Modelling-and-Analysing-the-Hydraulic-Variable-pit

ModellingandAnalysingtheHydraulicVariable-pitchMechanismforaVariable-speedWindTurbineYigangKongandZhixinWangDepartmentofElectricalEngineering,ShanghaiJiaoTongUniversity,P.R.ChinaEmail:[e-mail]31,NO.5,2007PP341–352341ABSTRACTModernwindturbinesarecontrolledinvaryingwindspeedbybladepitchingforpowercontrol.Tosatisfytherequirementoflargedrivingforcesandtorques,fastresponseandhighstiffness,hydraulictechnologyisusuallyusedinthevariable-pitchmechanism.Themodelofthehydraulicvariable-pitchmechanism(HVPM)issimplifiedbyafirst-orderinertiasysteminmostliterature.ThissimplifiedrepresentationneglectstheactualcharacteristicsoftheHVPM,anditisnotpreciseandreasonable.Therefore,HVPMmodellingisimplementedandanalyzedinthispaper.Simulationresultsshowthatconsequentlythevariable-speedwindturbineperformswellatabove-ratedwindspeeds.Keywords:modelling,variablepitch,electro-hydraulic,proportional,windturbineNOMENCLATUREPgeneratorpower(MW)τβtimeconstantλTip-speedratioωtturbinemechanicalangularvelocity(rad/s)νwindspeed(m/s)svariableofLaplacetransformρairdensity(kg/m3)Rrotorradius(m)βpitchangle(°)θcrankangle(°)CPpowercoefficientCTtorquecoefficienticontrolcurrentoftheelectro-hydraulicproportionalvalve(mA)Kipressure-currentamplificationfactoroftheelectro-hydraulicproportionalvalve(N/mA)Ksfspringcoefficientoftheelectro-hydraulicproportionalvalve(N/mm)Ksgainofthelinear-variabledifferentialtransformer(LVDT)(mA/mm)Kqflowamplificationgainoftheelectro-hydraulicproportionalvalve(m2/s)Kcflow-pressureamplificationgainoftheelectro-hydraulicproportionalvalve(l/N)xvdisplacementoftheelectro-hydraulicproportionalvalve(mm)ydisplacementofthecylinder(mm)Wind31-5_final19/12/073:53pmPage341Qlflowoftheelectro-hydraulicproportionalvalve(l/s)pcloadpressure(Pa)Acareaofthecylinderinnon-rodchamber(mm2)βeeffectivebulkmodulus(N/m2)Vctotalvolumeofthecylinder(mm3)ClcoefficientofleakageMequivalentmassofthecylinderandtheload(kg)BcresistantcoefficientofthecylinderKspringcoefficientofthecylinder(N/mm)FLexternaldisturbance(N)ωhnaturalfrequencyofthehydraulicsystemξhdampingratioofthehydraulicsystemrlengthofthecrank(mm)llengthofthelinklever(mm)GmGainMarginPmPhaseMarginωggaincrossoverfrequencywcphasecrossoverfrequencyKb,Kd,KecombinedcoefficentsSYSTEMDATACommonsystembase:Windturbineratedcapacity1.5MWGeneratorpoles=4Cutinwindspeed=4m/sStatorresistance(pu)=0.0076Ratedpower=1.5MWCutoutwindspeed=25m/sRotorresistance(pu)=0.0073Ratedfrequency=50HzRatedwindspeed=12.2m/sStatorleakageinductance(pu)=0.1248Powerfactor=1Statorratedvoltage=690VRotorleakageinductance(pu)=0.0884Gearboxratio=1:90Rotorratedvoltage=690VMagnetizinginductance(pu)=1.8365R=35.25mOptimumtipspeedratio=10Rotorspeedrange:11.1-22.2r/minr=480mmOptimumpowercoefficient=0.44Ki=0.3N/mAl=600mmTurbinerotorinertia=320000kg·m2.Kc=0.026×10-10m3/N·sM=5000kgGeneratorrotorinertia=60kg·m2βe=7000×105N/m2Ac=12.7cm2Ksf=8.4N·m/radKa=0.356m2/sVc=8.38×10-4m3Ks=0.4mA/mm1.INTRODUCTIONDuringthelastfewyears,variable-speedpitch-controlledwindturbineshavebecomethemostcommontypeofinstalledwindturbines,buttheirmorecontinuousenergycaptureissubjecttothephysicallimitationsoftheturbineathighwindspeed(Hansen,A.D.,2004).Theturbinerotorspeedandpowerproductionmustbeheldbelowcertainthresholdvaluesandthefatigueofthemechanismthatrestrictstherotorspeedshouldbeminimized(KendallLewis,1997).Hydraulicsystemsareimportantactuatorsinmodernindustry,principallybecausetheyhaveahighpower/massratio,fastresponse,andhighstiffness:acombinationunmatchedbyanyothercommercialtechnology(Andrew,2000).Thestudyofthevariable-pitchhydraulictechnologyisthereforeimportant.TheadoptionofHVPMhastwoprimemotivations:(i)optimisingthewindpower,and(ii)protectingthemachineatwindspeedsabovecut-out.342MODELLINGANDANALYSINGTHEHYDRAULICVARIABLE-PITCHMECHANISMFORAVARIABLE-SPEEDWINDTURBINEWind31-5_final19/12/073:53pmPage342Inthisstudy,themodelofthevariable-pitchwindturbinewithadoubly-fedinductiongenerator(DFIG),hasbeendesignedandimplementedinthesimulationtoolMATLAB/SIMULINK.Thesystem,Fig1,canbedividedintoseveralblocks:controller,amplifier,HVPM,slider-crankmechanism(SCM),windturbine(blade,gearbox,DFIG).Themeasuredvalueofpoweriscomparedwiththepowerreferencevalue,andtheerrorsignalisfedtothecontroller.ThecontrolsignalisamplifiedandsenttotheHVPM.TheHVPMisaninterfacebetweenlow-powerelectricalsignalandhighhydraulicpower.Consequently,theHVPMactivatestheSCMttoadjustthepitchangleofwindturbineblade.ThereismuchliteraturesconcerningtheHVPMmodelingandmanyauthorssimplifythemodelofthepitchregulationsystembyafirst-orderinertiasystem(Camblong,2004),(HansenM.H.,2005):(1)Withsuchasimulation,theinputandtheoutputvariablesare(a)thepitchangleβ,and(b)thetimeconstantdifferencebetweentheinputvariableandtheoutputvariable,τβ.Therefore,thissimplifiedrepresentationneglectsmanyactualcharacteristicsoftheHVPM.Inthispaper,basedonwindturbineelectro-hydraulicproportionalpitch-controlledtechnology,animprovedmodeloftheHVPMispresentedandthesimulationresultspresented.2.AERODYNAMICMODELAwindturbineischaracterizedb