飽和鐵心型超導(dǎo)限流器控制系統(tǒng)建模與仿真

飽和鐵心型超導(dǎo)限流器控制系統(tǒng)建模與仿真ControlSystemModelingandSimulationofSuperconductingCurrentLimiterwithSaturatedIron51015202530CoreAbstractThispaperpresentsabasicstructureofsuperconductingcurrentlimiterSFCLwithsaturatedironcoreandcomparestheadvantagesanddisadvantagesofseveralkindsofSFCLOnthisbasistheworkingprincipleofSFCLwithsaturatedironcoreisanalyzedandadynamicsystemmathematicalmodelofthistypeofSFCLisestablishedSimulationresultsshowthattheSFCLwithsaturatedironcorecanlimittheshortcircuitfaultcurrentquicklyandeffectivelyInthispaperacontrolsystemmodelwithinputofDCbiascurrentandacsupplyvoltageoutputofacimpedanceofSFCLispresentedThroughsimulationitshowsthatwhenshortcircuitfaultoccursthentheDCbiascurrentiscutofftheacimpedanceofSFCLincreasesgraduallyatlasturnintoasteadystateKeywordssystemmodelingSFCLsaturatedironcoredynamiccontrolsystemmodelacimpendance0IntroductionWiththelevelofshort-circuitcurrentofpowersystemgraduallyincreasestheeffectivelimitingshort-circuitcurrenthasbecomeanurgentproblemtobesolvedFortraditionallimitingmeasuresthoughitcouldbesomeresolutionoftheshort-circuitcurrentinhibitionbutwithoutexceptionitwillbringanegativeimpactontheoperationofthepowergridThesuperconductingfaultcurrentlimiterwithsaturatedironcorekeepsnotonlythemicro-impedancelowpowerlossintheperformanceduringnormaloperationbutalsowhenshortcircuitfaultoccursinthepowergriditcouldquicklyturnintohighimpedancetolimitfaultcurrentItcanreducesystemprotectionequipmentspecificationstoimprovetheexistingpowergridcapacitybringhighersystemreliabilityandpowerqualitywithevenbroaderapplications1TheAdvantagesandDisadvantagesoftheTypesofSuperconductingfaultcurrentlimiter11ResistiveSFCLResistance-typeSFCLwithsimplestructureshortresponsetimelowcurrentoverload3540coefficientlowpressuredropundernormaloperationetcisclosetopracticaluseintheworldHoweverthetotalcurrentflowsthroughthesuperconductingcoilduringnormaloperationHigh-currentsuperconductingcablesarerequiredwithlowAClossesAtpresenttheheavycurrentsuperconductingcablesespecially4-5kAabovearedifficulttomanufactureforthemechanicalandthermalproblemsThereforeintheresistance-typeSFCLtheratedcurrentisnotmorethan2kAMeanwhiletheresistance-typeSFCLofsuperconductingrecoverytimeistoolongtocopewiththeimplementationoffastre-closing-1-12Induction-typeSFCLInduction-typeSFCLwithoutcurrentleadsofsuperconductingcoilswithsimplestructurelessheatlosshasbothfunctionsoftransformerandcurrentlimiterHoweverwhenthequenching45ofoverallsuperconductingcoilsoccursthedevicewillnotproduceover-voltageAnditrequireshigh-currentACsuperconductingcablesInadditiontheneededassemblingnon-metallicDewarisstillinresearchstage13Mixed-typeSFCLMixed-typeSFCLisusingonlythesuperconductingcableswithmuchsmallercurrentlevel5055thanthelinecurrentItbringsthatsuperconductingcablesiseasytomakethesystemismoresimpleandthereducedweightofthesuperconductorwhichgreatlyreducesthetemperaturelossAtthesametimeduetothefaultduringthesaturationitlimitsandreducesRMSvalueofvoltageandcurrentthatcausesthereducingoftheheatingofthesuperconductingcoilItisconducivetotherecoveryofthesuperconductingstateHoweverfortheadoptionofconventionaltransformerstructurethetotallossofSFCLisgreaterandtheweightisheavierInadditionahigherbreakdownvoltageisgeneratedduringthefaultcurrentoccursAndthesaturationvoltagecancausedistortionItissimilarwiththeresistance-typeSFCLthekindofSFCLtakeslongtimetorecoversoitisnotconductivetotheimplementationoffastre-closing6014MagneticshieldingtypeSFCLFormagneticshieldingtypeSFCLtherequiredamountofhigh-temperaturesuperconductorsistheleastofavarietyofSFCLbecausesuperconductingshieldingcylinderislow-lossnotrequiringcurrentleadsandwithsosmallheatloadthatyoucanuseGMrefrigeratortocoolitInadditionthestraymagneticfieldoutsideissmallHowevertheweightofequipmentisheavyitsweightismoreheavythanresistance-typeSFCLinanorderofmagnitudefaultrecoverytime65islongeritneedstomaketwosetsofequipmentforrapidre-closingalongwithaswitchAtthesametimethetransientover-voltageisgeneratedduringcurrentlimitingAndthedevelopmentofashieldingcylinderhassomedifficulties15Non-inductivetypeSFCLThemainadvantagesofnon-inductivetypeSFCLareshortresponsetimeoffault70currentaboutthesub-microsecondlevellowimpedanceduringnormaloperationhalfoftheratedcurrentflowsthroughtriggercoilandthelimitingcoilindividuallyrequirementsforsuperconductingcableoftriggercoilarebelowtheresistance-typeSFCLsimplestructureButthedevicesrecoverytimeisaboutafewsecondsnotsuitableforrapidre-closing7516Bridge-typeSFCLBridge-typeSFCLsmainadvantagesarebelowIn05secondsitcouldrecoveryfromthesecondfailurewithouttheneedforthesecondsetofsystemitissuitableforre-closingBecausesuperconductingcoilisaDCcoiltherearenodifficultproblemofhigh-currentsuperconductingcableandnon-metallicDewarFortheabsenceofironcoreandcopperwindingpartsthetotalweightislightandlowcostDuringnormaloperationperiodthedevicedoesnotcausevoltage80dropharmonicandtransientThereducedrateoffaultcurrentcanbeadjustedHoweverduringnormaloperationtheamplitudeofsuperconductingcoilcurrentismorethantheDClineandsothecurrentlossinlowtemperaturefromleadsislargeAlsothepowerdiodebridgeandthebiassupplyarerequired-2-8517SaturatedcoretypeSFCLSaturatedcoretypeSFCLhasmanyadvantagesSuperconductingcoilduringthefaultcurrentlimitingdoesnotquenchItiscapableofauto-startmanytimessuitableformultiplere-closingoperationsSuperconductingcoilisaDCcoilsotheneededDCsuperconductingcablesiseasiertomanufacturethemetalDewaralsocanbeusedthevacuumcontainersforelectromagneticshieldingaremadeofaluminumalloyHoweverthecoreandconventional9095100105110115windingsaredesignedaccordingtotwotimesthesizeofthefaultpowersoitismoreheavyequipmentIroncoreinsaturationduringnormaloperationthereissignificantleakagemagneticfieldItwouldcausesignificantvoltageharmonicsduetorepeatchangingfromthecoresaturationtode-saturation[1-6]2TheBasicStructureofSuperconductingFaultCurrentlimiterwithSaturatedIronCoreSFCLswithdiverseprincipleshavebeenproposedabovesuchasresistiveinductivemagneticshieldingandsaturatedcoreSFCLsetc[7–9]MostofthemarebasedontheprincipleofthetransitionfromthesuperconductingtonormalconductingstateSNtransitionHoweverthesaturatedcoreHTSFCLachievesthepurposeoflimitingshortcurrentnotbyusingtheSNtransitionbutbythenonlinearpermeabilityofthemagneticcorewhichdoesnothavetheproblemofrecoverytimeSuperconductingcoilduringthefaultcurrentlimitingdoesnotquenchAtthesametimethehightemperaturesuperconductingcoilsaresuppliedbyadcsourceHenceitdoesnothaveacpowerlossForthiskindofSFCLitsstructureisshowninFigure1[1]ItconsistsofapairofsameironcoresEachcorehasanAClimitingwindingAsuperconductingwindingissuppliedbyadcsourcecontrolledbyaswitchIGBTorMOSFETTwoACwindingsareinserieswithoppositepolaritieswhiletheDCsuperconductingcoilisimposedbyDCbiascurrentUnderthenormalconditiontheDCbiascurrentmakecoressaturatedandtheimpedanceofACcoilsdecreasesgreatlyWhenfaultcurrentoccursshortcircuitcurrentcouldbedetectedintimeandtheIGBTswitchinDCcircuitiscontrolledoffwhichmakestheACcoilstobede-saturationwiththeinductanceofACcoilsincreasinggreatlyandthefaultcurrentcouldbelimited[1][2][3]ThiskindofSFCLisintheuseofthenonlinearchangesofmagneticpermeabilityofironcoretorestrictshort-circuitingfaultcurrentAndthesaturatedstatesofACcoilsmaketheimpedancegreatlylessthantheresistanceoftheratedloadAndtheIGBTswitchisconvenientlyandquicklycontrolledtochangetheimpedanceofACcoilsfromthecoresaturationtode-saturationwhichissuitableforre-closingButinevitablythesuperconductingcoilwillinduceanundesirablehighvoltageduringtheswitchoffwhichmaydestroythedccoilThisproblemhasbeendiscussedinauthorsanotherpaper[1]Inthispaperitdoesnotrepeatanymore-3-120Figure1TheStructureofSFCLwithSaturatedIronCore3WorkingPrincipleofSuperconductingFaultCurrentlimiterwithSaturatedIronCoreTheΨ-IcurveofbothacwindingsofSFCLcanbedescribedapproximatelybyfivelinear125130135segmentswithdifferentslopesasshowninFig2Curve1illustratesthemagnetizationcurveofsinglecorewithoutthedcbiaswhereitshowsabasiccharacterofaninductancewithironcoreCurves2and3plotthemagnetizationcurvesoftwocoresrespectivelywhenadcbiascurrentisimposedCurve4istheΨ-IcurveofthesaturatedcoreSFCLwhichisachievedbysummationofcurves2and3WhentheDCcurrentequalszeroidc0whiletheIGBTturnsofffromcurve1wecanseethattheACcurrentiacislimitedbythebothACwindingswithironcoreWhenthefluxΨΨ1theironcoreisnotsaturatedtheinductanceoftheACcoilingisrelativelylargeAndthetotalinductanceofsuperconductingfaultcurrentlimiterisLlimiter2dΨdtsoLlimiter2tgβ1WhentheACcurrentiacincreasesuntilΨ?Ψ1theironcoreissaturatedtheinductanceisrelativelysmallandLlimiter2tgβ2tgβ1tgβ2WhentheDCcurrentdoesnotequalzeroidc?0whiletheIGBTturnsontheinductanceofthesingle-phasecorecouldbeacquiredfromthecurve-4asfollowsLlimiter2tg2IIaLlimitertg1tg2IaIIb1Llimiter2tg2IIbWhensystemisinnormaloperationwithdcbiascurrentitworksinb-csectionofcurve4140145thesuperconductingDCcurrentmakesthetwocoresdeepsaturationandtheACcurrentcantmaketheACwindingde-saturationasshowninfig3AndtheimpedanceofSFCLturnstobeverysmallWhenACfaultcurrentoccursitworksina-bsectionanda-bsectiontheACwindingcurrentincreasesrapidlyasuddenincreaseofshortcircuitcurrentoftheACwindingmakesthetwocoresde-saturationinturnthefaultcurrentlimiterwithlargetransientimpedanceislimitingthefaultcurrentAtthistimethecontrolsystemdetectsthefaultACcurrentandturnsofftheIGBTimmediatelyItmeansthattheSFCLwithnoDCbiascurrentwouldbeequivalenttothewindingswithironcorewhichhaslargeACinductanceandcouldeffectivelimittheACfaultcurrentasshowninfig4[4][7][8][9]-4-150Figure2TheMagnetizationCurveofSingle-phaseSFCLwithSaturatedIronCoreFigure3TheWorkingPointofSingle-phaseSFCLwithDCBiasCurrentunderNormalWorkingConditions155Figure4TheWorkingPointofSingle-phaseSFCLwithoutDCBiasCurrentunderFaultWorkingConditions4MathematicalModelofSuperconductingFaultCurrentLimiterwithSaturatedIronCoreUndernormalworkingconditiontheequivalentcircuitofpowergridisshowninFigure5160165TheSFCLsironcoreisoversaturatedandtheimpedanceoftheACcoilsissmallItisalmostequivalenttotransmissionlineresistanceandhaslittleinfluenceonthegridHoweverwhenshort-circuitfaultoccursR0theIGBTturnsoffandtheironcoreofthelimiterisnotsaturatedanymoreTheimpedanceoftheACcoilsincreasesrapidlyandithasaprotectiveeffectonthegridandtheequivalentcircuitisshowninFigure6Single-phasesaturatedcoretypeSFCLhastwocoreshereinordertofacilitatethecalculationfirstlyconsideringacoreofhalf-wavecurrentlimiteritisonlyahalfcycleoffaultcurrentlimitingWeconsiderasinglephasehalf-wavecircuitwhichisshowninthefigure7Fromwhichwecangettheequation-5-UtLdiacddtdt2170whereutUsinωtisthepowersupplyvoltageListheinductanceforthetransformerandtransmissionlineristhetransmissionlineresistanceiacistheinstantaneousvalueofACcurrentNacisthenumberofACcoilsΦisthefluxofACcoilsAccordingtoAmperecircuitaltheoremwegetHlNaciacNdcidc3175whereHisthemagneticfielddensityofironcorelisthemagneticcircuitlengthoftheironcoreNdcstandsfortheDCcoilturnsidcstandsfortheinstantaneousDCcoilcurrentTotakeΦBSandBμhfBHintotheformula2whereSisthecross-sectionalareaoftheironcoreHfBisthemagnetizationcharacteristicB-HcurveandμfBstandsforthepermeabilityweget180didBdtdtdiacdBdtdtsimultaneousequations3thereareequations4diacdHdtdtHlNaciacNdcidc5Theaboveequationsdescribethesingle-phasehalf-wavesaturationmathematicalmodelofsaturatedcore-typeSFCLTheSFCLonlylimitsthecurrentinanegativehalf-cycleThefault185190currentisstillverylargeinapositivehalf-cycleBecauseACcurrenthastwodirectionsonedirectionmakesthemagneticfieldde-saturationanotherdirectionmakesthesaturationmagneticfieldfurtherdeepAfull-wavelimitershouldbeadoptedintheactualdesignAscanbeseenfromfigure8itconsistsoftwocoilsinserieswithoppositepolarityThemagneticfieldinthecentralcylindergeneratedbythetwocoilsinseriescancelsouteachotherThederivationofmathematicalmodelsissimilartotheaboveprocessThismathematicalmodelonthewholeisgivendirectlyasfollowsForthesinglephasefull-wave-typeSFCLwithsaturatedironcoresupposingthatthemagneticfieldofitsleftironcoreisHLandwhichofitsrightironcoreisHRlisthelengthofironcoremagneticcircuitNacisthenumberofACcoilturnsNdcisthenumberofDCcoilturns195iacistheACcoilcurrentidcisthebiascurrentofDCbiascoilgridvoltageisUtheratedloadisRtheequivalentinductanceoftransformersandtransmissionlinesisLtheequivalentresistanceoftransmissionlineisrRelatedequationsareHLfBLHRRSdBLBRdiacdtHLlNaciacNdcidcHRacacdcdc-6-6UtLLimiterrR200Figure5TheEquivalentCircuitofPowerGridunderNormalWorkingConditionFigure6TheEquivalentCircuitofPowerGridunderFaultCondition205Figure7Figure8TheSinglePhaseHalf-waveTheSinglePhaseFull-wave5TheMathematicalModelofTheControlSystemofSaturatedIronCore-typeSuperconductingFaultCurrentLimiter23210theACvoltageuandthesuperconductingbiasDCcurrentidcasthesysteminputandtheZacastheoutputUsuallytheACvoltageuisutUsinωtandchangingtheidcwecouldchangetheACimpedanceZacofSFCLWithrespecttothecircuitweknow-7-ZacUlimiterTIac1t21t21t21t2TT7Soasfollowswewillbuildstateequationsandoutputequationsaboutcontrolsystemof215SFCLAccordingtotheequation67werewritethemas2T1tiacdtLetsdefinestatevariablexiacandcontrolvariableu1uu2idcyZacandtakethemintoformula8wegetx1LR1t21t2T89220AccordingtoLetsdefineRl1NaciacNdcidcl1NaciacNdcidcFxu2NacSLNacNacSNacNacxNdcu2LNacxNdcu2llNacSNdcNacSNdcLNacxNdcu2LNacxNdcu2llwecouldrewrite9as225rR1gxu22221t1t2xdt106TheMATLABSimulationofMathematicalModelofSaturated-8-IronCore-typeSuperconductingFaultCurrentLimiterIntheMatlabplatformthe220V100AsaturatedcoretypeSFCLwassimulatedwithtwostatesofnormalstateR?0andshortcircuitfaultstateR0230ThemodelparametersofthesaturatedironcoretypeSFCLareasfollowspowervoltageuis220VsuperconductingDCcurrentidcis100ApowergridloadresistanceRis2Ωthetransmissionlineresistanceris005Ωmagneticpathlengthofironcorelis136mironcorecross-sectionalareaSis001254m2thenumberofACwindingturnsNdcis18ACinductanceLis686×10-5HDCwindingturnsNdcis10023561WaveformofFaultCurrentwithoutSFCLOnthisbasisasimulationofshort-circuitexperimentispresentedWhentheSFCLisnotusedthepowergridinnormalworkingconditionsduetotheexistenceofthepowersystemloadthevoltageandcurrentcanbekeptatalowerlevelWhenafaultoccurspowersystemloadquicklyreducestozerothenonlythepowertransmissionlineimpedancepresentswhichwill240leadtoarapidincreaseinthelevelofgridcurrentthatwillbringdamagetothepowerequipmentWhenthegridshort-circuitfaultoccursintimet50msthegridcurrentwaveformisshowninFigure9Figure9ShortCircuitCurrentWaveformwithoutSFCL245AscanbeseenfromFigure9whenthereisnocurrentlimiterthepowergridcurrentofashortcircuitfaultstateincreasedbynearlymanytimesthantheratedcurrentvalueexcessiveshort-circuitcurrentcandamageelectricalequipmentthereforeaddingcurrentlimiterisnecessary25062WaveformofFaultCurrentwithSFCLIfSFCLisadoptedundernormalworkingconditionsSFCLshowsverylowimpedanceithadnoeffectonthebasicoperationofthegridWhentheshort-circuitfaultoccurstheDCcurrentiscutoffthesaturatedcoretypeSFCLcanquicklyturnintoahighimpedanceandlimittheshort-circuitcurrentWhenthegridshort-circuitfaultoccursintimet50msthegridcurrentwaveformisshown255inFigure10andtheimpedanceofSFCLwaveformshowninFigure11-9-Figure10ShortCircuitCurrentWaveformwithSFCLFigure11ImpedanceofSFCLWaveformwithSFCL2607ThesimulationshowsthatthiskindofSFCLhasanobviouscurrentlimitingeffectiveConclusionandOutlookThroughsimulationwecanseethatsaturatedcore-typesuperconductingfaultcurrentlimitercanbeeffectiveinlimitingshort-circuitfaultcurrentofgridThiskindofcurrentlimitercansolvetheproblemofinsufficientbreakingcapacityofbreakerandreducetheassociatedtechnology265270targetsinelectricitymachineryhotetcaswellasreducethecostsandimprovedynamicstabilityofpowersystemAccordingtothismodelinBeijingInnopowersuperconductorcableCoLtdsuccessfullydevelopedtheexperimentalprototypeofathree-phase380V50AwiththeBi2223AgstripOnAprilthe35kV90MVAmajorsaturatedcoretypeSFCLishangingonPuJitransformersubstationinKunmingYunnanandrunningsuccessfullyItscontrolsystemwasdevelopedbyTianjinUniversityInordertofurtherimproveitsreliabilityimprovesystemoperationitisnecessarytoestablishitsdynamicsystemmodelAlsotheestablishmentoffaultdiagnosismodelandafaultdiagnosissystemisfurtherneededtowork-10-AcknowledgementsOptionalThankstoSpecializedResearchFundfortheDoctoralProgramofHigherEducationof275280285290295ChinaGrantNo003211References[1]HeYiLiChang-binWuAi-guoXinYingExperimentalofOver-voltageSuppressioninaHTSThree-phaseSaturatedCoreFaultCurrentLimiterbyaZnOVaristor[J]HighVoltageEngineering339154-158[2]HeYiWuAiguoXinYingRapidPatternRecognitionofFaultCurrentforHTSThreePhaseSaturatedIronCoreFaultCurrentLimiter[J]TransactionsOfChinaElectrotechnicalSociety24181-87[3]HeYiWuAi-guoXinYingResearchofrapidpatternrecognitionoffaultcurrentbasedonsupportvectormachineforHTSthree-phasesaturatedco