TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 5869 ~ 5876
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.605
4
5869
Re
cei
v
ed Ap
ril 4, 2014; Re
vised J
une 2,
2014; Accept
ed Ju
ne 18, 2
014
Optimal Location of Wind Turbines in a Wind Farm
using Genetic Algorithm
C. Bala
Krish
n
a Moorth
y
*
, M.K. Deshm
u
kh, Dar
s
ha
na Mukhe
r
ej
ee
Dept. of EEE
and Instrume
nt
ation,
BIT
S
, Pilani K K Birla G
oa Cam
pus,
Goa-4
037
26, Ind
i
a
Cores
pon
di
ng
author, ema
il: cbkmoorth
y@
g
m
ail.com*, mk
d@g
oa.bits-p
il
ani.ac.i
n
,
mukherj
ee.d
9
2
@
gmai
l.com
A
b
st
r
a
ct
In the pr
ese
n
t study, ge
netic
alg
o
rith
m h
a
s
bee
n us
ed to
r
e
solv
e the
pl
ac
ement of w
i
n
d
turbin
es i
n
a w
i
n
d
park
givi
ng
maxi
mu
m
pow
er
an
d effici
ency
w
i
th mini
mu
m nu
mber
of tur
b
in
es. Un
like
past a
ppro
a
ch
es
w
here e
a
ch
pl
ot w
a
s sub
d
iv
i
ded
int
o
s
m
a
l
l
e
r sq
uare
gr
i
d
s
at the
ce
ntre
of w
h
ich
a tur
b
ine
can
b
e
p
l
a
c
ed,
the pr
ese
n
t stu
d
y d
oes
not r
e
quir
e
d
i
visi
on
o
f
the p
l
o
t. Thus
, a turb
in
e n
o
w
has
more
flex
i
b
ility t
o
b
e
plac
e
d
anyw
here
outsi
de
a ra
dius
of
200
m
of e
a
ch
other yi
el
din
g
b
e
tter resu
lts. T
he c
a
se
of un
i
d
irecti
ona
l u
n
if
or
m
w
i
nd is co
nsi
d
ered
an
d 60
0
indiv
i
d
uals
evo
l
ve 3
000
ge
ne
rations. Al
on
g
w
i
th the opti
m
al l
a
yout, fitne
s
s
valu
e, total p
o
w
er output, efficiency
an
d n
u
m
b
e
r of tu
r
b
in
es hav
e a
l
so
bee
n re
ported.
Co
mp
ariso
n
w
i
th
results of earl
i
e
r
study and p
o
ssible
expl
an
ation is a
l
so prov
ide
d
.
Ke
y
w
ords
:
w
i
nd turbi
ne, opti
m
i
z
at
io
n, w
a
ke effect, genetic alg
o
rith
m
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
One of the major
con
c
e
r
ns today is i
n
crea
sed con
s
umptio
n,
increa
sed co
st,
deplete
d
natural
re
sou
r
ce
s, ou
r de
p
ende
nce on f
o
reig
n
source
s, and the im
pact on th
e e
n
vironm
ent a
nd
the dang
er o
f
global wa
rming. Alterna
t
ive energy
source
s, also
calle
d
ren
e
wable re
so
urces,
deliver p
o
we
r with mi
nim
a
l impa
ct on
the enviro
n
m
ent. The
s
e
sou
r
ces
are
typically mo
re
gree
n/cle
an than traditio
n
a
l method
s such a
s
oil
or coal. One
such
sou
r
ce o
f
energy is wind.
This is a gre
a
t self-re
ne
wable so
urce
of energy tha
t
will never run out. Also it has additio
nal
advantag
es li
ke
no p
o
lluti
on o
r
g
r
ee
nh
ouse ga
s
em
issi
on
s an
d i
s
ple
n
tiful, cl
ean a
nd
wid
e
ly
distrib
u
ted.
Wind tu
rbin
e
s
al
so ta
ke u
p
less
spa
c
e
and
can
be p
l
ace
d
in a
n
y terrai
n
or re
mote
locatio
n
s li
ke
offshore, mo
untain
s
and d
e
se
rts.
Co
st of the wind e
nergy te
chnol
ogy is re
du
ci
ng
rapidly
and
t
hus be
ginni
n
g
to a
c
tually
co
mpete
wi
th existing
fossil-fuel
po
wer p
r
od
ucti
on
method
s.
