From b612769e820a3c98d13f9b15374c2d3621b4b2f7 Mon Sep 17 00:00:00 2001 From: facat Date: Thu, 15 Aug 2013 20:59:36 +0800 Subject: [PATCH] =?UTF-8?q?=E6=8E=A8=E5=AF=BC=E5=85=AC=E5=BC=8F=E9=94=99?= =?UTF-8?q?=E4=BA=86?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Signed-off-by: facat --- run.asv | 92 ++-- run.m | 71 ++- 公式/公式.aux | 1 - 公式/公式.log | 918 ------------------------------------ 公式/公式.pdf | Bin 9774 -> 0 bytes 公式/公式.tex | 145 +++++- 公式/公式.tex.bak | 21 - 公式/鍏紡.synctex.gz(busy) | Bin 1625 -> 0 bytes 8 files changed, 255 insertions(+), 993 deletions(-) delete mode 100644 公式/公式.aux delete mode 100644 公式/公式.log delete mode 100644 公式/公式.pdf delete mode 100644 公式/公式.tex.bak delete mode 100644 公式/鍏紡.synctex.gz(busy) diff --git a/run.asv b/run.asv index ae2ebc2..c132cff 100644 --- a/run.asv +++ b/run.asv @@ -37,11 +37,13 @@ cmpBranchI=(cmpV(lineI)-cmpV(lineJ))./(lineR+1j*lineX);% rBranchI=abs(cmpBranchI);% ֧·ֵ mBranchI=rBranchI.*(normrnd(0,sigma,length(rBranchI),1)+1);%֧· %% ֧· -rBranchP=real((cmpV(lineI)-cmpV(lineJ)).*conj(cmpBranchI)); -rBranchP=rBranchP(abs(rBranchP)>1e-5); +rBranchP=real((cmpV(lineI)-cmpV(lineJ)).*conj(cmpBranchI))+real(cmpV(lineI) .*conj(1j*lineB2.*cmpV(lineI) ) ); +rV=abs(cmpV); +rA=imag( +% rBranchP=rBranchP(abs(rBranchP)>1e-5); mBranchP=rBranchP.*(normrnd(0,sigma,length(rBranchP),1)+1);%֧· -rBranchQ=imag((cmpV(lineI)-cmpV(lineJ)).*conj(cmpBranchI)); -rBranchQ=rBranchQ(abs(rBranchQ)>1e-5); +rBranchQ=imag((cmpV(lineI)-cmpV(lineJ)).*conj(cmpBranchI))+imag(cmpV(lineI) .*conj(1j*lineB2.*cmpV(lineI) ) ); +% rBranchQ=rBranchQ(abs(rBranchQ)>1e-5); mBranchQ=rBranchQ.*(normrnd(0,sigma,length(rBranchQ),1)+1);%֧· %% ע빦 rPD=PD; @@ -97,56 +99,92 @@ Busnum=length(Volt); % ¶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));%ѹ΢ 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))... + lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... )... +2*(lineG).*SEVolt(lineI) ... ,length(lineI),length(mVolt));%· dLPij_dVj=sparse(1:length(lineI),lineJ, ... -SEVolt(lineI).*( ... - lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineX.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... + lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... + ) ... + ,length(lineI),length(mVolt));%· +dLPij_dThetai=sparse(1:length(lineI),lineJ, ... + SEVolt(lineI).*SEVolt(lineJ).*( ... + lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))... + )... + ,length(lineI),length(mVolt));%· +dLPij_dThetaj=sparse(1:length(lineI),lineJ, ... + -SEVolt(lineI).*SEVolt(lineJ).*( ... + lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))... + )... + ,length(lineI),length(mVolt));%· + +dLQij_dVi=sparse(1:length(lineI),lineJ, ... + -SEVolt(lineJ).*( ... + lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... + )... + -2*(lineB+lineB2).