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CharacterizingWindSpeedandDirectionShearwithSoDARDataNielsLaWhite,ElizabethWalls,andKenCohn
SecondWindInc.
ABSTRACTSoDARdatafromthreesiteswereanalyzedtoidentifyfrequencyofoccurrenceofatypicalwind
conditionssufficienttoimpactresourcesuitabilityorturbineperformance.Windspeedanddirection
measurementswereobtainedforasetofheightsspanningatypicalwindturbinerotor.Foreachsite,
10minutewindaverageswerecollectedforathreemonthperiod.Apowerlawshearcoefficientwas
then
fit
to
each
10
minute
set
of
wind
speed
measurements,
yielding
an
accurate
short
term
measure
of
windspeedshear.Similaranalysiswasperformedforwinddirectionshear(alsocalledveer)byfittinga
straightlinetoeachsetof10minutewinddirectionmeasurements.Thewinddirectionchangefrom
lowertoupperbladetipwasthenusedasashorttermmeasureofveer.
Tohighlighttheeffectofspeedanddirectionshearonturbineoperation,datasampleswithhubheight
windspeedbelow6m/swereremovedfromthedataset.Histogramrepresentationisusedtoshowthe
frequencyofoccurrenceofspeedanddirectionshearvalues,andtheheavytaileddistributionssuggest
thatextremeshearandveer,whilesomewhatrare,occursurprisinglyoftenandusuallyatnight,when
atmosphericstabilityreducescouplingbetweenupperandlowerlevelair.Areversecumulative
distribution,orfrequencyofexceedanceplot,isshowntobeusefulincomparingthefrequencyof
occurrenceofdegreesofshearatthethreeexamplesites.
OBJECTIVESTheprimaryobjectiveofwindresourceassessmentistoidentifysiteswithsufficientwindsforpower
generation.Whenacandidatesiteisidentified,thewinddataforthesitearefurtheranalyzedtoensure
suitabilityofthelocalwindconditionsforwindturbineoperation.Oneaspectofsuitabilitythatisoften
neglectedistheoccurrenceofextremewindshear. Often,onlyasingle,seasonal,averageshear
coefficientisobtainedforasite,eventhoughsuchlongaveragesmaskthepresenceofwindshear
extremesthatoccurinfrequently.
Acommonreasonforoveraveragingwindshearisthelackofaccuratedata.Whentheonlyavailable
dataarefrombelowhubheightmetmasts,windshearvaluesmustbeextrapolatedfromasmallsetof
readings.Astowershadowandanemometeroverspeedingcancausesmallerrorsinthosereadings,the
extrapolatedshearvalueswillhaveuncertaintywhenaveragedovershorttimeintervals.Also,itis
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commontoignorewinddirectionshearaltogether,becausemanymettowersareinstrumentedwith
winddirectionvanesatonlyasingleheight.
Thedevelopmentofinexpensiveremotesensingtechnology,suchasSonicDetectionandRanging,or
SoDAR,hasmadeitpracticaltoobtainaccuratemeasurementsofwindspeedanddirectionatseveral
heightsacross
the
swept
area
of
atypical
wind
turbine
rotor.
Because
modern
SoDAR
equipment
is
robust,iseasytodeploy,andcanruncontinuously,itisanidealchoiceforstudyingthevarietyoflocal
shearconditionspresentatanypotentialwindfarmsite.
Forthisresearch,weusedmeasurementsfromaSecondWindTritonSonicWindProfiler,which
measures10minuteaveragewindspeedanddirectionatsixdifferentheightsspanningatypicalrotor
sweptarea,asshowninFigure1.
Figure1: ExampleTritonWindSpeedandDirectionMeasurementswithExtremeShear.
TheSoDARmeasurementsareeasilyanalyzedtocompute10minutevaluesforbothspeedand
directionshearoveranentiremeasurementcampaign.However,withoutastandardpracticefor
incorporatingshorttermshearmeasurements,itisnotclearwhattodowithsuchalargequantityof
sheardata.Thispaperdevelopsasimpletechniqueforplottingshearfrequencyofoccurrenceinorder
tohighlightsitetositedifferencesthatwouldaffectwindturbineperformanceandreliability.
VALIDATIONBeforeexaminingthewindsheardistribution,acorrelationstudywasconductedforeachthreemonth
datasetinordertoconfirmitsvalidity. Toensurethatnoisyorerroneousdatawerenotincludedinthe
analysis,theTritondatawerefilteredbasedonaminimumqualityfactorof90%andamaximum
verticalwindspeedof+/ 1.5m/s. Thequalityfactorisaparametercalculatedateveryheightandisa
functionofthesignaltonoiseratio(SNR)andthenumberofvaliddatapointscollectedoverthe10
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minuteinterval. Implementingaminumumqualityfactorof
90%removesanynoisyorinvaliddatathatmayhavebeen
recorded. Theverticalwindspeedfilterremoveserroneous
dataordataaffectedbyprecipitation.
