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First release of PowerSAS.m
This commit is contained in:
Rui Yao
801
internal/hemMachinePFSalientcontinueAlgebraicMultiArea.m
Normal file
801
internal/hemMachinePFSalientcontinueAlgebraicMultiArea.m
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@@ -0,0 +1,801 @@
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function [Vm,Wm,Qm]=hemMachinePFSalientcontinueAlgebraicMultiArea(SimData,SysData,SysPara,SysDataList,SysParaList,links,grossMaps,sysMaps,x0)
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% Compute HE coefficients for solving algebraic equations in multiple areas (parallel computation enabled)
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%
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% FUNCTION hemMachinePFSalientcontinueAlgebraicMultiArea
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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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% INPUT
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% SimData - Simulation parameters
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% SysData - System data for simulation
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% SysPara - Parameters representing the events happening in the system
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% SysDataList - The list of sub system data
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% SysParaList - The list of sub system parameters
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% links - the links connecting the sub systems
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% grossMaps - Mapping from agglomerated system to subsystem
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% sysMaps - Mapping from subsystem to agglomerated system
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% x0 - Initial system state
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%
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% OUTPUT
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% Vm, Wm, Qm - HE oefficients of algebraic variables
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%
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%
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nSys=length(SysDataList);
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auxList=cell(nSys,1);
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[~,~,~,nlvl,~,~,~,~,~]=unfoldSimData(SimData);
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[busMain,swMain,pvMain,pqMain,shuntMain,lineMain,indMain,zipMain,synMain,excMain,tgMain,agcMain,cacMain,clusterMain]=unfoldSysData(SysData);
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[~,~,~,~,~,~,Rzip0Main,~,~,~,~,~,~,~,~,~,~]=unfoldSysPara(SysPara);
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[V0,Q0]=unfoldX(x0,SysData);
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nbusMain=size(busMain,1);
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Vm=zeros(nbusMain,nlvl+1);
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Vm(:,1)=V0;
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Wm=zeros(nbusMain,nlvl+1);
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Wm(:,1)=1./V0;
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busTypeMain=zeros(nbusMain,1);
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if isempty(pvMain)
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pvMain=zeros(0,6);
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end
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if isempty(pqMain)
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pqMain=zeros(0,6);
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end
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if isempty(shuntMain)
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shuntMain=zeros(0,7);
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end
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if isempty(swMain)
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swMain=zeros(0,13);
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end
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busTypeMain(pvMain(:,1))=1;
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busTypeMain(swMain(:,1))=2;
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iswMain=find(busTypeMain==2);
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ipvMain=find(busTypeMain==1);
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ipqMain=find(busTypeMain==0);
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npqMain=size(ipqMain,1);
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npvMain=size(ipvMain,1);
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qVecMain=zeros(nbusMain,1);
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% vSp=zeros(nbus,1);
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qVecMain(pqMain(:,1))=qVecMain(pqMain(:,1))-pqMain(:,5);
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if ~isempty(zipMain)%zipMode=0, account for the PQ components in ZIP loads
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qVecMain=qVecMain-accumarray(zipMain(:,1),Rzip0Main.*zipMain(:,10).*zipMain(:,12),[nbusMain,1]);
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end
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qVecMain(ipvMain)=Q0(ipvMain);
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Qm=zeros(nbusMain,nlvl+1);
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Qm(:,1)=qVecMain;
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p = gcp('nocreate'); % If no pool, do not create new one.
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if isempty(p)
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poolsize = 0;
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else
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poolsize = p.NumWorkers;
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end
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for iSys=2:nSys
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[bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg]=unfoldSysData(SysDataList{iSys});
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busInX=[sysMaps{iSys}.busMap';sysMaps{iSys}.extBusMap(:,2)];
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V0a=V0(busInX);
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Q0a=Q0(busInX);
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nbus=size(bus,1);
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nline=size(line,1);
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[pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,MatGV0,MatGV1,MatGRhs0,MatGRhs1]=unfoldSysPara(SysParaList{iSys});
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%
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Pls=zeros(nbus,1);Pls(pq(:,1))=pqIncr(:,1);if ~isempty(pv);Pls(pv(:,1))=Pls(pv(:,1))-pvIncr;end
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Qls=zeros(nbus,1);Qls(pq(:,1))=pqIncr(:,2);
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% [Y,Ytr,Ysh,ytrfr,ytrto,yshfr,yshto]=getYMatrix(nbus,line);
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Ytr=Ytr0;
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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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if isempty(sw)
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sw=zeros(0,13);
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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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isw=find(busType==2);
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ipv=find(busType==1);
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ipq=find(busType==0);
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npq=size(ipq,1);
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npv=size(ipv,1);
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% yShunt=zeros(nbus,1);
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% yShunt(shunt(:,1))=shunt(:,5)+1j*shunt(:,6);
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% if ~isempty(zip)%zipMode=0
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% yShunt=yShunt+accumarray(zip(:,1),(zip(:,5)+1j*zip(:,8)).*zip(:,12),[nbus,1]);
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% end
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% Ysh=Ysh+yShunt;
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% Y=Y+sparse(1:nbus,1:nbus,yShunt,nbus,nbus);
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if ~isempty(zip)%zipMode=0
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Ysh0=Ysh0+accumarray(zip(:,1),Rzip0.*(zip(:,5)+1j*zip(:,8)).*zip(:,12),[nbus,1]);
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Ysh1=Ysh1+accumarray(zip(:,1),Rzip1.*(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,Ysh0,nbus,nbus);
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pVec=zeros(nbus,1);
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qVec=zeros(nbus,1);
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% vSp=zeros(nbus,1);
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pVec(pv(:,1))=pVec(pv(:,1))+pv(:,4);
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pVec(pq(:,1))=pVec(pq(:,1))-pq(:,4);