*SEVolt(lineI) ... + ,length(lineI),length(mVolt));%· +dLQij_dVj=sparse(1:length(lineI),lineJ, ... + -SEVolt(lineI).*( ... + lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))... + ) ... + ,length(lineI),length(mVolt));%· +dLQij_dThetai=sparse(1:length(lineI),lineJ, ... + -SEVolt(lineI).*SEVolt(lineJ).*( ... + lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... + ) ... + ,length(lineI),length(mVolt));%· +dLQij_dThetaj=sparse(1:length(lineI),lineJ, ... + SEVolt(lineI).*SEVolt(lineJ).*( ... + lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... ) ... ,length(lineI),length(mVolt));%· % ·翹Ϊ0NaN 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));%· -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));%· +dLPij_dThetai=dLPij_dThetai(setdiff( 1:size(dLPij_dThetai,1),zerosRXInd),:); +dLPij_dThetaj=dLPij_dThetaj(setdiff( 1:size(dLPij_dThetaj,1),zerosRXInd),:); dLQij_dVi=dLQij_dVi(setdiff( 1:size(dLQij_dVi,1),zerosRXInd),:); dLQij_dVj=dLQij_dVj(setdiff( 1:size(dLQij_dVj,1),zerosRXInd),:); +dLQij_dThetai=dLQij_dThetai(setdiff( 1:size(dLQij_dThetai,1),zerosRXInd),:); +dLQij_dThetaj=dLQij_dThetaj(setdiff( 1:size(dLQij_dThetaj,1),zerosRXInd),:); %% -H=[dV_dV ;dV_dTyta]'; +H=[dV_dV ,dV_dTyta; + dLPij_dVi+dLPij_dVj, dLPij_dThetai+dLPij_dThetaj; + dLQij_dVi+dLQij_dVj, dLQij_dThetai+dLQij_dThetaj];%jacobi +% 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); % ƽڵǺ㶨; -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; +% 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+ +SEVolt=SEVolt+dX(1:length(mVolt)); +Iteration=Iteration+1; +SEVAngel=SEVAngel+dX(length(mVolt)+1:end); +end %% +fprintf('%d\n',Iteration); +h=SEVolt; +fval=full((z-h)'*W*(z-h)); fprintf('Ŀ꺯Ϊ:%f\n',fval); fprintf('\n'); (abs(rVolt-double(SEVolt)))./(rVolt) MaxDeviation(rVolt,SEVolt,rVAngel,SEVAngel) -plotAndComparison( rVolt,rVAngel,SEVolt,SEVAngel ) -seOpti.fun(x); \ No newline at end of file +plotAndComparison( rVolt,rVAngel,SEVolt,SEVAngel ) \ No newline at end of file diff --git a/run.m b/run.m index 45d9943..ffb79c8 100644 --- a/run.m +++ b/run.m @@ -31,17 +31,21 @@ lineJ=newwordParameter.line.lineJ; lineR=newwordParameter.line.lineR; lineX=newwordParameter.line.lineX; lineB2=newwordParameter.line.lineB2; -lineG=1./lineR; -lineB=1./lineX; +lineG=real(1./(lineR+1j*lineX)); +lineB=imag(1./(lineR+1j*lineX)); cmpBranchI=(cmpV(lineI)-cmpV(lineJ))./(lineR+1j*lineX);%֧· rBranchI=abs(cmpBranchI);% ֧·ֵ mBranchI=rBranchI.*(normrnd(0,sigma,length(rBranchI),1)+1);%֧· %% ֧· -rBranchP=real((cmpV(lineI)-cmpV(lineJ)).*conj(cmpBranchI)); -rBranchP=rBranchP(abs(rBranchP)>1e-5); +rBranchP=real((cmpV(lineI)-cmpV(lineJ)).*conj(cmpBranchI))+real(cmpV(lineI) .*conj(1j*lineB2.