An advantag
e of a wind farm is that the fix
ed cost
s are spread ove
r
a bigger inve
stment,
thus, ma
kin
g
wind
en
ergy
com
petitive. Thu
s
, t
he
o
p
timal de
sig
n
of win
d
farms i
s
of
cap
i
tal
intere
st as it
govern
s
the
energy
obtain
ed from th
e wind
while
re
duci
ng the
co
st of installati
on.
One of the most impo
rtant asp
e
ct
s
of wind farm de
sig
n
is the relati
ve distributio
n of the turbine
s
for obtainin
g
an optimal g
eometry of the wind fa
rm,
becau
se the
turbine
s
re
ceive lowe
r wi
nd
spe
e
d
s
and l
e
ss en
ergy
capture
s
if the
y
are lo
cated behin
d
one a
nother or clo
s
e
togethe
r.
T
h
is
effect is calle
d the
wa
ke
ef
fect an
d i
s
di
scusse
d
late
r. Thu
s
, ou
r p
r
imary
con
c
e
r
n in thi
s
proje
c
t
is to
develop
an effici
ent al
gorithm
which can g
ene
ra
te the o
p
timal
layout of the
turbin
es in t
he
farm that can
give us maxi
mum po
wer
with lea
s
t expenditure.
Our work is
con
d
u
c
ted a
s
sumin
g
that the co
nc
erned farm fulfils all the criteria of site
sele
ction
an
d
tech
nical a
s
pect
s
. Th
e p
r
ogra
m
cod
e
f
o
r o
p
timisatio
n
is devel
ope
d in MA
TLAB,
based on g
e
n
e
tic algo
rithm
.
2. Past
Approa
ches
Acco
rdi
ng to
Bansal
et al
.[1], 10ha/M
W
can
be ta
ke
n as th
e land
requi
rem
ent
of wind
farms
inc
l
uding infras
truc
t
u
re. Further s
t
udies
do
ne
by Patel [2] indicate th
a
t
the optimu
m
spa
c
in
g i
s
fo
und i
n
rows
8–12
-rotor
di
ameters
apa
rt in the
win
d
dire
ction,
a
nd 1.5
–3-rot
o
r
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 586
9 –
5876
5870
diamete
r
s a
p
a
rt in the cro
s
swin
d directi
on. But Ammara
et al.
[3] in 2002 fo
und
it inefficient and
prop
osed a d
ense and
sta
ggered sch
e
m
e giving sim
ilar
produ
c
tio
n
with less la
nd req
u
ireme
n
ts.
The first app
roach u
s
ing
g
enetic
algo
rithm
in mi
cro-siting
wa
s m
ade by M
o
se
tti
et al.
[4].
The
aim was to
m
a
ximise th
e total po
we
r ge
nerate
d
a
nd
minimise the
investment
cost. But si
nce
the
results di
d n
o
t yield even
the simpl
e
st
empiri
cal pl
a
c
eme
n
t sche
mes, G
r
ady
et al.
[5] in 2005
made a
stud
y base
d
ag
ain on g
eneti
c
algorith
m
u
s
i
ng compute
r
i
s
ed
pro
g
ram
in MATLAB. G.
Marmidi
s
et al.
(200
8) [6]
use
d
a totall
y different ap
proa
ch
kn
own as M
onte
-
Carl
o si
mulat
i
on.
This was foll
owe
d
by the
study based
on
geneti
c
al
gorithm do
ne
in 2010 by Emami
et al.
[7]
usin
g a modi
fied objective
function. Th
e pre
s
ent st
udy is done
usin
g the sa
me optimisation
algorith
m
b
u
t
we t
r
y to
obtain
better and
mo
re
efficient
conf
iguratio
ns by
ch
angi
ng t
he
placement
cri
t
erion. Howe
ver, the basi
c
app
ro
ac
h remain
s the same an
d hen
ce the
results of
the studie
s
are comp
arable
.
3. Modelling
The wa
ke mo
del use
d
in this analysi
s
is
simila
r to the
one develo
p
e
d
by N.O.Jen
s
en [8].