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qVec(pq(:,1))=qVec(pq(:,1))-pq(:,5);
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if ~isempty(zip)%zipMode=0, account for the PQ components in ZIP loads
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pVec=pVec-accumarray(zip(:,1),Rzip0.*zip(:,7).*zip(:,12),[nbus,1]);
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qVec=qVec-accumarray(zip(:,1),Rzip0.*zip(:,10).*zip(:,12),[nbus,1]);
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end
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qVec(ipv)=Q0a(ipv);
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% vSp(ipv)=pv(:,5);
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V=zeros(nbus,nlvl+1);
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V(:,1)=V0a;
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W=zeros(nbus,nlvl+1);
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W(:,1)=1./V0a;
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P=zeros(nbus,nlvl+1);
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P(:,1)=pVec;
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% P(isw,2:end)=0;
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Q=zeros(nbus,nlvl+1);
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Q(:,1)=qVec;
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P(:,2:(size(Pls,2)+1))=-Pls;
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Q(:,2:(size(Qls,2)+1))=-Qls;
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if ~isempty(zip)
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P(:,2)=P(:,2)-accumarray(zip(:,1),Rzip1.*zip(:,7).*zip(:,12),[nbus,1]);
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Q(:,2)=Q(:,2)-accumarray(zip(:,1),Rzip1.*zip(:,10).*zip(:,12),[nbus,1]);
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end
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Q(busType~=0,2:end)=0;
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C0=real(V(:,1));
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D0=imag(V(:,1));
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E0=real(W(:,1));
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F0=imag(W(:,1));
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C0M=sparse(1:nbus,1:nbus,C0,nbus,nbus);
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D0M=sparse(1:nbus,1:nbus,D0,nbus,nbus);
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E0M=sparse(1:nbus,1:nbus,E0,nbus,nbus);
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F0M=sparse(1:nbus,1:nbus,F0,nbus,nbus);
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P0x=P(:,1);Q0x=Q(:,1);
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P0M=sparse(1:nbus,1:nbus,P0x,nbus,nbus);
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Q0M=sparse(1:nbus,1:nbus,Q0x,nbus,nbus);
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G=real(Y);
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B=imag(Y);
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nZip=size(zip,1);
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zipIdx=zip(:,1);
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if ~isempty(zip)
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IiL=zeros(nZip,nlvl+1);
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BiL=zeros(nZip,nlvl+1);
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Bi0=abs(V0a(zipIdx));
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JI=zip(:,6);
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KI=-zip(:,9);
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Ii0L=Rzip0.*(JI+1j*KI).*V0a(zipIdx)./Bi0;
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Ji0L=real(Ii0L);
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Ki0L=imag(Ii0L);
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IiL(:,1)=Ii0L;
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BiL(:,1)=Bi0;
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Ci0=real(V0a(zipIdx));
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Di0=imag(V0a(zipIdx));
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LHS_MatZip_p=[Rzip0.*JI./Bi0-Ci0.*Ji0L./Bi0./Bi0,-Rzip0.*KI./Bi0-Di0.*Ji0L./Bi0./Bi0,...
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Rzip0.*KI./Bi0-Ci0.*Ki0L./Bi0./Bi0,Rzip0.*JI./Bi0-Di0.*Ki0L./Bi0./Bi0];
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Mat_BZip=[Ci0./Bi0,Di0./Bi0];
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auxList{iSys}.LHS_MatZip=LHS_MatZip_p;
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auxList{iSys}.Mat_BZip=Mat_BZip;
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else
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IiL=zeros(nZip,nlvl+1);
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BiL=zeros(nZip,nlvl+1);
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end
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synIdx=syn(:,1);
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if ~isempty(syn)
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MatGCD_p=-[sparse(synIdx,synIdx,MatGV0(:,1),nbus,nbus),sparse(synIdx,synIdx,MatGV0(:,2),nbus,nbus);...
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sparse(synIdx,synIdx,MatGV0(:,3),nbus,nbus),sparse(synIdx,synIdx,MatGV0(:,4),nbus,nbus)];
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end
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Y11=-G;Y12=B;Y21=-B;Y22=-G;
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YEF11=P0M;YEF12=-Q0M;YEF21=-Q0M;YEF22=-P0M;
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if ~isempty(zip)
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Y11=Y11-sparse(1:nbus,1:nbus,accumarray(zipIdx,LHS_MatZip_p(:,1),[nbus,1]),nbus,nbus);
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Y12=Y12-sparse(1:nbus,1:nbus,accumarray(zipIdx,LHS_MatZip_p(:,2),[nbus,1]),nbus,nbus);
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Y21=Y21-sparse(1:nbus,1:nbus,accumarray(zipIdx,LHS_MatZip_p(:,3),[nbus,1]),nbus,nbus);
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Y22=Y22-sparse(1:nbus,1:nbus,accumarray(zipIdx,LHS_MatZip_p(:,4),[nbus,1]),nbus,nbus);
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end
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YLHS=[Y11,Y12;Y21,Y22];
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if ~isempty(syn)
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YLHS=YLHS+MatGCD_p;
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end
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idxNonSw=find(busType~=2);
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idxStackMat=[idxNonSw;idxNonSw+nbus];
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%
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% if nbus<=500
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% [L_LHS_mat,U_LHS_mat,p_LHS_mat]=lu(LHS_mat,'vector');
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% end
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%
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% p_amd = colamd (LHS_mat) ;
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% MxI = speye (size(LHS_mat)) ;
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% MxQ = MxI (:, p_amd) ;
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% [MxL,MxU,MxP] = lu (LHS_mat*MxQ) ;
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auxList{iSys}.nbus=nbus;
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auxList{iSys}.nline=nline;
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auxList{iSys}.busType=busType;
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auxList{iSys}.isw=isw;
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auxList{iSys}.ipv=ipv;
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auxList{iSys}.ipq=ipq;
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auxList{iSys}.npv=npv;
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auxList{iSys}.npq=npq;
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auxList{iSys}.Y=Y;
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auxList{iSys}.V=V;
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auxList{iSys}.W=W;
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auxList{iSys}.P=P;
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auxList{iSys}.Q=Q;
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auxList{iSys}.IiL=IiL;
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auxList{iSys}.BiL=BiL;
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if iSys>=2
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busTag=zeros(nbus,1);
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busTag(sysMaps{iSys}.extBusMap(:,4))=1;
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busTagx=busTag(busType~=2);
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nY=npv+npq;
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busIdxB=find(busTagx==1);
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busIdxI=find(busTagx==0);
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busIdxPurgeB=find(busTag==0&busType~=2);
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busIdxRemainB=find(busTag==1&busType~=2);
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nPurgeB=size(busIdxPurgeB,1);
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LHS_mat=[YLHS(idxStackMat,idxStackMat),...