*cmpV(lineI) ) ); +rV=abs(cmpV); +rA=angle(cmpV); +a=rV(lineI).^2.*(lineG)-rV(lineI).*rV(lineJ).*(lineG.*cos(rA(lineI)-rA(lineJ) )+lineB.*sin(rA(lineI)-rA(lineJ) ) ); +b=-rV(lineI).^2.*(lineB+lineB2)-rV(lineI).*rV(lineJ).*(lineG.*sin(rA(lineI)-rA(lineJ) )-lineB.*cos(rA(lineI)-rA(lineJ) ) ); +% rBranchP=rBranchP(abs(rBranchP)>1e-5); mBranchP=rBranchP.*(normrnd(0,sigma,length(rBranchP),1)+1);%֧· -rBranchQ=imag((cmpV(lineI)-cmpV(lineJ)).*conj(cmpBranchI)); -rBranchQ=rBranchQ(abs(rBranchQ)>1e-5); +rBranchQ=imag((cmpV(lineI)-cmpV(lineJ)).*conj(cmpBranchI))+imag(cmpV(lineI) .*conj(1j*lineB2.*cmpV(lineI) ) ); +% rBranchQ=rBranchQ(abs(rBranchQ)>1e-5); mBranchQ=rBranchQ.*(normrnd(0,sigma,length(rBranchQ),1)+1);%֧· %% ע빦 rPD=PD; @@ -104,34 +108,61 @@ 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))... + lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... )... +2*(lineG).*SEVolt(lineI) ... ,length(lineI),length(mVolt));%· dLPij_dVj=sparse(1:length(lineI),lineJ, ... -SEVolt(lineI).*( ... - lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineX.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... + lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... + ) ... + ,length(lineI),length(mVolt));%· +dLPij_dThetai=sparse(1:length(lineI),lineJ, ... + SEVolt(lineI).*SEVolt(lineJ).*( ... + lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))... + )... + ,length(lineI),length(mVolt));%· +dLPij_dThetaj=sparse(1:length(lineI),lineJ, ... + -SEVolt(lineI).*SEVolt(lineJ).*( ... + lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))... + )... + ,length(lineI),length(mVolt));%· + +dLQij_dVi=sparse(1:length(lineI),lineJ, ... + -SEVolt(lineJ).*( ... + lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... + )... + -2*(lineB+lineB2).*SEVolt(lineI) ... + ,length(lineI),length(mVolt));%· +dLQij_dVj=sparse(1:length(lineI),lineJ, ... + -SEVolt(lineI).*( ... + lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))... + ) ... + ,length(lineI),length(mVolt));%· +dLQij_dThetai=sparse(1:length(lineI),lineJ, ... + -SEVolt(lineI).*SEVolt(lineJ).*( ... + lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... + ) ... + ,length(lineI),length(mVolt));%· +dLQij_dThetaj=sparse(1:length(lineI),lineJ, ... + SEVolt(lineI).*SEVolt(lineJ).*( ... + lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))... ) ... ,length(lineI),length(mVolt));%· % ·翹Ϊ0NaN 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));%· -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));%· +dLPij_dThetai=dLPij_dThetai(setdiff( 1:size(dLPij_dThetai,1),zerosRXInd),:); +dLPij_dThetaj=dLPij_dThetaj(setdiff( 1:size(dLPij_dThetaj,1),zerosRXInd),:); dLQij_dVi=dLQij_dVi(setdiff( 1:size(dLQij_dVi,1),zerosRXInd),:); dLQij_dVj=dLQij_dVj(setdiff( 