I
nte
rna
t
io
na
l J
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urna
l o
f
P
o
wer
E
lect
ro
nics
a
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Driv
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y
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em
s
(
I
J
P
E
DS
)
Vo
l.
1
2
,
No
.
4
,
Dec
em
b
er
202
1
,
p
p
.
2
2
0
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I
SS
N:
2088
-
8
6
9
4
,
DOI
: 1
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1
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s
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v
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4
.
pp
2
2
0
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-
2
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0
8
2201
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
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e.
co
m
A new
per
turb
a
n
d obs
erve M
P
PT
a
lg
o
rithm bas
ed on two s
teps
v
a
ria
ble vo
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e control
H
us
s
a
in At
t
ia
1
,
Su
ley
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a
n Ulus
o
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2
1
De
p
a
rtme
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o
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El
e
c
tri
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l,
El
e
c
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C
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m
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s E
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Am
e
rica
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Un
i
v
e
rsity
o
f
Ra
s Al
Kh
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,
UEA
2
De
p
a
rtme
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M
a
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ti
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Na
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Am
e
rica
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iv
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f
Ra
s Al
K
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Art
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I
nfo
AB
S
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RAC
T
A
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ticle
his
to
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y:
R
ec
eiv
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J
u
n
1
1
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2
0
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1
R
ev
is
ed
Sep
2
2
,
2
0
2
1
Acc
ep
ted
Sep
29
,
2
0
21
Ba
se
d
o
n
t
h
e
fa
c
t
th
a
t
t
h
e
e
ffe
c
ti
v
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f
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n
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m
in
a
m
a
x
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m
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trac
k
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m
a
x
imu
m
p
o
we
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p
o
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n
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trac
k
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(
M
P
P
T)
i
n
a
p
h
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to
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o
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ic
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a
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f
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ri
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th
e
tran
sie
n
t
re
sp
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a
n
d
th
e
o
sc
il
latio
n
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ro
u
n
d
th
e
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le
lev
e
l
d
u
ri
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t
h
e
ste
a
d
y
sta
te
re
sp
o
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se
.
To
h
a
v
e
a
h
ig
h
trac
k
in
g
sp
e
e
d
,
in
c
re
m
e
n
tal
ste
p
sh
o
u
ld
b
e
h
ig
h
,
b
u
t
th
is
h
ig
h
in
c
re
m
e
n
ta
l
ste
p
in
c
re
a
se
s
th
e
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sc
il
latio
n
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e
l
a
ro
u
n
d
th
e
ste
a
d
y
lev
e
l
o
f
M
P
P
T
,
wh
e
re
a
s a
d
o
p
ti
n
g
l
o
w i
n
c
re
m
e
n
tal
ste
p
r
e
d
u
c
e
s th
e
a
lg
o
rit
h
m
re
sp
o
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se
ti
m
e
b
u
t
i
m
p
ro
v
e
th
e
re
sp
o
n
se
d
u
rin
g
t
h
e
ste
a
d
y
sta
te
c
o
n
d
i
ti
o
n
.
T
h
is
p
a
p
e
r
p
re
se
n
ts
a
n
e
w
p
e
rtu
rb
a
n
d
o
b
se
rv
e
a
lg
o
rit
h
m
b
a
se
d
o
n
two
ste
p
v
a
riab
le
c
o
n
tro
l
fo
r
M
P
P
T
a
p
p
li
c
a
ti
o
n
s
.
A
two
v
a
riab
le
i
n
c
re
m
e
n
tal
ste
p
c
o
n
tr
o
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se
d
t
o
g
a
in
t
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e
m
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rit
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f
h
i
g
h
ste
p
f
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g
u
a
ra
n
te
e
in
g
a
fa
st
re
sp
o
n
se
d
u
r
in
g
trac
k
in
g
p
ro
c
e
ss
,
a
n
d
a
lso
fo
r
g
u
a
ra
n
tee
in
g
t
h
e
m
e
rit
o
f
lo
w
o
sc
il
latio
n
d
u
rin
g
t
h
e
ste
a
d
y
sta
te
wo
rk
i
n
g
c
o
n
d
it
i
o
n
t
h
ro
u
g
h
a
d
o
p
ti
n
g
a
lo
w
ste
p
d
u
rin
g
ste
a
d
y
sta
te
re
sp
o
n
se
.
Th
e
e
ffe
c
ti
v
e
n
e
ss
o
f
t
h
e
p
ro
p
o
sa
l
is
p
r
o
v
e
d
by
th
e
a
n
a
l
y
sis
o
f
th
e
sim
u
latio
n
re
su
lt
s
v
ia
M
AT
LAB/S
imu
l
in
k
so
ftwa
re
,
a
n
d
b
y
th
e
c
o
m
p
a
riso
n
o
f
t
h
e
si
m
u
latio
n
re
su
lt
s
wi
th
a
c
o
n
v
e
n
t
io
n
a
l
p
e
rt
u
rb
a
n
d
o
b
se
rv
e
M
P
P
T
a
l
g
o
rit
h
m
.
K
ey
w
o
r
d
s
:
C
o
n
v
en
tio
n
al
p
e
r
tu
r
b
DC
-
DC
b
o
o
s
t c
o
n
v
er
ter
MA
T
L
AB
/S
im
u
lin
k
Du
ty
cy
cle
Ob
s
er
v
e
alg
o
r
ith
m
two
s
tep
co
n
tr
o
l
Ob
s
er
v
e
alg
o
r
ith
m
two
s
tep
s
p
er
tu
r
b
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Hu
s
s
ain
Attia
Dep
ar
tm
en
t o
f
E
lectr
ical,
E
lec
tr
o
n
ics an
d
C
o
m
m
u
n
icatio
n
E
n
g
in
ee
r
in
g
Am
er
ican
Un
iv
er
s
ity
o
f
R
as Al
Kh
aim
ah
R
as Al
Kh
aim
ah
,
1
0
0
2
1
,
UAE
E
m
ail: h
attia@
au
r
ak
.
ac
.
ae
N
O
M
E
N
CL
A
T
UR
E
I
PV
:
PV c
ell
o
u
tp
u
t c
u
r
r
en
t (
A)
R
s
:
PV c
ell
s
er
ies r
esi
s
to
r
(
Ω
)
I
SC
:
L
ig
h
t g
en
e
r
ated
cu
r
r
en
t (
A)
R
sh
:
PV c
ell
s
h
u
n
t r
esis
to
r
(
Ω
)
I
D
:
Dio
d
e
cu
r
r
e
n
t
(
A)
N
s
:
No
.
o
f
PV c
ells
in
s
er
ies
I
sh
:
Sh
u
n
t c
u
r
r
e
n
t
(
A)
N
sh
:
No
.
o
f
PV c
ells
in
p
ar
allel
V
D
:
Dio
d
e
Vo
ltag
e
(
V)
V
PV
-
Tot
:
T
o
tal
o
u
tp
u
t
v
o
ltag
e
f
r
o
m
a
PV m
o
d
u
le
V
T
:
T
em
p
er
atu
r
e
v
o
ltag
e
(
V)
I
PV
-
Tot
:
T
o
tal
o
u
tp
u
t c
u
r
r
e
n
t f
r
o
m
a
P
V
m
o
d
u
le
I
o
:
Dio
d
e
s
atu
r
atio
n
cu
r
r
en
t (
A
)
Δ
V
:
Vo
ltag
e
d
if
f
er
e
n
ce
V
(
t)
-
V(t
-
Δ
t)
V
PV
:
PV c
ell
o
u
tp
u
t v
o
ltag
e
(
V)
Δ
P
:
Po
wer
d
if
f
er
en
c
e
P
(
t)
-
P
(
t
-
Δ
t)
D
:
Du
ty
cy
cle
o
f
DC
-
DC
co
n
v
er
t
er
V
step
:
An
in
cr
em
en
t/d
ec
r
em
en
t in
t
r
a
ck
in
g
v
o
ltag
e
ɛ
:
A
s
m
all
ab
s
o
lu
te
Δ
P/
Δ
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
220
1
–
22
08
2202
1.
I
NT
RO
D
UCT
I
O
N
So
lar
r
en
ewa
b
le
e
n
er
g
y
is
r
e
p
r
esen
tin
g
as
a
v
al
u
ab
le
s
o
u
r
ce
o
f
d
ir
ec
t
cu
r
r
en
t
elec
tr
ical
p
o
wer
d
u
e
t
o
its
av
ailab
ilit
y
ev
er
y
wh
er
e,
cl
ea
n
n
ess
with
o
u
t
an
y
p
o
llu
ted
em
is
s
io
n
,
an
d
with
o
u
t
an
y
co
s
t
o
f
p
r
o
d
u
cin
g
.
