只以电压作为量测量,收敛.

Signed-off-by: facat <facat@facat.cn>
This commit is contained in:
facat 2013-08-14 22:25:16 +08:00
parent 006adb9fc0
commit 6f5326f93e
8 changed files with 1090 additions and 59 deletions

98
run.asv
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@ -10,10 +10,11 @@ addpath('.\Powerflow')
% 电压 相角
%%
%% 开始生成量测量
sigma=0.01;% ±ê×¼²î
sigma=0.05;% 标准差
%% 电压
%电压幅值
rVolt=Volt; %幅值
BalanceVolt=Volt(Balance);
mVolt=rVolt.*(normrnd(0,sigma,length(Volt),1)+1);%电压量测量
rVAngel=Vangle;
%% 电流
@ -29,15 +30,18 @@ lineI=newwordParameter.line.lineI;
lineJ=newwordParameter.line.lineJ;
lineR=newwordParameter.line.lineR;
lineX=newwordParameter.line.lineX;
lineB2=newwordParameter.line;
lineB2=newwordParameter.line.lineB2;
lineG=1./lineR;
lineB=1./lineX;
cmpBranchI=(cmpV(lineI)-cmpV(lineJ))./(lineR+1j*lineX);%复数支路电流
rBranchI=abs(cmpBranchI);% 支路电流幅值
mBranchI=rBranchI.*(normrnd(0,sigma,length(rBranchI),1)+1);%支路电流量测量
%% 支路功率
rBranchP=real((cmpV(lineI)-cmpV(lineJ)).*conj(cmpBranchI));
rBranchP=rBranchP(abs(rBranchP)>1e-5);
mBranchP=rBranchP.*(normrnd(0,sigma,length(rBranchP),1)+1);%支路功率量测量
rBranchQ=imag((cmpV(lineI)-cmpV(lineJ)).*conj(cmpBranchI));
rBranchQ=rBranchQ(abs(rBranchQ)>1e-5);
mBranchQ=rBranchQ.*(normrnd(0,sigma,length(rBranchQ),1)+1);%支路功率量测量
%% 注入功率
rPD=PD;
@ -71,7 +75,6 @@ measurements=length(mVolt)+length(mBranchI)+length(mBranchP)+length(mBranchQ)+le
fprintf('冗余度 %f\n',measurements/stateVarCount);
%% Opti ToolBox
Busnum=length(Volt);
seOpti=SEOpti();
%% save
% save('mVolt','mVolt');
% save('mPG','mPG');
@ -82,36 +85,65 @@ seOpti=SEOpti();
% save('mTransP','mTransP');
% save('mTransQ','mTransQ');
%% load
load('mVolt');
load('mPG');
load('mQG');
load('mBranchI');
load('mBranchP');
load('mBranchQ');
load('mTransP');
load('mTransQ');
seOpti=seOpti.init(Busnum, mVolt,sigma,newwordParameter,zerosInjectionIndex,cmpY,onlyPG,onlyQG,mPG,mQG,Balance,mBranchI,mBranchP,mBranchQ,mTransP,mTransQ);
opts = optiset('solver','ipopt');
opts.maxiter=85500;
opts.maxtime=3000;
opts.maxfeval=85000;
opts.maxnodes=85000;
opts.tolrfun=1e-4;
opts.tolafun=1e-4;
opts.warnings='all';
opts.display='off';
% x0=[ones(Busnum,1);zeros(Busnum,1)];
x0=[rVolt;rVAngle];
[~,seOpti]=seOpti.equ(x0);
nlrhs=seOpti.nlrhs();
nle=seOpti.nle();
Opt = opti('fun',@seOpti.fun,'ndec',length(Volt)*2,'nlmix',@seOpti.equ,nlrhs,nle,'options',opts)
% Opt = opti('fun',@seOpti.fun,'ndec',length(Volt)*2,'options',opts)
[x,fval,exitflag,info] = solve(Opt,x0);
info
% load('mVolt');
% load('mPG');
% load('mQG');
% load('mBranchI');
% load('mBranchP');
% load('mBranchQ');
% load('mTransP');
% load('mTransQ');
%% 自己写的微分代码
% 以下都是Jacobi矩阵
SEVolt=sparse(ones(length(mVolt),1));
SEVAngel=sparse(zeros(length(mVolt),1));
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));
dLPij_dVi=sparse(1:length(lineI),lineJ, ...
