#2062400 FGV - 2022 - Analista de Pesquisa Energética (EPE)/Transmissão de Energia

O sistema elétrico acima tem a Barra 1 escolhida como barra de referência, a Barra 2 é do tipo barra de carga e a Barra 3 é do tipo barra de geração.

Desta forma, o problema de fluxo de potência pelo método de Newton fica

\begin{bmatrix} \Delta P_1\\ \Delta Q_1 \end{bmatrix} = \begin{bmatrix} \frac{\delta P_1}{\Delta \theta_1}&\frac{\delta P_1}{\delta V_1} \\ \frac{\delta Q_1}{\delta \theta_1}& \frac{\delta Q_1}{\delta V_1} \end{bmatrix} \cdot \begin{bmatrix} \Delta \theta_1 \\ \Delta V_1 \end{bmatrix}
\begin{bmatrix} \Delta P_2\\ \Delta Q_3 \end{bmatrix} = \begin{bmatrix} \frac{\delta P_2}{\Delta \theta_2}&\frac{\delta P_2}{\delta V_3} \\ \frac{\delta Q_3}{\delta \theta_2}& \frac{\delta Q_3}{\delta V_3} \end{bmatrix} \cdot \begin{bmatrix} \Delta \theta_2 \\ \Delta V_3 \end{bmatrix}
\begin{bmatrix} \Delta P_3\\ \Delta Q_2 \end{bmatrix} = \begin{bmatrix} \frac{\delta P_3}{\Delta \theta_3}&\frac{\delta P_3}{\delta V_2} \\ \frac{\delta Q_2}{\delta \theta_3}& \frac{\delta Q_2}{\delta V_2} \end{bmatrix} \cdot \begin{bmatrix} \Delta \theta_3 \\ \Delta V_2 \end{bmatrix}
\begin{bmatrix} \Delta P_2\\ \Delta P_3 \\ \Delta Q_2 \end{bmatrix} = \begin{bmatrix} \frac{\delta P_2}{\Delta \theta_2}&\frac{\delta P_2}{\delta \theta_3}&\frac{\delta P_2}{\delta V_2} \\ \frac{\delta P_3}{\delta \theta_2}& \frac{\delta P_3}{\delta \theta_3} & \frac{\delta P_3}{\delta V_2} \\ \frac{\delta Q_2}{\delta \theta_2}& \frac{\delta Q_2}{\delta \theta_3}&\frac{\delta Q_2}{\delta V_2} \end{bmatrix} \cdot \begin{bmatrix} \Delta \theta_2 \\ \Delta \theta_3 \\ \Delta V_2 \end{bmatrix}
\begin{bmatrix} \Delta P_2\\ \Delta Q_2 \\ \Delta Q_3 \end{bmatrix} = \begin{bmatrix} \frac{\delta P_2}{\Delta \theta_2}&\frac{\delta P_2}{\delta V_2}&\frac{\delta P_2}{\delta V_2} \\ \frac{\delta Q_2}{\delta \theta_2}& \frac{\delta Q_2}{\delta V_2} & \frac{\delta Q_2}{\delta V_3} \\ \frac{\delta Q_3}{\delta \theta_2}& \frac{\delta Q_3}{\delta V_2}&\frac{\delta Q_3}{\delta V_3} \end{bmatrix} \cdot \begin{bmatrix} \Delta \theta_2 \\ \Delta V_2 \\ \Delta V_3 \end{bmatrix}