A
p
h
o
to
v
o
ltaic
(
PV)
p
an
el
ab
s
o
r
b
s
th
e
s
o
lar
en
er
g
y
an
d
c
o
n
v
er
ts
th
e
s
u
n
lig
h
t
in
to
elec
tr
icity
wh
en
it’
s
eith
er
wo
r
k
in
g
with
in
a
s
tan
d
alo
n
e
PV
s
y
s
tem
o
r
with
in
g
r
id
co
n
n
e
cted
s
y
s
tem
[1
]
,
[
2
]
.
T
h
e
d
esire
d
o
u
tp
u
t
v
o
ltag
e
an
d
/o
r
o
u
t
p
u
t
cu
r
r
en
t
o
r
p
o
wer
c
an
b
e
o
b
tain
e
d
th
r
o
u
g
h
a
s
p
ec
if
ic
d
esig
n
o
f
th
e
PV
ar
r
ay
.
I
n
o
th
er
wo
r
d
s
,
th
e
way
o
f
PV
p
an
els’
ar
r
an
g
em
en
t
i
n
th
e
s
y
s
tem
PV
ar
r
ay
will
af
f
ec
t
th
e
lev
el
o
f
o
u
tp
u
t
v
o
ltag
e
an
d
o
u
tp
u
t
cu
r
r
en
t
[
3
]
.
T
o
in
cr
ea
s
e
th
e
lev
el
o
f
o
u
tp
u
t
v
o
ltag
e
f
r
o
m
th
e
PV
ar
r
ay
,
th
e
n
u
m
b
er
o
f
s
er
ially
co
n
n
ec
ted
p
an
els
in
th
e
b
r
a
n
ch
es
o
f
PV
ar
r
ay
s
h
o
u
ld
b
e
in
cr
ea
s
ed
.
W
h
er
ea
s
to
in
cr
ea
s
e
th
e
lev
el
o
f
o
u
tp
u
t c
u
r
r
en
t
f
r
o
m
t
h
e
PV
ar
r
ay
,
th
e
n
u
m
b
e
r
o
f
p
ar
a
llel b
r
an
ch
es
s
h
o
u
ld
b
e
in
c
r
ea
s
ed
[
4
]
,
[
5
]
.
Ma
n
y
r
esear
c
h
s
tu
d
ies
in
s
tan
d
alo
n
e
o
r
in
g
r
id
co
n
n
e
cted
p
h
o
to
v
o
ltaic
s
y
s
tem
s
d
esig
n
an
d
im
p
lem
en
tatio
n
h
av
e
b
ee
n
f
o
c
u
s
ed
o
n
in
cr
ea
s
in
g
th
e
q
u
an
tity
o
f
h
ar
v
ested
s
o
lar
en
er
g
y
th
r
o
u
g
h
co
n
s
id
er
in
g
th
e
ch
ar
ac
ter
is
tics
o
f
s
o
lar
PV
p
an
els,
an
d
h
o
w
th
e
g
en
er
ate
d
elec
tr
icity
f
r
o
m
th
e
p
a
n
el
is
n
o
n
lin
ea
r
ly
af
f
ec
ted
b
y
th
e
lig
h
t
in
ten
s
ity
an
d
am
b
ien
t
tem
p
er
atu
r
e
[
6
]
-
[
8
]
.
B
ased
o
n
th
ese
ch
ar
ac
ter
is
tics
,
th
er
e
is
an
o
p
p
o
r
tu
n
ity
to
let
a
PV
p
an
el
wo
r
k
in
th
e
ar
ea
f
r
o
n
t
o
f
th
e
s
u
n
lig
h
t
d
u
r
in
g
wo
r
k
in
g
d
a
y
h
o
u
r
s
to
h
ar
v
est
th
e
m
a
x
im
u
m
p
o
wer
th
r
o
u
g
h
an
elec
tr
o
m
e
ch
an
ically
tr
ac
k
in
g
s
y
s
tem
[
9
]
.
Dif
f
er
en
t
al
g
o
r
ith
m
s
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
to
g
u
ar
an
tee
th
e
m
a
x
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT
)
wo
r
k
in
g
co
n
d
itio
n
,
a
n
d
ea
ch
alg
o
r
ith
m
h
as
d
if
f
er
en
t
p
r
o
ce
s
s
to
r
ea
ch
t
o
th
e
MPP
p
o
in
t w
ith
d
if
f
er
en
t sp
ec
if
icatio
n
s
o
r
m
er
its
[
1
0
]
-
[
21]
.
I
n
[
1
0
]
-
[
1
2
]
,
m
a
n
y
alg
o
r
ith
m
s
f
o
r
MPPT
o
b
jectiv
e
h
av
e
b
ee
n
p
r
o
p
o
s
ed
,
s
u
ch
as
in
cr
em
en
tal
co
n
d
u
cta
n
ce
(
I
C
)
alg
o
r
ith
m
,
Per
tu
r
b
an
d
Ob
s
er
v
e
(
P
an
d
O)
a
lg
o
r
ith
m
,
o
p
en
v
o
ltag
e
m
eth
o
d
,
an
d
s
h
o
r
t
cir
c
u
it
cu
r
r
en
t
m
eth
o
d
.
All
o
f
th
e
m
en
tio
n
ed
alg
o
r
ith
m
s
wer
e
ch
a
r
ac
ter
ized
b
y
s
im
p
licity
an
d
n
eg
ativ
ely
af
f
ec
ted
r
esp
o
n
s
e
b
y
th
e
alg
o
r
ith
m
p
r
o
ce
s
s
.
Fo
r
h
ig
h
er
r
o
b
u
s
tn
ess
p
er
f
o
r
m
an
ce
,
f
u
zz
y
lo
g
ic
co
n
tr
o
l
(
FLC)
h
as
p
r
o
p
o
s
ed
in
[
1
3
]
,
in
wh
ich
,
t
h
e
FLC
h
av
e
in
s
er
ted
to
s
u
p
p
o
r
t
th
e
Hill
-
C
lim
b
in
g
alg
o
r
it
h
m
in
tr
ac
k
in
g
th
e
MPP
f
o
e
PV
s
y
s
tem
ap
p
licati
o
n
s
.
Fo
r
f
ast
an
d
ac
cu
r
ate
r
es
p
o
n
s
e
o
f
MPPT
f
u
n
ctio
n
,
FL
C
h
as
b
ee
n
in
clu
d
ed
in
a
ce
r
tain
PV
s
y
s
tem
s
d
esi
g
n
in
[
1
4
]
.
Oth
er
s
tu
d
ies
h
av
e
f
o
cu
s
ed
o
n
a
h
i
g
h
s
tab
ili
ty
p
er
f
o
r
m
an
ce
in
th
e
MPPT
f
u
n
ctio
n
b
ased
o
n
FLC,
wh
ich
wer
e
s
h
o
wn
in
[
1
5
]
-
[
1
8
]
.
All
th
e
r
esear
ch
s
tu
d
ies
b
a
s
ed
o
n
FLC
r
ef
lect
d
if
f
icu
lties
in
d
esig
n
in
g
th
e
s
tep
s
,
b
lo
ck
s
,
m
em
b
er
s
h
ip
s
’
r
u
l
es
o
f
FLC,
lead
in
g
to
an
ad
d
itio
n
o
f
a
d
em
e
r
it
to
ap
p
ly
in
g
th
e
FLC i
n
PV
s
y
s
te
m
s
.
R
ec
en
tly
,
ar
tific
ial
n
eu
r
al
n
etwo
r
k
s
(
ANN)
alg
o
r
ith
m
s
h
av
e
p
r
o
p
o
s
ed
as
Ma
ch
in
e
lear
n
in
g
alg
o
r
ith
m
s
in
[
1
9
]
-
[
2
2
]
f
o
r
f
ast
tr
ac
k
in
g
t
h
e
MPP
d
u
r
in
g
d
if
f
er
en
t
wea
th
er
c
o
n
d
itio
n
s
.
ANN
alg
o
r
ith
m
d
em
o
n
s
tr
ates
f
ast
an
d
ac
cu
r
at
e
r
esp
o
n
s
e,
b
u
t
at
th
e
s
am
e
tim
e,
it
n
ee
d
s
a
f
ast
an
d
co
m
p
l
icate
d
p
r
o
ce
s
s
o
r
to
ex
ec
u
te
th
e
in
ter
n
al
ca
lcu
latio
n
s
.
