TELKOM
NIKA
, Vol.12, No
.3, Septembe
r 2014, pp. 5
49~556
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i3.91
549
Re
cei
v
ed Ma
rch 1
4
, 2014;
Re
vised July
25, 2014; Accepted Augu
st
10, 2014
Simple Hawt Prototype
Efficiency at S
m
all Scale Wind
Speed
Melda Lati
f
1
, Mumuh Muh
a
ram
2
, Yonggi Puriza
3
, Gusri
w
a
ndi
4
1,2
Basic Electrical En
gin
eeri
n
g Lab
orator
y,
Dep
a
rtment of Electrical E
ngi
neer
ing,
F
a
cult
y
of Eng
i
ne
erin
g, Univ
e
r
sit
y
of And
a
la
s, Indonesi
a
3
Department o
f
Electrical Eng
i
ne
erin
g, F
a
cul
t
y
of
Engi
ne
eri
ng, Univ
ersit
y
of Andal
as, Ind
ones
ia
4
Department o
f
Mechanic
a
l E
ngi
neer
in
g, F
a
cult
y
of
Engin
e
e
rin
g
, Univers
i
ty of And
a
las, Indo
nesi
a
email : mel
da_
l
a
tif@ft.unand.
a
c
.id
1
, mumuh
@
ft.unand.ac.i
d
2
, yon
ggi
puriz
a@
ya
hoo.com
3
,
gusri
w
a
n
d
i@ft.una
nd.ac.i
d
4
A
b
st
r
a
ct
Now
adays, the
w
i
nd ener
gy researc
h
for alt
e
rnat
if an
ergy
has be
en pr
og
ress. W
i
nd en
ergy ca
n
be fo
und
if the
w
i
nd turb
ine
i
s
avai
la
ble.T
h
i
s
pap
er ex
pl
ai
ns s
m
al
l sca
le
of Hori
z
o
nta
l
Axis W
i
nd T
u
rbin
e
(HAW
T
)
prototype by usi
ng 2
00 oh
m
res
i
sto
r
and LED at s
m
a
ll scal
e
w
i
nd spee
d. T
he bla
de
materi
al
is
acrilic. T
h
is
ma
terial
pro
perty
i
s
li
ght, n
o
easy
brok
en,
no
cor
r
osive
an
d
eas
y to fin
d
it. The
bl
ade
mo
del
i
s
flat plate
secti
on. Rotor
di
a
m
eter
i
s
1
m
e
te
r. Th
e
re
search
wa
s d
i
d at
the b
each. P
e
rman
ent
ma
g
net
synchro
nous
g
ener
ator is us
ed to ch
an
ge
w
i
nd en
ergy
t
o
el
ectric en
er
gy. T
he resu
lt show
s that th
e
gen
erator incr
ease l
i
ne
arly
w
i
th
w
i
nd speed. Measur
ed
w
i
nd spee
d w
a
s 1.9 m/s to 3.9 m/s. Averag
e
efficiency of H
A
W
T
prototype w
a
s 6.2% at delta
con
necte
d loa
d
an
d 3.7%
at w
y
e connect
ed lo
ad.
Ke
y
w
ords
: HA
W
T
prototype, flat pl
ate bl
ad
e mo
de
l, efficien
cy
1. Introduc
tion
One of the
most promo
s
i
ng alternative
ener
gie
s
as
rene
wa
ble e
nergy i
s
win
d
energy
whi
c
h ha
s ab
unda
nt and free re
sou
r
ce. Many re
sea
r
chers have be
en st
udyin
g the wind
spe
e
d
cha
r
a
c
teri
stics a
nd its p
o
tential a
s
a wi
nd tu
rbi
ne g
ene
ratio
n
(WTG
) in
many
cou
n
t
ries
worl
dwi
de [1]
.
Indone
sia
whi
c
h i
s
a
n
archipel
ago
u
s
cou
n
try ha
s p
o
tential
wi
nd for devel
o
p
ing
wind
turbi
n
e
gene
ration
(WTG
).
