rugged,egenerationcurrguidelines2PowerSystemNetworkDescriptionbinecanenterself-excitationoperation.Thevoltageandfre-quencyduringoff-gridoperationaredeterminedbythebalancebetweenthesystemsreactiveandrealpower.Downloaded28Mar2008to0.RedistributionsubjecttoASMElicenseorcopyright；see/terms/Terms_Use.cfmWeinvestigateaverysimplepowersystemnetworkconsistingofone1.5MW,fixed-speedwindturbinewithaninductiongen-eratorconnectedtoalinefeederviaatransformerH208492MVA,3phase,60Hz,690V/12kVH20850.Thelow-speedshaftoperatesat22.5rpm,andthegeneratorrotorspeedis1200rpmatitssyn-chronousspeed.AdiagramrepresentingthissystemisshowninFig.1.Thepowersystemcomponentsanalyzedincludethefollowing:AninfinitebusandalonglineconnectingthewindturbinetothesubstationAtransformeratthepadmountOnepotentialproblemarisingfromself-excitationisthesafetyaspect.Becausethegeneratorisstillgeneratingvoltage,itmaycompromisethesafetyofthepersonnelinspectingorrepairingthelineorgenerator.Anotherpotentialproblemisthatthegeneratorsoperatingvoltageandfrequencymayvary.Thus,ifsensitiveequipmentisconnectedtothegeneratorduringself-excitation,thatequipmentmaybedamagedbyover/undervoltageandover/underfrequencyoperation.Inspiteofthedisadvantagesofoper-atingtheinductiongeneratorinself-excitation,somepeopleusethismodefordynamicbrakingtohelpcontroltherotorspeedduringanemergencysuchasagridlosscondition.WiththeproperchoiceofcapacitanceandresistorloadH20849todumptheenergyfromthewindturbineH20850,self-excitationcanbeusedtomaintainthewindturbineatasafeoperatingspeedduringgridlossandme-chanicalbrakemalfunctions.Theequationsgoverningthesystemcanbesimplifiedbylook-ingattheimpedanceoradmittanceoftheinductionmachine.ToContributedbytheSolarEnergyDivisionofTHEAMERICANSOCIETYOFMECHANI-CALENGINEERSforpublicationintheASMEJOURNALOFSOLARENERGYENGINEERING.Manuscriptreceived:February28,2005；revisedreceived:July22,2005.AssociateEditor:DaleBerg.JournalofSolarEnergyEngineeringNOVEMBER2005,Vol.127/581Copyright2005byASMEE.MuljadiC.P.ButterfieldNationalRenewableEnergyLaboratory,Golden,Colorado80401H.RomanowitzOakCreekEnergySystemsInc.,Mojave,California93501R.YingerSouthernCaliforniaEdison,Rosemead,California91770Self-ExcitationWindPowerTraditionalwindturbinestheyareinexpensive,tiongeneratorsrequirisoftenused.Becausethecapacitorcompensationamongthewindturbine,tantaspectsofwindcontentintheoutputenaandgivessomeH20851DOI:10.1115/1.20475901IntroductionManyoftodaysoperatingwindturbineshavefixedspeedin-ductiongeneratorsthatareveryreliable,rugged,andlowcost.Duringnormaloperation,aninductionmachinerequiresreactivepowerfromthegridatalltimes.Thus,thegeneralpracticeistocompensatereactivepowerlocallyatthewindturbineandatthepointofcommoncouplingwherethewindfarminterfaceswiththeoutsideworld.Themostcommonlyusedreactivepowercom-pensationiscapacitorcompensation.Itisstatic,lowcost,andreadilyavailableindifferentsizes.Differentsizesofcapacitorsaregenerallyneededfordifferentlevelsofgeneration.Abankofparallelcapacitorsisswitchedinandouttoadjustthelevelofcompensation.Withpropercompensation,thepowerfactorofthewindturbinecanbeimprovedsignificantly,thusimprovingover-allefficiencyandvoltageregulation.Ontheotherhand,insuffi-cientreactivepowercompensationcanleadtovoltagecollapseandinstabilityofthepowersystem,especiallyinaweakgridenvironment.Althoughreactivepowercompensationcanbebeneficialtotheoveralloperationofwindturbines,weshouldbesurethecompen-sationisthepropersizeandprovidespropercontrol.Twoimpor-tantaspectsofcapacitorcompensation,self-excitationH208511,2H20852andharmonicsH208513,4H20852,arethesubjectsofthispaper.InSec.2,wedescribethepowersystemnetwork；inSec.3,wediscusstheself-excitationinafixedspeedwindturbine；andinSec.4,wediscussharmonics.Finally,ourconclusionsarepre-sentedinSec.5.andHarmonicsinGenerationarecommonlyequippedwithinductiongeneratorsbecauseandrequireverylittlemaintenance.Unfortunately,induc-reactivepowerfromthegridtooperate；capacitorcompensationthelevelofrequiredreactivepowervarieswiththeoutputpower,mustbeadjustedastheoutputpowervaries.Theinteractionsthepowernetwork,andthecapacitorcompensationareimpor-thatmayresultinself-excitationandhigherharmonicent.Thispaperexaminesthefactorsthatcontrolthesephenom-onhowtheycanbecontrolledoreliminated.H20852Capacitorsconnectedinthelowvoltagesideofthetrans-formerAninductiongeneratorFortheself-excitation,wefocusontheturbineandthecapaci-torcompensationonlyH20849therighthalfofFig.1H20850.Forharmonicanalysis,weconsidertheentirenetworkshowninFig.1.3Self-Excitation3.1TheNatureofSelf-ExcitationinanInductionGenerator.Self-excitationisaresultoftheinteractionsamongtheinductiongenerator,capacitorcompensation,electricalload,andmagneticsaturation.Thissectioninvestigatestheself-excitationprocessinanoff-gridinductiongenerator；knowingthelimitsandtheboundariesofself-excitationoperationwillhelpustoeitherutilizeortoavoidself-excitation.Fixedcapacitorsarethemostcommonlyusedmethodofreac-tivepowercompensationinafixed-speedwindturbine.Aninduc-tiongeneratoralonecannotgenerateitsownreactivepower；itrequiresreactivepowerfromthegridtooperatenormally,andthegriddictatesthevoltageandfrequencyoftheinductiongenerator.Althoughself-excitationdoesnotoccurduringnormalgrid-connectedoperation,itcanoccurduringoff-gridoperation.Forexample,ifawindturbineoperatinginnormalmodebecomesdisconnectedfromthepowerlineduetoasuddenfaultordistur-banceinthelinefeeder,thecapacitorsconnectedtotheinductiongeneratorwillprovidereactivepowercompensation,andthetur-Downloaded28Mar2008to0.RedistributionsubjecttoASMElicenseorcopyright；see/terms/Terms_Use.cfmoperateinanisolatedfashion,thetotaladmittanceoftheinduc-tionmachineandtherestoftheconnectedloadmustbezero.Thevoltageofthesystemisdeterminedbythefluxandfrequencyofthesystem.Thus,itiseasiertostarttheanalysisfromanodeatoneendofthemagnetizingbranch.Notethattheterm“imped-ance”inthispaperistheconventionalimpedancedividedbythefrequency.Theterm“admittance”inthispapercorrespondstotheactualadmittancemultipliedbythefrequency.3.2Steady-StateRepresentation.Thesteady-stateanalysisisimportanttounderstandtheconditionsrequiredtosustainortodiminishself-excitation.Asexplainedabove,self-excitationcanbeagoodthingorabadthing,dependingonhowweencounterthesituation.Figure2showsanequivalentcircuitofacapacitor-compensatedinductiongenerator.Asmentionedabove,self-excitationoperationrequiresthatthebalanceofbothrealandreactivepowermustbemaintained.EquationH208491H20850givesthetotaladmittanceofthesystemshowninFig.2:YS+YMH11032+YRH11032=0,H208491H20850whereYSH11005effectiveadmittancerepresentingthestatorwinding,thecapacitor,andtheloadseenbynodeMYMH11032H11005effectiveadmittancerepresentingthemagnetizingbranchasseenbynodeM,referredtothestatorsideYRH11032H11005effectiveadmittancerepresentingtherotorwindingasseenbynodeM,referredtothestatorsideH20849Note:thesuperscript“H11032”indicatesthatthevaluesarereferredtothestatorside.H20850EquationH208491H20850canbeexpandedintotheequationsforimaginaryandrealpartsasshowninEqs.H208492H20850andH208493H20850:R1L/H9275H20849R1L/H9275H208502+L1L2+RRH11032/SH9275H20849RRH11032/SH9275H208502+LLRH110322=0H208492H20850whereFig.1ThephysicaldiagramofthesystemunderinvestigationFig.2Perphaseequivalentcircuitofaninductiongeneratorunderself-excitationmode582/Vol.127,NOVEMBER20051LMH11032+L1LH20849R1L/H9275H208502+L1L2+LLRH11032H20849RRH11032/SH9275H208502+LLRH110322=0H208493H20850R1L=RS+RLH20849H9275CRLH208502+1L1L=LLSCRLH20849H9275CRLH208502+1RSH11005statorwindingresistanceLLSH