A Tutorial on the Dynamics and Control of Wind Turbines ...

1 Windenergyiscurrentlythefastest-growinge n-ergysourceintheworld, power, , , , ,theinstalledcapacityofwindgrewatanavera gerateof29%peryearovertheyears2002-2007[ 1].Attheendof2007,theinstalledcapacityin theUnitedStateswasnearly17,000megawatts( MW)andtheworldwideinstalledcapacitywasov er94,000MW( ).Windisrecognizedworldwideasacost-effec tive, [1],thatfigureinDenmarkismorethan15%[2]. [3]laystheframeworkforachieving20% ,manufacturing,transmissionandintegratio n,market,environmental, theinstalledcapacityofwindturbinesinrece ntyears, ,thetypicalsizeofutility-scalewindturbin eshas growndramaticallyoverthelastthreedecades ( ).Modernwindturbinesarelarge,flexiblestr ucturesoperating sworkwassupportedinpartbytheUniversityof ColoradoatBoulderEnergyInitiative, ,theMillerInstituteforBasicResearchinSci enceattheUniversityofCaliforniaatBerkele y, (NSFG rantCMMI-0700877).

2 KathrynJohnson (NSFG rantECCS-0725752). [Graphreproducedfromdatain[4]] byincreasingtheeffi-ciency,andthustheene rgycapture, , ,wewillfocusonhorizontal-axiswindturbine s(HAWTs) theentirerotorcanbeplacedatopatalltower, ,improvedpowercaptureandstructuralperfor mance,andnoneedforguywires(whicharetensi onedcablesusedtoaddstructuralstability). VAWT saremuchmorecommonassmallerturbines, (andhencedecreasingmaintenancerequiremen tsand/orextendinglifetime) [Diagramandschematicsfrom[5], [6],[7]] (kW) ,andthereforethistutorialwillfocuson walk aroundthewindturbine controlloop, ,whichisthenfollowedbyadiscussionoftheis suesandopportunitiesinwindturbineandwind farmcontrolinSectionsV,VI,VII, ,nacelle,androtor, , , , (a)(b) (a)vertical-axisturbinesspinliketopsanda readvantageousbecausetheydon tneedtoturnintothewindandtheirheavycompo nents,likegenerators,canbelocatedonthegr ound.

3 [Figurefrom[8]](b)horizontal-axisturbine sareusuallyplacedontalltowerstocatchmore ofthewindathigherlevelsabovetheground.[ ] , , , ,usedtoturnthenacellesothattherotorfaces intothewind.( [9].)Windturbine upwind, withtherotorontheupwindsideofthetower,or downwind. Thechoiceofupwindversusdownwindconfigura tionaffectsthechoiceofyawcontrollerandth eturbinedynamics, , , WindPower powerin , , , , , , ,whenthewindspeedislow(inthiscase,below6 m/s), ,Region3( ), ,Region2, (10m/sinthisexample), [10],[11]havingashapeparameterk=2andscal eparameterc= , , highwindcut-out, , ,actuatordisctheoryshowsthatthetheoretic almaximumaerodynamicefficiency,whichisca lledtheBetzLimit,isapproximately59%ofthe windpower[12].Thereasonthatanefficiencyo f100%cannotbeachievedisthatthewindmustha ve somekineticenergyremainingafterpassingth roughtherotordisc;ifitdidnot, powerandisknownastheturbine spowercoefficient, ,(1) Av3,(2)where istheairdensity,Aisthe sweptarea oftherotor, ,or R2, (2), [10]and[11] ,itisoftenassumed(asin(2)) ,asshownbythe instantaneouswindfield , , ,whichcanbecalled supervisorycontrol, operationalcontrol, and subsystemcontrol.