Thewind
speeds
as
measured
by
the
Triton
were
compared
toadjacenttowerwindspeeddataandcorrelation
coefficientsweredetermined.Figure2showsscatterplots
ofTritonandanemometerwindspeedsmeasuredat50,
100,and150mattheBoulderAtmosphericObservatory
fromSeptember1st,2008toNovember30th,2008.The
correlationcoefficientswerefoundtobeveryhighat0.985,
0.985,and0.973at50,100,and150m,respectively.
InFigure2,thesolidredlinerepresentsa1:1relationship
betweentheTritonandtowerwindspeeds. Asshown,at
allthreeheights,thewindspeeddatahaveanarrow
distributionandarescatteredaroundthe1:1line. The
averagewindspeedsasmeasuredbytheTritonandtower
werealsocompared. Forthiscomparison,thetowerdata
weredirectionallyfilteredtoreducetowershadowortower
speedupeffects. At50,100and150m,thedifferencein
averagewindspeed(TritonwindspeedTowerwind
speed)wasfoundtobe1.7%,0.8%and0.0%,respectively.
Uponsuccessfulcompletionofeachvalidationstudy,the
wind
shear
and
veer
distributions
were
analyzed.
METHODS
Inordertocomputeshorttermaverageshearvaluesfrom
SoDARdata,weuseasetof10minuteaveragewindspeed
anddirectionmeasurementsfromheightsspanninga
typicalwindturbinerotor. Forthispaper,arepresentative
windturbinewasassumedtohavean80mhubheightand
an80mbladediameter. Fromlowertipheighttouppertip
height,thesetofmeasurementsfromtheSecondWind
Tritonincluded
heights
40m,
50m,
60m,
80m,
100m,
and
120m.
Incomputingthewindspeedshearvalueforeach10minuteinterval,thesetofmeasurementsisfittoa
powerlawcurve,wheremeasuredwindspeedsatdifferentheightsareassumedtoberatiometrically
relatedbytheheightratioraisedtothepoweralpha(),whereistheshearexponentusedhereas
Figure2: ScatterplotsShowingCorrelationsbetweTowerandTritonMeasurements.
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windspeedshearvalue. Thefollowingderivationshowshowtofindabestfitshearexponent,givena
setofmeasurementsfrommanyheights.
Thefollowingpowerlawformulashowshowthewindspeedratioisequatedtotheheightratioraised
tothepower.
whereU1andU2arewindspeedmeasurementsatheightsH1andH2.
Takingthelogarithmofbothsides,theequationbecomes:
Tofind
an
aggregate
shear
exponent,
or
best
fit
,given
aset
of
measured
wind
speeds,
Ui,
taken
at
heightsHi,thepowerlawequationisreducedtotheformofastraightlinefit,bytakingthelogarithmof
theUandHvaluestoyieldthepoints
{log(Hi),log(Ui)}.Withasetofsuchpoints,alinearleastsquares,orstraightlinefitisperformed. The
straightlinecorrespondstotheequation:
log(Ui)=log(Hi)+c
Whiletheconstantoffsetterm,c,isdiscarded,theslopeofthefitlineis,theaggregateshear
exponentthatbestfitsthewindshearprofileacrossthesetofmeasuredwindspeeds.Figure3shows
howatypicalcomputedshearcoefficientreflectstheoriginal10minuteaveragewindspeeddata.The
plotshowshowtheSoDARdatafromheightsspanningaturbinerotornicelycapturethe10minute
averageshearcharacteristicwithoutextrapolation.
Winddirectionshearwascalculatedusingastraightlinefittothewinddirectionmeasurementsfrom
thesamesetofheights. Inthiscase,thewinddirectionisassumedtochangelinearlywithheight,notas
apowerlawfunctionofheight. Thusastraightlineisfittothepoints{Hi,Di},whereDiisthemeasured
winddirectionfromheightsHi,unwrappedtoavoidjumpsof360degrees. Figure3showsatypicalline
fittoasetof10minutewinddirectionmeasurements.
Theslopeofthebestfitlineisameasureofhowmuchthewinddirectionchangespermeterof
elevation.Multiplying
the
slope
by
the
rotor
diameter
then
yields
atotal
wind
direction
change
from
lowerbladetiptoupperbladetip. Forthispaper,thetotalwinddirectionchange,indegrees,overan
80mrotor,isusedasameasureofwinddirectionshear,orveer.
