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powersas.m/internal/convertSteadyDynModels.m

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function [SysDataNew,xNew]=convertSteadyDynModels(SysData,SysDataOrig,x,deltax,xOrig,SysPara,convMode)
% Conversion between QSS and dynamic model
% 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
% SysData - System data for conversion
% SysDataOrig - Original system data for reference (for guiding conversion from QSS to dynamic model)
% x - Current system states
% deltax - Time derivative of system states
% xOrig - Original system state
% SysPara -
% convMode
% 0 - QSS -> Dynamic
% 1 - Dynamic -> QSS
%
% OUTPUT
% SysDataNew - Converted system data
% xNew - new system state
%
%
% [busBase,swBase,pvBase,pqBase,shuntBase,lineBase,indBase,zipBase,synBase,excBase,tgBase,agcBase,cacBase,clusterBase]=unfoldSysData(BaseSysData);
[bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg,agc,cac,cluster]=unfoldSysData(SysData);
[V,Q,s,d,w,eq1,eq2,ed1,ed2,psid,psiq,Pm,Ef,Vavrm,Vavrr,Vavrf,Vavrref,tgovg,tgovm,tgovmech,f,dpg,qplt,vg]=unfoldX(x,SysData);
[~,~,ds,dd,dw,deq1,deq2,ded1,ded2,dpsid,dpsiq,dPm,~,dVavrm,dVavrr,dVavrf,~,dtgovg,~,dtgovmech,df,ddpg,dqplt,dvg]=unfoldX(deltax,SysData);
[pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,...
MatGV0,MatGV1,MatGRhs0,MatGRhs1,Tmech1,Varref1,Ef1,Pm1,Eq11,fault]=unfoldSysPara(SysPara);
[nIslands,islands]=searchIslands(bus(:,1),line(:,[1,2]));
if convMode==0 % To full dynamic model, i.e. convert all sw and pv to syn
[buso,swo,pvo,pqo,shunto,lineo,indo,zipo,syno,exco,tgo,agco,caco,clustero]=unfoldSysData(SysDataOrig);% SysDataOrig must not be empty
%
nbus=size(bus,1);
nline=size(line,1);
[nIslands,islands,refs]=searchIslands(bus(:,1),line(:,1:2));
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
if isempty(Ytr0)
[~,Ytr0,Ysh0]=getYMatrix(nbus,line,fault);
end
Ysh0=Ysh0+yShunt;
Y=Ytr0+sparse(1:nbus,1:nbus,Ysh0,nbus,nbus);
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;
agcExt=zeros(nbus,4);
if ~isempty(agc)
agcExt(agc(:,1),:)=agc;
end
fdk=agcExt(:,2)+agcExt(:,3);
D0=imag(V);
% Determine the frequency model of each island
freqTypeTag=zeros(nIslands,1);%0:sw,1:syn,2:steady-state f
freqKeptTag=zeros(nIslands,1);
frefs=refs;
fswTag=zeros(nbus,1);
fsynTag=zeros(nbus,1);
fswTag(sw(:,1))=1;
fswTagxD=fswTag;
fsynTag(syn(:,1))=1;
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);
pVec=zeros(nbus,1);
qVec=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
pVec=pVec-accumarray(zip(:,1),zip(:,7).*zip(:,12),[nbus,1]);
