(0)+Δx2)f\left( x_{1}, x_{2} \right) = f_1\left( x_{1}^{(0)} + \Delta x_1, x_{2}^{(0)} + \Delta x_2 \right)

Essa expressão pode ser resumida em:

[ΔK1(0)ΔK2(0)]=[J](0)[Δx1(0)Δx2(0)]\begin{bmatrix} \Delta K_1^{(0)}\\ \Delta K_2^{(0)} \end{bmatrix} = \begin{bmatrix} J \end{bmatrix}^{(0)} \begin{bmatrix} \Delta x_{1}^{(0)}\\ \Delta x_{2}^{(0)} \end{bmatrix}

Em que [J][J] é a Matriz Jacobiana

Com a equação acima é possível calcular os valores de Δx1(0)\Delta x_{1}^{(0)} e Δx2(0)\Delta x_{2}^{(0)}. Entretanto, esses valores somados às estimativas iniciais não determinam a solução correta, sendo necessário repetir o processo de determinação das constantes, formação da matriz jacobiana e solução da equação acima, o qual será refeito determinando novas estimativas Δx1(1)\Delta x_{1}^{(1)} e Δx2(1)\Delta x_{2}^{(1)}.

Esse processo é repetido até que as correções se tornem tão pequenas que satisfaçam uma precisão escolhida.

Para aplicar o método de Newton-Raphson à solução das equações do fluxo de carga, utiliza-se as equações que representam as potências ativa e reativa injetadas em uma barra.

Assim como no método de Gauss-Seidel, a barra de referência é omitida da solução iterativa para determinar as tensões, pois a tensão complexa dessa barra é especificada. Como é conhecido o valor da potência ativa injetada (PiespP_i^{esp}) nas barras do tipo PQ e PV, além da potência reativa injetada (QiespQ_i^{esp}) nas barras PQ pode-se definir PiespP_i^{esp} e QiespQ_i^{esp} como os valores de KK. Os valores estimados do módulo e ângulo da tensão correspondem aos valores estimados para x1x_1 e x2x_2.

O jacobiano consiste nas derivadas parciais de PiP_i e QiQ_i em relação a cada uma das variáveis das equações injeção de potência líquida na barra ii. A matriz coluna formada por Δx1\Delta x_{1} e Δx2\Delta x_{2} corresponde às correções de ângulo (Δθi\Delta \theta_i) e módulo (ΔVi\Delta V_i) das tensões de barra.

Com isso pode-se escrever a equação matricial de um sistema de nn barras, em que a barra número 1 corresponde à barra de referência e as barras de número 2 a n são barras do tipo PQ:

NPQ+NPV{   NPQ{  [ΔP2⋮ΔPnΔQ2⋮ΔQn]=[∂P2∂θ2…∂P2∂θn∂P2∂V2…∂P2∂Vn⋮⋱⋮⋮⋱⋮∂Pn∂θ2…∂Pn∂θn∂Pn∂V2…∂Pn∂Vn∂Q2∂θ2…∂Q2∂θn∂Q2∂V2…∂Q2∂Vn⋮⋱⋮⋮⋱⋮∂Qn∂θ2…∂Qn∂θn∂Qn∂V2…∂Qn∂Vn][Δθ2⋮Δθ2ΔV2⋮ΔVn]\begin{array}{r} \text{NPQ} + \text{NPV} \begin{cases} ~\\ ~ \end{cases}\\ ~\\ \text{NPQ} \begin{cases} ~\\ ~ \end{cases} \end{array} \begin{bmatrix} \Delta P_2\\ \vdots\\ \Delta P_n\\ \Delta Q_2\\ \vdots\\ \Delta Q_n\\ \end{bmatrix} = \begin{bmatrix} \displaystyle\frac{\partial P_2}{\partial \theta_2} & \dots & \displaystyle\frac{\partial P_2}{\partial \theta_n} & \displaystyle\frac{\partial P_2}{\partial V_2} & \dots & \displaystyle\frac{\partial P_2}{\partial V_n}\\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots\\ \displaystyle\frac{\partial P_n}{\partial \theta_2} & \dots & \displaystyle\frac{\partial P_n}{\partial \theta_n} & \displaystyle\frac{\partial P_n}{\partial V_2} & \dots & \displaystyle\frac{\partial P_n}{\partial V_n}\\ \displaystyle\frac{\partial Q_2}{\partial \theta_2} & \dots & \displaystyle\frac{\partial Q_2}{\partial \theta_n} & \displaystyle\frac{\partial Q_2}{\partial V_2} & \dots & \displaystyle\frac{\partial Q_2}{\partial V_n}\\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots\\ \displaystyle\frac{\partial Q_n}{\partial \theta_2} & \dots & \displaystyle\frac{\partial Q_n}{\partial \theta_n} & \displaystyle\frac{\partial Q_n}{\partial V_2} & \dots & \displaystyle\frac{\partial Q_n}{\partial V_n} \end{bmatrix} \begin{bmatrix} \Delta \theta_2\\ \vdots\\ \Delta \theta_2\\ \Delta V_2\\ \vdots\\ \Delta V_n\\ \end{bmatrix}

Em que:

  • NPQ\text{NPQ} é o número de barras PQ
  • NPV\text{NPV} é o número de barras PV

O processo iterativo se inicia calculando as potências ativas (PicalcP_i^{calc}) para as barras PQ e PV e as potências reativas (QicalcQ_i^{calc}) para as barras PQ, ambas as equações utilizando as estimativas iniciais das tensões complexas. Calcula-se, então, as correções de potência (ΔP\Delta P e ΔQ\Delta Q):

ΔP=Piesp−PicalcΔQ=Qiesp−Qicalc\Delta P = P_i^{esp} - P_i^{calc}\\ \Delta Q = Q_i^{esp} - Q_i^{calc}

O passo seguinte é a formação da matriz jacobiana. Com isso é possível calcular as correções de módulo e ângulo das tensões de todas as barras (com exceção da barra de referência). Para tanto, no PSP-UFU utiliza-se o método de Eliminação Gaussiana e em sequência a substituição regressiva. Esse procedimento diminui o esforço computacional, uma vez que a inversão da matriz jacobiana em todas as iterações é evitada.

Com as correções de módulo e ângulo das tensões das barras calculados, aplicam-se as seguintes equações:

θi(v+1)=θi(v)+Δθi(v)Vi(v+1)=Vi(v)+ΔVi(v)\theta_i^{(v+1)}=\theta_i^{(v)}+\Delta \theta_i^{(v)}\\ V_i^{(v+1)}=V_i^{(v)}+\Delta V_i^{(v)}

O processo é então reiniciado e será repetido até que se obtenha a convergência, quando as correções se tornam tão pequenas que satisfaçam uma tolerância pré-estipulada.

O fluxograma abaixo mostra o método de Newton-Raphson para solução do fluxo de carga implementado.

Método numérico de Newton-Raphson para fluxo de carga

Controles e limites em um problema de fluxo de carga

Nas barras de geração e também naquelas em que se encontra um compensador síncrono conectado, o controle da magnitude da tensão no barramento é realizado por meio do ajuste da corrente de campo das máquinas síncronas, as quais podem operar sobrexcitadas (injetando reativos) ou subexcitadas (absorvendo reativos). Os valores limites de potência reativa que podem ser injetadas ou absorvidas dependem da máquina síncrona em estudo. Esses limites são incluídos no fluxo de carga com a criação de dois novos parâmetros, a potência reativa máxima (QimaˊxQ_i^{máx}) e potência reativa mínima (QiminQ_i^{min}), sendo esses valores a soma dos limites individuais das máquinas em uma mesma barra genérica ii.

A manutenção da potência reativa dentro dos limites é realizada pela troca do tipo de barra, ou seja, as barras violadoras que controlam a tensão (PV), passam a ser barras de carga (PQ), cuja potência é fixada como o limite que seria ultrapassado (QimaˊxQ_i^{máx} ou QiminQ_i^{min}) e a tensão deixa de ser controlada partir de então.

A verificação de violação e troca de tipo de barra pode ser realizada a cada iteração ou ao final da convergência do cálculo. No PSP-UFU foi implementada a última estratégia, uma vez que separa os conceitos de cálculo e de verificação de limites, tornando mais fácil o desenvolvimento de novos métodos numéricos e limites. Nessa abordagem, ao ajustar o sistema para a nova situação não violadora o cálculo iterativo deve ser retomado até que obtenha novamente a convergência.

Referências

  1. MONTICELLI, A. J. Fluxo de Carga em Redes de Energia Elétrica. São Paulo: Edgar Blücher, 1983.
  2. STEVENSON JR.; WILLIAN, D. Elementos de Análise de Sistemas de Potência. 2ª ed. São Paulo: McGraw-Hill, 1986.
  3. MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: https://doi.org/10.1007/978-3-642-13669-6
  4. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
  5. TINNEY, W. F.; HART, C. E. Power Flow Solution by Newton’s Method. IEEE Transaction on Power Apparatus and Systems, v. PAS-86, n. 11, nov. 1967. doi: https://doi.org/10.1109/TPAS.1967.291823
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Fluxo de Potência

Um estudo fundamental no planejamento da expansão e operação de um sistema elétrico é o fluxo de potência (ou fluxo de carga) uma vez que a operação satisfatória desse sistema depende do conhecimento dos efeitos da interligação, de novas cargas, de novas centrais geradoras e de novas linhas antes que elas sejam instaladas. Esse estudo tem como objetivo encontrar o fluxo de potência nos ramos e as tensões nodais do Sistema Elétrico de Potência (SEP) impostas pela geração e a carga.

As equações formuladas a partir dos modelos dos elementos presentes no estudo de fluxo de carga são não lineares e não possuem solução analítica explícita. Portanto é necessária a utilização de métodos numéricos iterativos para solução do problema de fluxo de carga.

Formulação do problema de fluxo de carga

O problema de fluxo de carga pode ser representado por um sistema de equações e inequações algébricas não-lineares que correspondem às leis de Kirchhoff e a um conjunto de restrições de operação impostos pelos componentes de uma rede elétrica. +Na formulação do problema a cada barra da rede são associadas quatro variáveis, sendo que duas delas surgem como dados e duas como incógnitas (em uma barra de índice ii):

  • ViV_i é a magnitude da tensão na barra ii;
  • θiθ_i é o ângulo da tensão na barra ii;
  • PiP_i é a injeção líquida de potência ativa na barra ii;
  • QiQ_i é a injeção líquida de potência reativa na barra ii.

Relativo às variáveis que são incógnitas e os dados do sistema, podem ser definidos três tipos de barras:

  • Barra PQ: PiP_i e QiQ_i são dados, ViV_i e θiθ_i são calculados;
  • Barra PV: PiP_i e ViV_i são dados, QiQ_i e θiθ_i são calculados;
  • Barra de Referência ViV_i e θiθ_i são dados, PiP_i e QiQ_i são calculados.
Informação

As barras PQ geralmente são representadas pelos barramentos de carga, os quais não há geração e controle de tensão.

As barras PV se caracterizam pelo controle de tensão mediante a injeção ou absorção de potência reativa por meio do controle da excitação de uma máquina síncrona.

A barra de Referência (ou de folga, de oscilação) tem como função, assim como o próprio nome diz, servir de referência de tensão e ângulo do sistema. Essa barra é necessariamente geradora, uma vez que ela é responsável pelo equilíbrio do balanço de potência do sistema.

Atenção!

O tipo de barra deve ser definido no elemento barramento.

Note que o sistema deve possuir somente uma barra de referência.

Como mencionado anteriormente, as equações são não-lineares e a solução analítica não é prática. As soluções dessas equações seguem processos iterativos, em que são atribuídos valores estimados (ou iniciais) para as barras com tensões desconhecidas e, baseado na potência ativa e reativa e módulo da tensão especificados, calcula-se por meio das equações previamente apresentadas as novas tensões complexas em cada nó do sistema.

