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I
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io
d
e
clam
p
ed
m
u
ltil
ev
el
in
v
er
ter
.
T
h
er
e
ar
e
m
a
n
y
r
esear
ch
e
r
s
ar
e
u
s
ed
th
e
m
u
ltil
ev
el
in
v
er
te
r
with
PV
s
y
s
tem
in
g
r
id
-
co
n
n
e
cted
m
o
d
e
as
[
4
]
,
[
8
]
,
[
9
]
.
T
h
is
p
ap
er
p
r
e
s
en
ts
a
f
iv
e
-
lev
el
H
-
b
r
i
d
g
e
i
n
v
er
ter
to
p
o
lo
g
y
t
h
at
is
ca
s
ca
d
ed
an
d
co
n
n
ec
ted
to
th
e
u
tili
ty
g
r
id
u
s
in
g
s
o
lar
p
an
els
as
a
D
C
s
o
u
r
ce
.
T
h
e
m
is
m
atch
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
el
is
o
n
e
o
f
th
e
m
o
s
t
s
er
io
u
s
is
s
u
e
s
with
th
is
s
y
s
te
m
,
as
ea
ch
PV
m
o
d
u
le
g
iv
es
its
p
o
wer
(
MPP)
o
win
g
to
ch
an
g
es
in
ir
r
ad
ian
ce
,
tem
p
er
atu
r
e.
As
a
r
es
u
lt,
th
e
p
o
wer
p
r
o
v
id
ed
t
o
th
e
in
v
er
te
r
is
u
n
b
alan
ce
d
,
r
esu
ltin
g
in
a
n
im
b
alan
ce
in
g
r
i
d
cu
r
r
en
t
i
n
jectio
n
.
I
n
o
r
d
e
r
to
s
o
lv
e
th
is
is
s
u
e,
th
is
p
r
o
p
o
s
e
d
ca
s
ca
d
e
H
-
b
r
id
g
e
with
a
s
ep
ar
ate
PV
g
r
o
u
p
is
u
s
ed
[
8
]
,
[
10
]
.
2.
SYST
E
M
DE
SCRI
P
T
I
O
N
T
h
e
p
r
o
p
o
s
ed
co
n
f
ig
u
r
atio
n
i
s
co
m
p
o
s
ed
o
f
s
ix
PV
g
r
o
u
p
s
an
d
ea
ch
g
r
o
u
p
s
u
p
p
lies
H
-
b
r
id
g
e
with
DC
v
o
ltag
e
2
1
8
.
5
V,
DC
-
D
C
co
n
v
er
ter
with
MPPT
to
ex
tr
ac
t
m
ax
im
u
m
p
o
wer
a
n
y
ce
r
tain
wea
th
er
co
n
d
itio
n
,
f
iv
e
-
lev
el
ca
s
ca
d
ed
H
b
r
id
g
e,
L
C
f
ilter
,
an
d
co
u
p
li
n
g
tr
an
s
f
o
r
m
er
f
o
r
in
ter
f
ac
e
th
e
p
r
o
p
o
s
ed
s
y
s
tem
with
th
e
m
ain
g
r
id
.
T
h
e
co
n
c
ep
tio
n
an
d
d
etails
o
f
ea
ch
co
m
p
o
n
e
n
t
in
Fig
u
r
e
1
a
r
e
ex
p
l
ain
ed
in
th
e
b
ello
w
s
ec
tio
n
s
is
b
ein
g
as
,
Fig
u
r
e
1
.
C
o
m
p
o
n
en
ts
o
f
a
p
r
o
p
o
s
ed
PV sy
s
tem
2
.
1
.
P
V
a
rr
a
y
T
h
e
s
o
lar
ce
ll
is
th
e
b
asic
u
n
it f
o
r
f
o
r
m
i
n
g
PV
p
an
els.
A
s
o
la
r
ce
ll
ca
n
b
e
d
e
f
in
ed
as
a
s
em
ico
n
d
u
ct
o
r
m
ater
ial
th
at
co
n
v
er
ts
s
o
lar
r
ad
iatio
n
in
to
elec
tr
ical
e
n
er
g
y
an
d
th
e
s
o
lar
ce
ll
co
n
s
is
ts
o
f
a
th
in
lay
er
o
f
a
s
em
ico
n
d
u
cto
r
m
ater
ial
th
at
i
s
f
ab
r
icate
d
o
n
a
PN
ju
n
ctio
n
s
u
ch
as
s
ilico
n
,
ca
d
m
iu
m
tell
u
r
id
e,
g
alliu
m
,
an
d
ar
s
en
id
e,
its
o
p
er
atio
n
al
p
r
o
p
e
r
ties
ar
e
s
im
ilar
to
th
at
o
f
a
d
i
o
d
e
p
-
n
as
it
r
elies
o
n
s
o
lar
r
a
d
iatio
n
an
d
s
u
r
f
ac
e
tem
p
er
atu
r
e
t
o
g
e
n
er
ate
elec
t
r
ical
cu
r
r
e
n
t.
A
p
h
o
to
v
o
ltaic
ce
ll
ca
n
g
en
e
r
ate
alm
o
s
t
a
v
o
ltag
e
0
.
5
to
0
.
8
V
d
ep
en
d
i
n
g
o
n
th
e
a
d
v
an
ce
d
te
ch
n
o
lo
g
y
an
d
ty
p
e
o
f
s
em
ico
n
d
u
cto
r
m
ate
r
ial
u
s
ed
.
T
h
e
v
o
ltag
e
g
en
er
ated
b
y
a
s
in
g
le
s
o
lar
ce
ll
is
in
s
u
f
f
icien
t
f
o
r
th
e
ap
p
licatio
n
s
,
s
o
th
e
s
o
l
ar
ce
lls
ar
e
co
n
n
ec
ted
in
o
n
e
f
r
am
e
in
s
er
ies
an
d
p
ar
allel
to
th
eir
c
o
m
p
o
n
en
t
ca
lled
th
e
s
o
lar
p
an
el.
T
h
e
eq
u
iv
alen
t
cir
cu
it
o
f
a
s
o
lar
ce
ll
ca
n
co
n
s
is
t
o
f
a
s
in
g
le
o
r
d
o
u
b
le
d
io
d
e,
an
d
a
s
in
g
le
d
io
d
e
is
m
o
r
e
e
f
f
i
cien
t
an
d
ea
s
ier
to
an
aly
ze
.
Fig
u
r
e
2
s
h
o
ws
th
e
e
q
u
iv
alen
t
cir
c
u
it
o
f
a
s
o
lar
ce
ll
with
a
s
in
g
le
d
io
d
e
[
9
]
,
[
1
1
]
.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
o
u
tp
u
t
v
o
ltag
e
(
VP
V)
an
d
o
u
tp
u
t
cu
r
r
en
t
(
I
PV)
in
th
e
eq
u
iv
ale
n
t
cir
c
u
it
o
f
a
s
in
g
le
d
io
d
e
ca
n
b
e
an
aly
ze
d
m
ath
e
m
atica
lly
is
b
ein
g
as
[
1
2
]
.
