TELKOM
NIKA
, Vol.13, No
.3, Septembe
r 2015, pp. 7
45~751
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i3.1439
745
Re
cei
v
ed Ap
ril 20, 2015; Revi
sed
Jun
e
24, 2015; Accepted July 2,
2015
A Review on Perturb and Observe Maximum Power
Point Tracking in Photovoltaic System
Ro
zana Alik*
1,
A
w
a
ng Ju
s
o
h
2
,
Tole Sutikno
3
1,2
Department of Electrical Po
w
e
r, F
a
cult
y
of Electr
ical E
ngi
neer
ing, Un
iver
siti T
e
knologi
Mala
ysi
a
UT
M Skudai, 8131
0 Joh
o
r Ba
hru, Johor, Mal
a
y
s
ia
3
Departme
n
t of Electrical En
gi
neer
ing, F
a
cult
y of
Industri
a
l
T
e
chnolog
y, U
n
iversit
a
s Ahm
ad Da
hla
n
Jantura
n
, Yog
y
akarta 55
16
4, Indo
nesi
a
*Corres
p
o
ndi
n
g
author, em
ail
:
rozanaa
lik1
6
@
gmai
l.com
1
, a
w
a
ng@fke.ut
m.m
y
2
, tole@e
e.uad.ac.i
d
3
A
b
st
r
a
ct
Solar e
nergy i
s
beco
m
i
ng po
pul
ar and h
a
s
draw
n lo
ts of attention fro
m
researc
hers no
w
adays.
How
e
ver, the output p
o
w
e
r of
the photov
ol
taic (PV) arrays varies w
i
th solar irra
di
ation
and te
mper
ature
,
w
h
ich affect t
he
efficie
n
cy
of PV
arrays.
T
herefor
e, M
a
xi
mu
m Pow
e
r Poi
n
t T
r
acki
ng (MPPT
) c
o
ntrol
techni
qu
e is
us
ed to
extract t
h
e
max
i
mu
m
av
aila
bl
e
pow
er fr
om the
PV
arra
ys. Perturb
an
d
Observe
(P&O
)
alg
o
rith
m
is o
ne
of the
favo
rite tech
niq
ues
frequ
ent
ly us
ed due
to its simplic
ity
a
nd low
cost.
Yet, the
conventional P
&
O algorithm
has sev
e
ral dr
awbacks, which
leads to
power
loss
and lack
of efficiency. This
pap
er pres
ents
comparis
on
of
the bas
ic P&
O algorit
h
m
w
i
th the mod
i
fied
P&O algor
ith
m
us
ed for
par
tial
shad
ing c
ond
iti
on in ter
m
s of compl
e
xity, accu
racy, cost, and bas
ic conc
e
p
t of each method.
Ke
y
w
ords
:
max
i
mu
m p
o
w
er point tracking, Perturb
and Ob
serv
e alg
o
rith
m, partia
l
shad
in
g, sola
r
photov
olta
ic
Copy
right
©
2015 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Fulfilling the
energy dem
a
nd fro
m
the
p
eople
a
ll ove
r
the worl
d wo
uld be
not
en
ough if
the ene
rgy source
s a
r
e o
n
ly limited to utilizati
on of
non-ren
e
wa
ble source
s
su
ch a
s
fuel,
gas
and
coal. B
e
side
s, mo
st n
on-ren
e
wable
ene
rgie
s
ca
u
s
e
pollution
a
nd le
ss no
n-e
n
vironm
entally
friendly. He
n
c
e, re
ne
wabl
e ene
rgie
s a
r
e introd
uc
ed i
n
the pa
st two decade
s to
fulfill the energy
deman
d. On
e of the po
pular
ren
e
wable en
ergie
s
is
sola
r e
nergy
whi
c
h
is extra
c
ted
by
conve
r
ting su
nlight into ele
c
tri
c
al po
we
r usin
g
the pho
tovoltaic syst
em.
