Layout Optimization of Offshore Wind Energy Project for Maximum Energy Capture with Variable Hub Height

Optimizingthelayoutofoffshorewindenergyprojects 1LAYOUTOPTIMIZATIONOFFSHOREWINDENERGYPROJECTFORMAXIMUM ENERGY
CAPTUREWITHVARIOUSHUBHEIGHT
BrianO.Eliaud
RenewableEnergyTechnologyAndManagement
ResearchPaperTutor:Team Nerdyturtlerz
DuetoDate:11March,2019

Optimizingthelayoutofoffshorewindenergyprojects 2Abstract
Turbine wakesreduce powerproduction in a wind farm.Currentwind farmsare
generallybuiltwithturbinesthatareallthesameheight,butifwindfarmsincluded
turbineswithdifferenttowerheights,thecostofenergy(COE)maybereduced.We
usedgradientbasedoptimizationtodemonstrateamethodtooptimizewindfarmswith
variedhubheights.OurstudyincludesamodifiedversionoftheFLORISwakemodel
thataccommodatesthree-dimensionalwakesintegratedwithatowerstructuralmodel.
OurpurposewastodesignaprocesstominimizetheCOEofawindfarm through
layoutoptimizationandvaryingturbinehubheights.Resultsindicatethatwhenafarm is
optimizedforlayoutandheightwithtwoseparateheightgroups,COEcanbeloweredby
asmuchas5%-9%,comparedtoasimilarlayoutandheightoptimizationwhereallthe
towersarethesame.
Introduction
Aswindturbinesextractenergyfrom theairandconvertittopower,anareaofreduced
windspeedisformedbehindeachwindturbineknownasawake.Becausetheairina
wakehaslessmomentum,awindturbineinawakecannotextractasmuchenergyand
thereforeproduceslesspower.Severalsolutionshavebeendevelopedtohelpremedy
thisproblem,includinglayoutoptimizationofthewindfarm1–3androtoryawcontrol.4,
5 .In general,wind farmsarebuiltwith oneturbinetypeand height,and layout
optimizationstudiesonlyanalyzewindfarmswithidenticalturbines.Includingmore
thanoneturbineheightinthesamewindfarm coulddecreasewakeinterferenceeven
furtherandresultinhigherenergyproduction.Severalstudieshaveexploredtheuseof
differentturbineheightsinthesamewindfarm.Chenetal.usedageneticalgorithm to
optimizeawindfarm layoutof25turbinesbychangingthepositionandheightofeach
turbinebetweentwopredefinedheights.Theyfoundthatthepowerincreasedbyas
muchas13.53%andthecostperunitofenergyproduceddecreased0.37%.6Hazraet
al.usedaparticleswarm methodtooptimizeawindfarm,inwhichtheturbineheight
androtorradiusarebothdesignvariables.Thenumberofdesignvariablesincreasesby
uptothenumberofturbinesinthewindfarm;oneforeachtowerheight.Additionally,a
wakemodelmustbedevelopedormodifiedtooperateinthreedimensions,anda
structuralmodelforthetowermustbeaddedtoaccountforpotentialfailureasthe
heightchanges.Hazraetal.includedrotordiameterasadesignvariableintheir

Optimizingthelayoutofoffshorewindenergyprojects 3optimization.Gradient-basedoptimizationisfasterthangradient-freemethodsandis
necessaryforoptimizinglargewindfarmsincludingmanydesignvariables,suchasyaw
controlcoupledwiththevariablesmentionedabove.Whenyawcontrolisaddedtothe
optimization,thousandsofdesignvariablescanbeadded,becauseeachturbinemust
beoptimizedforeachwinddirectioninconsideration.Specifically,wewilloptimizewind
farmswithdifferenthubheights,anddemonstrategainsofwindfarmswithmultiple
hubheightscomparedtothosewithturbinesatanidenticalheight.Combiningmultiple
hubheightsinwindfarmswhilecontinuingtooptimizetheirlayoutmayhavesignificant
impactonthecostofenergy(COE)inwindfarms.
Methodology
Inthissection,wedescribethemodelusedtopredicttheCOEofawindfarm.First,the
wakemodelisdiscussed,whichisneededtocalculatethewindspeedatanypointin
thewindfarm.Next,wediscusstheannualenergyproduction(AEP)andhow itis
calculated.Consideringstructuralcalculationsmadealongthelengthofthetowerthat
areimportantasconstraintsinouroptimization,eachofthesecomponentswasusedin
ouroptimization.
A.WakeModel
Tocalculatetheeffectivewindspeedateachturbine,weusedtheFLORISwake
modelpresentedbyGebraadetal.4TheFLORISwakemodelisderivedfrom the
Jensenmodel,8butratherthanuseonespeedtodescribethewindacrossthe
wake,threeseparatezonesaredefined,eachwithadifferentexpansionand
decayrate.A simpleoverlapratioisusedbetweenzonestodefinethetotal
effectivewindspeedateachturbine.Figure1showsthethreeseparatewake
zones,aswellastheiroverlaponarotor.Withoutanalyticgradients,finite
differencegradientsmustbeused,whichoftenexperiencenumericaldifficulties,
anddonotscalewell.Becausethiswakemodelwasdesignedtodescribethe
wakeinthehorizontalplane,itwasmodifiedtocalculatetheeffectivewind
speedatanypointinthree-dimensional(3-Dspace.Weassumethatthewakeis

