南昌大学电力系统学科导论(双语)指导书

Laboratory：SectricPower^stemandItsAutomationTheGuideofExperimentIntroductiontopower

systemsInformationEngineeringSchoolNanchangUniversitySep.2010CONTENTSTOC\o"1-5"\h\z\o"CurrentDocument"EXPERIMENT1 1\o"CurrentDocument"BusAdmittanceMatrix 1Mathmaticsmodel. 2SystemRequirement. 3Procedure 4Exercises. 4Theflowchart. 6\o"CurrentDocument"EXPERIMENT2 12Objective 12Discussion 12\o"CurrentDocument"ZbusCALCULATION 13\o"CurrentDocument"Addingzbfromanewbusptothereferencebus0 14\o"CurrentDocument"Addingzbfromanewbusptoanexistingbusk 14Addingzbfromanexistingbusktothereferencebus0 15\o"CurrentDocument"Addingzbfromtwoexistingbusesjandk 16\o"CurrentDocument"Commentsonthealgorithm 18SystemRequirement. 19Procedure 79Mathmaticsmodel. 19Exercises. 20\o"CurrentDocument"Example1 20\o"CurrentDocument"EXPERIMENT3 25\o"CurrentDocument"SHORT-CIRCUETCALCULATIONSWITHBUSIMPEDANCEMATRIX 25Mathmaticsmodel. 25SystemRequirement. 25Procedure 25j6.Exercises. 25MatrixMethodsforNetworkSolutions 27\o"CurrentDocument"EXPERIMENT4 39Gauss-SeidelPowerFlowSolution 40LineFlowsandLosses 42SystemRequirement. 43Procedure 43Exercises. 44TheflowchartofGaussSeidelPowerFlow(Quitted) 44ReferencePogrom. 45\o"CurrentDocument"EXPERIMENT5 48Objective 48Discussion 48Mathmaticsmodel. 48\o"CurrentDocument"Newton-RaphsionPowerFlowSolution 49LineFlowsandLosses 52SystemRequirement. 52Exercises.. 53TheflowchartofNewtonRaphsionsolution(Qnmited) 54Referenceprogram 55\o"CurrentDocument"EXPERIMENT6 58\o"CurrentDocument"FastDecoupledPowerFlow 58LObjective 58Discussion 58FastDocouplGcl^jwerFlowSolution 59L/fiGandLosssstt1SystemRequirement. 62Procedure 62Exercises. 63TheflowchartofFastDecoupledPowerFlow(Quitted) 63ReferenceFYogram 70\o"CurrentDocument"THEIMPEDANCEMATRIXZBUS 72\o"CurrentDocument"YBUSMODIFICATIONS 84\o"CurrentDocument"MATRIXINVERSIONLEMMA(矩阵求逆弓I理) 85Experiment1Hour:4BusAdmittanceMatrixObjective•TowriteasimpleprograminMATLAB®forthealgorithmofbusadmittancematrix.DiscussionBusAdmittancematrix…4rDue=Ybu8VbusThenode-voltageequationofanw-buspowersystemcanbewritteninmatrixformas…4rDue=Ybu8Vbus(2)isthecolumnvectorof(2)isthecolumnvectorofbusWhereLJsthecolumnvectoroftheinjectedbuscurrents.V、busvoltagesmeasuredfromthereferencenode.Ybusisknownasthebusadmittancematrix.Calculationmethod:Thediagonalelementofeachnodeisthesumofadmittancesconnectedtoit.Itisknownastheself-admittanceordrivingpointadmittance,i.e.,

(3)(3)Theoff-diagonalelementisequaltothenegativeoftheadmittancebetweenthenodes.Itisknownasthemutualadmittanceortransferadmittance,i.e.Result:Baseontheequations(3)and(4),thealgorithmofbusadmittancematrixcanbeusedtobuildthebusadmittancematrix(Y^).MathmaticsmodelThemathematicsmodelsofpowersystemelementsaretwokinds,oneistransmissionlineorcableandanotheristransformer,andtheyareequivalentintopitypeequivalentcircuit,anddescribedasfollowing:TransmissionlineorcableAccordingtothePisectionalcircuitoftransmissionlineorcable,wecangettheelementsofnodalAdmittancematrixvalue,asthefollowingFigure:Thepisectionequivalentcircuitoftransmissionlineorcable++%)(6)Yii=Yii~XRu+JXu) ⑺Yji=% (8)transformer1:K 工丁i-GD―j-iT*4ij-Asshowasthetransfonnercircuit,wehave-KI)(10)-KI)(10)Accordingtoequations(10)and(9),wehaveI；Accordingtoequations(10)and(9),wehaveI；— (V.-KVi)=—V-H (匕一匕)一J7\3 1f7J ¥(11)A=-KI)—vi--vj=—vi

