187 lines
7.1 KiB
Mathematica
187 lines
7.1 KiB
Mathematica
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function ddh=func_ddh(AngleIJMat,GB,Volt,Init_Y,Busnum)
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%% deltaPi/deltaThytai_deltaThytaj <EFBFBD>ǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t1=-Volt'*Volt;
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t2=real(GB).*cos(AngleIJMat)+imag(GB).*sin(AngleIJMat);
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dPdTidTj=t1.*t2; %%(<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>˶Խ<EFBFBD>Ԫ<EFBFBD>ص<EFBFBD>)
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dPidTidTj_2=dPdTidTj-diag(diag(dPdTidTj));%ȥ<EFBFBD><EFBFBD><EFBFBD>˶Խ<EFBFBD>Ԫ<EFBFBD>ص<EFBFBD>
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t3=repmat(Init_Y',1,size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dPidTidTj_2=dPidTidTj_2.*t3(1:2:size(Init_Y,2),1:2:size(Init_Y,2));
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t2=real(GB).*cos(AngleIJMat)-imag(GB).*sin(AngleIJMat);
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t3=t1.*t2;
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dPjdTidTj=t3-diag(diag(t3));%ȥ<EFBFBD><EFBFBD><EFBFBD>˶Խ<EFBFBD>Ԫ<EFBFBD>ص<EFBFBD>
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t3=repmat(Init_Y,size(Init_Y,2),1);
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dPjdTidTj=dPjdTidTj.*t3(1:2:size(Init_Y,2),1:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dPdTidTj=dPidTidTj_2+dPjdTidTj;%<EFBFBD><EFBFBD><EFBFBD>շǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@@
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%% deltaP/deltaThyta_deltaThyta <EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t1=sum(-dPidTidTj_2,2);
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t2=diag(t1'.*Init_Y(1:2:size(Init_Y,2)));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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t3=sum(-dPidTidTj_2,1);
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t4=diag(t3.*Init_Y(1:2:size(Init_Y,2)));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dPdTidTi=t2+t4;%%<EFBFBD><EFBFBD><EFBFBD>նԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@@
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%% deltaP/deltaThytai_dVi <EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t1=ones(Busnum,1)*Volt.*(real(GB).*sin(AngleIJMat)-imag(GB).*cos(AngleIJMat));
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t2=diag(t1);
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t3=t1-diag(t2);%ȥ<EFBFBD><EFBFBD><EFBFBD>˶Խ<EFBFBD>Ԫ<EFBFBD>ص<EFBFBD>
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t4=sum(t3,2);
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t4=t4'.*Init_Y(1:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dPidTidVi=diag(t4);
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dPidTjdVj=-t3;
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t6=sum(dPidTjdVj,1);
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t6=t6.*Init_Y(1:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dPdTidVi=dPidTidVi+diag(t6);%%<EFBFBD><EFBFBD><EFBFBD>նԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@@
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%% deltaP/deltaThytai_dVj <EFBFBD>ǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t1=ones(Busnum,1)*Volt.*(real(GB).*sin(AngleIJMat)-imag(GB).*cos(AngleIJMat));
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dPidTidVj=t1-diag(diag(t1));%%ȥ<EFBFBD><EFBFBD><EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD>ص<EFBFBD>
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t2=repmat(Init_Y',1,size(Init_Y,2));
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dPidTidVj=dPidTidVj.*t2(1:2:size(Init_Y,2),1:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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t1=ones(Busnum,1)*Volt.*(real(GB).*sin(AngleIJMat)+imag(GB).*cos(AngleIJMat));
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dPjdTidVj=t1-diag(diag(t1));%ȥ<EFBFBD><EFBFBD><EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD>ص<EFBFBD>
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t2=t2';
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dPjdTidVj=dPjdTidVj.*t2(1:2:size(Init_Y,2),1:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dPdTidVj=dPidTidVj+dPjdTidVj;%<EFBFBD><EFBFBD><EFBFBD>շǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@@
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%% deltaP/dVi_deltaThytaj <EFBFBD>ǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t1=-ones(Busnum,1)*Volt.*(real(GB).*sin(AngleIJMat)-imag(GB).*cos(AngleIJMat));
