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m
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h
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r
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tic
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d
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n
v
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tio
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al
o
p
tim
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n
s
tech
n
iq
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f
o
r
th
e
g
r
id
c
o
n
n
ec
te
d
p
h
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to
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ltaic
s
o
lar
s
y
s
tem
.
T
h
e
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
a
n
d
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
alg
o
r
ith
m
s
ar
e
p
r
o
p
o
s
ed
to
tr
ac
k
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
o
f
th
e
p
h
o
to
v
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ltaic
s
o
lar
s
y
s
tem
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PVSS
)
.
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h
e
r
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lar
izatio
n
o
f
th
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u
r
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t
s
u
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ed
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e
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r
al
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s
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y
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e
g
e
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ith
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GA)
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h
e
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th
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s
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ith
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ar
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s
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f
to
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ar
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T
HD)
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ey
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r
d
s
:
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en
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le
e
n
er
g
y
PV
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id
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tem
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tim
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ith
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m
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m
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am
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u
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u
.
s
n
1.
I
NT
RO
D
UCT
I
O
N
D
u
e
t
o
t
h
e
e
n
v
i
r
o
n
m
e
n
t
a
l
a
n
d
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c
o
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T
h
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m
a
n
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it
s
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t
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o
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a
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m
i
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s
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o
n
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i
m
p
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v
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d
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g
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q
u
a
l
i
t
y
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e
t
t
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s
y
s
t
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m
e
f
f
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c
ie
n
c
y
a
n
d
r
e
l
i
a
b
le
s
e
r
v
i
c
e
.
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h
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t
o
v
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l
t
ai
c
s
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s
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m
(
P
V
)
i
s
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n
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o
f
t
h
e
t
y
p
e
s
o
f
r
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n
e
w
a
b
l
e
s
e
n
e
r
g
y
.
B
u
t
,
t
h
e
m
a
i
n
p
r
o
b
l
e
m
s
o
f
t
h
e
P
V
s
y
s
t
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m
a
r
e
t
h
e
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te
r
m
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t
te
n
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o
f
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t
s
s
o
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r
c
e
a
n
d
t
h
e
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p
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d
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o
f
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t
s
c
h
a
r
a
ct
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r
is
t
i
cs
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n
c
l
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m
at
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c
c
o
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ti
o
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s
a
n
d
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l
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t
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g
y
i
n
j
e
ct
e
d
i
n
t
o
t
h
e
g
r
i
d
.
Hen
ce
,
s
ev
er
al
r
esear
ch
e
r
s
h
av
e
ca
r
r
ied
o
u
t
s
o
m
e
wo
r
k
s
to
o
v
e
r
co
m
e
its
ch
allen
g
es
b
y
u
s
in
g
o
p
tim
izatio
n
s
tech
n
iq
u
es.
T
h
e
r
e
ar
e
m
an
y
m
et
h
o
d
s
o
f
p
o
wer
o
p
tim
izatio
n
.
Fo
r
ex
a
m
p
le,
i
n
o
r
d
er
to
m
i
n
im
ize
p
o
wer
lo
s
s
es,
an
in
cr
em
en
tal
c
o
n
d
u
cta
n
ce
(
I
C
)
b
ased
v
ar
iab
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tep
s
ize
Neu
r
o
-
Fu
zz
y
(
NF)
co
n
tr
o
l
is
ea
r
ly
p
r
o
p
o
s
ed
[
1
]
.
T
h
is
m
eth
o
d
r
e
d
u
ce
s
co
n
s
eq
u
en
tly
th
e
p
o
wer
lo
s
s
es.
U
s
in
g
a
ter
m
in
al
s
lid
i
n
g
m
o
d
e
c
o
n
tr
o
ller
co
m
b
in
ed
to
PS
O
[
2
]
,
it
is
s
h
o
wn
th
at
th
e
PS
O
-
T
SMC
o
f
f
er
s
th
e
b
est
r
esu
lts
.
W
ith
th
e
PS
O
an
d
GA
alg
o
r
ith
m
s
,
th
e
PID
an
d
N
-
D
PID
MPPT
co
n
tr
o
ller
s
p
er
m
it
ted
a
g
o
o
g
o
p
tim
izatio
n
’
s
ac
h
iev
em
en
t
[
3
]
.
T
h
e
PS
O
p
r
o
v
id
es
a
f
lex
ib
le
r
esp
o
n
s
e
u
n
d
er
f
ast
-
ch
an
g
in
g
we
ath
er
co
n
d
itio
n
s
.
An
ar
tific
ial
b
ee
c
o
lo
n
y
(
AB
C
)
in
teg
r
ated
PO
as
MPPT
alg
o
r
ith
m
is
alo
s
u
s
ed
f
o
r
o
p
tim
izin
g
th
e
d
u
ty
cy
cle
o
f
a
b
o
o
s
t
co
n
v
er
ter
[
4
]
.
T
h
is
p
r
o
p
o
s
ed
m
eth
o
d
allo
ws
f
o
r
h
ig
h
er
p
er
f
o
r
m
an
c
e
an
d
g
r
ea
t
er
p
r
ec
is
io
n
.
An
a
p
p
r
o
ac
h
b
a
s
ed
o
n
a
n
o
v
el
s
alp
s
war
m
o
p
tim
izatio
n
(
SS
O)
d
em
o
n
s
tr
ated
c
o
n
s
id
er
ab
le
s
u
c
ce
s
s
an
d
r
eliab
ilit
y
[
5
]
.
T
h
e
B
at
-
P&
O,
B
at
-
B
eta,
an
d
B
at
-
I
C
MPPT
ar
e
also
s
t
u
d
ied
an
d
c
o
m
p
a
r
ed
b
etwwe
n
th
em
[
6
]
.
I
t
is
n
o
ted
t
h
at
th
e
B
at
-
B
eta
co
m
m
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
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I
SS
N:
2088
-
8
694
A
co
mp
a
r
a
tive
s
tu
d
y
o
f m
eta
-
h
eu
r
is
tic
a
n
d
co
n
ve
n
tio
n
a
l o
p
timiz
a
tio
n
tech
n
iq
u
es o
f
… (
Ma
ma
d
o
u
Tr
a
o
r
e
)
2493
p
er
f
o
r
m
s
b
etter
u
n
d
er
all
test
co
n
d
itio
n
s
.
