lawhite shear veer paper wdshear

8/8/2019 LaWhite Shear Veer Paper WDShear

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CharacterizingWindSpeedandDirectionShearwithSoDARData|LaWhite,Walls,&Cohn,SecondWindInc.|Page1

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.

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