zrZA=-KI)—vi--vj=—vi

zrZTJzr'Z7K1-V,+月匕-匕）(12)KZZrFigure:thePIsectionequivalentcircuitofTransformerK2AssumeAssumeYTZ/Rg+jxu(13)4F+(14)“广务+/(13)4F+(14)“广务+/x0)(15)(16)SystemRequirementComputerwithMATLAB@6oraboveinstalled.Procedure1.0LaunchtheMATLABprogram.Figure12.0GotoFILENEWM-file.Figure23.0WriteafunctionY=The_Node_Admittance_Matrix(TopoStructureAndBranchPara)fortheformationofthebusadmittancematrix.4.0TopoStructureAndBranchParaisthetransmissionline,cableandtransformerinputdataandcontainsfivecolumnsparameters.Thefirsttwocolumnsarethelinebusnumbersandtheremainingcolumnscontainthelineresistanceandreactanceinper-unitandtransformertapratioorcapacitoroftransmissionline.5.0Thefunctionshouldreturnthebusadmittancematrix.6.BcercisesUsethewrittenfunction,Y=The_Node_Admittance_Matrix(TopoStructureAndBranchPara)toobtaintheYbusofthefollowingpowersystemnetwork:Q1.YouarerequiredtowritetheYbustopologicalstructureandparameterintoatextfile.(Hint:usethematlabtextcompilertowritedownthetable1data,usingthecommatoseparatetheparameters,andsaveitusethenameof4_Power_System_Data.dbf)Q2.Youarerequiredtowriteouttheprogramflowfigureofforminganodaladmittancematrix.Hint.YouarerequiredtocompileaprogramtoformtheYbusMatrix,thefollowing