4 Thetop-levelsupervisorycontroldetermines whentheturbinestartsandstopsinresponseto changesinthewindspeed, ,powerelectronics,yawdrive,pitchdrive, ,wewillmovethroughtheoperationalcontroll oopsshowninFig. 6,describingthewindinflow,sensors, ,andthereaderisreferredto[10],[11] satmosphereisthedrivingmechanismfortheea rth ,suchasthenocturnallow-leveljet,seabreez es,frontalpassages,andmountainandvalleyf lows,af-fectthewindinflowacrossawindturb ine srotorplane[10]. , ,andthevariabilityofwind, , ,thefrequencydistributionofwindspeeds,th etemporalandspatialvariationinwindspeed, themostfrequentwinddirection( ,prevailingwinddirection),andthefrequenc yofotherwinddirections[10]. s(orwindfarm s)energyoutputoveraperiodoftimetotheamou ntofenergytheturbinewouldhaveproducedifi thadrunatfullcapacityforthesameamountoft ime:CapacityFactor=actualenergyoutputove rtimeperiodenergyoutputifturbineoperated atmaxoutputoversametimeperiodToaccuratel ypredictcapacityfactorsandmaintenancereq uirementsforwindturbines,itisimportantto beabletounderstandwindcharacteristicsove rlong(multi-year)aswellasshort(secondand sub-second) (ordaily) variationiscausedbythedifferentialheatin goftheearth ssurfaceduringthedailysolarradiationcycl e.

5 ,knowledgeofshort-termwindspeedvariation s,suchasgustsandturbulence, (TKE), , [13].variableacrosstheturbine srotorplane,nearlyallmodeling,design,and controlisbasedonassumptionsofuniformandc onstantwindacrosstherotorplane,including equations(1)-(2)above(aswellallotherequa tionsin theremainderofthispaper).Whilethisassump tionsimplifiesmodelsandhencethedesignand controlofwindturbines,aswindturbinesbeco melarger, (whicharenon-uniformwinds) ,whenturbinesweresmallerandplacedatopsho rtertowers,theeffectsofthesestructureshi ttingtheturbineswaseithernotwellundersto od, slargerturbinesareoftenhitwithturbulents tructuresthatarecomparableorsmallerinsiz ethanturbinerotorplanes, hit differentbladesofalargeturbine,causingse riousfatigueandextremeloadingissuesthatc ancauseexcessivewearordamagetotheturbine structure[14].Bettercapabilitiesformeasu ringandpredictingturbulenteventsareneede d[15], (TKE)inalow-leveljet, , ,withoneexamplebeing wind s(NREL s)NationalWindTechnologyCenter(NWTC)near Boulder, (highervelocityatthetop,andloweroreven negativevelocityatthebottom).

6 Con-trollersdesignedtoalleviatestructura lloadinginresponsetoturbulentstructuresa redescribedin[16]. , ,speedcanbemeasuredoneitherthehighspeed( generator)orlowspeed(rotor) ,windturbinesusuallyhaveanemometersforsu pervisorycontrolpurposes,inparticulartod etermineifthewindspeedissufficientto vanelocatedontopofthenacelle(atapproxima telyhubheight) ,becauseoftheinteractionbetweentherotora ndthewind, ,theinteractionextendsbothupwindanddownw indoftherotor, , windturbinesandwhosemeasurementshavebeen usedinmoreadvancedwindturbinecontrollers include: straingaugesonthetowerandblades, accelerometers, positionencodersonthedriveshaftandbladep itchactuationsystems,and (CART3)nacelle,showingthehigh-speedshaft (insidetheyellowcageatleft),thegenerator (largegreenunitinthemiddle),theyawmotor( smallergreenunittowardtheright),andthe3- stageyawgearbox(largewhiteboxin lowerright).

7 Anothergearboxconnectsthehigh-speedshaft onthelefttothelow-speedshaftandrotor(not shownhere). , , [17], ,forexample, ,auto-calibrationtechniques,adaptivecont rol, ,whichturnsthewindturbinetoalignitwithth ewind,isnearlyalwaysincludedonlargeturbi nes, ,duetodangerousgyroscopicforces, ,investigationofadvancedcontrollersforya wcontrolisnotof asmuchinterestasadvancedcontrollers ,eitherofwhichcanallowpassiveyawmotion , ,which,dependingontypeofgeneratorand powerprocessingequipment,canbeforcedto command , , ,generatortorquecanbe upwind fromtheturbine, , (CART3)locatedattheNationalRenewableEner gyLaboratory s(NREL s)NationalWindTechnologyCenter(NWTC) , [11], [18].Thisteeterhingeallowsonebladetomove upwindwhiletheothermovesdownwindinrespon setodifferentialwindloads, ,whenonebladeisattheuppermostposition,an otherbladewillbeintheslowerwindcausedbyt ower shadow behindthetowerorthe bowwake , , ,a2-bladed,600kWwindturbinewitha43mdiame terrotoratNREL ,thepitchrateisrestrictedtoapproximately 5 ,the2-bladedControlsAdvancedResearchTurb ineatNREL (desired)pitchandactualpitchanglesaresho wnduringanormalshutdowneventasthebladesa repitchedfrom-1to90deg, , deg/sfor600kWresearchturbinesdownto8 stall orto feather, ,butmoreinformationisprovidedin[10],[19] .