A
n
ew
p
r
o
p
o
r
tio
n
al
in
teg
r
al
(
PI)
f
r
ac
tio
n
al
o
r
d
e
r
in
cr
e
m
en
tal
(
FOI
)
tech
n
iq
u
e
o
p
tim
iz
ed
b
y
s
alp
s
war
m
alg
o
r
ith
m
(
SS
A)
is
d
e
v
elo
p
ed
in
o
r
d
er
to
o
p
er
ate
t
h
e
PV
s
y
s
tem
at
t
h
e
esti
m
ated
PP
M
[
7
]
.
As
a
r
esu
lt,
th
e
au
th
o
r
s
r
em
ar
k
ed
th
at
t
h
eir
alg
o
r
ith
m
o
f
f
er
s
a
b
etter
tr
ac
k
in
g
ca
p
ab
ilit
y
th
an
th
e
o
t
h
er
s
.
A
v
a
r
iab
le
-
w
ea
th
er
-
p
ar
am
ete
r
(
VW
P)
co
m
m
an
d
is
p
r
o
p
o
s
ed
[
8
]
.
An
d
t
h
e
s
im
u
latio
n
r
esu
lts
s
h
o
wed
th
at
th
e
ap
p
lied
ap
p
r
o
ac
h
is
ap
p
licab
le
f
o
r
th
e
tr
ac
k
i
n
g
o
f
th
e
MPP.
C
o
n
s
id
er
in
g
a
n
ew
Har
r
is
Haw
k
o
p
tim
izatio
n
[
9
]
,
it
is
s
h
o
w
n
t
h
at
th
e
m
o
s
t
im
p
o
r
tan
t
ad
v
a
n
tag
es
o
f
th
is
ap
p
r
o
ac
h
is
to
all
o
w
q
u
ick
ly
o
f
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t.
Pro
p
o
s
in
g
an
asy
m
m
etr
ical
in
ter
v
al
ty
p
e
-
2
f
u
zz
y
lo
g
ic
co
n
t
r
o
l
(
I
T
-
2
AFLC)
[
1
0
]
,
P.
Ver
m
a
et
a
l
.
[
1
0
]
co
n
cl
u
d
ed
t
h
at
th
is
tech
n
i
q
u
e
h
as
th
e
m
ax
im
u
m
o
u
tp
u
t
p
o
wer
in
all
s
h
a
d
in
g
s
ce
n
a
r
io
s
.
T
h
e
p
o
s
s
ib
ilit
y
o
f
ex
tr
ac
tin
g
th
e
MPPT
o
f
ea
c
h
PV
p
an
el
is
d
em
o
n
s
tr
ated
in
a
n
o
v
el
f
ee
d
f
o
r
war
d
tech
n
iq
u
e
[
1
1
]
.
T
o
o
p
tim
ize
th
e
PV
en
e
r
g
y
p
r
o
d
u
ctio
n
,
t
h
e
P&
O
an
d
I
n
C
co
m
m
an
d
s
ar
e
im
p
r
o
v
ed
[
1
2
]
.
T
h
e
s
im
u
latio
n
r
esu
lts
s
h
o
wed
th
at
I
C
MPP
T
co
n
tr
o
l
tech
n
iq
u
e
is
m
o
r
e
ef
f
ec
tiv
e
th
an
P&
O.
A
m
o
d
if
ied
P&
O
alg
o
r
ith
m
s
tu
d
y
p
r
o
v
ed
th
at
th
e
u
s
ed
m
et
h
o
d
[
1
3
]
is
f
aster
th
an
P&
O
co
n
v
en
tio
n
al
a
n
d
ef
f
icien
cy
is
in
cr
ea
s
ed
.
I
n
th
e
liter
atu
r
e,
m
an
y
tech
n
i
q
u
es a
r
e
p
r
o
p
o
s
ed
to
ac
h
iev
e
b
e
tter
p
er
f
o
r
m
a
n
ce
o
f
th
e
PV
-
g
r
i
d
s
y
s
tem
.
A
co
o
r
d
in
ated
co
n
tr
o
l
[
1
4
]
is
u
s
ed
to
r
ed
u
c
e
th
e
o
u
t
p
u
t
v
a
r
iatio
n
.
I
n
[
1
5
]
,
with
a
n
o
n
lin
ea
r
co
m
m
an
d
,
th
e
T
HD
r
ea
ch
es
2
.
4
4
%.
T
o
o
p
ti
m
ize
th
e
Pro
p
o
r
tio
n
al
an
d
th
e
Pro
p
o
r
tio
n
al
I
n
teg
r
al
c
o
n
tr
o
ller
s
,
an
alg
o
r
ith
m
[
1
6
]
p
e
r
m
itted
to
r
ed
u
ce
b
y
2
7
%
th
e
T
HD.
A
m
o
d
if
ied
d
r
o
o
p
c
o
n
tr
o
ller
[
1
7
]
lead
e
d
t
o
th
e
co
n
tr
o
l
o
f
th
e
r
ea
ctiv
e
p
o
wer
in
jectio
n
o
f
t
h
e
in
v
er
ter
in
th
e
s
itu
atio
n
wh
er
e
th
e
v
o
ltag
es
o
f
ea
ch
cu
s
t
o
m
er
a
r
e
less
th
an
1
0
.
0
2
%
o
f
t
h
e
n
o
m
in
al
v
o
ltag
e.
B
y
an
o
th
er
m
eth
o
d
o
f
co
n
tr
o
l
[
1
8
]
,
it
is
s
h
o
wn
th
at
it
p
o
s
s
ib
le
to
m
in
im
ize
th
e
h
ig
h
f
r
eq
u
e
n
cy
o
f
th
e
g
r
id
.
T
h
e
v
o
ltag
e
co
n
tr
o
l
is
also
a
p
p
lied
[
1
9
]
.
T
h
is
ap
p
r
o
ac
h
k
e
ep
s
co
n
s
tan
t
th
e
d
c
lin
k
v
o
ltag
e.
A
p
r
e
d
ictiv
e
m
et
h
o
d
r
ed
u
ce
s
th
e
T
HD
to
1
.