Na sequência, esse conjunto de valores para as tensões em cada barra é utilizado para novamente calcular outro grupo de tensões. Cada cálculo de um novo conjunto de tensões é chamado iteração. O processo iterativo é repetido até que as mudanças em todas as barras sejam menores do que um valor pré-estipulado, obtendo assim a convergência.

Execução do fluxo de carga no PSP-UFU

Após a construção do diagrama unifilar no editor de potência, a execução do fluxo de carga é realizada no menu Simulação clicando no botão Fluxo de carga.

Menu Simulação
Dica

Caso o fluxo de carga tenha sido executado com sucesso, as setas de potência serão exibidas, a barra de status indicará sucesso na operação e os elementos de texto serão atualizados.

Outra possibilidade é a execução por meio do cálculo contínuo, também presente no menu Simulação e seu acionamento é realizado co clicar no botão Habilitar solução. Com essa opção, os cálculos estáticos selecionados nas configurações de simulação são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).

Atenção!

Evite construir o circuito com o cálculo contínuo habilitado, uma vez que configurações temporárias podem levar a erros de execução da simulação.

Para desabilitar o cálculo contínuo clique no botão Desabilitar solução.

Os resultados do fluxo de carga são exibidos nos elementos de texto vinculado, ao posicionar o mouse sobre os elementos e em relatórios tabulares.

Erros comuns na execução do fluxo de carga

A seguir são apresentados os erros mais comuns relacionados ao fluxo de carga.

A seguinte mensagem de erro é exibida: "O número máximo de iterações foi alcançado"

Essa mensagem de erro é exibida quando o método de solução numérica selecionado nas configurações de simulação atinge o número máximo de iterações inserido. As seguintes situações podem ocasionar esse erro:

  • Os parâmetros do circuito estão incorretos. caso parâmetros muito fora dos valores padrão dos elementos elétricos sejam inseridos, o cálculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente.
  • Algum elemento possui parâmetros discrepantes dos demais. Caso um dos elementos inseridos possua um valor de impedância muito distinto dos demais, como por exemplo uma linha com impedância muito elevada ou uma carga muito pequena, pode levar à divergência do método numérico. Nesse caso, reconsidere a necessidade de representação desses elementos no circuito e alterne entre os métodos numéricos de solução disponíveis.
  • O número máximo de iterações está muito baixo. Alguns circuitos exigem um número maior de iterações, portanto altere o valor do máximo de iterações nas configurações de simulação. Também tente alternar entre os métodos numéricos de solução disponíveis.
  • Os parâmetros de simulação estão inadequados. Caso um parâmetro do método de solução esteja inadequado, como fator de aceleração ou tolerância, o cálculo pode não alcançar a convergência. Altere esses parâmetros nas configurações de simulação.

Os dados de saída são exibidos como "NaN" ou "nan"

Isso ocorre devido a erros de operações matemáticas nos cálculos de fluxo de carga. "NaN" significa Not a Number.

  • Algum barramento está isolado. Esse erro é bastante comum e pode ocorrer ao inserir um barramento sem conectá-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solução é eliminar essa barra do diagrama.
  • Os parâmetros do circuito estão incorretos. caso parâmetros muito fora dos valores padrão dos elementos elétricos sejam inseridos, o cálculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente.
  • Algum elemento possui parâmetros discrepantes dos demais. Caso um dos elementos inseridos possua um valor de impedância muito distinto dos demais, como por exemplo uma linha com impedância muito elevada ou uma carga muito pequena, pode levar à divergência do método numérico. Nesse caso, reconsidere a necessidade de representação desses elementos no circuito e alterne entre os métodos numéricos de solução disponíveis.

Métodos de solução numérica do fluxo de carga no PSP-UFU

Os métodos implementados no programa para solução do problema de fluxo de carga no PSP-UFU são Gauss-Seidel (GS) e Newton-Raphson (NR). Além desses métodos clássicos, um método híbrido pode ser utilizado (definido nas configurações de simulação), em que é utilizado inicialmente o GS e na sequência o NR, aumentando a chance de convergência do NR.

Gauss-Seidel

O método de Gauss-Seidel tem sido bastante utilizado nas últimas décadas para solução do problema de fluxo de carga, uma vez que não há a necessidade de fatorar a matrizes, reduzindo o esforço computacional. Atualmente, restrições computacionais são menos problemáticas e outros métodos são normalmente escolhidos, porém o Gauss-Seidel ainda possui valor didático e, visto que o PSP-UFU também possui fins educacionais, optou-se pela implementação desse método.

Para iniciar as iterações do método são necessários valores iniciais para as tensões (V˙i0\dot{V}_i^0) que devem ser calculadas. Normalmente para barras do tipo PQ tem-se V˙i0=1,0+j0,0 p.u.\dot{V}_i^0=1{,}0+j0{,}0~p.u. e para barras do tipo PV V˙i0=Viesp+j0,0\dot{V}_i^0=V_i^{esp}+j0{,}0 [p.u.], em que ViespV_i^{esp} é o módulo da tensão especificada para a barra PV. A barra de referência tem o módulo e ângulo de tensão fixos e não participam no processo iterativo.

O método de Gauss-Seidel mostra um número excessivo de iterações e, com o intuito reduzi-los, multiplicam-se as correções de tensões por uma constante. Essa operação amplia o valor da correção, trazendo a tensão para mais perto do valor do valor final. Os multiplicadores que realizam essa convergência melhorada são chamados de fatores de aceleração. Para qualquer sistema existem valores ótimos para os fatores de aceleração e uma escolha inadequada pode resultar em uma convergência mais lenta ou torná-la impossível. Normalmente é utilizado um fator de aceleração igual a 1,6, valor definido como padrão no programa. A utilização do fator de aceleração é realizada por meio da equação:

V˙iAC(v+1)=α(V˙i(v+1)−V˙iAC(v))+V˙iAC(v)\dot{V}_{i_{AC}}^{(v + 1)} = \alpha \left( \dot{V}_{i}^{(v + 1)}- \dot{V}_{i_{AC}}^{(v)} \right) + \dot{V}_{i_{AC}}^{(v)}

Em que:

  • V˙iAC(v+1)\dot{V}_{i_{AC}}^{(v + 1)} é a tensão complexa da iteração atual com fator de aceleração aplicado
  • V˙i(v+1)\dot{V}_{i}^{(v + 1)} é a tensão complexa da iteração atual
  • V˙iAC(v)\dot{V}_{i_{AC}}^{(v)} é a tensão complexa da iteração anterior com fator de aceleração aplicado
  • α\alpha é o fator de aceleração

O fluxograma abaixo demonstra como o método de Gauss-Seidel foi implementado no PSP-UFU:

Método numérico de Gauss-Seidel para fluxo de carga

Newton-Raphson

O método de Newton-Raphson (também conhecido como método de Newton ou Newton-Fourier) para solução do fluxo de carga é descrito em vários livros e artigos. Atualmente é o algoritmo mais utilizado para solução do fluxo de carga. Para casos bem condicionados, esse método geralmente converge em 4 a 5 iterações, porém existe a possibilidade da técnica contornar o ponto da solução sem nunca atingi-la, o que também justifica implementação do método de Gauss-Seidel no software.

A expansão da série de Taylor para uma função de duas ou mais variáveis é a base do método de Newton-Raphson para resolver o problema do fluxo de carga. Fazendo a expansão em série de Taylor, para duas equações e duas incógnitas (f1(x1,x2)f_1\left( x_{1}, x_{2} \right) e f2(x1,x2)f_2\left( x_{1}, x_{2} \right)), sem listar as derivadas parciais maiores que 1 na forma matricial, obtêm-se:

[K1−f1(x1(0),x2(0))K2−f2(x1(0),x2(0))]=[∂f1∂x1∂f1∂x2∂f2∂x1∂f2∂x2][Δx1(0)Δx2(0)]\begin{bmatrix} K_1 - f_1\left( x_{1}^{(0)}, x_{2}^{(0)} \right)\\ K_2 - f_2\left( x_{1}^{(0)}, x_{2}^{(0)} \right) \end{bmatrix} = \begin{bmatrix} \displaystyle\frac{\partial f_1}{\partial x_1} & \displaystyle\frac{\partial f_1}{\partial x_2}\\ \displaystyle\frac{\partial f_2}{\partial x_1} & \displaystyle\frac{\partial f_2}{\partial x_2} \end{bmatrix} \begin{bmatrix} \Delta x_{1}^{(0)}\\ \Delta x_{2}^{(0)} \end{bmatrix}

Em que:

  • KK é o resultado da equação f(x1,x2)f\left( x_{1}, x_{2} \right)
  • x(0)x^{(0)} é a estimativa iniciais de xx
  • Δx\Delta x é o valor acrescido de x(0)x^{(0)} que resulta em xx, ou seja: f(x1,x2)=f1(x1(0)+Δx1,x2(0)+Δx2)f\left( x_{1}, x_{2} \right) = f_1\left( x_{1}^{(0)} + \Delta x_1, x_{2}^{(0)} + \Delta x_2 \right)

Essa expressão pode ser resumida em:

[ΔK1(0)ΔK2(0)]=[J](0)[Δx1(0)Δx2(0)]\begin{bmatrix} \Delta K_1^{(0)}\\ \Delta K_2^{(0)} \end{bmatrix} = \begin{bmatrix} J \end{bmatrix}^{(0)} \begin{bmatrix} \Delta x_{1}^{(0)}\\ \Delta x_{2}^{(0)} \end{bmatrix}

Em que [J][J] é a Matriz Jacobiana

Com a equação acima é possível calcular os valores de Δx1(0)\Delta x_{1}^{(0)} e Δx2(0)\Delta x_{2}^{(0)}. Entretanto, esses valores somados às estimativas iniciais não determinam a solução correta, sendo necessário repetir o processo de determinação das constantes, formação da matriz jacobiana e solução da equação acima, o qual será refeito determinando novas estimativas Δx1(1)\Delta x_{1}^{(1)} e Δx2(1)\Delta x_{2}^{(1)}.

Esse processo é repetido até que as correções se tornem tão pequenas que satisfaçam uma precisão escolhida.

Para aplicar o método de Newton-Raphson à solução das equações do fluxo de carga, utiliza-se as equações que representam as potências ativa e reativa injetadas em uma barra.

Assim como no método de Gauss-Seidel, a barra de referência é omitida da solução iterativa para determinar as tensões, pois a tensão complexa dessa barra é especificada. Como é conhecido o valor da potência ativa injetada (PiespP_i^{esp}) nas barras do tipo PQ e PV, além da potência reativa injetada (QiespQ_i^{esp}) nas barras PQ pode-se definir PiespP_i^{esp} e QiespQ_i^{esp} como os valores de KK. Os valores estimados do módulo e ângulo da tensão correspondem aos valores estimados para x1x_1 e x2x_2.

O jacobiano consiste nas derivadas parciais de PiP_i e QiQ_i em relação a cada uma das variáveis das equações injeção de potência líquida na barra ii. A matriz coluna formada por Δx1\Delta x_{1} e Δx2\Delta x_{2} corresponde às correções de ângulo (Δθi\Delta \theta_i) e módulo (ΔVi\Delta V_i) das tensões de barra.

