风电英文资料

Chapter2WindTurbines2.1GeneralThehistoryofwindmillsgoesbackmorethan2000years.Theyhavebeenusedpredominantlyforgrindingcerealsandforpumpingwater.ImportantexamplesofmorerecenttimesaretheDutchWindmillswhichappearedindifferentvariantsandwereerectedinlargenumbersinthe17thand18thcenturyinEurope.Anothermemorabledevelopmentofthe19thcenturywastheWesternMill,foundinruralareasespeciallyintheUSAuptothepresentday.Modernconstructionsofwindenergyconvertersweredevelopedinthe1920s,butitwasnotbeforethe1980sthattheyfoundprofessionalinterestasaprominentapplicationofrenewableenergies.Fromthestandpointoffluidengineeringwehavetodistinguishwindenergyconverterswithdragforcerotorandwithbuoyantforcerotor.Whiledragforcerotorsutilizedirectlythewindpressureandattainonlylowefficienciesintheorderof0,1...0,2,buoyantforcerotorsdevelopconsiderablyhighervalues,inherentlylimitedatapproximately0,59.Asuitabletheorywaspublishednotbeforethestartofthe19thcentury(Joukowski1907).Modernwindturbinesaremostlyconstructedasfastrunningmachineswithhori-zontalshaft,upwindarrangementandpreferably3rotorblades.Themachineratingshavesteadilyincreasedsothattheaverageinstalledpowerperunitiscurrentlyabove1.700kW.Foroffshore-wind-parksratingsofupto6.000kWareinpilotstage.Aselectionofrelevantbookliteratureonwindturbinesisin[Hau06,Gas02,Gas07].2.2BasicsofWindEnergyConversion2.2.1PowerConversionandPowerCoefficientFromtheexpressionforkineticenergyinflowingairfollowsthepowercontainedinthewindpassinganareaAwiththewindvelocity(2.1)M.Stiebler,WindEnergySystemsforElectricPowerGeneration.GreenEnergy11andTechnology,cSpringer-VerlagBerlinHeidelberg2008122WindTurbinesHereρisthespecificairmasswhichdependsonairpressureandmoisture;forpracticalcalculationsitmaybeassumedρ≈1.2kg/m3.Theairstreamsinaxialdirectionthroughtheawindturbine,ofwhichAisthecircularsweptarea.Theusefulmechanicalpowerobtainedisexpressedbymeansofthepowercoefficient(2.2)Incaseofhomogenousairflowthewindvelocity,whosevaluebeforethetur-bineplaneisv1,suffersaretardationduetothepowerconversiontoaspeedv3wellbehindthewindturbine,seeFig.2.1.Simplifiedtheoryclaimsthatintheplaneofthemovingbladesthevelocityisofaveragevaluev2=(v1+v3)/2.OnthisbasisBetz[Bet26]hasshownbyasimpleextremumcalculationthatthemaximumusefulpowerisobtainedforv3/v1=1/3;wherethepowercoefficientbecomescp=16/27≈0,59.Inrealitywindturbinesdisplaymaximumvaluescp,max=0,4...0,5duetolosses(profileloss,tiplossandlossduetowakero-tation).Inordertodeterminethemechanicalpoweravailablefortheloadmachine(electricalgenerator,pump)theexpression(2.2)hastobemultipliedwiththeeffi-ciencyofthedrivetrain,takinglossesinbearings,couplingsandgearboxesintoaccount.Animportantparameterofwindrotorsisthetip-speedratioλwhichistheratioofthecircumferentialvelocityofthebladetipsandthewindspeed(2.3)HereDistheouterturbinediameterandΩistheangularrotorspeed.Notethattherotationalspeedn(conventionallygiveninmin−1)isconnectedwithΩ(ins−1)byΩ=2πn/60.ConsideringthatintherotatingmechanicalsystemthepoweristheproductoftorqueTandangularspeedΩ(P=T·Ω),thetorquecoefficientcTcanbederivedfromthepowercoefficient:cT(λ)=cp(λ)λ(2.4)Fig.2.1Idealizedfluidmodelforawindrotor(Betz)2.2BasicsofWindEnergyConversion13Thetorqueconnectedwiththepoweraccordingto(1.2)isthen(2.5)Notethatthetorquevarieswiththesquare(v12)andthepowervarieswiththethirdpower(v13)ofthewindspeed.Figure2.2showstypicalcharacteristicscp(λ)fordifferenttypesofrotor.BesidestheconstantmaximumvalueaccordingtoBetzthefigureindicatesarevisedcurvecp(Schmitz)whichtakesthedownstreamdeviationfromaxialairflowdirectionintoaccount.Thedifferenceisnotableintheregionoflowertipspeedratios,ascalcu-latedbySchmitzand,before,Glauert.TogetherwithFig.2.3indicatingassociatedcharacteristicscT(λ),thecurrentpreferenceforthree-bladerotorswithhorizontalshaftisunderstood.Theso-calledfast-runningturbineswith3,2oronebladesdis-playthelargervaluesofcp,whilethecurvescTindicatethepoorstartingtorquecapabilityofthefast-runningtypes.Sinceoneandtwobladerotorsarealsoprob-lematicwithrespecttotorquevariationsandnoise,thethree-bladerotorsarecur-rentlypredominantinallmodernwindenergysystems.TherotorsarenormallydesignedtovaluesλA=5...8.Fig.2.2Typicalpowercoefficientsofdifferentrotortypesovertip-speedratio142WindTurbinesFig.2.3Typicaltorquecoefficientsofdifferentrotorwithhotizontalshaft2.2.2ForcesandTorqueThemainrotorpropertiesfollowfromliftingforceanddragforceofabladeasdescribedbyaerofoiltheory.Letanaerofoilelementofdepthtandwidthbbesubjectedtoawindspeedv1,seeFig.2.4.Dependentontheangleofattackαbetweenwinddirectionandthebladeprofilecord,theliftingforceFAanddragforceFWare:1·t·bindirectionofoncomingflow(2.6)Notethattheseforcecomponentsaredirectedperpendicularandparalleltotheoncomingwind,respectively.CoefficientscAandcWarecharacteristicforagivenbladeprofile;theydependonbladeangleα.TheexampleinFig.2.4appliestorealunsymmetricprofiles[Schm56].Forsmallvaluesofα(0≤α≤10◦)analmostproportionaldependenceofcA=(5,1...5,8)·αisobserved,whilecWiscompar-ativelysmallintheconsideredintervalofα.Theratioε=cA/cWiscalledtheglideratioorlift/dragratio.When