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[YEF11(busType~=2,busIdxPurgeB),YEF12(busType~=2,busIdxPurgeB),-F0M(busType~=2,ipv);...
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YEF21(busType~=2,busIdxPurgeB),YEF22(busType~=2,busIdxPurgeB),-E0M(busType~=2,ipv)];...
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C0M(ipv,busType~=2),D0M(ipv,busType~=2),sparse(npv,2*nPurgeB+npv);...
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E0M(busIdxPurgeB,busType~=2),-F0M(busIdxPurgeB,busType~=2),C0M(busIdxPurgeB,busIdxPurgeB),-D0M(busIdxPurgeB,busIdxPurgeB),sparse(nPurgeB,npv);...
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F0M(busIdxPurgeB,busType~=2),E0M(busIdxPurgeB,busType~=2),D0M(busIdxPurgeB,busIdxPurgeB),C0M(busIdxPurgeB,busIdxPurgeB),sparse(nPurgeB,npv);];
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% Note that for sub-systems, the E and F terms for boundary
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% variables will be purged.
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lhsTag=zeros(size(LHS_mat,1),1);
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lhsTag([busIdxB;busIdxB+nY])=1;
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LHS_bb=LHS_mat(lhsTag==1,lhsTag==1);
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LHS_bi=LHS_mat(lhsTag==1,lhsTag==0);
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LHS_ib=LHS_mat(lhsTag==0,lhsTag==1);
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LHS_ii=LHS_mat(lhsTag==0,lhsTag==0);
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p_amd = colamd (LHS_ii) ;
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MxI = speye (size(LHS_ii)) ;
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MxQ = MxI (:, p_amd) ;
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[MxL,MxU,MxP] = lu (LHS_ii*MxQ) ;
|
||||
|
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LHS_biii=(((LHS_bi*MxQ)/MxU)/MxL)*MxP;
|
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LHS_iiib=MxQ*(MxU\(MxL\(MxP*LHS_ib)));
|
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LHS_reduce_bb=LHS_bb-LHS_biii*LHS_ib;
|
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|
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auxList{iSys}.MxQ=MxQ;
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auxList{iSys}.MxL=MxL;
|
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auxList{iSys}.MxU=MxU;
|
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auxList{iSys}.MxP=MxP;
|
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auxList{iSys}.busIdxPurgeB=busIdxPurgeB;
|
||||
auxList{iSys}.busIdxRemainB=busIdxRemainB;
|
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auxList{iSys}.LHS_bb=LHS_bb;
|
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auxList{iSys}.LHS_bi=LHS_bi;
|
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auxList{iSys}.LHS_ib=LHS_ib;
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auxList{iSys}.LHS_ii=LHS_ii;
|
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auxList{iSys}.LHS_biii=LHS_biii;
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auxList{iSys}.LHS_iiib=LHS_iiib;
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auxList{iSys}.LHS_reduce_bb=LHS_reduce_bb;
|
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end
|
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end
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iSys=1;
|
||||
|
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[bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg]=unfoldSysData(SysDataList{iSys});
|
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busInX=[sysMaps{iSys}.busMap';sysMaps{iSys}.extBusMap(:,2)];
|
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V0a=V0(busInX);
|
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Q0a=Q0(busInX);
|
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|
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nbus=size(bus,1);
|
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nline=size(line,1);
|
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[pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,MatGV0,MatGV1,MatGRhs0,MatGRhs1]=unfoldSysPara(SysParaList{iSys});