-SEVolt(lineJ).*( ...
lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineX.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
)...
+2*(lineG).*SEVolt(lineI) ...
,length(lineI),length(mVolt));%线路的
dLPij_dVj=sparse(1:length(lineI),lineJ, ...
-SEVolt(lineI).*( ...
lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineX.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
) ...
,length(lineI),length(mVolt));%线路的
% 处理线路电阻或电抗为0的情况即消除NaN
zerosRXInd=union(find(abs(lineR)<1e-5),find(abs(lineX)<1e-5));
dLPij_dVi=dLPij_dVi(setdiff( 1:size(dLPij_dVi,1),zerosRXInd),:);
dLPij_dVj=dLPij_dVj(setdiff( 1:size(dLPij_dVj,1),zerosRXInd),:);
dLQij_dVi=sparse(1:length(lineI),lineJ, ...
-SEVolt(lineJ).*( ...
lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) -lineX.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
)...
-2*(lineB+lineB2).*SEVolt(lineI) ...
,length(lineI),length(mVolt));%线路的
dLQij_dVj=sparse(1:length(lineI),lineJ, ...
-SEVolt(lineI).*( ...
lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineX.*cos(SEVAngel(lineI)-SEVAngel(lineJ))...
) ...
,length(lineI),length(mVolt));%线路的
dLQij_dVi=dLQij_dVi(setdiff( 1:size(dLQij_dVi,1),zerosRXInd),:);
dLQij_dVj=dLQij_dVj(setdiff( 1:size(dLQij_dVj,1),zerosRXInd),:);
%% 进入迭代
H=[dV_dV ;dV_dTyta]';
h=SEVolt;
z=mVolt;
W=sparse(1:length(mVolt),1:length(mVolt),1/sigma.^2,length(mVolt),length(mVolt));
G=H'*W*H;
g=-H'*W*(z-h);
% 平衡节点相角恒定;
G(length(mVolt)+Balance,:)=0;
G(:,length(mVolt)+Balance)=0;
G=G+sparse(length(mVolt)+Balance,length(mVolt)+Balance,1,length(mVolt)*2,length(mVolt)*2);
g(length(mVolt)+Balance)=0;
dX=-g\G;
% 更新变量
SEVolt=SEVolt+
%% 输出结果
SEVolt=x(1:length(Volt));
SEVAngel=x(length(Volt)+Balance:2*length(Volt));
fprintf('目标函数为:%f\n',fval);
fprintf('相对误差\n');
(abs(rVolt-double(SEVolt)))./(rVolt)

88
run.m
View File

@ -30,8 +30,9 @@ lineI=newwordParameter.line.lineI;
lineJ=newwordParameter.line.lineJ;
lineR=newwordParameter.line.lineR;
lineX=newwordParameter.line.lineX;
lineB2=newwordParameter.line;
lineB2=newwordParameter.line.lineB2;
lineG=1./lineR;
lineB=1./lineX;
cmpBranchI=(cmpV(lineI)-cmpV(lineJ))./(lineR+1j*lineX);%
rBranchI=abs(cmpBranchI);%
mBranchI=rBranchI.*(normrnd(0,sigma,length(rBranchI),1)+1);%
@ -74,7 +75,6 @@ measurements=length(mVolt)+length(mBranchI)+length(mBranchP)+length(mBranchQ)+le
fprintf(' %f\n',measurements/stateVarCount);
%% Opti ToolBox
Busnum=length(Volt);
seOpti=SEOpti();
%% save
% save('mVolt','mVolt');
% save('mPG','mPG');
@ -93,31 +93,69 @@ seOpti=SEOpti();
% load('mBranchQ');
% load('mTransP');
% load('mTransQ');
seOpti=seOpti.init(Busnum, mVolt,sigma,newwordParameter,zerosInjectionIndex,cmpY,onlyPG,onlyQG,mPG,mQG,Balance,mBranchI,mBranchP,mBranchQ,mTransP,mTransQ,BalanceVolt,rVolt,rVAngel);
opts = optiset('solver','ipopt');
opts.maxiter=85500;
opts.maxtime=3000;
opts.maxfeval=85000;
opts.maxnodes=85000;
