添加变压器支路的公式

Signed-off-by: facat <facat@facat.cn>

run.m

@@ -2,7 +2,7 @@ clear
 clc
 % yalmip('clear')
 addpath('.\Powerflow')
-[~, ~, ~, ~,Volt,Vangle,Y,Yangle,r,c,newwordParameter,PG,QG,PD,QD,Balance]=pf('ieee14.dat', '0');
+[~, ~, ~, ~,Volt,Vangle,Y,Yangle,r,c,newwordParameter,PG,QG,PD,QD,Balance]=pf('ieee4.dat', '0');
 %% 量测量
 % 电压 节点电流 支路电流 节点功率 支路功率
 %%
@@ -170,9 +170,9 @@ dLQij_dThetaj=dLQij_dThetaj(setdiff( 1:size(dLQij_dThetaj,1),zerosRXInd),:);
 %   dLPij_dVi+dLPij_dVj, dLPij_dThetai+dLPij_dThetaj;
 %   dLQij_dVi+dLQij_dVj, dLQij_dThetai+dLQij_dThetaj];%jacobi
 
-H=[dV_dV;
-    dLPij_dVi+dLPij_dVj ;
-    dLQij_dVi+dLQij_dVj ];%jacobi
+H=[dV_dV,dV_dTyta;
+    dLPij_dVi+dLPij_dVj,dLPij_dThetai+dLPij_dThetaj ;
+    dLQij_dVi+dLQij_dVj,dLQij_dThetai+dLQij_dThetaj ];%jacobi
 
 SEBranchI=BranchI( SEVolt.*exp(1j*SEVAngel),lineI,lineJ,lineR,lineX );%复数支路电流
 SEBranchP=BranchP( SEVolt.*exp(1j*SEVAngel),SEBranchI,lineI,lineB2 );
@@ -194,9 +194,9 @@ g=-H'*W*(z-h);
 dX=G\-g;
 maxD=max(abs(dX))
 % 更新变量
-SEVolt=SEVolt+dX(1:length(mVolt));
+% SEVolt=SEVolt+dX(1:length(mVolt));
 Iteration=Iteration+1;
-% SEVAngel=SEVAngel+dX(length(mVolt)+1:end);
+SEVAngel=SEVAngel+dX(1:end);
 end
 %% 输出结果
 fprintf('迭代%d次\n',Iteration);

公式/公式.tex

@@ -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}