1:size(dLQij_dVj,1),zerosRXInd),:); +dLQij_dThetai=dLQij_dThetai(setdiff( 1:size(dLQij_dThetai,1),zerosRXInd),:); +dLQij_dThetaj=dLQij_dThetaj(setdiff( 1:size(dLQij_dThetaj,1),zerosRXInd),:); %% -H=[dV_dV ,dV_dTyta]; +H=[dV_dV ,dV_dTyta; + dLPij_dVi+dLPij_dVj, dLPij_dThetai+dLPij_dThetaj; + dLQij_dVi+dLQij_dVj, dLQij_dThetai+dLQij_dThetaj];%jacobi % H=[dV_dV]; h=SEVolt; z=mVolt; diff --git a/公式/公式.aux b/公式/公式.aux deleted file mode 100644 index f23e546..0000000 --- a/公式/公式.aux +++ /dev/null @@ -1 +0,0 @@ -\relax diff --git a/公式/公式.log b/公式/公式.log deleted file mode 100644 index d64fc4d..0000000 --- a/公式/公式.log +++ /dev/null @@ -1,918 +0,0 @@ -This is XeTeX, Version 3.1415926-2.3-0.9997.5 (MiKTeX 2.9) (preloaded format=xelatex 2013.5.6) 14 AUG 2013 12:13 -entering extended mode -**公式.tex -(D:\Matlab\StateEstimation-self-derivatives\公式\公式.tex -LaTeX2e <2011/06/27> -Babel and hyphenation patterns for loaded. -(C:\CTEX\MiKTeX\tex\latex\base\report.cls -Document Class: report 2007/10/19 v1.4h Standard LaTeX document class -(C:\CTEX\MiKTeX\tex\latex\base\size10.clo 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234) - defining Unicode char U+00EB (decimal 235) - defining Unicode char U+00EC (decimal 236) - defining Unicode char U+00ED (decimal 237) - defining Unicode char U+00EE (decimal 238) - defining Unicode char U+00EF (decimal 239) - defining Unicode char U+00F0 (decimal 240) - defining Unicode char U+00F1 (decimal 241) - defining Unicode char U+00F2 (decimal 242) - defining Unicode char U+00F3 (decimal 243) - defining Unicode char U+00F4 (decimal 244) - defining Unicode char U+00F5 (decimal 245) - defining Unicode char U+00F6 (decimal 246) - defining Unicode char U+00F8 (decimal 248) - defining Unicode char U+00F9 (decimal 249) - defining Unicode char U+00FA (decimal 250) - defining Unicode char U+00FB (decimal 251) - defining Unicode char U+00FC (decimal 252) - defining Unicode char U+00FD (decimal 253) - defining Unicode char U+00FE (decimal 254) - defining Unicode char U+00FF (decimal 255) - defining Unicode char U+0102 (decimal 258) - defining Unicode char U+0103 (decimal 259) - defining Unicode char U+0104 (decimal 260) - defining Unicode char U+0105 (decimal 261) - defining Unicode char U+0106 (decimal 262) - defining Unicode char U+0107 (decimal 263) - defining Unicode char U+010C (decimal 268) - defining Unicode char U+010D (decimal 269) - defining Unicode char U+010E (decimal 270) - defining Unicode char U+010F (decimal 271) - defining Unicode char U+0110 (decimal 272) - defining Unicode char U+0111 (decimal 273) - defining Unicode char U+0118 (decimal 280) - defining Unicode char U+0119 (decimal 281) - defining Unicode char U+011A (decimal 282) - defining Unicode char U+011B (decimal 283) - defining Unicode char U+011E (decimal 