牛顿法潮流计算的高效综合稀疏技术

：7111211．4000302．400010：。、。，，，。，，。，，。IEEE5727465：，。：；；；；；：TM744：A：1004-9649（2010）07-0019-05：2009-10-11；：2010-05-04：（1968—），，，，，。E-mail:[e-mail]0［1-2］，［3-10］。:［3］、［4］、［5］；［7-9］、［8］、［1］；LU［10］，3。，、、［7-9］3。2×2HijNijJijLij!、HijNijRijSij!（），。，2，2。，，2，，，。，。，，，；。。1。，［10］，（n-m）（n-m），，。，。1.1N，2×2HijNijJijLij!，HijNijRijSij!（Hij，Nij、JijLij）：ELECTRICPOWER43720107Vol．43，No．7Jul.20101943i≠j：Hij=-Bijei+GijfiRij=0Sij=≠≠≠≠≠≠≠≠≠0i=j：Hij=-Biiei+2Giifi+Biiei+j=nj=1,j≠iΣ（Gijfj+Bijej）Rij=2fiSii=2ei≠≠≠≠≠≠Σ≠≠≠≠≠≠。，，i≠j，2×2（i，j）。i=j，2×2i，。：，2×2，。，，，2。，，，，2。1.2：n，（m-1）PQ；（n-m）PV；1；，k（）。1.2.1。，，，。，，，，2×2，，。，2×2，（n-1）；，2（n-1）。，（n-1）；2（n-1），，。1.2.2、。，、，。，，、，。，、（）。，PQ，m≈n，，m=n，PV，。，2×2，。：=（n-1）2；2×2=（n-1）+2k；=［（n-1）+2k］/（n-1）2。：=［2（n-1）］2=4（n-1）2；=4［（n-1）+2k］；=［（n-1）+2k］/（n-1）2。，，，，。2，，，，、。2.12：、（）。，，。，，。14。1：（1），，，。（2），，，，。（3）（）（），（）。（4）20：72383IEEE300IEEE118IEEE570.257350.013280.004060.001880.815780.064630.014220.007660.315470.205480.285510.2454327460.350000.926600.37773/s1Fig.1Structureofthetwo-layerlinkedlisttableAij=HijNijJijLij!HijNijRijSij!，Yij=［GijBij］，，YijAij。2.2，，2×2，。，：（）。，，，。2。：，，？，，，，，。，，，。2.3，，，。，，，。，。、，。，、。，，、，。“，”，，。，，，。3：Pentium（R）4CPU2.26GHz，512MB，WindowsXP，VC6.0。2746、2383IEEE300、118、57。、，。3.11。：。3.2，，。2“”，。：1Tab.1Comparisonofthecalculationtime2143。3.32：，。3“”，。：2，，。3.4、；，，。2：，；3（、），。4：，1∶4，。4：、。，。，。：，、。，，、。，，30%，，。：［1］,,.［M］.:,2004.WUJian-ping,WANGZheng-hua,LIXiao-mei.Efficientsolutionsandparallelcomputingofsparselinearequations［M］.Changsha:HunanScience&TechnologyPress,2004.［2］BENZIM.Preconditioningtechniquesforlargelinearsystems:Asurvey［J］.JournalofComputationalPhysics,2002,18（2）:418-477.［3］TINNEYW,WALKERJ.Directsolutionsofsparsenetworkequationsbyoptionallyorderedtriangularfactorization［J］.ProceedingsoftheIEEE,1967,55（11）:1801-1809．［4］DAIVSTA,GLLBERTJR,LARIMORESI.Acolumnapproximateminimumdegreeorderingalgorithm［J］.ACMTransactionsonMathematicalSoftware,2004,30（3）:353-376.［5］KRISHNAM,SAMBARAPUS,HALPINM.Sparsematrixtechniques3Tab．3Comparisonofthelinerequationssolvingtimeandquantityofinputelements4Tab．4Comparisonofthequantityofstoringelementsandmemoryoperationtime2Tab．2ComparisonoftheJacobianmatrixformation&modificationtime2383IEEE300IEEE118IEEE5766550.035470.001330.000590.00014274650.037500.142660.248630.008860.1501120.002920.202060.001090.128440.149850.25025/s2383IEEE300IEEE118IEEE576655274650.188700.523400.006570.030620.001440.004540.000720.002780.253100.607806600171440.360530.3849751017560.214570.290431582620.317180.603051163580.258990.3240210478209000.416420.50134//s2383IEEE300IEEE118IEEE570.040600.003750.001330.0005827460.051600.1765081550.0193711180.006884760.003562130.198509756306780.230020.2658342020.193600.2660615380.193310.309497690.162920.27698352060.259950.27711/s/22：7IntegratedsparsetechniqueofNewtonpowerflowcalculationYANWei1,HUANGZheng-bo1,YUJuan1,ZHANGHai-bing2,XiangBo11．StateKeyLaboratoryofPowerTransmissionEquipment&SystemSecurityandNewTechnology,ChongqingUniversity,Chongqing400030,China;2．ElectricPowerMaintenanceandInstallationInstituteofChongqingElectriePowerCompany,Chongqing400010,ChinaAbstract:AnintegratedsparsetechniqueofNewtonpowerflowcalculationwasproposedtoenhancetheefficiencyofthecalculation.Aboveall,throughthesystemsanalysis,itisadvancedthatthestructureoftheblockconformationoftheJacobianmatrixundertherealbusinnetworksisabletoenhancetheefficienciesofthesetwoparts,whicharetheformation&modificationofJacobianmatricesandthedecomposition&solvingoflinearequations.Andakindoftwo-layerlinkedlisttablewasconstructedfurther.Thetwo-layerlinkedlistiscomposedofcrosslinkedlistandbinarylinkedlist,suchthatthecrosslinkedliststorestheblockJacobianmatrixandthebinarylinkedliststoresbusadmittancematrix,andthecorrespondingcellsbetweenthetwolayersarelinkedviathepointer.First,whenformattingandmodifyingtheJacobianmatrix,thevalueofadmittanceisobtainedthroughthelinkingbetweenthetwokindsoflinkedlists,whichavoidingtheeffectofthechangingoftheoriginalJacobiansturctureafterGaussdecomposition,andspeedinguptheefficiency.Second,thelayerofthecrosslinkedlistthatispreservedduringtheiterationisusedtosolvelinearequationsdirectly,whichspeedinguptheefficiency.Theresultoffivenetworksfrom57to2746busesaregiven:comparedwiththetraditionaltechniques,theintegratedsparsetechniqueofNewtonpowerflowdescribedinthisthesisismorecapableofimprovingtheefficiency.Keywords:Newtonpowerflowcalculation;sparsetechnique;Jacobianmatrixmodification;blockmatrix;linearequations;dynamiclinkedlistinpowersystems［C］//39thSoutheasternSymposiumonSystemTheory,2007．［6］,.［J］.,2003,27（8）:54-58．WANAShou-xiang,WANACheng-shan.Comparativestudyofoptimalnodeindexingschemesfordistributionsystems［J］.AutomationofElectricPowerSystems,2003,27（8）:54-58．［7］,,.［J］.,1999,19（6）:31-33．YOUZhong-xiao,JINYong,LIShu-mao.Theapplicationoforthogonallinkedlistinpowerflowcalculation［J］.ElectricPowerAutomationEquipment,1999,19（6）:31-33．［8］,.［J］．,2005,10（8）:28-31．YEJian-hua,LINJi-keng.StudyontheefficiencyoftwosparsestoragemodesforNewtonpowerflowcalculation［J］.TheWaterConservancyandElectricityi