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powersas.m/internal/hemMachinePFmultiStageAlgeb...

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function [Vx,Wx,Qx,fx,xx,finalAlpha,alphas,diffRec]=hemMachinePFmultiStageAlgebraic(SimData,SysData,SysPara,x0,xNew,SysDataNew)
% Multi-stage scheme for solving algebraic equations
%
% FUNCTION hemMachinePFmultiStageAlgebraic
%
% Author: Rui Yao <ruiyao@ieee.org>
%
% Copyright (C) 2021, UChicago Argonne, LLC. All rights reserved.
%
% OPEN SOURCE LICENSE
%
% Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
%
% 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
% 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.
% 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.
%
%
% ******************************************************************************************************
% DISCLAIMER
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
% WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
% PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY
% DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
% PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
% CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
% OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
% ***************************************************************************************************
%
% INPUT
% SimData - Simulation parameters
% SysData - System data for simulation
% SysPara - Parameters representing the events happening in the system
% x0 - Initial system state
% xNew - Updated system state (algebraic variables to be solved)
% SysDataNew - (optional) updated system data
%
% OUTPUT
% Vx, Wx, Qx, fx - Last HE coefficients of algebraic variables
% xx - Solved updated system state
% finalAlpha - The ending length of this segment of simulation
% alphas - Record of alphas
% diffRec - A list of errors
%
setting_func_hemMachinePFmultiStageAlgebraic;
[bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg,agc,cac,cluster]=unfoldSysData(SysData);
if nargin>=6&&~isempty(SysDataNew)
[~,~,~,~,~,~,~,~,synNew,~,~]=unfoldSysData(SysDataNew);
deltaSyn=synNew(:,[7:10,13:15])-syn(:,[7:10,13:15]);
else
synNew=[];
deltaSyn=zeros(size(syn,1),7);
end
nbus=size(bus,1);
nline=size(line,1);
nSyn=size(syn,1);
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);
[V0,Q0,s0,d0,w0,eq10,eq20,ed10,ed20,psid0,psiq0,Pm0,Ef0,Vavrm0,Vavrr0,Vavrf0,Vavrref0,tgovg0,tgovm0,tgovmech0,f0,dpg0,qplt0,vg0]=unfoldX(x0,SysData);
eq0=Ef0;ed0=zeros(size(Ef0));
[~,~,sNew,dNew,~,eq1New,eq2New,ed1New,ed2New,psidNew,psiqNew,~,EfNew,~,~,~,~,~,~,~,fNew,dpgNew,qpltNew,vgNew]=unfoldX(xNew,SysData);
