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First release of PowerSAS.m
This commit is contained in:
Rui Yao
527
internal/solveAlgebraicNR.m
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527
internal/solveAlgebraicNR.m
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function [stateNew,flag,diffRec,loop]=solveAlgebraicNR(SimData,SysData,SysPara,x0,xNew,SysDataNew)
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% General Newton-Raphson computation for solving the algebraic equations
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%
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% FUNCTION restorationAlgebraicNR (will be renamed in a future version)
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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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% x0 - Initial system state
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% xNew - New system state (algebraic variables need to be solved)
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% SysDataNew - NOT USED
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%
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% OUTPUT
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% stateNew - Solved state (only algebraic variables changed)
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% flag
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% 0 - returned normally
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% -1- Fail
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% diffRec - Final maximum difference
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% loop - number of loops to finish NR
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%
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% TODO % Check input argument SysDataNew if it is necessary
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setting_func_restorationAlgebraicNR;
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addLog('[#START#]Solving algebraic equations - NR.','INFO');
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[bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg,agc,cac,cluster]=unfoldSysData(SysData);
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if nargin>=6
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[~,~,~,~,~,~,~,~,synNew,~,~]=unfoldSysData(SysData);
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else
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synNew=[];
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end
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[nState,idxs]...
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=getIndexDyn(SysData);
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% [V0,Q0,s0,d0,w0,eq10,eq20,ed10,ed20,psid0,psiq0,Pm0,Ef0,Vavrm0,Vavrr0,Vavrf0,Vavrref0,tgovg0,tgovm0,tgovmech0]=unfoldX(x0,SysData);
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% [~,~,sNew,dNew,~,eq1New,eq2New,ed1New,ed2New,psidNew,psiqNew,~,EfNew,~,~,~,~,~,~,~]=unfoldX(xNew,SysData);
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[maxTime,segTime,dt,nlvl,taylorN,alphaTol,diffTol,diffTolMax,method]=unfoldSimData(SimData);
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AEmethod=round(10*mod(method,1));
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if isempty(AEmethod)
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AEmethod=1;
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end
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[pqIncr,pvIncr,Rind0,Rind1,~,~,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,VspSq2,MatGV0,MatGV1,MatGRhs0,MatGRhs1]=unfoldSysPara(SysPara);
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% The Y matrices may be with faults, so don't re-generate them!
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[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);
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eq0=Ef0;ed0=zeros(size(Ef0));
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[~,~,sNew,dNew,~,eq1New,eq2New,ed1New,ed2New,psidNew,psiqNew,~,EfNew,~,~,~,~,~,~,~]=unfoldX(xNew,SysData);
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eqNew=EfNew;edNew=zeros(size(EfNew));
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[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);
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nbus=size(bus,1);
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if ~isempty(ind)
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[YshInd0,Yshind1]=getLinearInterpolatorInd(nbus,ind,s0,sNew);
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Ysh0=Ysh0+YshInd0;
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Ysh1=Ysh1+Yshind1;
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end
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[nIslands,islands,refs]=searchIslands(bus(:,1),line(:,1:2));
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nbus=size(bus,1);
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nline=size(line,1);
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nInd=size(ind,1);
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nZip=size(zip,1);
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nSyn=size(syn,1);
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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~=0);
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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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if isempty(VspSq2)
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V0=x0(idxs.vIdx);
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VspSq2=[abs(V0).*abs(V0),zeros(nbus,1)];
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end
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% Determine the frequency model of each island
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freqTypeTag=zeros(nIslands,1);%0:sw,1:syn,2:steady-state f
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freqKeptTag=zeros(nbus,1);
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frefs=refs;
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fswTag=zeros(nbus,1);
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fsynTag=zeros(nbus,1);
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fswTag(isw)=1;