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dPidVidTj=t1-diag(diag(t1));
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t2=repmat(Init_Y',1,size(Init_Y,2));
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dPidVidTj=dPidVidTj.*t2(1:2:size(Init_Y,2),1:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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t1=-ones(Busnum,1)*Volt.*(real(GB).*sin(AngleIJMat)+imag(GB).*cos(AngleIJMat));
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dPjdVidTj=t1-diag(diag(t1));
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t2=t2';
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dPjdVidTj=dPjdVidTj.*t2(1:2:size(Init_Y,2),1:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dPdVidTj=dPidVidTj+dPjdVidTj;%<EFBFBD><EFBFBD><EFBFBD>շǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@@
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%% deltaPi/dVi_deltaThyta <EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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dPdVidTi=dPdTidVi;%<EFBFBD><EFBFBD><EFBFBD>նԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@
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%% deltaP/dVi_dVj <EFBFBD>ǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t1=-(real(GB).*cos(AngleIJMat)+imag(GB).*sin(AngleIJMat));
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dPidVidVj=t1-diag(diag(t1));%ȥ<EFBFBD><EFBFBD><EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD>ص<EFBFBD>
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t2=repmat(Init_Y',1,size(Init_Y,2));
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dPidVidVj=dPidVidVj.*t2(1:2:size(Init_Y,2),1:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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t1=-(real(GB).*cos(AngleIJMat)-imag(GB).*sin(AngleIJMat));
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dPjdVidVj=t1-diag(diag(t1));
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t2=t2';
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dPjdVidVj=dPjdVidVj.*t2(1:2:size(Init_Y,2),1:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dPdVidVj=dPidVidVj+dPjdVidVj;%<EFBFBD><EFBFBD><EFBFBD>շǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@@@
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%% deltaP/dVi_dVi <EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t0=real(GB).*cos(AngleIJMat)+imag(GB).*sin(AngleIJMat);
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t1=diag(t0);
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t2=t1'.*Init_Y(1:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dPidVidVi=-2*diag(t2);
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dPidVjdVj=0;
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dPdVidVi=dPidVidVi+dPidVjdVj;%<EFBFBD><EFBFBD><EFBFBD>նԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@@
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%% <EFBFBD><EFBFBD><EFBFBD><EFBFBD>APi
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APi=zeros(2*Busnum,2*Busnum);
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APi(1:2:2*Busnum,1:2:2*Busnum)=dPdTidTj;%%<EFBFBD>ǶԽ<EFBFBD> TT
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APi(1:2:2*Busnum,2:2:2*Busnum)=dPdTidVj;%%<EFBFBD>ǶԽ<EFBFBD> TV
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APi(2:2:2*Busnum,1:2:2*Busnum)=dPdVidTj;%%<EFBFBD>ǶԽ<EFBFBD> VT
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APi(2:2:2*Busnum,2:2:2*Busnum)=dPdVidVj;%%<EFBFBD>ǶԽ<EFBFBD> VV
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APi(1:2:2*Busnum,1:2:2*Busnum)=dPdTidTi;%%<EFBFBD>Խ<EFBFBD>
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APi(1:2:2*Busnum,2:2:2*Busnum)=dPdTidVi;%%<EFBFBD>Խ<EFBFBD>
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APi(2:2:2*Busnum,1:2:2*Busnum)=dPdVidTi;%%<EFBFBD>Խ<EFBFBD>
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APi(2:2:2*Busnum,2:2:2*Busnum)=dPdVidVi;%%<EFBFBD>Խ<EFBFBD>
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%% deltaQ/deltaThyta_deltaThyta <EFBFBD>ǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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%t1=-Volt'*Volt;
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t1=Volt'*Volt;
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t2=real(GB).*sin(AngleIJMat)-imag(GB).*cos(AngleIJMat);
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dQidTidTj=t1.*t2;%<EFBFBD><EFBFBD>ȥ<EFBFBD><EFBFBD><EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD>ˣ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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t3=repmat(Init_Y',1,size(Init_Y,2));
