导论.docx
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导论
课程名称：
电力系统导论（双语）
学院：
信息工程学院
专业班级：
电力系统101班
学号：
学生姓名：
Experiment1
BusAdmittanceMatrix
1.Objective
•TowriteasimpleprograminMATLAB®forthealgorithmofbusadmittancematrix.
2.Discussion
BusAdmittancematrix
Thenode-voltageequationofann-buspowersystemcanbewritteninmatrixformas
（1）
Or
（2）
WhereIbusisthecolumnvectoroftheinjectedbuscurrents.Vbusisthecolumnvectorofbusvoltagesmeasuredfromthereferencenode.Ybusisknownasthebusadmittancematrix.
Calculationmethod:
1.Thediagonalelementofeachnodeisthesumofadmittancesconnectedtoit.Itisknownastheself-admittanceordrivingpointadmittance,i.e.,
（3）
2.Theoff-diagonalelementisequaltothenegativeoftheadmittancebetweenthenodes.Itisknownasthemutualadmittanceortransferadmittance,i.e.
（4）
Result:
Baseontheequations（3）and（4）,thealgorithmofbusadmittancematrixcanbeusedtobuildthebusadmittancematrix（Ybus）.
3.Mathmaticsmodel
Themathematicsmodelsofpowersystemelementsaretwokinds,oneistransmissionlineorcableandanotheristransformer,andtheyareequivalentintopitypeequivalentcircuit,anddescribedasfollowing:
1）Transmissionlineorcable
AccordingtothePisectionalcircuitoftransmissionlineorcable,wecangettheelementsofnodalAdmittancematrixvalue,asthefollowing
Figure:
Thepisectionequivalentcircuitoftransmissionlineorcable
（5）
（6）
（7）
（8）
2）transformer
Asshowasthetransformercircuit,wehave
（9）
（10）
Accordingtoequations（10）and（9）,wehave
（11）
（12）
Figure:
thePisectionequivalentcircuitofTransformer
Assume
（13）
（14）
（15）
（16）
4.SystemRequirement
ComputerwithMATLAB®6oraboveinstalled.
5.Procedure
1.0LaunchtheMATLABprogram.
2.0GotoFILENEWM-file.
3.0WriteafunctionY=The_Node_Admittance_Matrix（TopoStructureAndBranchPara）fortheformationofthebusadmittancematrix.
4.0TopoStructureAndBranchParaisthetransmissionline,cableandtransformerinputdataandcontainsfivecolumnsparameters.Thefirsttwocolumnsarethelinebusnumbersandtheremainingcolumnscontainthelineresistanceandreactanceinper-unitandtransformertapratioorcapacitoroftransmissionline.
5.0Thefunctionshouldreturnthebusadmittancematrix.
6.Exercises
Usethewrittenfunction,Y=The_Node_Admittance_Matrix（TopoStructureAndBranchPara）toobtaintheYbusofthefollowingpowersystemnetwork:
Q1.YouarerequiredtowritetheYbustopologicalstructureandparameterintoatextfile.（Hint:
usethematlabtextcompilertowritedownthetable1data,usingthecommatoseparatetheparameters,andsaveitusethenameof4_Power_System_Data.dbf）
Q2.Youarerequiredtowriteouttheprogramflowfigureofforminganodaladmittancematrix.
Hint.YouarerequiredtocompileaprogramtoformtheYbusMatrix,thefollowingprogramisareferenceprogramtoyou.
Figure:
One-linediagramofpowersystem
Forexample,fromthetextbook“powersystemanalysis”No.2edition3onpage61~62
Table1：
TransformerandtransmissssionLinedata
FromBus#
ToBus#
R（p.u）
X（p.u）
B（p.u）orratioK
Others
1
2
0.1
0.4
j0.01528
1
3
0
0.3
1.1
1
4
0.12
0.5
j0.01920
2
4
0.08
0.40
J0.01413
7.Theflowchart
Figure:
TheflowchartofFormingNodalAdmittanceMatrix
Theprogramis:
%functionOutPut=The_Node_Admittance_Matrix（handles）
%isasubroutineofPowerSystemCalculation
functionOutPut=The_Node_Admittance_Matrix（handles）
%thefollowingprogramisopenadatafileandgettheNumberof
%NodeandBranchdatatoformanodaladdmittancematrix
%thefollowingcodeisopenafileandreadthedataofpowersystemnetwork
[fname,pname]=uigetfile（'*.dbf','Selectthenetworkparametredata-file'）;
TopoStructureAndBranchPara=csvread（fname）;
[NumberOfBranch,NumberOfPara]=size（TopoStructureAndBranchPara）;
Temporary1=max（TopoStructureAndBranchPara（:
1））;
Temporary2=max（TopoStructureAndBranchPara（:
2））;
ifTemporary1>Temporary2
NumberOfNode=Temporary1;
else
NumberOfNode=Temporary2;
end
%ThefollowingprogramistoformtheNodalAdmittanceMatrix
%andtheTopologicstructureandBranchParametresarearranged
%I,J,R,X,C/K,andpayattentiontotheinpedenceoftransformerisinthe
%sideofNodeJandtheratiooftransformer1:
KisinthesideofNodeI
forCircleNumber1=1:
NumberOfBranch
forCircleNumber2=1:
NumberOfBranch
NodalAdmittanceMatrix（CircleNumber1,CircleNumber2）=0;
end
end
forCircleNumber=1:
NumberOfBranch
ifTopoStructureAndBranchPara（CircleNumber,5）>0.85
NodalAdmittanceMatrix（TopoStructureAndBranchPara（TopoStructureAndBranchPara（CircleNumber,1）,TopoStructureAndBranchPara（CircleNumber,1）））=...