opts.tolrfun=1e-4;
opts.tolafun=1e-4;
opts.warnings='all';
opts.display='off';
x0=[ones(Busnum,1);-0.2*ones(Busnum,1)];
% x0=[rVolt;rVAngel];
[~,seOpti]=seOpti.equ(x0);
nlrhs=seOpti.nlrhs();
nle=seOpti.nle();
Opt = opti('fun',@seOpti.fun,'ndec',length(Volt)*2,'nlmix',@seOpti.equ,nlrhs,nle,'options',opts)
% Opt = opti('fun',@seOpti.fun,'ndec',length(Volt)*2,'options',opts)
[x,fval,exitflag,info] = solve(Opt,x0);
info
%%
% Jacobi
SEVolt=sparse(ones(length(mVolt),1));
SEVAngel=sparse(zeros(length(mVolt),1));
maxD=1000;
Iteration=0;
while maxD>1e-3;
dV_dV=sparse(1:length(mVolt),1:length(mVolt),1,length(mVolt),length(mVolt));%
dV_dTyta=sparse(length(mVolt),length(mVolt));
dLPij_dVi=sparse(1:length(lineI),lineJ, ...
-SEVolt(lineJ).*( ...
lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineX.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
)...
+2*(lineG).*SEVolt(lineI) ...
,length(lineI),length(mVolt));%线
dLPij_dVj=sparse(1:length(lineI),lineJ, ...
-SEVolt(lineI).*( ...
lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineX.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
) ...
,length(lineI),length(mVolt));%线
% 线0NaN
zerosRXInd=union(find(abs(lineR)<1e-5),find(abs(lineX)<1e-5));
dLPij_dVi=dLPij_dVi(setdiff( 1:size(dLPij_dVi,1),zerosRXInd),:);
dLPij_dVj=dLPij_dVj(setdiff( 1:size(dLPij_dVj,1),zerosRXInd),:);
dLQij_dVi=sparse(1:length(lineI),lineJ, ...
-SEVolt(lineJ).*( ...
lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) -lineX.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
)...
-2*(lineB+lineB2).*SEVolt(lineI) ...
,length(lineI),length(mVolt));%线
dLQij_dVj=sparse(1:length(lineI),lineJ, ...
-SEVolt(lineI).*( ...
lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineX.*cos(SEVAngel(lineI)-SEVAngel(lineJ))...
) ...
,length(lineI),length(mVolt));%线
dLQij_dVi=dLQij_dVi(setdiff( 1:size(dLQij_dVi,1),zerosRXInd),:);
dLQij_dVj=dLQij_dVj(setdiff( 1:size(dLQij_dVj,1),zerosRXInd),:);
%%
H=[dV_dV ,dV_dTyta];
% H=[dV_dV];
h=SEVolt;
z=mVolt;
W=sparse(1:length(mVolt),1:length(mVolt),1/sigma.^2,length(mVolt),length(mVolt));
G=H'*W*H;
g=-H'*W*(z-h);
% ;
% G(length(mVolt)+Balance,:)=0;
% G(:,length(mVolt)+Balance)=0;
% G=G+sparse(length(mVolt)+Balance,length(mVolt)+Balance,1,length(mVolt)*2,length(mVolt)*2);
% g(length(mVolt)+Balance)=0;
dX=G\-g;
maxD=max(abs(dX))
%
SEVolt=SEVolt+dX(1:length(mVolt));
Iteration=Iteration+1;
SEVAngel=SEVAngel+dX(length(mVolt)+1:end);
end
%%
SEVolt=x(1:length(Volt));
SEVAngel=x(length(Volt)+Balance:2*length(Volt));
fprintf('%d\n',Iteration);
h=SEVolt;
fval=full((z-h)'*W*(z-h));
fprintf(':%f\n',fval);
fprintf('\n');
(abs(rVolt-double(SEVolt)))./(rVolt)
MaxDeviation(rVolt,SEVolt,rVAngel,SEVAngel)
plotAndComparison( rVolt,rVAngel,SEVolt,SEVAngel )
seOpti.fun(x);

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. Adjusting the maths setup (use [no-math] to avoid this).