Unfort
unately, Pad
ang,
whi
c
h i
s
a b
e
a
c
h
city
in Indo
ne
sia,
has
wind
sp
eed
a
t
low rate sca
l
e (
≤
7 m/
s) [
2
]. To ca
pture this
small
scale
win
d
sp
eed, it is
nee
ded
some
te
chn
o
logie
s
i
n
wind tu
rbine
s
for
getting
high
er efficient en
ergy
conve
r
tion f
r
om
mech
ani
cal e
nergy to ele
c
tri
c
al ene
rg
y. From
the literatures, it is kno
w
n th
at the maximum
efficiency is
generated
by wind e
nergy is about 53% [3],[4]. Alth
ough the
resulting efficiency is
small, but the research rel
a
ted
to the ut
ilization
of wi
nd energy
as an alternativ
e energy
source
contin
ue
s to gro
w
.
As the
gen
eral form
of wi
nd turbine
s
,
Hori
zo
ntal Axis
Wind tu
rbi
nes (HAWT
)
are
still
built even though the dime
nsio
n of rotor blade be
co
me disa
dvant
age
s. The first disadva
n
ta
ge,
the effect on turbine bl
ade
cro
s
sed by wind ca
u
s
e the vibration a
nd deform
a
tion give additi
onal
stre
ss and inf
l
uen
ce the st
rength
of the blade [5
]. Another di
sadva
n
tage, due to
the large
rot
o
r
blade fault, several a
cci
de
nts and al
so
other in
ci
de
nts hap
pene
d not only in UK [6] but also in
other count
rie
s
[7].
In this pa
pe
r, to anticip
ate
the disadvan
tages
of the l
a
rge
scale
wi
nd turbine, th
e sm
all
scale wi
nd tu
rbine i
s
propo
sed
with so
m
e
polici
e
s.
First, the prototype sh
ould b
e
able to ha
rve
s
t
energy at l
o
w
speed
of wind [1
],[8],[9]. Second, the
built wi
nd tu
rbine should be
applicable
f
o
r
rural or re
sid
ence utility. F
i
nally, consi
d
ering
the first and se
con
d
policy, the turbine sh
ould
be
built by using
che
ap mate
ri
als an
d also it need
s just small spa
c
e fo
r installatio
n
[10].
2. Rese
arch
Metho
d
Wind ene
rgy conve
r
si
on sy
stem
s
is a system wh
i
c
h ai
ms to tran
sfor
m the ki
netic
energy
of the wind i
n
to mech
ani
ca
l energy to the turb
in
e shaf
t and then m
o
dified agai
n b
y
the gene
rat
o
r
into elect
r
ical
energy. Win
d
kineti
c
en
e
r
gy with
ma
ss "m" is mov
i
ng with velo
city v has th
e
equatio
n [3]:
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 54
9 – 556
550
(1)
Wind p
o
wer i
s
the ene
rgy per unit of time, then:
.
.
(2)
.
.
(3)
whe
r
e:
P
T
= me
ch
ani
cal po
we
r in the moving ai
r (Watt)
C
p
= po
we
r coefisie
nt, C
p
< 0,
6
=
a
i
r
de
ns
ity (
k
g
/m
3
)
A = area
swe
p
t by the rotor blade
s (m
2
) =
v = wind sp
e
ed (m/s)
The pe
rform
ance of the
HAWT
protot
ype wa
s al
so determined
from the tip
spe
ed
ratio.Tip
sp
e
ed
ratio i
s
th
e oute
r
mo
st
side
s
pee
d compa
r
ison of
the rotor
ag
ainst
th
e win
d
spe
ed. Equati
on tip spe
ed ratio is:
ts
r =
.
π
.D/60/v (4)
whe
r
e:
=
shaft sp
eed (rpm)
π
= 3
.
14
D = rotor diam
eter oh the blade
(m)
v = wind sp
eed (m/s)
the tsr was
selecte
d
amon
g the 5 s/d 8.
2.1 Blade
De
sign
The materi
al use
d
for the manufa
c
ture of t
he blade is acrilic. Rea
s
on
s for choo
sing th
i
s
material
beca
u
se it was
e
a
sy, lightweig
ht and not
p
r
one to corro
s
ion. The
radi
us of the bl
a
d
e
use
d
is 0.5
m and
blad
e
desi
gn i
s
flat
plate sectio
n.
