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powersas.m/internal/simulationTimeDomainNI.m

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function [stateCurve,tt,diffList,nxtDt,exitflag]=simulationTimeDomainNI(SimData,SysData,SysPara,x0)
% Numerical integration approach for dynamic simulation
%
% FUNCTION simulationTimeDomainNI
% 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
%
% OUTPUT
% stateCurve - A list of states in the order of time
% tt - A list of time points (starting with 0)
% diffList - A list of errors
% nxtDt - ending time step
% exitFlag -
% 0 - Success and normally exit
% -1 - Fail to finish (due to computation errors or failures)
%
% MODES (controlled by SimData.method)
% SimData.method has format X.YZ
% X - Method for solving differential equations (DE)
% 0 - HE
% 1 - Modified Euler
% 2 - RK4
% 3 - Trapezoidal
%
% Y - Method for solving algebraic equations (AE)
% 0 - HE
% 1 - NR
%
% Z - Variable step (only applies to X>1)
% 0 - Fixed step
% 1 - Adaptive step
%
%%
[bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg,agc,cac,cluster]=unfoldSysData(SysData);
[nState,idxs]...
=getIndexDyn(SysData);
% [V0,Q0,s0,d0,w0,eq10,eq20,ed10,ed20,psid0,psiq0,Pm0,Ef0,Vavrm0,Vavrr0,Vavrf0,Vavrref0,tgovg0,tgovm0,tgovmech0]=unfoldX(x0,SysData);
% [~,~,sNew,dNew,~,eq1New,eq2New,ed1New,ed2New,psidNew,psiqNew,~,EfNew,~,~,~,~,~,~,~]=unfoldX(xNew,SysData);
[maxTime,segTime,dt,nlvl,taylorN,alphaTol,diffTol,diffTolMax,method,varOpt]=unfoldSimData(SimData);
[pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,~,~,~,~,Tmech1,Varref1,Ef1,Pm1,Eq11]=unfoldSysPara(SysPara);
if ~isempty(varOpt) && isfield(varOpt,'absT')
useAbsT=1;
absT=varOpt.absT;
else
useAbsT=0;
end
[~,~,~,~,~,~,~,~,method]=unfoldSimData(SimData);
DEmethod =floor(method);
AEmethod =round(10*mod(method,1));
varStep =round(100*mod(method,0.1));
eval('setting_func_simulationTimeDomainNI');
if varStep~=0
% some temporary parameters
dt=min([maxStep,max([minStep,dt])]);
%
end
% dt = 0.01;
tt=0;
diffList=0;
% tt=0:dt:maxTime;
% if maxTime>tt(end)+1e-9;tt=[tt,maxTime];end
% if length(tt)<2;tt=[0,maxTime];end
% diffList=zeros(size(tt));
nbus=size(bus,1);
nline=size(line,1);
nInd=size(ind,1);
nZip=size(zip,1);
nSyn=size(syn,1);
nTg=size(tg,1);
nExc=size(exc,1);
if isempty(pqIncr);pqIncr=zeros(size(pq,1),2);end
if isempty(pvIncr);pvIncr=zeros(size(pv,1),1);end
if isempty(Rind0);Rind0=ones(nInd,1);end
if isempty(Rind1);Rind1=zeros(nInd,1);end
if isempty(Reind0);Reind0=ones(nInd,1);end
if isempty(Reind1);Reind1=zeros(nInd,1);end
if isempty(Rzip0);Rzip0=ones(nZip,1);end
if isempty(Rzip1);Rzip1=zeros(nZip,1);end
if isempty(Ytr0)||isempty(Ytr1)||isempty(Ysh0)||isempty(Ysh1)
[~,Ytr0x,Ysh0x,~,~,~,~]=getYMatrix(nbus,line);
if isempty(Ytr0);Ytr0=Ytr0x;end
if isempty(Ytr1);Ytr1=0*Ytr0;end
if isempty(Ysh0);Ysh0=Ysh0x;end
if isempty(Ysh1);Ysh1=0*Ysh0;end