Fig
u
r
e
2
.
E
q
u
iv
alen
t c
ir
c
u
it o
f
a
s
in
g
le
d
io
d
e
s
o
lar
ce
ll
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
E
n
h
a
n
ci
n
g
p
erfo
r
ma
n
ce
o
f
g
r
id
-
co
n
n
ec
ted
p
h
o
to
vo
lta
ic
s
ystems
b
a
s
ed
o
n
…
(
Ma
r
w
a
n
E
.
A
h
ma
d
)
2297
=
ℎ
–
–
ℎ
(
1
)
W
h
er
e
:
-
I
PV
: Cu
r
r
en
t o
f
PV
ce
ll,
-
A.
I
Ph
: p
h
o
t
o
-
cu
r
r
en
t
-
(
A)
; g
en
er
ated
b
y
t
h
e
p
h
o
to
ele
ctr
ic
ef
f
ec
t,
-
I
D
: D
io
d
e
cu
r
r
en
t (
A)
.
Ph
=
s
c
+
i
(
−
)
G
Gno
m
(
2
)
W
h
er
e:
I
s
c
:
s
h
o
r
t
cir
c
u
it
cu
r
r
e
n
t
(
A
),
Ki:
s
h
o
r
t
cir
c
u
it
cu
r
r
en
t
o
f
a
ce
ll
at
(
STC)
s
tan
d
a
r
d
t
est
co
n
d
itio
n
2
5
°C
an
d
1
0
0
0
W
/m
2
,
T:
o
p
er
atin
g
tem
p
er
atu
r
e
(
K)
,
T
r
:
r
ef
e
r
en
ce
tem
p
er
atu
r
e
o
f
th
e
PV
ce
ll
(
2
9
8
.
1
5
K)
,
G:
s
o
lar
r
ad
iatio
n
in
W
/m
2
,
G
nom
:
n
o
m
in
al
s
o
lar
r
ad
iatio
n
1
0
0
0
W
/m
2
,
in
(
2
)
s
h
o
ws
th
e
d
ep
e
n
d
en
ce
o
f
th
e
v
o
ltag
e
a
n
d
cu
r
r
en
t
o
f
th
e
s
o
lar
ce
ll
o
n
r
a
d
iatio
n
lev
el,
tem
p
er
at
u
r
e,
an
d
t
h
eir
ch
an
g
es.
Io
=
Ir
s
[
r
]
3
e
xp
×
(
1
−
1
)
(
3
)
Ir
s
=
Is
c
r
/
e
xp
(
q
V
o
c
Ns
KA
T
)
−
1
(
4
)
W
h
er
e
:
-
-
Io
:
R
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t
.
-
Irs
:
c
ell
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t a
t T
r
.
-
Q
:
t
h
e
ch
ar
g
e
o
f
th
e
elec
tr
o
n
is
eq
u
al
to
1
.
6
×1
0
-
19
co
u
lo
m
b
.
-
E
g
o
: b
an
d
g
a
p
en
er
g
y
o
f
th
e
s
em
ic
o
n
d
u
ct
o
r
=
1
.
1
e
V
.
-
A
:
t
h
e
id
ea
lity
f
ac
to
r
o
f
th
e
d
io
d
e,
K:
B
o
ltzm
an
n
’
s
co
n
s
tan
t e
q
u
al
1
.
3805
×
10
−
23
J
/k
.
-
Vo
c
:
o
p
en
cir
c
u
it v
o
ltag
e
.
-
N
s:
n
u
m
b
er
o
f
ce
lls
co
n
n
ec
ted
i
n
s
er
ies
.
No
w,
th
e
o
u
tp
u
t c
u
r
r
en
t o
f
th
e
PV c
ell
is
in
th
e
f
o
llo
win
g
eq
u
atio
n
.
I
pv
=
I
ph
−
I
o
[
V
pv
+
Ip
v
×
Rs
−
1
]
+
ℎ
(
5
)
W
h
er
e
I
sh
=
V
pv
+
I
PV
R
s
R
sh
(
6
)
an
d
R
s
: ser
ies r
esis
tan
ce
(
Ω
)
,
R
s
h
:
s
h
u
n
t r
esis
tan
ce
(
Ω
)
,
V
PV
:
o
u
tp
u
t
v
o
ltag
e
f
r
o
m
PV p
a
n
e
l
.
A
PV
ar
r
ay
ca
n
b
e
d
e
f
in
ed
as
a
s
et
o
f
p
h
o
to
v
o
ltaic
p
an
els
th
at
ar
e
co
n
n
ec
ted
in
s
er
ies
an
d
p
ar
allel
to
o
b
tain
s
p
ec
if
ic
elec
tr
ical
en
er
g
y
th
at
is
p
r
ac
tically
u
s
ed
to
p
o
wer
th
e
lo
a
d
s
[
9
]
,
[
13
]
.
In
(
7
)
r
ep
r
esen
ts
th
e
r
elatio
n
s
h
ip
b
etwe
en
I
-
V
in
th
e
PV a
r
r
ay
.
I
pv
=
N
×
I
ℎ
−
N
×
I
{
e
x
p
[
(
q
V
PV
+
Ns
N
p
I
Rs
)
Ns
A
K
T
]
}
−
1
+
V
Ns
N
p
+
I
PV
Rs
R
sh
(
7)
W
h
er
e
: N
P
:
n
u
m
b
er
o
f
PV m
o
d
u
les
co
n
n
ec
ted
in
p
a
r
allel
, N
s
:
n
u
m
b
er
o
f
PV m
o
d
u
les co
n
n
ec
ted
in
s
er
ies
.
2
.
2
.
B
o
o
s
t
c
o
nv
er
t
er
T
h
e
b
o
o
s
t
co
n
v
e
r
ter
is
ca
lled
a
s
tep
-
u
p
c
o
n
v
e
r
ter
b
ec
a
u
s
e
th
e
o
u
tp
u
t
v
o
ltag
e
is
g
r
ea
ter
t
h
a
n
th
e
in
p
u
t
v
o
ltag
e
.
Fig
u
r
e
3
s
h
o
ws
th
e
s
tr
u
ctu
r
e
o
f
th
e
b
o
o
s
t
co
n
v
er
te
r
,
wh
ich
co
n
s
is
ts
o
f
two
s
em
ico
n
d
u
ct
o
r
s
(
d
io
d
e
an
d
MO
SF
E
T
)
,
an
d
th
e
in
d
u
ct
o
r
,
wh
ich
is
th
e
p
o
wer
s
to
r
ag
e
s
o
u
r
ce
in
ad
d
itio
n
to
th
e
ca
p
a
citan
ce
s
u
ch
as
th
e
f
ilter
,
lo
ad
im
p
e
d
an
ce
,
a
n
d
D
C
v
o
ltag
e
s
o
u
r
ce
(
PV
ar
r
a
y
o
r
b
atter
y
)
.