As a refere
nce to determine the ch
ord
width equation is [11]:
2
6(
/
)
9
R
Rr
C
B
(5)
whe
r
e :
C = cho
r
d wi
dth (m)
R = the radiu
s
of the rotor
= 0.5 m
r = the di
stan
ce from the m
i
dline chord (m)
λ
= tip sp
eed
ratio = 7
B = blade nu
mbers = 3
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
9
30
Sim
p
le Hawt Prototyp
e Efficien
cy at Small Scale Wi
n
d
Speed (M
el
da Latif)
551
(a) One bla
de
(b)Th
r
ee
Blades
Figure 1. HAWT Blade
De
sign
Figure 1 sh
o
w
s the
sha
p
e
of the blade is pro
d
u
c
ed. T
h
ree bl
ade i
s
mounted o
n
the hub
are ea
ch a 1
2
0
o
.
2.2 The Esti
mated Po
w
e
r at HAWT Proto
t
y
p
e
Estimated of the output po
wer at
HAWT
pr
ototype wit
h
low wi
nd sp
eed was b
a
sed on
equatio
n (2
), can b
e
se
en i
n
Figure 2.
Figure 2. Estimated Power from small
scale
wind
spe
e
d
2.3 The Liais
on bet
w
e
e
n the Blade a
n
d Shaft
Liaison bet
ween the bl
ad
es an
d shafts using
an
iro
n
bar
whi
c
h i
s
mad
e
in th
e sha
pe of
the letter "T".
Liaison in
this twist of
th
e b
l
ade
wa
s o
b
tained
by a bit
slop
e a
bout
5
0
. T
h
e
pu
r
pos
e
of this i
s
to
m
a
ke
the a
c
q
u
i
r
ed
-twi
sting li
ft and d
r
ag
fo
rce
that i
s
g
o
od
so that
wi
nd turbine
s
can
work
well [3],[4],[11].
9 c
m
1.
5 c
m
14 c
m
3 c
m
Figure 3. The
Liaiso
n between shaft and
blade
0.0
2.0
4.0
6.0
1.9
2
.1
2.3
2
.5
2.7
2
.9
3.1
3
.3
3.5
3
.7
3.9
v
(m/s)
P
T
(W)
Cord
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 54
9 – 556
552
2.4 Gener
a
to
r
Gene
rato
rs
synchrono
us g
enerators u
s
ed are
three
pha
se with
magneti
c
excitation of
harve
sters. T
h
is i
s
a u
s
ed
gen
erato
r
at
win
d
tu
rb
in
es
w
i
th
a ca
pa
c
i
ty o
f
w
a
ter
-
X
-p
ow
e
r
4
00
Watts. Thi
s
Gene
rato
r is con
s
id
ere
d
according to
the de
sign
of wind tu
rbi
nes to
be m
a
d
e
becau
se it is
a type of gen
erato
r
that is
made for th
e purp
o
ses
of small-scale wi
nd turbi
ne wh
ich
has 6
pole
s
excitation. Ba
sed o
n
the te
chni
cal
spe
c
if
ication
s
on th
e User M
anu
al Wind tu
rbi
ne
Air-X win
d
turbin
e is kn
own that be
gan spinni
n
g
at wind sp
e
eds of 3.0
m/s. Ho
weve
r, on
hori
z
ontal
Axis wi
nd tu
rbin
e de
sign
s
are
expecte
d to
be sta
r
ting th
e turbi
ne
win
d
sp
eed
s
ca
n
be
lowe
r than 3.
0 m/s.
In general the
voltage gene
rated by t
he g
enerator h
a
s
the equatio
n [12]:
e = B.l.v
(6)
whe
r
e,
e = Indu
ction
Voltage (V)
B = magneti
c
field (Wb/m
2
)
l = the long e
n
tanglem
ent (m)
v = rotation speed (rpm
)
Usually the p
o
we
r equ
atio
n for altern
ating voltage so
urce is:
S =
P
L
+ jQ
(7)
whe
r
e,
S = appa
rent
power = V.I (VA)
(8)
P
L
=
ac
tive power or load
power =
V.I.cos
= I
2
R (Watt)
(9)
Q =
reac
tive
power =
V.I.s
in
= I
2
X (VAR)
(10
)
R =
r
esi
s
to
r (
Ω
)
X =
r
e
ac
ta
nce
=
X
L
- X
C
(
Ω
)
X
L
= inductive
reacta
nce =
2.