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fswTagxD=fswTag;
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fsynTag(syn(:,1))=1;
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D0=imag(V0);
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for isl=1:nIslands
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if isempty(find(fswTag(islands==isl)==1, 1))
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if isempty(find(fsynTag(islands==isl)==1, 1))
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freqTypeTag(isl)=2;
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busesInIsland=find(islands==isl);
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[~,imin]=min(abs(D0(busesInIsland)));
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frefs(isl)=busesInIsland(imin(1));
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fswTagxD(frefs(isl))=1;
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freqKeptTag(busesInIsland)=1;
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else
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freqTypeTag(isl)=1;
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end
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end
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end
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freqKeptTagxRef=freqKeptTag;
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freqKeptTagxRef(frefs)=0;
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nFreqKept=sum(freqKeptTag);
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if ~isempty(agc)
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agcExt=zeros(nbus,size(agc,2));
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agcExt(agc(:,1),:)=agc;
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fdk=agcExt(:,2)+agcExt(:,3); %1/R+D
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else
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fdk=zeros(nbus,1);
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end
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yShunt=zeros(nbus,1);
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yShunt(shunt(:,1))=shunt(:,5)+1j*shunt(:,6);
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Ysh0=Ysh0+yShunt;
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Ysh0=Ysh0+accumarray(zip(:,1),(Rzip0).*(zip(:,5)+1j*zip(:,8)),[nbus,1]);
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Ysh1=Ysh1+accumarray(zip(:,1),(Rzip1).*(zip(:,5)+1j*zip(:,8)),[nbus,1]);
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% VspSq2=zeros(nbus,1);
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% pqIncrS=zeros(size(pq,1),2);pvIncrS=zeros(size(pv,1),1);
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% Rzip0S=ones(nZip,1);Rzip1S=zeros(nZip,1);
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% Rind0S=ones(nInd,1);Rind1S=zeros(nInd,1);
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Reind0=ones(nInd,1);Reind1=zeros(nInd,1);
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if ~isempty(Ytr1)
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YtrNew=Ytr0+Ytr1;
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else
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YtrNew=Ytr0;
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end
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YshNew=Ysh0+Ysh1;
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YNew=YtrNew+sparse(1:nbus,1:nbus,YshNew,nbus,nbus);
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MatGVNew=MatGV0+MatGV1;
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MatGRhsNew=MatGRhs0+MatGRhs1;
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SNew=-accumarray(pq(:,1),pq(:,4)+1j*pq(:,5),[nbus,1])+accumarray(pv(:,1),pv(:,4),[nbus,1]);
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SNew=SNew-accumarray(pq(:,1),pqIncr(:,1)+1j*pqIncr(:,2),[nbus,1])+accumarray(pv(:,1),pvIncr,[nbus,1]);
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SNew=SNew-accumarray(zip(:,1),(Rzip0+Rzip1).*(zip(:,7)+1j*zip(:,10)),[nbus,1]);
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INew=-accumarray(zip(:,1),(Rzip0+Rzip1).*(zip(:,6)-1j*zip(:,9)),[nbus,1]);
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JNew=real(INew);
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KNew=imag(INew);
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GNew=real(YNew);BNew=imag(YNew);
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J1=GNew+sparse(syn(:,1),syn(:,1),MatGVNew(:,1),nbus,nbus);
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J2=-BNew+sparse(syn(:,1),syn(:,1),MatGVNew(:,2),nbus,nbus);
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J3=BNew+sparse(syn(:,1),syn(:,1),MatGVNew(:,3),nbus,nbus);
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J4=GNew+sparse(syn(:,1),syn(:,1),MatGVNew(:,4),nbus,nbus);
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P2freq=sparse(1:nbus,1:nbus,-freqKeptTag.*fdk,nbus,nbus);
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Freq2freq=sparse([1:nbus,1:nbus],[1:nbus,frefs(islands)'],[ones(1,nbus),-ones(1,nbus)],nbus,nbus);
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Vtemp=V0;
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ftemp=f0;
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QTemp=Q0;
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busTag=ones(nbus,1);
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busTag(sw(:,1))=0;
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jacRowTag=[busTag;busTag;freqKeptTagxRef];
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jacColTag=[busTag;fswTagxD==0;freqKeptTag];
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idxNonSw=find(busType~=2);
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idxNonSwD=find(busType~=2&fswTagxD==1);
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if AEmethod==1 % NR and damped NR
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for loop=1:maxLoop
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Ctemp=real(Vtemp);
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Dtemp=imag(Vtemp);
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Atemp=abs(Vtemp);
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Vgtemp=Vtemp(syn(:,1));
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Ig=accumarray(syn(:,1),MatGRhsNew(:,1)+1j*MatGRhsNew(:,2),[nbus,1])-...