|
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%
|
||||
Pls=zeros(nbus,1);Pls(pq(:,1))=pqIncr(:,1);if ~isempty(pv);Pls(pv(:,1))=Pls(pv(:,1))-pvIncr;end
|
||||
Qls=zeros(nbus,1);Qls(pq(:,1))=pqIncr(:,2);
|
||||
|
||||
% [Y,Ytr,Ysh,ytrfr,ytrto,yshfr,yshto]=getYMatrix(nbus,line);
|
||||
Ytr=Ytr0;
|
||||
|
||||
busType=zeros(nbus,1);
|
||||
if isempty(pv)
|
||||
pv=zeros(0,6);
|
||||
end
|
||||
if isempty(pq)
|
||||
pq=zeros(0,6);
|
||||
end
|
||||
if isempty(shunt)
|
||||
shunt=zeros(0,7);
|
||||
end
|
||||
if isempty(sw)
|
||||
sw=zeros(0,13);
|
||||
end
|
||||
busType(pv(:,1))=1;
|
||||
busType(sw(:,1))=2;
|
||||
|
||||
isw=find(busType==2);
|
||||
ipv=find(busType==1);
|
||||
ipq=find(busType==0);
|
||||
npq=size(ipq,1);
|
||||
npv=size(ipv,1);
|
||||
|
||||
% yShunt=zeros(nbus,1);
|
||||
% yShunt(shunt(:,1))=shunt(:,5)+1j*shunt(:,6);
|
||||
% if ~isempty(zip)%zipMode=0
|
||||
% yShunt=yShunt+accumarray(zip(:,1),(zip(:,5)+1j*zip(:,8)).*zip(:,12),[nbus,1]);
|
||||
% end
|
||||
% Ysh=Ysh+yShunt;
|
||||
% Y=Y+sparse(1:nbus,1:nbus,yShunt,nbus,nbus);
|
||||
if ~isempty(zip)%zipMode=0
|
||||
Ysh0=Ysh0+accumarray(zip(:,1),Rzip0.*(zip(:,5)+1j*zip(:,8)).*zip(:,12),[nbus,1]);
|
||||
Ysh1=Ysh1+accumarray(zip(:,1),Rzip1.*(zip(:,5)+1j*zip(:,8)).*zip(:,12),[nbus,1]);
|
||||
end
|
||||
|
||||
Y=Ytr+sparse(1:nbus,1:nbus,Ysh0,nbus,nbus);
|
||||
|
||||
pVec=zeros(nbus,1);
|
||||
qVec=zeros(nbus,1);
|
||||
% vSp=zeros(nbus,1);
|
||||
|
||||
pVec(pv(:,1))=pVec(pv(:,1))+pv(:,4);
|
||||
pVec(pq(:,1))=pVec(pq(:,1))-pq(:,4);
|
||||
qVec(pq(:,1))=qVec(pq(:,1))-pq(:,5);
|
||||
if ~isempty(zip)%zipMode=0, account for the PQ components in ZIP loads
|
||||
pVec=pVec-accumarray(zip(:,1),Rzip0.*zip(:,7).*zip(:,12),[nbus,1]);
|
||||
qVec=qVec-accumarray(zip(:,1),Rzip0.*zip(:,10).*zip(:,12),[nbus,1]);
|
||||
end
|
||||
qVec(ipv)=Q0a(ipv);
|
||||
% vSp(ipv)=pv(:,5);
|
||||
|
||||
V=zeros(nbus,nlvl+1);
|
||||
V(:,1)=V0a;
|
||||
W=zeros(nbus,nlvl+1);
|
||||
W(:,1)=1./V0a;
|
||||
P=zeros(nbus,nlvl+1);
|
||||
P(:,1)=pVec;
|
||||
% P(isw,2:end)=0;
|
||||
Q=zeros(nbus,nlvl+1);
|
||||
Q(:,1)=qVec;
|
||||
P(:,2:(size(Pls,2)+1))=-Pls;
|
||||
Q(:,2:(size(Qls,2)+1))=-Qls;
|
||||
if ~isempty(zip)
|
||||
P(:,2)=P(:,2)-accumarray(zip(:,1),Rzip1.*zip(:,7).*zip(:,12),[nbus,1]);
|
||||
Q(:,2)=Q(:,2)-accumarray(zip(:,1),Rzip1.*zip(:,10).*zip(:,12),[nbus,1]);
|
||||
end
|
||||
Q(busType~=0,2:end)=0;
|
||||
|
||||
C0=real(V(:,1));
|
||||
D0=imag(V(:,1));
|
||||
E0=real(W(:,1));
|
||||
F0=imag(W(:,1));
|
||||
|
||||
C0M=sparse(1:nbus,1:nbus,C0,nbus,nbus);
|
||||
D0M=sparse(1:nbus,1:nbus,D0,nbus,nbus);
|
||||
E0M=sparse(1:nbus,1:nbus,E0,nbus,nbus);
|
||||
F0M=sparse(1:nbus,1:nbus,F0,nbus,nbus);
|
||||
|
||||
P0x=P(:,1);Q0x=Q(:,1);
|
||||
if iSys==1
|
||||
for iSysi=2:nSys
|
||||
P0x(sysMaps{iSysi}.extBusMap(:,2))=P0x(sysMaps{iSysi}.extBusMap(:,2))+auxList{iSysi}.P(sysMaps{iSysi}.extBusMap(:,4),1);
|
||||
Q0x(sysMaps{iSysi}.extBusMap(:,2))=Q0x(sysMaps{iSysi}.extBusMap(:,2))+auxList{iSysi}.Q(sysMaps{iSysi}.extBusMap(:,4),1);
|
||||
end
|
||||
end
|
||||
P0M=sparse(1:nbus,1:nbus,P0x,nbus,nbus);
|
||||
Q0M=sparse(1:nbus,1:nbus,Q0x,nbus,nbus);
|
||||
|
||||
G=real(Y);
|
||||
B=imag(Y);
|
||||
|
||||
nZip=size(zip,1);
|
||||
zipIdx=zip(:,1);
|
||||
if ~isempty(zip)
|
||||
IiL=zeros(nZip,nlvl+1);
|
||||
BiL=zeros(nZip,nlvl+1);
|
||||
|
||||
Bi0=abs(V0a(zipIdx));
|
||||
JI=zip(:,6);
|
||||
KI=-zip(:,9);
|
||||
|
||||
Ii0L=Rzip0.*(JI+1j*KI).*V0a(zipIdx)./Bi0;
|
||||
Ji0L=real(Ii0L);
|
||||
Ki0L=imag(Ii0L);
|
||||
|
||||
IiL(:,1)=Ii0L;
|
||||
BiL(:,1)=Bi0;
|
||||
|
||||
Ci0=real(V0a(zipIdx));
|
||||
Di0=imag(V0a(zipIdx));
|
||||
|
||||
LHS_MatZip=[Rzip0.*JI./Bi0-Ci0.*Ji0L./Bi0./Bi0,-Rzip0.*KI./Bi0-Di0.*Ji0L./Bi0./Bi0,...
|
||||
Rzip0.*KI./Bi0-Ci0.*Ki0L./Bi0./Bi0,Rzip0.*JI./Bi0-Di0.*Ki0L./Bi0./Bi0];
|
||||
Mat_BZip=[Ci0./Bi0,Di0./Bi0];
|
||||
|
||||
auxList{iSys}.LHS_MatZip=LHS_MatZip;
|
||||
auxList{iSys}.Mat_BZip=Mat_BZip;
|
||||
else
|
||||
IiL=zeros(nZip,nlvl+1);
|
||||
BiL=zeros(nZip,nlvl+1);
|
||||
end
|
||||
|
||||
synIdx=syn(:,1);
|
||||
if ~isempty(syn)
|
||||
MatGCD=-[sparse(synIdx,synIdx,MatGV0(:,1),nbus,nbus),sparse(synIdx,synIdx,MatGV0(:,2),nbus,nbus);...
