Homework, wind energy

8/9/2019 Homework, wind energy

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RCL 563: Homework 2 - Wind Power

Student: Tulio Marcondes Moreira

Proessor: !e"in Hallinan



1. Describe where the relation for wind speed according to: V2 = (H2/H1)αV1 came from and

wh this approach is considered conser!ati!e. Describe also the conditions where it fails.

T#e Wind Proile Power Law is an em$irical e%uation de"elo$ed as a wa& to sim$li& "elocit&

and $ower $otential $redictions' (t)s sim$licit& #owe"er comes wit# t#e cost o a lower

*$recision+ w#en com$ared to t#e Lo,arit#m Law or t#e Lo, Law e%uation. not onl& t#erou,#ness o t#e terrain is accounted or. /ut also t#e atmos$#eric sta/ilit&0'

T#e Wind Proile Law tends also to /e conser"ati"e. /& t#e sometimes e1cessi"e use o t#e 4

correlation also called one-se"ent#-$ower-law' See Reerences0' T#e $ro/lem in t#is. is t#at t#e

rou,#ness coeicient is considered constant. e"en t#ou,# it can c#an,e si,niicantl& wit# surace

rou,#ness. time o da&. season. etc Reerence: #tt$:es'ucsc'eduno/lewinde1tra$0' T#is

issue is tackled in some articles as well: *T#e 4t# $ower law is amon, t#e met#ods t#at #a"e

/een used to e1tra$olate wind s$eed to t#e #u/ #ei,#ts o wind tur/ines rom t#e measurin,

le"els' Howe"er. it tends to underestimate t#e actual lon,-term a"era,e wind s$eeds 789 T#e

a"era,e $ower law e1$onent o/tained at t#e test site was ';4. a "alue t#at is su/stantiall& #i,#er t#an t#e 4t# $ower law e1$onent+ < =>T>RM(?@T(A? AB TH> PAW>R L@W

>PA?>?T BAR SADTH>R? H(EHL@?=S AB T@?F@?(@ - HH Mwan&ika and RM

!ainkwa0'

T#is model tends to ail w#en in t#e $resence o o/stacles. #i,# rou,#ness "alues. and w#en t#e

estimati"e or t#e rou,#ness coeicient c#an,es si,niicantl& o"er time Reerence: Wind

>ner,& >1$lained < W(L>G. and Touma. 'S'. I44. =e$endence o t#e wind $roile $ower law

on sta/ilit& or "arious locations. ' @ir Pollution Control @ssociation. Jol' 24. $$' K63-K660'

2. "onsidering Van #ert$ %hio (&se 't. #ane$ data where applicable)$ the location ofthe wind farm we will be !isiting$ area wind speeds$ determine the ann*al energ fl*+

(,#h /s-.m) potential a!ailable at a height of m$ 2 m$ and m.

Results rom >1cell See attac#ment0:

0. #hat are the classes of t*rbines nt*iti!el$ which t*rbine class is most s*ited to the

Van #ert site and wh

http://es.ucsc.edu/~jnoble/wind/extrap/

http://es.ucsc.edu/~jnoble/wind/extrap/



@ccordin, to t#e international standard (>C 6;- ed'2. tur/ine classes are created in order to

select t#e most a$$ro$riate tur/ine or eac# en"ironment' T#e idea /e#ind t#is is to not onl&

o$timie $ower out$ut. /ut to a"oid dama,e t#at could /e caused in #i,# wind s$eed

en"ironments'

T#e current classes are: (a.(/.((a.((/.(((a.(((/ and (J'

>ac# class is assi,ned accordin,l& to t#ree $arameters: @nnual a"era,e wind s$eed. Tur/ulence

and >1treme 5 &ear wind ,ust' T#e lower t#e class. t#e #i,#er wind s$eed one Tur/ine can

recei"e'

Since wit# t#e a"aila/le data rom ?rel Tm&3 we can onl& o/tain t#e wind s$eed or eac# #our

in a w#ole &ear. is $ossi/le to calculate t#e annual a"era,e annual ma1imum was taken ust or

curiosit&0:

T#us. onl& considerin, t#e annual a"era,e wind s$eed. or t#e t#ree #ei,#ts we would c#oose

class (J Wind Tur/ines ,ood or c#oice u$ to wind s$eeds o 6' ms < Reerence: (>C 6;-

ed'2. see links on reerence0'

. 3he Vestas V42 !ariable aw wind t*rbine has a rated power c*r!e as gi!en below. 3he

lower a+is is wind speed in m/s.



a0 =e"elo$ a Ra&lei,# distri/ution or t#e Jan Wert. A# use Bt' Wa&ne. (? data0 area wind

s$eed' >stimate t#e num/er o #ours t#at t#e wind s$eed will /e /etween 2 and 32 ms'

Ra&lei,# =istri/ution can /e $lotted t#rou,# t#e e%uation:

Ra&lcdD0 e1$- DN

2

2ODmeanN

2

00

W#en $lottin, t#e Ra&lei,# unction in e1cel we o/tain t#e ,ra$#:

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

1.2

Rayleigh Distribution

We see t#at. w#en close to 6 ms. t#e cumulati"e $ro/a/ilit& unction is $racticall& '

Bor Ra&lcd20. at 4Km #u/ #ei,#t. we o/tain: 3'23Q' T#is means t#at durin, a &ear.