Com isso pode-se escrever a equação matricial de um sistema de nn barras, em que a barra número 1 corresponde à barra de referência e as barras de número 2 a n são barras do tipo PQ:

NPQ+NPV{   NPQ{  [ΔP2⋮ΔPnΔQ2⋮ΔQn]=[∂P2∂θ2…∂P2∂θn∂P2∂V2…∂P2∂Vn⋮⋱⋮⋮⋱⋮∂Pn∂θ2…∂Pn∂θn∂Pn∂V2…∂Pn∂Vn∂Q2∂θ2…∂Q2∂θn∂Q2∂V2…∂Q2∂Vn⋮⋱⋮⋮⋱⋮∂Qn∂θ2…∂Qn∂θn∂Qn∂V2…∂Qn∂Vn][Δθ2⋮Δθ2ΔV2⋮ΔVn]\begin{array}{r} \text{NPQ} + \text{NPV} \begin{cases} ~\\ ~ \end{cases}\\ ~\\ \text{NPQ} \begin{cases} ~\\ ~ \end{cases} \end{array} \begin{bmatrix} \Delta P_2\\ \vdots\\ \Delta P_n\\ \Delta Q_2\\ \vdots\\ \Delta Q_n\\ \end{bmatrix} = \begin{bmatrix} \displaystyle\frac{\partial P_2}{\partial \theta_2} & \dots & \displaystyle\frac{\partial P_2}{\partial \theta_n} & \displaystyle\frac{\partial P_2}{\partial V_2} & \dots & \displaystyle\frac{\partial P_2}{\partial V_n}\\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots\\ \displaystyle\frac{\partial P_n}{\partial \theta_2} & \dots & \displaystyle\frac{\partial P_n}{\partial \theta_n} & \displaystyle\frac{\partial P_n}{\partial V_2} & \dots & \displaystyle\frac{\partial P_n}{\partial V_n}\\ \displaystyle\frac{\partial Q_2}{\partial \theta_2} & \dots & \displaystyle\frac{\partial Q_2}{\partial \theta_n} & \displaystyle\frac{\partial Q_2}{\partial V_2} & \dots & \displaystyle\frac{\partial Q_2}{\partial V_n}\\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots\\ \displaystyle\frac{\partial Q_n}{\partial \theta_2} & \dots & \displaystyle\frac{\partial Q_n}{\partial \theta_n} & \displaystyle\frac{\partial Q_n}{\partial V_2} & \dots & \displaystyle\frac{\partial Q_n}{\partial V_n} \end{bmatrix} \begin{bmatrix} \Delta \theta_2\\ \vdots\\ \Delta \theta_2\\ \Delta V_2\\ \vdots\\ \Delta V_n\\ \end{bmatrix}

Em que:

  • NPQ\text{NPQ} é o número de barras PQ
  • NPV\text{NPV} é o número de barras PV

O processo iterativo se inicia calculando as potências ativas (PicalcP_i^{calc}) para as barras PQ e PV e as potências reativas (QicalcQ_i^{calc}) para as barras PQ, ambas as equações utilizando as estimativas iniciais das tensões complexas. Calcula-se, então, as correções de potência (ΔP\Delta P e ΔQ\Delta Q):

ΔP=Piesp−PicalcΔQ=Qiesp−Qicalc\Delta P = P_i^{esp} - P_i^{calc}\\ \Delta Q = Q_i^{esp} - Q_i^{calc}

O passo seguinte é a formação da matriz jacobiana. Com isso é possível calcular as correções de módulo e ângulo das tensões de todas as barras (com exceção da barra de referência). Para tanto, no PSP-UFU utiliza-se o método de Eliminação Gaussiana e em sequência a substituição regressiva. Esse procedimento diminui o esforço computacional, uma vez que a inversão da matriz jacobiana em todas as iterações é evitada.

Com as correções de módulo e ângulo das tensões das barras calculados, aplicam-se as seguintes equações:

θi(v+1)=θi(v)+Δθi(v)Vi(v+1)=Vi(v)+ΔVi(v)\theta_i^{(v+1)}=\theta_i^{(v)}+\Delta \theta_i^{(v)}\\ V_i^{(v+1)}=V_i^{(v)}+\Delta V_i^{(v)}

O processo é então reiniciado e será repetido até que se obtenha a convergência, quando as correções se tornam tão pequenas que satisfaçam uma tolerância pré-estipulada.

O fluxograma abaixo mostra o método de Newton-Raphson para solução do fluxo de carga implementado.

Método numérico de Newton-Raphson para fluxo de carga

Controles e limites em um problema de fluxo de carga

Nas barras de geração e também naquelas em que se encontra um compensador síncrono conectado, o controle da magnitude da tensão no barramento é realizado por meio do ajuste da corrente de campo das máquinas síncronas, as quais podem operar sobrexcitadas (injetando reativos) ou subexcitadas (absorvendo reativos). Os valores limites de potência reativa que podem ser injetadas ou absorvidas dependem da máquina síncrona em estudo. Esses limites são incluídos no fluxo de carga com a criação de dois novos parâmetros, a potência reativa máxima (QimaˊxQ_i^{máx}) e potência reativa mínima (QiminQ_i^{min}), sendo esses valores a soma dos limites individuais das máquinas em uma mesma barra genérica ii.

A manutenção da potência reativa dentro dos limites é realizada pela troca do tipo de barra, ou seja, as barras violadoras que controlam a tensão (PV), passam a ser barras de carga (PQ), cuja potência é fixada como o limite que seria ultrapassado (QimaˊxQ_i^{máx} ou QiminQ_i^{min}) e a tensão deixa de ser controlada partir de então.

A verificação de violação e troca de tipo de barra pode ser realizada a cada iteração ou ao final da convergência do cálculo. No PSP-UFU foi implementada a última estratégia, uma vez que separa os conceitos de cálculo e de verificação de limites, tornando mais fácil o desenvolvimento de novos métodos numéricos e limites. Nessa abordagem, ao ajustar o sistema para a nova situação não violadora o cálculo iterativo deve ser retomado até que obtenha novamente a convergência.

Referências

  1. MONTICELLI, A. J. Fluxo de Carga em Redes de Energia Elétrica. São Paulo: Edgar Blücher, 1983.
  2. STEVENSON JR.; WILLIAN, D. Elementos de Análise de Sistemas de Potência. 2ª ed. São Paulo: McGraw-Hill, 1986.
  3. MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: https://doi.org/10.1007/978-3-642-13669-6
  4. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
  5. TINNEY, W. F.; HART, C. E. Power Flow Solution by Newton’s Method. IEEE Transaction on Power Apparatus and Systems, v. PAS-86, n. 11, nov. 1967. doi: https://doi.org/10.1109/TPAS.1967.291823
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Limitador de taxa

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 (rr) é calculada de acordo com a equação:

r=un−yn−1hr = \frac{u_n - y_{n-1}}{h}

Em que:

  • unu_n é a entrada atual do bloco
  • yn−1y_{n-1} é o valor de saída anterior do bloco
  • hh é o passo de integração

Obtida a taxa, o bloco irá resultar em um valor calculado pelas seguintes condições:

{h×Rcre,se r>Rcreun,se Rdec≤r≤Rcreh×Rdec,se r<Rdec\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:

  • RcreR_{cre} e RdecR_{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.

Formulário de edição de dados do bloco limitador de taxa no PSP-UFU

Esse bloco é definido pelo limite superior (taxa de crescimento máxima) e inferior (taxa de decrescimento máxima), inseridos pelo usuário.

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.

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Limitador de taxa

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 (rr) é calculada de acordo com a equação:

r=un−yn−1hr = \frac{u_n - y_{n-1}}{h}

Em que:

  • unu_n é a entrada atual do bloco
  • yn−1y_{n-1} é o valor de saída anterior do bloco
  • hh é o passo de integração

Obtida a taxa, o bloco irá resultar em um valor calculado pelas seguintes condições:

{h×Rcre,se r>Rcreun,se Rdec≤r≤Rcreh×Rdec,se r<Rdec\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:

  • RcreR_{cre} e RdecR_{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.

Formulário de edição de dados do bloco limitador de taxa no PSP-UFU

Esse bloco é definido pelo limite superior (taxa de crescimento máxima) e inferior (taxa de decrescimento máxima), inseridos pelo usuário.

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.

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Configurações da Simulação

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Configurações da Simulação

As parametrizações e configurações das simulações são acessadas no menu Simulação clicando no ícone do botão Configurações de simulação.

Menu Simulação

Formulário de edição das configurações de simulação

A imagem abaixo apresenta o formulário de edição das configurações de simulação:

Configurações de simulação

Esse formulário é subdividido em quatro contextos distintos:

Potência base

Potência base do sistema utilizada para conversão dos dados reais em p.u.p.u. e vice-versa. Pode ser inserido em VA, kVA ou MVA.

Dica

A potência base de cada elemento pode ser distinta da potência base do sistema. Para isso, basta marcar a opção "Utilizar potência nominal [do elemento] como base", presente em seus respectivos formulários de edição da dados.

Frequência do sistema

Define a frequência nominal do sistema.

Cuidado!

Ao alterar a frequência nominal atente-se ao campo "Frequência de circuito aberto" das máquinas síncronas.

Cálculo contínuo

Habilita ou desabilita o cálculo contínuo para os cálculos de curto-circuito, nível de curto-circuito e distorções harmônicas. O cálculo contínuo para o fluxo de carga é sempre habilitado.

Dica

Para habilitar o cálculo contínuo aperte o botão Habilitar solução presente no menu Simulação.

Com essa opção, os cálculos estáticos selecionados são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).

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Estabilidade

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Estabilidade

Estabilidade de sistemas de potência é a habilidade de um Sistema Elétrico de Potência (SEP), para uma certa condição de operação, de reestabelecer um estado de operação de equilíbrio após ser submetido a um distúrbio físico. A estabilidade é reconhecida como um importante problema para a segurança da operação desde a década de 1920. Muitos blackouts de grande porte causados pela instabilidade do SEP têm ilustrado a importância desse fenômeno.

Estabilidade

Normalmente são realizados dois tipos de estudos de estabilidade (uma classificação mais aprofundada pode ser observada nesse artigo). A recuperação de uma rápida e brusca perturbação é chamada de estabilidade transitória, e sua solução é geralmente obtida no domínio do tempo. Outro estudo é denominado estabilidade dinâmica, utilizado para descrever a resposta do sistema frente a pequenas perturbações ao longo de muito tempo, o qual pode ser resolvido tanto no domínio da frequência quanto no domínio do tempo.

Informação

No PSP-UFU, a estabilidade dinâmica é tratada como uma extensão da estabilidade transitória, em que os efeitos de pequenas constantes de tempo devem ser ignorados.

O modelo para representação do SEP em um estudo de estabilidade transitória é feito por meio do sistema de equações algébrico-diferenciais (EADs), em que o estado inicial é considerado estável e originado de um estudo de fluxo de carga. A solução das equações se dá por meio de um método de integração numérica e, então, é observada a resposta do sistema de potência.

Caso a solução no domínio do tempo, após alguma perturbação, leve um ou mais parâmetros do sistema a valores fisicamente impossíveis ou, até mesmo, a solução das equações diferenciais não obtenha convergência em processos iterativos, o sistema é dito instável. Em contrapartida, caso as variáveis de estado dos elementos do sistema oscilem após uma perturbação e se estabeleçam em um novo ponto de operação, mesmo que distinto dos valores iniciais, o sistema é considerado estável.

Execução do estudo de estabilidade no PSP-UFU

Após a construção do diagrama unifilar no editor de potência, assim como os controles das máquinas síncronas, a execução da estabilidade é realizada no menu Simulação clicando no ícone do botão Executar Estabilidade. Ao clicar na parte inferior do botão "Executar Estabilidade" será exibido um menu suspenso com a opção Lista de eventos de estabilidade.

Menu Simulação

Ao executar o cálculo de estabilidade, uma caixa com o status do processo de simulação será exibida, indicando primeiramente a inicialização do estudo e posteriormente o tempo de simulação calculado.

