PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution

A Ans

Discuss : Cost of wind energy !"e cost of #ind energy is com$ara%le to &on'entional(fuel)%ased energy* #"en cost of green"ouse gas emissions is ta+en into account A'erage cost of energy from coal is a%out ,80 $er MW"* #"ile #ind energy at a site #it" a'erage annual #ind s$eed of 7 m-s is slig"tly less t"an ,80 $er MW" Figure %elo# is a $lot of le'eli.ed cost of energy from coal* natural gas* nuclear* and ons"ore and off(s"ore #ind for a'erage #ind s$eed in t"e range of / to 10 m-s !"e ad'antage of #ind is t"at it "as no fuel cost According to t"e D0E re$ort* t"e amount of economically 'ia%le ons"ore #ind $o#er is 8000 1W t"at can %e $roduced at a cost of 283 $er MW" or less

4 Ans

A Ans

Fig. Levelized cost of energy from different sources. Costs are in euros per MWh. Cost of wind energy is a function of wind speed Discuss : Benefits of wind energy 4enefits of #ind energy are listed %elo# 5rimary %enefits is en'ironmental %enefits Secondary %enefits is cost com$are to &on'entional source of $o#er li+e coal* natural gas* nuclear Wind energy $roduction results in .ero emissions Wind energy is among t"e c"ea$est sources of rene#a%le energy #ind energy is a'aila%le in a%undance in most &ountries W"ere e'er electricity grid is not $ossi%le t"ere #e can use as $rime source of electricity E7$lain : Kinetic energy of wind
The kinetic energy contained in wind is:

E =

8 m'6

Cylinder of air in front of the rotor.

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
!"e mass (m) from #"ic" energy is e7tracted is t"e mass contained in t"e 'olume of air t"at #ill flo# t"roug" t"e rotor For a "ori.ontal a7is #ind tur%ine (9AW!)* t"e 'olume of air is cylindrical* as s"o#n in Fig +inetic energy of a solid o%:ect of fi7ed mass Wit" air flo#* it is con'enient to t"in+ of mass in a cylinder of air of radius r Since v m-s is t"e #ind s$eed* t"e mass contained in cylinder of lengt" v meters and radius r is t"e amount of mass t"at #ill $ass t"roug" t"e rotor of tur%ine $er second ;t is* t"erefore* con'enient to use mass $er second (m< )
E= m.v2 m = Av

#"ere is air density and A is t"e cross(section area m< is t"e amount of matter contained in a cylinder of air of lengt" v <E is energy $er second* #"ic" is t"e same as $o#er <E = = 1!6 Avv6 = 1/2 Av3 4 Ans E7$lain : Sensitivity of power to rotor radius and wind speed !"e im$act of c"ange in radius %y a small amount >r * #"ile all else is constant* can %e e7$ressed as: >5-5 = 6>r-r !"is means t"at if t"e radius is increased-decreased %y 1?* $o#er #ill increase-decrease %y 6? For larger c"anges in radius* t"e a%o'e formula does not a$$ly@ for instance* a 10? increase in radius #ill lead to increase %y 61? in $o#er A 60? increase in radius #ill lead to AA? increase in $o#er ;f s$eed is c"anged %y a small amount and all else is constant* t"en >5-5 = B>'-' !"is means t"at if t"e s$eed is increased-decreased %y 1?* energy #ill increase-decrease %y B? 9o#e'er* if t"e #ind s$eed is increased %y 60?* t"e $o#er #ill increase %y: 1- 6 = v"1v"6= (1.6)B = 1.768 !"is is a 76 8? increase in $o#er !"e relations"i$ %et#een $o#er and #ind s$eed* and $o#er and rotor diameter are seen in Figs %elo# :
Cubic relationship between power and wind speed for a horizontal axis wind rotor with radius = 1 m.

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution

Cu#ic relationship #etween power and wind speed for a horizontal a$is wind rotor with radius % & m.

'uadratic relationship #etween power and rotor size. Wind speed is ( m!s. & Ans E7$lain : &onser'ation of Mass For calculation of conser'ation of energy follo#ing Assum$tions are made: All air t"at enters at A0 lea'es from A6 Fluid flo# is streamlined and so t"ere is no loss of mass from t"e surface of t"e control 'olume Fluid is incom$ressi%le* t"at is* t"ere is no c"ange in density