3'23Q o t#e time t#e wind "elocit& was a/o"e 2 ms and /elow 32 ms nearl& im$ossi/le

accordin, to t#e cur"e0' T#us:

?um/er o #ours 3'23QOK462 5I'2 5I #ours and 2 minutes'

b) 5pplied to the Van #ert$ %H area and gi!en the 678 390 tpical weather data$

determine the ann*al energ potential for this t*rbine. "ompare this to the ann*al



energ e+tracted *sing the a!erage wind speed and 6aleig1h distrib*tion. 7+plain the

differences.

T#is $re"ious ,ra$# can /e di"ided into i"e unctions:

Power D0 . or D ;'0

Power D0 2OD< K. or ;' D 2'50

Power D0 4. or 2'5 D 30

Power D0 -4OD524. or 3 D 30

Power D0 . or 3 D0

Considerin, a constant wind s$eed or eac# #our in t#e TMG3 data. we can o/tain t#e Power or

eac# #our in e1cel. /& codin,: (BD3;..(BD32'5.2OD3-K.(BD33.4.(BD33.-

4OD3524.0000

T#us. ater summin, t#e total annual ener,& $otential or 4Km #u/ #ei,#t accordin, to t#e ,ra$#.

we o/tain:

Calculatin, t#rou,# a"era,e annual wind s$eed we #a"e:



P @O'5O$O U 3 O! e. in w#ic# @ 5.2K m2 or t#e Jestas JK2'

@lso. Ke=

1

Nhr ( year)∗ U 3 ∑i=1

N

U i3

T#rou,# Ra&lei,# distri/ution:

Pw ∫o

∞

Pw (U )∗ p (U )dU ' (n t#is case we are dealin, wit# t#ree inte,rals or eac# unction:

(1700 )∗ p (U )dU +¿∫30

31

(−1700∗U +52700 )∗ p (U )dU

(200∗U −800 )∗ p (U )dU +¿∫12.5

30

¿

Pw=∫4

12.5

¿

(n w#ic#: p (U )=exp(−U 2/ (2∗U mean2 ))

Bor 4Km #u/ #ei,#t. D a"era,e 5'I66 ms' T#us:

71.186−U 2/¿

¿¿

p (U )=e¿

Trou,# e1cel. we can a$$ro1imate t#e inte,ral /& summin, a$$ro1imated rectan,les area "alues.

t#us o/tainin,:

T#e Ra&lei,# distri/ution $resents a muc# #i,#er "alue t#an t#e actual. since it su$$oses a #i,#er

$resence o #i,# s$eed winds t#an t#e actuall& o/ser"ed' T#e a"era,e annual Power estimati"e is

s#own to /e actuall& conser"ati"e in t#is case. as alread& o/ser"ed in %uestion '



. "onsider the following possible Vestas t*rbines for the Van #ert site. ;i!en a ro*gh

capital cost of <2/#att$ which t*rbine(s) are the most economical for the Van #ert site

ote: o* will need to e+plore the prod*ct specification sheets to get data o* ma need

abo*t each t*rbine. 3he prod*ced electrical energ can be ass*med sellable to the grid at

<./,#h. resent a s*mmar table showing for each t*rbine tpe: (i) ann*al deli!ered

energ (,#h)> (ii) ann*al prod*ced electricit (cost)> (iii) estimated capital cost> and (i!)

simple pabac,. Describe wh the t*rbine o*?!e specified as the best is in fact best.

Wit# t#e use o t#e tool We/$lot=i,itier. we can estimate t#e $ower unctions D0 or eac# o

t#e si1 s#own Tur/ines' T#us o/tainin,: see e1cel s#eet or more detail0

Turbine 1 Turbine 2 Turbine 3 Turbine 4 Turbine 5

Turbine 6

Wit# t#is anal&sis we see t#at Tur/ine 6 would /e t#e most interestin, one to ac%uire. since it #as

t#e lowest sim$le $a&/ack' T#e reasons t#at culminate or t#is Tur/ine to /e t#e c#ea$est are:

• Lowest initial cost'

• Cut in s$eed o 3' ms t#e lowest "alue amon, dierent tur/ines0'

• T#e stee$est inclination o t#e cur"e PD0. /eore reac#in, t#e constant "alue t#is was

,ood considerin, t#at. accordin,l& to t#e TMG3 data. t#ere is a #i,# occurrence o low

s$eed winds0' T#is latest statement can /e $ro"en in ,ra$# /&:



Vestas V112-3.0 MW

V100-2.6MW







6eferences:

#tt$:www'"estas'comen$roductsandser"iceso$tionsandsolutionsU"estas-uni"ers.

#tt$:en'wiki$edia'or,wiki(>C6;citenote-2'

#tt$:aro#at,i'inoWe/Plot=i,itiera$$V'

http://www.vestas.com/en/products_and_services/options_and_solutions#!/vestas-univers

http://en.wikipedia.org/wiki/IEC_61400#cite_note-12

http://arohatgi.info/WebPlotDigitizer/app/

http://www.vestas.com/en/products_and_services/options_and_solutions#!/vestas-univers

http://en.wikipedia.org/wiki/IEC_61400#cite_note-12

http://arohatgi.info/WebPlotDigitizer/app/

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Homework, wind energy