|
||||
sparse(synIdx,synIdx,MatGV0(:,3),nbus,nbus),sparse(synIdx,synIdx,MatGV0(:,4),nbus,nbus)];
|
||||
end
|
||||
|
||||
Y11=-G;Y12=B;Y21=-B;Y22=-G;
|
||||
YEF11=P0M;YEF12=-Q0M;YEF21=-Q0M;YEF22=-P0M;
|
||||
|
||||
if ~isempty(zip)
|
||||
Y11=Y11-sparse(1:nbus,1:nbus,accumarray(zipIdx,LHS_MatZip(:,1),[nbus,1]),nbus,nbus);
|
||||
Y12=Y12-sparse(1:nbus,1:nbus,accumarray(zipIdx,LHS_MatZip(:,2),[nbus,1]),nbus,nbus);
|
||||
Y21=Y21-sparse(1:nbus,1:nbus,accumarray(zipIdx,LHS_MatZip(:,3),[nbus,1]),nbus,nbus);
|
||||
Y22=Y22-sparse(1:nbus,1:nbus,accumarray(zipIdx,LHS_MatZip(:,4),[nbus,1]),nbus,nbus);
|
||||
end
|
||||
YLHS=[Y11,Y12;Y21,Y22];
|
||||
|
||||
if ~isempty(syn)
|
||||
YLHS=YLHS+MatGCD;
|
||||
end
|
||||
|
||||
idxNonSw=find(busType~=2);
|
||||
idxStackMat=[idxNonSw;idxNonSw+nbus];
|
||||
|
||||
%
|
||||
% if nbus<=500
|
||||
% [L_LHS_mat,U_LHS_mat,p_LHS_mat]=lu(LHS_mat,'vector');
|
||||
% end
|
||||
%
|
||||
% p_amd = colamd (LHS_mat) ;
|
||||
% MxI = speye (size(LHS_mat)) ;
|
||||
% MxQ = MxI (:, p_amd) ;
|
||||
% [MxL,MxU,MxP] = lu (LHS_mat*MxQ) ;
|
||||
|
||||
auxList{iSys}.nbus=nbus;
|
||||
auxList{iSys}.nline=nline;
|
||||
auxList{iSys}.busType=busType;
|
||||
auxList{iSys}.isw=isw;
|
||||
auxList{iSys}.ipv=ipv;
|
||||
auxList{iSys}.ipq=ipq;
|
||||
auxList{iSys}.npv=npv;
|
||||
auxList{iSys}.npq=npq;
|
||||
auxList{iSys}.Y=Y;
|
||||
auxList{iSys}.V=V;
|
||||
auxList{iSys}.W=W;
|
||||
auxList{iSys}.P=P;
|
||||
auxList{iSys}.Q=Q;
|
||||
auxList{iSys}.IiL=IiL;
|
||||
auxList{iSys}.BiL=BiL;
|
||||
for iSysi=2:nSys
|
||||
idxOverlay=sysMaps{iSysi}.extBusMap(:,2);
|
||||
idxOverlayMat=[idxOverlay;idxOverlay+nbus];
|
||||
YLHS(idxOverlayMat,idxOverlayMat)=YLHS(idxOverlayMat,idxOverlayMat)+auxList{iSysi}.LHS_reduce_bb;
|
||||
end
|
||||
|
||||
LHS_mat=[YLHS(idxStackMat,idxStackMat),...
|
||||
[YEF11(busType~=2,busType~=2),YEF12(busType~=2,busType~=2),-F0M(busType~=2,ipv);...
|
||||
YEF21(busType~=2,busType~=2),YEF22(busType~=2,busType~=2),-E0M(busType~=2,ipv)];...
|
||||
C0M(ipv,busType~=2),D0M(ipv,busType~=2),sparse(npv,2*npq+3*npv);...
|
||||
E0M(busType~=2,busType~=2),-F0M(busType~=2,busType~=2),C0M(busType~=2,busType~=2),-D0M(busType~=2,busType~=2),sparse(npq+npv,npv);...