T
h
e
r
em
ain
in
g
o
f
th
is
p
ap
er
is
o
r
g
an
ized
as
s
h
o
wn
:
T
h
e
p
r
o
ce
s
s
an
d
s
tep
s
o
f
co
n
v
en
tio
n
al
Pan
d
O
alg
o
r
ith
m
f
o
r
MPPT
o
b
jectiv
e
ar
e
s
h
o
wn
in
Sectio
n
2
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
i
f
ie
d
Pan
d
O
alg
o
r
ith
m
with
all
d
if
f
er
en
ce
s
with
r
esp
ec
t
to
t
h
e
co
n
v
en
tio
n
al
o
n
e
is
d
em
o
n
s
tr
ated
in
Sectio
n
3
.
Pro
v
in
g
th
e
m
er
its
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
i
f
ied
alg
o
r
ith
m
is
s
h
o
wn
in
Sectio
n
4
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
s
im
u
latio
n
p
r
o
g
r
am
.
T
h
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
ar
e
s
u
m
m
ar
ized
an
d
co
n
clu
d
ed
in
Sectio
n
5
.
2.
CO
NVEN
T
I
O
NA
L
P
E
R
T
U
RB
AND
O
B
SE
RVE (
P
O
)
AL
G
O
RIT
H
M
T
h
e
m
eth
o
d
o
lo
g
y
o
f
th
is
alg
o
r
ith
m
is
to
c
o
n
s
id
er
th
e
b
eh
av
io
r
o
f
p
h
o
to
v
o
ltaic
m
o
d
u
le/p
an
el
with
r
esp
ec
t to
th
e
wea
th
er
c
o
n
d
itio
n
v
ar
iatio
n
s
,
n
am
ely
lig
h
t
i
n
ten
s
ity
an
d
am
b
ie
n
t te
m
p
er
atu
r
e
:
2
.
1
.
So
la
r
ph
o
t
o
v
o
lt
a
ic
re
pr
esenta
t
io
n
T
h
e
s
o
lar
ce
ll
h
as
n
o
n
-
lin
ea
r
b
eh
av
io
r
o
f
th
e
o
u
tp
u
t
cu
r
r
e
n
t
an
d
p
o
wer
with
r
esp
ec
t
to
o
u
tp
u
t
v
o
ltag
e
v
ar
iatio
n
b
ased
o
n
th
e
in
s
tan
t
an
eo
u
s
wea
th
er
co
n
d
itio
n
s
.
T
h
e
o
u
t
p
u
t
p
o
wer
is
p
o
s
itiv
ely
af
f
ec
ted
b
y
th
e
lev
el
o
f
ir
r
a
d
ian
ce
o
r
lig
h
t
in
te
n
s
ity
,
wh
er
ea
s
it
is
n
eg
ativ
ely
af
f
ec
ted
b
y
th
e
lev
el
o
f
a
m
b
ien
t
tem
p
er
at
u
r
e
[
2
2
]
-
[
2
4
]
.
T
h
e
eq
u
iv
alen
t
elec
tr
ical
cir
cu
it
wh
ich
r
ep
r
esen
ts
th
e
p
h
o
to
v
o
ltaic
ce
ll
is
s
h
o
w
n
in
Fig
u
r
e
1
.
T
h
e
lev
el
o
f
d
r
o
p
v
o
ltag
e
in
t
h
e
c
ell
is
p
r
o
p
o
r
tio
n
al
to
t
h
e
v
alu
e
o
f
s
er
ies
r
esis
tan
ce
R
s
.
T
h
e
cu
r
r
en
t
I
PV
p
ass
in
g
th
r
o
u
g
h
th
e
s
er
ies
r
esis
to
r
ca
n
b
e
d
eter
m
in
ed
b
y
s
u
b
tr
ac
tin
g
t
h
e
s
h
u
n
t
cu
r
r
en
t
I
sh
wh
ich
is
p
ass
in
g
th
r
o
u
g
h
th
e
s
h
u
n
t
r
esis
to
r
R
sh
an
d
th
e
d
i
o
d
e
cu
r
r
en
t
I
D
f
r
o
m
th
e
lig
h
t
-
g
e
n
er
ated
c
u
r
r
e
n
t
I
sc
.
T
h
e
to
tal
o
u
tp
u
t
v
o
ltag
e
f
r
o
m
th
e
P
V
m
o
d
u
le
V
PV
-
Tot
ca
n
b
e
r
ep
r
esen
ted
b
y
th
e
p
r
o
d
u
ct
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
o
n
e
PV
ce
ll
V
PV
an
d
th
e
n
u
m
b
er
o
f
s
er
ially
co
n
n
ec
te
d
PV
ce
lls
N
s
,
wh
er
ea
s
th
e
to
tal
o
u
tp
u
t
c
u
r
r
en
t
f
r
o
m
th
e
PV
m
o
d
u
le
I
PV
-
Tot
ca
n
b
e
r
ep
r
esen
ted
b
y
th
e
p
r
o
d
u
ct
o
f
th
e
o
u
t
p
u
t
cu
r
r
en
t
f
r
o
m
o
n
e
PV
ce
ll
I
PV
an
d
th
e
n
u
m
b
er
o
f
p
ar
allel
co
n
n
ec
ted
PV c
ells
N
sh
as sh
o
wn
in
th
e
r
elate
d
r
elatio
n
s
h
ip
s
(
1
)
t
o
(
6
)
[
2
2
]
-
[
2
4
]
.
=
−
−
ℎ
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
A
n
ew p
ertu
r
b
a
n
d
o
b
s
erve
MPP
T a
lg
o
r
ith
m
b
a
s
ed
o
n
tw
o
s
tep
s
va
r
ia
b
le
vo
lta
g
e
c
o
n
tr
o
l
(
Hu
s
s
a
in
A
ttia
)
2203
=
{
−
1
}
(
2
)
ℎ
=
ℎ
(
3
)
=
−
(
4
)
−
=
×
(
5
)
−
=
×
ℎ
(
6
)
Fig
u
r
e
1
.
A
p
h
o
to
v
o
ltaic
ce
ll c
ir
cu
its
T
h
e
s
o
lar
p
h
o
to
v
o
ltaic
p
an
el
m
o
d
u
le
1
So
ltech
1
STH
-
215
-
P
is
s
elec
ted
to
d
em
o
n
s
tr
ate
th
e
p
ar
ticip
atio
n
o
f
th
is
s
tu
d
y
.
T
h
e
elec
tr
ical
ch
ar
ac
te
r
is
tics
o
f
th
e
s
elec
ted
PV
m
o
d
u
le
ar
e
s
h
o
wn
in
T
ab
le
1
,
wh
er
ea
s
Fig
u
r
e
2
s
h
o
ws
th
e
c
u
r
v
es
o
f
th
e
o
u
tp
u
t
cu
r
r
en
t
an
d
p
o
wer
f
r
o
m
th
e
PV
m
o
d
u
le
f
o
r
d
if
f
e
r
en
t
lev
els
o
f
ir
r
ad
ia
n
ce
(
lig
h
t
in
ten
s
ity
)
2
0
0
W
/m
2
,
4
0
0
W
/m
2
,
6
0
0
W
/m
2
,
8
0
0
W
/m
2
,
an
d
1
0
0
0
W
/m
2
all
at
a
co
n
s
tan
t
am
b
ien
t
tem
p
er
at
u
r
e
2
5
°C
.
T
h
e
p
o
s
itiv
e
p
r
o
p
o
r
tio
n
o
f
th
e
o
u
tp
u
t
cu
r
r
en
t
an
d
p
r
o
d
u
ce
d
p
o
wer
with
r
esp
ec
t
to
th
e
lig
h
t in
ten
s
ity
ar
e
clea
r
l
y
d
em
o
n
s
tr
ated
.
Fig
u
r
e
2
.
T
h
e
cu
r
v
es o
f
th
e
o
u
tp
u
t c
u
r
r
e
n
t a
n
d
p
o
wer
f
r
o
m
th
e
PV
m
o
d
u
le
T
ab
le
1
.
Sp
ec
if
icatio
n
s
o
f
th
e
PV M
ODUL
E
:
1
So
ltech
1
STH
-
2
1
5
-
P
P
V
p
a
n
e
l
P
a
r
a
me
t
e
r
V
ALUE
M
a
x
i
m
u
m
p
o
w
e
r
2
1
3
.
1
5
W
V
o
l
t
a
g
e
a
t
M
P
P
2
9
V
C
u
r
r
e
n
t
a
t
M
P
P
7
.
3
5
A
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
V
oc
3
6
.
3
V
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
I
sc
7
.
8
4
A
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
V
oc
(
%/
d
e
g
.
C
)
-
0
.
3
6
0
9
9
V
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
I
sc
(
%/
d
e
g
.
C
)
0
.
1
0
2
A
N
u
mb
e
r
o
f
c
e
l
l
s
p
e
r
mo
d
u
l
e
(
N
c
e
l
l
)
60
Li
g
h
t
-
g
e
n
e
r
a
t
e
d
c
u
r
r
e
n
t
I
sc
7
.
8
6
4
9
A
D
i
o
d
e
s
a
t
u
r
a
t
i
o
n
c
u
r
r
e
n
t
I
o
2
.
9
2
5
9
e
-
1
0
A
S
h
u
n
t
r
e
si
st
a
n
c
e
R
sh
3
1
3
.
3
9
9
1
Ω
S
e
r
i
e
s r
e
si
s
t
a
n
c
e
R
s
0
.
3
9
3
8
3
Ω
2
.
2
.
T
he
pro
ce
s
s
o
f
co
nv
ent
i
o
na
l P
a
nd
O
a
lg
o
rit
h
m
T
h
e
b
e
h
av
io
r
o
f
th
e
o
u
tp
u
t
p
o
wer
o
f
th
e
PV
p
a
n
el
with
r
e
s
p
ec
t
to
th
e
o
u
tp
u
t
v
o
ltag
e
is
s
h
o
wn
in
Fig
u
r
e
3
,
in
w
h
ich
th
e
m
ax
i
m
u
m
p
o
wer
p
o
in
t
MPP
is
lo
ca
ted
in
th
e
p
o
in
t
o
f
n
o
c
h
an
g
e
in
o
u
tp
u
t
p
o
wer
d
u
r
in
g
th
e
ch
a
n
g
e
in
o
u
tp
u
t v
o
ltag
e
[
2
5
]
-
[
2
7
]:
=
0
(
7
)
T
h
e
P
an
d
O
alg
o
r
ith
m
co
n
s
id
er
s
th
is
f
ac
t
in
th
e
p
r
o
ce
s
s
o
f
s
ea
r
ch
in
g
t
o
th
e
ac
cu
r
ate
v
alu
e
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
at
MPP.
T
h
e
p
r
o
ce
s
s
o
f
th
e
a
lg
o
r
ith
m
is
s
tar
ted
,
as
s
h
o
wn
in
Fig
u
r
e
4
o
f
t
h
e
alg
o
r
ith
m
f
lo
wch
ar
t,
b
y
m
ea
s
u
r
in
g
th
e
in
s
tan
tan
eo
u
s
v
alu
es
o
f
th
e
P
V
p
an
el
o
u
tp
u
t
v
o
ltag
e
V
(
t)
an
d
cu
r
r
e
n
t
I
(
t)
as
p
r
esen
t
d
ata,
an
d
r
e
p
ea
ts
m
ea
s
u
r
in
g
PV
v
o
ltag
e
an
d
c
u
r
r
en
t
af
ter
a
ce
r
tain
s
am
p
le
p
e
r
io
d
t
o
h
a
v
e
V
(
t)
,
V
(
t
-
Δ
t)
,
I
(
t)
,
an
d
I(t
-
Δ
t)
.
T
h
e
s
ec
o
n
d
s
tep
is
in
s
tan
tan
eo
u
s
v
alu
es
o
f
th
e
cu
r
r
en
t
o
u
t
p
u
t
p
o
wer
P
(
t)
,
an
d
th
e
p
r
ev
io
u
s
p
o
wer
s
am
p
le
v
alu
e
P(t
-
Δ
t)
,
in
ad
d
itio
n
to
ca
lcu
late
th
e
d
if
f
er
en
ce
in
o
u
tp
u
t
v
o
ltag
e
Δ
V
,
a
n
d
th
e
d
if
f
e
r
en
ce
i
n
o
u
tp
u
t
p
o
wer
Δ
P
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
220
1
–
22
08
2204
P
(
t
)
=
V
(
t
)
×
I
(
t
)
(
8)
P
(
t
−
Δ
t
)
=
V
(
t
−
Δ
t
)
×
I
(
t
−
Δ
t
)
(
9)
Δ
V
=
V
(
t
)
−
V
(
t
−
Δ
t
)
(
10)
Δ
V
=
V
(
t
)
−
V
(
t
−
Δ
t
)
(
11)
T
h
en
th
e
s
ea
r
ch
in
g
p
r
o
ce
s
s
o
f
th
e
alg
o
r
ith
m
wo
r
k
s
o
n
g
iv
in
g
an
ad
d
itio
n
o
r
s
u
b
tr
ac
tio
n
o
f
a
ce
r
tain
co
n
s
tan
t v
o
ltag
e
s
tep
b
ased
o
n
th
e
in
s
tan
tan
eo
u
s
m
ea
s
u
r
em
e
n
t o
f
th
e
PV p
an
el
o
u
tp
u
t c
u
r
r
en
t a
n
d
v
o
ltag
e
an
d
b
ased
o
n
co
m
p
ar
is
o
n
d
ec
is
io
n
s
.
I
n
s
p
ite
o
f
th
e
s
im
p
licity
o
f
th
e
co
n
v
e
n
tio
n
al
alg
o
r
it
h
m
,
t
h
e
d
em
er
its
o
f
th
e
co
n
s
tan
t
v
o
ltag
e
s
tep
MPP
s
ea
r
ch
in
g
m
eth
o
d
o
f
th
e
co
n
v
en
ti
o
n
al
P
an
d
O
alg
o
r
ith
m
ar
e
r
e
p
r
esen
tin
g
b
y
th
at
it
n
ee
d
s
to
h
av
e
a
h
ig
h
v
o
ltag
e
s
tep
to
g
u
ar
an
tee
f
ast
r
esp
o
n
s
e
f
r
o
m
th
e
alg
o
r
ith
m
.
On
th
e
o
th
e
r
s
id
e,
if
co
n
s
id
er
in
g
a
h
ig
h
v
o
l
tag
e
s
t
ep
,
th
is
lead
s
to
h
av
e
a
h
ig
h
lev
el
o
f
o
s
cillatio
n
d
u
r
in
g
s
t
ea
d
y
s
tate
wea
th
er
co
n
d
itio
n
s
[
2
5
]
-
[
2
7
].
Fig
u
r
e
3
.
T
h
e
o
u
t
p
u
t p
o
wer
cu
r
v
e
with
r
esp
ec
t to
o
u
tp
u
t
v
o
lt
ag
e
an
d
MPP p
o
i
n
t o
f
th
e
PV
m
o
d
u
le
Fig
u
r
e
4
.
T
h
e
f
lo
wch
a
r
t o
f
t
h
e
co
n
v
e
n
tio
n
al
P
an
d
O
alg
o
r
ith
m
3.
P
RO
P
O
SE
D
P
a
nd
O
AL
G
O
RIT
H
M
B
A
SE
D
O
N
T
WO
ST
E
P
S VO
L
T
AG
E
CO
N
T
R
O
L
T
h
e
d
em
e
r
its
o
f
t
h
e
co
n
s
tan
t
v
o
l
tag
e
s
tep
in
ter
m
s
o
f
th
e
d
i
f
f
icu
lty
ar
e
g
u
ar
an
teein
g
a
f
ast
r
esp
o
n
s
e
u
s
in
g
a
h
ig
h
v
o
ltag
e
s
tep
,
b
e
ca
u
s
e
th
is
lead
s
to
h
av
e
a
h
ig
h
lev
el
o
f
o
s
cillatio
n
at
a
s
tead
y
s
tate
wea
th
er
co
n
d
itio
n
.
Fo
r
th
e
o
b
jectiv
e
o
f
av
o
id
i
n
g
th
ese
d
em
er
its
,
th
is
s
tu
d
y
p
r
o
p
o
s
es
a
two
-
v
o
ltag
e
s
tep
co
n
tr
o
l
b
ased
o
n
co
n
tin
u
o
u
s
m
ea
s
u
r
em
en
t o
f
th
e
p
o
wer
d
if
f
e
r
en
ce
b
etwe
e
n
p
o
wer
s
am
p
les.
Fig
u
r
e
5
s
h
o
ws th
e
f
lo
wch
ar
t o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
A
n
ew p
ertu
r
b
a
n
d
o
b
s
erve
MPP
T a
lg
o
r
ith
m
b
a
s
ed
o
n
tw
o
s
tep
s
va
r
ia
b
le
vo
lta
g
e
c
o
n
tr
o
l
(
Hu
s
s
a
in
A
ttia
)
2205
th
e
p
r
o
p
o
s
ed
en
h
a
n
ce
d
P
an
d
O
alg
o
r
ith
m
in
clu
d
i
n
g
t
h
e
t
wo
v
o
ltag
e
s
tep
s
co
n
tr
o
l.