This i
s
the
same
model
use
d
by the earli
er
stu
d
ies. It is b
a
se
d on gl
o
bal mome
ntum
con
s
e
r
vation
in the wake d
o
wn
stre
am of
the win
d
turb
ine. The
nea
r field behi
nd t
he wi
nd tu
rbi
n
e
is n
egle
c
ted;
therefo
r
e th
e
resulting
wa
ke is mo
d
e
lled
as a tu
rb
ulen
t wa
ke
or neg
ative jet. Since
it negle
c
ts th
e contrib
u
tio
n
of tip vo
rtices, thi
s
wa
ke
model
is ap
plica
b
le o
n
ly
in the fa
r
wa
ke
regio
n
.
Figure 1. Sch
e
matic of Wa
ke Mod
e
l
Several assu
mptions h
a
ve been ma
d
e
in the
anal
ysis to simpli
fy the model. At the
turbine
the wake ha
s
a ra
dius r
0
. As th
e wave
prop
agate
s
(as
shown in Fi
gu
re 1
)
the
radi
us of
the wa
ke in
creases p
r
o
portionally
to the down
s
tream
distan
ce, x. with the help
of Betz theo
ry
and
ap
plying the
contin
uity
equation we can sho
w
tha
t
:
Momentum b
a
lan
c
e give
s:
v
r
u
r
r
v
r
2
2
0
2
0
2
0
)
(
(
1
)
A
ssu
ming
u
v
o
3
1
a
nd
0
r
x
r
, we get:
]
)
(
3
2
1
[
2
0
0
x
r
r
u
v
(
2
)
Takin
g
the axial indu
ction factor,
3
1
a
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TELKOM
NIKA
ISSN:
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046
Optim
a
l Loca
t
ion of Wind
Turbi
n
e
s
in a Wind F
a
rm
using G
eneti
c
… (C.BalaK
ri
shn
a
Moo
r
thy)
5871
The velocity of wake at a distan
ce, ’x’ simplifies to:
]
)
1
(
2
1
[
2
0
r
x
a
u
v
,
(
3
)
Whe
r
e
u i
s
th
e mea
n
wind
sp
eed,
α
i
s
t
he e
n
train
m
e
n
t co
nsta
nt a
nd r is the
do
wn
strea
m
rotor
radiu
s
.
Powe
r pro
d
u
c
ed,
P =
3
2
1
Au
(
4
)
A
ssu
ming
η
=
40%,
ρ
= 1.2 kg/m³ an
d A =
π
x 20
2
s
q
.m, we get:
Power,
P = 0.3u
3
k
W
(
5
)
Her
e
,
η
s
t
ands
for effic
i
ency,
ρ
for density and A for area.
The do
wn
stre
am roto
r radi
us r1 a
nd the
turbine
coeffi
cient C
T
ar
e
:
)
2
1
/(
)
1
(
0
1
a
a
r
r
(6)
C
T
=
4a
(1-a)
(7)
The entrainm
ent con
s
tant i
s
given empi
rically as:
)
/
ln(
5
.
0
0
z
z
(
8
)
Wwhere z is t
he hub h
e
ight
of the wind turbin
e and
z
0
is the su
rface roug
hne
ss of the site.
Assu
ming
th
at the
kineti
c
ene
rgy d
e
ficit of a mixed
wa
ke
is equ
al to the
su
m of the
energy deficit
s, the resulting velo
city down
s
tr
e
a
m o
f
N turbi
nes
can
be
cal
c
u
l
ated u
s
ing t
he
followin
g
expression:
2
1
0
2
0
/
1
/
1
N
i
i
u
u
u
u
(9)
In orde
r to calcul
ate the total co
st, we
used
the
co
st model u
s
e
d
by Mosetti et al. in
orde
r to optimise the mo
del. They co
nsid
ere
d
t
hat the total cost/year of a wind farm can be
formulate
d
as:
)
(
2
00174
.
0
3
1
3
2
N
e
N
Cost
(10)
Efficiency of the win
d
farm
can b
e
cal
c
ul
ated as:
Effic
i
enc
y =
P
total
/(0.3Nu
0
3
)
(11)
The
obje
c
tive fun
c
tion
th
at we
con
s
i
dere
d
i
n
o
u
r wo
rk to
fin
d
the
optim
al result
(minimu
m
co
st per u
n
it of energy pro
d
u
c
ed
) is:
Objective = cost/P
total
(12)
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TELKOM
NI
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Vol. 12, No. 8, August 2014: 586
9 –
5876
5872
4.
