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8/3/2019 Wind Turb Lecture Full
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WindPowerSystems
Fall2010
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HistoryofWindPowerDevelopment
WindPower'sBeginnings
(1000B.C.
1300
A.D.)
SailBoat
PersianPanemone
500900A.D.
Verticalaxiswindstructureforseed
grindingorwaterpump
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WindmillsintheWesternWorld
(13001875
A.D.)
ThefirstwindmillstoappearinwesternEurope
wereofthehorizontalaxisconfiguration.
Thereasonforthesuddenevolutionfromthe
verticalaxisPersiandesignapproachisunknown
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Mediterraneanwindmill(Hills:1996)
Itusestheconceptofsailboat
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TheDutchman
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Asteel
bladed
water
pumping
windmill
in
the
American
Midwest(late1800's).
Between1850and1970,oversixmillionmostlysmall(1
horsepowerorless)mechanicaloutputwindmachineswere
installedintheU.S.alone.Theprimaryusewaswater
pumpingandthemainapplicationswerestockwateringand
farmhomewaterneeds.Verylargewindmills,withrotorsup
to18metersindiameter,wereusedtopumpwaterforthe
steamrailroadtrainsthatprovidedtheprimarysourceofcommercialtransportationinareaswheretherewereno
navigablerivers.
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Waterpumpusingwindenergy
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From:DevelopingWindPower
ProjectsbyToreWizelius (2007)
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Disaster
Palmer
Putnam's
1.25
megawatt
wind
turbine
wasoneoftheengineeringmarvelsofthelate
1930's,butthejumpinscalewastoogreatfor
availablematerials.
Thishorizontalaxisdesignfeaturedatwobladed,175footdiameterrotororienteddownwindof
thetower.The16tonstainlesssteelrotorused
fullspanbladepitchcontroltomaintainoperation
at28RPM.In1945,afteronlyseveralhundred
hoursofintermittentoperation,oneoftheblades
brokeoffnearthehub,apparentlyasaresultof
metalfatigue.
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Typicala3bladeturbine
system
Lowspeed;1530RPM
Noticethepoleheight;50m
Rotordiameter=oneblade
lengthx2
Sweptarea= (D/2)2
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ThebiggesteggbeaterDarrieus,thenearly
100mheight60mdiameter4MWratedgiganticeggbeaterEOLE,asshownintheleftpicture,locatedatCapChat,Quebec,Canada.Thegiantwasoperatedatlowerspeednowtoensure
longevitythusoutputreducedto2.5MW.AnotherEole pictureishere.
The42mheight34mdiameter625kWSandiaLaboratoryprototype wasbuiltspeciallyforresearchatBushland,Texas.ItcanbeidentifiedeasilyfromthefatcolumnwithUSDA,DOE,andaneaglelogoonit.
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http://rotor.fb12.tu-berlin.de/picture.eole.htmlhttp://rotor.fb12.tu-berlin.de/picture.eole.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://telosnet.com/wind/govprog.htmlhttp://rotor.fb12.tu-berlin.de/picture.eole.html8/3/2019 Wind Turb Lecture Full
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From:Mukund Patel
WindandSolarPower
System(2006)
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NationalRenewableEnergy
Laboratory(NREL)Mt.Newall,Antarctica(NREL)
4NEGMicon225kW,Ascension
IslandinmidAtlanticOcean(NREL)16
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HornsRev Denmark'sLargestWindFarm HornsRevissituatedofthecoastof,Blvandhuk,themostwesternpointofDenmark.
ThelargestwindfarminDenmarkistheoffshorewindfarmofHornsRev,whichwascompletedin2002.ItissituatedintheNorthSea,1420kmoffthecoastofJutland.Withits80Vestas 2MWturbines,thewindfarmhasatotalcapacityof160MW.Thatmakesitthelargestoffshorewindfarmin
theworldtoday(2003).Thefarmsuppliestheequivalentof150,000(Danish)households.ThelargerproductioncomparedtoNysted isduetobetterwindconditions.Learnmoreatwww.hornsrev.dk
(PhotographClausBjle Mller,2003DWIA)
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http://www.hornsrev.dk/Engelsk/default_ie.htmhttp://www.hornsrev.dk/Engelsk/default_ie.htmhttp://www.hornsrev.dk/Engelsk/default_ie.htm8/3/2019 Wind Turb Lecture Full
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InBrunsbuttel,Germany(2006),two5megawatts
offshorewindturbineswereonline.Theblade
diameterof126meterssweepinganareaof
12,000m2.
Maximumpoweriswhenthewindspeedis30
mph.Therotorsstarttoturnfor7mphwindspeed.
Fewmegawattsduringfreshbreeze.