T
h
e
p
r
o
p
o
s
ed
v
ar
iab
le
co
n
tr
o
l
ad
o
p
ts
two
v
o
ltag
e
s
tep
s
f
o
r
in
cr
em
e
n
t,
th
e
h
ig
h
v
o
l
tag
e
s
tep
is
u
s
ed
d
u
r
in
g
tr
ac
k
i
n
g
th
e
MPP
wh
en
th
e
d
if
f
er
e
n
ce
in
o
u
tp
u
t
p
o
wer
Δ
P
is
h
ig
h
o
r
m
o
r
e
th
a
n
a
ce
r
tain
lim
it
lik
e
ɛ
as
s
h
o
wn
in
Fig
u
r
e
3
,
a
n
d
in
t
h
e
p
r
o
p
o
s
ed
f
lo
wch
ar
t
o
f
Fig
u
r
e
5
.
I
n
o
th
er
wo
r
d
s
,
if
|
Δ
P|
>
ɛ
,
wh
er
e
ɛ
is
a
s
m
all
lim
ited
c
h
an
g
e
in
th
e
p
o
wer
d
if
f
er
en
ce
b
etwe
en
two
s
u
cc
e
s
s
iv
e
p
o
wer
s
am
p
les
,
th
e
alg
o
r
ith
m
will
ad
o
p
t
a
h
ig
h
v
o
lt
ag
e
s
tep
wh
er
ea
s
if
|
Δ
P|
<
ɛ
it a
d
o
p
ts
a
lo
w
v
o
l
tag
e
s
tep
.
B
y
th
is
p
r
o
p
o
s
ed
p
r
o
ce
s
s
,
th
e
en
h
an
ce
d
P
an
d
O
alg
o
r
ith
m
g
u
ar
an
tees
th
e
f
ast
r
esp
o
n
s
e
d
u
r
in
g
t
h
e
d
y
n
am
ic
co
n
d
itio
n
b
y
c
o
n
s
id
er
in
g
a
h
ig
h
s
tep
v
o
ltag
e,
wh
er
ea
s
it
g
u
ar
a
n
tees
a
s
m
all
o
s
cillatio
n
d
u
r
in
g
th
e
s
tead
y
wea
th
er
co
n
d
itio
n
s
b
y
co
n
s
id
er
in
g
a
lo
w
s
tep
v
o
ltag
e
.
Fo
r
i
=
1
,
2
…;
W
h
en
T
h
e
p
r
o
ce
s
s
will
s
elec
t
a
h
ig
h
v
o
lta
g
e
s
tep
,
w
h
er
ea
s
wh
en
th
e
p
r
o
ce
s
s
will
r
ep
lace
th
e
f
u
ll v
o
ltag
e
s
tep
b
y
th
e
o
n
e
ten
th
v
o
ltag
e
s
tep
0.
1
×
V
s
tep
,
wh
ich
is
s
u
itab
le
f
o
r
lo
w
lev
el
o
f
Δ
P
.
|
Δ
P
Δ
|
>
(
1
3
)
|
Δ
P
Δ
|
>
(
1
4
)
Fig
u
r
e
5
.
Flo
wch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
en
h
a
n
ce
d
P
an
d
O
alg
o
r
it
h
m
4.
CO
M
P
ARA
T
I
V
E
ANA
L
YS
I
S O
F
SI
M
UL
AT
I
O
N
RE
S
UL
T
S
T
h
e
p
r
o
p
o
s
ed
en
h
a
n
ce
P
an
d
O
alg
o
r
ith
m
is
ev
alu
ated
t
h
r
o
u
g
h
d
o
i
n
g
a
p
er
f
o
r
m
a
n
ce
c
o
m
p
ar
ativ
e
an
aly
s
is
with
th
e
c
o
n
v
e
n
tio
n
a
l
P
an
d
O
alg
o
r
ith
m
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
.
T
h
e
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
is
d
esig
n
ed
b
ased
o
n
d
esig
n
s
tep
s
o
f
[
7
]
,
th
e
co
n
v
er
te
d
is
co
n
tr
o
llin
g
b
y
co
n
tr
o
l
th
e
in
s
tan
tan
eo
u
s
v
alu
e
o
f
d
u
ty
cy
cle
D
,
T
ab
le
2
s
h
o
ws
th
e
co
n
v
er
ter
d
esig
n
ed
p
a
r
am
eter
s
.
T
h
e
s
im
u
lated
p
h
o
to
v
o
lt
aic
PV
s
y
s
tem
ad
o
p
ts
o
n
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
220
1
–
22
08
2206
PV
p
an
el
m
o
d
u
le
1
So
ltech
1
STH
-
215
-
P,
wh
ich
is
co
n
n
ec
te
d
with
th
e
DC
-
D
C
co
n
v
er
ter
.
Fo
r
MPPT
p
u
r
p
o
s
e,
th
e
d
u
ty
cy
cle
o
f
th
e
co
n
v
er
te
r
is
,
f
ir
s
tly
,
co
n
tr
o
lled
u
s
in
g
t
h
e
co
n
v
e
n
tio
n
al
P
an
d
O
alg
o
r
ith
m
p
r
o
ce
s
s
with
a
h
ig
h
v
o
ltag
e
s
tep
to
d
em
o
n
s
tr
ate
th
e
n
eg
ativ
e
ef
f
ec
t
o
f
ad
o
p
tin
g
a
co
n
s
tan
t
h
ig
h
s
tep
v
o
l
tag
e.
Af
ter
th
at
th
e
p
r
o
ce
s
s
o
f
th
e
co
n
v
en
tio
n
alg
o
r
ith
m
is
r
ep
ea
ted
with
a
lo
w
v
o
ltag
e
s
tep
to
d
em
o
n
s
tr
ate
th
e
n
eg
ativ
e
ef
f
ec
t
o
f
a
co
n
s
tan
t lo
w
s
tep
v
o
ltag
e
.
Fig
u
r
e
6
s
h
o
ws
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
MPPT
PV
s
y
s
t
em
co
n
tr
o
lled
b
y
a
h
ig
h
v
o
ltag
e
s
tep
co
n
v
en
tio
n
al
P
an
d
O
alg
o
r
ith
m
.
Fig
u
r
e
6
(
a
)
s
h
o
ws
th
e
s
el
ec
ted
r
eg
u
lar
f
iv
e
p
er
i
o
d
d
u
r
in
g
1
.
2
5
s
ec
o
n
d
s
o
f
d
if
f
er
en
t
ir
r
ad
ian
ce
lev
els
(
4
0
0
W
/m
2
,
6
0
0
W
/m
2
,
8
0
0
W
/m
2
,
1
0
0
0
W
/m
2
,
an
d
7
0
0
W
/m
2
).
Fig
u
r
e
6
(
b
)
s
h
o
ws
th
e
d
u
ty
cy
cle
v
ar
iatio
n
d
u
r
in
g
th
ese
f
iv
e
p
er
io
d
s
.
I
t
is
clea
r
ly
n
o
ted
th
at
a
h
i
g
h
f
lu
ctu
atio
n
in
th
e
in
s
tan
tan
eo
u
s
lev
el
o
f
d
u
ty
cy
cle
wh
en
a
h
i
g
h
s
tep
v
o
ltag
e
i
s
u
s
ed
,
at
t
h
e
s
am
e
tim
e
it h
as f
ast
tr
ac
k
in
g
d
u
r
in
g
th
e
i
r
r
ad
ia
n
ce
lev
els
v
ar
iat
io
n
.
Fig
u
r
e
6
(
c
)
c
o
n
f
ir
m
s
t
h
e
m
at
ch
in
g
b
etwe
en
th
e
v
ar
iatio
n
i
n
th
e
o
u
tp
u
t
p
o
wer
lev
els
with
r
esp
ec
t
to
th
e
v
ar
iatio
n
in
th
e
d
u
ty
cy
cle
d
em
o
n
s
tr
atin
g
th
e
f
ast
r
esp
o
n
s
e
an
d
h
ig
h
-
p
o
wer
f
lu
ctu
atio
n
at
th
e
s
am
e
tim
e.
Fig
u
r
e
7
s
h
o
ws
th
e
s
y
s
tem
p
er
f
o
r
m
a
n
ce
co
n
t
r
o
lled
b
y
a
l
o
w
v
o
ltag
e
s
tep
th
r
o
u
g
h
a
co
n
v
en
tio
n
al
P
an
d
O
alg
o
r
ith
m
.