8 ,thispowercoefficientisafunctionofthetur bine stip-speedratio ,whichisdefinedas = Rv.(3)In(3), istherotationalspeedoftherotor,andRandva retherotorradiusandinstantaneouswindspee d, ,thetip-speedratioistheratioofthelinear( tangential)speedofthebladetiptothewindsp eed,whereRisfixedforagiventurbine,visalw aystime-varying,and ,therelationshipbetweenthepowercoefficie ntCpandthetip-speedratio , ,theCART3atNREL = = ,theturbinewilloperateatitshighestaerody namicefficiencypoint,Cpmax, , , , ,Region3controlistypi-callyperformedviaa separatepitchcontrolloop, , , andaerodynamictorque aerobyP= aero .(4)Ifthepowerandrotorspeedareheldconsta nt, ,thelimitofwhichisknownastheturbine ,thepitchcontrolloopregulatestherotorspe ed (attheturbine s ratedspeed ) ,wewillprovidefurtherinformationre-gardi ngwhatcontrolalgorithmsaretypicallyusedf orthe TorqueControl and PitchControl , curvefortheCART3whenthebladepitchangle = whentheredcurve(representing(8))islessth anthebluecurve( CARTCpvs.)

9 , [19]foramoredetaileddescriptionofwindtur binecontrol, , ,wepresentonetypeofgeneratortorquecontro linuseonCART2atNREL ,wewillrefertothiscontrollerasthe standard (nonlinear)controlisachievedbysettingthe generator( Control )torque cas c=K 2,(5)where isthemeasurementoftherotorspeed,andKisgi venbyK=12 R5 Cpmax 3 ,(6)whereCpmaxisthemaximumpowercoefficie ntachievablebytheturbine,and = (perfectmeasurements),thetorquecontrolgi venby(5)and(6) ,werelatenettorqueandangularacceleration by =1J( aero c),(7) (7)with(1)-(6),wefindthat =12J R5 2(Cp 3 Cpmax 3 ). ;whenthisratedvalueisreached, , <0whenCp<Cpmax 3 3and >0whenCp>Cpmax 3 3(8)andweseethatthecontrollawgivenby(5)a nd(6) (8) (generator)speed,thecontroltorquesignalg ivenby(5), ,thewindspeedislowenoughthatcontrolisbas edon(5).Afterthattime,windspeedshaveincr easedandtheratedspeedof1800rpmisreached, verysteepsectionsofthetorquecontrolsigna latapproximately417sand427sareduetoatowe rresonanceavoidancecontrollerdescribedfu rtherin[17].

10 ForadditionalinformationaboutthisRegion2 standardtorquecontroller,aswellasanadapt ivetorquecontroller,pleasesee[20]. ,pitchcontrolinRegion3isfrequentlyperfor medusingaproportional-integral-derivativ e(PID)collectivepitchcontrol: c(t)=KP e(t)+KI t0 e( )d +KDd e(t)dt(9)where e= d istherotorspeederror,thedifferencebetwee nthedesiredrotorspeed dandthemeasuredrotorspeed .Becauseofitssensitivity tomeasurementnoise,thederivativetermisof tencombinedwithalow-passfilter,ortheterm issometimesomittedaltogether( ,KD=0) [21].AsystematicmethodforselectingthePID pitchcontrolgainsispresentedin[22]. ,whichchangesfromitsnominalvalueonlyinRe gion3, ,the600kWCART2hasahighermaximumpitchrate (18deg/s)thanmostmodern(andoftenlarger) ,single-output(SISO)controller, ,multi-input,multi-output(MIMO)individua lbladepitchcontrollerscanbedesignedforin creasedper-formance[23],[24].