2
6
%
[
2
0
]
.
A
n
o
v
el
Sp
ac
e
Vec
to
r
Mo
d
u
latio
n
(
SVM)
wh
o
s
e
aim
is
to
r
ed
u
ce
th
e
T
HD
is
im
p
r
o
v
e
d
b
y
Naja
f
i
et
a
l.
[
2
1
]
.
T
h
e
r
esu
lts
v
alid
ated
th
at
th
e
SVM
allo
wed
to
o
b
tain
1
.
7
6
%
o
f
T
HD.
R
o
s
ely
n
et
a
l
.
[
2
2
]
,
u
s
ed
a
f
u
zz
y
lo
g
ic
co
m
m
a
n
d
wh
ich
o
p
er
ates
s
ig
n
if
ican
tly
to
im
p
o
v
e
th
e
g
r
i
d
cu
r
r
en
t.
A
n
o
th
er
v
o
ltag
e
co
n
tr
o
l
m
eth
o
d
[
2
3
]
s
h
o
wed
a
T
HD
wh
ich
d
o
es
n
o
t
ex
ce
ed
3
.
5
%.
Ap
p
ly
in
g
h
y
s
ter
esis
co
n
tr
o
ller
,
Gan
esan
et
a
l.
[
2
4
]
o
b
tain
ed
an
in
c
r
ea
s
e
b
y
2
.
5
%
o
f
th
e
T
HD.
I
n
an
o
th
er
h
an
d
,
m
an
y
tech
n
iq
u
es
o
f
co
n
tr
o
l
ar
e
u
s
ed
t
o
co
n
tr
o
l
t
h
e
o
u
tp
u
t
cu
r
r
en
t
[
2
5
]
.
All
o
f
th
em
co
n
clu
d
e
d
th
at
th
e
ca
s
ca
d
e
co
n
tr
o
l
g
av
e
a
lo
wer
T
HD.
T
h
u
s
,
o
u
r
r
esear
ch
is
d
e
v
elo
p
p
e
d
to
u
s
e
two
m
eta
-
h
eu
r
is
tics
tech
n
iq
u
es
t
o
o
p
tim
ize
th
e
PV
p
o
wer
an
d
im
p
o
v
e
th
e
p
e
r
f
o
r
m
an
ce
o
f
a
s
i
n
g
le
-
p
h
ase
in
v
er
ter
co
n
n
ec
ted
t
o
g
r
id
.
T
h
e
r
e
f
o
r
e
,
i
n
t
h
is
w
o
r
k
,
a
co
m
p
a
r
a
t
i
v
e
r
e
v
i
ew
o
f
t
h
e
P&
O
a
n
d
t
h
e
P
SO
is
p
r
o
p
o
s
ed
.
T
h
e
b
o
t
h
a
l
g
o
r
i
t
h
m
s
a
r
e
u
s
e
d
t
o
e
x
t
r
ac
t
t
h
e
M
PP
o
f
t
h
e
P
V
u
n
d
er
s
e
v
e
r
a
l
v
a
r
i
at
i
o
n
s
o
f
s
o
la
r
i
r
r
a
d
i
a
t
i
o
n
a
n
d
t
h
e
t
e
m
p
e
r
a
t
u
r
e
.
T
h
e
o
b
j
e
ct
i
v
e
o
f
th
i
s
c
o
m
p
a
r
a
ti
v
e
s
t
u
d
y
i
s
t
o
c
h
o
o
s
e
t
h
e
b
es
t
e
f
f
i
c
i
e
n
c
y
t
o
e
x
t
r
ac
t
t
h
e
MP
P
.
O
n
t
h
e
A
C
s
i
d
e
,
t
h
e
g
e
n
e
t
i
c
al
g
o
r
i
t
h
m
u
n
d
e
r
M
A
T
L
A
B
is
u
s
e
d
t
o
o
p
t
i
m
i
z
e
t
h
e
P
I
p
a
r
a
m
et
e
r
s
.
As
w
e
k
n
o
w
,
t
h
e
r
e
a
r
e
s
e
v
e
r
a
l
m
et
h
o
d
s
t
o
d
e
t
e
r
m
i
n
e
th
e
p
a
r
a
m
e
t
e
r
s
o
f
a
c
o
r
r
e
c
t
o
r
:
Z
i
e
g
l
e
r
-
N
i
c
h
o
ls
,
Na
s
li
n
,
p
l
a
c
e
m
e
n
t
o
f
t
h
e
p
o
l
e
s
,
e
tc
.
E
a
c
h
o
f
t
h
e
m
f
i
x
es
at
le
a
s
t
th
e
o
r
e
t
i
c
a
l
l
y
o
n
e
v
a
r
i
a
b
l
e
o
f
th
e
t
r
a
n
s
f
e
r
f
u
n
c
ti
o
n
o
f
t
h
e
c
o
r
r
e
c
t
o
r
.
T
h
i
s
is
t
h
e
d
i
f
f
e
r
e
n
c
e
w
i
t
h
t
h
e
p
r
o
p
o
s
e
d
m
e
t
h
o
d
(
G
A
-
P
I
)
.
H
e
n
c
e
,
t
h
e
p
r
i
n
c
i
p
a
l
o
b
j
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c
t
i
v
e
o
f
t
h
i
s
w
o
r
k
is
t
o
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x
t
r
a
c
t
t
h
e
M
PP
o
f
t
h
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P
V
s
y
s
t
e
m
a
n
d
t
o
i
n
j
e
ct
in
t
o
t
h
e
g
r
i
d
a
g
o
o
d
q
u
a
l
i
t
y
o
f
e
n
e
r
g
y
w
i
t
h
a
z
e
r
o
r
e
a
c
ti
v
e
p
o
we
r
a
n
d
a
l
o
w
T
H
D
.
2.
DE
SCR
I
P
T
I
O
N
O
F
T
H
E
S
T
UDI
E
D
S
YST
E
M
T
h
e
F
ig
u
r
e
1
r
e
p
r
esen
ts
th
e
s
t
u
d
ied
s
y
s
tem
.