Optimizingthelayoutofoffshorewindenergyprojects 4axisymmetric,suchthatanycrosssectioniscircular.FLORISusesprecomputed
data,uniquetotheturbinemodelused,fortheCPandCTcurvesthatareusedin
theturbinepowercalculation.Arealwakemaymoveintheverticalplaneand
maynotmaintainaperfectlycircularcrosssection.Tolearnwhetherornotthe
assumptionswemadewerereasonable,wecomparedthemodelresultsto
SimulatorforWindFarm Applications(SOWFA).SOWFA,ahigh-fidelitylarge
eddysimulation toolthatwasdeveloped attheNationalRenewableEnergy
Laboratory(NREL)forwindfarm studies,isbasedonOpenFOAM andiscoupled
withNREL’sFASTmodelingtool.SOWFAsolvesthe3-DincompressibleNavier-
Stokesequationsandtransportofpotentialtemperatureequations,whichtake
intoaccountthethermalbuoyancyandEarthrotation(Carioles)effectsinthe
atmosphere.Theinflow conditionsforthesesimulationsaregeneratedusinga
periodic atmospheric boundary layerprecursorwith no turbines.SOWFA
calculatestheunsteadyflow fieldtocomputethetime-varyingpower,velocity
deficits,andloadsateachturbineinawindplant.SOWFAhasbeencompared
withthe48-Lillgrundwindfarm fielddataandshowsgoodagreementthrough
thefirstfiveturbinesinarowalignedwiththewinddirection.Inaddition,SOWFA
hasbeentestedtoverifythatitcapturestheinertialrangeintheturbulentenergy
spectra and log layerin the mean flow,both ofwhich characterize a real
atmosphericboundarylayer.TheturbinesweresimulatedusingtheNREL5-MW
reference turbine17 and were spaced 7 rotordiameters (7D)apartin the
downstream direction. These scenarios were simulated under neutral
atmosphericconditionswithan8m/smeanwindspeedand10% turbulence
intensity .A baseline scenario was run in which both the upstream and
downstream turbinesweresimulatedatahubheightof90m.Next,thehub
heightofthedownstream turbinewasvariedtoverifythatFLORIS-3D could

Optimizingthelayoutofoffshorewindenergyprojects 5capturetheeffectsofvaryinghubheights.Specifically,theupstream turbine
remainedata90m hubheightandthedownstream turbinewassetat65m and
115m hubheights.Figure2showstheseresultscomparedtotheFLORIS-3D
wakemodel.Whentunedforneutralatmosphericconditionsand10%turbulence,
FLORISandSOWFApredictverysimilarpowerproductionofeachturbineforthe
turbineswithdifferenthubheights.Thereareonlyafew datapointsobtained
from oneatmosphericcondition,butthisindicatesthateventhissimplewake
modelcanbeusefultopredictwakelossesinthreedimensions.
B.AnnualEnergyProductionCalculation
Theinstantaneouspowerproductionofawindfarm ishighlydependentonthe
winddirection,duetothewakescreatedbehindwindturbines.Forthisreason,
AEP isamuchbetterindicatorofaproductivefarm thanpower.Thewind
directionfrequencyandwindspeeddatausedinthisstudyarefrom thePrincess
AmaliaWindFarm,anoffshorefarm intheNetherlands.Thedirectionfrequency
dataisbinnedinto5◦incrementsandthewindspeedsareaveragedforeachof
the72bins.
Toaccountforheightdifferencesforourinflow velocity,weadjustedthewind
speeddataforwindshear.

Optimizingthelayoutofoffshorewindenergyprojects 6Weusedapowerlawtoestimatethewindspeedatdifferentheights(z):
U(z)=Uref(z)/zref^α
wherethereferenceheight,zref,ofthereferenceturbineis90m,andtheshear
coefficient,wasvariedaswillbediscussedlater.
C.TowerModel
Becausethetowerheightwasallowedtovary,itwasnecessarytoincludea
modelto calculatemassandperform structuralanalysisofthetower.The
structuralanalysiswasusedtoconstraintheoptimization,keepingthetowers
from growingunrealisticallytallwherefailurefrom stressorbucklingwouldbe
anissue.Itwasalsonecessarytoprovidegradientsforallofourconstraints,
whichincludedthevonMisesstress,shellbuckling,andglobalbucklingatany
pointalongthetower;thetowertaperratio;andthefirstnaturalfrequencyofthe
structure.NRELdevelopedafiniteelementmodelcalledTowerSEthatmakes
variouscalculationsalongthelengthofatower.Itisapowerfultool,butdoesnot
provideanalyticgradients.WeoptimizedseveralwindfarmsusingTowerSEand
finitedifferencegradients,andidentifiedtheshellbucklingandfirstnatural
frequencyastheonlyactiveconstraints.Wewerethenabletopulloutthe
necessarycalculationsfrom TowerSEandfindtheassociatedgradients.The
towermass was a simple calculation from the volume ofthe tower.The
gradientsweresimpletosolvebyhand.Wefoundshellbucklingasafunctionof
thetowergeometryandthestressesateachlocation,followingthemethod
outlinedinEurocode.ThesecalculationsweremadeinFortran90andexact
gradientswereobtainedwiththeTapenadeautomaticdifferentiationtool.We
simplifiedthefrequencycalculationbyapproximatingthetowerasacantilever
beam ofconstantcross section with an end mass.We used the method
describedbyErturketal.tocalculatethenaturalfrequency.Becausetheturbine
towerdoesnotreallyhaveaconstantmassdensityalongthelengthandthe
massfrom therotornacelleassemblyisslightlyoffsetatthetop,ourcalculation
isslightlymoreconservativethanthatpredictedbyTowerSEbyabout10%.For
thisreasonwescaledourfrequencycalculationby10%tomorecloselymatch
thefrequencycalculatedbyTowerSE.Wechosethissimplifiedmodelsothatwe
couldfindgradients,whichwereobtainedusinganalyticsensitivityequations.