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accumarray(syn(:,1),(MatGVNew(:,1).*real(Vgtemp)+MatGVNew(:,2).*imag(Vgtemp))+1j*(MatGVNew(:,3).*real(Vgtemp)+MatGVNew(:,4).*imag(Vgtemp)),[nbus,1]);
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diff=conj(SNew)+INew.*abs(Vtemp)+Ig.*conj(Vtemp)-(YNew*Vtemp).*conj(Vtemp);
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diffP=real(diff)+freqKeptTag.*(-fdk.*ftemp+dpg0);
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diffVQ=imag(diff);
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diffF=ftemp-ftemp(frefs(islands));
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if ~isempty(pv)
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diffVQ(pv(:,1))=abs(Vtemp(pv(:,1))).*abs(Vtemp(pv(:,1)))-sum(VspSq2(pv(:,1)),2);
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end
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tDiff=[diffP(idxNonSw);diffVQ(idxNonSw);diffF(freqKeptTagxRef==1)];
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if max(abs(tDiff))<diffTol
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QTemp=imag(diff);
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break;
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end
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dCtemp=sparse(1:nbus,1:nbus,Ctemp,nbus,nbus);
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dDtemp=sparse(1:nbus,1:nbus,Dtemp,nbus,nbus);
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Jac1=[dCtemp*J1+dDtemp*J3,dCtemp*J2+dDtemp*J4;...
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dCtemp*J3-dDtemp*J1,dCtemp*J4-dDtemp*J2];
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Jac2=[sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus),sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus);...
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sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus),-sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus)];
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Jac3=[sparse(1:nbus,1:nbus,JNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,JNew.*Dtemp./Atemp,nbus,nbus);...
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sparse(1:nbus,1:nbus,KNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,KNew.*Dtemp./Atemp,nbus,nbus)];
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Jac4=[sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus),sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus);...
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sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus),-sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus)];
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Jac=Jac3+Jac4-Jac1-Jac2;
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JacVc=sparse(1:nbus,1:nbus,2*Ctemp,nbus,nbus);
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JacVd=sparse(1:nbus,1:nbus,2*Dtemp,nbus,nbus);
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Jac(nbus+ipv,:)=[JacVc(ipv,:),JacVd(ipv,:)];
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JacExt=[Jac,[P2freq;sparse(nbus,nbus)];...
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sparse(nbus,2*nbus),Freq2freq];
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corr=-JacExt(jacRowTag==1,jacColTag==1)\tDiff*stepRatio;
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corrFull=zeros(3*nbus,1);
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corrFull(jacColTag==1)=corr;
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Vtemp=Vtemp+corrFull(1:nbus)+1j*corrFull((nbus+1):(2*nbus));
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ftemp=ftemp+corrFull((2*nbus+1):(3*nbus));
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QTemp=imag(diff);
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% QTemp(idxNonSw)
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end
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elseif AEmethod==2 % NRJ - jacobian adjustment once
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for loop=1:maxLoop
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VtempOrig=Vtemp;
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ftempOrig=ftemp;
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QTempOrig=QTemp;
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% 1st step
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Ctemp=real(Vtemp);
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Dtemp=imag(Vtemp);
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Atemp=abs(Vtemp);
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Vgtemp=Vtemp(syn(:,1));
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Ig=accumarray(syn(:,1),MatGRhsNew(:,1)+1j*MatGRhsNew(:,2),[nbus,1])-...
