外文翻译原文-变压器励磁涌流和相位跳变电流的研究

3506IEEETRANSACTIONSONPOWERELECTRONICS,VOL.31,NO.5,MAY2016InvestigationofTransformer-BasedSolutionsfortheReductionofInrushandPhase-HopCurrentsRasimDogan,SaeedJazebi,Member,IEEE,andFranciscodeLeon,Fellow,IEEEAbstractAcomprehensiveliteraturereviewshowsthattransformer-basedsolutionsaresuperiorforthemitigationofin-rushcurrentsthanexternal(tothetransformer)solutions.Theuseofairgapsandlow-permeability(iron)materialsareknowntech-niquesforthispurpose.Thispaperinvestigatestheeffectivenessoftheseapproachesforreducinginrushandphase-hopcurrents.Studiesarecarriedoutontoroidaltransformers,duetotheirbroadapplicationinpowerelectronicsdevices.Contrarytocommonbe-lief,thispaperdemonstratesthatairgapsdonotreducetheinrushcurrentswhenatransformerisfullydemagnetized.However,in-rushcurrentscanbemitigatedbytheuseoflow-permeabilityironmaterials.Itisalsodemonstratedthatair-gapssignificantlyre-duceinrushcurrentswhentransformershaveresidualflux,e.g.,forphase-hopconditions.Analyticalexpressionsarederivedtocomputethemitigationfactorforaspecificgaplength.Theresultsandformulaepresentedinthispaperareverifiedwithlaboratoryexperiments,transientsimulationswithvalidatedcircuitmodels,and2-Dfiniteelementsimulations.IndexTermsAir-gap,inrushcurrents,low-permeabilitymate-rials,phase-hopcurrent,toroidaltransformers,UPS.I.INTRODUCTIONINRUSHcurrentsareusuallyobservedwhenatransformercoreisdrivenintoverydeepsaturationatthetimeofen-ergization.Themagnitudeofinrushcurrentscouldbetento30timeslargerthantheratedcurrentdependingonthefollow-ingparameters:switchingangle,magnitudeandpolarityofthevoltage,residualfluxinthecore,saturationinductanceoftheen-ergizedwinding,windingresistance,impedanceofthesource,geometryofthetransformercore,andthecorematerial1,2.Transformerscandrawmoredestructivecurrentscomparedtoinrushcurrentswhenthecoreshaveresidualflux,orwhenaphenomenoncalled“phase-hop”occurs3.Themagnitudeofphase-hopcurrentsmightbetwiceaslargeasthezero-crossinginrushcurrents.Phase-hopisnotacommonlyusedtermintheliterature.However,itneedstobeknownbypowerengineers,sinceawiderangeofpowerelectronicdevicesmaycreateop-eratingconditionswhichleadatransformertodrawphase-hopcurrents.Possiblereasonsfortheoccurrenceofphase-hopcur-rentaretheswitchingofuninterruptiblepowersupply(UPS)systems,voltageinterruptions,voltagesags,andnotching3.ManuscriptreceivedFebruary15,2015;revisedJune8,2015;acceptedJuly14,2015.DateofpublicationJuly21,2015;dateofcurrentversionDecember10,2015.RecommendedforpublicationbyAssociateEditorM.Duffy.TheauthorsarewiththeDepartmentofElectricalandComputerEngineering,NewYorkUniversity,Brooklyn,NY11201USA(e-mail:;;).Colorversionsofoneormoreofthefiguresinthispaperareavailableonlineat.DigitalObjectIdentifier10.1109/TPEL.2015.2459032Phase-hopandinrushcurrentsareundesirabletransientphe-nomenainpowersystems.Theseabnormaleventsmayresultinsignificantvoltagedrops,whichmightcausefalsetrippingofprotectionsorproducemechanicalstressesonpowersystemcomponents4.Thus,powerquality,reliability,andstabilityofthesystemcanbeaffected.Severalsolutions(externaltothetransformer)havebeenpro-posedinthepasttomitigateinrushcurrents.Theseinclude:preinsertionresistors1,negativetemperaturecoefficientther-mistors5,controlledswitching69,transformercorede-magnetization10,sequentialphaseenergization11,12,voltagesagcompensators13,14,andtheapplicationofse-riesdcreactors1518.Preinsertionresistors,controlledswitching,andcoredemag-netizationneedadditionalcontrolunitsanddetectioncircuits.Therefore,thesecircuitsreducethereliabilityofthesystem,andincreasethecomplexityandthefinalcost.Furthermore,theyarenotapplicableformitigatingthephase-hopcurrents,becauseoftheunpredictabilityoftheiroccurrenceandthelackoftimetoreactevenifdetected.Transformer-basedsolutions,suchasreducedfluxdensityde-signs,air-gaps,useoflowpermeability(unannealed)ironcore,andvirtualair-gapsaremorerobustandeffectivealternatives3.Theinfalliblesolutionistodesigntransformersatsuffi-cientlylowfluxdensitiessothattheyneversaturate.However,transformersbecomelarger,moreexpensive,andinsomeap-plicationstheremaynotbesufficientspacetoaccommodatebulkiertransformers.Thevirtualair-gaptechniqueusesexter-naldcwindingsonthecore19.Theironcoregoesintoalocalsaturationwhenthedccurrentisinjected.Computersimulationstudiesin20showthatthedcexcitationcreatesthesameeffectasair-gapintheironcore.Itisbelievedthattheuseofunannealedcoresgivessimilarperformancetotheair-gapswithadditionaladvantages21.Inthispaper,theeffectofair-gapsandlow-permeabilityironma-terialsisinvestigatedandtheadvantagesanddisadvantagesarediscussed.Numerouslaboratoryexperimentsaccompaniedwithcomputersimulationsindicatethatair-gapsarenotalwaysca-pabletomitigateinrushcurrentsespeciallywhenatransformerisfullydemagnetized.Forthefirsttime,solutionstomitigatethephase-hopcurrentsarepresented.Itisshownvialaboratorymeasurementsthatfortheinrushcaseswithinitialresidualfluxandphase-hop,thecurrentamplitudereducesappreciablyevenwithsmallair-gaps.Itisalsodemonstratedthatspecialdesignswithlow-permeabilityironmaterialscouldsignificantlyreduceinrushandphase-hopcurrents.Theprincipaladvantageofthesemethodsistheirsimplicity.ThesemethodsdonotrequireanycontroluniEEE.Personaluseispermitted,butrepublication/redistributionrequiresIEEEpermission.See/publicationsstandards/publications/rights/index.htmlformoreinformation.DOGANetal.:INVESTIGATIONOFTRANSFORMER-BASEDSOLUTIONSFORTHEREDUCTIONOFINRUSHANDPHASE-HOPCURRENTS3507Fig.1.(a)Transformerprimaryvoltage.(b)Currentwaveformsduringinrushandphase-hop.ormonitoringdevicetodetectthephase-hop.Hence,theyhaveperennialfunctionality.Thephase-hopcurrentisproducedbytwoconsecutivesemi-cyclesofvoltageseeFig.1(a).Thefirstsemicyclebuildsmagneticfluxinthecore,whichistrappedasresidualflux.Thiscausesahighervalueofinrushcurrentswhenthesecondsemicycleofthevoltageisappliedtothetransformerterminals.Theair-gapdrainstheresidualfluxandconsequentlyreducesthephase-hopcurrent.Unannealedcoreshavereducedresidualfluxwhencomparedtoannealedcores.Lessresidualfluxleadstodiminishedphase-hopcurrents.Theeffectivityofthemethodsisdemonstratedwithvalidatedtimedomain(transient)modelsusingtheEMTP-RVandalsowithfiniteelements(FEM)simulationsusingANSYSMaxwellin2-D.TransientsimulationsareperformedusingthereversiblemodelexplainedinSectionIV.Laboratoryexperimentsareper-formedonseveraltransformerstocorroboratethesimulationresultsandtheproposedsolutions.II.DESCRIPTIONOFINRUSHANDPHASE-HOPCURRENTSA.InrushCurrentsInrushcurrentsaretransientsthatoccurwhentransformersareconnectedtothesource.Theyhappenbecausethemagneticfluxisdrivenbythevoltageandthetransformerironcoresatu-rates.Thepeakofthisphenomenonisafunctionofthetimeofswitching,residualfluxinthecore,resistanceandinductanceofthesystem.Theworstcasehappenswhenthetransformerisinopencircuit,residualfluxisatmaximum(seerinFig.2),andtheswitchinghappensatvoltagezerocrossingwithapolaritythatincreasesthefluxinthecore.Fig.2.Hysteresiscurveandresidualflux.Afterthetransformerisdisconnectedfromthesource,theresidualfluxdependsontheoperatingpointbeforedisconnec-tion.Astheresult,atthemomentofreconnection,theinrushcurrentsmayoccuratdifferentlevelsdependingontheresidualflux.Therefore,inthispaper,inrushcurrentexperimentsareper-formedondemagnetizedtransformerstoobtainconsistentmea-surementsandtobeabletovalidatethetransientsimulations.Azero-crossingsinusoidalvoltageisappliedtothetransformerontheprimarysidewhenthesecondarysideisopencircuit.TheprimaryvoltageisillustratedinFig.1(a).Afterahalfcycle,themagnitudeofthefluxinthecoreis(theoretically)doubledwhencomparedtothemaximumfluxofthesteady-statecondition4.Thishighfluxdrivesthecoreintosaturationandinrushcurrentsaredrawnfromthesource.B.Phase-HopCurrentsPhase-hopcurrentsoccurwhenthetransformergoesintosu-persaturation(morethandoubleofratedflux).Supersaturationisobservedwhenthetransformerisenergizedwithazero-crossingvoltageandsimultaneouslythecorehasmaximumresidualfluxwiththesamepolarity3.ThiscouldbeexplainedfromthetransformerterminalvoltageshowninFig.1(a).Thefirsthalfcycleofvoltageimpressesahighlevelfluxinthemagneticcore.Then,thevoltageiszeroforahalfcycle.Therefore,fluxremainsinthecoreatthemomentthesecondvoltagepositivesemicycleisapplied.Hence,thefluxmagnitudebecomes(theo-retically)largerthandouble.Thislargerfluxdrivesthecoreintomuchdeepersaturationwhencomparedwiththeinrushcurrentcondition,andthus,alargercurrentisdrawnfromthesourceseeFig.1(b).Thephase-hopconditionissimilarinnaturetoinrushcur-rentswithresidualflux.However,therearesomeimportantdifferenceswhencomparingtheresidualfluxofphase-hopandinrushconditions.Themagnitudeofinrushcurrentsdependsontheinitialconditions,beforethezerovoltageswitching.Ifthetransformerisdisconnectedfromthecircuit,thentheoperatingpointisontheaxisatthepointofzerocurrentonthemag-netizingcharacteristic;rinFig.2.Therefore,theworstcasescenarioofinrushcurrentshappenswiththeinitialfluxofrandatthemomentofzerovoltageswitching,withapolarityofvoltagewhichbuildsuptheflux(inthiscasepositive).Ontheotherhand,phase-hopisatransientthathappenswhenthetrans-formerismagnetizedhigherthanr.Forexample,inthecaseofafaultattheprimaryterminalsorwhenvoltagesagshappen,the3508IEEETRANSACTIONSONPOWERELECTRONICS,VOL.31,NO.5,MAY2016Fig.3.Phase-hopcausedbythenormaloperationofaUPSsystem.(a)Normaloperatingcondition.Utilitypowerison.(b)Nopowerisdeliveredtotheload.(c)PowerissuppliedbytheUPS.terminalcurrentwillnotjumptozeroandwillkeepcirculatingintheprimarywinding.Therefore,magneticfluxwillbetrappedinthecoreforaperiodoftimethatdependsonthetimeconstant(totalresistanceandinductanceofthesystem).Theoperatingpointinsomecasesmaystayonthesaturatedsectionofthemagnetizingcurve;forexample,sinFig.2.Inthiscondition,theworstcasescenarioalsohappensatthemomentofzerovolt-ageswitchingwiththepolarityofvoltagewhichbuildsupflux.Therefore,phase-hopandtheworstcaseofinrushcurrent(withresidualflux)aresimilarinnature,butthephase-hopconditionyieldshighercurrentssincethecoreisatahigherinitialflux.Toobservethephase-hopcurrent,twoconsecutivesemicyclesofvoltageseeFig.1(a)isappliedtothetransformerontheprimarysidewhenthesecondarysideisopencircuitedandthetransformerisdemagnetized.Thefirsthalfcycleofvoltageimpressesahighlevelfluxinthemagneticcore.Theworstcaseofphase-hopoccurswhenthereisa0.5cycledelaybetweentwoconsecutivevoltagesemicyclesofthesamepolarity3.Ifthereislongerdelaythana0.5cycle,theresidualfluxdecreases.Therefore,allphase-hopexperimentsandsimulationsinthispaperareperformedbasedonahalfcycledelaytoassuretheworstpossiblecase.Severaloperatingconditionsofelectroniccircuitscreatephase-hopcurrents.Phase-hopcanhappenbynotching,voltagesags,maloperationofUPSsystems,andvoltageinterruptionsinthenetwork.Thesephenomenacanbeclassifiedintotwomaincategories:1)phase-hopcausedbyaparallelswitchingaction;2)phase-hopcausedbyaseriesswitchingaction.1)SeriesSwitching:Asdiscussedin3,themaloperationofofflineUPSsystemsmaycausephase-hopcurrents.ThisphenomenonhappensbecauseoftheseriesdisconnectionoftheUPSsystemattheterminalofthetransformers(seeFig.3).Whenthemainsourceisnotavailable,theUPSisswitchedontofeedtheload.ThetimedelaybetweendisconnectionofthemainsandconnectionoftheUPSmaycreateaphase-hopphenomenon.Therefore,thisoperationismodeledbyseriesswitching.Aninterruptionisdefinedasacompletelossofvoltageforaspecificperiodoftime22.Thistimeperiodcouldbemo-mentary(from0.5to180cycles),temporary(from180to3600cycles),orsustained(morethan3600cycles)ina60Hzsystem.Possiblereasonsforinterruptionaretheopeningofalineastheresultofpowersystemfaults,equipmentfailures,andcontrolsystemsmalfunctions23.TheyallcanberepresentedwithaseriesswitchingasillustratedinFig.3.TheonlydifferencebetweeninterruptionandmalfunctionofUPSscenariosisthatFig.4.Phase-hopcausedbyashortcircuit.(a)Normaloperatingcondition.Theutilitypowerison.(b)Shortcircuit.(c)Shortcircuitisclearedandpowerisback.TABLEIINFORMATIONOFTHETOROIDALTRANSFORMERSCoreDimensions(mm)WindingCharacteristicsInnerOuterHeightPrimarySecondaryWireDiameterDiameterTurnsTurnsGauge85.7149.250.819619613intheinterruptiontheutilitypowerisrecoveredinsteadofUPSreconnection.2)ParallelSwitching:Voltagesagsaredefinedasapercent-agemagnitudevalueintermsofregularvoltagelevel23.Theyareoftentheresultoffaults,typicallysingleline-to-groundfault(SLG),inpowersystems.Therefore,thisphenomenoncouldbesimulatedwiththeswitchingofaparallelresistancewiththeterminalsofthetransformer.Thisresistancerepresentsthefaultimpedance(seeFig.4).Notchingisadisturbanceofoppositepolaritytothevoltagewaveformwhichisfrequentlycausedbymalfunctionsoftheelectronicswitchesorpowerconditioners24.Voltagenotch-ingisprimarilycausedbythree-phaserectifiersorconverters.Voltagenotcheshappenwhenthecurrentcommutatesfromonephasetoanother.Subsequently,amomentaryshortcircuitbe-tweentwophaseswilloccurduringthisperiod23.Theworstcaseiswhenthefaultresistanceisnegligible.Also,itshouldbenotedthatthisphenomenonlastatmostforhalfacycle.Therefore,notchingisaparticularsituationofthevoltagesagcasewhenRfisequalzeroandcanberepresentedwithparallelswitchingasshowninFig.4.III.EFFECTOFAIR-GAPANDLOW-PERMEABILITYMATERIALONTHEELECTROMAGNETICBEHAVIOROFTRANSFORMERSInthispaper,severaltoroidaltransformersarestudiedforthemitigationofinrushandphase-hopcurrents.Alltransformersaregeometricallysimilar,single-phase,samevoltage(120V),andhave1kVAratedpower.Thecoredimensionsandwind-ingscharacteristicsareshowninTableI.Thefirstprototype(T1)showninFig.5doesnothaveanair-gapandiswoundonanannealedironcore.PrototypesT2toT7arewoundonannealedironcoresandhave2,4,8,16,32,and64miltotalair-gaps(=2g),respectively.Thelasttransformer(T8)isman-ufacturedonanunannealedcoreofthesamematerial(M4),thushavingadifferentmagneticpermeabilitythantherestsincethemanufacturingstresseshavenotbeenrelieved.ToroidaltransformershaveverysharphysteresiscurveswhencomparedtostandardtransformersbecausetheydonothaveDOGANetal.:INVESTIGATIONOFTRANSFORMER-BASEDSOLUTIONSFORTHEREDUCTIONOFINRUSHANDPHASE-HOPCURRENTS3509Fig.5.Toroidaltransformerunderstudy(T1).Fig.6.Hysteresischaracteristicofuncutandallgappedtransformersobtainedbymeasurements.air-gapsinthecore.Thesharphysteresiscurveresultsinlargeresidualfluxbecausethemagnetizingcurvecrossesatahighervalueoffluxwhenthecurrentiszero.Theuseofair-gapsandlow-permeabilitymaterialschangethischaracteristicasdemon-stratedinthefollowingsections.A.Air-GapEffectontheMagnetizingCharacteristicsofTransformersOpen-circuittestsareperformedontransformerswithdiffer-entair-gaplengthsaccordingtotheIEEEStandardC57.12.91-199525.Hence,theopen-circuittestsareperformedwith120Vappliedtotheprimaryterminal.Theprimarycurrentandsecondaryvoltagearemeasured.Thelinkagefluxisde-rivedfromtheintegrationofthesecondaryvoltage26.Asaresult,thehysteresiscurvesforuncutandallsixgappedtrans-formersareshowninFig.6.Themeasuredresidualfluxes(fluxcorrespondingtozeroterminalcurrent)foreachtransformerarepresentedinTableII(seeFig.6aswell).Measurementsdemonstratedramaticchangesinthemagneticbehaviorofthetransformerswithdifferentair-gapslengths.OnecanobservethatthefluxfollowsdifferentmagnetizingpathsdependingonTABLEIIMEASUREDRESIDUALFLUXFORTRANSFORMERSTransformerresidualmWbUncut(T1)5412mil(T2)574mil(T3)518mil(T4)4516mil(T5)2832mil(T6)1964mil(T7)17Fig.7.Dimensionsandthemagneticequivalentcircuitofthecorewithair-gap.Notethatgishalfofthetotalair-gap.Tocreateair-gapsintheironcore,transformermanufacturersdiametricallycutthecoreintotwohalves.Thenthesurfacesaregrinded,burnished,andkeptapartwithMylarorepoxyfiberglasslaminatesgluedandbandedtokeeptheseparationdistancewellcontrolled.Finally,thetransformeriswoundasusual.Fig.8.Hysteresischaracteristic(L)oftransformerironcorerepresentedbytwoconstantslopes;theeffectofthegap(Lg)onthehysteresiscurveisshown.thelengthoftheair-gap.Mostimportantly,theresidualfluxreducesnoticeably.Therefore,foratransformerwithanair-gap,whentheterminalcurrenttendstozeroatthemomentofdisconnectionfromthesource,thefluxalsotendstozero,andthecorewillbedemagnetized.Theoretically,alargergapresultsinalowerslope(seeFig.6).ThereasoncanbeexplainedfromthereluctancecircuitofthetoroidaltransformershowninFig.7andapiecewiselinearapproximationofthehysteresiscurve(seeFig.8).Accordingtotheprincipleofdualitybetweenmagneticandequivalentelectricalcircuits,theair-gapcanberepresentedwithaparallellinearinductancewiththenonlinearmagnetizingbranchasshowninFig.727.Theparallelconnectionofthelinearinductance(Lg),changestheslopeofthemagnetizingcurve(L)thatisshowninFig.8.Accordingtothisfigure,the3510IEEETRANSACTIONSONPOWERELECTRONICS,VOL.31,NO.5,MAY2016Fig.9.Magneticfluxlinesfora64milgaptransformerobtainedfrom2-DFEMsimulations.followingexpressionscanbewrittenfor=0:0=Lm1(Ic)+r1Ic=r1/Lm1(1)0=Lm2(Ic)+r2Ic=r2/Lm2(2)whereIcisthecoercivecurrent28.Therefore,wegetr2=Lm2Lm1r1.(3)Themagnetizinginductanceofthetransformerwithair-gap(Lm2)issmallerthanthemagnetizinginductanceoftheuncuttransformer(Lm1).Therefore,theair-gapdecreasestheresidualfluxfromr1tor2accordingto(3).NotefromFig.7that,Lm2=Lm1|Lg,hencesubstitutingLm2in(3)yieldsr2=LgLm1+Lgr1.(4)Neglectingthefringingeffectsandassumingauniformmag-neticfield(seeFig.9)Rfracturg1=g0(ODID)2HT(5)Rfracturg1=2g0(ODID)HT(6)Lg1=Lg2=N2Rfracturg1=N20(ODID)HT2g(7)whereLg1andLg2aretheequivalentmagnetizinginductancesoftheair-gap,Nisthenumberofturnsoftheenergizedwinding,gishalfofthetotalairgap(i.e.,forthe2miltransformer,g=1mil),andRfracturg1isthereluctanceofoneofair-gaps.ParametersHT,ID,OD,andlmstandforheight,innerdiameter,outerdiameter,andthemeanlengthofthefluxpathinthecore,respectively(seeFig.7).Also,0isthepermeabilityofvacuum4107H/m,andristherelativepermeabilityoftheironcoremeasuredas4000attheoperatingvoltage(120V).Theinductanceofthetotalair-gapisLg=Lg1|Lg2=Lg12=N20(ODID)HT4g.(8)Therefore,wehaver2=N20(ODID)HT4gLm1+N20(ODID)HTr1(9)whereLm1iscalculatedfromtheopen-circuittestontheuncutcoretransformer29asLm1=(VOCRsIOC)22fQOC(10)whereVOC,IOCarethermsv