π
.f.L (
Ω
)
X
C
= capa
citi
ve reacta
nce = 1/(2.
π
.f.C) (
Ω
)
f = frequen
cy
(Hz)
L = indu
ctan
ce (He
n
ry)
C = capa
cita
nce (Fa
r
ad
)
From e
quatio
n 2 and 9, the
n
the effi
cien
cy of the HAWT prototype
is:
100%
(11
)
whe
r
e.
=
effic
i
enc
y
HAWT Prototype
P
L
= load po
wer
(W)
P
T
= turbine
mech
ani
cal p
o
we
r (W)
3. Eksperiment Results and An
aly
s
is
Prior to the fi
eld, the pe
rm
anent ma
gnet
sync
hro
nou
s gene
rato
r u
s
ed to be te
ste
d
in the
laboratory. By providing t
he en
ergy o
f
moti
on co
ming from t
he moto
r, the gen
erato
r
will
gene
rate el
ectrical e
n
e
r
gy. Figure 4a
sh
ows the
circui
t for testing p
e
rma
nent ma
gnet ge
nerator.
Figure 4b
sh
ows the
re
su
lting vo
ltage
perm
ane
nt magnet g
ene
ra
tor for
seve
ral rou
n
d
s
of
the
s
haft. By providing the 300 rpm to
2500 rpm, gene
rator produces
a voltage from 2.1 Volts
up to
21.1 volts.
The p
r
o
c
edu
re for testin
g a
r
e a
s
follo
w. First, Prototy
pe was te
ste
d
without lo
a
d
to kno
w
wethe
r
the
r
e
wa
s
cu
rrent
or n
o
t. The
n
, circuit
wa
s l
oade
d by LE
D. The
LE
D
use
d
i
s
a
kin
d
of
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
9
30
Sim
p
le Hawt Prototyp
e Efficien
cy at Small Scale Wi
n
d
Speed (M
el
da Latif)
553
sup
e
r b
r
ight
white LE
D which
con
s
i
s
ts
of two gr
oup
s of LED. Each gro
up
con
s
i
s
ts of ten LE
Ds.
In the first group, LED
constructio
n
a
r
e parallel which is a m
a
ximum of 5 k
Ω
re
sist
a
n
c
e
con
n
e
c
ted. While in the seco
nd group,
every two
LED is arrang
ed parallelly and co
nne
cte
d
to a
1 k
Ω
, so the circuit will consi
s
t of the simillar fi
ve groups of LE
D. Before being connected
to
LED, alte
rnat
ing voltage
must b
e
re
ctified by
dio
d
e
re
ctifier.Final
ly, the experi
m
ent cond
uct
e
d
with load in
and Y conn
e
c
tion. The
circuit for testin
g can b
e
depi
cted in Figu
re
5.
,
a.
Circuit
b.
Result
Voltage
Figure 4. Permanent Ma
gn
et Synchro
n
o
u
s Ge
nerator
Testing
V1
V2
V3
Li
n
e
2
Li
n
e
3
Li
n
e
1
0
‐
5
k
Ω
A
1
k
Ω
1
k
Ω
1
k
Ω
1
k
Ω
1
k
Ω
Li
n
e
1
Li
n
e
2
Li
ne
3
V
a
.
b
.
A
V
Li
n
e
1
Li
n
e
2
Lin
e
3
Be
b
a
n
V
‐
LL
V
‐
LN
A
Lin
e
1
Lin
e
2
Lin
e
3
Ne
tr
a
l
c
.
d
.