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution

;llustration of a control 'olume t"at follo#s streamlines t"at $ass t"roug" t"e rotor v0) vr ) v6 are u$stream* rotor* and do#nstream #ind s$eeds A0) Ar ) A6 are u$stream* rotor* and do#nstream cross(sectional areas Cnder t"ese assum$tions* conser'ation of mass is: m< = A0v0 = Arvr = A6v6 #"ere v6 is t"e a'erage #ind s$eed* #"ere t"e a'erage is ta+en o'er cross(sectional A6@ vr is assumed to %e uniform o'er Ar * #"ere Ar is t"e area of t"e rotor Since t"e rotor of tur%ine is e7tracting energy from air* t"e +inetic energy of air #ill reduce* so* v0 * vr * v6 D Ans E7$lain : Conservation of energy A sim$lified conser'ation of energy eDuation is used initially* under t"e assum$tions listed %elo# !otal energy = Einetic energy F 5ressure energy F 5otential energy !"e +inetic energy is %ecause of t"e directed motion of t"e fluid@ $ressure energy is %ecause of t"e random motion of $articles in t"e fluid@ $otential energy is %ecause of relati'e $osition of t"e fluid Assum$tions: Fluid is incom$ressi%le* meaning t"e density does not c"ange Gote t"at $ressure can c"ange Fluid flo# is in'iscid* meaning t"e eDuation a$$lies to fluid flo# outside a %oundary layer !"e %oundary layer is #"ere t"e friction %et#een a surface and fluid causes slo#er fluid flo# All t"e flo# is along streamlines !"ere is no #or+ done %y s"ear forces !"ere is no "eat e7c"ange !"ere is no mass transfer Helati'e $osition of fluid #it" res$ect to t"e eart"Is surface does not c"ange* t"at is* t"e $otential energy remains constant !"e first t#o assum$tions define an ideal fluid !"e a%o'e assum$tions lead to 4ernoulli s eDuation: !otal energy $er unit 'olume = v6-6F p = constant v+!+ is t"e +inetic energy term* #"ic" is also called t"e dynamic $ressure* and p is t"e static $ressure 4ernoullis eDuation* t"erefore* states t"at along a stream line #"en s$eed increases* t"en $ressure decreases and #"en s$eed decreases* t"en $ressure increases !"e

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
magnitude of c"ange in $ressure is go'erned %y t"e Duadratic relations"i$ E Ans E7$lain : Conservation of momentum

Since t"e #ind rotor is a mac"ine t"at #or+s %y e7tracting +inetic energy from #ind* t"e #ind s$eed is reduced Since momentum is mass multi$lied %y s$eed* t"ere is a c"ange in momentum According to Ge#tonIs second la#* t"e rate of c"ange of momentum in a control 'olume is eDual to t"e sum of all t"e forces acting ;n order to sim$lify t"e eDuations* t"e follo#ing assum$tions are reDuired: !"ere are no s"ear forces in t"e $(direction !"e $ressure forces on edges A0 and A6 are eDual !"ere is no momentum loss or gain ot"er t"an from A0 and A6 !"e eDuation for Ge#tonIs second la# along t"e $(a7is %ecomes: m<0v0 m<6v6 = F 4ecause of c"ange in momentum in t"e control 'olume* t"ere must %e e7ternal force acting ;n t"is case* rotor $ro'ides t"e e7ternal force According to Ge#tonIs t"ird la#* t"ere must %e an eDual* %ut o$$osite* force t"at acts on t"e rotor !"is force is e7erted %y #ind 4ecause #ind is e7erting a force on t"e rotor* t"ere must %e a $ressure difference across t"e rotor eDual to t"e force di'ided %y t"e area of rotor Since t"e rotor "inders t"e flo# of air* t"e $ressure at t"e front of t"e rotor (p0r) is "ig"er t"an t"e free(stream $ressure (p0)@ t"e $ressure at t"e %ac+ surface of rotor (p6r) is %elo# t"e free(stream $ressure 4ecause t"e $ressure is "ig"er at t"e front of t"e rotor* according to 4ernoulliIs eDuation* t"e #ind s$eed decreases from t"e free(stream #ind s$eed ( v0) as it a$$roac"es t"e front of t"e rotor 4ecause vr* t"e #ind s$eed in front rotor* is less t"an v0* conser'ation of mass mandates t"at t"e area increase@ since v0*vr* cross(sectional areas must "a'e t"e relations"i$ A0 , Ar Gote* t"e #ind s$eed does not c"ange as it $asses t"roug" t"e rotor@ t"at is* t"e #ind s$eed is t"e same immediately in front of t"e rotor and immediately %e"ind t"e rotor 4ecause t"e $ressure is lo# immediately after #ind "as $assed t"roug" t"e rotor and t"e $ressure #ill increase to t"e free(stream $ressure as air mo'es to#ard A6* t"e #ind s$eed #ill decrease and* t"erefore* t"e area #ill increase from t"e rig"t face of rotor to A6* t"at is* A6 * Ar !"e 'olume to t"e rig"t of t"e rotor is called t"e #a+e B Ans
!hat is Betz limit" derive its mathematical expression.

4et. $ostulated a t"eory a%out t"e efficiency of rotor%ased tur%ines Csing sim$le conce$ts of conser'ation of mass* momentum* and energy* "e $ostulated t"at a #ind tur%ine #it" a disc(li+e rotor cannot ca$ture more t"an 3J B? of energy contained in a mass of air t"at #ill $ass t"roug" t"e rotor !"e 4et. limit is deri'ed ne7t A$$lying conser'ation of mass* in control 'olume A0* Ar * and A6 #it" constant density A0'0 = Ar'r = A6'6