Ao clicar na lista de eventos de estabilidade, será exibida uma janela com a descrição dos eventos de estabilidade inseridos.

Lista de eventos de estabilidade

Inserindo um evento de estabilidade

Os distúrbios mais comuns aplicados em estudos de estabilidade transitória são faltas e chaveamentos. Tais operações são facilmente realizadas no PSP-UFU:

  • Faltas: Curtos-circuitos trifásicos podem ser inseridos nos barramentos do sistema por meio da inclusão da impedância de falta na matriz admitância de barras da mesma maneira realizada em um elemento shunt. Tal valor é definido pelo usuário e caso seja um curto-circuito franco, um valor não nulo, mas suficientemente próximo de zero, é aplicado, de forma que a tensão no barramento é levada a zero durante o distúrbio.

  • Chaveamento de ramo: Da mesma forma que as faltas, o chaveamento de ramos é realizado por meio da alteração na matriz admitância, removendo ou inserindo os parâmetros do elemento a ser chaveado. +Cada elemento de potência possui um botão de "Chaveamento" ou "Estabilidade", em que pode ser inserido os tempos de remoção e/ou inserção do componente.

  • Chaveamento de máquinas: A remoção de uma máquina síncrona é efetivada com a retirada de sua participação no vetor de correntes, além da remoção de sua admitância fictícia. +Assim como os elementos de potência, as máquinas síncronas possui um botão "Chaveamento", em que pode ser inserido os tempos de remoção e/ou inserção do componente.

    Atenção!

    Mesmo que removida da barra, os parâmetros das máquinas síncronas continuam a ser calculados com a corrente do estator nula, podendo fornecer resultados em uma eventual reconexão.

Dica

Eventos nos sistemas de controle podem ser facilmente introduzidos com o bloco de expressão matemática. Nesse caso, tais eventos não serão exibidos na lista de eventos de estabilidade.

Erros comuns na execução do estudo de estabilidade

A seguir são apresentados os erros mais comuns relacionados ao estudo de estabilidade.

A seguinte mensagem de erro é exibida: "Não foi possível construir a matriz admitância"

Essa mensagem de erro é exibida quando não é possível construir a matriz admitância de barras. As seguintes situações podem ocasionar esse erro:

  • Os parâmetros do circuito estão incorretos. Caso parâmetros muito fora dos valores padrão dos elementos elétricos sejam inseridos, o cálculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente.
  • Algum barramento está isolado. Esse erro é bastante comum e pode ocorrer ao inserir um barramento sem conectá-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solução é eliminar essa barra do diagrama.
  • Algum elemento possui parâmetros discrepantes dos demais. Caso um dos elementos inseridos possua um valor de impedância muito distinto dos demais, como por exemplo uma linha com impedância muito elevada ou uma carga muito pequena, pode levar à divergência do método numérico. Nesse caso, reconsidere a necessidade de representação desses elementos no circuito e alterne entre os métodos numéricos de solução disponíveis.

A seguinte mensagem de erro é exibida: "Erro ao inicializar os valores de saturação do..."

Essa mensagem de erro é exibida quando não é possível calcular os fatores de saturação da máquina síncrona. As seguintes situações podem ocasionar esse erro:

  • O fator de saturação é menor que 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.
  • Os parâmetros da máquina síncrona estão incorretos. Caso parâmetros muito fora dos valores padrão das máquinas síncronas sejam inseridos, o cálculo dos fatores de saturação pode divergir. Verifique se os dados foram inseridos corretamente.

A seguinte mensagem de erro é exibida: "Erro ao inicializar o AVR / regulador de velocidade..."

Essa mensagem de erro é exibida quando não é possível inicializar o sistema de controle de uma máquina síncrona. As seguintes situações podem ocasionar esse erro:

  • O sistema de controle está vazio. Caso esteja habilitado o AVR e/ou o regulador de velocidade e o controle não foi inserido, esse erro pode ser acionado. Insira o controle da máquina ou desmarque a opção de utilização do AVR e/ou regulador de velocidade.
  • O sistema de controle não possui ao menos uma entrada e uma saída. O sistema de controle deve ter ao menos uma entrada e uma saída, caso contrário apresentará erro de execução.
  • O passo de integração está muito pequeno. Caso o passo de integração esteja muito pequeno, os cálculos gerarão erros e irão divergir. Reduza o passo de integração nas configurações de simulação.

A seguinte mensagem de erro é exibida: "Impossível resolver as máquinas do sistema"

Essa mensagem de erro é exibida quando não é possível resolver as EADs das máquinas síncronas inseridas no sistemas. As seguintes situações podem ocasionar esse erro:

  • Os parâmetros da máquina síncrona estão incorretos. Caso parâmetros muito fora dos valores padrão das máquinas síncronas sejam inseridos, o cálculo das EADs pode se tornar impossível. Verifique se os dados foram inseridos corretamente.
  • O passo de integração está muito pequeno. Caso o passo de integração esteja muito pequeno, os cálculos gerarão erros e irão divergir. Reduza o passo de integração nas configurações de simulação.
  • Os parâmetros do circuito estão incorretos. Caso parâmetros muito fora dos valores padrão dos elementos elétricos sejam inseridos, o cálculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente.
  • Algum barramento está isolado. Esse erro é bastante comum e pode ocorrer ao inserir um barramento sem conectá-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solução é eliminar essa barra do diagrama.
  • Algum elemento possui parâmetros discrepantes dos demais. Caso um dos elementos inseridos possua um valor de impedância muito distinto dos demais, como por exemplo uma linha com impedância muito elevada ou uma carga muito pequena, pode levar à divergência do método numérico. Nesse caso, reconsidere a necessidade de representação desses elementos no circuito e alterne entre os métodos numéricos de solução disponíveis.

A seguinte mensagem de erro é exibida: "Erro ao inicializar o escorregamento do motor..."

Essa mensagem de erro é exibida quando não é possível calcular o valor de escorregamento inicial do motor de indução. As seguintes situações podem ocasionar esse erro:

  • Os parâmetros de estabilidade do motor estão incorretos. Caso parâmetros muito fora dos valores padrão dos motores de indução sejam inseridos, o cálculo do escorregamento pode se tornar impossível. Verifique se os dados foram inseridos corretamente.

Estrutura da ferramenta de estabilidade

A estabilidade de um SEP é um problema dinâmico e necessita de modelos mais elaborados de elementos de potência comparados àqueles apresentados nos outros estudos. Esses modelos são descritos individualmente, com destaque às máquinas síncronas, cargas ZIP e motores de indução.

A representação dos demais componentes do sistema elétrico: linhas de transmissão, transformadores e elementos shunt (com exceção de cargas ZIP), que formam a rede de transmissão ou distribuição balanceada, é realizada utilizando os mesmos modelos do fluxo de carga.

Os modelos dinâmicos para a análise no domínio do tempo são na forma de um sistema de equações algébrico-diferenciais (EADs), descritas a seguir:

dxdt=f(x,y,u)g=f(x,y)\dfrac{dx}{dt}= f(x,y,u)\\ g = f(x,y)

Em que:

  • xx são as variáveis de estado
  • yy são as variáveis de algébricas
  • uu são as variáveis de entrada

As variáveis de entrada são inseridas pelo usuário e permanecem constantes durante todo o processo de cálculo. Para o problema de estabilidade, as variáveis algébricas iniciais correspondem às tensões e ângulos das barras calculadas no fluxo de carga. As variáveis de estado iniciais são estimadas após a convergência do fluxo de potência (inicialização dos elementos dinâmicos).

Na sequência é apresentado, na forma de fluxogramas, a estrutura do módulo de estabilidade implementado no PSP-UFU. O fluxograma abaixo mostra a estrutura geral da ferramenta de estabilidade.

Estrutura geral da ferramenta de estabilidade

A inicialização da rede elétrica e dos elementos dinâmicos, assim como o precesso iterativo para solução das EADs são apresentados nos dois fluxogramas conseguintes.

Inicialização da ferramenta de estabilidade
Processo iterativo para cálculo dos elementos dinâmicos

Integração numérica

Para resolver as equações diferenciais da máquina é necessário um método de integração numérica. Tais métodos são classificados em dois grupos: métodos explícitos e métodos implícitos. Os métodos explícitos, devido à sua formulação, calculam diretamente o estado do sistema em um instante de tempo posterior, enquanto métodos implícitos envolvem estados atuais e posteriores em suas equações, exigindo, portanto, um processo iterativo.

As constantes de tempo presentes no estudo de estabilidade têm uma grande variação em seu valor (podem variar de 10−3 s10^{-3}~s a 10 s10~s). Isso torna o sistema de equações diferenciais da máquina síncrona como um sistema rígido (stiff equation). Caso a análise da estabilidade numérica tanto das equações diferenciais rígidas quanto do método de integração obtenham o mesmo comportamento, o método é chamado de absolutamente estável, ou A-estável.

Métodos de integração numérica explícitos, como por exemplo o Runge-Kutta de quarta ordem, não podem ser A-estáveis e, portanto, normalmente possuem comportamento ruim em problemas com equações diferenciais rígidas. Por outro lado, métodos implícitos podem ser A-estáveis. Um método implícito adequado para solução do comportamento dinâmico de sistemas elétricos é o Trapezoidal Implícito, por possuir as seguintes vantagens:

  • É numericamente estável (A-estável);
  • É bastante rápida;
  • Possui boa precisão (dependendo somente do passo de integração utilizado).

Tal método foi implementado no PSP-UFU tanto para solução das equações diferenciais da máquina síncrona quanto nas funções transferência do sistema de controle. Sua formulação é dada pela seguinte expressão:

yn+1=yn+0,5h(yn+1′+yn′)y_{n+1}=y_n + 0{,}5 h \left(y_{n+1}' + y_{n}' \right)

Em que:

  • hh é o passo de integração
  • yny_n é o valor do estado no passo anterior (instante tnt_n)
  • yn+1y_{n+1} é o valor do estado no passo atual (instante tn+1t_{n+1})
  • yn′y_{n}' é a equação diferencial no passo anterior
  • yn+1′y_{n+1}' é a equação diferencial no passo atual

Nota-se nessa equação que o método é implícito devido ao termo n+1n+1 aparecer em ambos os lados da equação, por isso é necessário um processo iterativo para sua solução.

Referências

  1. MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: https://doi.org/10.1007/978-3-642-13669-6
  2. KUNDUR, P.; et al. Definition and classification of power system stability. IEEE Transactions Power Systems, v. 19, n. 2, mai 2004, p. 1387-1401. doi: https://doi.org/10.1109/TPWRS.2004.825981
  3. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
  4. PARK, R. H. Two-reactions Theory of Synchronous Machine. Generalized Method of Analysis – Part I. AIEE Transactions, v. 48, n. 3, jul 1929. doi: https://doi.org/10.1109/T-AIEE.1929.5055275
  5. ANDERSON, P. M.; FOUAD, A. A. Power System Control and Stability. Wiley-IEEE Press, New York, 2002. doi: https://doi.org/10.1109/9780470545577
  6. SAUER, P. W.; PAI, M. A. Power System Dynamics and Stability. Pretience Hall, Upper Saddle River, 1998.
  7. KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994.
  8. 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: https://doi.org/10.1109/TPAS.1972.293341
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Somador

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.

Formulário de edição de dados do somador no PSP-UFU

No seu único campo “Sinais” é inserida uma lista de sinais separados por espaços contendo os símbolos “+” para uma entrada positiva e “-” para negativa.

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).

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Somador

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.

Formulário de edição de dados do somador no PSP-UFU

No seu único campo “Sinais” é inserida uma lista de sinais separados por espaços contendo os símbolos “+” para uma entrada positiva e “-” para negativa.

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).

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Gerador Síncrono

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.

