1.推导的潮流公式是对的，已经验证过

2.已经做成了只有负荷功率以及电压幅值量测的WLS方法。

3.如果ieee输电网算例不收敛，是因为不满足客观性（要考虑0注入约束）
4.ieee4-DN.dat是在原有ieee4节点算例上修改，改成所有节点都有负荷的形式。

Signed-off-by: dmy@lab <dmy@lab.lab>

run.m

@@ -2,7 +2,8 @@ clear
 clc
 % yalmip('clear')
 addpath('.\Powerflow')
-[~, ~, ~, ~,Volt,Vangle,Y,Yangle,r,c,newwordParameter,PG,QG,PD,QD,Balance]=pf('E:\ËãÀý\feeder33\feeder33ieee.txt', '0');
+[~, ~, ~, ~,Volt,Vangle,Y,Yangle,r,c,newwordParameter,PG,QG,PD,QD,Balance]=pf('ieee4-DN.dat', '0');
+% 'E:\算例\feeder33\feeder33ieee.txt'
 %% 开始生成量测量
 sigma=0.03;% 标准差
 %% 电压
@@ -74,6 +75,7 @@ onlyQG=setdiff(QGi,PDQDi);
 measureSigma=abs(([rVolt;rPD(PDi);rQD(QDi);].*sigma));
 measureSigma(measureSigma<1e-6)=mean(measureSigma(measureSigma>1e-6));
 W=sparse(diag(1./measureSigma.^2)) ;
+% W=eye(length(W));
 % W=sparse(1:length(W),1:length(W),400,length(W),length(W));
 %% 冗余度计算
 stateVarCount=2*length(Volt);
@@ -102,17 +104,19 @@ fprintf('
 SEVolt=sparse(ones(length(mVolt),1));
 SEVolt(Balance)=rVolt(Balance);
 SEVAngle=sparse(-0.00*ones(length(mVolt),1));
+% SEVolt=rVolt;
+% SEVAngle=rVAngel;
 maxD=1000;
 Iteration=0;
 optimalCondition=100;
-eps=1e-4;
+eps=1e-5;
 mu=0;
 v=2;
 ojbFunDecrease=1000;% 目标函数下降
 % 以下都是Jacobi矩阵
 % while max(abs(g))>1e-5;
 % while maxD>1e-5
-while max(abs(maxD))>eps
+while max(abs(optimalCondition))>eps
     % 电压
     dV_dV=sparse(1:length(mVolt),1:length(mVolt),1,length(mVolt),length(mVolt));%电压量测量的微分
     dV_dTyta=sparse(length(mVolt),length(mVolt));
@@ -213,8 +217,8 @@ while max(abs(maxD))>eps
     YdotCos=Y.* ( spfun (@cos, VAngleIJ ) );
     diag_Volt_YdotCos=diag(SEVolt)*YdotCos;
     diag_Volt_YdotSin=diag(SEVolt)*YdotSin;
-    YdotCosVolt=YdotCos*Volt;
+    YdotCosVolt=YdotCos*SEVolt;
-    YdotSinVolt=YdotSin*Volt;
+    YdotSinVolt=YdotSin*SEVolt;
     diag_Volt_YdotCosVolt=diag_Volt_YdotCos*Volt;
     diag_Volt_YdotSinVolt=diag_Volt_YdotSin*Volt;
     diag_YdotSinVolt_=diag(YdotSinVolt);
@@ -223,6 +227,23 @@ while max(abs(maxD))>eps
     dQdTyta=-diag_Volt_YdotCos*diag(SEVolt)+diag_YdotCosVolt_*diag(SEVolt);%dQ/dThyta
     dPdV=diag_YdotCosVolt_+diag_Volt_YdotCos;%dP/dV
     dQdV=diag_YdotSinVolt_+diag_Volt_YdotSin;%dQ/dV
+    %采用我自己推导的公式
+    dPdV_=diag(SEVolt)*YdotCos+diag(YdotCos*SEVolt);
+    dQdV_=diag(SEVolt)*YdotSin+diag(YdotSin*SEVolt);
+    dPdTyta_=diag(SEVolt)*(YdotSin*diag(SEVolt)-diag(YdotSin*SEVolt));
+    dQdTyta_=diag(SEVolt)*(-YdotCos*diag(SEVolt)+diag(YdotCos*SEVolt));
+    if any(abs(dPdV_-dPdV)>1e-5)
+        abc=1;
+    end
+    if any(abs(dQdV_-dQdV)>1e-5)
+        abc=1;
+    end
+    if any(abs(dPdTyta_-dPdTyta)>1e-5)
+        abc=1;
+    end
+    if any(abs(dQdTyta_-dQdTyta)>1e-5)
+        abc=1;
+    end
     %     % C 是等式约束 c 的Jacobi
     %     C=[dPdV dPdTyta;
     %         dQdV dQdTyta];
@@ -269,23 +290,25 @@ while max(abs(maxD))>eps
 %         dTPij_dVi+dTPij_dVj,dTPij_dThetai+dTPij_dThetaj;
 %         dTQij_dVi+dTQij_dVj,dTQij_dThetai+dTQij_dThetaj];%jacobi
     H=[dV_dV,dV_dTyta;
-        -dPdV(PDi,:),-dPdTyta(PDi,:);
+        dPdV(PDi,:),dPdTyta(PDi,:);
-        -dQdV(QDi,:),-dQdTyta(QDi,:)];%jacobi
+        dQdV(QDi,:),dQdTyta(QDi,:)];%jacobi
     