eqNew=EfNew;edNew=zeros(size(EfNew));
[maxAlpha,segAlpha,dAlpha,nlvl,taylorN,alphaTol,diffTol,diffTolMax,method]=unfoldSimData(SimData);
[pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,MatGV0,MatGV1,MatGRhs0,MatGRhs1]=unfoldSysPara(SysPara);
%
[MatGV0,MatGV1,MatGRhs0,MatGRhs1]=getLinearInterpolatorSyn(syn,synNew,d0,dNew,ed0,ed10,ed20,edNew,ed1New,ed2New,eq0,eq10,eq20,eqNew,eq1New,eq2New,psid0,psiq0,psidNew,psiqNew);
Ysh0Orig=Ysh0;
Ysh1Orig=Ysh1;
if ~isempty(ind)
[YshInd0,Yshind1]=getLinearInterpolatorInd(nbus,ind,s0,sNew);
Ysh0=Ysh0+YshInd0;
Ysh1=Ysh1+Yshind1;
end
[nIslands,islands,refs]=searchIslands(bus(:,1),line(:,1:2));
% Determine the frequency model of each island
freqTypeTag=zeros(nIslands,1);%0:sw,1:syn,2:steady-state f
freqKeptTag=zeros(nbus,1);
frefs=refs;
fswTag=zeros(nbus,1);
fsynTag=zeros(nbus,1);
fswTag(isw)=1;
fswTagxD=fswTag;
fsynTag(syn(:,1))=1;
D0=imag(V0);
for isl=1:nIslands
if isempty(find(fswTag(islands==isl)==1, 1))
if isempty(find(fsynTag(islands==isl)==1, 1))
freqTypeTag(isl)=2;
busesInIsland=find(islands==isl);
[~,imin]=min(abs(D0(busesInIsland)));
frefs(isl)=busesInIsland(imin(1));
fswTagxD(frefs(isl))=1;
freqKeptTag(busesInIsland)=1;
else
freqTypeTag(isl)=1;
end
end
end
freqKeptTagxRef=freqKeptTag;
freqKeptTagxRef(frefs)=0;
nFreqKept=sum(freqKeptTag);
if ~isempty(agc)
agcExt=zeros(nbus,size(agc,2));
agcExt(agc(:,1),:)=agc;
fdk=agcExt(:,2)+agcExt(:,3); %1/R+D
else
fdk=zeros(nbus,1);
end
if ~isempty(pv)
extraPV=freqKeptTag.*(dpgNew-dpg0);
pvIncr=pvIncr+extraPV(pv(:,1));
end
pqx=pq;
pvx=pv;
shuntx=shunt;
indx=ind;
zipx=zip;
synx=syn;
V0x=V0;
Q0x=Q0;
f0x=f0;
Rzip0x=Rzip0;
Ysh0x=Ysh0;
Ysh0Origx=Ysh0Orig;
Ytr0x=Ytr0;
Vsp0x=real(V0.*conj(V0));
MatGV0x=MatGV0;
MatGRhs0x=MatGRhs0;
alphaConfirm=0;
busType=zeros(nbus,1);
if ~isempty(pv);busType(pv(:,1))=1;end
if ~isempty(sw);busType(sw(:,1))=2;end
vc=zeros(nbus,1);
qc=zeros(size(Q0,1),1);
alphas=0;
skip=0;
heCounter=0;
noMove=0;
while alphaConfirm<1
alpha=1-alphaConfirm;
alphax=alpha/alphaPreMult;
if skip==0
SysDatax=foldSysData(bus,sw,pvx,pqx,shuntx,line,indx,zipx,synx,exc,tg,agc,cac,cluster);
xx=foldX(SysDatax,V0x,Q0x,s0,d0,w0,eq10,eq20,ed10,ed20,psid0,psiq0,Pm0,Ef0,Vavrm0,Vavrr0,Vavrf0,Vavrref0,tgovg0,tgovm0,tgovmech0,f0x,dpg0,qplt0,vg0);
SysParax=foldSysPara(pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0x,Rzip1,Ytr0x,Ytr1,Ysh0x,Ysh1,[Vsp0x,VspSq2(:,2)],MatGV0x,MatGV1,MatGRhs0x,MatGRhs1);
if isfield(SysPara,'iden')&&isfield(SysPara,'p_amd')
SysParax.iden=SysPara.iden;
SysParax.p_amd=SysPara.p_amd;
if isempty(SysPara.p_amd)
if exist([SysPara.iden,'.mat'],'file')