TheGuideofExperimentofShortCircuitCalculationprogramisareferenceprogramtoyou.Figure:One-linediagramofpowersystemForexample,fromthetextbook“powersystemanalysis"No.2edition3on62Table1：TransformerandtransmissssionLinedataFromBus#ToBus#R(pu)X(p.u)B(p.u)orratioKOthers120.10.4j0.015281300.31.1140.120.5j0.01920240.080.40J0.014137.TheflowchartFigure:TheflowchartofFormingNodalAdmittanceMatrix “____Reference1%functionOutPut=The_Node_Admittance_Matrix(handles)%isasubroutineofPowerSystemCalculationfunctionOutPut=The_Node_Admittance_Matrix(handles)%thefollowingprogramisopenadatafileandgettheNumberof%NodeandBranchdatatoformanodaladdmittancematrix%thefollowingcodeisopenafileandreadthedataofpowersystemnetwork[fnamefpname]=uigetfile('".dht.','Selectthenetworkparametredata-filer);TopoStruetureAndBranchPara=csvread(fname);[NumberOfBranchfNumberOfPara]=size(TopoStructureAndBranchPara);Temporaryl=max(TopoStructureAndBranchPara(:f1));Temporary2=max(TopoStructureAndBranchPara(:,2));ifTemporaryl>Temperary2NumberOfNode=Temporaryl;elseNumberOfNode=Temporary2;end%ThefollowingprogramistoformtheNodalAdmittanceMatrix%andtheTopologicstructureandBranchParametresarearranged%I,JfR,X,C/K,andpayattentiontotheinpedenceoftransformerisinthe%sideofNodeJandtheratiooftransformer1:KisinthesideofNode工forCirdeNumberl=1:NumberOfBranchforCircleNumber2=l:NumberOfBranchNodalAdmittanceMatrix(CirdeNumberl,CirdeNumber2)=0;endendforCircleNumber=l:NumberOfBranchifTopoStructureAndBranchPara(CircleNumber,5)>0.85NodalAdmittanceMatrix(TopoStructureAndBranchPara(TopoStructureAndBranchPara(CirdeNumber,1)fTopoStructureAndBranchPara(CircleNumberf1)))=.NodalAdmittanceMatrix(TopoStructureAndBranchPara(TopoStructureAndBranchPara(CirdeNumber,1)fTopoStructureAndBranchPara(CirdeNumberf1)))-i-.TopoStructureAndBranchPara(CirdeNumber,5)2/・..(TopoStructureAndBranchPara(CircleNumber,3)+・,・j★TopoStructureAndBranchPara(CirdeNumberf4));NodalAdmittanceMatrix(TopoStructureAndBranchPara(CirdeNumber,2),TopoStructureAndBranchPara(CircleNumberf2))=,..NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,2),TopoStructureAndBranchPara(CircleNumber,2))+・,,1/((TopoStructureAndBranchPara(CirdeNumberf3)+j*TopoStructureAndBranchPara(CirdeNumber,4)));NodalAdmittanceMatrix(TopoStructureAndBranchPara(CirdeNumberf1),TopoStructureAndBranchPara(CircleNumberf2))=...NodalAdmittanceMatrix(TopoStructureAndBranchPara(CirdeNumberf1)fTopoStructureAndBranchPara(CirdeNumberf2))...-TopoStructureAndBranchPara(CircleNumberf5)/...((TopoStructureAndBranchPara(CircleNumberf3)-f-j±TopoStructureAndBranchPara(CircleNumberf4)));NodalAdmittanceMatrix(TopoStructureAndBranchPara(CirdeNumber,2),TopoStructureAndBranchPara(CircleNumberf1))=,..NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumberf1),TopoStructureAndBranchPara(CircleNumber,2));elseNodalAdmittanceMatrix(TopoStructureAndBranchPara(CirdeNumber,1)fTopoStructureAndBranchPara(CircleNumberf1))=...NodalAdmittanceMatrix(TopoStructureAndBranchPara(CirdeNumberf1),TopoStructureAndBranchPara(CirdeNumberf!.))+・,,-t-1/(TopoStructureAndBranchPara(CircleNumberf3)-t-...j★TopoStructureAndBranchPara(CircleNumberf4)) ★TopoStructureAndBranchPara(CirdeNumberf5);NodalAdmittanceMatrix(TopoStructureAndBranchPara(CirdeNumberf2),TopoStructureAndBranchPara(CircleNumberf2))=»..NodalAdmittanceMatrix(TopoStructureAndBranchPara(CirdeNumberf2),TopoStructureAndBranchPara(CircleNumberf2))+...+1/(TopoStructureAndBranchPara(CircleNumberf3)+...j★TopoStructureAndBranchPara(CircleNumberf4))-i-j★TopoStructureAndBrancTheGuideofExperimentofShortCircuitCalculationhPara(CirdeNumberf5)NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumberf1),TopoStructureAndBranchPara(CircleNumber,2))=...NodalAdmittanceMatrix(TopoStructureAndBranchPara(CirdeNumberf1)fTopoStructureAndBranchPara(CirdeNumberf2))...-1/(TopoStructureAndBranchPara(CirdeNumberf3)+,..j±TopoStructureAndBranchPara(CirdeNumber,4));NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumberf2),TopoStruetureAndBranchPara(CirdeNumberf1))=.,.NodalAdmittanceMatrix(TopoStructureAndBranchPara(CircleNumber,1),TopoStructureAndBranchPara(CirdeNumber,2));endendReference2不一定要重新编写Matalab程序,可以在装上Matpower,其中的"makeYbus.m”文件中的源码是最标准的生成导纳矩阵程序。Matpower可以下载得到,若实在找不到就给我你的邮箱,我发给你。这里先把文件的内容给你贴上。事先声明:这是从Matpower中拷下的,仅供教学交流之用,其他后果与本人无关。function[Ybus,YffYt]=makeYbus(baseMVA,bus,branch)%MAKEYBUSBuildsthebusadmittancematrixandbranchadmittancematrices.%[Ybus,Yf9Yt]=makeYbus(baseMVAfbus,branch)returnsthefull%busadmittancematrix(i.e.forallbuses)andthematricesYfandYt%which,whenmultipliedbyacomplexvoltagevector,yieldthevector%currentsinjectedintoeachlinefromthe''from"anduto"buses%respectivelyofeachline.Doesappropriateconversionstop.u.%MATPOWER%$Id:makeYbus.myv1.42004/08/2320:56:42rayExp$%byRayZimmerman,PSERCCornell%Copyright(c)1996-2004byPowerSystemEngineeringResearchCenter(PSERC)%Seehttp://www.pserc,/matpower/formoreinfo.%%constantsj=sqrt(-l);nh=size(busf1); %%numberofbusesnl=size(branchfI); %%numberoflines%%definenamedindicesintobus,branchmatrices[PQ,PV,REF,NONE,BUS」,BUS_TYPE,PD,QD,GS,BS,BUS_AREA,VM,...VA,BASE_KV9ZONE,VMAX,VMIN,LAM_PfLAM_Q,MU_VMAX9MUJVMIN]=idx_bus;[F_BUS,T_BUS,BR_R,BR_X,BR_B,RATE_AfRATE_B,...RATEJC,TAP,SHIFT,BR_STATUSfPRQF,PT,QT,MU_SF,MU_ST]=idxj)rch;%%checkthatbusnumbersareequaltoindicestobus(onesetofbusnumbers)ifany(bus(:,BUSJ)errorCbusesmustappearinorderbybusnumber')end%%foreachbranch,computetheelementsofthebranchadmittancematrixwhere%%%%\yffyft\1V/l%%11=11*1%%\It\\YtfYtt1\Vt\%%stat-branch(:,BR_STATUS); %%onesatin-servicebranches