end
if isempty(Tmech1);Tmech1=zeros(nTg,1);end
if isempty(Varref1);Varref1=zeros(nExc,1);end
if isempty(Ef1);Ef1=zeros(nSyn,1);end
if isempty(Pm1);Pm1=zeros(nSyn,1);end
if isempty(Eq11);Eq11=zeros(nSyn,1);end
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~=0);
ipq=find(busType==0);
npq=size(ipq,1);
npv=size(ipv,1);
yShunt=zeros(nbus,1);
yShunt(shunt(:,1))=shunt(:,5)+1j*shunt(:,6);
Ysh0=Ysh0+yShunt;
shunt=zeros(0,7);
if isempty(VspSq2)
V0=x0(idxs.vIdx);
VspSq2=[abs(V0).*abs(V0),zeros(nbus,1)];
end
segAlpha=min([maxTime,segTime]);
maxLvlHe=3;
if nlvl>maxLvlHe
nlvl=maxLvlHe;
end
SimDatax=foldSimData(maxTime,segAlpha,dt,nlvl,taylorN,alphaTol,diffTol,diffTolMax,method);
stateCurve=zeros(size(x0,1),1);
stateCurve(:,1)=x0;
iden=[datestr(clock,30),'_dyn'];
%
% [t,stateCurve,finalAlpha,alphaList,diffList]=hemMachinePFmultiStageDyn(SimDatax,SysData,SysParax,x0);
V0=x0(idxs.vIdx);
SysDatax=foldSysData(bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg,agc,cac,cluster);
dxc=integ(SysDatax,SysPara,x0,dt)/dt;
SysParaxx=foldSysPara(pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,[],Ysh0,[],[abs(V0).*abs(V0),zeros(nbus,1)],[],[],[],[],Tmech1,Varref1,Ef1,Pm1,Eq11);
diff=checkEquationBalanceSynDyn(SysDatax,SysParaxx,x0,dxc);
diffList(1)=max(abs(diff));
it=1;
stepCnt=0;
errPtoX=zeros(0,1);
nxtDt=dt;
correctRatio=1;
while tt(end)+dt<=maxTime+stepSizeEps
xt=stateCurve(:,end);
nxtDt=dt;
% dt=tt(it)-tt(it-1);
if DEmethod==1 % Improved Euler
SysParaOrig=foldSysPara(pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,[],[],[],[],Tmech1,Varref1,Ef1,Pm1,Eq11);
SysDataOrig=foldSysData(bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg,agc,cac,cluster);
[xTemp,diff,exitflag]=singleStepME(SimDatax,SysDataOrig,SysParaOrig,xt,tt(end),dt,iden,AEmethod);
if exitflag~=0
if varStep
dt=max([minStep,dt/10]);
[xTemp,diff,exitflag]=singleStepME(SimDatax,SysDataOrig,SysParaOrig,xt,tt(end),dt,iden,AEmethod);
if exitflag~=0
break;
end
else
break;
end
end
stateCurve=[stateCurve,xTemp];
diffList=[diffList,max(abs(diff))];
if varStep&&stepCnt>=stepCntThreshold
[xTempMid,~,tmpExitflag]=singleStepME(SimDatax,SysDataOrig,SysParaOrig,xt,tt(end),dt/2,iden,AEmethod);
if tmpExitflag==0
[xTemp1,~,tmpExitflag]=singleStepME(SimDatax,SysDataOrig,SysParaOrig,xTempMid,tt(end)+dt/2,dt/2,iden,AEmethod);
end
if tmpExitflag==0
errX=max(abs(xTemp1-xTemp));
maxErrX=max(abs(errX));
errPtoX=[errPtoX;maxErrX/diffList(end)];
stepRatio=min([max([(diffTol*mean(errPtoX)/2/maxErrX)^(1/3),0.3]),2]);
nxtDt=correctRatio^1.5*0.95*dt*stepRatio;
correctRatio=sqrt(correctRatio);
disp('');
end
stepCnt=0;
end
elseif DEmethod==2% R-K 4
SysParaOrig=foldSysPara(pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,[],[],[],[],Tmech1,Varref1,Ef1,Pm1,Eq11);
SysDataOrig=foldSysData(bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg,agc,cac,cluster);