|
||||
F0M(busType~=2,busType~=2),E0M(busType~=2,busType~=2),D0M(busType~=2,busType~=2),C0M(busType~=2,busType~=2),sparse(npq+npv,npv);];
|
||||
|
||||
p_amd = colamd (LHS_mat) ;
|
||||
MxI = speye (size(LHS_mat)) ;
|
||||
MxQ = MxI (:, p_amd) ;
|
||||
[MxL,MxU,MxP] = lu (LHS_mat*MxQ) ;
|
||||
|
||||
auxList{iSys}.MxQ=MxQ;
|
||||
auxList{iSys}.MxL=MxL;
|
||||
auxList{iSys}.MxU=MxU;
|
||||
auxList{iSys}.MxP=MxP;
|
||||
% Merge the blocks of sub-systems into the main system's matrix
|
||||
|
||||
for i=1:nlvl
|
||||
seq2=getseq(i,2);
|
||||
% seq2p=getseq(i+1,2);
|
||||
% seq3=getseq(i,3);
|
||||
idxSeq2=sum(seq2==i,2);
|
||||
seq2R=seq2(idxSeq2==0,:);
|
||||
|
||||
for iSys=2:nSys
|
||||
[bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg]=unfoldSysData(SysDataList{iSys});
|
||||
[pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,MatGV0,MatGV1,MatGRhs0,MatGRhs1]=unfoldSysPara(SysParaList{iSys});
|
||||
nbus=auxList{iSys}.nbus;
|
||||
busType=auxList{iSys}.busType;
|
||||
IiL=auxList{iSys}.IiL;
|
||||
BiL=auxList{iSys}.BiL;
|
||||
V=auxList{iSys}.V;
|
||||
W=auxList{iSys}.W;
|
||||
P=auxList{iSys}.P;
|
||||
Q=auxList{iSys}.Q;
|
||||
Y=auxList{iSys}.Y;
|
||||
ipv=auxList{iSys}.ipv;
|
||||
isw=auxList{iSys}.isw;
|
||||
busIdxPurgeB=auxList{iSys}.busIdxPurgeB;
|
||||
|
||||
RHSILr=zeros(nbus,1);
|
||||
RHSILi=zeros(nbus,1);
|
||||
|
||||
RHSIiLr=zeros(nbus,1);
|
||||
RHSIiLi=zeros(nbus,1);
|
||||
if ~isempty(zip)
|
||||
zipIdx=zip(:,1);
|
||||
JI=zip(:,6);
|
||||
KI=-zip(:,9);
|
||||
Ji0L=real(IiL(:,1));
|
||||
Ki0L=imag(IiL(:,1));
|
||||
Bi0=BiL(:,1);
|
||||
|
||||
RHS_BZip_p=(real(sum(V(zipIdx,seq2R(:,1)+1).*conj(V(zipIdx,seq2R(:,2)+1)),2))-sum(BiL(:,seq2R(:,1)+1).*BiL(:,seq2R(:,2)+1),2))./Bi0/2;
|
||||
RHZ_BIConv=sum(IiL(:,seq2R(:,1)+1).*BiL(:,seq2R(:,2)+1),2);
|
||||
RHSILr_full_p=Rzip1.*(JI.*real(V(zipIdx,i))-KI.*imag(V(zipIdx,i)))./Bi0-real(RHZ_BIConv)./Bi0-Ji0L.*RHS_BZip_p./Bi0;
|
||||
RHSILi_full_p=Rzip1.*(KI.*real(V(zipIdx,i))+JI.*imag(V(zipIdx,i)))./Bi0-imag(RHZ_BIConv)./Bi0-Ki0L.*RHS_BZip_p./Bi0;
|
||||
RHSIiLr=accumarray(zipIdx,RHSILr_full_p,[nbus,1]);
|
||||
RHSIiLi=accumarray(zipIdx,RHSILi_full_p,[nbus,1]);
|
||||
|
||||
auxList{iSys}.RHSILr_full=RHSILr_full_p;
|
||||
auxList{iSys}.RHSILi_full=RHSILi_full_p;
|
||||
auxList{iSys}.RHS_BZip=RHS_BZip_p;
|
||||
end
|
||||
|
||||
RHSIGr=zeros(nbus,1);
|
||||
RHSIGi=zeros(nbus,1);
|
||||
if ~isempty(syn)
|
||||
synIdx=syn(:,1);
|
||||
RHSIGr=-accumarray(synIdx,MatGV1(:,1).*real(V(synIdx,i))+MatGV1(:,2).*imag(V(synIdx,i)),[nbus,1]);
|
||||
RHSIGi=-accumarray(synIdx,MatGV1(:,3).*real(V(synIdx,i))+MatGV1(:,4).*imag(V(synIdx,i)),[nbus,1]);
|
||||
if i==1
|
||||
RHSIGr=RHSIGr+accumarray(synIdx,MatGRhs1(:,1),[nbus,1]);
|
||||
RHSIGi=RHSIGi+accumarray(synIdx,MatGRhs1(:,2),[nbus,1]);
|
||||
end
|
||||
end
|
||||
|
||||
% HEM Body
|
||||
RHS1=sum((-P(:,seq2(:,1)+1)+1j*Q(:,seq2(:,1)+1)).*conj(W(:,seq2(:,2)+1)),2)+Ysh1.*V(:,i)+Ytr1*V(:,i);
|
||||
RHS2=-0.5*real(sum(V(:,seq2R(:,1)+1).*conj(V(:,seq2R(:,2)+1)),2));
|
||||
RHS3=sum(-W(:,seq2R(:,1)+1).*V(:,seq2R(:,2)+1),2);
|
||||
|
||||
if i==1
|
||||
RHS2=RHS2+0.5*VspSq2(:,2);
|
||||
end
|
||||
|
||||
compactRHS1=RHS1(busIdxPurgeB);
|
||||
if ~isempty(isw);compactRHS1=compactRHS1+Y(busIdxPurgeB,isw)*V(isw,i+1);end
|
||||
RHS=[real(compactRHS1)+RHSILr(busIdxPurgeB)+RHSIiLr(busIdxPurgeB)-RHSIGr(busIdxPurgeB);...
|
||||
imag(compactRHS1)+RHSILi(busIdxPurgeB)+RHSIiLi(busIdxPurgeB)-RHSIGi(busIdxPurgeB);...
|
||||
RHS2(ipv);...
|
||||
real(RHS3(busIdxPurgeB));...