Gerador Síncrono no PSP-UFU

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.

Atenção!

Somente barramentos que possuem esse elemento conectado podem ser considerados barras de referência. Barras do tipo PV devem conter um gerador síncrono ou um motor síncrono (compensador síncrono).

O formulário de dados é dividido em dois, sendo o primeiro responsável pelos dados gerais, de fluxo de carga e de falta e um segundo pelos dados de estabilidade . Esse último também permite o acesso aos controles das máquinas síncronas manipulados pelo editor de controle.

Informação

Os dados referentes às impedâncias de sequência positiva do gerador síncrono inseridas no contexto (aba) "Falta" são utilizados tanto para os estudos de curto-circuito quanto para os estudos de harmônicos.

Esses dados são ignorados nos estudos de fluxo de carga (não são utilizado nesse estudo) e estabilidade (são utilizados dados inseridos em formulário específico).

Gerador Síncrono no fluxo de carga

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:

  • Barra de referência: 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;
  • Barra PV: 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;
  • Barra PQ: Para os geradores conectados a essa barra tanto a potência ativa quanto reativa inseridas são consideradas.
Atenção

Caso o limite de potência reativa seja excedido, o programa automaticamente transforma a Barra PV conectada em uma Barra PQ, utilizando o valor limite de potência reativa que seria ultrapassado.

Gerador Síncrono no estudo de curto-circuito

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.

Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero

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.

A corrente que circula na impedância z‾n\overline{z}_n entre o neutro e a terra é 3I˙a03\dot{I}_{a0}. Pela figura acima (c), observa-se que a queda de tensão de sequência zero do ponto a para terra (V˙a0\dot{V}_{a0}) é:

V˙a0=−3I˙a0z‾n−I˙a0z‾g0\dot{V}_{a0} = -3\dot{I}_{a0}\overline{z}_n - \dot{I}_{a0}\overline{z}_{g0}

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:

z‾0=3z‾n+z‾g0\overline{z}_{0} = 3\overline{z}_n + \overline{z}_{g0}
Dica

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:

"Falha ao inverter a matriz admitância de sequência zero"

Isso ocorre porque a matriz admitância de sequência zero é singular. Para contornar esse problema escolha uma das duas soluções abaixo:

  1. Marque a opção "Neutro aterrado" e insira um alto valor de reatância de aterramento (j9999 p.u.j9999~p.u., por exemplo);
  2. Ou, na barra do gerador, insira um reator de baixo valor de potência reativa (1,0 var1,0~var, por exemplo).

Gerador Síncrono no estudo de estabilidade

A relação de valores observados em testes adequados (definidos na IEEE Std. 115-2019), denominados parâmetros padrões, são utilizados para modelar a máquina síncrona no estudo de estabilidade do PSP-UFU.

Os parâmetros da máquina síncrona que influenciam rapidamente no decaimento de valores são chamados subtransitórios (indicados por ′′''), aqueles que influenciam mais lentamente são chamados transitórios (indicados por ′') e, finalmente, aqueles que influenciam continuamente são chamados de parâmetros síncronos (sem indicação de sobrescrito).

Um conjunto de equações algébrico-diferenciais determinam o comportamento da máquina síncrona no estudo de estabilidade:

Eq′−Vq=raIq−xds′IdEd′−Vd=raId−xqs′IqEq′′−Vq=raIq−xds′′IdEd′′−Vd=raId−xqs′′Iq dEq′dt=Vfd+(xd−xd′)Id−sdEq′Td0′dEd′dt=−(xq−xq′)Iq−sqEd′Tq0′dEq′′dt=sdEq′+(xd′−xd′′)Id−sdEq′′Td0′′dEd′′dt=sdEd′+(xq′−xq′′)Iq−sdEd′′Tq0′′ dωdt=ωr2H[Pm−Pe−Da(ω−ωr)]dδdt=Ωb(ω−ωr)E_{q}' - V_q = r_aI_q - x_{ds}'Id\\ E_{d}' - V_d = r_aI_d - x_{qs}'Iq\\ E_{q}'' - V_q = r_aI_q - x_{ds}''Id\\ E_{d}'' - V_d = r_aI_d - x_{qs}''Iq\\ ~\\ \frac{dE_{q}'}{dt} = \frac{V_{fd} + \left( x_d - x_{d}' \right)I_d - s_d E_{q}'}{T_{d0}'}\\ \frac{dE_{d}'}{dt} = \frac{- \left( x_q - x_{q}' \right)I_q - s_q E_{d}'}{T_{q0}'}\\ \frac{dE_{q}''}{dt} = \frac{s_dE_{q}' + \left( x_{d}' - x_{d}'' \right)I_d - s_d E_{q}''}{T_{d0}''}\\ \frac{dE_{d}''}{dt} = \frac{s_dE_{d}' + \left( x_{q}' - x_{q}'' \right)I_q - s_d E_{d}''}{T_{q0}''}\\ ~\\ \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)

As duas últimas equações diferenciais são as equações mecânicas da máquina; e as demais são equações elétricas (consulte essa tese para maiores detalhes acerca dos parâmetros dessas equações).

Utilizando as equações transitórias e subtransitórias podem-se definir cinco modelos de distintas complexidades.

Atenção!

O modelo da máquina síncrona é selecionado automaticamente de acordo com os dados fornecidos ao programa.

Na sequência são apresentados tais modelos, incluídos os efeitos da saturação magnética, em conjunto com seus diagramas de blocos:

  • Modelo 1: Corresponde a uma tensão constante atrás de uma reatância transitória de eixo direto (xd′x_{d}'), não exigindo equações diferenciais;
  • Modelo 2: São representados os efeitos transitórios de eixo direto, sendo necessária a solução de uma equação diferencial (dEq′dt\frac{dE_{q}'}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 2 das máquinas síncronas
  • Modelo 3: São representados os efeitos transitórios de eixo direto e em quadratura, exigindo duas equações diferenciais (dEq′dt\frac{dE_{q}'}{dt} e dEd′dt\frac{dE_{d}'}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 3 das máquinas síncronas
  • Modelo 4: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de três equações diferenciais (dEq′dt\frac{dE_{q}'}{dt}, dEq′′dt\frac{dE_{q}''}{dt} e dEd′′dt\frac{dE_{d}''}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 4 das máquinas síncronas
  • Modelo 5: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de quatro equações diferenciais (dEq′dt\frac{dE_{q}'}{dt}, dEd′dt\frac{dE_{d}'}{dt}, dEq′′dt\frac{dE_{q}''}{dt} e dEd′′dt\frac{dE_{d}''}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 4 das máquinas síncronas
Nota

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 (xpx_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 (xlx_l), aqui substituída de forma aproximada por xpx_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 (EpE_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 (sds_d) e outro no eixo em quadratura (sqs_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.

Portanto as reatâncias saturadas, que devem ser inseridas nas equações algébricas da máquina, são definidas pelas seguintes equações:

xds=xd−xpsd+xpxqs=xq−xpsq+xpx_{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.

No PSP-UFU a representação de um barramento infinito 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 (9999 s9999~s, por exemplo) em relação às demais máquinas do sistema, e o valor de xd′x_{d}' deve ser um valor muito pequeno (10−3 p.u.10^{-3}~p.u., por exemplo).

Centro de inércia

Normalmente utiliza-se a velocidade de referência como sendo a síncrona e portanto, nesse caso, ωr=ωb=1,0 p.u.\omega_r = \omega_b = 1,0~p.u. 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, Center of Inertia), que constitui uma soma ponderada das velocidades das máquinas presentes no sistema:

ωr=(∑i=1nHiωi)(∑i=1nHi)\omega_r=\frac{\left( \sum_{i=1}^{n} H_i \omega_i \right)}{\left( \sum_{i=1}^{n} H_i \right)}

Em que: -nn é o número de máquinas síncronas conectadas no sistema.

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 definida pelo usuário.

Formulário de edição dos geradores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos geradores síncronos:

Formulário dos geradores síncronos no PSP-UFU

Um segundo pelos dados de estabilidade, como mostra a figura abaixo, acessado ao clicar no botão "Estabilidade" do formulário principal. Nele é possível também acessar aos controles das máquinas síncronas manipulados pelo editor de controle.

Formulário de estabilidade dos geradores síncronos no PSP-UFU

No formulário de estabilidade pode ser observado o botão "Chaveamento" 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 estabilidade.

Formulário de chaveamento do gerador síncrono

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do gerador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador.

Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.

Atenção!

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.

Potências reativas máxima e mínima

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.

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.

Acesso aos controles da máquina síncrona

Como já mencionado anteriormente, 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". Ambas as opções irão acessar o editor de controles.

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".

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.

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
  3. KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994.
  4. 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: https://doi.org/10.1109/TPAS.1972.293341
  5. IEEE Std 1110-2002 IEEE Guide for Synchronous Generator Modeling Practices and Applications in Power System Stability Analyses. IEEE, New York, nov. 2003. doi: https://doi.org/10.1109/IEEESTD.2003.94408
  6. KIMBARK, E. W. Power System Stability: Volume III – Synchronous Machine. New York: Wiley-IEEE Press, 1995.
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Gerador Síncrono

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.

Gerador Síncrono no PSP-UFU

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.

Atenção!

Somente barramentos que possuem esse elemento conectado podem ser considerados barras de referência. Barras do tipo PV devem conter um gerador síncrono ou um motor síncrono (compensador síncrono).

O formulário de dados é dividido em dois, sendo o primeiro responsável pelos dados gerais, de fluxo de carga e de falta e um segundo pelos dados de estabilidade . Esse último também permite o acesso aos controles das máquinas síncronas manipulados pelo editor de controle.

Informação

Os dados referentes às impedâncias de sequência positiva do gerador síncrono inseridas no contexto (aba) "Falta" são utilizados tanto para os estudos de curto-circuito quanto para os estudos de harmônicos.

Esses dados são ignorados nos estudos de fluxo de carga (não são utilizado nesse estudo) e estabilidade (são utilizados dados inseridos em formulário específico).

Gerador Síncrono no fluxo de carga

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:

  • Barra de referência: 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;
  • Barra PV: 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;
  • Barra PQ: Para os geradores conectados a essa barra tanto a potência ativa quanto reativa inseridas são consideradas.
Atenção

Caso o limite de potência reativa seja excedido, o programa automaticamente transforma a Barra PV conectada em uma Barra PQ, utilizando o valor limite de potência reativa que seria ultrapassado.

Gerador Síncrono no estudo de curto-circuito

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.

Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero

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.

A corrente que circula na impedância z‾n\overline{z}_n entre o neutro e a terra é 3I˙a03\dot{I}_{a0}. Pela figura acima (c), observa-se que a queda de tensão de sequência zero do ponto a para terra (V˙a0\dot{V}_{a0}) é:

V˙a0=−3I˙a0z‾n−I˙a0z‾g0\dot{V}_{a0} = -3\dot{I}_{a0}\overline{z}_n - \dot{I}_{a0}\overline{z}_{g0}

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:

z‾0=3z‾n+z‾g0\overline{z}_{0} = 3\overline{z}_n + \overline{z}_{g0}
Dica

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:

"Falha ao inverter a matriz admitância de sequência zero"

Isso ocorre porque a matriz admitância de sequência zero é singular. Para contornar esse problema escolha uma das duas soluções abaixo:

  1. Marque a opção "Neutro aterrado" e insira um alto valor de reatância de aterramento (j9999 p.u.j9999~p.u., por exemplo);
  2. Ou, na barra do gerador, insira um reator de baixo valor de potência reativa (1,0 var1,0~var, por exemplo).

Gerador Síncrono no estudo de estabilidade

A relação de valores observados em testes adequados (definidos na IEEE Std. 115-2019), denominados parâmetros padrões, são utilizados para modelar a máquina síncrona no estudo de estabilidade do PSP-UFU.