Fig
u
r
e
7
(
b
)
s
h
o
ws th
e
d
u
ty
c
y
cle
v
ar
iatio
n
d
u
r
i
n
g
th
ese
f
iv
e
p
er
io
d
s
.
I
t
is
clea
r
ly
n
o
ted
th
at
th
er
e
is
a
lo
w
f
lu
ctu
atio
n
in
th
e
in
s
tan
tan
eo
u
s
lev
el
o
f
d
u
ty
cy
cle
as
well
as
th
e
s
lo
w
r
es
p
o
n
s
e
in
MPP
tr
ac
k
in
g
d
u
r
in
g
th
e
v
ar
iatio
n
i
n
ir
r
ad
ian
ce
lev
els.
Fig
u
r
e
7
(
c
)
d
em
o
n
s
tr
ates
th
e
o
u
tp
u
t
p
o
wer
v
ar
iatio
n
wit
h
lo
w
f
lu
ctu
atio
n
d
u
r
in
g
s
tead
y
wea
th
er
c
o
n
d
itio
n
s
,
at
t
h
e
s
a
m
e
tim
e
it
r
ef
lects
th
e
s
lo
w
r
esp
o
n
s
e
d
u
r
in
g
th
e
v
ar
iatio
n
in
ir
r
ad
ian
ce
l
e
v
els.
Fig
u
r
e
8
s
h
o
ws
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
en
h
a
n
ce
d
P
an
d
O
alg
o
r
ith
m
,
wh
ich
ad
o
p
ts
two
s
tep
s
v
o
ltag
e
co
n
tr
o
l.
Hig
h
s
tep
v
o
ltag
e
f
o
r
f
ast
r
esp
o
n
s
e
d
u
r
in
g
d
y
n
am
ic
wea
th
er
co
n
d
itio
n
s
,
wh
er
ea
s
lo
w
s
tep
v
o
ltag
e
f
o
r
lo
w
o
s
cillatio
n
d
u
r
in
g
th
e
s
tead
y
w
ea
th
e
r
co
n
d
itio
n
s
.
Fig
u
r
e
8
(
b
)
s
h
o
ws
th
e
d
u
ty
c
y
cle
r
esp
o
n
s
e
wh
ich
d
em
o
n
s
tr
ates
th
e
f
ast
r
esp
o
n
s
e
f
o
r
MPP
tr
ac
k
in
g
an
d
lo
w
o
s
cillatio
n
f
o
r
t
h
e
wea
th
er
s
tead
y
co
n
d
itio
n
s
as
m
ar
k
ed
b
y
b
lack
co
lo
r
o
v
als.
Fig
u
r
e
8
(
c
)
d
em
o
n
s
tr
ates
an
d
co
n
f
ir
m
s
th
e
m
er
its
o
f
t
h
e
p
r
o
p
o
s
ed
en
h
a
n
ce
d
alg
o
r
ith
m
in
ter
m
s
o
f
d
e
liv
er
ed
p
o
wer
.
T
h
e
en
h
an
ce
m
e
n
ts
ar
e
r
ep
r
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ted
b
y
f
ast tr
ac
k
in
g
an
d
lo
w
o
s
cillatio
n
d
u
r
i
n
g
s
tead
y
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th
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r
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n
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itio
n
s
.
T
ab
le
2
.
Par
am
eter
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o
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d
es
ig
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DC
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DC
b
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t c
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ter
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(
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(
b
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(
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Fig
u
r
e
6
.
PV sy
s
tem
p
er
f
o
r
m
a
n
ce
u
s
in
g
a
c
o
n
v
e
n
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n
al
P
an
d
O
alg
o
r
ith
m
w
ith
h
i
g
h
s
tep
v
o
ltag
e,
(
a)
f
iv
e
eq
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ally
p
er
i
o
d
s
o
f
d
if
f
er
e
n
t ir
r
ad
ian
ce
,
(
b
)
d
u
ty
cy
cle
r
esp
o
n
s
e,
(
c)
o
u
tp
u
t p
o
wer
r
esp
o
n
s
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
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&
Dr
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N:
2088
-
8
694
A
n
ew p
ertu
r
b
a
n
d
o
b
s
erve
MPP
T a
lg
o
r
ith
m
b
a
s
ed
o
n
tw
o
s
tep
s
va
r
ia
b
le
vo
lta
g
e
c
o
n
tr
o
l
(
Hu
s
s
a
in
A
ttia
)
2207
(
a)
(
a)
(
b
)
(
b
)
(
c)
(
c
)
Fig
u
r
e
7
.
PV sy
s
tem
p
er
f
o
r
m
a
n
ce
u
s
in
g
a
co
n
v
en
tio
n
al
P
an
d
O
alg
o
r
ith
m
with
lo
w
s
tep
v
o
ltag
e,
(
a
)
f
iv
e
e
q
u
ally
p
er
io
d
s
o
f
d
if
f
e
r
en
t
ir
r
ad
ian
ce
,
(
b
)
d
u
ty
c
y
cle
r
esp
o
n
s
e,
(
c)
o
u
tp
u
t
p
o
wer
r
esp
o
n
s
e
Fig
u
r
e
8
.
PV sy
s
tem
p
er
f
o
r
m
a
n
ce
u
s
in
g
th
e
p
r
o
p
o
s
ed
en
h
an
ce
d
P
an
d
O
alg
o
r
i
th
m
wi
th
v
ar
iab
le
s
tep
v
o
ltag
e,
(
a
)
f
iv
e
e
q
u
ally
p
er
io
d
s
o
f
d
if
f
e
r
en
t
ir
r
ad
ian
ce
,
(
b
)
d
u
ty
c
y
cle
r
esp
o
n
s
e,
(
c)
o
u
tp
u
t
p
o
wer
r
esp
o
n
s
e
5.
CO
NCLU
SI
O
N
A
n
ew
en
h
an
ce
d
P
an
d
O
alg
o
r
ith
m
co
m
p
ar
ed
to
t
h
e
co
n
v
en
tio
n
al
a
P
an
d
O
alg
o
r
ith
m
h
as
b
ee
n
p
r
o
p
o
s
ed
in
th
is
s
tu
d
y
b
y
two
s
tep
s
v
o
ltag
e
v
ar
iab
le
co
n
tr
o
l
to
in
teg
r
ate
th
e
p
e
r
f
o
r
m
an
ce
o
f
t
h
e
p
h
o
to
v
o
ltaic
MPPT
s
y
s
tem
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
av
o
i
d
s
th
e
d
e
m
er
it
s
o
f
th
e
co
n
v
en
tio
n
al
P
an
d
O
alg
o
r
ith
m
wh
ic
h
is
r
ep
r
esen
ted
b
y
th
e
tr
ad
e
o
f
f
b
etwe
en
th
e
f
ast
MPP
tr
ac
k
in
g
d
u
r
i
n
g
th
e
d
y
n
am
ic
r
esp
o
n
s
e
an
d
t
h
e
lo
w
o
s
cillatio
n
d
u
r
i
n
g
th
e
s
tead
y
wea
th
er
co
n
d
itio
n
s
.
Pro
p
o
s
in
g
two
s
tep
s
v
o
ltag
e
co
n
tr
o
l
g
u
ar
an
tees
th
e
f
ast
-
tr
ac
k
in
g
r
esp
o
n
s
e,
an
d
at
th
e
s
am
e
tim
e
g
u
ar
a
n
tees
th
e
lo
w
o
s
cillatio
n
in
th
e
o
u
tp
u
t
p
o
wer
p
er
f
o
r
m
a
n
ce
d
u
r
in
g
th
e
s
tead
y
s
tate
wo
r
k
co
n
d
itio
n
s
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
is
e
v
a
lu
ated
t
h
r
o
u
g
h
a
co
m
p
ar
ativ
e
a
n
aly
s
is
with
th
e
co
n
v
en
tio
n
al
P
an
d
O
alg
o
r
ith
m
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
a
u
t
h
o
r
s
a
p
p
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ci
a
t
e
t
h
e
f
i
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l
s
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p
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p
r
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v
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d
b
y
o
f
f
i
c
e
o
f
r
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e
a
r
c
h
a
n
d
c
o
m
m
u
n
i
t
y
s
e
r
v
i
ce
,
A
m
e
r
i
c
a
n
U
n
i
v
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r
s
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t
y
o
f
R
a
s
A
l K
h
a
i
m
a
h
-
UA
E
,
h
t
t
p
s
:
//
a
u
r
a
k
.
ac
.
a
e
/
e
n
/
a
ca
d
e
m
i
cs
/
o
f
f
i
c
e
-
of
-
r
ese
a
r
c
h
-
c
o
m
m
u
n
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t
y
-
s
e
r
v
i
c
e
/
RE
F
E
R
E
NC
E
S
[1
]
H.