I
t
co
n
s
is
ts
o
f
a
p
h
o
to
v
o
ltaic
g
en
e
r
ato
r
,
a
DC
/
DC
b
o
o
s
t
co
n
v
er
ter
an
d
a
s
in
g
le
-
p
h
ase
co
n
v
er
ter
,
l
o
w
v
o
ltag
e
elec
tr
ical
g
r
id
.
An
d
t
h
e
s
y
s
tem
s
f
o
r
th
e
o
p
tim
is
atio
n
o
f
th
e
p
o
wer
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
el
an
d
th
e
r
eg
u
latio
n
o
f
th
e
o
u
tp
u
t
cu
r
r
en
t
o
f
th
e
s
in
g
l
e
-
p
h
ase
in
v
e
r
ter
ar
e
illu
s
tr
ated
.
Fig
u
r
e
1
.
Stu
d
ie
d
s
y
s
tem
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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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
:
2492
–
2
5
0
0
2494
2
.
1
.
PV
pa
nels
T
h
er
e
ar
e
s
ev
er
al
m
o
d
els
o
f
PV
p
an
els.
T
h
e
m
o
s
t
p
o
p
u
lar
m
o
d
el
in
p
o
wer
elec
tr
o
n
ics
is
th
e
s
in
g
le
d
io
d
e
m
o
d
el
as
s
h
o
wn
in
Fig
u
r
e
2
(
a)
[
2
6
]
.
T
h
is
is
b
ec
au
s
e
i
t
h
as
a
g
o
o
d
co
m
p
r
o
m
is
e
b
etwe
en
p
r
ec
is
io
n
an
d
s
im
p
licity
.
T
h
e
PV
p
an
el
p
ar
am
eter
s
is
r
ep
r
esen
ted
b
y
(
1
)
.
Fig
u
r
e
2
(
b
)
s
h
o
ws
th
e
n
u
m
b
er
o
f
p
an
els,
th
e
co
n
n
ec
tio
n
’
s
ty
p
es
an
d
PV
p
ar
am
eter
s
(
o
p
en
an
d
s
h
o
r
t
-
cir
c
u
it
v
o
ltag
e
an
d
cu
r
r
en
t
r
esp
ec
t
iv
ely
an
d
m
ax
im
u
m
p
o
wer
)
.
=
ℎ
−
[
+
.
.
.
−
1
]
−
+
.
ℎ
(
1
)
(
a)
(
b
)
Fig
u
r
e
2
.
T
h
er
e
f
i
g
u
r
es a
r
e;
(
a
)
T
h
e
elec
tr
ical
eq
u
iv
alen
t c
ir
c
u
it o
f
PV c
ell
,
(
b
)
T
y
p
ical
PV
ch
ar
ac
ter
is
tics
at
1000
W
/m²
an
d
2
5
C
W
h
er
e
I
d
is
th
e
d
io
d
e
s
atu
r
atio
n
cu
r
r
en
t
,
I
p
v
is
th
e
p
h
o
to
-
c
u
r
r
en
t,
R
s
h
is
th
e
s
h
u
n
t r
esis
tan
ce
an
d
Rs
is
th
e
s
er
ies r
esis
tan
ce
,
k
is
th
e
B
o
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an
n
’
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co
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s
tan
t; T
is
th
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am
b
ien
t te
m
p
e
r
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r
e
,
n
is
th
e
th
e
d
io
d
e
f
ac
to
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o
f
th
e
ju
n
ctio
n
.
T
a
b
le
1
r
e
p
r
es
en
ts
th
e
PV p
an
el
p
ar
am
eter
s
u
s
ed
in
th
is
wo
r
k
.
T
ab
le
1
.
PV p
an
el
p
ar
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eter
s
P
a
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2
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1
6
V
I
max
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a
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m
C
u
r
r
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t
2
.
7
A
V
O
C
V
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t
a
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o
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n
c
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2
0
V
I
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C
C
u
r
r
e
n
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o
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h
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t
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c
i
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c
u
i
t
3
A
R
s
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e
r
i
e
s r
e
si
s
t
a
n
c
e
0
.
5
7
3
7
3
Ω
R
sh
S
h
u
n
t
r
e
si
st
a
n
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e
1
0
3
.
3
8
4
3
Ω
a
I
d
e
a
l
i
t
y
f
a
c
t
o
r
0
.
8
9
6
4
9
Is
S
a
t
u
r
a
t
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o
n
c
u
r
r
e
n
t
9
.
4
4
9
8
*
1
0
-
11
2
.
2
.
B
o
o
s
t
c
o
nv
er
t
er
T
h
e
b
o
o
s
t
co
n
v
er
ter
is
a
n
elec
tr
o
n
ic
co
m
p
o
n
en
t
wh
ich
ca
n
c
o
n
v
er
t
th
e
lo
w
v
o
ltag
e
to
h
ig
h
v
o
ltag
e
.
I
ts
elec
tr
ical
cir
cu
it
is
r
ep
r
ese
n
ted
b
y
Fig
u
r
e
3
.
T
h
e
b
o
o
s
t
c
o
n
v
er
ter
is
u
s
ed
in
th
is
wo
r
k
t
o
p
r
o
v
id
e
a
co
n
tr
o
l
s
ig
n
al
th
at
is
g
en
er
ated
b
y
th
e
P&
O
an
d
PS
O
co
n
tr
o
ls
to
th
e
s
y
s
tem
to
r
u
n
at
th
e
m
ax
im
u
m
p
o
in
t a
n
d
p
r
o
d
u
c
e
PV e
n
er
g
y
.
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
co
mp
a
r
a
tive
s
tu
d
y
o
f m
eta
-
h
eu
r
is
tic
a
n
d
co
n
ve
n
tio
n
a
l o
p
timiz
a
tio
n
tech
n
iq
u
es o
f
… (
Ma
ma
d
o
u
Tr
a
o
r
e
)
2495
Fig
u
r
e
3.
B
o
o
s
t c
o
n
v
er
ter
3.
P
RO
P
O
SE
D
M
E
T
H
O
D
S
3
.
1
.
Alg
o
rit
hm
o
f
pa
rt
icle
s
wa
rm
o
pti
m
iza
t
io
n
T
h
e
PS
O
i
s
an
o
p
tim
is
atio
n
m
eth
o
d
th
at
is
ab
le
to
r
ea
ch
a
g
lo
b
al
b
est
s
o
lu
tio
n
.