qVec=qVec-accumarray(zip(:,1),zip(:,10).*zip(:,12),[nbus,1]);
end
IInj=Y*V;
if ~isempty(zip)%zipMode=0
IInj=IInj+accumarray(zip(:,1),(zip(:,6)-1j*zip(:,9)).*zip(:,12).*V(zip(:,1))./abs(V(zip(:,1))),[nbus,1]);
end
SInjRHS=V.*conj(IInj);
% qVec(busType~=0)=0;
if ~isempty(ind)
nInd=size(ind,1);
indIdx=ind(:,1);
Rm1=ind(:,7);
Xm1=ind(:,8);
Zm1=ind(:,7)+1j*ind(:,8);
Xmm=ind(:,13);
Zme=1j*ind(:,13);
Rm2=ind(:,9);
Xm2=ind(:,10);
Tm0=ind(:,15)+ind(:,16)+ind(:,17);
Tm1=-ind(:,16)-2*ind(:,17);
Tm2=ind(:,17);
Hm=ind(:,14);
Zind=Zm1+Zme.*(Rm2+1j*Xm2.*s)./(Rm2+(1j*Xm2+Zme).*s);
ILind=V(indIdx)./Zind;
SInjRHS=SInjRHS+V.*conj(accumarray(indIdx,ILind,[nbus,1]));
end
diffSInj=SInjRHS-(pVec+1j*qVec);
% diffSInj=diffSInj-1j*Q;
% diffSInj(busType==2)=0;
sg=diffSInj;
sgSyn=sg(syno(:,1));
IgSyn=conj(sgSyn./V(syno(:,1)));
w=f(syno(:,1));
Qx=zeros(nbus,1);
Eq=V(syno(:,1))+IgSyn.*(syno(:,7)+1j*syno(:,13));
dg=atan2(imag(Eq),real(Eq));
unitEq=Eq./abs(Eq);
unitEd=-1j*unitEq;
Id=unitEd.*(real(unitEd).*real(IgSyn)+imag(unitEd).*imag(IgSyn));
Efx=Eq+1j*Id.*(syno(:,8)-syno(:,13));
synIdx=syno(:,1);
Rga=syno(:,7);
Xgd=syno(:,8);
Xgd1=syno(:,9);
Xgd2=syno(:,10);
Xgq=syno(:,13);
Xgq1=syno(:,14);
Xgq2=syno(:,15);
Vgx=real(V(synIdx));
Vgy=imag(V(synIdx));
Igx=real(IgSyn);
Igy=imag(IgSyn);
Vgd=Vgx.*sin(dg)-Vgy.*cos(dg);
Vgq=Vgx.*cos(dg)+Vgy.*sin(dg);
Igd=Igx.*sin(dg)-Igy.*cos(dg);
Igq=Igx.*cos(dg)+Igy.*sin(dg);
eq1=Vgq+Igd.*Xgd1+Igq.*Rga;
ed1=Vgd+Igd.*Rga-Igq.*Xgq;
SysDataNew=foldSysData(buso,swo,pvo,pq,shunt,lineo,ind,zip,syno,exco,tgo,agc,caco,clustero);
[nState,idxs]...
=getIndexDyn(SysDataNew);
xx=zeros(nState,1);
xx(idxs.vIdx)=V;
xx(idxs.qIdx)=Qx;
xx(idxs.sIdx)=s;
xx(idxs.deltaIdx)=dg;
xx(idxs.omegaIdx)=w;
xx(idxs.efIdx)=abs(Efx);
deltaxx=zeros(nState,1);
deltaxx(idxs.omegaIdx)=df(syno(:,1));
% deltaxx(tgovgIdx)=ddpg(syno(tgo(:,1),1))+tgo(:,8)./tgo(:,7)./tgo(:,4).*df(syno(tgo(:,1),1));
deltaxx(idxs.tgovgIdx)=-(1-tgo(:,8)./tgo(:,7))./tgo(:,4).*df(syno(tgo(:,1),1));
xNew=perpareInitialState(SysDataNew,xx,deltaxx);
SysDataNew.agc=agco;
xNew(idxs.fIdx)=f;
% xNew(eq1Idx)=xOrig(eq1Idx);
% xNew(eq2Idx)=xOrig(eq2Idx);
% xNew(ed1Idx)=xOrig(ed1Idx);
% xNew(ed2Idx)=xOrig(ed2Idx);
% xNew(psidIdx)=xOrig(psidIdx);
% xNew(psiqIdx)=xOrig(psiqIdx);
xNew(idxs.vavrmIdx)=xOrig(idxs.vavrmIdx);
xNew(idxs.vavrrIdx)=xOrig(idxs.vavrrIdx);
xNew(idxs.vavrfIdx)=xOrig(idxs.vavrfIdx);
xNew(idxs.vavrrefIdx)=xOrig(idxs.vavrrefIdx);
elseif convMode==1 % To QSS model, i.e. convert all syn to sw and pv (or pv if agc is on)
[nState,idxs]...