Ys=stat./(hranch(:9BR_R)+j*hranch(:,BR_X)); %%seriesadmittanceBe=statbranch(:9BR_B); %%linechargingsusceptancetap=ones(nl,1); %%defaulttapratio=1i=find(branch(:,TAP)); %%indicesofnon-zerotapratiostap(i)=branch(i9TAP); %%assignnon-zerotapratiostap=tap.*exp(-j*pi/180*branch(:,SHIFT));%%addphaseshiftersYtt=Ys+产Bc/2;Yjf=YttJ(tap.*conj(tap));Yfi=-Ys./conj(tap);Ytf YsJtap;%%computeshuntadmittance%%ifPshistherealpowerconsumedbytheshuntatV-1.0p.u,%%andQshisthereactivepowerinjectedbytheshuntatV=1,0p.u.%%thenPsh-jQsh=V*conj(Ysh*V)=conj(Ysh)=Gs-jBs9%%i.e,Ysh=Psh+jQsh,so...Ysh=(bus(:,GS)+j*bus(:,BS))/baseMVA;%%vectorofshuntadmittances%%buildYbusf=branch(:,F_BUS);%%buildYbusf=branch(:,F_BUS);t=branch(:,T_BUS);Cf=sparse(f,l:nl9ones(nl,1),nb,nl);Ct=sparseft,l:nlfones(nl,I),nb,nl);Ybus=spdiags(Yshf0,nb,nb)+...Cf^spdiags(Yff,0,M,川)*C7+・・・Cf^spdiags(Yftf0,nl,nl)*Ct'+...Ct*spdiags(Ytf,0,nl,nl)*Cf+...Ct*spdiags(Yttf0,nl,nl)*Ct';%%listof"fromnbuses%%listofntonbuses%%connectionmatrixforline&frombuses%%connectionmatrixforline&tobuses%%shuntadmittance%%Yjftermofbranchadmittance%%Yfttermofbranchadmittance%%Ytftermofbranchadmittance%%Ytttermofbranchadmittance%%BuildYfandYtsuchthatYf*Visthevectorofcomplexbranchcurrentsinjected%%ateachbranch's"from"bus,andYtisthesameforthentonbusendifnargout>1i=Ul:nl]';[l:nl]r]; %%doublesetofrowindicesYf=sparser[f;t]9[Yff；Yft]);Yt=sparse(i,[f;t],[Ytf;Ytt]);endreturn;Experiment2Hour:4PowerGridBusImpedanceMatrixObjective•TowriteasimpleprograminMATLABRforthealgorithmofbusimpedancematrix.DiscussionBusImpedancematrixThenode-currentequationofann-buspowersystemcanbewritteninmatrixformasWherelbusisthevectoroftheinjectedbuscurrents.isthevectorofbusvoltagesmeasuredfromthereferencenode.Z.isknownasthebusimpedancematrix.ZbusCALCULATIONTherearetwomajormethods:InversionofYbusZ^sbuildingalgorithmLUfactorization.Matrixinversionforverylarge-scalenetworksisveryslowandavoided.Ontheotherhand,theZbusbuildingalgorithmistheacceptablemethodforlargenetworks.Itismuchfasterandeasiertoupdate.ZbusBuildingAlgorithmThisisaverysystematicwayofformingZbusandallowforeasyimplementationonthedigitalcomputer.AdvantagesEasytoimplementAvoidsmatrixinversionItiseasytohandleZbusmodificationsduetolineswitchingsandchangesinnetworktopologySolution：Notationexisting matrix)-7ne>\-乙bus-7ne>\-乙bustrequiredZbtts(?matrix)i,jtk—existingbusesp —►anewbus(notintheoriginalnehvork)Theadditionofabranchofimpedancezbfallsinto4categoriesasfollows.Addingzbfromanewbusptothereferencebus0Here,Z黑willbe(n+lX^+l)matrixInjectedcurrentIpwillnotchangethebusvoltagesoftheoriginalnetwork"工Then,AddingzbfromanewbusptoanexistingbuskHere,Zwillbe(〃+1+1)matrixInjectedcurrentIpwillchangethebusvoltagesoftheoriginalnetworkInjectedcurrentatbuskbecomesIk+1p