Os parâmetros da máquina síncrona que influenciam rapidamente no decaimento de valores são chamados subtransitórios (indicados por ′′''), aqueles que influenciam mais lentamente são chamados transitórios (indicados por ′') e, finalmente, aqueles que influenciam continuamente são chamados de parâmetros síncronos (sem indicação de sobrescrito).

Um conjunto de equações algébrico-diferenciais determinam o comportamento da máquina síncrona no estudo de estabilidade:

Eq′−Vq=raIq−xds′IdEd′−Vd=raId−xqs′IqEq′′−Vq=raIq−xds′′IdEd′′−Vd=raId−xqs′′Iq dEq′dt=Vfd+(xd−xd′)Id−sdEq′Td0′dEd′dt=−(xq−xq′)Iq−sqEd′Tq0′dEq′′dt=sdEq′+(xd′−xd′′)Id−sdEq′′Td0′′dEd′′dt=sdEd′+(xq′−xq′′)Iq−sdEd′′Tq0′′ dωdt=ωr2H[Pm−Pe−Da(ω−ωr)]dδdt=Ωb(ω−ωr)E_{q}' - V_q = r_aI_q - x_{ds}'Id\\ E_{d}' - V_d = r_aI_d - x_{qs}'Iq\\ E_{q}'' - V_q = r_aI_q - x_{ds}''Id\\ E_{d}'' - V_d = r_aI_d - x_{qs}''Iq\\ ~\\ \frac{dE_{q}'}{dt} = \frac{V_{fd} + \left( x_d - x_{d}' \right)I_d - s_d E_{q}'}{T_{d0}'}\\ \frac{dE_{d}'}{dt} = \frac{- \left( x_q - x_{q}' \right)I_q - s_q E_{d}'}{T_{q0}'}\\ \frac{dE_{q}''}{dt} = \frac{s_dE_{q}' + \left( x_{d}' - x_{d}'' \right)I_d - s_d E_{q}''}{T_{d0}''}\\ \frac{dE_{d}''}{dt} = \frac{s_dE_{d}' + \left( x_{q}' - x_{q}'' \right)I_q - s_d E_{d}''}{T_{q0}''}\\ ~\\ \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)

As duas últimas equações diferenciais são as equações mecânicas da máquina; e as demais são equações elétricas (consulte essa tese para maiores detalhes acerca dos parâmetros dessas equações).

Utilizando as equações transitórias e subtransitórias podem-se definir cinco modelos de distintas complexidades.

Atenção!

O modelo da máquina síncrona é selecionado automaticamente de acordo com os dados fornecidos ao programa.

Na sequência são apresentados tais modelos, incluídos os efeitos da saturação magnética, em conjunto com seus diagramas de blocos:

  • Modelo 1: Corresponde a uma tensão constante atrás de uma reatância transitória de eixo direto (xd′x_{d}'), não exigindo equações diferenciais;
  • Modelo 2: São representados os efeitos transitórios de eixo direto, sendo necessária a solução de uma equação diferencial (dEq′dt\frac{dE_{q}'}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 2 das máquinas síncronas
  • Modelo 3: São representados os efeitos transitórios de eixo direto e em quadratura, exigindo duas equações diferenciais (dEq′dt\frac{dE_{q}'}{dt} e dEd′dt\frac{dE_{d}'}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 3 das máquinas síncronas
  • Modelo 4: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de três equações diferenciais (dEq′dt\frac{dE_{q}'}{dt}, dEq′′dt\frac{dE_{q}''}{dt} e dEd′′dt\frac{dE_{d}''}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 4 das máquinas síncronas
  • Modelo 5: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de quatro equações diferenciais (dEq′dt\frac{dE_{q}'}{dt}, dEd′dt\frac{dE_{d}'}{dt}, dEq′′dt\frac{dE_{q}''}{dt} e dEd′′dt\frac{dE_{d}''}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 4 das máquinas síncronas
Informação

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 (xpx_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 (xlx_l), aqui substituída de forma aproximada por xpx_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 (EpE_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 (sds_d) e outro no eixo em quadratura (sqs_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.

Portanto as reatâncias saturadas, que devem ser inseridas nas equações algébricas da máquina, são definidas pelas seguintes equações:

xds=xd−xpsd+xpxqs=xq−xpsq+xpx_{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.

No PSP-UFU a representação de um barramento infinito 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 (9999 s9999~s, por exemplo) em relação às demais máquinas do sistema, e o valor de xd′x_{d}' deve ser um valor muito pequeno (10−3 p.u.10^{-3}~p.u., por exemplo).

Centro de inércia

Normalmente utiliza-se a velocidade de referência como sendo a síncrona e portanto, nesse caso, ωr=ωb=1,0 p.u.\omega_r = \omega_b = 1,0~p.u. 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, Center of Inertia), que constitui uma soma ponderada das velocidades das máquinas presentes no sistema:

ωr=(∑i=1nHiωi)(∑i=1nHi)\omega_r=\frac{\left( \sum_{i=1}^{n} H_i \omega_i \right)}{\left( \sum_{i=1}^{n} H_i \right)}

Em que: +nn é o número de máquinas síncronas conectadas no sistema.

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 definida pelo usuário.

Formulário de edição dos geradores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos geradores síncronos:

Formulário dos geradores síncronos no PSP-UFU

Um segundo pelos dados de estabilidade, como mostra a figura abaixo, acessado ao clicar no botão "Estabilidade" do formulário principal. Nele é possível também acessar aos controles das máquinas síncronas manipulados pelo editor de controle.

Formulário de estabilidade dos geradores síncronos no PSP-UFU

No formulário de estabilidade pode ser observado o botão "Chaveamento" 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 estabilidade.

Formulário de chaveamento do gerador síncrono

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do gerador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador.

Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.

Atenção!

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.

Potências reativas máxima e mínima

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.

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.

Acesso aos controles da máquina síncrona

Como já mencionado anteriormente, 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". Ambas as opções irão acessar o editor de controles.

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".

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.

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
  3. KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994.
  4. 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: https://doi.org/10.1109/TPAS.1972.293341
  5. IEEE Std 1110-2002 IEEE Guide for Synchronous Generator Modeling Practices and Applications in Power System Stability Analyses. IEEE, New York, nov. 2003. doi: https://doi.org/10.1109/IEEESTD.2003.94408
  6. KIMBARK, E. W. Power System Stability: Volume III – Synchronous Machine. New York: Wiley-IEEE Press, 1995.
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Compensador Síncrono

Uma máquina síncrona operando sem carga mecânica e fornecendo ou absorvendo energia reativa. tradução livre - IEC 60050.

Compensador Síncrono no PSP-UFU

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 fluxo de carga, no PSP-UFU esse elemento tem comportamento idêntico ao gerador síncrono, porém a sua potência ativa é inserida nos algoritmos de solução com sinal negativo.

Sua parametrização para o estudo de fluxo de carga, falta e harmônicos é idêntica ao gerador síncrono.

Cuidado!

O compensador síncrono não foi implementado no estudo de estabilidade e sua presença no circuito pode causar erros durante os cálculos.

Não inclua esse elemento para os estudos de estabilidade. Versões futuras do PSP-UFU irão contemplar esse elemento para esse estudo.

Dica

É possível utilizar um gerador síncrono com potência ativa nula ou negativa para representar o compensador síncrono nos estudos de estabilidade.

Formulário de edição dos compensadores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos compensadores síncronos:

Formulário dos compensadores síncronos no PSP-UFU

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do compensador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do compensador.

Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.

Atenção!

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.

Potências reativas máxima e mínima

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.

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.

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Compensador Síncrono

Uma máquina síncrona operando sem carga mecânica e fornecendo ou absorvendo energia reativa. tradução livre - IEC 60050.

Compensador Síncrono no PSP-UFU

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 fluxo de carga, no PSP-UFU esse elemento tem comportamento idêntico ao gerador síncrono, porém a sua potência ativa é inserida nos algoritmos de solução com sinal negativo.

Sua parametrização para o estudo de fluxo de carga, falta e harmônicos é idêntica ao gerador síncrono.

Cuidado!

O compensador síncrono não foi implementado no estudo de estabilidade e sua presença no circuito pode causar erros durante os cálculos.

Não inclua esse elemento para os estudos de estabilidade. Versões futuras do PSP-UFU irão contemplar esse elemento para esse estudo.

Dica

É possível utilizar um gerador síncrono com potência ativa nula ou negativa para representar o compensador síncrono nos estudos de estabilidade.

Formulário de edição dos compensadores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos compensadores síncronos:

Formulário dos compensadores síncronos no PSP-UFU

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do compensador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do compensador.

Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.

Atenção!

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.

Potências reativas máxima e mínima

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.

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.

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Relatórios Tabulares

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Relatórios Tabulares

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Texto Vinculado

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Texto Vinculado

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Função Transferência

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.

Informação

Nesses blocos é utilizado a letra “s” para representação no domínio da frequência, pois essa é a terminologia mais utilizada em sistemas de controle.

Função Transferência no PSP-UFU

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.

Dada uma função transferência genérica abaixo:

Y(s)U(s)=b0sk+b1sk−1+⋯+bk−1s+bksk+a1sk−1+⋯+ak−1s+ak\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}

A transformação em espaço de estado na forma canônica controlável ficará da seguinte forma:

[sx1sx2⋮sxk−1sxk]=[010⋯0001⋯0⋮⋮⋮⋱⋮000⋯1−ak−ak−1−ak−2⋯−a1][x1x2⋮xk−1xk]+[00⋮01]unyn=[(bn−anb0)(bn−1−an−1b0)⋯(b1−a1b0)][x1x2⋮xk]+b0un\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 & 1 & 0 & \cdots & 0\\ 0 & 0 & 1 & \cdots & 0\\ \vdots & \vdots & \vdots & \ddots & \vdots\\ 0 & 0 & 0 & \cdots & 1\\ -a_k & -a_{k-1} & -a_{k-2} & \cdots & -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) & \left( b_{n-1} - a_{n-1} b_0 \right) & \cdots & \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

A equação diferencial matricial é resolvida pelo método Trapezoidal Implícito. 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 (xx) calculados obtém-se o valor da saída do bloco (yny_n).

Formulário de edição de dados da Função Transferência

A figura abaixo apresenta o formulário de edição de dados da função transferência.

Formulário de edição de dados da função transferência no PSP-UFU

A função transferência é definida pelos coeficientes do numerador e denominador, separados por espaço.

Atenção!

Os elementos não presentes são representados como coeficientes de valor zero.

Por exemplo, um parâmetro inserido igual a “10,502\begin{matrix} 1 & 0{,}5 & 0 & 2 \end{matrix}” irá gerar: “s3+0,5s2+2s^3+0{,}5s^2+2”.

Referências

  1. OGATA, K. Modern Control Engineering. Prentice Hall Inc., New Jersey, 2004.
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Função Transferência

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.

Informação

Nesses blocos é utilizado a letra “s” para representação no domínio da frequência, pois essa é a terminologia mais utilizada em sistemas de controle.

Função Transferência no PSP-UFU

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.

Dada uma função transferência genérica abaixo:

Y(s)U(s)=b0sk+b1sk−1+⋯+bk−1s+bksk+a1sk−1+⋯+ak−1s+ak\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}

A transformação em espaço de estado na forma canônica controlável ficará da seguinte forma:

[sx1sx2⋮sxk−1sxk]=[010⋯0001⋯0⋮⋮⋮⋱⋮000⋯1−ak−ak−1−ak−2⋯−a1][x1x2⋮xk−1xk]+[00⋮01]unyn=[(bn−anb0)(bn−1−an−1b0)⋯(b1−a1b0)][x1x2⋮xk]+b0un\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 & 1 & 0 & \cdots & 0\\ 0 & 0 & 1 & \cdots & 0\\ \vdots & \vdots & \vdots & \ddots & \vdots\\ 0 & 0 & 0 & \cdots & 1\\ -a_k & -a_{k-1} & -a_{k-2} & \cdots & -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) & \left( b_{n-1} - a_{n-1} b_0 \right) & \cdots & \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

A equação diferencial matricial é resolvida pelo método Trapezoidal Implícito. 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 (xx) calculados obtém-se o valor da saída do bloco (yny_n).

