1.更新了公式
2.修复了dQij_dVi的公式 Signed-off-by: facat <facat@facat.cn>
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facat
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5e07471ce3
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run.m
47
run.m
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@ -33,6 +33,8 @@ lineX=newwordParameter.line.lineX;
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lineB2=newwordParameter.line.lineB2;
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lineG=real(1./(lineR+1j*lineX));
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lineB=imag(1./(lineR+1j*lineX));
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% 处理线路电阻或电抗为0的情况，即消除NaN
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zerosRXInd=union(find(abs(lineR)<1e-5),find(abs(lineX)<1e-5));
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cmpBranchI=BranchI( cmpV,lineI,lineJ,lineR,lineX );%复数支路电流
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rBranchI=abs(cmpBranchI);% 支路电流幅值
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mBranchI=rBranchI.*(normrnd(0,sigma,length(rBranchI),1)+1);%支路电流量测量
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@ -47,6 +49,9 @@ mBranchP=rBranchP.*(normrnd(0,sigma,length(rBranchP),1)+1);%֧·
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rBranchQ=BranchQ( cmpV,cmpBranchI,lineI,lineB2 );
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% rBranchQ=rBranchQ(abs(rBranchQ)>1e-5);
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mBranchQ=rBranchQ.*(normrnd(0,sigma,length(rBranchQ),1)+1);%支路功率量测量
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% 处理线路电阻或电抗为0的情况，即消除NaN
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mBranchP=mBranchP(setdiff( 1:length(mBranchP),zerosRXInd));
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mBranchQ=mBranchQ(setdiff( 1:length(mBranchQ),zerosRXInd));
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%% 注入功率
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rPD=PD;
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PDi=find(PD~=0);
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@ -106,7 +111,7 @@ Iteration=0;
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while maxD>1e-3;
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dV_dV=sparse(1:length(mVolt),1:length(mVolt),1,length(mVolt),length(mVolt));%电压量测量的微分
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dV_dTyta=sparse(length(mVolt),length(mVolt));
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dLPij_dVi=sparse(1:length(lineI),lineJ, ...
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dLPij_dVi=sparse(1:length(lineI),lineI, ...
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-SEVolt(lineJ).*( ...
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lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
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)...
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@ -117,7 +122,7 @@ dLPij_dVj=sparse(1:length(lineI),lineJ, ...
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lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
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) ...
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,length(lineI),length(mVolt));%线路的
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dLPij_dThetai=sparse(1:length(lineI),lineJ, ...
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dLPij_dThetai=sparse(1:length(lineI),lineI, ...
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SEVolt(lineI).*SEVolt(lineJ).*( ...
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lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))...
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)...
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@ -128,9 +133,9 @@ dLPij_dThetaj=sparse(1:length(lineI),lineJ, ...
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)...
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,length(lineI),length(mVolt));%线路的
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dLQij_dVi=sparse(1:length(lineI),lineJ, ...
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dLQij_dVi=sparse(1:length(lineI),lineI, ...
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-SEVolt(lineJ).*( ...
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lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
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lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))...
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)...
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-2*(lineB+lineB2).*SEVolt(lineI) ...
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,length(lineI),length(mVolt));%线路的
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@ -139,7 +144,7 @@ dLQij_dVj=sparse(1:length(lineI),lineJ, ...
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lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))...
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) ...
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,length(lineI),length(mVolt));%线路的
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dLQij_dThetai=sparse(1:length(lineI),lineJ, ...
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dLQij_dThetai=sparse(1:length(lineI),lineI, ...
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-SEVolt(lineI).*SEVolt(lineJ).*( ...
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lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
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) ...
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@ -150,7 +155,6 @@ dLQij_dThetaj=sparse(1:length(lineI),lineJ, ...
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) ...
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,length(lineI),length(mVolt));%线路的
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% 处理线路电阻或电抗为0的情况，即消除NaN
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zerosRXInd=union(find(abs(lineR)<1e-5),find(abs(lineX)<1e-5));
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dLPij_dVi=dLPij_dVi(setdiff( 1:size(dLPij_dVi,1),zerosRXInd),:);
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dLPij_dVj=dLPij_dVj(setdiff( 1:size(dLPij_dVj,1),zerosRXInd),:);
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dLPij_dThetai=dLPij_dThetai(setdiff( 1:size(dLPij_dThetai,1),zerosRXInd),:);
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@ -160,16 +164,26 @@ dLQij_dVj=dLQij_dVj(setdiff( 1:size(dLQij_dVj,1),zerosRXInd),:);
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dLQij_dThetai=dLQij_dThetai(setdiff( 1:size(dLQij_dThetai,1),zerosRXInd),:);
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dLQij_dThetaj=dLQij_dThetaj(setdiff( 1:size(dLQij_dThetaj,1),zerosRXInd),:);
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% 对量测值做同样处理
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mBranchP=mBranchP(setdiff( 1:length(mBranchP),zerosRXInd));
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mBranchQ=mBranchQ(setdiff( 1:length(mBranchQ),zerosRXInd));
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%% 进入迭代
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H=[dV_dV ,dV_dTyta;
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dLPij_dVi+dLPij_dVj, dLPij_dThetai+dLPij_dThetaj;
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dLQij_dVi+dLQij_dVj, dLQij_dThetai+dLQij_dThetaj];%jacobi
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% H=[dV_dV];
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h=[SEVolt;mBranchP;mBranchQ];
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z=[mVolt;mBranchP;mBranchQ];
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W=sparse(1:length(mVolt),1:length(mVolt),1/sigma.^2,length(mVolt),length(mVolt));
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% H=[dV_dV ,dV_dTyta;
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% dLPij_dVi+dLPij_dVj, dLPij_dThetai+dLPij_dThetaj;
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% dLQij_dVi+dLQij_dVj, dLQij_dThetai+dLQij_dThetaj];%jacobi
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H=[dV_dV;
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dLPij_dVi+dLPij_dVj ;
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dLQij_dVi+dLQij_dVj ];%jacobi
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SEBranchI=BranchI( SEVolt.*exp(1j*SEVAngel),lineI,lineJ,lineR,lineX );%复数支路电流
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SEBranchP=BranchP( SEVolt.*exp(1j*SEVAngel),SEBranchI,lineI,lineB2 );
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SEBranchQ=BranchQ( SEVolt.*exp(1j*SEVAngel),SEBranchI,lineI,lineB2 );