=getIndexDyn(SysData);
nbus=size(bus,1);
nline=size(line,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;
agcExt=zeros(nbus,4);
agcExt(1:nbus,1)=1:nbus;
if ~isempty(agc)
agcExt(agc(:,1),:)=agc;
end
synIsland=islands(syn(:,1));
synV=V(syn(:,1));
dg=x(idxs.deltaIdx);
wg=x(idxs.omegaIdx);
eq1=x(idxs.eq1Idx);
eq2=x(idxs.eq2Idx);
ed1=x(idxs.ed1Idx);
ed2=x(idxs.ed2Idx);
psid=x(idxs.psidIdx);
psiq=x(idxs.psiqIdx);
vbus=x(idxs.vIdx);
Ef=x(idxs.efIdx);
if ~isempty(syn)
nSyn=size(syn,1);
synIdx=syn(:,1);
Vgx=real(vbus(synIdx));
Vgy=imag(vbus(synIdx));
Vgd=Vgx.*sin(dg)-Vgy.*cos(dg);
Vgq=Vgx.*cos(dg)+Vgy.*sin(dg);
wgb=syn(:,4);
model=syn(:,5);
Xgl=syn(:,6);
Rga=syn(:,7);
Xgd=syn(:,8);
Xgd1=syn(:,9);
Xgd2=syn(:,10);
Tgd1=syn(:,11);
Tgd2=syn(:,12);
Xgq=syn(:,13);
Xgq1=syn(:,14);
Xgq2=syn(:,15);
Tgq1=syn(:,16);
Tgq2=syn(:,17);
Mg=syn(:,18);
Dg=syn(:,19);
TgAA=syn(:,24);
gammad=Tgd2./Tgd1.*Xgd2./Xgd1.*(Xgd-Xgd1);
gammaq=Tgq2./Tgq1.*Xgq2./Xgq1.*(Xgq-Xgq1);
Igd=zeros(nSyn,1);
Igq=zeros(nSyn,1);
for i=1:nSyn
if model(i)==8
Igd(i)=(eq2(i)-psid(i))/Xgd2(i);
Igq(i)=(-ed2(i)-psiq(i))/Xgq2(i);
elseif model(i)==6
Igd(i)=(Rga(i)*(ed2(i)-Vgd(i))+Xgq2(i)*(eq2(i)-Vgq(i)))/(Rga(i)*Rga(i)+Xgd2(i)*Xgq2(i));
Igq(i)=(-Xgd2(i)*(ed2(i)-Vgd(i))+Rga(i)*(eq2(i)-Vgq(i)))/(Rga(i)*Rga(i)+Xgd2(i)*Xgq2(i));
elseif model(i)==5
Igd(i)=(Rga(i)*(ed2(i)-Vgd(i))+Xgq2(i)*(eq2(i)-Vgq(i)))/(Rga(i)*Rga(i)+Xgd2(i)*Xgq2(i));
Igq(i)=(-Xgd2(i)*(ed2(i)-Vgd(i))+Rga(i)*(eq2(i)-Vgq(i)))/(Rga(i)*Rga(i)+Xgd2(i)*Xgq2(i));
elseif model(i)==4
Igd(i)=(Rga(i)*(ed1(i)-Vgd(i))+Xgq1(i)*(eq1(i)-Vgq(i)))/(Rga(i)*Rga(i)+Xgd1(i)*Xgq1(i));
Igq(i)=(-Xgd1(i)*(ed1(i)-Vgd(i))+Rga(i)*(eq1(i)-Vgq(i)))/(Rga(i)*Rga(i)+Xgd1(i)*Xgq1(i));
elseif model(i)==3
Igd(i)=(Rga(i)*(-Vgd(i))+Xgq(i)*(eq1(i)-Vgq(i)))/(Rga(i)*Rga(i)+Xgd1(i)*Xgq(i));
Igq(i)=(-Xgd1(i)*(-Vgd(i))+Rga(i)*(eq1(i)-Vgq(i)))/(Rga(i)*Rga(i)+Xgd1(i)*Xgq(i));
elseif model(i)==2
Igd(i)=(Rga(i)*(-Vgd(i))+Xgq(i)*(Ef(i)-Vgq(i)))/(Rga(i)*Rga(i)+Xgd(i)*Xgq(i));
Igq(i)=(-Xgd(i)*(-Vgd(i))+Rga(i)*(Ef(i)-Vgq(i)))/(Rga(i)*Rga(i)+Xgd(i)*Xgq(i));
end
end
Ig=(Igd.*sin(dg)+Igq.*cos(dg))+1j*(-Igd.*cos(dg)+Igq.*sin(dg));
else
Ig=zeros(0,1);
end
synS=synV.*conj(Ig);
synP=real(synS);
Qx=Q;
Qx(syn(:,1))=Qx(syn(:,1))+imag(synS);
pgTotal=zeros(nbus,1);
pgTotal(pv(:,1))=pv(:,4);
pgTotal(syn(:,1))=pgTotal(syn(:,1))+synP;
% pgTotal(pq(:,1))=pgTotal(pq(:,1))-pq(:,4);
busTypeNew=busType;
busTypeNew(syn(:,1))=1;
busTypeNew(sw(:,1))=2;
f0=f;
for island=1:nIslands
busesInIsland=find(islands==island);
agcCoeffInIsland=agcExt(busesInIsland,4);