Then,CASE3:Addingzbfromanexistingbusktothereferencebus0Here,Z黑willbenxnmatrixThisisaspecialcaseofCASE2exceptthat=0Then,SinceVp=0,thelastrowcanbeeliminatedbyKronreduction(onekindofmathematicsmethod)toyieldannxnmatrixasSummaryofCase3ProceedasinCASE2EliminatethelastrowCASE4:AddingzbfromtwoexistingbusesjandkHere,Z黑willbenxnmatrixBranchcurrentIpwillchangethebusvoltagesoftheoriginalnetworkInjectedcurrentatbusjbecomesIi+1pInjectedcurrentatbuskbecomesIk-Ip匕一匕=4〃0=匕一匕+z应willchangethebusvoltagesoftheoriginalnetworkInjectedcurrentatbuskbecomesIk+1/tVP=Vk+ZbIp'buswillbenniatiixBranchcimentIpwillchangethebusvoltagesoftheoriginalnetworkInjectedcimentatbusjbecomes %Injectedcimentatbuskbecomesh-Ip%一匕=』"-0=匕—匕+二5Then,ThelastrowcanbeeliminatedbyKronreductiontoyieldannxnmatrixas7 7乙〃（〃+ThelastrowcanbeeliminatedbyKronreductiontoyieldannxnmatrixas7 7乙〃（〃+l）乙（“+1”Zu+Zkk—2Zjk+zbSummaryofSummaryofCase41.Proceedasfollows2.Eliminatethelastrow2.Eliminatethelastrowofinodiflcat沁"ofexisiiiiwCas。ofinodiflcat沁"ofexisiiiiwCas。Addbranch二"a"NewbusptoreferencebusExistingbusktoreferencebusPROCEDUREFORBUILDINGALGORITHMStepsPrepareatransmissionlinelistFirstlineconsideredmusthaveatietothereferenceAllsubsequentlinesinthelistmusthaveatleastonebusalreadyseenAlgorithmDeterminewhichofthecases(1-4)applyandproceedaccordingly.Readaline.Ifthelastlinehasbeenprocessed,thenstopelseconsideranotherlineCommentsonthealgorithmLoopsmustbeclosedasearlyaspossibleTheaxesofthefinalmatrixmaynotcorrespondwiththebusesinnumericalorderThelinelistorderaffectstheefficiencyofcalculationIfthereisnotietothereference,placeafictitiousgroundtieatoneofthebuses.Lineoutageismodeledbyusing-zbinsteadofzb