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\symlegacymaths=\mathgroup6
LaTeX Font Info: Overwriting symbol font `legacymaths' in version `bold'
(Font) OT1/cmr/m/n --> OT1/cmr/bx/n on input line 11.
LaTeX Font Info: Redeclaring math accent \acute on input line 11.
LaTeX Font Info: Redeclaring math accent \grave on input line 11.
LaTeX Font Info: Redeclaring math accent \ddot on input line 11.
LaTeX Font Info: Redeclaring math accent \tilde on input line 11.
LaTeX Font Info: Redeclaring math accent \bar on input line 11.
LaTeX Font Info: Redeclaring math accent \breve on input line 11.
LaTeX Font Info: Redeclaring math accent \check on input line 11.
LaTeX Font Info: Redeclaring math accent \hat on input line 11.
LaTeX Font Info: Redeclaring math accent \dot on input line 11.
LaTeX Font Info: Redeclaring math accent \mathring on input line 11.
LaTeX Font Info: Redeclaring math symbol \Gamma on input line 11.
LaTeX Font Info: Redeclaring math symbol \Delta on input line 11.
LaTeX Font Info: Redeclaring math symbol \Theta on input line 11.
LaTeX Font Info: Redeclaring math symbol \Lambda on input line 11.
LaTeX Font Info: Redeclaring math symbol \Xi on input line 11.
LaTeX Font Info: Redeclaring math symbol \Pi on input line 11.
LaTeX Font Info: Redeclaring math symbol \Sigma on input line 11.
LaTeX Font Info: Redeclaring math symbol \Upsilon on input line 11.
LaTeX Font Info: Redeclaring math symbol \Phi on input line 11.
LaTeX Font Info: Redeclaring math symbol \Psi on input line 11.
LaTeX Font Info: Redeclaring math symbol \Omega on input line 11.
LaTeX Font Info: Redeclaring math symbol \mathdollar on input line 11.
LaTeX Font Info: Redeclaring symbol font `operators' on input line 11.
LaTeX Font Info: Encoding `OT1' has changed to `EU1' for symbol font
(Font) `operators' in the math version `normal' on input line 11.
LaTeX Font Info: Overwriting symbol font `operators' in version `normal'
(Font) OT1/cmr/m/n --> EU1/宋体(0)/m/n on input line 11.
LaTeX Font Info: Encoding `OT1' has changed to `EU1' for symbol font
(Font) `operators' in the math version `bold' on input line 11.
LaTeX Font Info: Overwriting symbol font `operators' in version `bold'
(Font) OT1/cmr/bx/n --> EU1/宋体(0)/m/n on input line 11.
LaTeX Font Info: Overwriting symbol font `operators' in version `normal'
(Font) EU1/宋体(0)/m/n --> EU1/宋体(0)/m/n on input line 1
1.
LaTeX Font Info: Overwriting math alphabet `\mathrm' in version `normal'
(Font) EU1/宋体(0)/m/n --> EU1/宋体(0)/m/n on input line 1
1.
LaTeX Font Info: Overwriting math alphabet `\mathit' in version `normal'
(Font) OT1/cmr/m/it --> EU1/宋体(0)/m/it on input line 11.
LaTeX Font Info: Overwriting math alphabet `\mathbf' in version `normal'
(Font) OT1/cmr/bx/n --> EU1/宋体(0)/bx/n on input line 11.
LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `normal'
(Font) OT1/cmss/m/n --> EU1/lmss/m/n on input line 11.
LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `normal'
(Font) OT1/cmtt/m/n --> EU1/lmtt/m/n on input line 11.