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Figure3: SampleWindMeasurementsShowingShearandVeerFit.Aswindshearatlowwindspeedshaslittleornoconsequence,all10minutedatawithhubheightwind
speedbelow6m/swereremovedfromthedataset.Inalllikelihood,theremainingshearvalues
occurredwellwithintheoperatingrangeofmostwindturbines.Histogramsareshownforwindspeed
shearand
wind
direction
shear
in
Figure
4.
Also
shown
are
the
time
series
SoDAR
data
from
times
of
fairlyextreme,yetfrequentlyoccurringshearandveer.Thespeedsheartimeseriesexamplehasatip
totipwindspeedratioof2:1(=0.63).Theveertimeseriesexampleshowsatiptotipdirection
discrepancyof15degrees.Thehistogramsshowthat,atleastforshortperiodsoftime,fargreatershear
valuesoccur.Theseshearextremesaremostoftenmaskedinresourceassessment,becauseshear
coefficientsarederivedfromlongtermdataaverages.
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Figure4: HistogramsforWindSpeedShearExponentandDirectionalShearwithMatchingTimeSeriesData.
RESULTSAthreemonthdatasetwasobtainedforeachofthreeexamplesites:
SITE PERIOD LOCATION DESCRIPTION
BAO SeptNov2008BoulderAtmospheric
ObservatoryNearby300mTower
CapeCod MayJuly2008 Massachusetts CoastalCranberryBog
Windfarm NovJan2008/9 Texas OperatingWindfarm
Windshear
is
reduced
by
coupling
between
layers
of
air
during
periods
of
atmospheric
instability,
such
aswhensolarheatingcausesconvectivemixingoftheair.Forthisreason,mostextremeshearevents
occurduringperiodsofhighatmosphericstability,usuallyatnight.Evenonovercastdays,atmospheric
stabilityisusuallysomewhatreduced,providingadegreeofprotectionagainstextremeshear.
Thediurnaltrendisdemonstratedbysegregatingtheshearandveerhistogramsbytimeofday. Todo
this,weplotthehistogramusingalinechartinsteadofabarchart. Threelinesareplotted:thetotal
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histogram,includingalldatawithhubheightwindspeed>6m/s,thedaytimehistogram,includingonly
databetweenonehouraftersunriseandonehourbeforesunset,andthenighttimehistogram,
includingdatafromothertimes. Thehourbiasisintroducedbecausethesunmustreachasufficient
angleintheskybeforeconvectionbeginstoovercomeatmosphericstability.
Figure5shows
the
wind
speed
shear
histograms
for
the
BAO
test
site.
The
vertical
dotted
line
correspondstoafairlyextremeshearvalueof0.63,wheretheupperbladetipwindspeedistwicethat
ofthelowerbladetip. Forthisdataset,shearinexcessof0.4isshowntooccuratnight,becausethe
daytimehistogramisapproximatelyzero,andnighttimehistogramisapproximatelyequaltothe
daytimehistogram.
Figure5: HistogramofBAOShearExponentwithDay/NightDecomposition.ThewindveerhistogramoftheBAOsiteisshowninFigure6. Hereagain,extremeshearisseento
occurmostlyatnight,asthedaytimehistogramisapproximatelyzeroforveervaluesinexcessof+/ 15
degrees.It
is
interesting
to
note
that
the
veer
histogram
tails
are
right
sided,
with
veer
more
often
havingincreasinganglewithincreasingheight. ThisphenomenonisrelatedtotheEkmanspiral,where
frictionandtheCoriolisforcevectorintheNorthernHemispheremoreoftencauseapositiveshiftof
winddirectionwithincreasingheight.
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Figures7and8showtheshearandveerhistogramsfortheCapeCodsite,whichisacranberrybog
aboutamiledownwindofanopenoceanbay.Thewindspeedshearatthissiteisoftenveryextremeat
night,withvaluesexceeding1.0,wheretheupperbladetipwindspeedisthreetimesthatofthelower
bladetip.
Veer
at
this
site
is
less
severe
than
at
the
other
sites,
but
the
histograms
are
quite
noticeably
rightsided. Theextremevaluesontherightsideofthedistributionshowequaldaytime/nighttime
occurrence,whilethoseontheleftaredaytimeonly. Presumablythisisbecausethesummerdaytime
stormactivitycancausestrongveerduringtheday,whilethenighttimeatmosphericforcesfollowthe
positivedirectionpredictedbytheEkmanspiral.
Figure6: HistogramofBAOVeerwithDay/NightDecomposition.
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Figure7: HistogramofCapeCodShearExponentwithDay/NightDecomposition.