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dQidTidTj=dQidTidTj.*t3(2:2:size(Init_Y,2),2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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t2=real(GB).*sin(AngleIJMat)+imag(GB).*cos(AngleIJMat);
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dQjdTidTj=-t1.*t2;
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t3=t3';
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dQjdTidTj=dQjdTidTj.*t3(2:2:size(Init_Y,2),2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dQdTidTj=dQidTidTj+dQjdTidTj;%<EFBFBD><EFBFBD><EFBFBD>շǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@@
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%% deltaQ/deltaThyta_deltaThyta <EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t1=dQidTidTj-diag(diag(dQidTidTj));%ȥ<EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t2=sum(t1,2);
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t3=t2'.*Init_Y(2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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%dQidTidTi=diag(t3);
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dQidTidTi=-diag(t3);
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t1=-Volt'*Volt;
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t2=real(GB).*sin(AngleIJMat)-imag(GB).*cos(AngleIJMat);
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t3=t1.*t2;
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t4=t3-diag(diag(t3));
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t5=repmat(Init_Y',1,size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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t6=t4.*t5(2:2:size(Init_Y,2),2:2:size(Init_Y,2));
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t7=sum(t6,1);
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dQjdTidTi=diag(t7);
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dQdTidTi=dQjdTidTi+dQidTidTi;%<EFBFBD><EFBFBD><EFBFBD>նԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@@
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%% deltaQ/deltaThyta_deltaV <EFBFBD>ǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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%t1=-Volt;
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t1=Volt;
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t2=real(GB).*cos(AngleIJMat)+imag(GB).*sin(AngleIJMat);
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t3=t1'*ones(1,Busnum).*t2;
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t4=repmat(Init_Y',1,size(Init_Y,2));
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dQidTidVj=t3.*t4(2:2:size(Init_Y,2),2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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t2=real(GB).*cos(AngleIJMat)-imag(GB).*sin(AngleIJMat);
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t3=-Volt'*ones(1,Busnum).*t2;
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t4=t4';
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dQjdTidVj=t3.*t4(2:2:size(Init_Y,2),2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dQdTidVj=dQidTidVj+dQjdTidVj;%<EFBFBD><EFBFBD><EFBFBD>շǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD> @@@
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%% deltaQ/deltaThyta_deltaV <EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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%t1=sum(dQidTidVj,2)-diag(dQidTidVj);%ȥ<EFBFBD><EFBFBD><EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t1=real(GB).*cos(AngleIJMat)+imag(GB).*sin(AngleIJMat);
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t2=ones(Busnum,1)*Volt.*t1;
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t3=sum(t2,2);
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t4=t3'.*Init_Y(2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dQidTidVi=diag(t4);
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t1=-Volt'*ones(1,Busnum).*(real(GB).*cos(AngleIJMat)+imag(GB).*sin(AngleIJMat));
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t2=t1-diag(diag(t1));
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t3=repmat(Init_Y',1,size(Init_Y,2));
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t4=t2.*t3(2:2:size(Init_Y,2),2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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t5=sum(t4,1);
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dQjdTidVi=diag(t5);
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dQdTidVi=dQidTidVi+dQjdTidVi;% @@