Figure 5. HAWT prototype
experime
n
t: a. No load
circ
uit b. Circuit
with LED loa
d
c. Circuit wi
th
conn
ectio
n
d. Circuit with
Y conne
ction
0
5
10
15
20
25
100
300
500
700
900
1100
1300
1500
1700
1900
2100
2300
2500
(rpm)
V
L
(V)
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ISSN: 16
93-6
9
30
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 54
9 – 556
554
3.1 No Load
Eksperimen
t
Figure 6 sho
w
s th
e ci
rcui
t and the vo
ltage
wa
s p
r
odu
ced o
n
the HA
WT p
r
ototype
without loa
d
.
Figure 6. The
curve of line
voltage vs
wi
nd sp
eed at n
o
load conditi
o
n
The gra
ph shows that it look
s that the greater the
wind
spee
d the gre
a
ter re
sultin
g
voltage gene
rator will be. This is be
ca
u
s
e the gen
erat
or voltage is dire
ctly pro
portion
al to wind
spe
ed. Win
d
turbin
e begi
ns rotating in the wind
spe
e
d
1.9 m/s.
3.2 Eksperi
m
ent
w
i
th L
E
D
Figure 7 sh
o
w
s
HAWT p
r
ototype
that its blad
e are
spinnin
g
. It is seen that LED
is on.
a.
The Prototyp
e and ci
rcuit
b. The re
sult of LED Voltage
Figure 7. LED experi
m
ent
in the Beach
Figure 7b sh
ows that the resultin
g voltage rises lin
ea
rly with an in
cre
a
se in win
d
spe
ed.
The resulting
voltage of the gene
rato
r i
s
then
re
ctif
ied by the re
ctifier. The direct current from
rectifie
r is u
s
ed to light on the LEDs. LE
D st
a
r
ted ligh
t
on spee
d of wind at 2.3 m/s.
3.3 Eksperi
m
ent
w
i
th
Delta Co
nnec
t
ed Load
Figure 8a sh
ows the voltage pro
d
u
c
ed
on the
protot
ype delta rel
a
tionship wa
s HA
WT
with the load
resi
sto
r
200
Ω
. The re
sulti
ng voltage ge
nerato
r
will b
e
even gre
a
ter wh
en the
wind
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
1.
9
2
.
1
2.
3
2
.
5
2.
7
2
.
9
3.
1
3
.
3
3.
5
3
.
7
3.
9
4
.
1
v
(m/s)
V
L
(V
)
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
1.
9
2
.
1
2.
3
2
.
5
2.
7
2
.
9
3.
1
3
.
3
3.
5
3
.
7
3.
9
v
(m/s)
V
L
(Vol
t)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sim
p
le Hawt Prototyp
e Efficien
cy at Small Scale Wi
n
d
Speed (M
el
da Latif)
555
spe
ed th
at a
ppea
rs in
cre
a
sin
g
ly eleva
t
ed, be
ca
u
s
e
the
re
sulting
voltage i
s
proportio
nal to
the
given rotation
al spe
ed.
a.
The voltage o
f
Generator
b. The Load
power
Figure 8. HAWT Prototype
with
Conn
ected L
oad
Result
s
Figure 8b
sh
ows that loa
d
po
wer is
n
o
t equal to
turbin
e po
we
r. Load p
o
we
r P
L
is
cal
c
ulate
d
fro
m
eq. (8), turbine p
o
wer P
T
from eq. (2), effic
i
enc
y
from eq.
(11
)
.
The d
e
cre
a
se
of efficiency
becau
se the
r
e are lo
sse
s
at turbine
su
ch a
s
drag fo
rce
and at g
e
nerato
r
such
as
magneti
c
and
copp
er lo
sse
s
. The aver
ag
e efficien
cy is obtained i
s
6
.
2%.
3.4 Eksperi
m
ent
w
i
th
Wy
e
Connec
t
e
d
Load
Figure 9a
sh
ows the curv
e of line voltage versu
s
wi
nd sp
eed to 2
00
Ω
.re
s
i
s
tor load
wit
h
wye co
nne
cti
on. The curve
sho
w
s that li
ne
voltage in
cre
a
se linea
rl
y to wind spe
ed.
a.
The voltage o
f
Generator
b. The power lo
ad
Figure 9. HAWT Prototype
with Y Conn
ected L
oad
Result
s
Figure 9
b
sh
ows the
loa
d
power. Ba
se
d on
th
e
load
po
we
r, effici
ency i
s
cal
c
ul
ated.Th
e
efficien
cy, then is obtai
n
ed on the HAWT pr
ototype Y conn
ection wa
s sm
aller than d
e
l
ta
con
n
e
c
tion.