Furling canbeachievedeithermanually(bytheturbineownerhimselfphysicallycrankingthe
turbineoutandawayfromthewind),or
automatically(withhydraulicsandspringsfor
example)withthegoalofturningtheturbine
bladeedgesintothewindwhenthewindisdangerouslystrongandgusty.
WhatIsWindTurbineFurling
Ifthewindistoostrong,thepitchof
individualbladewillberotatedto
preventthewholestructurebeingdamaged(Furling)
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WindSpeedandEnergy
Mukund R.Patel(WindandSolar)
Joules
m =massflows
Thevolumetricflowrateis AV
Themassflowrateis AV kg/sec
SpeedandPowerRelations
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Thetotalmechanicalpowerontheupstream
windinwatts:
Sometimethesiteselectionisbasedon
thepowerdensityorspecificwind
power(watts/m2)or
NoticeonV3 variation
Theupstreamwindwillberetarded/slowdownbythe
bladesandhenceextractingtheenergy.However,notall
thewindenergywillberemoved;thedownstreamair
stillmovesatalowerspeed.
W/m2
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=therotorefficiency=Neverreach1.0
= Maxvalueis0.593
Canbearrangedintheform
Powerfromthebladesisexpressedintermsofupstreamwind(watts)
Where
Comparingtheaboveequationto
Notice: Cp isthefractionoftheupstreamwind
powerthatisextractedbytherotorbladesandfed
tothegenerators(usefulpower).
V=upstreamwindvelocityattheentranceoftherotorblades
V0 =downstreamwindvelocityattheexitofrotorblades
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28.97g/mol=Molecularweight(MW)
ofgas
Warmerairhaslessdensityandhence
produceslesspower.
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http://docs.engineeringtoolbox.com/documents/600/air_density_specific_we
ight_chart.pdf
http://docs.engineeringtoolbox.com/documents/600/air_density_specific_weight_chart.pdfhttp://docs.engineeringtoolbox.com/documents/600/air_density_specific_weight_chart.pdfhttp://docs.engineeringtoolbox.com/documents/600/air_density_specific_weight_chart.pdfhttp://docs.engineeringtoolbox.com/documents/600/air_density_specific_weight_chart.pdf8/3/2019 Wind Turb Lecture Full
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Theratiocanbeusedto
determinetherotorstress,as
inExample6.6P322.
P0 isthereferenceheightat10m
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FromFig3.3,thetheoretical
maximumvalueofCp is0.59
happenedwhenV0/Vof
about0.033or(1/3).
Cp canbeexpressedintermsof
therotortipspeedratio(TSR),whichisdefinedasthelinear
speedoftherotorstiptothe
upstreamwindspeed.
Whathappenatextremev0/vratio?
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InpracticaldesignsCpranges:
0.40.47formodernhighspeedtwobladeturbines
0.40.42forModernthreebladeturbines
FromFig3.4,wecanseethatuptonowthemaxvalueis0.47or
about0.5(50%efficiency).HenceaPracticalmaxpoweroutputis
Watts/m2 ofsweptarea
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Rotorsweptareaforthehorizontalaxis
turbineis:
whereDistherotor
diameter.
Sweptareaforverticalaxisturbine,like
Darrieus design,isverycomplicatedto
calculate.Theapproximationwithblade
shapeasaparabolagives:
Areaofparabola=2/3XbaseXheight
For33mdiameterand33mhalf
oftherotor,sweptarea=726m2
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AirDensity
Theairdensityatsealevelat1atm (14.7
psi)and60Fis1.225kg/m3.
ThefollowingtwoapproximatedEqs are
validupto6000m(~20,000ft):
OR
where,Hm isthesiteelevationinmeters.
Thetemperatureisrelatedtoelevationin Cas:
Varieswithpressureandtemperature
(GasLaw)
ToconvertCto F=multiply Cby9/5,thenadd32
Forthereverse,subtract32to F,thenmultiply5/9 20 C=68 F 34
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LargesyncgeneratorrequiresDCcurrentfeedingthefieldwindings.
DCsupplyusuallyobtainsfromacpowergridthroughrectifierand
capacitor.
TheinternalfieldingwindingsareexcitedbytheexternalDCcurrent
throughthesliprings(attachedontherotorshaft)andbrushes.
SmallgeneratorcanusetheresidualDCmagneticfieldleftover
insidethemachine.
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Thespeedforwindapplicationdoesnotturnasafixedspeed(asynchronousgenerator).
RotatingMagneticfield
Resultantmagneticfield
rotatesClockwise(CW)
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Inthistext,thesenseofpositiveflowofcurrentis
shownbelow:
Magnetic field
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SquirrelCageRotorMagneticfield
rotatesCWandat
thestartingthecage
aswellasthecrosswiresarestandstill.