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%% deltaQ/deltaV_deltaV <EFBFBD>ǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t1=real(GB).*sin(AngleIJMat)-imag(GB).*cos(AngleIJMat);
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t2=repmat(Init_Y',1,size(Init_Y,2));
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t3=t1.*t2(2:2:size(Init_Y,2),2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dQidVidVj=t3;
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t1=-real(GB).*sin(AngleIJMat)-imag(GB).*cos(AngleIJMat);
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t2=t2';
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t3=t1.*t2(2:2:size(Init_Y,2),2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dQjdVidVj=t3;
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dQdVidVj=dQidVidVj+dQjdVidVj;% @@@
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%% deltaQ/deltaV_deltaV <EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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t1=2*(real(GB).*sin(AngleIJMat)-imag(GB).*cos(AngleIJMat));
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t2=diag(t1);
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t3=t2'.*Init_Y(2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dQidVidVi=diag(t3);
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% t1=-real(GB).*sin(AngleIJMat)-imag(GB).*cos(AngleIJMat);
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% t2=diag(t1);
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% t3=t1-diag(t2);
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% t4=sum(t3,1);
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% t5=t4.*Init_Y(2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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% dQjdVidVi=diag(t5);
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dQjdVidVi=0;
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dQdVidVi=dQidVidVi+dQjdVidVi; % @@
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%% deltaQ/deltaV_deltaThyta <EFBFBD>ǶԽ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
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%t1=real(GB).*sin(AngleIJMat)+imag(GB).*cos(AngleIJMat);
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t1=real(GB).*cos(AngleIJMat)+imag(GB).*sin(AngleIJMat);
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t2=-ones(Busnum,1)*Volt.*(t1);
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t3=repmat(Init_Y',1,size(Init_Y,2));
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t4=t2'.*t3(2:2:size(Init_Y,2),2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dQidVidTj=t4;
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t1=real(GB).*cos(AngleIJMat)-imag(GB).*sin(AngleIJMat);
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t2=-ones(Busnum,1)*Volt.*(t1);
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t3=t3';
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t4=t2.*t3(2:2:size(Init_Y,2),2:2:size(Init_Y,2));%<EFBFBD><EFBFBD>y<EFBFBD><EFBFBD>ϵ<EFBFBD><EFBFBD>
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dQjdVidTj=t4;
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dQdVidTj=dQidVidTj+dQjdVidTj;% @
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%% deltaQ/deltaV_deltaThyta <EFBFBD>Խ<EFBFBD>Ԫ<EFBFBD><EFBFBD>
|
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|
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dQdVidTi=dQdTidVi;% @
|
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|
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%% <EFBFBD><EFBFBD><EFBFBD><EFBFBD>AQi
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AQi=zeros(2*Busnum,2*Busnum);
|
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AQi(1:2:2*Busnum,1:2:2*Busnum)=dQdTidTj;%%<EFBFBD>ǶԽ<EFBFBD> TT
|
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|
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AQi(1:2:2*Busnum,2:2:2*Busnum)=dQdTidVj;%%<EFBFBD>ǶԽ<EFBFBD> TV
|
|||
|
|
AQi(2:2:2*Busnum,1:2:2*Busnum)=dQdVidTj;%%<EFBFBD>ǶԽ<EFBFBD> VT
|
|||
|
|
AQi(2:2:2*Busnum,2:2:2*Busnum)=dQdVidVj;%%<EFBFBD>ǶԽ<EFBFBD> VV
|
|||
|
|
AQi(1:2:2*Busnum,1:2:2*Busnum)=dQdTidTi;%%<EFBFBD>Խ<EFBFBD>
|
|||
|
|
AQi(1:2:2*Busnum,2:2:2*Busnum)=dQdTidVi;%%<EFBFBD>Խ<EFBFBD>
|
|||
|
|
AQi(2:2:2*Busnum,1:2:2*Busnum)=dQdVidTi;%%<EFBFBD>Խ<EFBFBD>
|
|||
|
|
AQi(2:2:2*Busnum,2:2:2*Busnum)=dQdVidVi;%%<EFBFBD>Խ<EFBFBD>
|
|||
|
|
%% <EFBFBD><EFBFBD><EFBFBD><EFBFBD>ddh
|
|||
|
|
t=[zeros(4,14);
|
|||
|
|
zeros(2*5,4),AQi+APi;
|
|||
|
|
];
|
|||
|
|
ddh=t;
|
|||
|
|
end
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