     SEBranchI=BranchI( SEVolt.*exp(1j*SEVAngle),lineI,lineJ,lineR,lineX );%复数支路电流
     SEBranchP=BranchP( SEVolt.*exp(1j*SEVAngle),SEBranchI,lineI,lineB2 );
     SEBranchQ=BranchQ( SEVolt.*exp(1j*SEVAngle),SEBranchI,lineI,lineB2 );
     SETransP=TransPower( newwordParameter,SEVolt,SEVAngle );
     SETransQ=TransReactivePower( newwordParameter,SEVolt,SEVAngle );
-    SEPD=-diag(SEVolt)*Y.* ( spfun (@cos, VAngleIJ ) )*SEVolt;
+%     rAngleIJ=sparse(r,c,rVAngel(r)-rVAngel(c) -Yangle,length(mVolt),length(mVolt)) ;
-    SEQD=-diag(SEVolt)*Y.* ( spfun(@sin,VAngleIJ) )*SEVolt;
+%     diag(rVolt)*Y.* ( spfun (@cos, rAngleIJ ) )*rVolt;
+    SEPD=diag(SEVolt)*Y.* ( spfun (@cos, VAngleIJ ) )*SEVolt;
+    SEQD=diag(SEVolt)*Y.* ( spfun(@sin,VAngleIJ) )*SEVolt;
     
     h=[SEVolt;SEPD(PDi);SEQD(QDi);];
     
 %     h=[SEVolt;SEBranchP;SEBranchQ;SETransP;SETransQ];
 %     z=[mVolt;mBranchP;mBranchQ;mTransP;mTransQ];
 
-    z=[mVolt;mPD(PDi);mQD(QDi)];
+    z=[mVolt;-mPD(PDi);-mQD(QDi)];
 
 
     G=H'*W*H;

公式/公式.tex

@@ -399,6 +399,135 @@ V_2
 \right\}
 \end{equation}
 
+接下来推导潮流无功公式
+\begin{equation}
+\Delta Q =diag ( \left[
+\begin{array}{c}
+V_1\\
+V_2
+\end{array}
+\right]
+)
+\left[ 
+\begin{array}{cc}
+sin(t_1-t_1) & sin(t_1-t_2) \\
+sin(t_2-t_1) & sin(t_2-t_2)
+\end{array}	
+\right]
+\left[
+\begin{array}{c}
+V_1\\
+V_2
+\end{array}	
+\right]
+\end{equation}
+
+\begin{equation}
+\Delta Q=
+diag(
+\left[
+\begin{array}{c}
+V_1 \\
+V_2
+\end{array}
+\right]
+)
+\left[
+\begin{array}{c}
+V_1sin(t_1-t_1)+V_2sin(t_1-t_2) \\
+V_1sin(t_2-t_1)+V_2sin(t_2-t_2) \\
+\end{array}
+\right]
+\end{equation}
+
+\begin{equation}
+\dfrac{\partial \Delta Q}{\partial t}=
+diag(
+\left[
+\begin{array}{c}
+V_1 \\
+V_2
+\end{array}
+\right]
+)
+\left[
+\begin{array}{cc}
+V_2cos(t_1-t_2) & -V_2cos(t_1-t_2) \\
+-V_1cos(t_2-t_1) & V_1cos(t_2-t_1)
+\end{array}
+\right]
+\end{equation}
+
+\begin{equation}
+\dfrac{\partial \Delta Q}{\partial t}=
+\begin{array}{c}
+diag(
+\left[
+\begin{array}{c}
+V_1 \\
+V_2
+\end{array}
+\right]
+)\\
+\left[
+\begin{array}{cc}
+-V_1cos(t_1-t_1) & -V_2cos(t_1-t_2) \\
+-V_1cos(t_2-t_1) & -V_2cos(t_2-t_2)
+\end{array}
+\right]
++
+\left[
+\begin{array}{cc}
+V_1cos(t_1-t_1)+V_2cos(t_1-t_2) & 0  \\
+0 & V_1cos(t_2-t_1)+V_2cos(t_2-t_2)
+\end{array}
+\right]
+
+\end{array}
+\end{equation}
+
+\begin{equation}
+\dfrac{\partial \Delta Q}{\partial t}=
+diag(
+\left[
+\begin{array}{c}
+V_1 \\
+V_2
+\end{array}
+\right]
+)
+\left\{
+-
+\left[
+\begin{array}{cc}
+cos(t_1-t_1) & cos(t_1-t_2) \\
+cos(t_2-t_1) & cos(t_2-t_2)
+\end{array}
+\right]
+diag(
+\left[
+\begin{array}{c}
+V_1 \\
+V_2
+\end{array}
+\right]
+)
++diag(
+\left[
+\begin{array}{cc}
+cos(t_1-t_1) & cos(t_1-t_2) \\
+cos(t_2-t_1) & cos(t_2-t_2)
+\end{array}
+\right]
+\left[
+\begin{array}{c}
+V_1 \\
+V_2
+\end{array}
+\right]
+)
+\right\}
+\end{equation}
 
 
 潮流方程有功的公式为