MO
SF
E
T
is
u
s
ed
as
a
tr
ig
g
er
s
witch
in
th
e
cir
c
u
it,
an
d
th
e
b
o
o
s
t
s
witch
o
p
er
ates
in
two
m
o
d
es.
T
h
e
f
ir
s
t
is
wh
en
th
e
s
witch
is
clo
s
ed
in
t
h
e
ON
p
o
s
itio
n
,
th
e
c
u
r
r
e
n
t
is
s
to
r
ed
in
th
e
in
d
u
cto
r
f
o
r
a
ce
r
tain
p
er
io
d
a
n
d
th
e
d
io
d
e
p
r
ev
e
n
ts
th
e
cu
r
r
e
n
t f
r
o
m
f
lo
win
g
.
W
ith
t
h
e
lo
a
d
c
u
r
r
en
t
r
em
ain
i
n
g
co
n
s
tan
t
d
u
e
to
ca
p
ac
ito
r
d
is
ch
ar
g
e.
I
n
th
e
s
ec
o
n
d
p
o
s
itio
n
,
wh
en
th
e
s
witch
is
o
p
en
ed
,
cu
r
r
e
n
t
f
lo
ws
th
r
o
u
g
h
th
e
in
d
u
cto
r
an
d
d
io
d
e
,
an
d
th
e
ca
p
ac
ito
r
is
ch
ar
g
ed
an
d
f
r
o
m
th
er
e
to
th
e
lo
ad
wh
ile
th
e
lo
ad
cu
r
r
e
n
t
also
r
em
ain
s
co
n
s
tan
t
,
t
h
e
jo
b
o
f
th
e
b
o
o
s
t
co
n
v
er
ter
is
to
b
o
o
s
t
an
d
r
eg
u
late
th
e
p
h
o
to
v
o
ltaic
ar
r
a
y
v
o
ltag
e,
as
well
as
co
n
tr
o
l
th
e
d
u
ty
cy
cle
o
f
th
e
DC
-
DC
co
n
v
er
ter
u
s
in
g
MP
PT,
b
ef
o
r
e
s
en
d
in
g
p
o
wer
to
th
e
in
v
er
ter
v
ia
th
e
DC
-
lin
k
[
1
4
]
,
[
1
5
].
Usi
n
g
Far
ad
ay
'
s
law,
t
h
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
o
u
tp
u
t
an
d
in
p
u
t
v
o
ltag
e
o
f
th
e
b
o
o
s
t
co
n
v
er
ter
ca
n
b
e
f
o
u
n
d
as
s
h
o
wn
[
1
6
]
.
W
h
er
e
:
Vs:
in
p
u
t
v
o
ltag
e
,
Vo
:
o
u
tp
u
t
v
o
ltag
e
o
f
DC
-
DC
b
o
o
s
t c
o
n
v
er
ter
,
D:
d
u
ty
cy
cle
.
Vs.
DT
=(
Vo
-
Vs)
(
1
-
D)
T
(
8
)
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
:
2
295
–
23
04
2298
Fig
u
r
e
3
.
C
ir
cu
it d
iag
r
am
o
f
th
e
b
o
o
s
t c
o
n
v
er
ter
2
.
3
.
I
ncre
m
ent
a
l
c
o
nd
uct
a
nce
a
lg
o
rit
hm
(
I
NC)
I
n
Fig
u
r
e
4
r
e
p
r
esen
ts
a
f
lo
wch
ar
t
o
f
th
e
I
NC
alg
o
r
ith
m
,
f
ea
tu
r
es
o
f
th
is
alg
o
r
ith
m
in
clu
d
e
th
e
s
p
ee
d
o
f
p
r
o
ce
s
s
in
g
s
tead
y
-
s
tate
er
r
o
r
s
,
r
ap
id
r
esp
o
n
s
e
to
v
ar
iab
le
s
o
lar
r
ad
iatio
n
,
as
wel
l
as
th
e
s
p
ee
d
o
f
co
n
v
er
g
en
ce
,
as
it
co
m
b
in
es
a
cc
u
r
ac
y
a
n
d
s
p
ee
d
.
T
h
e
m
ax
i
m
u
m
p
o
wer
p
o
in
t
in
t
h
e
PV
m
atr
ix
is
tr
ac
ed
f
r
o
m
th
e
d
er
iv
atio
n
o
f
th
e
r
elatio
n
s
h
ip
P*
V
co
n
ce
r
n
in
g
v
o
ltag
e
o
r
cu
r
r
e
n
t.
MPP
ca
n
b
e
ca
lc
u
lated
u
s
in
g
th
e
d
p
/d
v
an
d
-
I
/
v
r
elatio
n
s
h
ip
a
n
d
as sh
o
wn
b
y
t
h
e
f
o
llo
win
g
d
er
i
v
atio
n
.
=
×
(
9
)
=
+
.
(
1
0
)
or
=
+
.
(
1
1
)
Fro
m
th
e
ca
lcu
latio
n
∆
a
n
d
∆
to
d
ep
e
n
d
o
n
th
e
v
alu
es
I
an
d
V,
th
e
MPP
v
alu
es
ca
n
b
e
in
f
er
r
e
d
f
r
o
m
th
e
ex
p
r
ess
io
n
s
;
∆
∆
>
−
T
h
e
o
p
er
atin
g
p
o
in
t is to
th
e
lef
t o
f
MPP
,
∆
∆
=
−
T
h
e
o
p
er
atin
g
p
o
in
t is ex
ac
tly
at
MPP
,
∆
∆
<
−
T
h
e
o
p
er
atin
g
p
o
in
t
i
s
to
th
e
r
ig
h
t
o
f
MPP
Acc
o
r
d
in
g
to
th
ese
c
o
m
p
a
r
is
o
n
s
,
th
e
alg
o
r
ith
m
in
cr
ea
s
es o
r
d
ec
r
ea
s
es th
e
v
o
lt
ag
e
in
th
e
PV
ar
r
a
y
[
17
]
,
[
18]
.
Fig
u
r
e
4
.
Flo
wch
ar
t
o
f
I
NC
al
g
o
r
ith
m
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
E
n
h
a
n
ci
n
g
p
erfo
r
ma
n
ce
o
f
g
r
id
-
co
n
n
ec
ted
p
h
o
to
vo
lta
ic
s
ystems
b
a
s
ed
o
n
…
(
Ma
r
w
a
n
E
.
A
h
ma
d
)
2299
2
.
4
.