However, the conversi
on
efficien
cy is relatively low
with the
rang
e of o
n
ly from
12%
up to
2
0
%, and
it is
highly d
epe
n
dent
on the solar i
rra
diation a
n
d
panel tem
p
eratu
r
e [1]. Thus, in thi
s
p
aper, M
a
ximum Powe
r P
o
int
Tra
cki
ng (MP
P
T) cont
rol techni
que is ex
plaine
d whi
c
h
can increa
se
the efficiency of
the overall
Photovoltaic (PV) system b
y
extracting the maximu
m
available po
wer from the P
V
array
s
[1-3]
.
There are
many MPPT techniq
u
e
s
t
hat have been intro
duced an
d elabo
rate
d
extensively b
y
rese
arche
r
s. Refe
ren
c
e
[4] stated
that at least 1
9
distin
ct me
thods
have b
een
prom
oted, de
veloped
and
impleme
n
ted
to improve
sola
r p
hotovoltaic. Ea
ch
method
differs in
theirs com
p
le
xity,
number of
sen
s
ors u
s
ed, co
st and
effectivene
ss.
The
simpl
e
st
techni
que t
h
a
t
can
be
used
is fi
xed
duty
cycle
metho
d
[5] sin
c
e
it d
oes not
need
any fe
edba
ck to b
e
implem
ent
ed; but wh
e
n
the op
erati
on environm
ent ch
ang
es,
the
efficien
cy will
be
come
lo
w. Fra
c
tional
open
ci
rcuit
voltage (OCV) an
d fra
c
ti
onal
sh
ort
circuit
curre
n
t (SCC) are al
so
sai
d
to be th
e e
a
sie
s
t o
ffline
methods
for
MPPT [3, 4], [6-8]. As
for the
OCV meth
od,
the voltage a
t
MPP (V
MP
P
)
is app
roximat
e
ly equal to t
he ope
n ci
rcu
i
t voltage (V
OC
)
of PV array with the facto
r
of
k
1
suc
h
t
h
a
t
V
MP
P
≈
k
1
V
OC
, where
k
1
ra
nge
s bet
wee
n
0.71
and
0.7
8
[9]. Similar with SCC method, the c
u
rrent at MPP (I
MPP
) is approximately linearl
y
related to the
sho
r
t ci
rc
uit c
u
rr
ent (I
SC
) of
PV array, su
ch that IMPP
≈
k
2
I
SC,
wh
er
e
k
2
ra
nge
s b
e
t
ween
0.78 a
nd
0.9 [4]. Rega
rdle
ss of thei
r simpli
city, the Maximum
Power Point
(MPP) obtai
ned from the
s
e
method
s is
n
o
t true du
e to the impreci
s
e MPP tra
c
king. Plu
s
, the co
nsta
nts
k
1
and
k
2
a
r
e
not
valid duri
ng p
a
rtial shadi
ng
conditio
n
. It have
bee
n im
proved
by sweepin
g
the PV array volta
ge
or current in
orde
r to up
da
te
k
1
and
k
2
, resp
ectively. Ho
wever,
sweepin
g
lead
s
to compl
e
xity
and
incu
rs m
o
re p
o
we
r los
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 3, September 20
15 : 745 – 751
746
A number
of soft com
putin
g based MP
PT method
s also h
a
ve be
en pro
p
o
s
ed,
such as
Fuzzy L
ogi
c
Control
(FL
C
) [10, 11]
an
d
Artificial
Neu
r
al Netwo
r
k (A
NN) [1
2]. The
advanta
g
e
s
of
usin
g FLC m
e
thod are it
doe
s not req
u
ire a
c
cura
te
mathematica
l
model and
can op
erate well
unde
r varyin
g atmosphe
ri
c co
ndition
s. Yet, the
effe
ctivene
ss of t
h
is meth
od d
epen
ds a lot
on
the u
s
e
r
kno
w
led
ge. Even
thoug
h MPP
T
with
ANN controlle
r ca
n provide
go
od perfo
rman
ce,
the
neural network mu
st be trai
ned spe
c
ifical
ly
beforeha
nd
with the PV
array [4, 13].
