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First release of PowerSAS.m
This commit is contained in:
Rui Yao
202
internal/getJacobianMod.m
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202
internal/getJacobianMod.m
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function [jac,pIdx,qIdx,vIdx,sIdx,busType]=getJacobianMod(nbus,nline,bus,sw,pv,pq,shunt,line,zip,ind,s,V,dyn,Ytr,Ysh)
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% Generate jacobian matrix
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%
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% FUNCTION getJacobianMod
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%
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% Author: Rui Yao <ruiyao@ieee.org>
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%
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% Copyright (C) 2021, UChicago Argonne, LLC. All rights reserved.
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%
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% OPEN SOURCE LICENSE
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%
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% Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
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%
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% 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
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% 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
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% 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
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%
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%
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% ******************************************************************************************************
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% DISCLAIMER
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%
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% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
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% WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
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% PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY
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% DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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% PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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% CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
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% OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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% ***************************************************************************************************
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%
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[~,Ytrx,Yshx,ytrfr,ytrto,yshfr,yshto]=getYMatrix(nbus,line);
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if nargin<14
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Ytr=Ytrx;
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end
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if nargin<15
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Ysh=Yshx;
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end
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yBr=[-ytrfr;-ytrto];
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busType=zeros(nbus,1);
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if isempty(pv)
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pv=zeros(0,6);
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end
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if isempty(pq)
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pq=zeros(0,6);
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end
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if isempty(shunt)
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shunt=zeros(0,7);
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end
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busType(pv(:,1))=1;
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busType(sw(:,1))=2;
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yShunt=zeros(nbus,1);
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yShunt(shunt(:,1))=shunt(:,5)+1j*shunt(:,6);
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Ysh=Ysh+yShunt;
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if ~isempty(zip)%zipMode=0
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Ysh=Ysh+accumarray(zip(:,1),(zip(:,5)+1j*zip(:,8)).*zip(:,12),[nbus,1]);
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end
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Y=Ytr+sparse(1:nbus,1:nbus,Ysh,nbus,nbus);
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if ~isempty(ind)
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nInd=size(ind,1);
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indIdx=ind(:,1);
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R1=ind(:,7);
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X1=ind(:,8);
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Z1=ind(:,7)+1j*ind(:,8);
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Xm=ind(:,13);
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Ze=1j*ind(:,13);
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R2=ind(:,9);
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X2=ind(:,10);
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Zind=Z1+Ze.*(R2+1j*X2.*s)./(R2+(1j*X2+Ze).*s);
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Y=Y+sparse(indIdx,indIdx,1./Zind,nbus,nbus);
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end
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isw=find(busType==2);
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ipv=find(busType==1);
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ipq=find(busType==0);
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busTypePvPq=busType(busType~=2);
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ipvInPvPq=find(busTypePvPq==1);
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npq=size(ipq,1);
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npv=size(ipv,1);