Ca
s
ca
ded H
-
bridg
e
inv
e
r
t
er
C
ascad
ed
H
-
b
r
id
g
es
ar
e
s
ev
e
r
al
s
in
g
le
-
p
h
ase
in
v
er
ter
s
o
r
ca
lled
H
-
b
r
id
g
e
in
v
er
ter
co
n
n
ec
ted
i
n
s
er
ies,
ea
c
H
-
b
r
id
g
e
co
n
s
is
ts
o
f
an
in
d
ep
e
n
d
en
t
DC
s
o
u
r
ce
i
n
ad
d
itio
n
to
s
witch
es,
as
s
h
o
wn
in
F
ig
u
r
e
5
T
h
is
in
v
er
ter
g
en
er
ates
a
s
in
u
s
o
id
a
l
o
u
tp
u
t
v
o
ltag
e
as
ea
ch
H
-
b
r
id
g
e
p
r
o
v
id
es
th
r
ee
lev
els
(
ze
r
o
,
p
o
s
itiv
e
o
u
tp
u
t
v
o
ltag
e,
a
n
d
n
e
g
ativ
e
o
u
tp
u
t
v
o
ltag
e)
.
T
h
e
to
tal
o
u
tp
u
t
v
o
l
ta
g
e
is
th
e
s
u
m
o
f
all
th
e
v
o
ltag
es
p
r
o
d
u
ce
d
b
y
th
e
co
n
n
ec
ted
H
-
b
r
i
d
g
e
ce
lls
in
t
h
e
ch
ain
.
W
h
er
e
if
th
e
n
u
m
b
er
o
f
H
-
b
r
id
g
e
ce
lls
is
M
th
e
to
tal
o
u
tp
u
t
v
o
ltag
e
eq
u
al
to
(2
M+
1
)
.
L
ittl
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
th
e
o
u
t
p
u
t
v
o
ltag
e,
a
h
ig
h
e
r
v
o
ltag
e
le
v
el,
o
p
e
r
a
tin
g
at
all
b
asic
an
d
h
ig
h
s
witch
in
g
f
r
e
q
u
en
cies,
litt
le
d
is
to
r
tio
n
in
th
e
in
p
u
t
cu
r
r
e
n
t
with
ea
s
y
s
to
r
ag
e
an
d
p
ac
k
in
g
,
a
n
d
less
s
tr
ess
d
u
e
to
th
e
co
m
m
o
n
m
o
d
e
o
f
th
e
v
o
ltag
e
ar
e
th
e
m
ain
b
en
ef
its
o
f
th
is
in
v
er
t
er
.
As
a
r
esu
lt,
it
is
p
r
ef
er
ab
le
t
o
u
s
e
it o
v
e
r
a
two
-
lev
el
th
r
ee
-
p
h
ase
in
v
er
ter
[1
9]
-
[
2
1
]
.
Fig
u
r
e
5
.
T
o
p
o
lo
g
y
o
f
th
e
m
o
d
u
lar
ca
s
ca
d
ed
H
-
b
r
id
g
e
m
u
lti
lev
el
in
v
er
ter
f
o
r
a
t
h
r
ee
-
p
h
ase
g
r
id
-
c
o
n
n
ec
ted
PV
s
y
s
tem
3.
CO
NT
RO
L
SCH
E
M
E
On
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
p
r
o
b
lem
s
f
ac
in
g
th
e
PV
s
y
s
tem
is
th
e
m
is
m
atch
o
f
th
e
P
V
p
an
els
d
u
e
to
th
e
u
n
e
v
en
r
ad
iatio
n
an
d
tem
p
er
atu
r
e
c
h
an
g
es
i
n
a
d
d
itio
n
to
th
e
life
tim
e
o
f
th
e
s
o
lar
p
an
els
,
wh
ich
m
ea
n
s
th
at
th
e
MPP
is
d
if
f
er
e
n
t
f
o
r
ea
c
h
PV
m
o
d
el.
T
h
is
r
ed
u
ce
s
th
e
ef
f
icien
cy
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
an
d
th
e
o
cc
u
r
r
e
n
ce
o
f
p
r
o
b
lem
s
in
th
e
th
r
ee
-
p
h
ase
s
y
s
tem
at
ea
ch
s
t
ag
e
d
u
e
to
th
e
lack
o
f
cu
r
r
en
t
b
alan
ce
in
th
e
g
r
id
,
s
o
th
er
e
m
u
s
t
b
e
a
n
MPPT
f
o
r
ea
ch
PV
ar
r
ay
i
n
d
ep
e
n
d
en
tly
,
co
n
tr
o
l
an
d
s
y
n
ch
r
o
n
izatio
n
b
etwe
en
m
icr
o
g
r
id
an
d
u
tili
ty
g
r
id
,
t
h
e
s
u
g
g
este
d
co
n
tr
o
l
ap
p
r
o
ac
h
is
clev
er
an
d
c
o
m
p
atib
le
with
t
h
e
g
r
id
'
s
A
C
Mic
r
o
g
r
id
co
n
n
ec
ted
m
o
d
e
,
as
it
m
o
n
ito
r
s
b
o
th
t
h
e
DC
MPPT
an
d
t
h
e
in
v
er
ter
o
u
tp
u
t
AC
p
o
wer
[
7
]
,
[
22
]
.
T
h
e
co
n
tr
o
l
p
r
o
ce
s
s
co
n
s
is
ts
o
f
two
clo
s
ed
lo
o
p
s
,
a
n
in
n
e
r
co
n
tr
o
l
lo
o
p
th
at
r
eg
u
lates
th
e
c
u
r
r
en
t
an
d
an
ex
ter
n
al
co
n
tr
o
l
lo
o
p
th
at
co
n
tr
o
ls
th
e
DC
v
o
l
tag
e
r
eg
u
latio
n
,
m
ain
tain
s
a
c
o
n
s
tan
t
DC
lin
k
v
o
ltag
e,
an
d
p
r
o
d
u
ce
s
s
ig
n
als
to
th
e
in
n
er
co
n
tr
o
l
lo
o
p
a
s
a
r
e
f
er
en
ce
f
o
r
t
h
e
cu
r
r
en
t
.
C
h
an
g
es
in
co
n
d
itio
n
s
af
f
ec
tin
g
th
e
PV
ar
r
ay
(
r
ad
iatio
n
an
d
tem
p
er
atu
r
e)
r
esu
lt
in
a
d
if
f
er
en
ce
in
th
e
p
o
wer
p
r
o
d
u
c
ed
f
r
o
m
it
wh
ich
r
ea
c
h
es
th
e
u
tili
ty
g
r
id
v
ia
th
e
DC
lin
k
.
T
h
er
ef
o
r
e
,
th
e
p
o
we
r
p
r
o
d
u
ce
d
d
o
es
n
o
t
m
atch
t
h
e
p
o
wer
th
at
r
ea
ch
es
th
e
u
tili
ty
g
r
id
,
h
en
ce
th
e
v
o
ltag
e
co
n
tr
o
l
u
n
it
p
r
o
v
id
es
a
m
atch
b
etwe
en
t
h
e
p
o
we
r
p
r
o
d
u
ce
d
f
r
o
m
th
e
PV
ar
r
ay
an
d
th
e
p
o
wer
d
eliv
er
ed
to
th
e
u
tili
ty
g
r
id
b
y
ch
an
g
in
g
th
e
ac
tiv
e
p
o
wer
o
f
t
h
e
r
ef
er
en
ce
cu
r
r
en
t
[
22
]
,
[
23
]
.