if ~exist('p_amd','var')
load([SysPara.iden,'.mat']);
end
SysParax.p_amd=p_amd;
end
end
end
[V,W,Q,f]=hemMachinePFSalientcontinueAlgebraic(SimData,SysDatax,SysParax,xx);
heCounter=heCounter+1;
[Va3,Vb3]=getPadeApproxHelm(V,0);
[Qa3,Qb3]=getPadeApproxHelm(Q,find(busType==0));
[fa3,fb3]=getPadeApproxHelm(f,0);
idxNanf=find(isnan(fa3(:,1))|isnan(fb3(:,1)));fa3(idxNanf,:)=0;fb3(idxNanf,:)=0;fa3(idxNanf,1:2)=f(idxNanf,1:2);
end
skip=0;
alphaLeft=0;
alphaRight=alpha/alphaPreMult;
while 1
vc=polyvalVec(Va3(:,end:-1:1),alphax)./polyvalVec([Vb3(:,end:-1:1),ones(size(Vb3,1),1)],alphax);
vc(isnan(vc))=V(isnan(vc),1)+alphax*V(isnan(vc),2);
qc=polyvalVec(Qa3(:,end:-1:1),alphax)./polyvalVec([Qb3(:,end:-1:1),ones(size(Qb3,1),1)],alphax);
qc(isnan(qc))=Q(isnan(qc),1)+alphax*Q(isnan(qc),2);
fc=polyvalVec(fa3(:,end:-1:1),alphax)./polyvalVec([fb3(:,end:-1:1),ones(size(fb3,1),1)],alphax);
Y=Ytr0x+alphax*Ytr1+sparse(1:nbus,1:nbus,Ysh0x+Ysh1*alphax,nbus,nbus);
Vsp2=Vsp0x+alphax*VspSq2(:,2);
pqxx=pqx;
pqxx(:,[4,5])=pqx(:,[4,5])+alphax*pqIncr;
pvxx=pvx;
if ~isempty(pvx);pvxx(:,4)=pvx(:,4)+alphax*pvIncr;end
zipxx=zipx;
if ~isempty(zipxx)
zipxx(:,5:10)=repmat(Rzip0x+alphax*Rzip1,1,6).*zipx(:,5:10);
end
synxx=synx;
if ~isempty(synxx)
synxx(:,[7:10,13:15])=synx(:,[7:10,13:15])+alphax*deltaSyn;
end
MatGVxx=MatGV0x+alphax*MatGV1;
MatGRhsxx=MatGRhs0x+alphax*MatGRhs1;
SysDataxx=foldSysData(bus,sw,pvxx,pqxx,shunt,line,indx,zipxx,synxx,exc,tg,agc,cac,cluster);
xxx=foldX(SysDataxx,vc,qc,s0,d0,w0,eq10,eq20,ed10,ed20,psid0,psiq0,Pm0,Ef0,Vavrm0,Vavrr0,Vavrf0,Vavrref0,tgovg0,tgovm0,tgovmech0,fc,dpg0,qplt0,vg0);
SysParaxx=foldSysPara([],[],[],[],[],[],[],[],Ytr0x+alphax*Ytr1,[],Ysh0Origx+Ysh1Orig*alphax,[],[Vsp2,zeros(size(Vsp2))],MatGVxx,[],MatGRhsxx,[]);
diff=checkEquationBalanceSynAlgebraic(SysDataxx,SysParaxx,xxx);
if heCounter<=1
Vx=V;Wx=W;Qx=Q;fx=f;
end
if max(abs(diff))<diffTol&&alphax==alpha
V0x=vc;
Q0x=qc;
f0x=fc;
alphaLeft=alphaRight;
else
if max(abs(diff))<diffTol
V0x=vc;
Q0x=qc;
f0x=fc;
alphaLeft=alphax;
alphax=(alphaLeft+alphaRight)/2;
else
alphaRight=alphax;
alphax=(alphaLeft+alphaRight)/2;
end
end
if alphaRight-alphaLeft<alphaTol
break;
end
end
diffParadigm=max(abs(diff))+1e-12;
countCheckAlpha=1;
alphax=alphaLeft*alphaPreMult;
if alpha-alphax<alphaTol/10
alphax=alpha;
end
while countCheckAlpha<maxCount
vc=polyvalVec(Va3(:,end:-1:1),alphax)./polyvalVec([Vb3(:,end:-1:1),ones(size(Vb3,1),1)],alphax);
vc(isnan(vc))=V(isnan(vc),1)+alphax*V(isnan(vc),2);
qc=polyvalVec(Qa3(:,end:-1:1),alphax)./polyvalVec([Qb3(:,end:-1:1),ones(size(Qb3,1),1)],alphax);
qc(isnan(qc))=Q(isnan(qc),1)+alphax*Q(isnan(qc),2);