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accumarray(syn(:,1),(MatGVNew(:,1).*real(Vgtemp)+MatGVNew(:,2).*imag(Vgtemp))+1j*(MatGVNew(:,3).*real(Vgtemp)+MatGVNew(:,4).*imag(Vgtemp)),[nbus,1]);
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diff=conj(SNew)+INew.*abs(Vtemp)+Ig.*conj(Vtemp)-(YNew*Vtemp).*conj(Vtemp);
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diffP=real(diff)+freqKeptTag.*(-fdk.*ftemp+dpg0);
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diffVQ=imag(diff);
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diffF=ftemp-ftemp(frefs(islands));
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if ~isempty(pv)
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diffVQ(pv(:,1))=abs(Vtemp(pv(:,1))).*abs(Vtemp(pv(:,1)))-sum(VspSq2(pv(:,1)),2);
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end
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tDiff=[diffP(idxNonSw);diffVQ(idxNonSw);diffF(freqKeptTagxRef==1)];
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if max(abs(tDiff))<diffTol
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QTemp=imag(diff);
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break;
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end
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dCtemp=sparse(1:nbus,1:nbus,Ctemp,nbus,nbus);
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dDtemp=sparse(1:nbus,1:nbus,Dtemp,nbus,nbus);
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Jac1=[dCtemp*J1+dDtemp*J3,dCtemp*J2+dDtemp*J4;...
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dCtemp*J3-dDtemp*J1,dCtemp*J4-dDtemp*J2];
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Jac2=[sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus),sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus);...
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sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus),-sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus)];
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Jac3=[sparse(1:nbus,1:nbus,JNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,JNew.*Dtemp./Atemp,nbus,nbus);...
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sparse(1:nbus,1:nbus,KNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,KNew.*Dtemp./Atemp,nbus,nbus)];
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Jac4=[sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus),sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus);...
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sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus),-sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus)];
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Jac=Jac3+Jac4-Jac1-Jac2;
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JacVc=sparse(1:nbus,1:nbus,2*Ctemp,nbus,nbus);
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JacVd=sparse(1:nbus,1:nbus,2*Dtemp,nbus,nbus);
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Jac(nbus+ipv,:)=[JacVc(ipv,:),JacVd(ipv,:)];
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JacExt=[Jac,[P2freq;sparse(nbus,nbus)];...
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sparse(nbus,2*nbus),Freq2freq];
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corr=-JacExt(jacRowTag==1,jacColTag==1)\tDiff*0.5*stepRatio;
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corrFull=zeros(3*nbus,1);
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corrFull(jacColTag==1)=corr;
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Vtemp=Vtemp+corrFull(1:nbus)+1j*corrFull((nbus+1):(2*nbus));
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ftemp=ftemp+corrFull((2*nbus+1):(3*nbus));
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QTemp=imag(diff);
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% 2nd step
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Ctemp=real(Vtemp);
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Dtemp=imag(Vtemp);
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Atemp=abs(Vtemp);
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Vgtemp=Vtemp(syn(:,1));
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Ig=accumarray(syn(:,1),MatGRhsNew(:,1)+1j*MatGRhsNew(:,2),[nbus,1])-...
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accumarray(syn(:,1),(MatGVNew(:,1).*real(Vgtemp)+MatGVNew(:,2).*imag(Vgtemp))+1j*(MatGVNew(:,3).*real(Vgtemp)+MatGVNew(:,4).*imag(Vgtemp)),[nbus,1]);
|
||||
diff=conj(SNew)+INew.*abs(Vtemp)+Ig.*conj(Vtemp)-(YNew*Vtemp).*conj(Vtemp);
|
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diffP=real(diff)+freqKeptTag.*(-fdk.*ftemp+dpg0);
|
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diffVQ=imag(diff);
|
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diffF=ftemp-ftemp(frefs(islands));
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if ~isempty(pv)
|
||||
diffVQ(pv(:,1))=abs(Vtemp(pv(:,1))).*abs(Vtemp(pv(:,1)))-sum(VspSq2(pv(:,1)),2);
|
||||
end
|
||||
tDiffx=[diffP(idxNonSw);diffVQ(idxNonSw);diffF(freqKeptTagxRef==1)];
|
||||
if max(abs(tDiffx))<diffTol
|
||||
QTemp=imag(diff);
|
||||
break;
|
||||
end
|
||||
dCtemp=sparse(1:nbus,1:nbus,Ctemp,nbus,nbus);
|
||||
dDtemp=sparse(1:nbus,1:nbus,Dtemp,nbus,nbus);
|
||||
Jac1=[dCtemp*J1+dDtemp*J3,dCtemp*J2+dDtemp*J4;...