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
#"ere '6 is t"e a'erage #ind s$eed at A6 A$$lying Ge#tonIs second la# Go# force e7erted on rotor %y #ind: F = m<r ('0 K '6) = LAr'r ('0 K '6) !"e force e7erted on t"e rotor is also %ecause of t"e $ressure difference across t"e rotor: F = Ar ($0r ( $6r) Go# EDuating A%o'e eDuation of Force F = Ar($0r( $6r) = LAr'r ('0 K '6) 4ernoullis la# is ne7t a$$lied in t#o 'olumes: (a) Flo# along streamlines from A0 to t"e front face of t"e rotor@ and (%) flo# from t"e %ac+ surface of rotor to A6. $0 F 1-6L'60= $0rF 1-6L'6r $r6 F 1-6L'6r = $0 F 1-6L'66 From A%o'e !#o EDuation 5r0 ( 5r6 = 8 L('60 ) '66) F- Ar = ($0r ( $6r) = L'r ('0( '6) = 8 L('60 ) '66) Mr = ('0( '6)-6 !"e $o#er deli'ered to t"e ideali.ed rotor %y t"e #ind is: 5 = FMr = ($0r ( $6r) ArMr = 8 LArMr('60 ) '66) = 1-6LArMr (M0 K M6) (M0 F M6) 5= 8 LArMr('60 ) '66) = 8 m('60 ) '66) 5= 1-6LAr'r6('0( '6) =6LAr'r6('0( 'r) Ma7imum $o#er is reali.ed #"en: N 5-N'r = 0 = 6MrM0 ) BMr6 Mr = 6-BM0 Mr = 6-BM0 5 = 6LArMr6(M0 ) Mr) = LArM0B(8-67)

Cp is called t"e $o#er coefficient Cp is referred to as t"e 4et. limit and states t"at t"e ma7imum $o#er an ideal rotor can e7tract from #ind is 3J B?

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
A Ans
!rite a note on wind speed measuring instrumentation li#e cap anemometer" propeller anemometer" sonic anemometer " S$%&'" ()%&' !ind Speed *easuring )nstruments are discuss as below

Cup Anemomete ! "

!"e cu$ anemometer is $ro%a%ly t"e most common instrument for measuring t"e #ind s$eed &u$ anemometers use t"eir rotation* #"ic" 'aries in $ro$ortion to t"e #ind s$eed* to generate a signal !odayIs most common designs feature t"ree cu$s mounted on a small s"aft !"e rate of rotation of t"e cu$s can %e measured %y: mec"anical counters registering t"e num%er of rotations@ electrical or electronic 'oltage c"anges (A& or D&)@ a $"otoelectric s#itc" !"e mec"anical(ty$e anemometers indicate t"e #ind flo# in distance !"e mean #ind s$eed is o%tained %y di'iding t"e #ind flo# %y time (t"is ty$e is also called a #ind(run anemometer) For remote sites* t"is ty$e of anemometer "as t"e ad'antage of not reDuiring a $o#er source
Some of the earliest types of mechanical anemometers also drove a pen recorder directly. +owever" these systems were expensive and difficult to maintain. &n electronic cup anemometer gives a measurement of instantaneous wind speed. ,he lower end of the rotating spindle is connected to a miniature &C or %C generator and the analog output is converted to wind speed via a variety of methods. ,he photoelectric switch type has a disc containing up to 1-. slots and a photocell. ,he periodic passage of the slots produces pulses during each revolution of the cup. ,he response and accuracy of a cup anemometer are determined by its weight" physical dimensions" and internal friction. By changing any of these parameters" the response of the instrument will vary. )f turbulence measurements are desired" small" lightweight" low/friction sensors should be used. ,ypically" the most responsive cups have a distance constant of about 1 m. !here turbulence data are not re0uired" the cups can be larger and heavier" with distance constants from - to 1 m. ,his limits the maximum usable data sampling rate to no greater than once every few seconds. ,ypical accuracy values 2based on wind tunnel tests3 for cup anemometers are about 4/-5. 6nvironmental factors can affect cup anemometers and reduce their reliability. ,hese include ice or blowing dust. %ust can lodge in the bearings" causing an increase in friction and wear and reducing anemometer wind speed readings. )f an anemometer ices up" its rotation will slow" or completely stop" causing erroneous wind speed signals" until the sensor thaws completely. +eated cup anemometers can be used" but they re0uire a significant source of power. Because of these problems" the assurance of reliability for cup anemometers depends on calibration and service visits. ,he fre0uency of these visits depends on the site environment and the value of the data.

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution

Cup anemometer

P ope##e Anemomete !
5ro$eller anemometers use t"e #ind %lo#ing into a $ro$eller to turn a s"aft t"at dri'es an A& or D& (most common) generator* or a lig"t c"o$$er to $roduce a $ulse signal !"e designs used for #ind energy a$$lications "a'e a fast res$onse and %e"a'e linearly in c"anging #ind s$eeds ;n a ty$ical "ori.ontal configuration* t"e $ro$eller is +e$t facing t"e #ind %y a tail('ane* #"ic" also can %e used as a direction indicator !"e accuracy of t"is design is a%out F(6?* similar to t"e cu$ anemometer !"e $ro$eller is usually made of $olystyrene foam or $oly$ro$ylene W"en mounted on a fi7ed 'ertical arm* t"e $ro$eller anemometer may %e used for measuring t"e 'ertical #ind com$onent A configuration for measuring t"ree com$onents of #ind 'elocity is s"o#n in 4elo# Figure !"e $ro$eller anemometer res$onds $rimarily to #ind $arallel to its a7is* and t"e #ind $er$endicular to t"e a7is "as no effect