Gene
tic Alg
o
rithm and
Optimisation
Cla
ssi
cal m
e
thod
s would
be very com
p
lex and diffi
cult to be
used to solve a
discrete
probl
em li
ke
wind fa
rm
po
sitionin
g
invol
v
ing a la
rge
numbe
r of va
riable
s
.
Unlike cal
c
ul
us-ba
s
e
d
method
s, we
requi
re an a
l
gorithm that
use
s
onl
y th
e obje
c
tive functio
n
and
do not req
u
ire its
derivatives fo
r sea
r
ch. Ge
netic
algo
rith
ms
(GAs
)
are search
met
hod
s b
a
se
d
on p
r
in
ciple
s
of
natural
sele
ct
ion and g
e
n
e
tics. GA
s e
n
co
de the d
e
ci
sion vari
a
b
les of a
se
arch problem
into
finite-length strings of
alph
abets of
ce
rta
i
n ca
rdin
ality. The
stri
ng
s whi
c
h
a
r
e ca
ndidate sol
u
tions
to the
sea
r
ch
problem
a
r
e
referred
to
as ch
ro
m
o
some
s, the
alph
ab
ets a
r
e
refe
rred to
as ge
n
e
s
and the
valu
es of
gen
es
are
call
ed all
e
les. An
ot
her importa
nt co
nce
p
t of GA
s is the
notion
of
popul
ation. Unli
ke
t
r
aditi
onal se
arch
method
s,
g
e
netic algo
rith
ms rely
o
n
a
po
pulatio
n
o
f
can
d
idate
sol
u
tions.
The
p
opulatio
n
size, whi
c
h
is u
s
ually
a u
s
e
r
-spe
cified
pa
rameter, i
s
on
e of
the impo
rtant
factors
affecting
the
scala
b
ility and p
e
rf
orma
nce of g
enetic
algo
rit
h
ms. O
n
ce th
e
probl
em i
s
e
n
co
ded
in
a
chromo
som
a
l
man
ner an
d
a fitne
s
s me
asu
r
e
for
discrimi
nating
g
ood
solutio
n
s fro
m
bad on
es has be
en
chosen, we
c
an sta
r
t to evolve solutio
n
s to the se
arch
probl
em [9].
For th
e initiali
sation
of the
rand
om in
divi
dual
s of the
popul
ation
ce
rtain p
a
ra
met
e
rs an
d
pro
c
ed
ure ne
ed to be follo
wed. Minim
u
m value of
objective fun
c
tion is then
co
mpared a
c
ro
ss a
rang
e of turbine
s
to find
the optimal
numbe
r. Pa
ramete
rs
co
nsid
ere
d
for the initialisa
t
ion
p
r
oc
es
s
ar
e
:
a)
Numb
er of va
riable
s
: Ta
ke
n as twi
c
e the
numbe
r of turbine
s
.
b)
Population
si
ze: is the tota
l numbe
r of solution
s in a set.
c)
Con
s
trai
nts: Size of the wi
nd farm.
d) Optimis
a
tion
c
r
iteria:
Ma
xi
mum n
u
mbe
r
of iterations,
stall
gen
erati
ons an
d fun
c
tion
toleran
c
e. Th
e flow ch
art u
s
ed for thi
s
st
udy is sh
own in Figure 2:
Figure 2. Flow Ch
art De
scribing G
eneti
c
Algorithm
5. Numerical
P
r
ocedu
r
e
A squ
a
re plot
(2
km X
2km
)
ha
s be
en
ch
ose
n
. Unlike
past
app
roa
c
hes which
div
i
de the
plot into 10
0
cell
s for
a m
a
ximum of 1
00 turbine
l
o
cation
s, the
pre
s
ent
study
just rest
rict
s the
minimum di
st
ance betwee
n
two adja
c
e
n
t turbine
s
to
200m (a
s 5
D
(2
00m
) sat
i
sfies the
rule
of
thumb
spa
c
in
g re
qui
reme
n
t
s). Thi
s
mini
mise
s the
co
nstrai
nts i
n
pl
acin
g the
turbine
s
giving
us
greate
r
flexibi
lity to increa
se efficie
n
cy
a
nd tota
l
power. The turbines, now,
do
n
o
t r
e
qu
ir
e to
be
put
in
colum
n
s one
after anothe
r but can
b
e
pl
aced
ra
ndomly
provided th
ey
are
20
0m a
p
a
rt.