The lo
w
effici
ency
of Y con
nectio
n
i
s
cau
s
ed
by in
ducti
ve rea
c
tan
c
e
at the lin
e. Th
e
averag
e effici
ency which re
sulted
o
n
this prototype is
3.7%.
Gene
rally, small scale wi
nd sp
eed giv
e
s lo
w effi
cie
n
cy of the protot
ype of wind turbin
e.
This result is the sam
e
re
sult as the stu
d
y by
[1] that little wind re
sou
r
ce gives
only 10% of the
0.0
1.0
2.0
3.0
4.0
5.0
1.9
2
.1
2.3
2
.5
2.7
2
.9
3.1
3
.3
3.5
3
.7
3.9
v
(m/s)
V
L
(V)
0.00
0.05
0.10
0.15
0.20
0.25
1.9
2
.1
2.3
2
.5
2.7
2
.9
3.1
3
.3
3.5
3
.7
3.9
v
(m/
s
)
P
L
(W)
0
1
2
3
4
5
1.9
2
.1
2.3
2
.5
2.7
2
.9
3.1
3
.3
3.5
3
.7
3.9
v
(m/s)
VL
(V)
0.00
0.05
0.10
0.15
0.20
1.9
2
.1
2.3
2
.5
2.7
2
.9
3.1
3
.3
3.5
3
.7
3.9
v
(m/s)
PL
(W)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 54
9 – 556
556
total output voltage of WT
G. Therefore,
it is need
ed
to increa
se t
he efficien
cy
by developin
g
a
spe
c
ial wi
nd
turbine
s
which is simple, e
ffective
and low-co
st win
d
turbine [13]. In addition, the
usin
g of spe
ed-in
crea
se
gearbox can
increa
se ge
nerato
r
rpm
even thoug
h
the gearbox
can
contri
bute to
vibration [14]
. The hybrid
betwe
en ho
ri
zontal a
nd vertical
axis can increa
se t
he
efficien
cy du
e to vertical
axis win
d
turbine c
an rota
te at smalle
r scale spee
d
rathe
r
than
the
hori
z
ontal
axi
s
[15]. Fin
a
lly, for the
gen
e
r
ator poi
nt
of
view, Refs. [
16] an
d [17]
can
in
cre
s
e
the
perfo
rman
ce
of the prototype.
4. Conclusio
n
The
simpl
e
HAWT p
r
ototy
pe h
a
s alrea
d
y bee
n ma
d
e
. Thi
s
p
r
otot
ype ha
s th
re
e bla
d
e
s
.
De
sign
of
bl
ade i
s
flat pl
ate se
ctio
n. By
usin
g re
sistor
20
0
Ω
,
average
efficien
cy
to
delta
con
n
e
c
tion is 6.2% and wye conn
ectio
n
is 3.7%. Ac
tually, the effi
cien
cy of both are still sm
all.
There are m
a
ny losses in t
h
is
prototype. Those
are lo
sses at
turbin
e, generator
and at line.
Ackn
o
w
l
e
dg
ment
This
wo
rk was
su
ppo
rted
by DG
HE
(Di
k
ti-De
c
entralisatio
n Research
) Proje
c
t No.
15/UN.16/PL-HB/2013 a
n
d
Enginee
ring
Faculty DI
PA, University
of Andalas, Indone
sia un
de
r
Project No. 035/PL/SPK/PNP/FT-Unand/2013.
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ces
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a
nto M, Su
w
a
rno, Ir
w
a
n Y.M, Gomesh N, A
h
mad N.S. Po
tenti
a
l of W
i
n
d
S
p
e
ed for W
i
n
d
Po
w
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i
on in Perlis, Northern Malay
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2011; 9(3):
575-5
82.
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Latif M. Savo
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rbin
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Protot
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cienc
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n
d
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Jur
nal Rekay
a
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Elektrika.
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2
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M.R.
W
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nd and So
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Evaluation Warning : The document was created with Spire.PDF for Python.