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution

Son$% Anemomete !
Cltrasonic Anemometers use ultrasonic sound #a'es to measure #ind s$eed and direction Wind 'elocity is measured %ased on t"e time of flig"t of sonic $ulses %et#een $airs of transducers A re'ie# of t"eir t"eory of o$eration is gi'en %y &uer'a and San.(Andres (6000) 0ne(* t#o(* or t"ree(dimensional flo# can %e measured 'ia signals from $airs of transducers !y$ical #ind engineering a$$lications use t#o( or t"ree(dimensional sonic anemometers !"e s$atial resolution is determined %y t"e $at" lengt" %et#een transducers (ty$ically 10 to 60 cm) Sonic anemometers can %e used for tur%ulence measurements #it" fine tem$oral resolution (60 9. or %etter)

A%ou!t$% Dopp#e Sen!o ! &SODAR'

S0DAH (standing for Sound Detection And Hanging) is classified as a remote sensing system* since it can ma+e measurements #it"out $lacing an acti'e sensor at t"e $oint of measurement Since suc" de'ices do not need tall (and e7$ensi'e) to#ers for t"eir use* t"e $otential ad'antages of t"eir use are o%'ious Hemote sensing is used e7tensi'ely for meteorological and aeros$ace $ur$oses* %ut only in recent times "as it %een used for #ind siting and $erformance measurements S0DAH is %ased on t"e $rinci$le of acoustic %ac+scattering ;n order to measure t"e #ind $rofile #it" S0DAH* acoustic $ulses are sent 'ertically and at a small angle to t"e 'ertical For measurement of t"ree(dimensional #ind 'elocity* at least t"ree %eams in different directions are needed !"e acoustic $ulse transmitted into t"e air e7$eriences %ac+scattering from $articles or fluctuations in t"e refracti'e inde7 of air !"ese fluctuations can %e caused %y #ind s"ear as #ell as %y tem$erature and "umidity gradients !"e acoustic energy scattered %ac+ to t"e ground is t"en collected %y micro$"ones Assuming t"at t"e sender and t"e recei'er are not se$arated* t"e S0DAH configuration is referred to as a monostatic S0DAH At t"e $resent time all commercial S0DAHs used for #ind energy a$$lications are monostatic (sim$lifying t"e system design and reducing its si.e)

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
;f t"e local s$eed of sound is +no#n* t"e tra'el time %et#een emission and rece$tion determines t"e "eig"t t"e signal re$resents A c"ange in t"e acoustic freDuency of t"e ec"o (Do$$ler s"ift) occurs if t"e scattering medium "as a com$onent of motion $arallel to t"e %eam motion !"us* estimation of t"e s$eed of t"e #ind s$eed $arallel to t"e %eam as a function of "eig"t can %e carried out 'ia freDuency s$ectrum analysis of t"e recei'ed %ac+( scattered signal S0DAHs "a'e %een used for %ot" ons"ore and offs"ore #ind siting studies #it" measurement of #ind s$eed u$ to B00m a%o'e t"e de'ice alt"oug" S0DAH systems can %e commercially $urc"ased* t"e follo#ing issues "a'e arisen:

L(!e Dopp#e Sen!o ! &LIDAR'

O;DAH (Oig"t Detection And Hanging)* similar to S0DAH* is also classified as a remote sensing de'ice* and can similarly %e used to ma+e measurements of a t"ree(dimensional #ind field ;n t"is de'ice* a %eam of lig"t is emitted* t"e %eam interacts #it" t"e air and some of t"e lig"t is scattered %ac+ to t"e O;DAH !"e returned lig"t is analy.ed to determine t"e s$eed and distances to t"e $articles from #"ic" it #as scattered ;n addition* t"e %asic O;DAH $rinci$le relies on t"e measurement of t"e Do$$ler s"ift of radiation scattered %y natural aerosols t"at are carried %y t"e #ind O;DAHs "a'e %een used e7tensi'ely in meteorological and aeros$ace a$$lications* #it" t"e cost of meteorological O;DAH systems %eing Duite "ig" 9o#e'er* de'elo$ments in commercially a'aila%le O;DAH systems "a'e $roduced lo#er cost systems for #ind s$eed determination at "eig"ts of interest in #ind energy a$$lications ;n addition* eye safety concerns "a'e %een o'ercome since t"e ma:ority of O;DAH lasers emit at t"e eye(safe #a'elengt" of 1 3 microns Csing t"ese ne# systems* O;DAH "as most recently %een a$$lied to %ot" ons"ore and offs"ore #ind system a$$lications At t"e $resent time* t"ere are t#o ty$es of commercial O;DAH de'ice a'aila%le for #ind engineering a$$lications: (1) a constant #a'e* 'aria%le focus design* and (6) a $ulsed O;DAH #it" a fi7ed focus Wind s$eeds at "eig"ts u$ to 600m "a'e %een measured %y %ot" ty$es of O;DAH system As an e7am$le of an a$$lication of a constant #a'e O;DAH system* a $orta%le and com$act O;DAH system #as used to determine "ori.ontal and 'ertical #ind s$eed and direction at "eig"ts u$ to 600 m As s"o#n in Figure %elo#* t"e O;DAH %eam is offset at B0 degrees to t"e 'ertical !"e %eam scans as it re'ol'es at one re'olution $er second As t"e %eam rotates it interce$ts t"e #ind at different angles* t"ere%y %uilding u$ a #ind s$eed ma$ around a disc of air ;n a ty$ical o$eration* t"ree scans are $erformed at eac" "eig"t* and #ind measurements are ta+en at fi'e "eig"ts