fc=polyvalVec(fa3(:,end:-1:1),alphax)./polyvalVec([fb3(:,end:-1:1),ones(size(fb3,1),1)],alphax);
Y=Ytr0x+alphax*Ytr1+sparse(1:nbus,1:nbus,Ysh0x+Ysh1*alphax,nbus,nbus);
Vsp2=Vsp0x+alphax*VspSq2(:,2);
pqxx=pqx;
pqxx(:,[4,5])=pqx(:,[4,5])+alphax*pqIncr;
pvxx=pvx;
if ~isempty(pvx);pvxx(:,4)=pvx(:,4)+alphax*pvIncr;end
zipxx=zipx;
if ~isempty(zipxx)
zipxx(:,5:10)=repmat(Rzip0x+alphax*Rzip1,1,6).*zipx(:,5:10);
end
synxx=synx;
if ~isempty(synxx)
synxx(:,[7:10,13:15])=synx(:,[7:10,13:15])+alphax*deltaSyn;
end
MatGVxx=MatGV0x+alphax*MatGV1;
MatGRhsxx=MatGRhs0x+alphax*MatGRhs1;
SysDataxx=foldSysData(bus,sw,pvxx,pqxx,shunt,line,indx,zipxx,synxx,exc,tg,agc,cac,cluster);
xxx=foldX(SysDataxx,vc,qc,s0,d0,w0,eq10,eq20,ed10,ed20,psid0,psiq0,Pm0,Ef0,Vavrm0,Vavrr0,Vavrf0,Vavrref0,tgovg0,tgovm0,tgovmech0,fc,dpg0,qplt0,vg0);
SysParaxx=foldSysPara([],[],[],[],[],[],[],[],Ytr0x+alphax*Ytr1,[],Ysh0Origx+Ysh1Orig*alphax,[],[Vsp2,zeros(size(Vsp2))],MatGVxx,[],MatGRhsxx,[]);
diff=checkEquationBalanceSynAlgebraic(SysDataxx,SysParaxx,xxx);
if max(abs(diff))<1.05*diffParadigm
break;
end
alphax=alphax*alphaPreMult;
countCheckAlpha=countCheckAlpha+1;
end
if countCheckAlpha>=maxCount;alphax=alphax/alphaPreMult;end
alpha=alphax;
pqx(:,[4,5])=pqx(:,[4,5])+alpha*pqIncr;
synx(:,[7:10,13:15])=synx(:,[7:10,13:15])+alpha*deltaSyn;
if ~isempty(pvx);pvx(:,4)=pvx(:,4)+alpha*pvIncr;end
Rzip0x=Rzip0x+alpha*Rzip1;
Ysh0x=Ysh0x+alpha*Ysh1;
Ysh0Origx=Ysh0Origx+alpha*Ysh1Orig;
Vsp0x=Vsp0x+alpha*VspSq2(:,2);
Ytr0x=Ytr0x+alpha*Ytr1;
MatGV0x=MatGV0x+alpha*MatGV1;
MatGRhs0x=MatGRhs0x+alpha*MatGRhs1;
alphaConfirm=alphaConfirm+alpha;
addLog(['Alpha=',num2str(alphaConfirm),', da=',num2str(alpha),', (maxdiff<',num2str(diffTol),').'],'INFO');
if alpha==0
addLog('Step did not move!','INFO');
noMove=noMove+1;
if noMove>=MaxNoMove
addLog('Reached consecutive max no move, exit!','INFO');
break;
end
if diffTol>=diffTolMax
addLog('Max DiffTol reached and not move, exit!','INFO');
break;
end
diffTol=max([diffTol*diffMul,max(abs(diff))+1e-9]);
if diffTol>diffTolMax
diffTol=diffTolMax;
end
addLog(['Enlarge tol! (Tol=',num2str(diffTol),')'],'INFO');
skip=0;
else
noMove=0;
V0x=vc;
Q0x=qc;
f0x=fc;
alphas=[alphas;alpha];
end
end
addLog(['Total Step=',num2str(alphaConfirm),'.'],'INFO');
VSol=V0x;
QSol=Q0x;
fSol=f0x;
dpgSol=dpg0;
if ~isempty(pv)
dpgSol=dpgSol+extraPV*alphaConfirm;
end
xx=foldX(SysData,VSol,QSol,s0,d0,w0,eq10,eq20,ed10,ed20,psid0,psiq0,Pm0,Ef0,Vavrm0,Vavrr0,Vavrf0,Vavrref0,tgovg0,tgovm0,tgovmech0,fSol,dpgSol,qplt0,vg0);
diffRec=max(abs(diff));
finalAlpha=alphaConfirm;
end
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