This furth
e
r h
e
lps in redu
ci
ng wa
ke effe
ct yielding bet
ter re
sults.
The turbi
ne consi
dered for
study ha
s pro
pertie
s
given
in Table 1:
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Optim
a
l Loca
t
ion of Wind
Turbi
n
e
s
in a Wind F
a
rm
using G
e
neti
c… (C.BalaK
ri
shn
a
Moo
r
thy)
5873
Table 1. Win
d
Turbi
ne Pro
pertie
s
Hub height
z
60m
Rotor radius
r
0
40m
Thrust coefficient
C
T
0.88
Grou
nd rou
ghne
ss
Z
0
0.3m
Wind velocity
u
0
12m/s
Axial induction factor
a
0.33
Entrainment con
s
tant
α
0.094
Do
w
n
stream roto
r
radius
r
1
55.75
The thru
st co
efficient is taken con
s
tant
throu
gho
ut the pro
c
e
s
ses
and groun
d rough
ne
ss
of the site is taken a
s
z
0
= 0.3m. The
power curve
pre
s
ente
d
in Mosetti
et al.
’s study for t
h
e
turbine u
nde
r con
s
ide
r
atio
n yields the followin
g
expression for p
o
w
er:
N
i
U
P
1
3
3
.
0
.
(
1
3
)
The ca
se a
ssessed h
e
re a
s
sume
s unifo
rm win
d
dire
ction with a wi
nd sp
eed of 1
2
m/s.
6. Resul
t
s
and
Comparis
on
s
Since
thi
s
ca
se con
s
id
ers wind sp
eed
o
f
12m/s
i
n
a
u
n
iform di
re
cti
o
n, the
wa
ke
cre
a
ted
depe
nd
s only
on the
do
wn
strea
m
di
stan
ce. As
expl
ai
ned e
a
rlie
r, o
u
r p
r
og
ram
d
oes
not rest
ri
ct
the pla
c
eme
n
t of the turbine
s
in spe
c
ific g
r
id
s bu
t can b
e
pla
c
ed
anywhere within the
are
a
provide
d
they
are minim
u
m 200m di
sta
n
ce a
p
a
r
t
an
d deliver b
e
tter outp
ut. Our study con
s
i
ders
600 i
ndividual
s to
evolve o
v
er 30
00
gen
eration
s
. Fi
gu
re
3 illu
strate
s fitne
s
s valu
e evolutio
n fo
r
a
maximum of 1200 g
ene
rati
ons.
Figure 3. Fitness Cu
rve (No. of
turbines
is 30)
Figure 4. Total power vs. no. of Turbin
es
The valu
es sugge
st that in
itia
lly the fitness value
is
very
high
but
then d
r
o
p
s
d
r
asti
cally
to settle down to a const
ant value of
.00142
1.
The
graph is
si
milar to the result
s in earl
ier
pape
rs.
Whe
n
the progra
m
wa
s run for differe
nt number
of
turbine
s
, the total power i
n
crea
sed
linearly
(till around
1.7 x 10
4
kW) for
a ma
ximum of ap
p
r
oximately 35
turbin
es. A
s
the num
be
r
of
turbine
s
wa
s further in
crea
sed, the
r
e were o
n
ly sligh
t
incre
a
se se
en in the tota
l powe
r outp
ut
and it settled
to a value of arou
nd 2.4x1
0
4
k
W
(
F
ig
ur
e
4
)
.
With the ne
w
approa
ch of
placi
ng the tu
rbine
s
, we found that ou
r result
s are bet
ter than
that of the previous
studie
s
. Re
sults
co
mputed for dif
f
erent num
be
r of turbine
s
a
r
e tabulate
d a
nd
sho
w
n. Tabl
e
2 is a com
p
a
r
iso
n
of the re
sult
s of the p
r
ese
n
t study a
n
d earli
er results.
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Table 2. Co
m
pari
s
on of Sol
u
tion Ch
ara
c
t
e
risti
c
s
Mos
e
tti et
al.
Grad
y et
al.
