外文翻译--基于优化的牛顿—拉夫逊法和牛顿法的潮流计算英文文献PowerFlowCalculationbyCombinationofNewton-RaphsonMethodandNewton’sMethodinOptimization.AndreyPazderin,SergeyYuferevURALSTATETECHNICALUNIVERSITY?UPIE-mail:pav@//0>.,usv@//.Abstract--Inthispaper,theapplicationoftheNewton’smethodinoptimizationforpowerflowcalculationisconsidered.Convergenceconditionsofthesuggestedmethodusinganexampleofathree-machinesystemareinvestigated.Itisshown,thatthemethodallowstocalculatenon-existentstatepointsandautomaticallypullsthemontotheboundaryofpowerflowexistencedomain.AcombinedmethodwhichiscomposedofNewton-RaphsonmethodandNewton’smethodinoptimizationispresentedinthepaper.IndexTerms?Newtonmethod,Hessianmatrix,convergenceofnumericalmethods,steadystatestabilityⅠ.INTRODUCTIONThesolutionofthepowerflowproblemisthebasisonwhichotherproblemsofmanagingtheoperationanddevelopmentofelectricalpowersystemsEPSaresolved.Thecomplexityoftheproblemofpowerflowcalculationisattributedtononlinearityofsteady-stateequationssystemanditshighdimensionality,whichinvolvesiterativemethods.Thebasicproblemofthepowerflowcalculationisthatofthesolutionfeasibilityanditerativeprocessconvergence[1].Thedesiretofindasolutionwhichwouldbeontheboundaryoftheexistencedomainwhenthegivennodalcapacitiesareoutsidetheexistencedomainofthesolution,anditisrequiredtopullthestatepointbackontothefeasibilityboundary,motivatestodevelopmethodsandalgorithmsforpowerflowcalculation,providingreliableconvergencetothesolution.ThealgorithmforthepowerflowcalculationbasedontheNewton'smethodinoptimizationallowstofindasolutionforthesituationwheninitialdataareoutsidetheexistencedomainandtopulltheoperationpointontothefeasibilityboundarybyanoptimalpath.AlsoitispossibletoestimateastaticstabilitymarginbyutilizingNewton'smethodinoptimization.AsthealgorithmbasedontheNewton’smethodinoptimizationhasconsiderablecomputationalcostandpowercontrolcannotberealizedinallnodes,thealgorithmbasedonthecombinationoftheNewton-RaphsonmethodsandtheNewton’smethodinoptimizationisofferedtobeutilizedforcalculatingspeed,enhancingthepowerflowcalculation.II.THEORETICALBACKGROUNDA.Steady-stateequationsThesystemofsteady-stateequations,ingeneral,canbeexpressedasfollows:whereisthevectorofparametersgivenforpowerflowcalculation.Inpowerflowcalculation,realandreactivepowersaresetineachbusexceptfortheslackbus.Ingenerationbuses,themodulusofvoltagecanbefixed.WX,Yisthenonlinearvectorfunctionofsteady-stateequations.VariablesYdefinethequasi-constantparametersassociatedwithanequivalentcircuitofanelectricalnetwork.Xisarequiredstatevector,itdefinessteadystateofEPS.Thedimensionofthestatevectorcoincideswiththenumberofnonlinearequationsofthesystem1.Therearevariousknownformsofnotationofthesteady-stateequations.Normally,theyarenodal-voltageequationsintheformofpowerbalanceorintheformofcurrentbalance.Complexquantitiesintheseequationscanbepresentedinpolarorrectangularcoordinates,whichleadstoasufficientlylargevarietyformsofthesteady-stateequationsnotation.Therearevariablemethodsofanonlinearsystemofsteady-stateequationssolution.TheyareunitedbytheincrementalvectorofindependentvariablesΔXbeingsearchedandtheconditionofconvergencebeingassessedateachiteration.B.TheNewton'smethodinoptimizationAnotherwayofsolvingtheproblemofpowerflowcalculationisrelatedtodefiningazerominimumofobjectivefunctionofsquaressumofdiscrep...