Formulário de edição de dados da Função Transferência

A figura abaixo apresenta o formulário de edição de dados da função transferência.

Formulário de edição de dados da função transferência no PSP-UFU

A função transferência é definida pelos coeficientes do numerador e denominador, separados por espaço.

Atenção!

Os elementos não presentes são representados como coeficientes de valor zero.

Por exemplo, um parâmetro inserido igual a “10,502\begin{matrix} 1 & 0{,}5 & 0 & 2 \end{matrix}” irá gerar: “s3+0,5s2+2s^3+0{,}5s^2+2”.

Referências

  1. OGATA, K. Modern Control Engineering. Prentice Hall Inc., New Jersey, 2004.
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Transformador

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.

Transformador no PSP-UFU

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 (tt) e defasagem (ϕ\phi), utilizando um transformador ideal de relação de transformação t‾:1\overline{t}:1 em série com sua impedância (y‾T=rT+jxT\overline{y}_T = r_T + jx_T), em que t‾\overline{t} é um número complexo (t∠ϕt\angle\phi)

Atenção

O modelo utilizado no PSP-UFU não considera o ramo magnetizante ou impedâncias mútuas entre as fases.

A figura abaixo mostra o modelo do transformador implementado no PSP-UFU:

Modelo PI da linha

Em que:

  • rT\bold{r_T} é a resistência total do transformador;
  • xT\bold{x_T} é a reatância indutiva total do transformador;
  • t‾\bold{\overline{t}} é a o tape complexo do transformador.

A relação entre as tensões e correntes das barras genéricas ii e jj é obtida pela equação matricial:

[I˙ijI˙ji]=[y‾Tt2−y‾Tt‾∗−y‾Tt‾y‾T]×[V˙iV˙j]\begin{bmatrix} \dot{I}_{ij}\\ \dot{I}_{ji} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} & -\displaystyle \frac{\overline{y}_T}{\overline{t}^*}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}} & \overline{y}_T \end{bmatrix} \times \begin{bmatrix} \dot{V}_{i}\\ \dot{V}_{j} \end{bmatrix}

Assim como nas linhas, o transformador de dois enrolamentos deve ser inserido entre barras, porém não há a necessidade das tensões nominais desses barramentos serem idênticas.

Atenção!

A primeira barra selecionada será o lado primário, 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 ferramentas CAD.

Transformadores no estudo de curto-circuito

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 faltas desbalanceadas é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.

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 (ϕ\phi) deve ser invertido, uma vez que os fasores da sequência negativa são deslocados na direção oposta. Com isso, a matriz que representa as admitâncias da equação anterior deve ser substituída pela seguinte expressão:

[Y‾iiY‾ijY‾jiY‾jj]=[y‾Tt2−y‾Tt‾−y‾Tt‾∗y‾T]\begin{bmatrix} \overline{Y}_{ii} & \overline{Y}_{ij}\\ \overline{Y}_{ji} & \overline{Y}_{jj} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} & -\displaystyle \frac{\overline{y}_T}{\overline{t}}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}^*} & \overline{y}_T \end{bmatrix}

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.

Circuitos equivalentes de sequência zero dos transformadores

Para os transformadores com conexão estrela aterrado, se a ligação do neutro para a terra apresentar uma impedância z‾n\overline{z}_n, o circuito equivalente de sequência zero deve ter impedância de 3z‾n3\overline{z}_n em série com a resistência e reatância equivalentes do transformador.

Formulário de edição dos transformadores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos transformadores:

Formulário dos transformadores no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais dos transformadores, informações do fluxo de carga, sua conexão e defasagem;
  • Falta: local onde as impedâncias de sequência zero e impedâncias de aterramento são inseridas.

Além desses dois contextos, pode ser observado o botão "Estabilidade" 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 estabilidade.

Formulário de chaveamento do transformador

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

Campo de informação não editável que apresenta a tensão primária e secundária do transformador. Para alterar esse campo é necessário editar o campo correspondente dos barramento conectados.

Tensão base

Tensão utilizada para converter os parâmetros de impedância inseridos em Ω\Omega para p.u.p.u. As tensões selecionadas por uma caixa de escolha são editadas nos formulários dos barramentos conectados.

Informação

A tensão base é ignorada caso os dados inseridos estejam em p.u.p.u.

Potência nominal

Potência nominal do transformador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Impedância do transformador

Impedância série do transformador (resistência e reatância indutiva), inserida em p.u.p.u. ou Ω\Omega. Caso as impedâncias sejam inseridas em Ω\Omega será utilizada a tensão base selecionada para conversão para p.u.p.u.

Conexão

Conexão do transformador utilizada para cálculo das correntes de sequência zero nas faltas desbalanceadas com presença de terra (fase-terra e fase-fase-terra).

As seguintes conexões estão disponíveis:

  1. Yaterrado−YaterradoY_{aterrado}-Y_{aterrado}
  2. Y−YaterradoY-Y_{aterrado}
  3. Yaterrado−YY_{aterrado}-Y
  4. Y−YY-Y
  5. Δ−Yaterrado\Delta-Y_{aterrado}
  6. Δ−Y\Delta-Y
  7. Yaterrado−ΔY_{aterrado}-\Delta
  8. Y−ΔY-\Delta
  9. Δ−Δ\Delta-\Delta

TAP

Tape do transformador em relação ao primário.

Atenção!

O tape no PSP-UFU deve ser inserido pela relação entre a tensão primária nominal e a tensão de tape (TAP=VnominalVtape)\left(\text{TAP} = \frac{V_{nominal}}{V_{tape}}\right).

Defasagem

Defasagem do transformador em relação ao primário, em graus. Esse valor independe do tipo de conexão, portanto para conexões diferentes de Y−YY-Y(aterrado ou não) e Δ−Δ\Delta-\Delta, deve-se inserir o ângulo de defasagem correto.

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.

Edit this page
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+

Transformador

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.

Transformador no PSP-UFU

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 (tt) e defasagem (ϕ\phi), utilizando um transformador ideal de relação de transformação t‾:1\overline{t}:1 em série com sua impedância (y‾T=rT+jxT\overline{y}_T = r_T + jx_T), em que t‾\overline{t} é um número complexo (t∠ϕt\angle\phi)

Atenção

O modelo utilizado no PSP-UFU não considera o ramo magnetizante ou impedâncias mútuas entre as fases.

A figura abaixo mostra o modelo do transformador implementado no PSP-UFU:

Modelo PI da linha

Em que:

  • rT\bold{r_T} é a resistência total do transformador;
  • xT\bold{x_T} é a reatância indutiva total do transformador;
  • t‾\bold{\overline{t}} é a o tape complexo do transformador.

A relação entre as tensões e correntes das barras genéricas ii e jj é obtida pela equação matricial:

[I˙ijI˙ji]=[y‾Tt2−y‾Tt‾∗−y‾Tt‾y‾T]×[V˙iV˙j]\begin{bmatrix} \dot{I}_{ij}\\ \dot{I}_{ji} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} & -\displaystyle \frac{\overline{y}_T}{\overline{t}^*}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}} & \overline{y}_T \end{bmatrix} \times \begin{bmatrix} \dot{V}_{i}\\ \dot{V}_{j} \end{bmatrix}

Assim como nas linhas, o transformador de dois enrolamentos deve ser inserido entre barras, porém não há a necessidade das tensões nominais desses barramentos serem idênticas.

Atenção!

A primeira barra selecionada será o lado primário, 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 ferramentas CAD.

Transformadores no estudo de curto-circuito

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 faltas desbalanceadas é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.

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 (ϕ\phi) deve ser invertido, uma vez que os fasores da sequência negativa são deslocados na direção oposta. Com isso, a matriz que representa as admitâncias da equação anterior deve ser substituída pela seguinte expressão:

[Y‾iiY‾ijY‾jiY‾jj]=[y‾Tt2−y‾Tt‾−y‾Tt‾∗y‾T]\begin{bmatrix} \overline{Y}_{ii} & \overline{Y}_{ij}\\ \overline{Y}_{ji} & \overline{Y}_{jj} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} & -\displaystyle \frac{\overline{y}_T}{\overline{t}}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}^*} & \overline{y}_T \end{bmatrix}

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.

Circuitos equivalentes de sequência zero dos transformadores

Para os transformadores com conexão estrela aterrado, se a ligação do neutro para a terra apresentar uma impedância z‾n\overline{z}_n, o circuito equivalente de sequência zero deve ter impedância de 3z‾n3\overline{z}_n em série com a resistência e reatância equivalentes do transformador.

Formulário de edição dos transformadores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos transformadores:

Formulário dos transformadores no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais dos transformadores, informações do fluxo de carga, sua conexão e defasagem;
  • Falta: local onde as impedâncias de sequência zero e impedâncias de aterramento são inseridas.

Além desses dois contextos, pode ser observado o botão "Estabilidade" 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 estabilidade.

Formulário de chaveamento do transformador

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

Campo de informação não editável que apresenta a tensão primária e secundária do transformador. Para alterar esse campo é necessário editar o campo correspondente dos barramento conectados.

Tensão base

Tensão utilizada para converter os parâmetros de impedância inseridos em Ω\Omega para p.u.p.u. As tensões selecionadas por uma caixa de escolha são editadas nos formulários dos barramentos conectados.

Informação

A tensão base é ignorada caso os dados inseridos estejam em p.u.p.u.

Potência nominal

Potência nominal do transformador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Impedância do transformador

Impedância série do transformador (resistência e reatância indutiva), inserida em p.u.p.u. ou Ω\Omega. Caso as impedâncias sejam inseridas em Ω\Omega será utilizada a tensão base selecionada para conversão para p.u.p.u.

Conexão

Conexão do transformador utilizada para cálculo das correntes de sequência zero nas faltas desbalanceadas com presença de terra (fase-terra e fase-fase-terra).

As seguintes conexões estão disponíveis:

  1. Yaterrado−YaterradoY_{aterrado}-Y_{aterrado}
  2. Y−YaterradoY-Y_{aterrado}
  3. Yaterrado−YY_{aterrado}-Y
  4. Y−YY-Y
  5. Δ−Yaterrado\Delta-Y_{aterrado}
  6. Δ−Y\Delta-Y
  7. Yaterrado−ΔY_{aterrado}-\Delta
  8. Y−ΔY-\Delta
  9. Δ−Δ\Delta-\Delta

TAP

Tape do transformador em relação ao primário.

Atenção!

O tape no PSP-UFU deve ser inserido pela relação entre a tensão primária nominal e a tensão de tape (TAP=VnominalVtape)\left(\text{TAP} = \frac{V_{nominal}}{V_{tape}}\right).

Defasagem

Defasagem do transformador em relação ao primário, em graus. Esse valor independe do tipo de conexão, portanto para conexões diferentes de Y−YY-Y(aterrado ou não) e Δ−Δ\Delta-\Delta, deve-se inserir o ângulo de defasagem correto.

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.

Edit this page
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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:"pot\xeancia-ativa"},"Pot\xeancia ativa"),Object(m.b)("p",null,"Parcela de pot\xeancia ativa da carga. 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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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-

PSP-UFU

Power System Platform of Federal University of Uberlândia

Download
User Guide
Samples
[object Object]

Complete Platform

PSP-UFU is a cross-platform, multilingual, Free and Open-Source Software (FOSS) with advanced GUI (Graphical User Interface) features and CAD (Computer-Aided Design) tools for electrical power system studies.