Marmi
d
is
et al.
Emami
et
al.
Present
st
udy
No. of
t
u
rbin
es
26
30
32
20
30
10
26
30
32
20
10
Total P
o
w
e
r
(kW/ye
ar)
1235
2.00
1431
0.00
1639
5.00
1016
4.00
1431
0.00
5184.
00
1347
1.00
1501
9.00
1655
2.18
1036
5.86
038
5184.
00
Fitne
ss val
u
e
0.001
62
0.001
544
0.001
410
7
Di
scre
pan
cie
s
pr
ese
n
t
0.001
500
0.001
40
0.001
397
3
0.001
607
0.001
826
3
Effici
enc
y
91.64
5
92.01
5
Not
reporte
d
98
92
100
99.8
96.57
00
99.77
99.97
100
wei
ght of cost
(w
1)
Take
n to
be s
m
al
l.
Value not
m
e
n
t
i
o
ne
d
wei
ght
s
not
con
s
id
ered
wei
ght
s
not
con
s
id
ered
0.35
0.2
0.6
wei
ght
s n
ot c
ons
ider
e
d
w2
0.65
0.8
0.4
The tabulate
d
data indicates that in
each
of th
e ca
se
s our turbine con
f
iguration
prod
uces
l
a
rger power o
u
tput
giving better
effi
ci
e
n
cy. The fitn
ess value
s
o
b
tained
are
also
lesser than
values ea
rlie
r repo
rted. T
h
is
wo
rk ha
s tried to
imp
r
ove u
pon
some d
r
a
w
ba
cks
pre
s
ent in the
earlie
r studi
e
s
. A detailed comp
ari
s
o
n
o
f
earlier
studi
es is give
n in Table 3.
Table 3. Deta
iled De
scripti
ons of Pa
st Appro
a
che
s
Mosetti et al. (19
94)
Grad
y et
al. (200
5)
Mar
m
idis et al.
(2008)
Emami et al. (20
10)
Objective function
(
m
inimise)
Single objective
Single objective
Single objective
Multi-objective
Cost/y
ear Same
sa
me same
same
Technique used
Genetic algor
ith
m
Genetic
algorith
m
Monte Carlo
simulation
Genetic algorith
m
Power
reporte
d
reporte
d
reporte
d
reporte
d
Efficiency
Not considered a
paramete
r
Not considered a
paramete
r
Neither
calculated nor
considered
Considered and
calculated in so
me cases
The layo
ut o
f
the earli
er
works a
nd th
e present st
udy is
given
belo
w
(Figu
r
e 5
)
for
c
o
mparis
on.
7. Conclu
sion
The present
study sho
w
s that
geneti
c
algo
rithm is very effective in predi
cting the
optimal turbi
n
e config
uratio
ns. Ou
r ne
w
approa
ch of
placi
ng the tu
rbine
s
a
n
ywh
e
re in the
are
a
at a minim
u
m dista
n
ce of
200m f
r
om
each othe
r
cl
early redu
ce
s the overall
wa
ke effe
ct i
n
the
farm a
nd
gen
erate
s
m
o
re
power. In
fact
, in real
wo
rld
it is not
difficult to pla
c
e
tu
rbine
s
with
co-
ordin
a
tes
me
asu
r
ed i
n
uni
ts of metre
s
.
Also o
u
r
stu
d
y has i
n
volved a
workin
g
out layouts f
o
r
different num
ber of turbi
n
e
s
ran
g
ing fro
m
10 to 32 an
d all have sh
own b
e
tter re
sults.
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TELKOM
NIKA
ISSN:
2302-4
046
Optim
a
l Loca
t
ion of Wind
Turbi
n
e
s
in a Wind F
a
rm
using G
e
neti
c… (C.BalaK
ri
shn
a
Moo
r
thy)
5875
Mosetti et al.’s optimal layo
ut
Grady et al.’s and Emami et al.’s optimal
layout
Marmidi
s
et a
l
.’s optimal la
yout
Present layou
t
for 20 turbin
es
Present layou
t
for 10 turbin
es
Present layou
t
for 32 turbin
es
Present layou
t
for 29 turbin
es
Present layou
t
for 30 turbin
es
Figure 5. Layouts of the Wi
nd Fa
rm from Different Studies
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5876
5876
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