I
t
is
a
p
o
wer
f
u
l
an
d
ef
f
icien
t
m
eth
o
d
f
o
r
th
e
s
o
lu
tio
n
o
f
co
m
p
lex
o
p
tim
is
atio
n
q
u
esti
o
n
s
.
I
t
h
as
b
ee
n
m
o
d
elled
af
ter
th
e
b
eh
av
i
o
u
r
o
f
b
ir
d
s
.
T
h
e
F
ig
u
r
e
4
illu
s
tr
ates th
e
PS
O
ap
p
r
o
ac
h
.
Fig
u
r
e
4
.
PS
O
alg
o
r
ith
m
T
h
e
PS
O
u
s
es a
p
o
p
u
latio
n
o
f
ag
en
t,
ca
lled
p
a
r
ticle.
T
h
e
latt
er
is
th
e
s
o
lu
tio
n
to
th
e
p
r
o
b
le
m
.
T
h
e
(
2
)
an
d
(
3
)
ar
e
u
s
ed
to
u
p
d
ate
th
e
p
o
s
itio
n
an
d
v
elo
city
.
+
1
=
.
+
1
.
1
(
,
−
)
+
2
.
2
(
−
)
(
2
)
+
1
=
+
+
1
(
3)
W
h
er
e
k
is
th
e
n
u
m
b
er
o
f
iter
a
tio
n
,
it is
th
e
n
u
m
b
er
o
f
p
ar
ticl
e,
x
i
an
d
V
i
th
e
p
o
s
itio
n
in
th
e
s
ea
r
ch
s
p
ac
e
an
d
v
elo
cit
y
,
r
esp
ec
tiv
ely
,
w
is
th
e
in
er
tia
o
f
p
ar
ticles,
P
best,
i
a
n
d
G
best
ar
e
th
e
b
est
an
d
th
e
g
lo
b
a
l b
est
p
o
s
itio
n
o
f
th
e
p
ar
ticle
,
c
1
an
d
c
2
ar
e
two
co
n
s
tan
ts
ca
lled
ac
ce
ler
atio
n
c
o
ef
f
icien
ts
an
d
r
1
an
d
r
2
ar
e
r
a
n
d
o
m
n
u
m
b
er
s
.
I
n
th
is
p
ap
er
,
eq
u
atio
n
1
r
ep
r
esen
ts
th
e
o
b
jectiv
e
f
u
n
ctio
n
.
3
.
2
.
P
er
t
urb a
nd
o
bs
er
v
e
(
P
&O
)
a
lg
o
rit
hm
T
h
is
m
eth
o
d
allo
ws
th
e
s
y
s
tem
to
b
e
d
is
tu
r
b
e
d
an
d
th
e
im
p
ac
t
o
n
th
e
p
o
wer
p
r
o
d
u
ce
d
b
y
th
e
GPV
to
b
e
o
b
s
er
v
ed
.
T
h
e
s
y
s
tem
co
n
tin
u
es
to
in
cr
em
en
t
th
e
o
p
er
a
tin
g
v
o
ltag
e
u
n
til
th
e
p
o
wer
g
en
er
atio
n
s
tar
ts
to
d
ec
r
ea
s
e
.
Fig
u
r
e
5
p
r
o
v
id
es
th
e
P&
O
alg
o
r
ith
m
f
l
o
wch
ar
t.
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
:
2492
–
2
5
0
0
2496
Fig
u
r
e
5
.
C
o
m
m
a
n
d
P&
O
f
lo
wch
ar
t
3
.
3
.
G
enet
ic
a
lg
o
rit
h
m
(
AG
)
T
h
e
GA
ar
e
in
s
p
ir
ed
b
y
th
e
p
r
o
ce
s
s
o
f
ev
o
lu
tio
n
p
r
esen
t
in
th
e
n
atu
r
al
wo
r
ld
,
s
u
c
h
as
s
elec
tio
n
,
m
u
tatio
n
in
h
e
r
itan
ce
an
d
r
ec
o
m
b
in
atio
n
to
s
o
lv
e
a
p
r
o
b
lem
.
I
n
th
e
GA
ap
p
r
o
ac
h
,
s
et
o
f
g
en
s
ar
e
r
ep
r
esen
ted
b
y
th
e
ch
r
o
m
o
s
o
m
e
o
r
in
d
iv
i
d
u
al.
E
ac
h
ch
r
o
m
o
s
o
m
e
r
ep
r
e
s
en
ts
a
s
o
lu
tio
n
o
r
th
e
g
iv
en
p
r
o
b
lem
.
T
h
e
GA
is
u
s
ed
in
t
h
is
p
ap
er
to
d
eter
m
in
e
th
e
o
p
tim
al
p
a
r
am
eter
s
(
K
p
et
K
i
)
o
f
th
e
PI
co
n
tr
o
ll
er
.
As
s
h
o
wn
(
4
)
g
iv
es
P
I
tr
an
s
f
er
f
u
n
ctio
n
:
(
S
)
=
+
(
4
)
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
s
in
g
le
-
p
h
ase
DC
/AC
in
v
er
ter
o
u
t p
u
t c
u
r
r
en
t is g
iv
e
n
b
y
(
5
)
:
(
)
=
0
.
(
5
)
T
h
e
f
ee
d
b
ac
k
co
n
tr
o
l o
f
th
e
in
v
er
ter
o
u
t p
u
t c
u
r
r
en
t is r
e
p
r
esen
ted
in
Fig
u
r
e
6.
Fig
u
r
e
6
.
Un
ity
f
ee
d
b
ac
k
co
n
t
r
o
l sy
s
tem
(
)
is
th
e
er
r
o
r
b
etwe
en
in
v
e
r
ter
c
u
r
r
en
t a
n
d
th
e
r
ef
er
en
ce
.
(
)
=
(
t)
-
(
t)
(
6
)
V(
t)
is
in
v
er
ter
in
p
u
t
ex
p
r
ess
ed
as:
V
(
t
)
=
e
(
t
)
+
∫
e
(
t
)
(
7
)
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
co
mp
a
r
a
tive
s
tu
d
y
o
f m
eta
-
h
eu
r
is
tic
a
n
d
co
n
ve
n
tio
n
a
l o
p
timiz
a
tio
n
tech
n
iq
u
es o
f
… (
Ma
ma
d
o
u
Tr
a
o
r
e
)
2497
T
h
e
f
itn
ess
f
u
n
ctio
n
is
g
iv
en
b
y
(
8
)
.