T
h
e
in
n
er
co
n
tr
o
l
u
n
it
(
cu
r
r
en
t
)
ca
n
b
e
d
esig
n
e
d
with
d
if
f
er
en
t
f
r
am
es
o
f
r
ef
er
en
ce
wh
ich
ar
e
s
y
n
ch
r
o
n
o
u
s
(
d
q
)
,
f
ix
ed
f
r
am
es
(
α
β),
an
d
n
atu
r
al
f
r
a
m
es
(
ab
c)
.
I
t
s
h
o
u
ld
b
e
ca
p
ab
le
o
f
h
ar
m
o
n
ic
co
m
p
e
n
s
atio
n
,
g
r
id
s
y
n
ch
r
o
n
izatio
n
,
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
co
n
t
r
o
l
wi
th
a
f
ast
d
y
n
am
ic
r
esp
o
n
s
e.
Si
n
ce
th
e
in
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ter
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ee
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ase
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ltil
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r
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abc
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V
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ab
c)
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s
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r
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d
q
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r
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C
lar
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o
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Par
k
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s
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ase
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PLL
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h
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ec
o
m
es
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
:
2
295
–
23
04
2300
ea
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r
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[
26
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T
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Fig
u
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6
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[
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[
]
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3
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s
in
(
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s
in
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−
2
3
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s
in
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+
2
3
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os
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3
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Fig
u
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6
.
C
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t
h
r
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p
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ase
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d
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H
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b
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e
m
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in
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r
4.
SI
M
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t
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is
n
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d
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d
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n
t
h
i
s
s
e
c
t
i
o
n
,
t
h
e
s
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m
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l
a
t
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o
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s
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l
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s
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t
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n
a
r
i
o
s
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s
b
e
i
n
g
a
s
:
T
ab
le
1.
T
h
e
elec
tr
ical
p
ar
am
e
ter
s
o
f
th
e
PV p
an
el
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
M
a
x
i
m
u
m
p
o
w
e
r
(
P
m
a
x
)
3
0
5
w
R
a
t
e
d
V
o
l
t
a
g
e
(
V
m
p
)
5
4
.
7
v
R
a
t
e
d
C
u
r
r
e
n
t
(
I
mp
)
5
.
5
8
A
O
p
e
n
C
i
r
c
u
i
t
V
o
l
t
a
g
e
(
V
o
c
)
6
4
.
2
v
S
h
o
r
t
C
i
r
c
u
i
t
C
u
r
r
e
n
t
(
I
sc
)
5
.
9
6
A
N
u
mb
e
r
o
f
c
e
l
l
s
i
n
t
h
e
p
a
n
e
l
96
4
.
1
.
Scena
rio
I
:
u
nd
er
s
t
a
nd
a
rd
t
est
co
nd
it
io
n (
ST
C)
(
1
0
0
0
W/m
2
,
2
5
°
C
)
T
h
e
r
esp
o
n
s
es
o
f
th
e
PV
s
y
s
t
em
f
o
r
o
n
e
g
r
o
u
p
ar
e
lis
ted
in
th
e
f
o
llo
win
g
f
ig
u
r
es,
as
th
e
n
u
m
b
er
o
f
p
an
els
u
s
ed
:
5
4
p
an
els,
two
p
a
n
els
in
s
er
ies,
an
d
2
8
p
an
els
in
p
ar
allel,
an
d
th
e
o
u
tp
u
t
v
o
lt
ag
e
o
f
o
n
e
PV
ar
r
ay
is
1
0
9
.
4
v
o
lts
as
in
Fig
u
r
e
7
(
a
)
,
t
h
e
o
u
tp
u
t
cu
r
r
en
t
o
f
th
e
PV
g
r
o
u
p
is
1
5
6
.
2
4
A,
as
s
h
o
wn
in
F
ig
u
r
e
7
(
b
)
an
d
th
e
p
h
o
to
v
o
ltaic
p
o
wer
o
u
tp
u
t
is
ap
p
r
o
x
im
ately
1
7
KW
,
as
s
h
o
wn
in
Fig
u
r
e
7
(
c
)
.
U
n
d
e
r
s
tan
d
ar
d
ir
r
a
d
ian
ce
co
n
d
itio
n
s
o
f
1
0
0
0
W
/m
2
an
d
a
tem
p
er
atu
r
e
o
f
2
5
°C
.
Sin
g
le
-
p
h
ase
DC
v
o
ltag
e
r
esp
o
n
s
e,
F
ig
u
r
e
8
(
a
)
s
h
o
ws
o
u
tp
u
t
DC
v
o
ltag
e
o
f
two
PV
g
r
o
u
p
s
o
f
a
p
p
r
o
x
im
ately
2
1
8
.
5
V
.
Fig
u
r
e
8
(
b
)
also
s
h
o
ws
th
e
VDC
o
u
tp
u
t
at
a
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
E
n
h
a
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ci
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p
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co
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ystems
b
a
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(
Ma
r
w
a
n
E
.
A
h
ma
d
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2301
DC
lin
k
o
f
a
p
p
r
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x
im
ately
5
0
0
V
.
W
av
ef
o
r
m
s
o
f
AC
lo
ad
s
id
e,
F
ig
u
r
e
9
(
a
)
s
h
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ws
th
e
o
u
t
p
u
t
v
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ltag
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f
f
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,
F
ig
u
r
es 9
(
b
)
-
(
d
)
s
h
o
w
th
e
o
u
tp
u
t v
o
ltag
e
,
cu
r
r
e
n
t,
an
d
p
o
wer
o
f
th
e
AC
b
u
s
.
(
a)
(
b
)
(
c)
Fig
u
r
e
7.
R
esp
o
n
s
es o
f
PV sy
s
tem
f
o
r
o
n
e
g
r
o
u
p
,
(
a)
o
u
tp
u
t
v
o
ltag
e
o
f
PV a
r
r
ay
,
(
b
)
o
u
tp
u
t c
u
r
r
en
t
o
f
PV
ar
r
ay
,
(
c
)
PV o
u
tp
u
t p
o
wer
(
a)
(
b
)
Fig
u
r
e
8
.
R
esp
o
n
s
e
o
f
DC
v
o
ltag
e
f
o
r
s
in
g
le
-
p
h
ase,
(
a)
o
u
tp
u
t D
C
v
o
ltag
e
o
f
two
PV g
r
o
u
p
s
,
(
b
)
o
u
tp
u
t V
DC
at
DC
lin
k
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
9
.
W
av
ef
o
r
m
s
o
f
AC
lo
ad
s
id
e,
(
a)
o
u
tp
u
t
v
o
ltag
e
o
f
f
iv
e
-
lev
el
C
HB
,
(
b
)
o
u
tp
u
t v
o
lt
ag
e
o
f
AC
b
u
s
,
(
c)
o
u
tp
u
t c
u
r
r
en
t o
f
AC
b
u
s
,
(
d
)
o
u
tp
u
t p
o
wer
o
f
AC
b
u
s
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
:
2
295
–
23
04
2302
4.