|
||||
dCtemp*J3-dDtemp*J1,dCtemp*J4-dDtemp*J2];
|
||||
Jac2=[sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus),sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus);...
|
||||
sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus),-sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus)];
|
||||
Jac3=[sparse(1:nbus,1:nbus,JNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,JNew.*Dtemp./Atemp,nbus,nbus);...
|
||||
sparse(1:nbus,1:nbus,KNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,KNew.*Dtemp./Atemp,nbus,nbus)];
|
||||
Jac4=[sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus),sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus);...
|
||||
sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus),-sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus)];
|
||||
Jac=Jac3+Jac4-Jac1-Jac2;
|
||||
|
||||
JacVc=sparse(1:nbus,1:nbus,2*Ctemp,nbus,nbus);
|
||||
JacVd=sparse(1:nbus,1:nbus,2*Dtemp,nbus,nbus);
|
||||
|
||||
Jac(nbus+ipv,:)=[JacVc(ipv,:),JacVd(ipv,:)];
|
||||
|
||||
JacExt=[Jac,[P2freq;sparse(nbus,nbus)];...
|
||||
sparse(nbus,2*nbus),Freq2freq];
|
||||
|
||||
corr=-JacExt(jacRowTag==1,jacColTag==1)\tDiff*stepRatio;
|
||||
corrFull=zeros(3*nbus,1);
|
||||
corrFull(jacColTag==1)=corr;
|
||||
|
||||
Vtemp=VtempOrig;
|
||||
ftemp=ftempOrig;
|
||||
QTemp=QTempOrig;
|
||||
|
||||
Vtemp=Vtemp+corrFull(1:nbus)+1j*corrFull((nbus+1):(2*nbus));
|
||||
ftemp=ftemp+corrFull((2*nbus+1):(3*nbus));
|
||||
QTemp=imag(diff);
|
||||
end
|
||||
elseif AEmethod==3 % NRM -
|
||||
for loop=1:maxLoop
|
||||
Ctemp=real(Vtemp);
|
||||
Dtemp=imag(Vtemp);
|
||||
Atemp=abs(Vtemp);
|
||||
Vgtemp=Vtemp(syn(:,1));
|
||||
Ig=accumarray(syn(:,1),MatGRhsNew(:,1)+1j*MatGRhsNew(:,2),[nbus,1])-...
|
||||
accumarray(syn(:,1),(MatGVNew(:,1).*real(Vgtemp)+MatGVNew(:,2).*imag(Vgtemp))+1j*(MatGVNew(:,3).*real(Vgtemp)+MatGVNew(:,4).*imag(Vgtemp)),[nbus,1]);
|
||||
diff=conj(SNew)+INew.*abs(Vtemp)+Ig.*conj(Vtemp)-(YNew*Vtemp).*conj(Vtemp);
|
||||
diffP=real(diff)+freqKeptTag.*(-fdk.*ftemp+dpg0);
|
||||
diffVQ=imag(diff);
|
||||
diffF=ftemp-ftemp(frefs(islands));
|
||||
if ~isempty(pv)
|
||||
diffVQ(pv(:,1))=abs(Vtemp(pv(:,1))).*abs(Vtemp(pv(:,1)))-sum(VspSq2(pv(:,1)),2);
|
||||
end
|
||||
tDiff=[diffP(idxNonSw);diffVQ(idxNonSw);diffF(freqKeptTagxRef==1)];
|
||||
lambda=1e-3*norm(tDiff)^2;
|
||||
if max(abs(tDiff))<diffTol
|
||||
QTemp=imag(diff);
|
||||
break;
|
||||
end
|
||||
dCtemp=sparse(1:nbus,1:nbus,Ctemp,nbus,nbus);
|
||||
dDtemp=sparse(1:nbus,1:nbus,Dtemp,nbus,nbus);
|
||||
Jac1=[dCtemp*J1+dDtemp*J3,dCtemp*J2+dDtemp*J4;...