Fit
n
ess
f
u
n
ctio
n
=
∫
(
(
e
(
t
)
)
2
+
(
V
(
t
)
)
2
)
d
t
(
8)
T
h
e
o
p
tim
izatio
n
o
f
th
e
PI
c
o
n
tr
o
ller
p
ar
am
eter
s
b
y
u
s
in
g
th
e
g
en
etic
al
g
o
ith
m
,
is
m
a
d
e
as
f
o
llo
w
u
n
d
er
MA
T
L
AB
;
i)
d
ef
in
e
th
e
f
u
n
ct
io
n
(
f
ile
n
am
e
)
;
ii)
d
ef
in
e
th
e
tr
an
s
f
er
t
f
u
n
ctio
n
:
tf
(
‘
S’)
;
iii)
d
ef
in
e
th
e
tr
a
n
s
f
er
t
f
u
n
ctio
n
o
f
th
e
s
tu
d
ied
s
y
s
tem
: (
5
)
;
iv
)
d
ef
in
e
t
h
e
p
ar
am
eter
s
o
f
th
e
co
n
tr
o
ller
:
et
;
v
)
d
ef
in
e
th
e
tr
an
s
f
er
t
f
u
n
ctio
n
o
f
th
e
co
n
tr
o
ller
:
(
4
)
;
v
i)
d
ef
in
e
th
e
er
r
o
r
:
(
6
)
;
an
d
v
ii)
d
ef
in
e
th
e
co
s
t
f
u
n
ctio
n
:
(
8
)
.
T
ab
le
2
r
ep
r
esen
ts
th
e
GA
p
ar
am
eter
s
.
T
ab
le
2.
GA
p
ar
am
eter
G
A
p
a
r
a
m
e
t
e
r
s
M
e
t
h
o
d
e
s
V
a
l
u
e
s
Lo
w
e
r
b
o
u
n
d
s [
K
p
,
K
i
]
[
0
0
]
U
p
p
e
r
b
o
u
n
d
s [
K
p
,
K
i
]
[
5
0
0
5
0
0
]
P
o
p
u
l
a
t
i
o
n
t
y
p
e
D
o
u
b
l
e
v
e
c
t
o
r
60
S
e
l
e
c
t
i
o
n
S
t
o
c
h
a
st
i
c
u
n
i
f
o
r
m
M
u
t
a
t
i
o
n
U
n
i
f
o
r
m
C
r
o
ss
o
v
e
r
A
r
i
t
h
m
e
t
i
c
C
r
o
sso
v
e
r
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
s
tu
d
ied
s
y
s
tem
is
im
p
le
m
en
ted
u
n
d
er
MA
T
L
AB
/Si
m
u
lin
k
So
f
twar
e.
Simu
latio
n
s
ar
e
f
ir
s
t
d
o
n
e
u
n
d
er
s
tan
d
ar
d
tem
p
e
r
at
u
r
e
co
n
d
itio
n
(
STC).
Fig
u
r
e
7
s
h
o
ws th
e
m
ax
im
u
m
p
o
wer
p
o
in
t o
f
th
e
PV
wh
en
th
e
tem
p
er
atu
r
e
an
d
s
o
lar
ir
r
ad
iatio
n
ar
e
at
1
0
0
0
W
/m²
an
d
2
5
d
eg
r
ee
s
C
elsi
u
s
(
STC)
,
r
esp
ec
tiv
ely
.
T
h
e
m
ax
im
u
m
p
o
wer
tr
ac
k
ed
a
r
e
8
4
6
.
1
4
W
an
d
8
3
6
.
8
7
W
with
P
SO
an
d
P&
O
r
esp
ec
tiv
ely
.
He
n
ce
,
th
e
ef
f
icien
cy
is
9
7
.
9
%
an
d
9
6
.
8
%
with
PS
O
th
e
P&
O
,
r
esp
ec
tiv
ely
.
I
t
ca
n
b
e
n
o
ted
t
h
at
th
e
m
eta
-
h
eu
r
is
tic
co
m
m
an
d
(
PS
O)
is
m
o
r
e
ef
f
icien
cy
to
ex
tr
ac
t t
h
e
m
ax
im
u
m
p
o
wer
th
a
n
th
e
c
o
n
v
en
tio
n
al
m
eth
o
d
(
P&
O)
.
T
o
ev
alu
ate
th
e
ef
f
icien
c
y
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
,
th
e
s
o
lar
ir
r
ad
iatio
n
an
d
th
e
tem
p
e
r
atu
r
e
h
av
e
be
en
v
ar
iated
as sh
o
wn
in
Fig
u
r
e
8
.
T
h
e
s
o
lar
ir
r
ad
iatio
n
(
W
/
m
²
)
is
v
ar
iated
f
r
o
m
8
0
0
to
5
0
0
,
f
r
o
m
5
0
0
to
8
0
0
an
d
f
r
o
m
8
0
0
to
6
0
0
.
An
d
th
e
tem
p
er
atu
r
e
(
in
d
eg
r
ee
C
elsi
u
s
)
is
al
s
o
v
ar
iated
f
r
o
m
2
5
to
3
7
an
d
f
r
o
m
3
7
to
2
2
.
Fig
u
r
e
9
illu
s
tr
ates
th
e
p
h
o
to
v
o
ltaic
o
u
tp
u
t
g
e
n
er
ated
b
y
th
e
two
MPPT
alg
o
r
ith
m
s
.
T
h
e
all
u
s
ed
m
eth
o
d
s
co
n
v
er
g
e
to
th
e
MPP
b
u
t
th
e
PS
O
is
f
aster
to
attain
th
e
MPP
th
an
P&
O
as
s
h
o
wn
in
Fi
g
u
r
e
9
(
a)
an
d
g
iv
es
less
o
s
ci
llatio
n
s
at
th
e
m
ax
im
u
m
p
o
in
t
in
Fig
u
r
e
9
(
b
)
.