2
.
Scena
rio
I
I
:
un
der
pa
rt
ia
l sh
a
din
g
co
nd
it
io
ns
(
5
0
0
W/m
2
,
3
2
°
C
)
T
h
er
e
ar
e
two
p
er
io
d
ic
in
th
e
p
r
o
f
ile
u
s
ed
f
o
r
t
h
is
test
ca
s
e.
F
o
r
th
e
f
ir
s
t
p
er
io
d
ic
(
t=0
s
-
1
.
2
s
)
,
t
h
e
ir
r
ad
iatio
n
is
r
ed
u
c
ed
to
5
0
0
W
/m
2,
an
d
th
e
tem
p
er
atu
r
e
is
m
ain
tain
ed
at
STC
(
2
5
C
°
).
W
h
ile
i
n
th
e
s
ec
o
n
d
p
er
io
d
ic
(
t=
1
.
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R
E
F
E
R
E
NC
E
S
[
1
]
P.
R
a
y
a
n
d
M
.
B
i
s
w
a
l
,
“
L
e
c
t
u
r
e
n
o
t
e
s
i
n
e
l
e
c
t
r
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
6
2
5
m
i
c
r
o
g
r
i
d
:
o
p
e
r
a
t
i
o
n
,
c
o
n
t
r
o
l
,
m
o
n
i
t
o
r
i
n
g
,
a
n
d
p
r
o
t
e
c
t
i
o
n
,
”
S
p
r
i
n
g
e
r
,
2
0
2
0
.
[
O
n
l
i
n
e
]
.
[
A
v
a
i
l
a
b
l
e
]
:
h
t
t
p
s
:
/
/
w
w
w
.
s
p
r
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n
g
e
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.
c
o
m
/
g
p
/
b
o
o
k
/
9
7
8
9
8
1
1
5
1
7
8
0
8
#
a
b
o
u
t
A
u
t
h
o
r
s
.
[2
]
P
.
K.
P
a
n
d
a
,
A.
S
a
h
o
o
,
A.
S
a
m
a
l,
D.
P
.
M
ish
ra
,
a
n
d
S
.
Re
d
d
y
,
“
Vo
l
tag
e
c
o
n
tr
o
l
o
f
AC
h
y
b
rid
m
icro
g
rid
,
”
In
ter
n
a
t
io
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
m
(IJ
PE
DS
)
,
v
o
l.
12
,
n
o
.
2
,
p
p
.
7
9
3
-
802
,
Ju
n
e
2
0
2
1
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
p
e
d
s
.
v
1
2
.
i
2
.
p
p
7
9
3
-
8
0
2
.
[3
]
S
.
Ba
y
h
a
n
,
H.
Ab
u
-
R
u
b
,
J.
I.
Le
o
n
,
S
.
Va
z
q
u
e
z
,
a
n
d
L
.
G
.
F
ra
n
q
u
e
lo
,
“
P
o
we
r
e
lec
tro
n
ic
c
o
n
v
e
rt
e
rs
a
n
d
c
o
n
tr
o
l
tec
h
n
iq
u
e
s
in
AC
m
icro
g
ri
d
s,
”
I
ECON
2
0
1
7
-
4
3
r
d
An
n
u
a
l
C
o
n
fer
e
n
c
e
o
f
th
e
I
EE
E
I
n
d
u
stri
a
l
El
e
c
tro
n
ics
S
o
c
iety
,
2
0
1
7
,
p
p
.
6
1
7
9
-
6
1
8
6
,
d
o
i:
1
0
.
1
1
0
9
/IE
CON
.
2
0
1
7
.
8
2
1
7
0
7
3
.
[4
]
G
.
Ja
y
a
ra
ju
,
a
n
d
G.
S.
Ra
o
,
“
In
t
e
ll
ig
e
n
t
c
o
n
tr
o
ll
e
r
b
a
se
d
p
o
we
r
q
u
a
li
ty
imp
ro
v
e
m
e
n
t
o
f
m
icr
o
g
ri
d
in
teg
ra
ti
o
n
o
f
p
h
o
to
v
o
lt
a
ic
p
o
we
r
sy
ste
m
u
sin
g
n
e
w
c
a
sc
a
d
e
m
u
lt
il
e
v
e
l
i
n
v
e
r
ter
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
E
n
g
in
e
e
rin
g
(IJ
ECE
)
,
v
o
l.
9
,
n
o
.
3
,
p
p
.
1
5
1
4
-
1
5
2
3
,
Ju
n
e
2
0
1
9
,
d
o
i:
1
0
.
1
1
5
9
1
/i
jec
e
.
v
9
i
3
.
p
p
1
5
1
4
-
1
5
2
3
.
[5
]
A.
Krish
n
a
R
,
a
n
d
L.
P
.
S
u
re
sh
,
“
A
b
rief
re
v
iew
o
n
m
u
lt
i
lev
e
l
in
v
e
rter
to
p
o
lo
g
ies
,
”
2
0
1
6
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Circ
u
it
,
P
o
we
r a
n
d
C
o
mp
u
ti
n
g
T
e
c
h
n
o
lo
g
ies
(ICCPCT
)
,
2
0
1
6
,
p
p
.
1
-
6
,
d
o
i:
1
0
.
1
1
0
9
/ICC
P
CT.
2
0
1
6
.
7
5
3
0
3
7
3
.
[6
]
I.
H.
S
h
a
n
o
n
o
,
N.
R.
H.
Ab
d
u
ll
a
h
,
a
n
d
A.
M
u
h
a
m
m
a
d
,
“
A
s
u
rv
e
y
o
f
m
u
lt
il
e
v
e
l
v
o
lt
a
g
e
so
u
rc
e
in
v
e
rter
to
p
o
lo
g
ies
,
c
o
n
tro
ls,
a
n
d
a
p
p
li
c
a
ti
o
n
s
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tr
o
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
8
6
-
1
2
0
1
,
S
e
p
tem
b
e
r
2
0
1
8
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
p
e
d
s
.
v
9
.
i3
.
p
p
1
1
8
6
-
1
2
0
1
.
[7
]
Er.
M
.
S
a
n
d
h
u
,
a
n
d
T.
T
h
a
k
u
r,
“
M
u
lt
il
e
v
e
l
i
n
v
e
rters
li
tera
tu
re
s
u
r
v
e
y
-
to
p
o
lo
g
ies
,
c
o
n
tro
l
tec
h
n
i
q
u
e
s
&
a
p
p
li
c
a
ti
o
n
s
o
f
re
n
e
wa
b
le
e
n
e
r
g
y
so
u
rc
e
s
-
g
ri
d
i
n
teg
ra
ti
o
n
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
En
g
in
e
e
rin
g
Res
e
a
rc
h
a
n
d
A
p
p
li
c
a
ti
o
n
s
,
v
o
l.