|
||||
dCtemp*J3-dDtemp*J1,dCtemp*J4-dDtemp*J2];
|
||||
Jac2=[sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus),sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus);...
|
||||
sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus),-sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus)];
|
||||
Jac3=[sparse(1:nbus,1:nbus,JNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,JNew.*Dtemp./Atemp,nbus,nbus);...
|
||||
sparse(1:nbus,1:nbus,KNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,KNew.*Dtemp./Atemp,nbus,nbus)];
|
||||
Jac4=[sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus),sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus);...
|
||||
sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus),-sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus)];
|
||||
Jac=Jac3+Jac4-Jac1-Jac2;
|
||||
|
||||
JacVc=sparse(1:nbus,1:nbus,2*Ctemp,nbus,nbus);
|
||||
JacVd=sparse(1:nbus,1:nbus,2*Dtemp,nbus,nbus);
|
||||
|
||||
Jac(nbus+ipv,:)=[JacVc(ipv,:),JacVd(ipv,:)];
|
||||
|
||||
JacExt=[Jac,[P2freq;sparse(nbus,nbus)];...
|
||||
sparse(nbus,2*nbus),Freq2freq];
|
||||
|
||||
filteredJac=JacExt(jacRowTag==1,jacColTag==1);
|
||||
corr=-(filteredJac'*filteredJac+lambda*speye(size(filteredJac)))\(filteredJac'*tDiff)*stepRatio;
|
||||
corrFull=zeros(3*nbus,1);
|
||||
corrFull(jacColTag==1)=corr;
|
||||
Vtemp=Vtemp+corrFull(1:nbus)+1j*corrFull((nbus+1):(2*nbus));
|
||||
ftemp=ftemp+corrFull((2*nbus+1):(3*nbus));
|
||||
QTemp=imag(diff);
|
||||
% QTemp(idxNonSw)
|
||||
end
|
||||
elseif AEmethod==4 % NRMJ -
|
||||
for loop=1:maxLoop
|
||||
VtempOrig=Vtemp;
|
||||
ftempOrig=ftemp;
|
||||
QTempOrig=QTemp;
|
||||
% 1st step
|
||||
Ctemp=real(Vtemp);
|
||||
Dtemp=imag(Vtemp);
|
||||
Atemp=abs(Vtemp);
|
||||
Vgtemp=Vtemp(syn(:,1));
|
||||
Ig=accumarray(syn(:,1),MatGRhsNew(:,1)+1j*MatGRhsNew(:,2),[nbus,1])-...