So
PS
O
i
s
b
etter
th
an
P&
O
to
tr
ac
k
th
e
m
ax
im
u
m
p
o
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ates
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Var
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[
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s
.
RE
F
E
R
E
NC
E
S
[1
]
A.
Ha
rra
g
a
n
d
,
a
n
d
S
.
M
e
ss
a
lt
i,
“
IC
-
b
a
se
d
v
a
ria
b
le
ste
p
siz
e
n
e
u
ro
-
f
u
z
z
y
M
P
P
T
Im
p
r
o
v
i
n
g
P
V
sy
ste
m
p
e
rfo
rm
a
n
c
e
s,”
En
e
rg
y
Pro
c
e
d
i
a
,
v
o
l
.
1
5
7
,
p
p
.
3
6
2
-
3
7
4
,
2
0
1
9
,
d
o
i:
1
0
.
1
0
1
6
/j
.
e
g
y
p
r
o
.
2
0
1
8
.
1
1
.
2
0
1
.
[2
]
F
.
E.
Lam
z
o
u
ri
,
E
-
M
.
B
o
u
f
o
u
n
a
s,
A.
Bra
h
m
i,
a
n
d
A.
El
Am
ra
n
i,
“
O
p
ti
m
ize
d
TS
M
C
Co
n
tr
o
l
Ba
se
d
M
P
P
T
fo
r
P
V
S
y
ste
m
u
n
d
e
r
Va
riab
le
Atm
o
sp
h
e
ric
Co
n
d
i
ti
o
n
s
Us
in
g
P
S
O
Alg
o
r
i
th
m
,
”
Pro
c
e
d
ia
C
o
mp
u
ter
S
c
ien
c
e
,
v
o
l.
1
7
0
,
p
p
.
887
-
8
9
2
,
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
p
ro
c
s.2
0
2
0
.
0
3
.
1
1
6
.
[3
]
D.
P
a
th
a
k
,
G
.
S
a
g
a
r,
a
n
d
P
.
G
a
u
r,
“
An
Ap
p
li
c
a
ti
o
n
o
f
In
tell
ig
e
n
t
No
n
-
li
n
e
a
r
Disc
re
te
-
P
ID
Co
n
tr
o
ll
e
r
fo
r
M
P
P
T
o
f
P
V S
y
ste
m
,
”
Pro
c
e
d
i
a
Co
m
p
u
ter
S
c
ien
c
e
,
v
o
l.
1
6
7
,
p
p
.
1
5
7
4
-
1
5
8
3
,
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
p
ro
c
s.2
0
2
0
.
0
3
.
3
6
8
.
[4
]
D.
P
il
a
k
k
a
t
a
n
d
S
.
Ka
n
t
h
a
lak
sh
m
i,
“
S
in
g
le
p
h
a
se
P
V
sy
ste
m
o
p
e
ra
ti
n
g
u
n
d
e
r
P
a
rti
a
ll
y
S
h
a
d
e
d
Co
n
d
it
io
n
s
wit
h
ABC
-
P
O
a
s
M
P
P
T
a
l
g
o
rit
h
m
f
o
r
g
ri
d
c
o
n
n
e
c
ted
a
p
p
li
c
a
ti
o
n
s,”
En
e
rg
y
Rep
o
rts
,
v
o
l.
6
,
p
p
.
1
9
1
0
-
1
9
2
1
,
2
0
2
0
,
d
o
i:
1
0
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0
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6
/j
.
e
g
y
r.
2
0
2
0
.
0
7
.
0
1
9
.
[5
]
A.
F
.
M
irza
,
M
.
M
a
n
s
o
o
r
,
Q.
Li
n
g
,
B
.
Yin
,
a
n
d
M
.
Ya
q
o
o
b
Ja
v
e
d
,
“
A
S
a
lp
-
S
wa
rm
Op
ti
m
iza
ti
o
n
b
a
se
d
M
P
P
T
tec
h
n
iq
u
e
fo
r
h
a
rv
e
sti
n
g
m
a
x
imu
m
e
n
e
rg
y
fr
o
m
P
V
sy
ste
m
s
u
n
d
e
r
p
a
rti
a
l
sh
a
d
in
g
c
o
n
d
it
io
n
s
,
”
En
e
r
g
y
Co
n
v
e
rs
io
n
a
n
d
M
a
n
a
g
e
me
n
t
,
2
0
9
,
p
p
.
1
1
2
-
6
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5
,
2
0
2
0
,
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o
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1
0
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0
1
6
/j
.
e
n
c
o
n
m
a
n
.
2
0
2
0
.
1
1
2
6
2
5
.
[6
]
M
.
V.
d
a
Ro
c
h
a
,
L.
P
.
S
a
m
p
a
io
,
a
n
d
S
.
A.
O.
d
a
S
il
v
a
,
“
Co
m
p
a
ra
ti
v
e
a
n
a
l
y
sis
o
f
M
P
P
T
a
lg
o
rit
h
m
s
b
a
se
d
o
n
Ba
t
a
lg
o
rit
h
m
fo
r
P
V
sy
ste
m
s
u
n
d
e
r
p
a
rti
a
l
sh
a
d
in
g
c
o
n
d
it
io
n
,
”
S
u
sta
i
n
a
b
le
E
n
e
rg
y
T
e
c
h
n
o
lo
g
ies
a
n
d
As
se
ss
me
n
ts
,
v
o
l.
4
0
,
p
p
.
1
0
0
-
7
6
1
,
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
se
ta.2
0
2
0
.
1
0
0
7
6
1
.
[7
]
M
.
K.
Be
h
e
ra
a
n
d
L.
C.
S
a
ik
ia,
“
A
n
e
w
c
o
m
b
in
e
d
e
x
trem
e
lea
rn
in
g
m
a
c
h
in
e
v
a
riab
le
ste
e
p
e
st
g
ra
d
ien
t
a
sc
e
n
t
M
P
P
T
fo
r
P
V
sy
ste
m
b
a
se
d
o
n
o
p
ti
m
ize
d
P
I
-
F
OI
c
a
sc
a
d
e
c
o
n
tro
ll
e
r
u
n
d
e
r
u
n
ifo
rm
a
n
d
p
a
rti
a
l
sh
a
d
in
g
c
o
n
d
it
io
n
s,”
S
u
sta
in
a
b
le E
n
e
rg
y
T
e
c
h
n
o
l
o
g
ies
a
n
d
Asse
ss
me
n
ts
,
v
o
l.