SystemFtequirementComputerwithMATLAB®6oraboveinstalled.Procedure1.0LaunchtheMATLABprogram.Figure12.0GotoFILENEWM-file.Figure23.0WriteafunctionZ=znbus(z)fortheformationofthebusimpedancematrix.4.0zisthelineinputandcontainsthreecolumns.Thefirsttwocolumnsarethelinebusnumbersandtheremainingcolumnscontainthelineresistanceinper-unit.5.0Thefunctionshouldreturnthebusimpedancematrix.MathmaticsmodelThemathmaticsmodelsofpowersystemelementsaretwokinds,oneistransmissionlineandanotheristransformation,andtheyareequivalentedintopitypeequivalentciucuit,anddricribledasfollowing:

ExercisesUsethewrittenfunction,Z=znbus(z)toobtaintheYbusofthefollowingpowersystemnetwork:Figure3:One-linediagramofpowersystemForexample,fromthetextbook“powersystemanalysis''No.2edition3on62Table1：TransformerandtransmissssionLinedataFromBus#ToBus#R(p.u)X(p.u)B(p.u)orratioKOthers120.10.4j0.015281300.31.1140.120.5j0.01920240.080.40J0.01413Q2.YouarerequiredtowritetheZbusintoatextfile.(Hint:usethematlabtextcompiler)Forthesystemshown,formZbusmatrixusingthebuildingalgorithmSolutionItAlinelistLine#Froin-toZbCase#10-3IC123-21Q232-11C241-31Q4Addline1reference3Z“3[1]Addline2(k=3,p=2. =2妹+3=2)32Addline3(k=2.p=1.马=Zh+二b=3)3213[iir