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution

-chematic of conically scanned L./A0 system 3 Ans 9o# #ind data analysis $erformed !"e data $roduced %y a #ind monitoring system can %e analy.ed in a num%er of #ays !"ese may include* %ut are not limited to: a'erage "ori.ontal #ind s$eeds o'er s$ecified time inter'als@ 'ariations in t"e "ori.ontal #ind s$eed o'er t"e sam$ling inter'als (standard de'iation* tur%ulence intensity* ma7ima)@ a'erage "ori.ontal #ind direction@ 'ariations in t"e "ori.ontal #ind direction o'er t"e sam$ling inter'als (standard de'iation)@ s$eed and direction distri%utions@ $ersistence@ determining gust $arameters@ statistical analysis* including autocorrelation* $o#er s$ectral density* lengt" and time scales* and s$atial and time correlations #it" near%y measurements@ steady and fluctuating u* '* # #ind com$onents@ diurnal* seasonal* annual* inter(annual and directional 'ariations of any of t"e a%o'e $arameters Some mention "as %een made of eac" of t"ese measures of #ind data* e7ce$t for $ersistence 5ersistence is t"e duration of t"e #ind s$eed #it"in a gi'en #ind s$eed range Also* "istograms of t"e freDuency of continuous $eriods of #ind %et#een t"e cut(in and cut(out #ind s$eeds #ould $ro'ide information on t"e e7$ected lengt" of $eriods of continuous tur%ine o$eration A#ind rose is a diagram s"o#ing t"e tem$oral distri%ution of #ind direction and a.imut"al distri%ution of #ind s$eed at a gi'en location A #ind rose (an e7am$le of #"ic" is s"o#n in Figure %elo#) is a con'enient tool for dis$laying anemometer data (#ind s$eed and direction) for siting analysis !"is figure illustrates t"e most common form* #"ic" consists of eDually s$aced concentric circles #it" 1/ eDually s$aced radial lines (eac" re$resents a com$ass $oint) !"e line lengt" is $ro$ortional to t"e freDuency of t"e #ind from t"e com$ass $oint* #it" t"e circles forming a scale !"e freDuency of calm conditions is indicated in t"e center !"e longest lines identify t"e $re'ailing #ind directions Wind roses generally are used to re$resent annual* seasonal* or mont"ly data

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution

E$ample of a wind rose diagram / A Ans Define and deri'e e7$ression for Po)e *en!$t+ 5o#er density gi'es t"e measure of $o#er a'aila%le in unit area 5o#er density is defined as:

;f t"e statistical distri%ution of #ind is ignored and it is assumed t"at t"ere is no 'ariation in #ind s$eed* t"en t"e $o#er density is incorrectly com$uted

#"ere ' is t"e a'erage #ind s$eed 9o#e'er* if t"e energy density is com$uted correctly #"ile ta+ing into account $ro%a%ility density of #ind s$eed* t"en t"e $o#er density num%ers are 'ery different

#"ere $d(') is t"eWei%ull $ro%a%ility density function

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution

.llustration of the power density function for wind speed with a Wei#ull distri#ution A % ( and 1 % +. 2he mean wind speed is 3.45 m!s. 6otice the power density curve pea1s at && m!s.

4 Ans

Define and deri'e e7$ression for ,$n* %#(!!e! As a con'ention* t"e strengt" of #ind at a site is classified %ased on $o#er density at an ele'ation of 30 m a%o'e t"e ground le'el (A1O) !a%le %elo# lists t"e definition of #ind classes in terms of $o#er density at 10 and 30 m B For sa+e of con'enience* #ind s$eed ranges are associated #it" t"e $o#er density ranges Gote* t"is ma$$ing of $o#er density to #ind s$eed is correct only if 1 = 6* t"at is* it is only correct if #ind at t"e location "as a Hayleig" distri%ution Alt"oug" #ind class definition in terms of #ind s$eed range is #idely used* it is an a$$ro7imation A $o$ular misconce$tion is t"at #ind class can %e determined if t"e annual a'erage #ind s$eed at 30 m is gi'en Alt"oug" t"is #or+s for certain $ro%a%ility density functions of #ind s$eed* it may not al#ays yield t"e correct #ind class