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i_fr=line(:,1);
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i_to=line(:,2);
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yDiag=diag(Y);
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C=real(V);
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D=imag(V);
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vMag=abs(V);
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G=real(Y);
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B=imag(Y);
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gcbdx=G*C-B*D;
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gcbd=sparse(1:nbus,1:nbus,gcbdx,nbus,nbus);
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bcgdx=B*C+G*D;
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bcgd=sparse(1:nbus,1:nbus,bcgdx,nbus,nbus);
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diagc=sparse(1:nbus,1:nbus,C,nbus,nbus);
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diagd=sparse(1:nbus,1:nbus,D,nbus,nbus);
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cg=diagc*G;
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cb=diagc*B;
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dg=diagd*G;
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db=diagd*B;
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Hmat=gcbd+cg+db; % P/C
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Nmat=bcgd-cb+dg; % P/D
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Jmat=-bcgd-cb+dg; % Q/C
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Lmat=gcbd-cg-db; % Q/D
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if ~isempty(zip)
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Czip=C(zip(:,1));
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Dzip=D(zip(:,1));
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vMagzip=vMag(zip(:,1));
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Hmat=Hmat+sparse(zip(:,1),zip(:,1),zip(:,6).*Czip./vMagzip,nbus,nbus);
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Nmat=Nmat+sparse(zip(:,1),zip(:,1),zip(:,6).*Dzip./vMagzip,nbus,nbus);
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Jmat=Jmat+sparse(zip(:,1),zip(:,1),zip(:,9).*Czip./vMagzip,nbus,nbus);
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Lmat=Lmat+sparse(zip(:,1),zip(:,1),zip(:,9).*Dzip./vMagzip,nbus,nbus);
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end
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% Hdiag=sparse(ones(2*nline+nbus,1),[i_to;i_fr;(1:nbus)'],[-(real(yBr).*C([i_to;i_fr])-imag(yBr).*D([i_to;i_fr]));-2*real(yDiag).*C],1,nbus);
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% Ndiag=sparse(ones(2*nline+nbus,1),[i_to;i_fr;(1:nbus)'],[-(real(yBr).*D([i_to;i_fr])+imag(yBr).*C([i_to;i_fr]));-2*real(yDiag).*D],1,nbus);
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% Jdiag=sparse(ones(2*nline+nbus,1),[i_to;i_fr;(1:nbus)'],[(real(yBr).*D([i_to;i_fr])+imag(yBr).*C([i_to;i_fr]));2*imag(yDiag).*C],1,nbus);
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% Ldiag=sparse(ones(2*nline+nbus,1),[i_to;i_fr;(1:nbus)'],[-(real(yBr).*C([i_to;i_fr])-imag(yBr).*D([i_to;i_fr]));2*imag(yDiag).*D],1,nbus);
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%
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% Hmat=sparse([i_fr;i_to;(1:nbus)'],[i_to;i_fr;(1:nbus)'],[-(real(yBr).*C([i_fr;i_to])+imag(yBr).*D([i_fr;i_to]));Hdiag.'],nbus,nbus);
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% Nmat=sparse([i_fr;i_to;(1:nbus)'],[i_to;i_fr;(1:nbus)'],[(imag(yBr).*C([i_fr;i_to])-real(yBr).*D([i_fr;i_to]));Ndiag.'],nbus,nbus);
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% Jmat=sparse([i_fr;i_to;(1:nbus)'],[i_to;i_fr;(1:nbus)'],[(imag(yBr).*C([i_fr;i_to])-real(yBr).*D([i_fr;i_to]));Jdiag.'],nbus,nbus);
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% Lmat=sparse([i_fr;i_to;(1:nbus)'],[i_to;i_fr;(1:nbus)'],[(real(yBr).*C([i_fr;i_to])+imag(yBr).*D([i_fr;i_to]));Ldiag.'],nbus,nbus);
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% VdC=sparse(1:nbus,1:nbus,-2*C,nbus,nbus);
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% VdD=sparse(1:nbus,1:nbus,-2*D,nbus,nbus);
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C0Mx=sparse(1:npv,ipvInPvPq,-2*C(ipv),npv,npv+npq);
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D0Mx=sparse(1:npv,ipvInPvPq,-2*D(ipv),npv,npv+npq);
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jac=[Hmat(busType~=2,busType~=2),Nmat(busType~=2,busType~=2);...
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Jmat(busType==0,busType~=2),Lmat(busType==0,busType~=2);...
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C0Mx,D0Mx];
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pIdx=1:(npv+npq);
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qIdx=npv+npq+(1:npq);
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vIdx=npv+npq+npq+(1:npv);
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sIdx=[];
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ind=ind(dyn==0,:);
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nInd=size(ind,1);
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if nInd>1
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indIdx=ind(:,1);
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s=s(dyn==0);
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R1=ind(:,7);
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X1=ind(:,8);
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Z1=ind(:,7)+1j*ind(:,8);
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Xm=ind(:,13);
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Ze=1j*ind(:,13);
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R2=ind(:,9);
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X2=ind(:,10);
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T0=ind(:,15)+ind(:,16)+ind(:,17);
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T1=-ind(:,16)-2*ind(:,17);
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T2=ind(:,17);
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H=ind(:,14);
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Vind=V(indIdx);
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C1=real(Vind);
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C2=imag(Vind);
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y2=-(R2.*Xm.*Xm)./(s.*(R2./s - X2*1i + (Xm.*(R1 - X1*1i)*1i)./...