Despite of t
he availability of other
MPPT
techni
ques, Pertur
b and Observe (P&O)
algorith
m
is
still the most common
a
nd broadl
y
use
d
due to
its simpli
city and low
cost
implementation [1], [3-4], [13-18]. Bes
i
de
s
,
it
c
a
n b
e
u
s
ed
pr
ac
tic
a
lly in
micr
oc
on
tr
o
ller
or
D
i
gita
l
Signal Proce
ssi
ng Syste
m
. Neve
rthel
ess, the
con
v
entional P&
O alg
o
rithm
still have
se
veral
dra
w
ba
cks. T
herefo
r
e, the
next sectio
n
of this
pape
r will de
scribe
more o
n
the
P&O algorit
hm
and the modif
i
cation ma
de by rese
arche
r
s to improv
e the algo
rithm, esp
e
ci
ally during the partial
sha
d
ing con
d
i
tion.
2. Perturb a
nd Observ
e
(P&O) MPPT
2.1. Conv
entional P&O M
PPT
The ba
si
c co
nce
p
t of Pert
urb a
nd O
b
se
rve (P&O
) alg
o
rithm involv
es the
pertu
rbation of
sola
r PV o
peration poi
nt co
rre
sp
ondi
ng t
o
the
sign
of
t
he la
st in
cre
m
ent of PV p
o
we
r [16,
18]. In
this metho
d
, any cha
nge
s of perturb v
o
ltage
∆
V are comm
and
e
d
by the alg
o
rithm to the
PV
module
op
erating voltage
. P&O will
determi
ne
whether
the o
peratin
g
volt
age sho
u
ld be
increa
sed o
r
decrea
s
e
d
by
∆
V after the
pro
c
e
ss of ob
servin
g outpu
t power h
a
s t
a
ke
n pla
c
e [1
9].
Figure 1
sho
w
s mo
re
deta
il on th
e o
p
e
r
ation of th
e
convention
a
l P
&
O alg
o
rithm
.
Base
d
on the obtai
ned informati
on, P&O algorithm is a
b
l
e
to predi
ct whe
n
the op
erating volta
ge is
approa
chin
g the V
MPP
by
comp
ari
ng th
e actual
and
the pr
eviou
s
state of the powe
r
, P, and
voltage, V. In sh
ort, the
next pertu
rba
t
ion to re
ach
the MPP wil
l
be the
sam
e
if there i
s
an
increme
n
t of P and vice versa [20], a
s
shown co
ncl
u
d
ed in Table 1.
Figure 1. Flow ch
art of co
nventional P
&
O algorithm
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Revie
w
on
Perturb a
nd
Observe Ma
xim
u
m Power
Point Tra
ckin
g
in… (Rozan
a Alik)
747
Table 1. Sum
m
ary of P&O Algorithm
Perturba
tio
n
∆
P
Next
Pert
urba
ti
on
Positi
v
e
Positive
Positive
Positi
v
e
Negative
Negative
Negati
v
e
Positive
Negative
Negati
v
e
Negative
Positive
The process of perturb
ation and ob
servat
ion will
be ca
rri
ed continuo
usly
until the
system
s re
a
c
h the MPP. Refere
nce [21] stated th
at the two
importa
nt parameters for this
algorith
m
are
the pertu
rba
t
ion step
size and the
ti
me between
algorith
m
iteration. Someh
o
w,
large p
e
rtu
r
b
a
tion step
size is nee
ded t
o
spe
ed up th
e respon
se, b
u
t it will contri
bute to the loss
of powe
r
du
e
to the impre
c
ise tra
cki
ng.
As the
step
size is redu
ced,
the MPP tracking
syst
em
will
slo
w
d
o
w
n th
e
re
spo
n
se.
Co
nseq
uently, time t
a
ke
n to
co
m
p
lete the
alg
o
rithm
be
co
mes
longe
r.
Many studi
es had be
en d
one to modif
y
the al
gorith
m
so that th
e trackin
g
sp
eed an
d
algorith
m
accuracy can be
impr
oved.
Many re
sea
r
ch
ers have
prop
osed variable ste
p
si
ze
concept since P&O MPPT
with fixed step
size does not provide a good tradeoff.
2.2. Modified
P&O MPPT
Referen
c
e [1,
22] used fu
zzy logi
c controller
(F
L
C
) to
vary the ste
p
size, as
presented in
Figure 2. FLC function
s to determi
ne the
suitabl
e
step
size to be u
s
ed in the algo
rithm.