|
||||
imag(RHS3(busIdxPurgeB));];
|
||||
|
||||
auxList{iSys}.RHS=RHS;
|
||||
end
|
||||
|
||||
iSys=1;
|
||||
[bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg]=unfoldSysData(SysDataList{iSys});
|
||||
[pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,MatGV0,MatGV1,MatGRhs0,MatGRhs1]=unfoldSysPara(SysParaList{iSys});
|
||||
nbus=auxList{iSys}.nbus;
|
||||
busType=auxList{iSys}.busType;
|
||||
IiL=auxList{iSys}.IiL;
|
||||
BiL=auxList{iSys}.BiL;
|
||||
V=auxList{iSys}.V;
|
||||
W=auxList{iSys}.W;
|
||||
P=auxList{iSys}.P;
|
||||
Q=auxList{iSys}.Q;
|
||||
Y=auxList{iSys}.Y;
|
||||
ipv=auxList{iSys}.ipv;
|
||||
isw=auxList{iSys}.isw;
|
||||
npv=auxList{iSys}.npv;
|
||||
npq=auxList{iSys}.npq;
|
||||
|
||||
MxQ=auxList{iSys}.MxQ;
|
||||
MxL=auxList{iSys}.MxL;
|
||||
MxU=auxList{iSys}.MxU;
|
||||
MxP=auxList{iSys}.MxP;
|
||||
|
||||
RHSILr=zeros(nbus,1);
|
||||
RHSILi=zeros(nbus,1);
|
||||
|
||||
RHSIiLr=zeros(nbus,1);
|
||||
RHSIiLi=zeros(nbus,1);
|
||||
if ~isempty(zip)
|
||||
zipIdx=zip(:,1);
|
||||
JI=zip(:,6);
|
||||
KI=-zip(:,9);
|
||||
Ji0L=real(IiL(:,1));
|
||||
Ki0L=imag(IiL(:,1));
|
||||
Bi0=BiL(:,1);
|
||||
|
||||
RHS_BZip=(real(sum(V(zipIdx,seq2R(:,1)+1).*conj(V(zipIdx,seq2R(:,2)+1)),2))-sum(BiL(:,seq2R(:,1)+1).*BiL(:,seq2R(:,2)+1),2))./Bi0/2;
|
||||
RHZ_BIConv=sum(IiL(:,seq2R(:,1)+1).*BiL(:,seq2R(:,2)+1),2);
|
||||
RHSILr_full=Rzip1.*(JI.*real(V(zipIdx,i))-KI.*imag(V(zipIdx,i)))./Bi0-real(RHZ_BIConv)./Bi0-Ji0L.*RHS_BZip./Bi0;
|
||||
RHSILi_full=Rzip1.*(KI.*real(V(zipIdx,i))+JI.*imag(V(zipIdx,i)))./Bi0-imag(RHZ_BIConv)./Bi0-Ki0L.*RHS_BZip./Bi0;
|
||||
RHSIiLr=accumarray(zipIdx,RHSILr_full,[nbus,1]);
|
||||
RHSIiLi=accumarray(zipIdx,RHSILi_full,[nbus,1]);
|
||||
|
||||
auxList{iSys}.RHSILr_full=RHSILr_full;
|
||||
auxList{iSys}.RHSILi_full=RHSILi_full;
|
||||
auxList{iSys}.RHS_BZip=RHS_BZip;
|
||||
end
|
||||
|
||||
RHSIGr=zeros(nbus,1);
|
||||
RHSIGi=zeros(nbus,1);
|
||||
if ~isempty(syn)
|
||||
synIdx=syn(:,1);
|
||||
RHSIGr=-accumarray(synIdx,MatGV1(:,1).*real(V(synIdx,i))+MatGV1(:,2).*imag(V(synIdx,i)),[nbus,1]);
|
||||
RHSIGi=-accumarray(synIdx,MatGV1(:,3).*real(V(synIdx,i))+MatGV1(:,4).*imag(V(synIdx,i)),[nbus,1]);
|
||||
if i==1
|
||||
RHSIGr=RHSIGr+accumarray(synIdx,MatGRhs1(:,1),[nbus,1]);
|
||||
RHSIGi=RHSIGi+accumarray(synIdx,MatGRhs1(:,2),[nbus,1]);
|
||||
end
|
||||
end
|
||||
|
||||
% HEM Body
|
||||
RHS1=sum((-P(:,seq2(:,1)+1)+1j*Q(:,seq2(:,1)+1)).*conj(W(:,seq2(:,2)+1)),2)+Ysh1.*V(:,i)+Ytr1*V(:,i);
|
||||
RHS2=-0.5*real(sum(V(:,seq2R(:,1)+1).*conj(V(:,seq2R(:,2)+1)),2));
|
||||
RHS3=sum(-W(:,seq2R(:,1)+1).*V(:,seq2R(:,2)+1),2);
|
||||
|
||||
if i==1
|
||||
RHS2=RHS2+0.5*VspSq2(:,2);
|
||||
end
|
||||
|
||||
compactRHS1=RHS1(busType~=2);
|
||||
if ~isempty(isw);compactRHS1=compactRHS1+Y(busType~=2,isw)*V(isw,i+1);end
|
||||
|
||||
RHSIiLrExt=zeros(nbus,1);
|
||||
RHSIiLiExt=zeros(nbus,1);
|
||||
for iSys=2:nSys
|
||||
RHSIiLExtCompact=auxList{iSys}.LHS_biii*auxList{iSys}.RHS;
|
||||
RHSIiLrExt(sysMaps{iSys}.extBusMap(:,2))=RHSIiLrExt(sysMaps{iSys}.extBusMap(:,2))+RHSIiLExtCompact(1:(size(RHSIiLExtCompact,1)/2));
|
||||
RHSIiLiExt(sysMaps{iSys}.extBusMap(:,2))=RHSIiLiExt(sysMaps{iSys}.extBusMap(:,2))+RHSIiLExtCompact((size(RHSIiLExtCompact,1)/2+1):end);
|
||||
end
|
||||
|
||||
RHS=[real(compactRHS1)+RHSILr(busType~=2)+RHSIiLr(busType~=2)-RHSIGr(busType~=2)-RHSIiLrExt(busType~=2);...
|
||||
imag(compactRHS1)+RHSILi(busType~=2)+RHSIiLi(busType~=2)-RHSIGi(busType~=2)-RHSIiLiExt(busType~=2);...
|
||||
RHS2(ipv);...
|
||||
real(RHS3(busType~=2));...