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(- R1 + X1*1i + Xm*1i)).*(R1 + X1*1i + Xm*1i).*(X2*1i + R2./s + (Xm.*(R1 + X1*1i)*1i)./(R1 + X1*1i + Xm*1i)).*(- R1 + X1*1i + Xm*1i)); % Te=V^2.*y2
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y2ds=(R2.*Xm.*Xm)./(s.*s.*(R2./s - X2*1i + (Xm.*(R1 - X1*1i)*1i)./(- R1 + X1*1i + Xm*1i)).*(R1 + X1*1i + Xm*1i).*(X2*1i + R2./s + (Xm.*(R1 + X1*1i)*1i)./(R1 + X1*1i + Xm*1i))...
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.*(- R1 + X1*1i + Xm*1i)) - (R2.*R2.*Xm.*Xm)./(s.*s.*s.*(R2./s - X2*1i + (Xm.*(R1 - X1*1i)*1i)./(- R1 + X1*1i + Xm*1i)).*(R1 + X1*1i + Xm*1i)...
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.*(X2*1i + R2./s + (Xm.*(R1 + X1*1i)*1i)./(R1 + X1*1i + Xm*1i)).^2.*(- R1 + X1*1i + Xm*1i)) - (R2.*Xm.*R2.*Xm)./(s.*s.*s.*(R2./s - X2*1i + (Xm.*(R1 - X1*1i)*1i)...
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./(- R1 + X1*1i + Xm*1i)).^2.*(R1 + X1*1i + Xm*1i).*(X2*1i + R2./s + (Xm.*(R1 + X1*1i)*1i)./(R1 + X1*1i + Xm*1i)).*(- R1 + X1*1i + Xm*1i));
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dTds=(T1+2*T2.*s-abs(Vind).*abs(Vind).*y2ds)/2./H;
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dTdC1=-2*C1.*real(y2)/2./H;
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dTdC2=-2*C2.*real(y2)/2./H;
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yIL=(R2 + s.*(X2 + Xm)*1i)./(R1.*R2 - s.*(X1.*X2 + X1.*Xm + X2.*Xm) + R2.*(X1 + Xm)*1i + R1.*s.*(X2 + Xm)*1i);
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yILds=(X2*1i + Xm*1i)./(R1.*R2 - s.*(X1.*X2 + X1.*Xm + X2.*Xm) + R2.*(X1 + Xm)*1i + R1.*s.*(X2 + Xm)*1i) ...
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+ (R2 + s.*(X2 + Xm)*1i).*(X1.*X2 + X1.*Xm + X2.*Xm - R1.*(X2 + Xm)*1i)./(R1.*R2 - s.*(X1.*X2 + X1.*Xm + X2.*Xm) + R2.*(X1 + Xm)*1i + R1.*s.*(X2 + Xm)*1i).^2;
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% VILdC1=-2*C1.*conj(yIL);
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% VILdC2=-2*C2.*conj(yIL);
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% Hmat=Hmat+sparse(indIdx,indIdx,real(VILdC1),nbus,nbus);
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% Nmat=Nmat+sparse(indIdx,indIdx,real(VILdC2),nbus,nbus);
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% Jmat=Jmat+sparse(indIdx,indIdx,imag(VILdC1),nbus,nbus);
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% Lmat=Lmat+sparse(indIdx,indIdx,imag(VILdC2),nbus,nbus);
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VILds=abs(Vind).*abs(Vind).*conj(yILds);
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PILdsmat=sparse(indIdx,1:nInd,-real(VILds),nbus,nInd);
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QILdsmat=sparse(indIdx,1:nInd,-imag(VILds),nbus,nInd);
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dTdC1mat=sparse(1:nInd,indIdx,dTdC1,nInd,nbus);
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dTdC2mat=sparse(1:nInd,indIdx,dTdC2,nInd,nbus);
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ind2ind=sparse(1:nInd,1:nInd,dTds,nInd,nInd);
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jac=[jac,[PILdsmat(busType~=2,:);QILdsmat(busType==0,:);sparse(npv,nInd)]...
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dTdC1mat(:,busType~=2),dTdC2mat(:,busType~=2),ind2ind];
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sIdx=vIdx(end)+(1:nInd);
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end
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end
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