A.
Atti
a
,
T.
K.
S
.
F
re
d
d
y
,
H.
S
.
Ch
e
,
W.
P
.
He
w
a
n
d
A.
H.
El
Kh
a
teb
,
“
Co
n
fi
n
e
d
Ba
n
d
Va
riab
le
S
witch
in
g
F
re
q
u
e
n
c
y
P
u
lse
Wi
d
t
h
M
o
d
u
lati
o
n
(CB
-
VS
F
P
W
M
)
fo
r
a
S
i
n
g
le
-
P
h
a
se
In
v
e
rter
wit
h
a
n
LCL
F
il
t
e
r,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
3
2
,
n
o
.
1
1
,
p
p
.
8
5
9
3
-
8
6
0
5
,
N
o
v
.
2
0
1
7
,
d
o
i:
1
0
.
1
1
0
9
/
TP
EL
.
2
0
1
6
.
2
6
4
5
7
3
9
.
[2
]
S
.
Alsa
d
i,
a
n
d
B
.
Alsa
y
id
,
“
M
a
x
i
m
u
m
P
o
we
r
P
o
in
t
Trac
k
in
g
S
imu
latio
n
f
o
r
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
s
Us
in
g
P
e
rtu
r
b
a
n
d
O
b
se
rv
e
Alg
o
rit
h
m
,
”
In
tern
a
t
io
n
a
l
Jo
u
r
n
a
l
o
f
En
g
in
e
e
rin
g
a
n
d
In
n
o
v
a
ti
v
e
Tec
h
n
o
l
o
g
y
(IJEIT
)
,
v
o
l.
2
,
Iss
.
6
,
p
p
.
8
0
-
8
5
,
2
0
1
2
.
[3
]
N
.
On
a
t,
“
Re
c
e
n
t
De
v
e
lo
p
m
e
n
ts
in
M
a
x
imu
m
P
o
we
r
P
o
i
n
t
Trac
k
in
g
Tec
h
n
o
lo
g
ies
fo
r
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
s,
”
In
tern
a
ti
o
n
a
l
Jo
u
rn
a
l
o
f
P
h
o
to
e
n
e
rg
y
,
v
o
l.
2
0
1
0
,
d
o
i:
1
0
.
1
1
5
5
/
2
0
1
0
/
2
4
5
3
1
6
.
[4
]
H.
Atti
a
,
a
n
d
K.
H
o
ss
in
,
“
I
n
teg
ra
ted
Re
n
e
wa
b
le
P
V
S
y
ste
m
th
r
o
u
g
h
Artif
icia
l
Ne
u
ra
l
Ne
two
rk
Ba
se
d
M
P
P
T
a
n
d
Wate
r
Co
o
li
n
g
Trea
tme
n
t,
”
2
0
1
9
In
tern
a
ti
o
n
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CTA),
2
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1
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p
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5
,
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1
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1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
0
8
8
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8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
220
1
–
22
08
2208
[5
]
J
.
-
S
.
Ko
,
J
.
-
H
.
H
u
h
,
a
n
d
J
.
-
C
.
Kim
,
”
Ov
e
rv
iew
o
f
M
a
x
imu
m
P
o
w
e
r
P
o
i
n
t
Trac
k
i
n
g
M
e
th
o
d
s
f
o
r
P
V
S
y
ste
m
in
M
icro
G
rid
”
,
El
e
c
tro
n
ics
2
0
2
0
,
9
,
8
1
6
;
d
o
i:
1
0
.
3
3
9
0
/ele
c
tro
n
ics
9
0
5
0
8
1
6
.
[6
]
H.
Atti
a
,
M
.
M
o
h
se
n
,
B.
Qa
d
o
o
r,
M
.
Al
S
h
a
m
si,
O.
Ab
d
u
l
sa
lam
,
a
n
d
Z.
Ra
h
m
a
n
,
“
Ne
w
De
sig
n
a
n
d
Im
p
lem
e
n
tatio
n
o
f
a
S
o
lar
Ca
r
o
f
th
e
Am
e
rica
n
Un
iv
e
rsit
y
o
f
Ra
s
Al
Kh
a
ima
h
:
El
e
c
tri
c
a
l
Visio
n
,
”
J
o
u
rn
a
l
o
f
S
u
sta
in
a
b
le
De
v
e
lo
p
me
n
t
o
f
En
e
rg
y
,
W
a
ter
a
n
d
E
n
v
iro
n
me
n
t
S
y
s
tem
s,
v
o
l.
8
,
n
o
.
3
,
p
p
.
4
52
-
4
6
3
,
2
0
2
0
,
d
o
i:
1
0
.
1
3
0
4
4
/j
.
s
d
e
we
s.d
7
.
0
2
8
1
.
[7
]
H.
A.
Att
ia,
Y.
I.
Al
-
M
a
sh
h
a
d
a
n
y
,
a
n
d
B.
N.
G
e
tu
,
“
De
sig
n
a
n
d
S
imu
latio
n
o
f
a
Hig
h
P
e
rfo
rm
a
n
c
e
S
tan
d
a
lo
n
e
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
,
”
ICRE
GA’1
4
-
Re
n
e
wa
b
le
E
n
e
rg
y
:
Ge
n
e
ra
t
io
n
a
n
d
Ap
p
li
c
a
ti
o
n
s,
p
p
.
6
8
3
-
6
9
7
,
2
0
1
4
,
d
o
i
:
1
0
.
1
0
0
7
/
9
7
8
-
3
-
3
1
9
-
0
5
7
0
8
-
8
_
5
6
.
[8
]
M
.
A.
Ab
d
o
u
rra
z
iq
a
n
d
M
.
M
a
a
r
o
u
fi,
“
Ex
p
e
rime
n
tal
Ve
rifi
c
a
ti
o
n
o
f
th
e
M
a
in
M
P
P
T
Tec
h
n
i
q
u
e
s
f
o
r
P
h
o
to
v
o
l
taic
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
,
v
o
l
.
8
,
n
o
.
1
,
p
p
.
3
8
4
-
3
9
1
,
M
a
rc
h
2
0
1
7
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
p
e
d
s
.
v
8
.
i1
.
p
p
3
8
4
-
3
9
1
.
[9
]
T.
Th
a
k
u
r
a
n
d
K.
S
.
Be
d
i,
“
Da
ta
b
a
se
d
M
P
P
T
tec
h
n
i
q
u
e
fo
r
p
h
o
to
v
o
lt
a
ic
sy
ste
m
,
”
2
0
1
1
A
n
n
u
a
l
IEE
E
In
d
i
a
Co
n
fer
e
n
c
e
,
2
0
1
1
,
p
p
.
1
-
5
,
d
o
i
:
1
0
.
1
1
0
9
/INDCO
N.2
0
1
1
.
6
1
3
9
5
1
1
.
[1
0
]
H.
A.
S
h
e
r,
A.
F
.
M
u
rtaz
a
,
A.
N
o
m
a
n
,
K.
E
.
A
d
d
o
we
e
sh
,
a
n
d
M
.
Ch
ia
b
e
rg
e
,
“
An
i
n
telli
g
e
n
t
c
o
n
tr
o
l
stra
teg
y
o
f
fra
c
ti
o
n
a
l
s
h
o
rt
c
ircu
i
t
c
u
rre
n
t
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
tec
h
n
i
q
u
e
fo
r
p
h
o
to
v
o
lt
a
ic
a
p
p
li
c
a
ti
o
n
s,
”
J
o
u
r
n
a
l
o
f
Ren
e
wa
b
le
a
n
d
S
u
sta
i
n
a
b
le E
n
e
rg
y
,
v
o
l
.
7
,
n
o
.
1
,
p
.
0
1
3
1
1
4
,
2
0
1
5
,
d
o
i:
1
0
.
1
0
6
3
/1
.
4
9
0
6
9
8
2
.
[1
1
]
B.
N.
Ala
jmi,
K.
H.
Ah
m
e
d
,
S
.
J.
F
in
n
e
y
a
n
d
B
.
W.
Wi
l
li
a
m
s,
“
F
u
z
z
y
-
Lo
g
ic
-
Co
n
tro
l
Ap
p
ro
a
c
h
o
f
a
M
o
d
if
ied
Hill
-
Cli
m
b
in
g
M
e
th
o
d
fo
r
M
a
x
i
m
u
m
P
o
we
r
P
o
i
n
t
in
M
icr
o
g
ri
d
S
tan
d
a
lo
n
e
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
i
c
s
,
v
o
l.
2
6
,
n
o
.
4
,
p
p
.
1
0
2
2
-
1
0
3
0
,
Ap
ril
2
0
1
1
,
d
o
i:
1
0
.
1
1
0
9
/
TP
EL
.
2
0
1
0
.
2
0
9
0
9
0
3
.
[1
2
]
S
u
b
i
y
a
n
t
o
,
A.
M
o
h
a
m
e
d
a
n
d
M
.
A.
Ha
n
n
a
n
,
“
M
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
in
g
in
g
rid
c
o
n
n
e
c
ted
P
V
sy
ste
m
u
sin
g
a
n
o
v
e
l
f
u
z
z
y
lo
g
ic
c
o
n
tr
o
ll
e
r,
”
2
0
0
9
IEE
E
S
tu
d
e
n
t
C
o
n
fer
e
n
c
e
o
n
Res
e
a
rc
h
a
n
d
De
v
e
lo
p
me
n
t
(S
C
ORe
D),
2
0
0
9
,
p
p
.
3
4
9
-
3
5
2
,
d
o
i:
1
0
.
1
1
0
9
/S
CORE
D.2
0
0
9
.
5
4
4
3
0
0
2
.
[1
3
]
A.
El
Kh
a
te
b
,
N.
A.
Ra
h
im,
J.
S
e
lv
a
ra
j
a
n
d
M
.
N.
Ud
d
in
,
“
F
u
z
z
y
-
Lo
g
ic
-
C
o
n
tr
o
ll
e
r
-
Ba
se
d
S
E
P
IC
Co
n
v
e
rter
f
o
r
M
a
x
imu
m
P
o
we
r
P
o
in
t
Trac
k
in
g
,
”
in
IE
EE
T
r
a
n
s
a
c
t
io
n
s
o
n
I
n
d
u
st
ry
Ap
p
li
c
a
ti
o
n
s
,
v
o
l.
5
0
,
n
o
.
4
,
p
p
.
2
3
4
9
-
2
3
5
8
,
Ju
ly
-
Au
g
.
2
0
1
4
,
d
o
i:
1
0
.
1
1
0
9
/T
I
A.2
0
1
4
.
2
2
9
8
5
5
8
.
[1
4
]
H.
El
Kh
a
teb
a
,
N.
Ab
d
Ra
h
ima
,
a
n
d
J.
S
e
lv
a
ra
ja,
“
F
u
z
z
y
lo
g
ic
c
o
n
tro
l
a
p
p
r
o
a
c
h
o
f
a
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
e
m
p
lo
y
i
n
g
S
EP
IC
c
o
n
v
e
rter
f
o
r
s
tan
d
a
lo
n
e
p
h
o
t
o
v
o
lt
a
ic
sy
ste
m
,
”
Pro
c
e
d
ia
E
n
v
iro
n
me
n
ta
l
S
c
ien
c
e
s
,
v
o
l
.
1
7
,
p
p
.
529
-
5
3
6
,
2
0
1
3
,
d
o
i:
1
0
.
1
0
1
6
/j
.
p
ro
e
n
v
.
2
0
1
3
.
0
2
.
0
6
8
.
[1
5
]
R.
S
a
m
u
e
l
Ra
jes
h
Ba
b
u
,
“
A
Co
m
p
a
ra
ti
v
e
An
a
ly
sis
o
f
I
n
teg
ra
ted
Bo
o
st
F
ly
b
a
c
k
C
o
n
v
e
rteru
sin
g
P
ID
a
n
d
F
u
z
z
y
Co
n
tr
o
ll
e
r,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(IJ
PE
DS
),
v
o
l.
5
,
n
o
.
4
,
p
p
.
4
8
6
-
5
0
1
,
2
0
1
5
,
d
o
i:
1
0
.
1
1
5
9
1
/i
j
p
e
d
s.
v
5
.
i
4
.
p
p
4
8
6
-
5
0
1
.
[1
6
]
H
.
Atti
a
,
“
F
u
z
z
y
L
o
g
ic
C
o
n
tro
ll
e
r
Eff
e
c
ti
v
e
n
e
ss
E
v
a
lu
a
ti
o
n
t
h
ro
u
g
h
Co
m
p
a
ra
ti
v
e
M
e
m
b
e
rsh
i
p
s
fo
r
P
h
o
t
o
v
o
lt
a
ic
M
a
x
imu
m
P
o
we
r
P
o
i
n
t
Trac
k
in
g
F
u
n
c
ti
o
n
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(IJ
PE
DS
)
,
v
o
l.
9
,
n
o
.
3
,
p
p
.
1
1
4
7
-
1
1
5
6
,
2
0
1
8
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
p
e
d
s
.
v
9
.
i
3
.
p
p
1
1
4
7
-
1
1
5
6
.
[1
7
]
F
.
A.
O.
Aa
sh
o
o
r,
“
M
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
in
g
tec
h
n
iq
u
e
s
fo
r
p
h
o
t
o
v
o
lt
a
ic
wa
ter
p
u
m
p
in
g
s
y
ste
m
,
”
P
h
.
D.
d
isse
rtatio
n
,
De
p
t.
El
e
c
t.
El
e
c
t.
E
n
g
.
,
Un
i
v
.
o
f
Ba
th
,
Clav
e
rt
o
n
D
o
wn
,
UK
,
2
0
1
5
.
[1
8
]
D.
M
a
th
u
r,
“
M
a
x
imu
m
P
o
we
r
P
o
in
t
Trac
k
i
n
g
with
Artifi
c
ial
Ne
u
ra
l
Ne
two
r
k
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Eme
rg
in
g
S
c
ien
c
e
a
n
d
En
g
in
e
e
ri
n
g
(IJ
E
S
E)
,
v
o
l.
2
,
n
o
.
3
,
2
0
1
4
,
d
o
i:
1
0
.
1
1
5
5
/
2
0
1
2
/5
0
6
7
0
9
.
[1
9
]
R.
Ha
q
u
e
,
“
Tra
n
sm
issio
n
lo
ss
a
ll
o
c
a
ti
o
n
u
sin
g
a
rti
ficia
l
n
e
u
ra
l
n
e
two
rk
s
,
”
M
a
ste
r
Th
e
sis,
Un
iv
e
rsity
o
f
S
a
sk
a
tch
e
wa
n
S
a
sk
a
to
o
n
,
S
a
sk
a
to
o
n
,
Ca
n
a
d
a
,
2
0
0
6
.
[2
0
]
N.
Ka
laia
ra
si,
S
.
P
a
ra
m
a
siv
a
m
,
a
n
d
S
.
K
u
n
d
u
,
“
C
o
n
tr
o
l
o
f
Z
-
S
o
u
r
c
e
In
v
e
rter Bas
e
d
P
V S
y
ste
m
with
M
P
P
T
Us
i
n
g
AN
F
IS
,
”
In
ter
n
a
ti
o
n
a
l
Rev
iew
o
n
M
o
d
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imu
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(
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5
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7
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.
[2
1
]
A.
Ra
v
i,
J.
S
h
a
m
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a
S
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lt
h
a
n
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S
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th
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R.
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n
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a
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“
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fo
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p
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to
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ise
re
v
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,
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Criti
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Rev
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o
.
6
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p
.
8
6
-
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9
,
2
0
2
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[2
2
]
A.
Yo
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e
f,
A.
M
il
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u
d
i,
R.
S
a
y
a
h
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n
d
H.
S
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h
,
“
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.
Pr
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8
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1
6
.
[2
3
]
M
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He
b
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A.
Ko
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,
a
n
d
A.
Ch
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m
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v
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M
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8
.
[2
4
]
Ba
h
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a
A.
Nu
m
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n
,
Am
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a
M
.
S
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k
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A
n
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L.
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,
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lec
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ics
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m
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.
[2
5
]
Kh
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ig
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ter
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p
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.
[2
6
]
V
.
KV
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m
b
a
ra
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,
A
.
Ba
ti
,
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d
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.
Zh
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,
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v
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ter
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p
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7
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.
[2
7
]
H.
J.
El
‑Kh
o
z
o
n
d
a
r,
R.
J.
El
‑K
h
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z
o
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d
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r,
K.
M
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a
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T
.
S
u
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,
“
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re
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x
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m
p
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k
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g
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m
s,”
Ren
e
wa
b
les
:
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in
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W
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ter
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.
3
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3
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1
1
8
6
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4
0
8
0
7
-
0
16
-
0
0
2
2
-
8.
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