更新电流，有功，无功计算公式。开始考虑接地支路。
Signed-off-by: facat <facat@facat.cn>
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facat
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@ -1,5 +1,5 @@
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function [ output_args ] = BranchI( V,lineI,lineJ,lineR,lineX )
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output_args=(V(lineI)-V(lineJ))./(lineR+1j*lineX);
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function [ output_args ] = BranchI( V,lineI,lineJ,lineR,lineX,lineB2 )
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output_args=(V(lineI)-V(lineJ))./(lineR+1j*lineX)+V(lineI).*lineB2;
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end
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@ -1,4 +1,4 @@
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function [ output_args ] = BranchP( V,I,lineI,lineB2 )
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output_args=real((V(lineI)).*conj(I))+real(V(lineI) .*conj(1j*lineB2.*V(lineI) ) );
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output_args=real((V(lineI)).*conj(I));
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end
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@ -1,4 +1,4 @@
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function [ output_args ] = BranchQ( V,I,lineI,lineB2 )
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output_args=imag((V(lineI)).*conj(I))+imag(V(lineI) .*conj(1j*lineB2.*V(lineI) ) );
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output_args=imag((V(lineI)).*conj(I));
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end
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9
run.m
9
run.m
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@ -2,7 +2,7 @@ clear
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clc
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% yalmip('clear')
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addpath('.\Powerflow')
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[~, ~, ~, ~,Volt,Vangle,Y,Yangle,r,c,newwordParameter,PG,QG,PD,QD,Balance]=pf('s1047.dat', '0');
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[~, ~, ~, ~,Volt,Vangle,Y,Yangle,r,c,newwordParameter,PG,QG,PD,QD,Balance]=pf('ieee14.dat', '0');
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%% 开始生成量测量
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sigma=0.03;% 标准差
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%% 电压
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@ -27,7 +27,7 @@ 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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cmpBranchI=BranchI( cmpV,lineI,lineJ,lineR,lineX );%复数支路电流
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cmpBranchI=BranchI( cmpV,lineI,lineJ,lineR,lineX,lineB2 );%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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%% 支路功率
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@ -232,13 +232,16 @@ while max(abs(optimalCondition))>eps
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% nodePQ=[nodeP;nodeQ];
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% c=nodePQ(zerosInjectionIndex);
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%% 进入迭代
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% 一阶导数
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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 ;
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dTPij_dVi+dTPij_dVj,dTPij_dThetai+dTPij_dThetaj;
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dTQij_dVi+dTQij_dVj,dTQij_dThetai+dTQij_dThetaj];%jacobi
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% 二阶导数
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SEBranchI=BranchI( SEVolt.*exp(1j*SEVAngle),lineI,lineJ,lineR,lineX );%复数支路电流
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SEBranchI=BranchI( SEVolt.*exp(1j*SEVAngle),lineI,lineJ,lineR,lineX,lineB2 );%复数支路电流
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SEBranchP=BranchP( SEVolt.*exp(1j*SEVAngle),SEBranchI,lineI,lineB2 );
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SEBranchQ=BranchQ( SEVolt.*exp(1j*SEVAngle),SEBranchI,lineI,lineB2 );
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SETransP=TransPower( newwordParameter,SEVolt,SEVAngle );
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80
公式/公式.tex
80
公式/公式.tex
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@ -61,11 +61,25 @@ Q_{ij}&=-[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]B_{ij}-V_1V_2sin (\theta_1 - \the
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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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考虑接地支路后(利用Ali Abur 书上的公式)
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\newline
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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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P_{ij}&=V_1^2(G_{ij}+G_{is})-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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Q_{ij}&=-V_1^2(B_{ij}+B_{is})-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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2V_1(G_{ij}+G_{is})-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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@ -94,7 +108,7 @@ Q_{ij}&=-[V_1^2-V_1V_2cos(\theta_1 - \theta_2)]B_{ij}-V_1V_2sin (\theta_1 - \the
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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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-2V_1(B_{12}+B_{is})-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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@ -206,20 +220,21 @@ ps.已检验过线路的公式。
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以上公式已经可以完成状态估计，若要实现更好的收敛性，需要利用二阶导数。
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\par
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线路支路功率二阶导数
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有功部分
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\begin{equation}
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\begin{aligned}
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\frac{\partial^2 P_{12}}{\partial V_1^2}&=
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\frac{-2}{k^2}B_{12}\\
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&=\frac{-2B_{12}}{k^2}
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\frac{2}{k^2}(G_{12}+G_{1s})\\
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&=\frac{2 (G_{12}+G_{1s} ) } {k^2}
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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^2 P_{12}}{\partial V_1 \partial V_2 }&=
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\frac{-1}{k}[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}] \\
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\frac{-1}{k}[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}] \\
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&=
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\frac{-[sin(\theta_1 - \theta_2)G_{ij}-cos (\theta_1 - \theta_2)B_{ij}]}{k}
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\frac{-[cos(\theta_1 - \theta_2)G_{ij}+sin (\theta_1 - \theta_2)B_{ij}]}{k}
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\end{aligned}
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\end{equation}
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@ -232,26 +247,69 @@ ps.已检验过线路的公式。
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\begin{equation}
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\begin{aligned}
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\frac{\partial P_{12}}{\partial \theta_1^2}&=
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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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\frac{V_1}{k} 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 \theta_1 \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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\frac{V_1}{k} V_2[-cos(\theta_1 - \theta_2)G_{ij}-sin (\theta_1 - \theta_2)B_{ij}] \\
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&=
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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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- \frac{V_1}{k} 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 \theta_2^2}&=
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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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- \frac{V_1}{k} V_2[-cos(\theta_1 - \theta_2)G_{ij}-sin (\theta_1 - \theta_2)B_{ij}] \\
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&=
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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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\frac{V_1}{k} 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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无功部分
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\begin{equation}
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\begin{aligned}
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\frac{\partial^2 Q_{12}}{\partial V_1 \partial V_1}&=
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-2\frac{( B_{12}+B_{1s})}{k^2}
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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^2 Q_{12}}{\partial V_1 \partial V_2}&=
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-\frac{1}{k}[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^2 Q_{12}}{\partial V_2^2}&=0
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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^2 Q_{12}}{\partial \theta_1^2}&=
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-\frac{V_1}{k}V_2[-sin(\theta_1 - \theta_2)G_{ij}+cos (\theta_1 - \theta_2)B_{ij}] \\
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&=\frac{V_1}{k}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^2 Q_{12}}{\partial \theta_1 \partial \theta_2}&=
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-\frac{V_1}{k}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^2 Q_{12}}{\partial \theta_2^2}
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&=\frac{V_1}{k}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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以上公式对线路和没有计及接地支路的变压器适用，只是线路中变比$k$为1.
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\end{document}
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