4
,
n
o
.
3
,
p
p
.
6
4
4
-
6
5
2
,
M
a
rc
h
2
0
1
4
.
[8
]
S
.
S
.
Ka
t
k
a
m
wa
r
,
a
n
d
V.
R.
Do
i
fo
d
e
,
“
Ca
sc
a
d
e
d
H
-
b
ri
d
g
e
m
u
lt
il
e
v
e
l
P
V
in
v
e
rter
with
M
P
P
T
f
o
r
g
rid
c
o
n
n
e
c
ted
a
p
p
li
c
a
ti
o
n
,
”
2
0
1
6
I
n
ter
n
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m
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lt
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0
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S
.
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re
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S
.
D.
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u
sh
i
k
,
a
n
d
Y.
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M
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d
h
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sim
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m
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0
1
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ti
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1
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2
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3
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n
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,
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ter
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4
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M.
Ku
m
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“
D
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sim
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l
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.
D
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b
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l
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Tec
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y
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P
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ste
m
(El
e
c
tri
c
a
l
En
g
i
n
e
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rin
g
)
De
p
a
rtme
n
t
Of
El
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c
tri
c
a
l
En
g
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n
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rin
g
,
2
0
1
6
.
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
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t J
Po
w
E
lec
&
Dr
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Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
295
–
23
04
2304
[1
5
]
R.
Na
g
a
ra
jan
,
J.
Ch
a
n
d
ra
m
o
h
a
n
,
a
n
d
S.
S
a
t
h
ish
k
u
m
a
r,
“
Im
p
lem
e
n
tatio
n
o
f
P
I
c
o
n
tr
o
ll
e
r
fo
r
b
o
o
st
c
o
n
v
e
rter
i
n
P
V
S
y
ste
m
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Ad
v
a
n
c
e
d
Res
e
a
rc
h
in
M
a
n
a
g
e
me
n
t,
Arc
h
it
e
c
tu
re
,
T
e
c
h
n
o
l
o
g
y
a
n
d
E
n
g
i
n
e
e
rin
g
(IJ
AR
M
AT
E)
,
v
o
l.
2
,
n
o
.
2
2
,
p
p
.
6
-
1
0
,
Ap
ril
,
6
-
10.
[1
6
]
M
.
H.
Ra
sh
i
d
,
P
o
we
r E
lec
tro
n
ics
Ha
n
d
b
o
o
k
,
Bu
tt
e
rwo
rt
h
-
He
in
e
m
a
n
n
,
2
0
1
8
.
[1
7
]
F
.
L
.
To
f
o
li
,
D.
D
e
C
.
P
e
re
ira
,
a
n
d
W
.
J.
d
e
P
a
u
la,
“
Co
m
p
a
r
a
ti
v
e
stu
d
y
o
f
m
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
i
n
g
tec
h
n
iq
u
e
s
fo
r
p
h
o
t
o
v
o
lt
a
ic
s
y
ste
m
s
,
”
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ter
n
a
t
io
n
a
l
J
o
u
r
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l
o
f
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h
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e
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e
rg
y
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v
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l.
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0
1
5
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,
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o
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:
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.
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5
5
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0
1
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2
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8
2
.
[1
8
]
M
.
H.
Ud
d
i
n
,
M
.
A.
Ba
ig
,
a
n
d
M.
Ali,
“
Co
m
p
a
risio
n
o
f
‘
p
e
rt
u
rb
&
o
b
se
r
v
e
’
a
n
d
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in
c
re
m
e
n
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o
n
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tan
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e
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m
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x
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m
p
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o
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n
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trac
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g
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lg
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re
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l
e
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m
e
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tal
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s
,”
2
0
1
6
I
n
t
.
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o
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f
.
o
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Co
m
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ti
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,
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e
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tro
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e
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trica
l
E
n
g
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2
0
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6
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7
4
9
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2
4
4
[1
9
]
B.
S
in
g
h
,
B.
Ve
rm
a
,
a
n
d
P
.
K.
P
a
d
h
y
,
“
S
t
u
d
y
o
f
P
&
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a
n
d
INC
P
V
M
P
P
T
tec
h
n
iq
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e
s
f
o
r
d
iffere
n
t
e
n
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n
m
e
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ti
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s,
”
2
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2
n
d
IEE
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n
t
e
rn
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l
Co
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fer
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n
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o
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P
o
we
r
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e
c
tro
n
ics
,
I
n
telli
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C
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n
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l
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En
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0
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8
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8
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7
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7
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.
[2
0
]
R.
M
a
h
a
lak
sh
m
i
,
a
n
d
K.
C.
S
.
Th
a
m
p
a
tt
y
,
“
G
rid
c
o
n
n
e
c
ted
m
u
lt
i
lev
e
l
in
v
e
rter
fo
r
re
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wa
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le
e
n
e
rg
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a
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ti
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n
s
,
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e
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T
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h
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o
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v
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l.
2
1
,
p
p
.
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4
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5
,
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:
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0
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1
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.
p
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tcy
.
2
0
1
5
.
1
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6
.
[2
1
]
L.
H.
P
ra
to
m
o
,
a
n
d
S
.
Riy
a
d
i,
“
De
sig
n
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n
d
im
p
lem
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n
tatio
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o
f
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si
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le
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p
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se
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lev
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l
in
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e
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si
n
g
a
DC
s
o
u
rc
e
with
v
o
lt
a
g
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lan
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e
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n
c
a
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r
,
”
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ter
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l
J
o
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rn
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l
o
f
Po
we
r
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c
tro
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ics
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n
d
Dr
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S
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ste
m
(IJ
PE
DS
)
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l
.
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,
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o
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2
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p
.
9
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s.
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.
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.
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p
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0
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.
[2
2
]
K.
A.
K.
Nia
z
i,
Y.
Ya
n
g
,
a
n
d
D.
S
e
ra
,
“
Re
v
iew
o
f
m
ism
a
t
c
h
m
it
ig
a
ti
o
n
tec
h
n
iq
u
e
s fo
r
P
V m
o
d
u
les
.
IET
Re
n
e
wa
b
le
P
o
we
r
G
e
n
e
ra
ti
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n
,
”
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T
Re
n
e
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le
P
o
we
r
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n
e
ra
ti
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n
,
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l.
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.
1
2
,
p
p
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0
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0
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0
,
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0
1
9
,
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o
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0
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9
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e
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-
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g
.
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0
1
9
.
0
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5
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.
[
2
3
]
M
.
N
.
M
o
h
s
i
n
,
“
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e
s
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o
f
a
g
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d
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c
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t
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p
o
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le
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t
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n
i
c
c
o
n
v
e
r
te
r
,
”
M
a
s
t
e
r
'
s
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h
e
si
s
,
U
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T
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,
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.
1
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p
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.
[
O
n
l
i
n
e
]
.
[
A
v
a
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l
a
b
l
e
]
:
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t
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:
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w
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[2
4
]
D.