LaTeX Font Info: Overwriting symbol font `operators' in version `bold'
(Font) EU1/宋体(0)/m/n --> EU1/宋体(0)/bx/n on input line
11.
LaTeX Font Info: Overwriting math alphabet `\mathrm' in version `bold'
(Font) EU1/宋体(0)/m/n --> EU1/宋体(0)/bx/n on input line
11.
LaTeX Font Info: Overwriting math alphabet `\mathit' in version `bold'
(Font) OT1/cmr/bx/it --> EU1/宋体(0)/bx/it on input line 11.
LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `bold'
(Font) OT1/cmss/bx/n --> EU1/lmss/bx/n on input line 11.
LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `bold'
(Font) OT1/cmtt/m/n --> EU1/lmtt/bx/n on input line 11.
Requested font "å®^^8bä½^^93/ICU:script=latn;language=DFLT;" at 7.0pt
-> C:/Windows/Fonts/simsun.ttc
Requested font "å®^^8bä½^^93/ICU:script=latn;language=DFLT;" at 5.0pt
-> C:/Windows/Fonts/simsun.ttc
Requested font "cmex7" at 7.0pt
-> cmex7
Requested font "cmex7" at 5.0pt
-> cmex7
LaTeX Font Info: Try loading font information for U+msa on input line 12.
(C:\CTEX\MiKTeX\tex\latex\amsfonts\umsa.fd
File: umsa.fd 2009/06/22 v3.00 AMS symbols A
)
Requested font "msam10" at 10.0pt
-> msam10
Requested font "msam7" at 7.0pt
-> msam7
Requested font "msam5" at 5.0pt
-> msam5
LaTeX Font Info: Try loading font information for U+msb on input line 12.
(C:\CTEX\MiKTeX\tex\latex\amsfonts\umsb.fd
File: umsb.fd 2009/06/22 v3.00 AMS symbols B
)
Requested font "msbm10" at 10.0pt
-> msbm10
Requested font "msbm7" at 7.0pt
-> msbm7
Requested font "msbm5" at 5.0pt
-> msbm5
[1
]
(D:\Matlab\StateEstimation-self-derivatives\å…¬å¼<C3A5>\å…¬å¼<C3A5>.aux) )
Here is how much of TeX's memory you used:
14250 strings out of 430478
297453 string characters out of 3191503
292163 words of memory out of 3000000
17264 multiletter control sequences out of 15000+200000
5427 words of font info for 33 fonts, out of 3000000 for 9000
14 hyphenation exceptions out of 8191
44i,8n,31p,604b,132s stack positions out of 5000i,500n,10000p,200000b,50000s
Output written on å…¬å¼<C3A5>.pdf (1 page).

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\documentclass[10pt,a4paper,final]{report}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{fontspec}%使用xetex
\setmainfont[BoldFont=黑体]{宋体} % 使用系统默认字体
\XeTeXlinebreaklocale "zh" % 针对中文进行断行
\XeTeXlinebreakskip = 0pt plus 1pt minus 0.1pt % 给予TeX断行一定自由度
\linespread{1.5} % 1.5倍行距
\begin{document}
\begin{equation}
\begin{aligned}
\frac{\partial P_{ij}}{\partial V_i}
&=
-V_{ij}(g_{ij}cos\theta_{ij}+b_{ij}sin\theta_{ij})+
2(g_{ij}+g_{si})V_i
\end{aligned}
\end{equation}
\end{document}

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\documentclass[10pt,a4paper,final]{report}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{fontspec}%使用xetex
\setmainfont[BoldFont=黑体]{宋体} % 使用系统默认字体
\XeTeXlinebreaklocale "zh" % 针对中文进行断行
\XeTeXlinebreakskip = 0pt plus 1pt minus 0.1pt % 给予TeX断行一定自由度
\linespread{1.5} % 1.5倍行距
\begin{document}
\begin{equation}
\begin{aligned}
\frac{\partial P_{ij}}{\partial V_i}
&=
-V_{ij}(g_{ij}cos\theta_{ij}+b_{ij}sin\theta_{ij})+
2(g_{ij}+g_{si})V_i
\end{aligned}
\end{equation}
\end{document}

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