For the
simu
lation pu
rpo
s
e, a Buck
DC-DC
co
nverter with Pul
s
e Width Mo
d
u
lation
(PWM
) controller
wa
s also
includ
ed in t
he PV syst
e
m
. As a re
sult
, the modified
P&O was
abl
e to
improve b
o
th the steady st
ate and dy
na
mic pe
rform
a
nce of the sy
stem.
Figure 2. Modified P&O Algorithm
with FLC
Figure 3. Modification of P&O Algorithm
The step si
ze also could
be varied b
y
m
odifying the deci
s
io
n part of the flowcha
r
t
(Figu
r
e 1) a
s
being pro
p
o
s
ed by [7]. As sh
own
in F
i
gure 3, wh
e
never the pe
rturbation mo
ved
away from th
e MPP i.e
∆
P < 0, the duty cycle
wa
s re
duced by dividing the voltage with A and
vice versa,
where
A i
s
a
consta
nt large
r
tha
n
1.
The
improved P&
O ha
d
su
cce
ssfully
co
mbi
ned
the spe
ed of relatively large
step si
ze an
d the
smooth
tracking of th
e small ste
p
size of P&O.
There a
r
e
so
me research
ers
who
com
b
ined
ot
he
r
method
with
the va
riable
st
ep
size of
P&O algorith
m
to prod
uce
better pe
rformance of MP
PT, as don
e
by [8]. The techni
que u
s
e
d
for
MPPT in that pape
r was a
com
b
ination
betwe
en variable
step
size pert
u
rb
atio
n and
co
nsta
nt
voltage tra
cki
ng. Basi
cally, whe
n
the li
ght inten
s
ity cha
nge
d dra
s
tically, the
consta
nt voltage
method
wo
ul
d take pl
ace,
and
wh
en the
ch
ang
e of lig
ht inten
s
ity tended
to b
e
st
able, the
n
P&
O
sho
u
ld
be
pre
f
erable.
Th
e
results obtain
ed from
the
S
i
mulink si
mul
a
tion p
r
oved
t
hat this meth
od
can
pro
m
ptly achi
eve MPP without a
n
y misjud
gme
n
ts of different l
i
ght inten
s
ity and temp
erature
condition.
2.3. Modifica
tion of P&O MPPT
The com
m
on
dra
w
ba
ck of conve
n
tional
P&O
MPPT, whi
c
h
i
s
the step
si
ze
p
r
obl
em,
can
literally be
so
lved by modif
y
ing the algo
rithm.
Most o
f
modified P&O MPPT are
sho
w
n
able t
o
N
Y
∆
P >
0
V
n
×A
V
n
÷A
∆
V>
0
∆
V<
0
D
e
cis
i
on P
a
r
t
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 3, September 20
15 : 745 – 751
748
prod
uce better pe
rform
a
nce
comp
ared to t
he convention
a
l MPPT. Table 2 sho
w
s the
comp
ari
s
o
n
b
e
twee
n three
modified P&O MPPT in terms of compl
e
xity, accura
cy and co
st.
According
to Tabl
e 2,
modificatio
n
made
by [7] is the
be
st
idea
sin
c
e it
doe
s n
o
t
requi
re a
n
y additional ele
c
tronic
com
p
o
nents a
nd is
simple
r than
other meth
od
s. Apart from
the
step si
ze i
s
su
e, P&O MPPT is also u
n
a
b
le to pr
od
uce high efficie
n
cy wh
en the
irradi
ation is
not
con
s
tant. T
h
e next
se
ctio
n will
explai
n
more m
odifi
cation
ma
de
on the
alg
o
rit
h
m to
overco
me
the sha
d
ing i
s
sue.
Table 2. Co
m
pari
s
on b
e
tween Modifie
d
P&O Algorith
m
s
Mod
i
fied MPPT
Characteristic
P&O w
i
th
Fuzz
y
Logic
Controller
P&O
w
i
th consta
nt A
P&O
w
i
th consta
nt
voltage tracking
Complex
i
t
y
Complex
Simple
Medium
Accuracy Good
Good
Good
Cost High
Lo
w
Lo
w
3. P&O MPPT for Partial
Shading Condition
3.1. O
v
er
v
i
e
w
o
n
P
&
O M
PPT under Partial Shadin
g Condition
The
su
n irra
diation
wo
uld
mo
st p
r
oba
bly be
come
non-unifo
rm
whe
n
the
r
e
i
s
p
a
rtial
sha
d
ing. In fact, the PV array rarely re
ce
ives unifo
rm irra
diation mo
st of the time, as pa
rts of the
PV arrays m
a
y be sha
d
e
d
by heavy clou
d, tree
s or nea
rby bu
ilding
s
, whi
c
h cau
s
e p
a
rt
ial
sha
d
ing
con
d
i
tion (PSC) [6
, 11], [13-14], [19], 23-27].