Y.
M
a
h
m
o
o
d
,
A.
H.
Nu
m
a
n
,
a
n
d
J.
K.
Ate
ih
,
“
S
imp
le
a
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d
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ffi
c
ien
t
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m
e
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b
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rg
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ig
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tratio
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h
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ic
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rra
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”
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ter
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a
rc
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o
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p
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3
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1
8
1
9
,
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a
y
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.
[2
5
]
M
.
R.
J.
De
v
i
,
a
n
d
M
.
S
.
S
.
Ka
d
a
m
,
“
S
y
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o
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iza
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p
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se
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rter
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lec
tri
c
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,
”
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ter
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ti
o
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a
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J
o
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.
[2
6
]
S
.
M
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Ka
v
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M
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v
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P
.
Ja
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n
,
a
n
d
A.
Ba
k
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sh
a
i
,
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A
re
v
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f
AC
m
icro
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rid
c
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tro
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m
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th
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s,
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2
0
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IEE
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8
t
h
In
ter
n
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a
l
S
y
mp
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m
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Po
we
r
El
e
c
tro
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ics
fo
r
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n
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ra
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.
2
0
1
7
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7
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4
9
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.
[2
7
]
G
.
J.
M
a
y
,
A.
Da
v
id
so
n
,
a
n
d
B.
M
o
n
a
h
o
v
,
“
Lea
d
b
a
tt
e
ries
fo
r
u
ti
l
it
y
e
n
e
rg
y
sto
ra
g
e
:
A
re
v
iew
,
”
J
o
u
rn
a
l
o
f
En
e
rg
y
S
to
ra
g
e
,
v
o
l
.
1
5
,
p
p
.
1
4
5
-
1
5
7
,
F
e
b
ru
a
ry
2
0
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8
,
d
o
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0
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1
0
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6
/j
.
e
st.
2
0
1
7
.
1
1
.
0
0
8
.
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
Ma
r
wa
n
S
a
d
e
d
Ahm
e
d
,
is
a
n
M
.
S
c
.
d
e
g
re
e
st
u
d
e
n
t
i
n
th
e
re
se
a
rc
h
lev
e
l
a
t
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
De
p
a
rtme
n
t,
Un
iv
e
rsity
o
f
Tec
h
n
o
lo
g
y
,
Ba
g
h
d
a
d
,
Ira
q
,
a
n
d
c
o
m
p
lete
a
B.
S
c
.
d
e
g
re
e
in
2
0
0
9
i
n
th
e
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
De
p
a
rtme
n
t,
Un
i
v
e
rsity
o
f
D
y
a
la,
Dy
a
la,
Ir
a
q
.
M
r.
M
a
rwa
n
is
in
tere
ste
d
i
n
P
o
we
r
El
e
c
tro
n
ic
C
o
n
v
e
rters
,
P
V
S
y
ste
m
s,
M
icro
g
ri
d
sy
ste
m
s,
a
n
d
S
to
ra
g
e
E
n
e
rg
y
S
y
ste
m
s
.
Ema
il
:
e
e
e
.
1
9
.
0
9
@g
ra
d
.
u
o
tec
h
n
o
l
o
g
y
.
e
d
u
.
iq
Ali
H
u
ss
e
in
Num
a
n
re
c
e
iv
e
d
t
h
e
BS
c
,
M
.
S
c
,
a
n
d
P
h
.
D.
in
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
fro
m
th
e
Un
iv
e
rsity
o
f
Tec
h
n
o
lo
g
y
,
i
n
1
9
9
9
,
2
0
0
3
,
a
n
d
2
0
0
9
,
re
sp
e
c
ti
v
e
l
y
.
Cu
rre
n
tl
y
,
h
e
is
a
n
As
so
c
iate
P
ro
fe
ss
o
r
o
f
E
lec
tri
c
a
l
En
g
i
n
e
e
rin
g
i
n
th
e
E
lec
tro
m
e
c
h
a
n
ica
l
En
g
in
e
e
rin
g
De
p
a
rtme
n
t
o
f
th
e
Un
iv
e
rsity
o
f
Tec
h
n
o
lo
g
y
(U
o
T)
.
He
h
a
s
c
o
-
a
u
t
h
o
re
d
th
e
tex
tb
o
o
k
S
m
a
ll
a
n
d
S
p
e
c
ial
El
e
c
tri
c
M
o
to
r
a
n
d
T
h
e
ir
Co
n
tro
l
Tec
h
n
i
q
u
e
,
2
0
1
6
,
a
n
d
p
u
b
li
s
h
e
d
3
7
j
o
u
r
n
a
ls
a
n
d
c
o
n
fe
re
n
c
e
s
p
a
p
e
rs.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
p
o
we
r
e
lec
tro
n
ics
,
v
a
riab
le
sp
e
e
d
d
riv
e
s,
r
e
n
e
wa
b
le
e
n
e
r
g
y
,
a
n
d
m
o
d
e
li
n
g
a
n
d
sim
u
lati
o
n
.
Ema
il
:
a
li
.
h
.
n
u
m
a
n
@u
o
tec
h
n
o
l
o
g
y
.
e
d
u
.
i
q
Dha
r
i
Yo
u
sif.
Ma
h
m
o
o
d
is
a
.
P
ro
f
a
t
th
e
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
a
t
t
h
e
Un
iv
e
rsity
o
f
Tec
h
n
o
l
o
g
y
–
Ba
g
h
d
a
d
–
Ira
q
.
He
wa
s
a
wa
rd
e
d
h
is
M
.
S
c
a
n
d
P
h
.
D.
i
n
El
e
c
tri
c
a
l
P
o
we
r
En
g
in
e
e
ri
n
g
fr
o
m
S
a
n
t.
P
e
terb
u
rg
P
o
ly
tec
h
n
ica
l
In
sti
tu
t
e
-
Ru
ss
a
in
1
9
8
6
a
n
d
1
9
9
0
re
sp
e
c
ti
v
e
ly
.
His
BS
c
d
e
g
re
e
wa
s
re
c
e
iv
e
d
in
1
9
8
1
fro
m
t
h
e
Un
i
v
e
rsity
o
f
Ba
g
h
d
a
d
-
Co
l
lag
e
o
f
En
g
i
n
e
e
rin
g
-
Ira
q
.
He
wo
r
k
s
i
n
t
h
e
field
o
f
re
n
e
wa
b
le
e
n
e
rg
y
a
n
d
p
o
we
r
sy
ste
m
a
n
a
ly
sis.
He
su
p
e
rv
ise
s a
larg
e
n
u
m
b
e
r
o
f
p
o
st
g
ra
d
u
a
te st
u
d
e
n
ts
in
b
o
th
m
a
ste
rs an
d
P
h
.
D.
d
e
g
re
e
s
.
Ema
il
:
d
h
a
ri.
y
.
m
a
h
m
o
o
d
@
u
o
tec
h
n
o
l
o
g
y
.
e
d
u
.
i
q
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