|
||||
accumarray(syn(:,1),(MatGVNew(:,1).*real(Vgtemp)+MatGVNew(:,2).*imag(Vgtemp))+1j*(MatGVNew(:,3).*real(Vgtemp)+MatGVNew(:,4).*imag(Vgtemp)),[nbus,1]);
|
||||
diff=conj(SNew)+INew.*abs(Vtemp)+Ig.*conj(Vtemp)-(YNew*Vtemp).*conj(Vtemp);
|
||||
diffP=real(diff)+freqKeptTag.*(-fdk.*ftemp+dpg0);
|
||||
diffVQ=imag(diff);
|
||||
diffF=ftemp-ftemp(frefs(islands));
|
||||
if ~isempty(pv)
|
||||
diffVQ(pv(:,1))=abs(Vtemp(pv(:,1))).*abs(Vtemp(pv(:,1)))-sum(VspSq2(pv(:,1)),2);
|
||||
end
|
||||
tDiff=[diffP(idxNonSw);diffVQ(idxNonSw);diffF(freqKeptTagxRef==1)];
|
||||
lambda=1e-3*norm(tDiff)^2;
|
||||
if max(abs(tDiff))<diffTol
|
||||
QTemp=imag(diff);
|
||||
break;
|
||||
end
|
||||
dCtemp=sparse(1:nbus,1:nbus,Ctemp,nbus,nbus);
|
||||
dDtemp=sparse(1:nbus,1:nbus,Dtemp,nbus,nbus);
|
||||
Jac1=[dCtemp*J1+dDtemp*J3,dCtemp*J2+dDtemp*J4;...
|
||||
dCtemp*J3-dDtemp*J1,dCtemp*J4-dDtemp*J2];
|
||||
Jac2=[sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus),sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus);...
|
||||
sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus),-sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus)];
|
||||
Jac3=[sparse(1:nbus,1:nbus,JNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,JNew.*Dtemp./Atemp,nbus,nbus);...
|
||||
sparse(1:nbus,1:nbus,KNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,KNew.*Dtemp./Atemp,nbus,nbus)];
|
||||
Jac4=[sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus),sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus);...
|
||||
sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus),-sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus)];
|
||||
Jac=Jac3+Jac4-Jac1-Jac2;
|
||||
|
||||
JacVc=sparse(1:nbus,1:nbus,2*Ctemp,nbus,nbus);
|
||||
JacVd=sparse(1:nbus,1:nbus,2*Dtemp,nbus,nbus);
|
||||
|
||||
Jac(nbus+ipv,:)=[JacVc(ipv,:),JacVd(ipv,:)];
|
||||
|
||||
JacExt=[Jac,[P2freq;sparse(nbus,nbus)];...
|
||||
sparse(nbus,2*nbus),Freq2freq];
|
||||
|
||||
filteredJac=JacExt(jacRowTag==1,jacColTag==1);
|
||||
corr=-(filteredJac'*filteredJac+lambda*speye(size(filteredJac)))\(filteredJac'*tDiff)*0.5*stepRatio;
|
||||
corrFull=zeros(3*nbus,1);
|
||||
corrFull(jacColTag==1)=corr;
|
||||
Vtemp=Vtemp+corrFull(1:nbus)+1j*corrFull((nbus+1):(2*nbus));
|
||||
ftemp=ftemp+corrFull((2*nbus+1):(3*nbus));
|
||||
QTemp=imag(diff);
|
||||
% 2nd step
|
||||
Ctemp=real(Vtemp);
|
||||
Dtemp=imag(Vtemp);
|
||||
Atemp=abs(Vtemp);
|
||||
Vgtemp=Vtemp(syn(:,1));
|
||||
Ig=accumarray(syn(:,1),MatGRhsNew(:,1)+1j*MatGRhsNew(:,2),[nbus,1])-...
|
||||
accumarray(syn(:,1),(MatGVNew(:,1).*real(Vgtemp)+MatGVNew(:,2).*imag(Vgtemp))+1j*(MatGVNew(:,3).*real(Vgtemp)+MatGVNew(:,4).*imag(Vgtemp)),[nbus,1]);
|
||||
diff=conj(SNew)+INew.*abs(Vtemp)+Ig.*conj(Vtemp)-(YNew*Vtemp).*conj(Vtemp);
|
||||
diffP=real(diff)+freqKeptTag.*(-fdk.*ftemp+dpg0);
|
||||
diffVQ=imag(diff);
|
||||
diffF=ftemp-ftemp(frefs(islands));
|
||||
if ~isempty(pv)
|
||||
diffVQ(pv(:,1))=abs(Vtemp(pv(:,1))).*abs(Vtemp(pv(:,1)))-sum(VspSq2(pv(:,1)),2);
|
||||
end
|
||||
tDiffx=[diffP(idxNonSw);diffVQ(idxNonSw);diffF(freqKeptTagxRef==1)];
|
||||
lambdax=1e-3*norm(tDiffx)^2;
|
||||
if max(abs(tDiffx))<diffTol
|
||||
QTemp=imag(diff);
|
||||
break;
|
||||
end
|
||||
dCtemp=sparse(1:nbus,1:nbus,Ctemp,nbus,nbus);
|
||||
dDtemp=sparse(1:nbus,1:nbus,Dtemp,nbus,nbus);
|
||||
Jac1=[dCtemp*J1+dDtemp*J3,dCtemp*J2+dDtemp*J4;...