11005statorwindingleakageinductanceRRH11032H11005rotorwindingresistanceLLRH11032H11005rotorwindingleakageinductanceLMH11032H11005statorwindingresistanceSH11005operatingslipH9275H11005operatingfrequencyRLH11005loadresistanceconnectedtotheterminalsCH11005capacitorcompensationR1LandL1Laretheeffectiveresistanceandinductance,respectively,representingthestatorwindingandtheloadasseenbynodeM.Oneimportantaspectofself-excitationisthemagnetizingchar-acteristicoftheinductiongenerator.Figure3showstherelation-shipbetweenthefluxlinkageandthemagnetizinginductanceforatypicalgenerator；anincreaseinthefluxlinkagebeyondacer-tainlevelreducestheeffectivemagnetizinginductanceLMH11032.Thisgraphcanbederivedfromtheexperimentallydeterminedno-loadcharacteristicoftheinductiongenerator.Tosolvetheaboveequations,wecanfixthecapacitorH20849CH20850andtheresistiveloadH20849RLH20850valuesandthenfindtheoperatingpointsfordifferentfrequencies.FromEq.H208492H20850,wecanfindtheoperatingslipataparticularfrequency.Then,fromEq.H208493H20850,wecanfindthecorrespondingmagnetizinginductanceLMH11032,and,fromFig.3,theoperatingfluxlinkageatthisfrequency.Theprocessisrepeatedfordifferentfrequencies.Asabaseline,weconsideracapacitorwithacapacitanceof3.8mFH20849milli-faradH20850connectedtothegeneratortoproduceap-proximatelyratedVARH20849voltamperereactiveH20850compensationforfullloadgenerationH20849highwindH20850.AloadresistanceofRL=1.0H9024isusedasthebaselineload.TheslipversusrotorspeedpresentedinFig.4showsthattheslipisroughlyconstantthroughoutthespeedrangeforaconstantloadresistance.Thecapacitancedoesnotaffecttheoperatingslipforaconstantloadresistance,butahigherresistanceH20849RLhigh=lowergeneratedpowerH20850correspondstoalowerslip.ThevoltageattheterminalsoftheinductiongeneratorH20849pre-sentedinFig.5H20850showstheimpactofchangesinthecapacitanceFig.3AtypicalmagnetizationcharacteristicTransactionsoftheASMEDownloaded28Mar2008to0.RedistributionsubjecttoASMElicenseorcopyright；see/terms/Terms_Use.cfmandloadresistance.AsshowninFig.5,theloadresistancedoesnotaffecttheterminalvoltage,especiallyatthehigherrpmH20849higherfrequencyH20850,butthecapacitancehasasignificantimpactonthevoltageprofileatthegeneratorterminals.Alargercapacitanceyieldslessvoltagevariationwithrotorspeed,whileasmallercapacitanceyieldsmorevoltagevariationwithrotorspeed.AsshowninFig.6,foragivencapacitance,changingtheeffectivevalueoftheloadresistancecanmodulatethetorque-speedcharacteristic.Theseconceptsofself-excitationcanbeexploitedtoprovidedynamicbrakingforawindturbineH20849asmentionedaboveH20850topre-venttheturbinefromrunningawaywhenitlosesitsconnectiontothegrid；onesimplyneedstochoosethecorrectvaluesforcapaci-tanceH20849ahighvalueH20850andloadresistancetomatchtheturbinepoweroutput.Appropriateoperationoverarangeofwindspeedscanbeachievedbyincorporatingavariableresistanceandadjust-ingitdependingonwindspeed.3.3DynamicBehavior.Thissectionexaminesthetransientbehaviorinself-excitationoperation.Wechooseavalueof3.8mFcapacitanceandaloadresistanceof1.0H9024forthissimu-lation.Theconstantdrivingtorqueissettobe4500Nm.Notethatthewindturbineaerodynamiccharacteristicandtheturbinecon-trolsystemarenotincludedinthissimulationbecausewearemoreinterestedintheself-excitationprocessitself.Thus,wefo-Fig.4Variationofslipforatypicalself-excitedinductiongeneratorFig.5TerminalvoltageversusrotorspeedfordifferentRLandCJournalofSolarEnergyEngineeringcusontheelectricalsideoftheequations.Figure7showstimeseriesoftherotorspeedandtheelectricaloutputpower.Inthiscase,theinductiongeneratorstartsfromrest.Thespeedincreasesuntilitreachesitsratedspeed.Itisinitiallyconnectedtothegridandatt=3.1secondsH20849sH20850,thegridisdiscon-nectedandtheinductiongeneratorentersself-excitationmode.Att=6