外文翻译（原文）AComparisonofPowerFlowbyDifferentOrderingSchemesAbstract—Nodeorderingalgorithms,aimingatkeepingsparsityasfaraspossible,arewidelyusedtoday.Insuchalgorithms,theirinfluenceontheaccuracyofthesolutionisneglectedbecauseitwon’tmakesignificantdifferenceinnormalsystems.While,alongwiththedevelopmentofmodernpowersystems,theproblemwillbecomemoreill-conditionedanditisnecessarytotaketheaccuracyintocountduringnodeordering.Inthispaperweintendtolaygroundworkforthemorerationalityorderingalgorithmwhichcouldmakereasonablecompromisingbetweenmemoryandaccuracy.Threeschemesofnodeorderingfordifferentpurposeareproposedtocomparetheperformanceofthepowerflowcalculationandanexampleofsimplesix-nodenetworkisdiscusseddetailed.Keywords—powerflowcalculation;nodeordering;sparsity;accuracy;Newton-Raphsonmethod;linearequationsI.INTRODUCTIONPowerflowisthemostbasicandimportantconceptinpowersystemanalysisandpowerflowcalculationisthebasisofpowersystemplanning,operation,schedulingandcontrol[1].Mathematicallyspeaking,powerflowproblemistofindanumericalsolutionofnonlinearequations.Newtonmethodisthemostcommonlyusedtosolvetheproblemanditinvolvesrepeateddirectsolutionsofasystemoflinearequations.ThesolvingefficiencyandprecisionofthelinearequationsdirectlyinfluencestheperformanceofNewton-Raphsonpowerflowalgorithm.Basedonnumericalmathematicsandphysicalcharacteristicsofpowersysteminpowerflowcalculation,scholarsdedicatedtotheresearchtoimprovethecomputationalefficiencyoflinearequationsbyreorderingnodes’numberandreceivedalotofsuccesswhichlaidasolidfoundationforpowersystemanalysis.Jacobianmatrixinpowerflowcalculation,similarwiththeadmittancematrix,hassymmetricalstructureandahighdegreeofsparsity.Duringthefactorizationprocedure,nonzeroentriescanbegeneratedinmemorypositionsthatcorrespondtozeroentriesinthestartingJacobianmatrix.Thisactionisreferredtoasfill-in.Iftheprogrammingtermsisusedwhichprocessedandstoresonlynonzeroterms,thereductionoffill-inreflectsagreatreductionofmemoryrequirementandthenumberofoperat