Twomainequations:
F=i (lXB)e=(VXB).L
Toapplythe
equations,themagneticfieldis
stationaryandthe
wiresmoveacross
thefield.Todothis,
weviewfromthe
movingwireandthe
fieldappears
standstill.
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InductionmachineasaMotor
Therotorspeedisabitslowerthan
synchronousspeed,duetoeitherfriction,coolingblades,orloadatthe
shaft.
Ex.6.8P333
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InductionMachineasaGenerator
Therotor/shaftspeedisabitfasterthanthesynchronousmagneticfield.
TheslipconceptisstillappliedbutonlythesignbecomesNEGATIVE.
(Rotorspeedismovingfasterthansynchronousspeed)
For60Hz,2polemachine,synchspeedis120f/p=3600rpm.
Theslipofgridconnectedgeneratoris
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Selfexcitedgenerator:
Useresonanceconcept
Makeuseoftheresidual
magneticfield
AdvantageusingInductionGeneratorforwindturbine
application
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http://livelypictures.blogspot.com/2008/05/inductionmotor.html
http://www.electricmotors.machinedesign.com/guiEdits/Co
ntent/bdeee11/bdeee11_7.aspx
Moreoninductionmachines
http://www.allaboutcircuits.com/vol_2/chpt_13/9.html
http://livelypictures.blogspot.com/2008/05/induction-motor.htmlhttp://livelypictures.blogspot.com/2008/05/induction-motor.htmlhttp://livelypictures.blogspot.com/2008/05/induction-motor.htmlhttp://www.electricmotors.machinedesign.com/guiEdits/Content/bdeee11/bdeee11_7.aspxhttp://www.electricmotors.machinedesign.com/guiEdits/Content/bdeee11/bdeee11_7.aspxhttp://www.allaboutcircuits.com/vol_2/chpt_13/9.htmlhttp://www.allaboutcircuits.com/vol_2/chpt_13/9.htmlhttp://www.electricmotors.machinedesign.com/guiEdits/Content/bdeee11/bdeee11_7.aspxhttp://www.electricmotors.machinedesign.com/guiEdits/Content/bdeee11/bdeee11_7.aspxhttp://livelypictures.blogspot.com/2008/05/induction-motor.html8/3/2019 Wind Turb Lecture Full
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Modern3bladesystem,Cp workswell
whenthetipspeed
ratioisbetween3
to5.5,with4being
thebest.
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PowerdeliveredbyModern3Bladesystem
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Rememberwindpowervariesasv3
DiscreteProbability
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Windstatisticinoneyear=8760hrs
Thissitehaswindat6m/sfor946hrs
Previousslide
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Hoursinayear Average
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Continuouscase
8760hr/yristhenormalized
factor
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Whenk=2,thep.d.f hasa
specialnamewhichweall
recognizeas,Rayleighpdf
Forthebestguessofthe
windpdf,usingk=2for
initialdesign.
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Shapefactor(k)=2
Rayleighpdf
Vistheaveragewindspeed
=0.886Xscaleparameter
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OnP342,thecorrectpowerdensityisabout1.9times
more.Thisisduetothefactthattheauthorusedthe
windhistogramthatfitsRayleighpdf.
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Sincewedontknowtheblade
sweptarea,thenwehavetoexpressthewindpowerinterms
ofW/m2
P 52 f th f ll i t Th fitti i W ib ll
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http://www.offshorewindenergy.org/reports/report_043.pdf
Page52ofthefollowingreport.ThecurvefittingusingWeibull
pdf andrealmeasureddata.
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FormulacommonlyusedinEurope
RoughnessClass1
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Sweptarea= r2 =
D2/4
Diameter=48m
Usuallywedeterminethe
energyperyear
Optimum Spacing of Towers for Wind farm
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OptimumSpacing ofTowersforWindfarm
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Twostrategies:increaserotordiameterorincreasethegeneratorsize
Increaserotorsize:theoutputpowerreachesmaxatlower
windspeed(SeeFig.6.33a)
IncreaseGensize:Thiswillincreasetheoutputpoweratthe
sitewherethereishighwindmostofthetime.
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k=2andC=6
Theavg.windspeed=5.32m/s
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Wh t i th b bilit th t th i d bl
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Whatistheprobability thatthewindblows
between
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Histogramoftheexceldata
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BasedonRayleighstatistic
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WecanestimatetheCapacityFactor
(CF)usingalinearequation,
Slope(m)=(0.40.13)/(85)
=0.09~0.087
Intersection=
7
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Energyproductionperyear
Onlyapproximation
Usingthisapproximation,theannualpoweris
2,899,560kWh/yrAscomparedto2,851,109kWh/yr(page365give
moreaccuratepower)
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