|
||||
dCtemp*J3-dDtemp*J1,dCtemp*J4-dDtemp*J2];
|
||||
Jac2=[sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus),sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus);...
|
||||
sparse(1:nbus,1:nbus,J3*Ctemp+J4*Dtemp,nbus,nbus),-sparse(1:nbus,1:nbus,J1*Ctemp+J2*Dtemp,nbus,nbus)];
|
||||
Jac3=[sparse(1:nbus,1:nbus,JNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,JNew.*Dtemp./Atemp,nbus,nbus);...
|
||||
sparse(1:nbus,1:nbus,KNew.*Ctemp./Atemp,nbus,nbus),sparse(1:nbus,1:nbus,KNew.*Dtemp./Atemp,nbus,nbus)];
|
||||
Jac4=[sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus),sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus);...
|
||||
sparse(syn(:,1),syn(:,1),MatGRhsNew(:,2),nbus,nbus),-sparse(syn(:,1),syn(:,1),MatGRhsNew(:,1),nbus,nbus)];
|
||||
Jac=Jac3+Jac4-Jac1-Jac2;
|
||||
|
||||
JacVc=sparse(1:nbus,1:nbus,2*Ctemp,nbus,nbus);
|
||||
JacVd=sparse(1:nbus,1:nbus,2*Dtemp,nbus,nbus);
|
||||
|
||||
Jac(nbus+ipv,:)=[JacVc(ipv,:),JacVd(ipv,:)];
|
||||
|
||||
JacExt=[Jac,[P2freq;sparse(nbus,nbus)];...
|
||||
sparse(nbus,2*nbus),Freq2freq];
|
||||
|
||||
filteredJac=JacExt(jacRowTag==1,jacColTag==1);
|
||||
corr=-(filteredJac'*filteredJac+lambda*speye(size(filteredJac)))\(filteredJac'*tDiff)*stepRatio;
|
||||
corrFull=zeros(3*nbus,1);
|
||||
corrFull(jacColTag==1)=corr;
|
||||
|
||||
Vtemp=VtempOrig;
|
||||
ftemp=ftempOrig;
|
||||
QTemp=QTempOrig;
|
||||
|
||||
Vtemp=Vtemp+corrFull(1:nbus)+1j*corrFull((nbus+1):(2*nbus));
|
||||
ftemp=ftemp+corrFull((2*nbus+1):(3*nbus));
|
||||
QTemp=imag(diff);
|
||||
end
|
||||
end
|
||||
|
||||
if loop>=maxLoop&&max(abs(tDiff))>=diffTol
|
||||
flag=-1;
|
||||
else
|
||||
flag=0;
|
||||
end
|
||||
|
||||
diffRec=max(abs(tDiff));
|
||||
|
||||
stateNew=xNew;
|
||||
stateNew(idxs.vIdx)=Vtemp;
|
||||
stateNew(idxs.qIdx)=QTemp;
|
||||
stateNew(idxs.fIdx)=ftemp;
|
||||
|
||||
addLog(['[#END#] Solving algebraic equations - NR finished. Exitflag = ',num2str(flag), ', loop = ',num2str(loop),'.'],'INFO');
|
||||
|
||||
end
|
||||
Reference in New Issue
Block a user