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1.更新了公式

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2.修复了dQij_dVi的公式

Signed-off-by: facat <facat@facat.cn>
This commit is contained in:
facat
2013-08-17 11:44:02 +08:00
parent 5e07471ce3
commit a4d726da90
2 changed files with 92 additions and 20 deletions
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65
公式/公式.tex
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@@ -25,7 +25,7 @@
\end{equation}
\begin{equation}
\begin{aligned}
\dot{S}^*_{12}&=V_1e^{j \theta_1}
\dot{S}_{12}&=V_1e^{j \theta_1}
\dot{I}^*_{12} \\
&=V_1e^{j \theta_1}
(V_1e^{-j \theta_1} - V_2e^{-j \theta_2})
@@ -50,15 +50,74 @@
有功传输功率
\begin{equation}
\begin{aligned}
\dot{P}_{ij}&=[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]G_{ij}-V_1V_2sin (\theta_1 - \theta_2)B_{ij} \\
P_{ij}&=[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]G_{ij}-V_1V_2sin (\theta_1 - \theta_2)B_{ij} \\
&=V_1^2G_{ij}-V_1V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
无功传输功率
\begin{equation}
\begin{aligned}
\dot{Q}_{ij}&=-[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]B_{ij}-V_1V_2sin (\theta_1 - \theta_2)G_{ij} \\
Q_{ij}&=-[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]B_{ij}-V_1V_2sin (\theta_1 - \theta_2)G_{ij} \\
&=-V_1^2B_{ij}-V_1V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
线路有功功率Jacobi
\begin{equation}
\begin{aligned}
\frac{\partial P_{ij}}{\partial V_1}=
2V_1G_{ij}-V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
\begin{equation}
\begin{aligned}
\frac{\partial P_{12}}{\partial V_2}=
-V_1[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
\begin{equation}
\begin{aligned}
\frac{\partial P_{12}}{\partial \theta_1}&=
-V_1V_2[-sin(\theta_1 - \theta_2)G_{ij}+cos (\theta_1 - \theta_2)B_{ij}] \\
&=V_1V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
\begin{equation}
\begin{aligned}
\frac{\partial P_{12}}{\partial \theta_2}&=
-V_1V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}] \\
\end{aligned}
\end{equation}
\begin{equation}
\begin{aligned}
\frac{\partial Q_{12}}{\partial V_1}&=
-2V_1B_{12}-V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
\begin{equation}
\begin{aligned}
\frac{\partial Q_{12}}{\partial V_2}&=
-V_1[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
\begin{equation}
\begin{aligned}
\frac{\partial Q_{12}}{\partial \theta_1}&=
-V_1V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
\begin{equation}
\begin{aligned}
\frac{\partial Q_{12}}{\partial \theta_2}&=
-V_1V_2[-cos(\theta_1 - \theta_2)G_{ij}-sin (\theta_1 - \theta_2)B_{ij}] \\
&=V_1V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
\end{document}