7 -I921123Addline4(/=3,k=1,4P=4+Z址・24"二广3)TOC\o"1-5"\h\z32 1311102122-1Zbia.4=.123一2（）-1-23TOC\o"1-5"\h\zApplyKronreductiontoeliminatethelastrow32 13T1 1 1-Z如=215/34/31[14/35/3Hint.YouarerequiredtocompileaprogramtoformtheZbusMatrix.thefollowingprogramisareferenceprogramtoyou.%functionOutPut=The_Node_impedance_Matrix(handles)%isasubroutineofPowerSystemCalculationfunctionOutPut=The_Node_impedance_Matrix(handles)%thefollowingprogramisopenadatafileandgettheNumberof%NodeandBranchdatatoformanodalimpedancematrix%thefollowingcodeisopenafileandreadthedataofpowersystemnetwork[fnamefpname]=uigetfile('★.dbf1,'Selectthenetworkparametredata-file*);Topo_Structure_And_Branch_Para=csvread(fname);%gettheelectricpowersystemthenumberofbranchandtheparametreof%elements[NumberOfBranch,NumberOfPara]=size(Topo_Structure_And_Branch_Para);%Temporaryl temporaryvariable1%Temporary2 temporaryvariable2Temporaryl=max(Topo_Structure_And_Branch_Para(:,1));Temporary2=max(Topo_Structure_And_Branch_Para(:f2));ifTemporaryl>Temporary2NumberOfNode=Temporaryl;elseNumberOfNode=Temporary2;end%ThefollowingprogramistoformtheNodalimpedanceMatrix%andtheTopologicstructureandBranchParametresarearranged%I,JfX,C/K,andpayattentiontotheinpedenceoftransformerisinthe%sideofNodeJandtheratiooftransformer1:KisinthesideofNode%I%settheinitialvalueofNodalAdmittanceMatrixtozeroforCirdeNumberl=1:NumberOfNodeforCircleNumber2=l:NumberOfNodeNodal_impedance_Matrix(CircleNumberl,CircleNumber2)=0;endendforCircleNumber-1:NumberOfBranchifTopo_Structure_And_Branch_Para(CircleNumberf5)>0.85Nodal_impedance_Matrix(Topo_Structure__And_Branch_Para(Topo_Structure_And_Branch_Para(CircleNumberf1)fTopo_Structure_And_Branch_Para(CirdeNumber,1)))=.,,Nodal_impedance_Matrix(Topo__Structure_And_Branch__Para(Topo_Structure_And_Branch_Para(CirdeNumberf1),Topo_Structure_And_Branch_Para(CirdeNumberf1)))-hTopo_Structure__And__Branch_Para(CircleNumber,5)^2/(Topo_Structure_And_Branch_Para(CirdeNumber,3)•j*Topo__Structure_And_Branch_Para(CirdeNumberf4));Nodal__impedance_Matrix(Topo_Structure_And_Branch_Para(CirdeNumberf2),Topo_Structure_And_Branch_Para(CirdeNumber,2)).Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,2),Topo_Structure_And_Branch__Para(CirdeNumberf2))+...1/((Topo_Structure_And_Branch__Para(CircleNumberf3)-bj*Topo_Structure_And__Branch_Para(CirdeNumber,4)));F沁 n工，，代.，/InformationPZn)*invvringSchoolTheGuideofExperimentofShortCircuitCalculation J，Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CirdeNumber,1),Topo_Structure__And_Branch_Para(CircleNumber,2))=...Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CirdeNumber,1),Topo_Structure_And_Branch_Para(CirdeNumber,2))...-Topo_Structure__And_Branch_Para(CirdeNumberf5)/...((Topo_Structure_And_Branch_Para(CirdeNumberf3)+j★Topo_Structure_And_Branch_Para(CirdeNumber,4)));Nodal_impedance__Matrix(Topo__Structure_And_Branch__Para(CirdeNumber,2),Topo_Structure_And_Branch__Para(CirdeNumberf1))=...Nodal_impedance_Matrix(Topo_Structure_And__Branch_Para(CirdeNumberf1)fTopo_Structure_And_Branch_Para(CircleNumber,2));elseNodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CirdeNumber,1),Topo_Structure_And_Branch_Para(CirdeNumber,!))=,•・Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CirdeNumberf1),Topo_Structure_And_Branch_Para(CirdeNumber,1))+...■Fl/(Topo_Structure_And__Branch_Para(CirdeNumber,3)+・,・j*Topo_Structure__And__Branch_Para(CircleNumber,4))+j*Topo_Structure_And_Branch_Para(CirdeNumberf5);Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,2),Topo_Structure_And_Branch_Para(CirdeNumber,2))=...Nodal_impedance_Matrix(Topo_Structure_And_Branch__Para(CirdeNumber,2),Topo_Structure_And_Branch_Para(CirdeNumberf2))+...+1/(Topo__Structure_And__Branch_Para(CirdeNumberf3)+・・,j±Topo_Structure_And_Branch__Para(CirdeNumberf4))-hj±Topo_Structure_And_Branch_Para(CircleNumberf5)Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumber,1)fTopo_Structure_And_Branch_Para(CircleNumberf2))=...Nodal_impedance_Matrix(Topo__Structure_And_Branch__Para(CirdeNumber,1),Topo_Structure_And_Branch_Para(CircleNumber,2))...-1/(Topo_Structure_And_Branch_Para(CirdeNumberf3)+...j*Topo_Structure_And_Branch_Para(CirdeNumber,4));Nodal_impedance_Matrix(Topo_Structure_And_Branch_Para(CircleNumberf2),Topo_Structure_And_Branch_Para(CircleNumberf1))=...Nodal_impedance__Matrix(Topo__Structure_And_Branch__Para(CirdeNumber,1),Topo_Structure_And__Branch_Para(CircleNumberf2));endendFlowchart(omitted)Experiment3Hour:8SHORT-CIRCUETCALCULATIONSWITHBUSIMPEDANCEMATRIXObjective•TowriteasimpleprograminMATLAB®forthealgorithmofshortcircuitcalculationwithbusimpedancematrix.DiscussionUsingthenodeimpedancematrixtowriteaprograminMATLAB®.MathmaticsmodelThemathmaticsmodelsofpowersystemelementsonekinds,itistransmissionline,anditisequivalentedintoanonlyoneimpedancebranchequivalentciucuit,anddricribledasfollowing:• - •i1 jX 」WstemFtequirementComputerwithMATLAB®6oraboveinstalled.ProcedureLimited:ZeroisesShort-circuitcalculationsusingbusimpedancematricesfollowthesamelogicasdevelopedin