The MPP
ca
n be
ea
sily tracke
d
whe
n
the sola
r irradian
ce i
s
consta
nt, as
shown in
Figure 4. Th
e
trackin
g
process is
sta
r
ted
at the prese
n
t value of P
&
O MPPT, which i
s
ze
ro.
The
voltage will
keep on i
n
crea
sing b
a
sed o
n
the increm
e
n
t of perturbe
d
voltage. Th
e PV powe
r
a
l
so
will increa
se
until it reach
e
s the MPP. Then,
furthe
r increme
n
t of array ope
ra
ting voltage will
lead the PV powe
r
to decre
ase.
The same tracking
pro
c
e
ss
doe
s n
o
t occu
r
wh
en t
he PV array
experie
nces
PSC. As
see
n
in Fig
u
re 5, the P-V
cha
r
a
c
teri
stic wa
s ob
se
rved to have
multiple lo
cal
MPP due to
the
three
di
stinct
sol
a
r irradi
a
n
ce
level
s
. T
he P-V
cha
r
acteri
stic h
a
p
pene
d to
be
nonli
nea
r
a
n
d
compl
e
x
.
Figure 4. Normal P-V cha
r
acteri
stic u
n
d
e
r
c
o
ns
ta
n
t
irr
a
dia
t
io
n
Figure 5. P-V characte
ri
stic und
er pa
rtia
l
sha
d
ing con
d
i
tion
In the
experi
m
ent, the
op
erating
voltag
e was
un
able
to in
crea
se
since
the
po
wer
starte
d
to de
crea
se.
As
a
re
sult, the
co
nventi
onal P&O
M
PPT wa
s t
r
a
pped
in th
e l
o
cal
MPP ev
en
though it wa
s supp
osedly able to gen
erate more el
ectrical en
ergy.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
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ISSN:
1693-6
930
A Revie
w
on
Perturb a
nd
Observe Ma
xim
u
m Power
Point Tra
ckin
g
in… (Rozan
a Alik)
749
2.3 Modified
P&O for Par
t
ial Shading Conditio
n
For thi
s
rea
s
on, re
se
arch
ers all ove
r
th
e wo
rld
attempt to modify the algorithm
s
o
that it
can
wo
rk
effectively unde
r any irradiati
on level.
Kou
t
roulis, E an
d
Blaabjerg, F
[6] propo
se
d
a
new i
dea
ba
sed on
controll
ing a
DC-DC
conve
r
ter
co
n
necte
d at the
PV array out
put, as
sh
own
in Figure 6.
Figure 6. Pro
posed metho
d
with additio
nal glob
al MPPT pro
c
e
s
s
The co
nverte
r acts a
s
a consta
nt input-po
w
e
r
load. The expe
rim
ental re
sults
sho
w
e
d
that und
er
an
y partial
sh
ad
ing
con
d
ition,
the al
gor
ith
m
wa
s still
a
b
le to t
r
a
c
k the gl
obal
MP
P. In
addition, the time taken fo
r the tracking
process
wa
s much sh
ort
e
r with si
gnifi
cantly less PV
array power
pertu
rbatio
n step
s. The m
a
in advanta
g
e
for this met
hod is that it can b
e
appli
e
d in
PV arrays
without req
u
iri
n
g
kno
w
led
ge o
n
t
he PV modules
config
uration within th
e PV.
Mean
while, referen
c
e [1
3] recomme
nd
ed a
simple
and effici
ent hybrid MPPT
algorit
h
m
for PV
syste
m
s. Fig
u
re 7
sho
w
s b
r
ief
d
e
scriptio
n a
b
out the
propo
sed
meth
od.
