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Diffstat (limited to 'docs/assets/js/109a3630.56afc9a7.js')
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",Object(n.b)("span",{parentName:"li",className:"math math-inline"},Object(n.b)("span",{parentName:"span",className:"katex"},Object(n.b)("span",{parentName:"span",className:"katex-mathml"},Object(n.b)("math",{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)("msub",{parentName:"mrow"},Object(n.b)("mi",{parentName:"msub"},"Q"),Object(n.b)("mi",{parentName:"msub"},"i"))),Object(n.b)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"Q_i")))),Object(n.b)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},Object(n.b)("span",{parentName:"span",className:"base"},Object(n.b)("span",{parentName:"span",className:"strut",style:{height:"0.8777699999999999em",verticalAlign:"-0.19444em"}}),Object(n.b)("span",{parentName:"span",className:"mord"},Object(n.b)("span",{parentName:"span",className:"mord 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admonition-info alert alert--info"},Object(n.b)("div",{parentName:"div",className:"admonition-heading"},Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",{parentName:"h5",className:"admonition-icon"},Object(n.b)("svg",{parentName:"span",xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"},Object(n.b)("path",{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",{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",{parentName:"div",className:"admonition-heading"},Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",{parentName:"h5",className:"admonition-icon"},Object(n.b)("svg",{parentName:"span",xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"},Object(n.b)("path",{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",{parentName:"div",className:"admonition-content"},Object(n.b)("p",{parentName:"div"},"O tipo de barra deve ser definido no ",Object(n.b)("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",{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",{parentName:"p",href:"powerEditor"},"editor de pot\xeancia"),", a execu\xe7\xe3o do fluxo de carga \xe9 realizada no ",Object(n.b)("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(p.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",{parentName:"div",className:"admonition-heading"},Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",{parentName:"h5",className:"admonition-icon"},Object(n.b)("svg",{parentName:"span",xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"},Object(n.b)("path",{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",{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",{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",{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",{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",{parentName:"div",className:"admonition-heading"},Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",{parentName:"h5",className:"admonition-icon"},Object(n.b)("svg",{parentName:"span",xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"},Object(n.b)("path",{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",{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",{parentName:"p",href:"text"},"elementos de texto vinculado"),", ao posicionar o mouse sobre os elementos e em ",Object(n.b)("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",{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",{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",{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",{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",{parentName:"p",className:"math math-inline"},Object(n.b)("span",{parentName:"span",className:"katex"},Object(n.b)("span",{parentName:"span",className:"katex-mathml"},Object(n.b)("math",{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",{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",{parentName:"semantics",encoding:"application/x-tex"},"\\dot{V}_i^0")))),Object(n.b)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},Object(n.b)("span",{parentName:"span",className:"base"},Object(n.b)("span",{parentName:"span",className:"strut",style:{height:"1.178854em",verticalAlign:"-0.258664em"}}),Object(n.b)("span",{parentName:"span",className:"mord"},Object(n.b)("span",{parentName:"span",className:"mord accent"},Object(n.b)("span",{parentName:"span",className:"vlist-t"},Object(n.b)("span",{parentName:"span",className:"vlist-r"},Object(n.b)("span",{parentName:"span",className:"vlist",style:{height:"0.9201900000000001em"}},Object(n.b)("span",{parentName:"span",style:{top:"-3em"}},Object(n.b)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),Object(n.b)("span",{parentName:"span",className:"mord"},Object(n.b)("span",{parentName:"span",className:"mord mathdefault",style:{marginRight:"0.22222em"}},"V"))),Object(n.b)("span",{parentName:"span",style:{top:"-3.25233em"}},Object(n.b)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),Object(n.b)("span",{parentName:"span",className:"accent-body",style:{left:"-0.13889em"}},Object(n.b)("span",{parentName:"span",className:"mord"},"\u02d9"))))))),Object(n.b)("span",{parentName:"span",className:"msupsub"},Object(n.b)("span",{parentName:"span",className:"vlist-t vlist-t2"},Object(n.b)("span",{parentName:"span",className:"vlist-r"},Object(n.b)("span",{parentName:"span",className:"vlist",style:{height:"0.8141079999999999em"}},Object(n.b)("span",{parentName:"span",style:{top:"-2.441336em",marginRight:"0.05em"}},Object(n.b)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),Object(n.b)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},Object(n.b)("span",{parentName:"span",className:"mord mathdefault mtight"},"i"))),Object(n.b)("span",{parentName:"span",style:{top:"-3.063em",marginRight:"0.05em"}},Object(n.b)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),Object(n.b)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},Object(n.b)("span",{parentName:"span",className:"mord mtight"},"0")))),Object(n.b)("span",{parentName:"span",className:"vlist-s"},"\u200b")),Object(n.b)("span",{parentName:"span",className:"vlist-r"},Object(n.b)("span",{parentName:"span",className:"vlist",style:{height:"0.258664em"}},Object(n.b)("span",{parentName:"span"})))))))))),") que devem ser calculadas. 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mtight"},Object(n.b)("span",{parentName:"span",className:"mord mathdefault mtight"},"c"),Object(n.b)("span",{parentName:"span",className:"mord mathdefault mtight"},"a"),Object(n.b)("span",{parentName:"span",className:"mord mathdefault mtight",style:{marginRight:"0.01968em"}},"l"),Object(n.b)("span",{parentName:"span",className:"mord mathdefault mtight"},"c"))))),Object(n.b)("span",{parentName:"span",className:"vlist-s"},"\u200b")),Object(n.b)("span",{parentName:"span",className:"vlist-r"},Object(n.b)("span",{parentName:"span",className:"vlist",style:{height:"0.247em"}},Object(n.b)("span",{parentName:"span"}))))))))))),Object(n.b)("p",null,"O passo seguinte \xe9 a forma\xe7\xe3o da matriz jacobiana. Com isso \xe9 poss\xedvel calcular as corre\xe7\xf5es de m\xf3dulo e \xe2ngulo das tens\xf5es de todas as barras (com exce\xe7\xe3o da barra de refer\xeancia). Para tanto, no PSP-UFU utiliza-se o m\xe9todo de ",Object(n.b)("a",{parentName:"p",href:"https://en.wikipedia.org/wiki/Gaussian_elimination"},"Elimina\xe7\xe3o Gaussiana")," e em sequ\xeancia a substitui\xe7\xe3o regressiva. 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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",{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",{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",{parentName:"li",href:"https://doi.org/10.1109/TPAS.1967.291823"},"https://doi.org/10.1109/TPAS.1967.291823"))))}N.isMDXComponent=!0}}]);
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