Chapter2.ConsiderthatthepositivenegativeandzerosequencebusimquencebusimpedancematricesZ\s,Z：,andZ：areknownandasingleline-to-groundfaultoccursattherthbus.Thepositivesequenceistheninjectedonlyattherthbusandallothercurrentsinthepositivesepuencecurrentvectorarezero.Thepositivesepuencevoltageatbusrisgivenby(3.76)v1=-z'/'(3.76)r rrrSimilarly,thenegativeandzerosequencesvoltagesareV2=-Z2I2

r rrrV°=-Z0/r rr.Fromthesequencenetworkconnectionsforaline-to-groundfault:1=/2=/°1.0Z：+ZV°=-Z0/r rr.Fromthesequencenetworkconnectionsforaline-to-groundfault:1=/2=/°1.0Z：+Z；+Z：+3Z/Thisshowsthatthefollowingequationscanbewrittenforashortedbuss.3.1Line-to-GroundFault2

ss0ss1.0Z',+Z：+Z°+3Zf3.2Line-to-LineFault1.0Z：+Z：+3Z/3.3DoubleLine-to-GroundFaultZ：(Z：+3Z/)"Z：+(Z：+3Z/)7/°= 久 llZ：+(Z：+3ZQ$-Z：+3Z/ /(3.83)Z：+(Z：+3Z”(3.83)Thephasecurrentsarecalculatedby(3.84)Thevoltageatbusjofthesystermis

Wherej=1,2 s, ,mThefaultcurrentfrombusxtobusyisgivenby1°zyy°xy00Y'00v°jrV'-v°y_y1xt0xy0Y2冲XV2Xy-V2yWhere2127°=xy213/°mmTheGuideofExperimentofShortCircuitCalculationV.0ZTheGuideofExperimentofShortCircuitCalculationV.0Z®0 0V-1-0 z'js 0V;0 0 0 zj.0(3.85)y°112,12Y°212,13y01\2,mn吸=yO113,12y0113.13y（）Y0mn,\2y°1mnA3Y°mnjnn(3.88.)WhereY^yistheinverseoftheprimitivematrixofthesysterm.Similarexpressionsapplytopositivesequenceandnegativesequencequantities.Example3Thepositive,negative,andzerosequencematricesofthesysteminFig.3-12arecalculatedinExample3.6.Adoubleline-to-groundfaultoccursatbus4.Usingthematricesalreadycalculated,itisrequiredtocalculate:Faultcurrentatbus4Voltageatbus4Voltageatbuses1,2,and3Faultcurrentflowsfrombuses3to4,1to4,2to3Currentflowinnode0tobus3Thefaultcurrentatbus4isfirstcalculatedasfollows:=8.408=8.408MatrixMethodsforNetworkSolutions~Z4., ,1Z：+Z：4=-3.022Thelinecurrentsaregivenby1a2aa~-24-3.0228.408-5.386Z：+Z；,abc4I\=-5.386r14I;Sequencevoltagesatbus4aregivenbyLinevoltagesare.therefore,Similarly,—0,1,21a2I：aa2-4.533-jl1.946-4.533+jl1.9460.1292z1乙4sz2乙4s0.07250.07250.39040.39040.390410.39041a200.01420.39040.39040.022312.777<249.2°12.777<110.78°-04-3.0228.408-5.3861.1820.0223-3.0228.408-5.3860.04290.8125_0.1201Sequencevoltagesatbuses2and3,similarlycalculated.are_0,1,2v20.0837=0.8310_0,1,2丫3 =0.13360.80910.12230.1083Thesequencevoltagesareconvertedintolinevoltages:0.976<0°V,ahc=0.734<125.2°V产

0.734<234.8°1.023<0°=0.735<121.5°匕血0.735<238.3°1.065<0°=0.681<119.2°0.681<240.8°Thesequencecurrentsflowingbetweenbuses3and4aregivenby0341/0.2000.1336-0.3904-10284134二01/0.100.8091-0.3904二4.1870234001/0.10.123-0.3904-2.6811/0.080 00.1336-0.08370.624—01/0.06 00.8091-0.8310二-0.36500 1/0.060.123-0.10830.233Thiscanbetransformedintolinecurrents0.4920.222rabc732 =0.69+j0.518jabc734二-2.037+,5.9480.69-J0.518-2.037+J5.948Similarly,thesequencecurrentsbetweenbus3to2areThelinesbetweenbuses1and4arecoupledinthezerosequencenetw