286) - defining Unicode char U+011F (decimal 287) - defining Unicode char U+0130 (decimal 304) - defining Unicode char U+0131 (decimal 305) - defining Unicode char U+0132 (decimal 306) - defining Unicode char U+0133 (decimal 307) - defining Unicode char U+0139 (decimal 313) - defining Unicode char U+013A (decimal 314) - defining 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diff --git a/公式/公式.tex b/公式/公式.tex index f687f23..38d99d8 100644 --- a/公式/公式.tex +++ b/公式/公式.tex @@ -9,13 +9,146 @@ \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} +线路功率（不考虑接地导纳） +\newline \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 +\dot{I}_{12}&=(V_1 e^{j\theta_1} - V_2 e^{j\theta_2} ) +(G+jB) \\ +&=[V_1 (cos\theta_1+jsin\theta_1) - V_2 (cos\theta_2+jsin\theta_2)](G+jB) \\ +&=(V_1 cos\theta_1+ jV_1 sin\theta_1- V_2 cos \theta_2 -j V_2 sin \theta_2)(G+jB) \\ +&=(V_1 cos \theta_1 -V_2 cos \theta_2)G + j(V_1 sin \theta_1- V_2 sin \theta_2)G +\\&+j( V_1 cos \theta_1 -V_2 cos \theta_2)B + j(jV_1 sin \theta_1-jV_2 sin \theta_2)B \\ +&=G(V_1 cos \theta_1- V_2 cos \theta_2) - B(V_1 sin \theta_1 -V_2 sin \theta_2) \\ +&+jB(V_1 cos \theta_1 - V_2 cos \theta_2) + jG(V_1 sin \theta_1 - V_2 sin \theta_2) \\ +&= V_1( G cos \theta_1-B sin \theta_1) -V_2 (G cos \theta_2 - B sin \theta_2) \\ +&+jV_1(Bcos \theta_1+Gsin\theta_1)-jV_2(Bcos\theta_2+Gsin\theta_2) \end{aligned} \end{equation} - -\end{document} \ No newline at end of file +电流的共轭复数 +\begin{equation} +\begin{aligned} +\dot{I}^*_{12}&=V_1( G cos \theta_1-B sin \theta_1) -V_2 (G cos \theta_2 - B sin \theta_2) \\ +&-jV_1(Bcos \theta_1+Gsin\theta_1)+jV_2(Bcos\theta_2+Gsin\theta_2) +\end{aligned} +\end{equation} +线路复功率 +\begin{equation} +\begin{aligned} +\dot{S}_{12}&=(V_1 e^{j\theta_1} - V_2 e^{j\theta_2} ) +\dot{I}^*_{12} \\ +&=[V_1 (cos\theta_1+jsin\theta_1) - V_2 (cos\theta_2+jsin\theta_2)]\dot{I}^*_{12} \\ +&=[V_1 (cos\theta_1+jsin\theta_1) - V_2 (cos\theta_2+jsin\theta_2)] \\ +&[V_1( G cos \theta_1-B sin \theta_1) -V_2 (G cos \theta_2 - B sin \theta_2) +-jV_1(Bcos \theta_1+Gsin\theta_1)+jV_2(Bcos\theta_2+Gsin\theta_2)]\\ +&=V_1( G cos \theta_1-B sin \theta_1) +[V_1( G cos \theta_1-B sin \theta_1) -V_2 (G cos \theta_2 - B sin \theta_2)]\\ +&-V_1( G cos \theta_1-B sin \theta_1) +[jV_1(Bcos \theta_1+Gsin\theta_1)-jV_2(Bcos\theta_2+Gsin\theta_2)] \\ +&- V_2 (cos\theta_2+jsin\theta_2) +[V_1( G cos \theta_1-B sin \theta_1) -V_2 (G cos \theta_2 - B sin \theta_2)]\\ +&V_2 (cos\theta_2+jsin\theta_2) +[jV_1(Bcos \theta_1+Gsin\theta_1)-jV_2(Bcos\theta_2+Gsin\theta_2)] +\end{aligned} +\end{equation} +另一种推导方式 +\begin{equation} +\begin{aligned} +\dot{I}_{12}=(V_1 e^{j\theta_1} - V_2 e^{j\theta_2} ) +(G+jB) +\end{aligned} +\end{equation} +电流的共轭复数 +\begin{equation} +\begin{aligned} +\dot{I}^*_{12}=(V_1 