Figure8: HistogramofCapeCodVeerwithDay/NightDecomposition.
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ThelastexamplesiteisanoperatingwindfarminTexas. Figure9showsthewindspeedshear,whichis
usuallyquitesmallduringtheday,butspansalargerangeatnight. Itisworthnotingthatthisthree
monthdatasetisfromwintermonths,andthuscontainsmorenighttimesamplesthandaytimesamples.
Theveerdataforthissite,showninFigure10,arequiteextreme,almostentirelyatnight,andright
sided.
Figure9: HistogramofWindfarmShearExponentwithDay/NightDecomposition.
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Figure10: HistogramofWindfarmVeerwithDay/NightDecomposition.
Theday/nighthistogramsfromthethreedifferentsitesshowninFigures510havesimilarcharacter,
butadetailedsitecomparisonisdifficultwithoutplottingonacommonaxis. Oneveryeffectivewayto
comparesitesistoplotthefrequencyofexceedancedistribution.Likeaninversecumulative
distribution,
the
frequency
of
exceedance
indicates
the
percentage
of
time
that
the
sheer
was
in
excess
ofavalue.Becausethedatawerefilteredtoremoveperiodswithlowwindspeed,thepercentages
indicatedarewithrespecttoturbineoperationaltime.Byplottingthefrequencyofexceedanceofwind
speedanddirectionshearforallthreesites,thesitetositedifferencesarequiteapparent.
Figure11showsthefrequencyofexceedanceofwindspeedshearforthethreeexamplesites.Fromthe
chart,itisevidentthatsweptareashearinexcessof2:1(=0.63)occursalmost10%ofturbine
operationaltimeattheCapeCodsite,whileonly2%attheBAOsite.
Figure12showsthefrequencyofexceedanceoftheabsolutevalueofwinddirectionshearforthethree
examplesites.Fromthechart,itisevidentthatsweptareaveerinexcessof20degreesoccursalmost
10%of
turbine
operational
time
at
two
of
the
sites,
but
only
occurs
2%
of
the
time
at
the
Cape
Cod
site.
Thusthesitewiththehighestspeedshearisseentohavethelowestdirectionalshear.
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Figure11: FrequencyofExceedanceofShearExponentatThreeExampleSites.
Figure12: FrequencyofExceedanceofVeeratThreeExampleSites.
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CONCLUSIONS
Shorttermwindspeedanddirectionshearvalueswerecomputedbasedon10minuteaverageSoDAR
measurements.Theresultsindicatethepresenceofextremeshearatallexamplesites,eventhoughthe
datawerefilteredtoremovelightwindperiods,whenthehubheightwindspeedwasbelowa
conservative,6m/s
cut
in
threshold.
Extreme
shear
is
shown
to
occur
mostly
at
night,
presumably
becausethemorestableatmosphereovernightdoeslittletorelievetheatmosphericforcegradients
thatcauseshear.Lastly,thefrequencyofoccurrenceofshearextremesisshownusingalogscale
frequencyofexceedanceplot,andthedistributionsareobservedtodiffersubstantiallyfromsitetosite.
Moreworkisneededtoassesstheimportanceofmeasuringshorttermwindshearvalues.Aswind
turbinetechnologyadvancestoincludeindividualbladepitchcontrol,theextenttowhichdiffering
windsacrosstherotorcauseperformanceandreliabilityproblemsmaychange.Atthecurrenttime,
however,extremewindshearisthoughttocontributetoperformancedegradationandoperational
downtime,sositestatisticsbeyondsimple,extrapolated,seasonalaveragesshouldbeevaluated,and
SoDARmeasurementtechnologyiswellsuitedtoprovidethedata.
REFERENCES1. Elliott,DennisL.,andJackCadogan(1990): EffectsofWindShearandTurbulenceonWind
TurbinePowerCurves,PresentedattheEuropeanCommunityWindEnergyConferenceandExhibition,Madrid,Spain,1014Sep.1990
2. Moore,KathleenE.,andBruceBailey(2007): ClassifyingRotorSpanShearProfileVariabilityandImprovingWindTurbineProductionPrediction,Windpower2007ConferenceProceedings(CDROM),
American
Wind
Energy
Association,
2007.
3. Schwartz,M.andD.Elliot(2006): WindShearCharacteristicsatCentralPlainsTallTowers,ReprintfromWindPower2006Conference,NREL/CP50040019,June2006.
4. Smith,K.,G.Randall,D.Malcolmetal.(2002): EvaluationofWindShearPatternsatMidwestWindEnergyFacilities,ReprintfromWindPower2002Conference,NREL/CP50032492,May2002.