busTypeInIsland=busTypeNew(busesInIsland);
pBusesInIsland=busesInIsland(busTypeInIsland>0);
swBusesInIsland=busesInIsland(busTypeInIsland==2);
f0(busesInIsland)=mean(f(busesInIsland));
if sum(agcCoeffInIsland(busTypeInIsland>0))>0 % Effective AGC
else % No Effective AGC in island
% if isempty(swBusesInIsland)&&~isempty(pBusesInIsland)
% busTypeNew(pBusesInIsland(1))=2;
% end
% f0(busesInIsland)=0.0;
end
if ~isempty(swBusesInIsland)
f0(busesInIsland)=0.0;
end
end
agcExt(syn(:,1),3)=agcExt(syn(:,1),3)+syn(:,19);
agcExt(syn(tg(:,1),1),2)=agcExt(syn(tg(:,1),1),2)+1./tg(:,4);
TagcOri=1./agcExt(:,4);
K=zeros(nbus,1);
K(syn(:,1))=K(syn(:,1))+syn(:,19);
K(syn(tg(:,1),1))=K(syn(tg(:,1),1))+1./tg(:,4);
Tagc=zeros(nbus,1);
Tagc(syn(:,1))=syn(:,18)./syn(:,19);
Mtg=syn(tg(:,1),18);
Dtg=syn(tg(:,1),18);
Rtg=tg(:,4);
T1tg=tg(:,8);
T2tg=tg(:,7);
Tagc(syn(tg(:,1),1))=2*Mtg.*T2tg.*Rtg./(Rtg.*Mtg+T1tg+Rtg.*Dtg.*T2tg-sqrt((Rtg.*Mtg-Rtg.*Dtg.*T2tg).*(Rtg.*Mtg-Rtg.*Dtg.*T2tg)+4*Rtg.*Mtg.*(T1tg-T2tg)));
recTagc=(K.*TagcOri-sqrt(K.*K.*TagcOri.*TagcOri-4*K.*TagcOri.*Tagc))/2./TagcOri./Tagc;
recTagc(isnan(recTagc))=0.0;
agcExt(:,4)=recTagc;
fdk=agcExt(:,2)+agcExt(:,3);
agcTag=zeros(nbus,1);
agcTag(agc(:,1))=1;
agcTag(fdk>0)=1;
agcTag(agcExt(:,4)~=0)=1;
agcNew=agcExt(agcTag==1,:);
pvNewIdx=find(busTypeNew==1);
swNewIdx=find(busTypeNew==2);
pqDel=pq(busTypeNew(pq(:,1))~=0,:);
pq(busTypeNew(pq(:,1))~=0,5)=0;
Qx(pqDel(:,1))=Qx(pqDel(:,1))-pqDel(:,5);
pvNew=[pvNewIdx,100.0*ones(size(pvNewIdx,1),1),bus(pvNewIdx,2),pgTotal(pvNewIdx),abs(V(pvNewIdx)),repmat([2.0,0.0,0,1],size(pvNewIdx,1),1)];
swNew=[swNewIdx,100.0*ones(size(swNewIdx,1),1),bus(swNewIdx,2),abs(V(swNewIdx)),atan2(imag(V(swNewIdx)),real(V(swNewIdx)))*180/pi,repmat([99.00000 -99.00000 1.1 0.9 0 1 1 1],size(swNewIdx,1),1)];
deltaFd=fdk.*f0;
pvNew(:,4)=pvNew(:,4)+deltaFd(pvNew(:,1));
deltaFd(pvNew(:,1))=0.0;
pqVal=zeros(nbus,2);
pqVal(pq(:,1),:)=pq(:,4:5);
pqVal(:,1)=pqVal(:,1)-deltaFd;
pqNew=[bus(:,1),100.0*ones(nbus,1),bus(:,2),pqVal,repmat([2.0,0.0,0,1],nbus,1)];
pqNew=pqNew(pqNew(:,4)~=0|pqNew(:,5)~=0,:);
SysDataNew=foldSysData(bus,swNew,pvNew,pqNew,shunt,line,ind,zip,zeros(0,26),zeros(0,14),zeros(0,8),agcNew,cac,cluster);
[nState,idxs]...
=getIndexDyn(SysDataNew);
xx=zeros(nState,1);
xx(idxs.vIdx)=V;
xx(idxs.qIdx)=Qx;
xx(idxs.sIdx)=s;
deltaxx=zeros(nState,1);
xNew=perpareInitialState(SysDataNew,xx,deltaxx);
xNew(idxs.fIdx)=f0;
dpg0=zeros(nbus,1);
xNew(idxs.dpgIdx)=dpg0;
end
end
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