e^{-j\theta_1} - V_2 e^{-j\theta_2} ) +(G-jB) +\end{aligned} +\end{equation} +线路复功率 +\begin{equation} +\begin{aligned} +\dot{S}_{12}&=(V_1 e^{j\theta_1} - V_2 e^{j\theta_2} )\dot{I}^*_{12} \\ +&=(V_1 e^{j\theta_1} - V_2 e^{j\theta_2} ) +(V_1 e^{-j\theta_1} - V_2 e^{-j\theta_2} ) +(G-jB) \\ +&=(V_1 e^{j\theta_1}V_1 e^{-j\theta_1} - V_1 e^{j\theta_1}V_2 e^{-j\theta_2} +- V_2 e^{j\theta_2}V_1 e^{-j\theta_1}+ V_2 e^{j\theta_2}V_2 e^{-j\theta_2} +) +(G-jB) \\ +&=(V_1^2+V_2^2-V_1V_2e^{j(\theta_1-\theta_2)} -V_1V_2e^{j(\theta_2-\theta_1)} ) +(G-jB) \\ +&=[V_1^2+V_2^2 +-V_1V_2(e^{j(\theta_1-\theta_2)}+e^{j(\theta_2-\theta_1)}) +](G-jB) \\ +&=\{V_1^2+V_2^2-V_1V_2[cos(\theta_1-\theta_2)+jsin(\theta_1-\theta_2) ++cos(\theta_2-\theta_1)+jsin(\theta_2-\theta_1)]\}(G-jB) \\ +&=\{V_1^2+V_2^2-V_1V_2[cos(\theta_1-\theta_2) ++cos(\theta_1-\theta_2)]\}(G-jB) \\ +&=[V_1^2+V_2^2-2V_1V_2cos(\theta_1-\theta_2)](G-jB) \\ +&=(V_1^2+V_2^2)G-j(V_1^2+V_2^2)B-j2V_1V_2cos(\theta_1-\theta_2)G-j2V_1V_2cos(\theta_1-\theta_2)(-jB) \\ +&=(V_1^2+V_2^2)G-2V_1V_2cos(\theta_1-\theta_2)B +-j(V_1^2+V_2^2)B-j2V_1V_2cos(\theta_1-\theta_2)G +\end{aligned} +\end{equation} +\begin{equation} +\begin{aligned} +P_{12}=(V_1^2+V_2^2)G+2V_1V_2sin(\theta_1-\theta_2)B +\end{aligned} +\end{equation} +\begin{equation} +\begin{aligned} +Q_{12}=-(V_1^2+V_2^2)B+2V_1V_2sin(\theta_1-\theta_2)G +\end{aligned} +\end{equation} +考虑接地支路,接地电流为 +\begin{equation} +\label{接地电流} +\dot{I}_{1}=V_1e^{j\theta_1}(G_d+jB_d) +\end{equation} +(\ref{接地电流})共轭为 +\begin{equation} +\dot{I}_{1}^{*}=V_1e^{-j\theta_1}(G_d-jB_d) +\end{equation} +%Sd +\begin{equation} +\begin{aligned} +\dot{S}_{1}&=V_1e^{j\theta_1}\dot{I}_{1}^{*} \\ +&=V_1e^{j\theta_1} +V_1e^{-j\theta_1}(G_d-jB_d) \\ +&=V_1^2(G_d-jB_d) +\end{aligned} +\end{equation} +因而 +\begin{equation} +\begin{aligned} +P_{1}&=V_1^2 G_d \\ +\end{aligned} +\end{equation} +\begin{equation} +\begin{aligned} +Q_{1}&=-V_1^2 B_d \\ +\end{aligned} +\end{equation} +考虑节点支路后的注入电流 +\begin{equation} +\begin{aligned} +\tilde{P}_{12}&=V_1^2 G_d ++(V_1^2+V_2^2)G+2V_1V_2sin(\theta_1-\theta_2)B +\end{aligned} +\end{equation} +\begin{equation} +\begin{aligned} +\tilde{Q}_{12}&=-V_1^2 B_d +-(V_1^2+V_2^2)B+2V_1V_2sin(\theta_1-\theta_2)G +\end{aligned} +\end{equation} +\end{document} diff --git a/公式/公式.tex.bak b/公式/公式.tex.bak deleted file mode 100644 index f687f23..0000000 --- a/公式/公式.tex.bak +++ /dev/null @@ -1,21 +0,0 @@ -\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} \ No newline at end of file diff --git a/公式/鍏紡.synctex.gz(busy) b/公式/鍏紡.synctex.gz(busy) deleted file mode 100644 index 56a8dc0ccf97f511815d074d07d7aaa9f5d15793..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1625 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