[object Object]

Advanced CAD Features

The software allows the construction of any electric transmission network and control systems through the deployment of visual elements.

[object Object]

Easy Visualization

For the visualization of results, the program offers linked text elements in the main screen, voltage heatmap display, and also table and graph editors.

[object Object]

Application

The PSP-UFU aims to provide efficient computer simulation tools for research and education purposes, in addition to industrial applications in electrical power systems.

Studies Performed

Power Flow

  • Newton-Raphson
  • Gauss-Seidel
  • Hybrid Newton-Gauss
  • Three-phase induction motors included

Short-Circuit calculation

  • Balanced
  • Unbalanced
  • Short-Circuit power in all system buses

Harmonics

  • Harmonic voltages and THD (Total Harmonic Distortion) calculation
  • Frequency scan

Transient and Dynamic Stability

  • Several synchronous machine models automatically selected
  • Three-phase induction motors
  • User-defined machine controls, exciters and prime moves created using block diagrams (Exciters, AVR, PSS, Hydro and Thermal turbines, Speed Governor, etc.)

Published Papers

Further details can be found in the published papers:
Oliveira, T. L., Guimarães, G. C., & Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. International Transactions on Electrical Energy Systems, e12185. doi: 10.1002/2050-7038.12185
Oliveira, T. L., Guimarães, G. C., Silva, L. R., & Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. The International Journal of Electrical Engineering & Education, 0020720919879058. doi: 10.1177/0020720919879058

Code Documentation

All detailed descriptions of the source-code can be found at Online Documentation, generated by Doxygen.

Screenshots

- - - - - - +
+

PSP-UFU

Power System Platform of Federal University of Uberlândia

Download
User Guide
Samples
[object Object]

Complete Platform

PSP-UFU is a cross-platform, multilingual, Free and Open-Source Software (FOSS) with advanced GUI (Graphical User Interface) features and CAD (Computer-Aided Design) tools for electrical power system studies.

[object Object]

Advanced CAD Features

The software allows the construction of any electric transmission network and control systems through the deployment of visual elements.

[object Object]

Easy Visualization

For the visualization of results, the program offers linked text elements in the main screen, voltage heatmap display, and also table and graph editors.

[object Object]

Application

The PSP-UFU aims to provide efficient computer simulation tools for research and education purposes, in addition to industrial applications in electrical power systems.

Studies Performed

Power Flow

  • Newton-Raphson
  • Gauss-Seidel
  • Hybrid Newton-Gauss
  • Three-phase induction motors included

Short-Circuit calculation

  • Balanced
  • Unbalanced
  • Short-Circuit power in all system buses

Harmonics

  • Harmonic voltages and THD (Total Harmonic Distortion) calculation
  • Frequency scan

Transient and Dynamic Stability

  • Several synchronous machine models automatically selected
  • Three-phase induction motors
  • User-defined machine controls, exciters and prime moves created using block diagrams (Exciters, AVR, PSS, Hydro and Thermal turbines, Speed Governor, etc.)

Published Papers

Further details can be found in the published papers:
Oliveira, T. L., Guimarães, G. C., & Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. International Transactions on Electrical Energy Systems, e12185. doi: 10.1002/2050-7038.12185
Oliveira, T. L., Guimarães, G. C., Silva, L. R., & Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. The International Journal of Electrical Engineering & Education, 0020720919879058. doi: 10.1177/0020720919879058

Code Documentation

All detailed descriptions of the source-code can be found at Online Documentation, generated by Doxygen.

Screenshots

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i.languages.go["class-name"],function(e){e.languages.handlebars={comment:/\{\{![\s\S]*?\}\}/,delimiter:{pattern:/^\{\{\{?|\}\}\}?$/i,alias:"punctuation"},string:/(["'])(?:\\.|(?!\1)[^\\\r\n])*\1/,number:/\b0x[\dA-Fa-f]+\b|(?:\b\d+\.?\d*|\B\.\d+)(?:[Ee][+-]?\d+)?/,boolean:/\b(?:true|false)\b/,block:{pattern:/^(\s*~?\s*)[#\/]\S+?(?=\s*~?\s*$|\s)/i,lookbehind:!0,alias:"keyword"},brackets:{pattern:/\[[^\]]+\]/,inside:{punctuation:/\[|\]/,variable:/[\s\S]+/}},punctuation:/[!"#%&'()*+,.\/;<=>@\[\\\]^`{|}~]/,variable:/[^!"#%&'()*+,.\/;<=>@\[\\\]^`{|}~\s]+/},e.hooks.add("before-tokenize",(function(t){e.languages["markup-templating"].buildPlaceholders(t,"handlebars",/\{\{\{[\s\S]+?\}\}\}|\{\{[\s\S]+?\}\}/g)})),e.hooks.add("after-tokenize",(function(t){e.languages["markup-templating"].tokenizePlaceholders(t,"handlebars")}))}(i),i.languages.json={property:{pattern:/"(?:\\.|[^\\"\r\n])*"(?=\s*:)/,greedy:!0},string:{pattern:/"(?:\\.|[^\\"\r\n])*"(?!\s*:)/,greedy:!0},comment:/\/\/.*|\/\*[\s\S]*?(?:\*\/|$)/,number:/-?\d+\.?\d*(e[+-]?\d+)?/i,punctuation:/[{}[\],]/,operator:/:/,boolean:/\b(?:true|false)\b/,null:{pattern:/\bnull\b/,alias:"keyword"}},i.languages.less=i.languages.extend("css",{comment:[/\/\*[\s\S]*?\*\//,{pattern:/(^|[^\\])\/\/.*/,lookbehind:!0}],atrule:{pattern:/@[\w-]+?(?:\([^{}]+\)|[^(){};])*?(?=\s*\{)/i,inside:{punctuation:/[:()]/}},selector:{pattern:/(?:@\{[\w-]+\}|[^{};\s@])(?:@\{[\w-]+\}|\([^{}]*\)|[^{};@])*?(?=\s*\{)/,inside:{variable:/@+[\w-]+/}},property:/(?:@\{[\w-]+\}|[\w-])+(?:\+_?)?(?=\s*:)/i,operator:/[+\-*\/]/}),i.languages.insertBefore("less","property",{variable:[{pattern:/@[\w-]+\s*:/,inside:{punctuation:/:/}},/@@?[\w-]+/],"mixin-usage":{pattern:/([{;]\s*)[.#](?!\d)[\w-]+.*?(?=[(;])/,lookbehind:!0,alias:"function"}}),i.languages.makefile={comment:{pattern:/(^|[^\\])#(?:\\(?:\r\n|[\s\S])|[^\\\r\n])*/,lookbehind:!0},string:{pattern:/(["'])(?:\\(?:\r\n|[\s\S])|(?!\1)[^\\\r\n])*\1/,greedy:!0},builtin:/\.[A-Z][^:#=\s]+(?=\s*:(?!=))/,symbol:{pattern:/^[^:=\r\n]+(?=\s*:(?!=))/m,inside:{variable:/\$+(?:[^(){}:#=\s]+|(?=[({]))/}},variable:/\$+(?:[^(){}:#=\s]+|\([@*%<^+?][DF]\)|(?=[({]))/,keyword:[/-include\b|\b(?:define|else|endef|endif|export|ifn?def|ifn?eq|include|override|private|sinclude|undefine|unexport|vpath)\b/,{pattern:/(\()(?:addsuffix|abspath|and|basename|call|dir|error|eval|file|filter(?:-out)?|findstring|firstword|flavor|foreach|guile|if|info|join|lastword|load|notdir|or|origin|patsubst|realpath|shell|sort|strip|subst|suffix|value|warning|wildcard|word(?:s|list)?)(?=[ 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i.languages.objectivec["class-name"],i.languages.ocaml={comment:/\(\*[\s\S]*?\*\)/,string:[{pattern:/"(?:\\.|[^\\\r\n"])*"/,greedy:!0},{pattern:/(['`])(?:\\(?:\d+|x[\da-f]+|.)|(?!\1)[^\\\r\n])\1/i,greedy:!0}],number:/\b(?:0x[\da-f][\da-f_]+|(?:0[bo])?\d[\d_]*\.?[\d_]*(?:e[+-]?[\d_]+)?)/i,type:{pattern:/\B['`]\w*/,alias:"variable"},directive:{pattern:/\B#\w+/,alias:"function"},keyword:/\b(?:as|assert|begin|class|constraint|do|done|downto|else|end|exception|external|for|fun|function|functor|if|in|include|inherit|initializer|lazy|let|match|method|module|mutable|new|object|of|open|prefix|private|rec|then|sig|struct|to|try|type|val|value|virtual|where|while|with)\b/,boolean:/\b(?:false|true)\b/,operator:/:=|[=<>@^|&+\-*\/$%!?~][!$%&*+\-.\/:<=>?@^|~]*|\b(?:and|asr|land|lor|lxor|lsl|lsr|mod|nor|or)\b/,punctuation:/[(){}\[\]|_.,:;]/},i.languages.python={comment:{pattern:/(^|[^\\])#.*/,lookbehind:!0},"string-interpolation":{pattern:/(?:f|rf|fr)(?:("""|''')[\s\S]+?\1|("|')(?:\\.|(?!\2)[^\\\r\n])*\2)/i,greedy:!0,inside:{interpolation:{pattern:/((?:^|[^{])(?:{{)*){(?!{)(?:[^{}]|{(?!{)(?:[^{}]|{(?!{)(?:[^{}])+})+})+}/,lookbehind:!0,inside:{"format-spec":{pattern:/(:)[^:(){}]+(?=}$)/,lookbehind:!0},"conversion-option":{pattern:/![sra](?=[:}]$)/,alias:"punctuation"},rest:null}},string:/[\s\S]+/}},"triple-quoted-string":{pattern:/(?:[rub]|rb|br)?("""|''')[\s\S]+?\1/i,greedy:!0,alias:"string"},string:{pattern:/(?:[rub]|rb|br)?("|')(?:\\.|(?!\1)[^\\\r\n])*\1/i,greedy:!0},function:{pattern:/((?:^|\s)def[ 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i.languages.reason.function,function(e){e.languages.sass=e.languages.extend("css",{comment:{pattern:/^([ \t]*)\/[\/*].*(?:(?:\r?\n|\r)\1[ \t]+.+)*/m,lookbehind:!0}}),e.languages.insertBefore("sass","atrule",{"atrule-line":{pattern:/^(?:[ \t]*)[@+=].+/m,inside:{atrule:/(?:@[\w-]+|[+=])/m}}}),delete e.languages.sass.atrule;var t=/\$[-\w]+|#\{\$[-\w]+\}/,n=[/[+*\/%]|[=!]=|<=?|>=?|\b(?:and|or|not)\b/,{pattern:/(\s+)-(?=\s)/,lookbehind:!0}];e.languages.insertBefore("sass","property",{"variable-line":{pattern:/^[ \t]*\$.+/m,inside:{punctuation:/:/,variable:t,operator:n}},"property-line":{pattern:/^[ \t]*(?:[^:\s]+ *:.*|:[^:\s]+.*)/m,inside:{property:[/[^:\s]+(?=\s*:)/,{pattern:/(:)[^:\s]+/,lookbehind:!0}],punctuation:/:/,variable:t,operator:n,important:e.languages.sass.important}}}),delete e.languages.sass.property,delete e.languages.sass.important,e.languages.insertBefore("sass","punctuation",{selector:{pattern:/([ \t]*)\S(?:,?[^,\r\n]+)*(?:,(?:\r?\n|\r)\1[ 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