[xTemp,diff,exitflag]=singleStepRK4(SimDatax,SysDataOrig,SysParaOrig,xt,tt(end),dt,iden,AEmethod);
if exitflag~=0
if varStep
dt=max([minStep,dt/10]);
[xTemp,diff,exitflag]=singleStepRK4(SimDatax,SysDataOrig,SysParaOrig,xt,tt(end),dt,iden,AEmethod);
if exitflag~=0
break;
end
else
break;
end
end
stateCurve=[stateCurve,xTemp];
diffList=[diffList,max(abs(diff))];
if varStep&&stepCnt>=stepCntThreshold
[xTempMid,~,tmpExitflag]=singleStepRK4(SimDatax,SysDataOrig,SysParaOrig,xt,tt(end),dt/2,iden,AEmethod);
if tmpExitflag==0
[xTemp1,~,tmpExitflag]=singleStepRK4(SimDatax,SysDataOrig,SysParaOrig,xTempMid,tt(end)+dt/2,dt/2,iden,AEmethod);
end
if tmpExitflag==0
errX=max(abs(xTemp1-xTemp));
maxErrX=max(abs(errX));
errPtoX=[errPtoX;maxErrX/diffList(end)];
stepRatio=min([max([(diffTol*mean(errPtoX)/2/maxErrX)^0.2,0.3]),2]);
nxtDt=correctRatio^1.9*0.99*dt*stepRatio;
correctRatio=sqrt(correctRatio);
disp('');
end
stepCnt=0;
end
else %trapezoidal rule
SysParaOrig=foldSysPara(pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,[],[],[],[],Tmech1,Varref1,Ef1,Pm1,Eq11);
SysDataOrig=foldSysData(bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg,agc,cac,cluster);
[xTemp,diff,exitflag]=singleStepTRAP(SimDatax,SysDataOrig,SysParaOrig,xt,tt(end),dt,iden,AEmethod);
if exitflag~=0
if varStep
dt=max([minStep,dt/10]);
[xTemp,diff,exitflag]=singleStepTRAP(SimDatax,SysDataOrig,SysParaOrig,xt,tt(end),dt,iden,AEmethod);
if exitflag~=0
break;
end
else
break;
end
end
stateCurve=[stateCurve,xTemp];
diffList=[diffList,max(abs(diff))];
if varStep&&stepCnt>=stepCntThreshold
[xTempMid,~,tmpExitflag]=singleStepTRAP(SimDatax,SysDataOrig,SysParaOrig,xt,tt(end),dt/2,iden,AEmethod);
if tmpExitflag==0
[xTemp1,~,tmpExitflag]=singleStepTRAP(SimDatax,SysDataOrig,SysParaOrig,xTempMid,tt(end)+dt/2,dt/2,iden,AEmethod);
end
if tmpExitflag==0
errX=max(abs(xTemp1-xTemp));
maxErrX=max(abs(errX));
errPtoX=[errPtoX;maxErrX/diffList(end)];
stepRatio=min([max([(diffTol*mean(errPtoX)/2/maxErrX)^(1/3),0.3]),2]);
nxtDt=correctRatio^1.9*0.99*dt*stepRatio;
correctRatio=sqrt(correctRatio);
disp('');
end
stepCnt=0;
end
end
tt=[tt,tt(end)+dt];
it=it+1;
if useAbsT
strPre=['T=',num2str(absT+tt(it),'%7.5f'),', '];
else
strPre=['TD time (in stage)=',num2str(tt(it),'%7.5f'),', '];
end
addLog([strPre,'(s), dt=',num2str(dt,'%7.5f'),',cr=',num2str(correctRatio,'%7.5f'),',nxt=',num2str(nxtDt,'%7.5f')],'INFO');
if tt(end)>=maxTime-stepSizeEps
break;
end
if varStep
stepCnt=stepCnt+1;
dt=nxtDt;
dt=min([maxStep,max([minStep,dt])]);
correctRatio=correctRatio*dt/nxtDt;
if mod(it,stepCntThreshold*20)==0
correctRatio=1;
end
end
if tt(end)+dt>=maxTime-stepSizeEps
dt=maxTime-tt(end);
end
end
stateCurve=stateCurve(:,1:it);
tt=tt(1:it);
diffList=diffList(1:it);
if exist([iden,'.mat'],'file')
delete([iden,'.mat']);
end
end
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