/efinition of Wind Classes & Ans Define and deri'e e7$ression for ,$n* !-e( Wind s"ear descri%es t"e c"ange in #ind s$eed as a function of "eig"t Assuming t"ere is no sli$$age on t"e surface* t"e surface #ind s$eed is .ero !"at is* #ind s$eed is .ero at an ele'ation of .ero !"ere are t#o met"ods to descri%e s"ear: 5o#er la# $rofile and logarit"m

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
$rofile !"e $o#er la# is t"e most common met"od to descri%e t"e relations"i$ of #ind s$eed and "eig"t !"is is an engineering a$$ro7imation and must %e used #it" caution

#"ere '6 and '1 are #ind s$eeds at "eig"ts "6 and "1* and e7$onent P is called #ind s"ear An alternate met"od to e7tra$olate #ind s$eed is to use t"e logarit"mic $rofile* #"ic" uses roug"ness of t"e surface

#"ere 70 is called t"e roug"ness lengt" ;f #ind s$eed 81 is a'aila%le at h1 = 10 m* t"en a%o'e ED may %e used to com$ute 86. !"e 'alue of s"ear can t"en %e deri'ed using a%o'e t#o EDs as:

lot of the ratio of wind speed to ratio of height for different values of shear. S"ear* t"erefore* de$ends on t"e "eig"ts and roug"ness lengt" 7 Ans Deri'e t"e e7$ression for t"e ma7imum $o#er coefficient for t"e rotor dis+ #it" res$ect to #ind tur%ine using 4et. t"eory 4et. $ostulated a t"eory a%out t"e efficiency of rotor%ased tur%ines Csing sim$le conce$ts of conser'ation of mass* momentum* and energy* "e $ostulated t"at a #ind tur%ine #it" a disc(li+e rotor cannot ca$ture more t"an 3J B? of energy contained in a mass of air t"at #ill $ass t"roug" t"e rotor !"e 4et. limit is deri'ed ne7t A$$lying conser'ation of mass* in control 'olume A0* Ar * and A6 #it" constant density A0'0 = Ar'r = A6'6

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
#"ere '6 is t"e a'erage #ind s$eed at A6 A$$lying Ge#tonIs second la# Go# force e7erted on rotor %y #ind: F = m<r ('0 K '6) = LAr'r ('0 K '6) !"e force e7erted on t"e rotor is also %ecause of t"e $ressure difference across t"e rotor: F = Ar ($0r ( $6r) Go# EDuating A%o'e eDuation of Force F = Ar($0r( $6r) = LAr'r ('0 K '6) 4ernoullis la# is ne7t a$$lied in t#o 'olumes: (a) Flo# along streamlines from A0 to t"e front face of t"e rotor@ and (%) flo# from t"e %ac+ surface of rotor to A6. $0 F 1-6L'60= $0rF 1-6L'6r $r6 F 1-6L'6r = $0 F 1-6L'66 From A%o'e !#o EDuation 5r0 ( 5r6 = 8 L('60 ) '66) F- Ar = ($0r ( $6r) = L'r ('0( '6) = 8 L('60 ) '66) Mr = ('0( '6)-6 !"e $o#er deli'ered to t"e ideali.ed rotor %y t"e #ind is: 5 = FMr = ($0r ( $6r) ArMr = 8 LArMr('60 ) '66) = 1-6LArMr (M0 K M6) (M0 F M6) 5= 8 LArMr('60 ) '66) = 8 m('60 ) '66) 5= 1-6LAr'r6('0( '6) =6LAr'r6('0( 'r) Ma7imum $o#er is reali.ed #"en: N 5-N'r = 0 = 6MrM0 ) BMr6 Mr = 6-BM0 Mr = 6-BM0 5 = 6LArMr6(M0 ) Mr) = LArM0B(8-67)

Cp is called t"e $o#er coefficient 8 Deri'e and $lot t"e relations %et#een lift coefficient (&c) and angle of attac+ (Q)and $lot a gra$" of &c 's Q and e7$lain different $oints in t"e gra$"

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
Ans !"e lift force $er unit lengt" of %lade is: Oift force is traditionally e7$ressed in terms of a lift coefficient (CL ) as:

#"ere - is t"e area of t"e %lade* #"ic" is eDual to c"ord lengt" ( c) multi$lied %y t"e lengt" of t"e %lade (l)

!"is is a t"eoretical relations"i$ %et#een CL and 9* t"e attac+ angle Em$irically* for small 'alues of 9* t"e relations"i$ is linear 9o# small de$ends on t"e airfoil design@ ty$ical 'alues for al$"a are in t"e range of K13 to 13R 0utside t"is range* t"e linear relations"i$ %et#een CL and Q ceases to e7ist As Q increase* t"e lift dro$s off resulting in a stall condition Salient features of t"e coefficient of lift cur'e in Figure are %elo# are: &ur'es are o%tained em$irically %y conducting e7$eriments on s$ecific airfoil s"a$es ;n t"e linear region* t"e slo$e is 6: For nonsymmetrical airfoils #it" cam%er line (line t"at is eDuidistant from u$$er and lo#er surface of t"e airfoil) t"at is "ig"er t"an c"ord line* t"e entire lift cur'e s"ifts u$* resulting in $ositi'e lift for .ero angle of attac+