.375s,thegeneratorisreconnectedtothegrid,terminatingtheself-excitation.Therotorspeedincreasesslightlyduringself-excitation,but,eventually,thegeneratortorquematchesthedriv-ingtorqueH208494500NmH20850,andtherotorspeedisstabilized.Whenthegeneratorisreconnectedtothegridwithoutsynchronization,thereisasuddenbrieftransientinthetorqueasthegeneratorresyn-chronizeswiththegrid.Oncethisoccurs,therotorspeedsettlesatthesamespeedasbeforethegriddisconnection.Figure8H20849aH20850plotsperphasestatorvoltage.Itshowsthatthestatorvoltageisoriginallythesameasthevoltageofthegridtowhichitisconnected.Duringtheself-excitationmodeH208493.1sH11021tH110216.375sH20850,whentherotorspeedincreasesasshowninFig.7,thevoltageincreasesandthefrequencyisabithigherthan60Hz.Thevoltageandthefrequencythenreturntotheratedvalueswhentheinductiongeneratorisreconnectedtothegrid.Figure8H20849bH20850isanexpansionofFig.8H20849aH20850betweent=3.0sandt=3.5stobetterillustratethechangeinthevoltagethatoccursduringthattransient.4HarmonicAnalysis4.1SimplifiedPerPhaseHigherHarmonicsRepresentation.Inordertomodeltheharmonicbehaviorofthenetwork,wereplacethepowernetworkshowninFig.1withtheperphaseequivalentcircuitshowninFig.9H20849aH20850.Inthiscircuitrepresentation,ahigherharmonicormultipleof60HzisdenotedFig.6Thegeneratortorquevs.rotorspeedfordifferentRLandCFig.7Thegeneratoroutputpowerandrotorspeedvs.timeNOVEMBER2005,Vol.127/5834.1.2Transformer.Weconsiderathree-phasetransformerwithleakagereactanceH20849XxfH20850of6percent.Becausethemagnetiz-Downloaded28Mar2008to0.RedistributionsubjecttoASMElicenseorcopyright；see/terms/Terms_Use.cfmbyh,wherehistheintegermultipleof60Hz.Thush=5indicatesthefifthharmonicH20849300HzH20850.Forwindturbineapplications,theinductiongenerator,transformer,andcapacitorsarethreephaseandconnectedineitherWyeorDeltaconfiguration,sotheevenharmonicsandthethirdharmonicdonotexistH208515,6H20852.Thatis,onlyh=5,7,11,13,17,.,etc.exist.4.1.1InfiniteBusandLineFeeder.Theinfinitebusandthelinefeederconnectingthewindturbinetothesubstationarerep-resentedbyasimpleTheveninrepresentationofthelargerpowersystemnetwork.Thus,weconsiderasimpleRLlinerepresenta-tion.Fig.8Theterminalvoltageversusthetime.aVoltageduringself-excitation.bVoltagebeforeandduringself-excitation,andafterreconnection.Fig.9Theperphaseequivalentcircuitofthesimplifiedmodelforharmonicanalysis584/Vol.127,NOVEMBER2005ingreactanceofalargetransformerisusuallyverylargecom-paredtotheleakagereactanceH20849XMH11032H11015H11009opencircuitH20850,onlytheleakagereactanceisconsidered.Assumingtheefficiencyofthetransformerisabout98percentatfullload,andthecopperlossisequaltothecorelossH20849ageneralassumptionforanefficient,largetransformerH20850,thecopperlossandcorelossareeachapproximately1percentor0.01perunit.Withthisassumption,wecancomputethecopperlossinperunitatfullloadcurrentH20849I1FullH6018Load=1.0perunitH20850,andwecandeterminethetotalwindingresistanceoftheprimaryandsecondarywindingH20849aboutonepercentinperunitH208CapacitorCompensation.Switchedcapacitorsrepresentthecompensationofthewindturbine.Thewindturbinewecon-siderisequippedwithanadditional1.9MVARreactivepowercompensationH208491.5MVARabovethe400kVARsuppliedbythemanufacturerH20850.Thewindturbineiscompensatedatdifferentlevelsofcompensationdependingonthelevelofgeneration.Theca-pacitorisrepresentedbythecapacitanceCinserieswiththepara-siticresistanceH20849RcH20850,representingthelossesinthecapacitor.Thisresistanceisusuallyverysmallforagoodqualitycapacitor.4.1.4InductionGenerator.TheinductiongeneratorH208491.5MW,480V,60HzH20850usedforthiswindturbinecanberepre-sentedastheperphaseequivalentcircuitshownFig.9H20849aH20850.TheslipofaninductiongeneratoratanyharmonicfrequencyhcanbemodeledasSh=hH9275sH9275rhH9275sH2