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添加变压器支路的公式

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Signed-off-by: facat <facat@facat.cn>
This commit is contained in:
facat
2013-08-17 16:35:46 +08:00
parent a4d726da90
commit 4ea4ceb639
2 changed files with 92 additions and 7 deletions
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公式/公式.tex
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@@ -90,7 +90,7 @@ Q_{ij}&=-[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]B_{ij}-V_1V_2sin (\theta_1 - \the
-V_1V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}] \\
\end{aligned}
\end{equation}
线路无功功率Jacobi
\begin{equation}
\begin{aligned}
\frac{\partial Q_{12}}{\partial V_1}&=
@@ -119,5 +119,90 @@ Q_{ij}&=-[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]B_{ij}-V_1V_2sin (\theta_1 - \the
&=V_1V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
变压器支路功率
\newline
变压器模型为
\newline
\begin{center}
----k:1----z----高压侧 \\
or \\
i----k:1----z----j \\
\end{center}
变压器支路功率
\newline
变压器有功输送功率
\begin{equation}
\begin{aligned}
P_{ij}&=[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]G_{ij}-V_1V_2sin (\theta_1 - \theta_2)B_{ij} \\
&=\frac{V_1^2}{k^2} G_{ij}-\frac{V_1}{k} V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
变压器无功输送功率
\begin{equation}
\begin{aligned}
Q_{ij}&=-[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]B_{ij}-V_1V_2sin (\theta_1 - \theta_2)G_{ij} \\
&=-\frac{V_1^2}{k^2}B_{ij}-\frac{V_1}{k} V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
变压器输送有功功率Jacobi
\begin{equation}
\begin{aligned}
\frac{\partial P_{ij}}{\partial V_1}=
2\frac{V_1}{k^2}G_{ij}-\frac{V_2}{k}[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}=
-\frac{V_1}{k}[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}
&=\frac{V_1}{k}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 P_{12}}{\partial \theta_2}&=
-\frac{V_1}{k}V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}] \\
\end{aligned}
\end{equation}
变压器输送无功功率Jacobi
\begin{equation}
\begin{aligned}
\frac{\partial Q_{12}}{\partial V_1}&=
-2\frac{V_1}{k^2}B_{12}-\frac{V_2}{k}[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}&=
-\frac{V_1}{k}[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}&=
-\frac{V_1}{k}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 Q_{12}}{\partial \theta_2}
&=\frac{V_1}{k}V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
\end{aligned}
\end{equation}
ps.已检验过线路的公式。
\end{document}