|
||||
imag(RHS3(busType~=2));];
|
||||
% Solve linear
|
||||
x = MxQ * (MxU \ (MxL \ (MxP * RHS))) ;
|
||||
|
||||
V(busType~=2,i+1)=x(1:(npq+npv))+1j*x(((npq+npv)+1):(2*(npq+npv)));
|
||||
W(busType~=2,i+1)=x((2*(npq+npv)+1):(3*(npq+npv)))+1j*x((3*(npq+npv)+1):(4*(npq+npv)));
|
||||
Q(ipv,i+1)=x((4*(npq+npv)+1):end);
|
||||
|
||||
iSys=1;
|
||||
if ~isempty(zip)
|
||||
zipIdx=zip(:,1);
|
||||
LHS_MatZip=auxList{iSys}.LHS_MatZip;
|
||||
Mat_BZip=auxList{iSys}.Mat_BZip;
|
||||
IiL(:,i+1)=(LHS_MatZip(:,1)+1j*LHS_MatZip(:,3)).*real(V(zipIdx,i+1))+(LHS_MatZip(:,2)+1j*LHS_MatZip(:,4)).*imag(V(zipIdx,i+1))+(RHSILr_full+1j*RHSILi_full);
|
||||
BiL(:,i+1)=Mat_BZip(:,1).*real(V(zipIdx,i+1))+Mat_BZip(:,2).*imag(V(zipIdx,i+1))+RHS_BZip;
|
||||
end
|
||||
auxList{iSys}.V=V;
|
||||
auxList{iSys}.W=W;
|
||||
auxList{iSys}.Q=Q;
|
||||
auxList{iSys}.IiL=IiL;
|
||||
auxList{iSys}.BiL=BiL;
|
||||
|
||||
busMap=sysMaps{iSys}.busMap';
|
||||
Vm(busMap,i+1)=V(1:size(busMap,1),i+1);
|
||||
Wm(busMap,i+1)=W(1:size(busMap,1),i+1);
|
||||
Qm(busMap,i+1)=Q(1:size(busMap,1),i+1);
|
||||
|
||||
% Finished main, start sub-systems
|
||||
auxList_p=auxList;
|
||||
for iSys=2:nSys
|
||||
aux_p=auxList_p{iSys};
|
||||
[bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg]=unfoldSysData(SysDataList{iSys});
|
||||
[pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,MatGV0,MatGV1,MatGRhs0,MatGRhs1]=unfoldSysPara(SysParaList{iSys});
|
||||
nbus=aux_p.nbus;
|
||||
busType=aux_p.busType;
|
||||
IiL=aux_p.IiL;
|
||||
BiL=aux_p.BiL;
|
||||
V=aux_p.V;
|
||||
W=aux_p.W;
|
||||
Q=aux_p.Q;
|
||||
Y=aux_p.Y;
|
||||
ipv=aux_p.ipv;
|
||||
isw=aux_p.isw;
|
||||
npv=aux_p.npv;
|
||||
npq=aux_p.npq;
|
||||
|
||||
busIdxPurgeB=aux_p.busIdxPurgeB;
|
||||
nPurgeB=size(busIdxPurgeB,1);
|
||||
busIdxRemainB=aux_p.busIdxRemainB;
|
||||
|
||||
MxQ=aux_p.MxQ;
|
||||
MxL=aux_p.MxL;
|
||||
MxU=aux_p.MxU;
|
||||
MxP=aux_p.MxP;
|
||||
|
||||
RHS=aux_p.RHS;
|
||||
|
||||
Vb=auxList_p{1}.V(sysMaps{iSys}.extBusMap(:,2),i+1);
|
||||
Wb=auxList_p{1}.W(sysMaps{iSys}.extBusMap(:,2),i+1);
|
||||
|
||||
% Solve linear
|
||||
x = MxQ * (MxU \ (MxL \ (MxP * RHS)))-auxList{iSys}.LHS_iiib*[real(Vb);imag(Vb)];
|
||||
|
||||
V(busIdxPurgeB,i+1)=x(1:nPurgeB)+1j*x((nPurgeB+1):(2*nPurgeB));
|
||||
W(busIdxPurgeB,i+1)=x((2*nPurgeB+1):(3*nPurgeB))+1j*x((3*nPurgeB+1):(4*nPurgeB));
|
||||
Q(ipv,i+1)=x((4*nPurgeB+1):end);
|
||||
V(busIdxRemainB,i+1)=Vb;
|
||||
W(busIdxRemainB,i+1)=Wb;
|
||||
|
||||
if ~isempty(zip)
|
||||
zipIdx=zip(:,1);
|
||||
RHSILr_full_p=auxList{iSys}.RHSILr_full;
|
||||
RHSILi_full_p=auxList{iSys}.RHSILi_full;
|
||||
RHS_BZip_p=auxList{iSys}.RHS_BZip;
|
||||
LHS_MatZip=auxList{iSys}.LHS_MatZip;
|
||||
Mat_BZip=auxList{iSys}.Mat_BZip;
|
||||
IiL(:,i+1)=(LHS_MatZip(:,1)+1j*LHS_MatZip(:,3)).*real(V(zipIdx,i+1))+(LHS_MatZip(:,2)+1j*LHS_MatZip(:,4)).*imag(V(zipIdx,i+1))+(RHSILr_full_p+1j*RHSILi_full_p);
|
||||
BiL(:,i+1)=Mat_BZip(:,1).*real(V(zipIdx,i+1))+Mat_BZip(:,2).*imag(V(zipIdx,i+1))+RHS_BZip_p;
|
||||
end
|
||||
|
||||
aux_p.V=V;
|
||||
aux_p.W=W;
|
||||
aux_p.Q=Q;
|
||||
aux_p.IiL=IiL;
|
||||
aux_p.BiL=BiL;
|
||||
|
||||
auxList{iSys}=aux_p;
|
||||
end
|
||||
for iSys=2:nSys
|
||||
busMap=sysMaps{iSys}.busMap';
|
||||
Vm(busMap,i+1)=auxList{iSys}.V(1:size(busMap,1),i+1);
|
||||
Wm(busMap,i+1)=auxList{iSys}.W(1:size(busMap,1),i+1);
|
||||
Qm(busMap,i+1)=auxList{iSys}.Q(1:size(busMap,1),i+1);
|
||||
end
|
||||
end
|
||||
end
|
||||
Reference in New Issue
Block a user