Basically, the
idea
is to id
entify the cl
assification of the
suitable
o
p
e
r
atin
g voltage
co
rrespon
ding
to the irra
dian
ce
level by using ANN. Next, P&O algorit
hm will be
used to track the MPP withi
n
the local area
based on th
e
classification
. In general, t
h
is meth
od combine
s
the
advantag
es o
f
P&O and ANN
MPPT. Base
d on
the
simu
lation a
nd
experim
ental
re
sults, thi
s
hyb
r
id MPPT
ha
s relatively lo
wer
co
st, faster re
spo
n
se, and
much
simpl
e
stru
ct
ure co
m
pare
d
to the convention
a
l tech
niqu
e.
Figure 7. The
tracking p
r
o
c
ess for Hyb
r
i
d
MPPT (P&O and ANN)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 3, September 20
15 : 745 – 751
750
An innovative
che
c
king me
thod for P&O
algorit
hm
was
sugg
este
d
by [14] to solve the
partial shadi
n
g
issue. It is a simple, fast
and reli
able t
e
ch
niqu
e, as
pre
s
ente
d
in the Figu
re 8.
Figure 8. P&O algorith
m
with the ch
ecking al
gorith
m
Princi
pally, the che
ckin
g
al
gorithm
is
used to
ve
rify if the alg
o
rith
m already a
c
hieves
a
real
MPP o
r
only a
lo
ca
l MPP. More
over, thi
s
al
gorithm
do
es not
req
u
ire
any
additio
nal
electroni
c co
mpone
nts an
d it can find the
true MPP unde
r any op
erating
con
d
itions.
3.3. Compari
s
on on Modi
fied P&O MP
PT for Partia
l Shading Co
ndition
In a nutshell, all of the modified P&O MPPT are able
to achieve the true MPP.
Table 3
depi
cts the compa
r
ison b
e
twee
n the three meth
od
s that have been elab
orat
ed in the pre
v
ious
se
ction. Th
e
prop
osed m
e
thod
with the
ch
ecking
al
g
o
rithm i
s
a
b
solutely the b
e
st
sin
c
e it h
a
s
lowe
r co
st an
d is the simpl
e
st than the o
t
her metho
d
s.
Table 3. Co
m
pari
s
on b
e
tween Modifie
d
P&O Algorith
m
s for PSC
Mod
i
fied MPPT
Characteristic
P&O
w
i
th
DC-DC
Converter as
a
constant input-po
w
e
r
load
P&O w
i
th
ANN
P&O w
i
th
innovat
ive
checking algorithm
Complex
i
t
y
Complex
Medium
Simple
Accuracy Good
Good
Good
Cost High
Lo
w
Lo
w
4. Conclusi
on
In short, P&O MPPT Algorithm is the
most
efficient
MPPT for photovoltaic
system due
to its characteristi
c
s of bei
ng si
mple
and low co
st im
plementation. Still,
the step si
ze
problem
and p
a
rtial
shadin
g
issue
affect the a
c
cura
cy of
the
algorith
m
to
achi
eve true
MPP, as well
as
contri
bution
f
o
r th
e p
o
wer
losse
s
. Th
us,
so
me
modifi
cation
s
mu
st
be m
ade
in
o
r
de
r to
imp
r
o
v
e
the perfo
rma
n
ce of P&O MPPT. This pape
r ha
s reviewe
d
and com
pare
d
three mod
i
fied
method
s
fo
r each
i
s
sue a
nd
a
s
a con
c
l
u
sio
n
;
the
be
st meth
od i
s
t
he o
ne th
at can p
r
ovide
g
ood
accuracy, sim
p
le and lo
w cost.
Ackn
o
w
l
e
dg
ements
The autho
rs woul
d like to thank Mini
stry of
Education of Malaysia
(MOE) an
d Universit
i
Tekn
ologi M
a
laysia (UTM
) for providin
g
Resear
ch
University Gra
n
t (RUG) u
n
der vote num
ber
Q.J.130
000.2
523.03
H4
0 for this re
se
arch work.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Revie
w
on
Perturb a
nd
Observe Ma
xim
u
m Power
Point Tra
ckin
g
in… (Rozan
a Alik)
751
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