;eneral CL form of the coefficient of lift as a function of attac1 angle for a symmetric airfoil. J Ans 5lot coefficient of drag 's angle of attac+ A Suestion 9o# can $ressure drag %e reducedT !"e ans#er is* %y mo'ing t"e %oundary layer se$aration $oint closer to t"e trailing edge !"e t#o $rimary factors t"at influence t"e location of %oundary layer se$aration $oint are angle of attac+ and surface roug"ness As t"e angle of attac+ increases* t"e se$aration $oint mo'es closer to t"e leading edge !"e $ressure drag is $ro$ortional to t"e sDuare of t"e attac+ angle !"e drag force is traditionally e7$ressed in terms of a drag coefficient (C/) as:

#"ere &fD* &$D are coefficients of s+in(friction drag and $ressure drag For normal #ind s$eeds (UU s$eed of sound)* s+in(friction drag is small and t"e $ressure drag is larger Since

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
&O is a linear function of Q* and & $D is a Duadratic function of Q* As s"o#n in %elo# Fig !"e relations"i$ %et#een drag and lift at normal #ind s$eeds and small 'alues of Q (less t"an 13

/rag as a function of attac1 angle. degrees) is:

W"ere is t"e s$an#ise efficiency factor* Ar is t"e as$ect ratio 1 0 Ans Discuss flo# of fluid o'er an aerofoil and e7$lain different regions for a flo# o'er an aerofoil

Airfoils are structures #it" s$ecific geometric s"a$es t"at are used to generate mec"anical forces due to t"e relati'e motion of t"e airfoil and a surrounding fluid Wind tur%ine %lades use airfoils to de'elo$ mec"anical $o#er !"e cross(sections of #ind tur%ine %lades "a'e t"e s"a$e of airfoils !"e mean cam%er line is t"e locus of $oints "alf#ay %et#een t"e u$$er and lo#er surfaces of t"e airfoil !"e straig"t line connecting t"e leading and trailing edges is t"e c"ord line of t"e airfoil* and t"e distance from t"e leading to t"e trailing edge measured along t"e c"ord line is designated t"e c"ord* c* of t"e airfoil Finally* t"e angle of attac+* a* is defined as t"e angle %et#een t"e relati'e #ind (Crel) and t"e c"ord line

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
Air flo# o'er an airfoil $roduces a distri%ution of forces o'er t"e airfoil surface !"e flo# 'elocity o'er airfoils increases o'er t"e con'e7 surface resulting in lo#er a'erage $ressure on t"e VsuctionI side of t"e airfoil com$ared #it" t"e conca'e or V$ressureI side of t"e airfoil Mean#"ile* 'iscous friction %et#een t"e air and t"e airfoil surface slo#s t"e air flo# to some e7tent ne7t to t"e surface L$.t .o %e ) defined to %e $er$endicular to direction of t"e oncoming air flo# !"e lift force is a conseDuence of t"e uneDual $ressure on t"e u$$er and lo#er airfoil surfaces D (/ .o %e ) defined to %e $arallel to t"e direction of t"e oncoming air flo# !"e drag force is due %ot" to 'iscous friction forces at t"e surface of t"e airfoil and to uneDual $ressure on t"e airfoil surfaces facing to#ard and a#ay from t"e oncoming flo# P$t%-$n/ moment ) defined to %e a%out an a7is $er$endicular to t"e airfoil cross(section !"e lift* drag* and $itc"ing moment coefficients of an airfoil are generated %y t"e $ressure 'ariation o'er t"e airfoil surface and t"e friction %et#een t"e air and t"e airfoil !"e $ressure 'ariations are caused %y c"anges in air 'elocity t"at can %e understood using 4ernoulliIs $rinci$le* #"ic" states t"at t"e sum of t"e static $ressure and t"e dynamic $ressure (assuming frictionless flo#) are constant: W"ere $ is t"e static $ressure and C is t"e local 'elocity along t"e airfoil surface As t"e air flo# accelerates around t"e rounded leading edge* t"e $ressure dro$s* resulting in a negati'e $ressure gradient As t"e air flo# a$$roac"es t"e trailing edge* it decelerates and t"e surface $ressure increases* resulting in a $ositi'e $ressure gradient ;f* gi'en t"e airfoil design and t"e angle of attac+* t"e air s$eeds u$ more o'er t"e u$$er surface t"an o'er t"e lo#er surface of t"e airfoil* t"en t"ere is a net lift force Similarly* t"e $itc"ing moment is a function of t"e integral of t"e moments of t"e $ressure forces a%out t"e Duarter c"ord o'er t"e surface of t"e airfoil

1 1 Ans

W"at is t"e difference %et#een constant s$eed tur%ine and 'aria%le s$eed tur%ineT E7$lain #it" necessary c"arts ;n &onstant S$eed !ur%ine (&S!) generator is directly connected to grid #"ere as in Maria%le S$eed !ur%ine (MS!) generator is not directly connected to grid ;n &S! A grid(connected async"ronous generator is t"e sim$lest and c"ea$est ty$e of generator %ecause t"e out$ut energy is at t"e grid freDuency W"ere as in MS! t"ere is also a reDuirement of $o#er electronics to rectify or in'ert (A& 7D&* D&7A&) So generator is costly ;n &S! constant(rotor s$eed tur%ines are una%le to deli'er t"e o$timal $o#er out$ut at different #ind s$eed #"ere as MS! are ena%le to deli'er t"e o$timal $o#er out$ut at

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
'aria%le #ind s$eed

ower output versus rotor speed for different wind speeds. ower curves for fi$ed speed rotor and varia#le speed rotor are illustrated. $<a$is is in rps =% rpm!>4?.

1 6 Ans 1 B A Ans

D$!%u!! /ene (#$!e* %on*$t$on!0

oto

*e!$/n

p o%e*u e

.o

!pe%$.$%

9o# #ill you design a #ind measurement cam$aign %ased on A Gum%er of met to#ers 4 5lacement of met to#ers Wind measurement cam$aign "as $rimary o%:ecti'e is to im$ro'e accuracy of $rediction of energy out$ut of t"e #ind $ro:ect* ot"er factors li+e economics and $ro:ect sc"edule So main factors are as %elo# Gum%er of met to#ers 5lacement of met to#ers a #ind measurement cam$aign must start #it" #"at is +no#n and design a $rocess t"at can economically generate reasona%ly accurate energy $redictions A $rocess for designing a #ind measurement cam$aign is descri%ed %elo# ;t may %e ada$ted to meet a $ro:ects s$ecific need 1 &onduct a $reliminary #ind resource assessment of t"e area under consideration !"is a$$lies to %ot" single tur%ine and #ind(farm installations !"e outcome of t"e $reliminary #ind assessment #ill %e a #ind resource ma$ of suita%le granularity For t"e $ur$oses of t"is discussion* it is assumed t"at #ind resources are a'aila%le for a 600mW 600mgrid !"e resource ma$ may %e %ased on com$uter simulations using numerical #eat"er $rediction models or #ind resource($rediction model li+e WAs5 or ot"ers !"e source of t"e #ind data for t"ese models may %e 10(m air$ort data and-or reanalysis data from Gational &enter for

PANDIT DEENDAYAL PETROLEUM UNIVERSITY SCHOOL OF TECHNOLOGY

Fundamental of Wind Energy (ME708) Assignment Solution
Atmos$"eric Hesearc" (G&AH) 6 !"e $reliminary location of Wind !ur%ine 1enerators (W!1s) may %e com$uted %y running a layout o$timi.ation model (e7am$le 0$timi.e in Wind5H0) #it" #ind resource ma$ from ste$ (1) and a 'ariety of constraints &onstraints include ma7imum #ind(farm ca$acity* minimum ca$acity factor* tur%ine to#er "eig"t and rotor diameter* distances %et#een tur%ines* and ot"er set%ac+ criteria li+e distance %et#een tur%ine and $ro$erty %oundary* $u%lic roads* transmission* and in"a%ited areas ;n t"is $"ase* t"e constraints are guidelines rat"er t"an $recise For a single tur%ine case* a location #it" t"e "ig"est #ind resource t"at satisfies all t"e constraints is t"e location of t"e met(to#er For a #ind farm* go to ste$ (B) B ;n t"e $reliminary W!1 layout* form clusters of W!1s ;f t"e #ind farm is in a com$le7 terrain* t"en 3 to 7 W!1s may %e grou$ed into one cluster ;f it is a sim$ler terrain #it" 'ery little c"anges in ele'ation and roug"ness* t"en 10 to 16 W!1s may %e grou$ed into one cluster !"e clusters #ill %e %ased on distance &lusters are %est formed 'isually@ t"e %orders of clusters may %e dra#n manually on a &om$uter Aided Design (&AD) dra#ing or on $a$er !"e ratio %et#een W!1 and met(to#ers of 3 to 7* or 10 to 16 are normal guidelines for determining num%er of fi7ed met(to#ers for #ind measurement Harely #ill all clusters "a'e t"e same num%er of W!1 A ;n eac" cluster* find t"e median #ind s$eed W!1 !"is W!1 location or a location in t"e 'icinity #ould %e a location for $lacement of met(to#er Measuring at t"e %est or #orst #ind resource location in t"e cluster #ould yield #ind measurements t"at "a'e to %e eit"er e7tra$olated do#n or e7tra$olated u$ to all $oints in t"e cluster* #"ic" #ould lead to "ig"er inaccuracies Gormally* a set of t#o or t"ree locations is c"osen in eac" cluster For instance* t"e t"ree locations are: Oocation #it" median #ind s$eed and t"e t#o locations #it" t"e smallest difference #it" t"e median #ind s$eed 3 !"e goal of t"is ste$ is to $ic+ one location in eac" cluster suc" t"at* for t"e #ind farm as a #"ole* t"e met(to#er locations are sufficiently s$read out geogra$"ically !"is ste$ is %est done 'isually* starting #it" t"e median #ind s$eed location in eac" cluster and t"en e7amining t"e $ro7imity of t"ese locations ;f t"e median locations of t#o clusters are geogra$"ically close* t"en alternate locations are c"osen from t"e set