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SEBranchP=SEBranchP(setdiff( 1:length(SEBranchP),zerosRXInd));
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SEBranchQ=SEBranchQ(setdiff( 1:length(SEBranchQ),zerosRXInd));
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% h=[SEVolt;SEBranchP;SEBranchQ];
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% z=[mVolt;mBranchP;mBranchQ];
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h=[SEVolt;SEBranchP;SEBranchQ];
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z=[mVolt;mBranchP;mBranchP];
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W=sparse(1:length(h),1:length(h),1/sigma.^2,length(h),length(h));
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G=H'*W*H;
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g=-H'*W*(z-h);
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% 平衡节点相角恒定;
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@ -182,11 +196,10 @@ maxD=max(abs(dX))
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% 更新变量
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SEVolt=SEVolt+dX(1:length(mVolt));
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Iteration=Iteration+1;
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SEVAngel=SEVAngel+dX(length(mVolt)+1:end);
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% SEVAngel=SEVAngel+dX(length(mVolt)+1:end);
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end
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%% 输出结果
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fprintf('迭代%d次\n',Iteration);
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h=SEVolt;
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fval=full((z-h)'*W*(z-h));
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fprintf('目标函数为:%f\n',fval);
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fprintf('相对误差\n');
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65
公式/公式.tex
65
公式/公式.tex
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@ -25,7 +25,7 @@
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\end{equation}
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\begin{equation}
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\begin{aligned}
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\dot{S}^*_{12}&=V_1e^{j \theta_1}
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\dot{S}_{12}&=V_1e^{j \theta_1}
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\dot{I}^*_{12} \\
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&=V_1e^{j \theta_1}
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(V_1e^{-j \theta_1} - V_2e^{-j \theta_2})
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@ -50,15 +50,74 @@
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有功传输功率
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\begin{equation}
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\begin{aligned}
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\dot{P}_{ij}&=[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]G_{ij}-V_1V_2sin (\theta_1 - \theta_2)B_{ij} \\
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P_{ij}&=[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]G_{ij}-V_1V_2sin (\theta_1 - \theta_2)B_{ij} \\
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&=V_1^2G_{ij}-V_1V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
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\end{aligned}
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\end{equation}
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无功传输功率
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\begin{equation}
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\begin{aligned}
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\dot{Q}_{ij}&=-[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]B_{ij}-V_1V_2sin (\theta_1 - \theta_2)G_{ij} \\
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Q_{ij}&=-[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]B_{ij}-V_1V_2sin (\theta_1 - \theta_2)G_{ij} \\
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&=-V_1^2B_{ij}-V_1V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}]
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\end{aligned}
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\end{equation}
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线路有功功率Jacobi
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\begin{equation}
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\begin{aligned}
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\frac{\partial P_{ij}}{\partial V_1}=
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2V_1G_{ij}-V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
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\end{aligned}
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\end{equation}
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\begin{equation}
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\begin{aligned}
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\frac{\partial P_{12}}{\partial V_2}=
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-V_1[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
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\end{aligned}
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\end{equation}
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\begin{equation}
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\begin{aligned}
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\frac{\partial P_{12}}{\partial \theta_1}&=
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-V_1V_2[-sin(\theta_1 - \theta_2)G_{ij}+cos (\theta_1 - \theta_2)B_{ij}] \\
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&=V_1V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}]
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\end{aligned}
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\end{equation}
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\begin{equation}
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\begin{aligned}
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\frac{\partial P_{12}}{\partial \theta_2}&=
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-V_1V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}] \\
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\end{aligned}
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\end{equation}
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\begin{equation}
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\begin{aligned}
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\frac{\partial Q_{12}}{\partial V_1}&=
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-2V_1B_{12}-V_2[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}]
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\end{aligned}
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\end{equation}
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\begin{equation}
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\begin{aligned}
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\frac{\partial Q_{12}}{\partial V_2}&=
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-V_1[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}]
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\end{aligned}
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\end{equation}
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\begin{equation}
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\begin{aligned}
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\frac{\partial Q_{12}}{\partial \theta_1}&=
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-V_1V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
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\end{aligned}
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\end{equation}
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\begin{equation}
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\begin{aligned}
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\frac{\partial Q_{12}}{\partial \theta_2}&=
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-V_1V_2[-cos(\theta_1 - \theta_2)G_{ij}-sin (\theta_1 - \theta_2)B_{ij}] \\
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&=V_1V_2[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]
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\end{aligned}
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\end{equation}
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\end{document}
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