NodalAdmittanceMatrix（TopoStructureAndBranchPara（TopoStructureAndBranchPara（CircleNumber,1）,TopoStructureAndBranchPara（CircleNumber,1）））+...
TopoStructureAndBranchPara（CircleNumber,5）^2/...
（TopoStructureAndBranchPara（CircleNumber,3）+...
j*TopoStructureAndBranchPara（CircleNumber,4））;
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,2）,TopoStructureAndBranchPara（CircleNumber,2））=...
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,2）,TopoStructureAndBranchPara（CircleNumber,2））+...
1/（（TopoStructureAndBranchPara（CircleNumber,3）+j*TopoStructureAndBranchPara（CircleNumber,4）））;
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,1）,TopoStructureAndBranchPara（CircleNumber,2））=...
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,1）,TopoStructureAndBranchPara（CircleNumber,2））...
-TopoStructureAndBranchPara（CircleNumber,5）/...
（（TopoStructureAndBranchPara（CircleNumber,3）+j*TopoStructureAndBranchPara（CircleNumber,4）））;
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,2）,TopoStructureAndBranchPara（CircleNumber,1））=...
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,1）,TopoStructureAndBranchPara（CircleNumber,2））;
else
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,1）,TopoStructureAndBranchPara（CircleNumber,1））=...
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,1）,TopoStructureAndBranchPara（CircleNumber,1））+...
+1/（TopoStructureAndBranchPara（CircleNumber,3）+...
j*TopoStructureAndBranchPara（CircleNumber,4））+j*TopoStructureAndBranchPara（CircleNumber,5）;
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,2）,TopoStructureAndBranchPara（CircleNumber,2））=...
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,2）,TopoStructureAndBranchPara（CircleNumber,2））+...
+1/（TopoStructureAndBranchPara（CircleNumber,3）+...
j*TopoStructureAndBranchPara（CircleNumber,4））+j*TopoStructureAndBranchPara（CircleNumber,5）
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,1）,TopoStructureAndBranchPara（CircleNumber,2））=...
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,1）,TopoStructureAndBranchPara（CircleNumber,2））...
-1/（TopoStructureAndBranchPara（CircleNumber,3）+...
j*TopoStructureAndBranchPara（CircleNumber,4））;
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,2）,TopoStructureAndBranchPara（CircleNumber,1））=...
NodalAdmittanceMatrix（TopoStructureAndBranchPara（CircleNumber,1）,TopoStructureAndBranchPara（CircleNumber,2））;
end
end
NodalAdmittanceMatrix=
1.0421-8.2429i-0.5882+2.3529i0+3.6667i-0.4539+1.8911i
-0.5882+2.3529i1.0690-4.7274i00
0+3.6667i00-3.3333i0
-0.4539+1.8911i000.9346-4.2616i
Experiment2
BusImpedanceMatrix
1.Objective
•TowriteasimpleprograminMATLAB®forthealgorithmofbusimpedancematrix.
2.Discussion
BusImpedancematrix
Thenode-currentequationofann-buspowersystemcanbewritteninmatrixformas
（1）
Or
（2）
WhereIbusisthevectoroftheinjectedbuscurrents.Vbusisthevectorofbusvoltagesmeasuredfromthereferencenode.Zbusisknownasthebusimpedancematrix.
ZbusCALCULATION
Therearetwomajormethods:
1.InversionofYbus
2.Zbusbuildingalgorithm
3.LUfactorization.
Matrixinversionforverylarge-scalenetworksisveryslowandavoided.Ontheotherhand,theZbusbuildingalgorithmistheacceptablemethodforlargenetworks.Itismuchfasterandeasiertoupdate.
ZbusBuildingAlgorithm
ThisisaverysystematicwayofformingZbusandallowforeasyimplementationonthedigitalcomputer.
Advantages
1.Easytoimplement
2.Avoidsmatrixinversion
3.ItiseasytohandleZbusmodificationsduetolineswitchingsandchangesinnetworktopology
Solution：
Notation
Theadditionofabranchofimpedancezbfallsinto4categoriesasfollows.
CASE1:
Addingzbfromanewbusptothereferencebus0
Here,
●
willbe
matrix
●Injectedcurrent
willnotchangethebusvoltagesoftheoriginalnetwork
●
Then,
CASE2:
Addingzbfromanewbusptoanexistingbusk
Here,
●
willbe
matrix
●Injectedcurrent
willchangethebusvoltagesoftheoriginalnetwork
●Injectedcurrentatbuskbecomes
●
Then,
SummaryofCase2
CASE3:
Addingzbfromanexistingbusktothereferencebus0
Here,
●
willbe
matrix
●ThisisaspecialcaseofCASE2exceptthat
Then,
SinceVp=0,thelastrowcanbeeliminatedbyKronreduction（onekindofmathematicsmethod）toyieldann×nmatrixas
SummaryofCase3
•ProceedasinCASE2
•Eliminatethelastrow
CASE4:
Addingzbfromtwoexistingbusesjandk
Here,
●
willbe
matrix
●Branchcurrent
willchangethebusvoltagesoftheoriginalnetwork
●Injectedcurrentatbusjbecomes
●Injectedcurrentatbuskbecomes
●
●willchangethebusvoltagesoftheoriginalnetwo
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