4
2
,
p
p
.
1
0
0
8
5
9
,
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/
j.
se
ta.2
0
2
0
.
1
0
0
8
5
9
.
[8
]
S
h
.
Li
,
“
A
v
a
riab
le
-
we
a
th
e
r
-
p
a
ra
m
e
ter
M
P
P
T
c
o
n
tro
l
stra
teg
y
b
a
s
e
d
o
n
M
P
P
T
c
o
n
stra
in
t
c
o
n
d
it
i
o
n
s
o
f
P
V
s
y
ste
m
with
i
n
v
e
rter,”
E
n
e
rg
y
Co
n
v
e
rs
io
n
a
n
d
M
a
n
a
g
e
me
n
t
,
v
o
l.
1
9
7
,
p
p
.
1
1
1
8
7
3
,
2
0
1
9
.
[9
]
M
.
M
a
n
s
o
o
r,
A
.
F
.
M
irza
,
a
n
d
Q.
Li
n
g
,
“
Ha
rris
h
a
wk
o
p
ti
m
iza
t
io
n
b
a
se
d
M
P
P
T
c
o
n
tro
l
fo
r
P
V
sy
ste
m
s
u
n
d
e
r
p
a
rti
a
l
sh
a
d
i
n
g
c
o
n
d
i
ti
o
n
s,”
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o
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Cle
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[1
0
]
P
.
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rm
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,
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G
a
rg
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a
n
d
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.
M
a
h
a
jan
,
“
As
y
m
m
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tri
c
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l
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terv
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fu
z
z
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V
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it
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o
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IS
A
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s
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isa
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[1
1
]
A.
El
m
e
leg
i,
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.
Aly
,
E.
A
h
m
e
d
,
a
n
d
A
b
d
u
ll
a
h
G
.
Alh
a
r
b
i,
“
A
sim
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li
fied
p
h
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se
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sh
ift
P
WM
-
b
a
se
d
fe
e
d
fo
rwa
rd
di
strib
u
ted
M
P
P
T
m
e
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ri
d
c
o
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c
ted
c
a
sc
a
d
e
d
P
V
i
n
v
e
rter
s,”
S
o
l
a
r
E
n
e
rg
y
,
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l.
1
8
7
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p
.
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so
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e
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0
5
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1
.
[1
2
]
A.
Ra
j,
S
.
R.
Ary
a
,
a
n
d
J.
G
u
p
ta,
“
S
o
lar
P
V
a
rra
y
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b
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se
d
DC
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DC
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o
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v
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h
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P
P
T
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o
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lo
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p
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we
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p
p
li
c
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ti
o
n
s
,
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e
w
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b
le E
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re
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0
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.
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.
[1
3
]
B.
A.
Nu
m
a
n
,
A.
M
.
S
h
a
k
ir
,
a
n
d
A.
L.
M
a
h
m
o
o
d
,
“
P
h
o
t
o
v
o
lt
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ic
a
rra
y
m
a
x
imu
m
p
o
we
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n
t
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k
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rb
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n
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se
rv
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ti
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n
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l
g
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
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l
o
f
Po
w
e
r
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e
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tro
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ics
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d
Dr
ive
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.
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.
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8
.
[1
4
]
X.
Zh
a
n
g
,
Q.
G
a
o
,
Z.
G
u
o
,
H.
Zh
a
n
g
,
M
.
Li
,
a
n
d
F
.
Li
,
“
Co
o
r
d
in
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ted
c
o
n
tr
o
l
stra
teg
y
fo
r
a
P
V
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sto
ra
g
e
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ri
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o
n
n
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ted
sy
ste
m
b
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se
d
o
n
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sy
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c
h
ro
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o
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g
e
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ra
to
r,
”
Gl
o
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En
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ter
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0
3
.
[1
5
]
M
.
Ao
u
ri
r
e
t
a
l
.
,
“
No
n
li
n
e
a
r
c
o
n
tro
l
o
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m
u
lt
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ll
u
lar
sin
g
le
sta
g
e
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rid
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o
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e
c
ted
p
h
o
to
v
o
lt
a
ic
sy
st
e
m
s
with
sh
u
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a
c
ti
v
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p
o
we
r
flt
e
rin
g
c
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p
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b
il
it
y
,
”
I
FAC
-
P
a
p
e
rs
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n
L
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v
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l.
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1
2
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0
9
1
.
[1
6
]
S
.
Na
d
we
h
,
O.
Kh
a
d
d
a
m
,
G
.
Ha
y
e
k
,
B.
Atieh
,
a
n
d
H.
H.
Alh
e
l
o
u
,
“
Op
ti
m
iza
ti
o
n
o
f
P
&
P
I
c
o
n
tr
o
ll
e
r
p
a
ra
m
e
ters
fo
r
v
a
riab
le
sp
e
e
d
d
riv
e
sy
ste
m
s
u
sin
g
a
n
o
we
r
p
o
ll
in
a
ti
o
n
a
l
g
o
rit
h
m
,
”
He
li
y
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,
v
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l
.
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p
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,
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.
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0
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e
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4
8
.
[1
7
]
M
.
S
Ch
o
n
g
,
D.
Um
so
n
st,
a
n
d
H.
S
a
n
d
b
e
rg
,
“
Lo
c
a
l
Lo
c
a
l
v
o
lt
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g
e
v
o
lt
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g
e
c
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tr
o
l
c
o
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tr
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c
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l
v
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lt
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g
e
with
Lo
c
a
l
v
o
lt
a
g
e
c
o
n
tro
l,
”
IFA
C
Pa
p
e
rs
On
L
in
e
,
v
o
l.
5
2
,
p
p
.
1
6
3
-
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6
/
j.
ifac
o
l.
2
0
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9
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1
2
.
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5
2
.
[1
8
]
A.
M
.
Ho
wla
d
e
r,
S
.
S
a
d
o
y
a
m
a
,
Leo
n
R.
Ro
o
se
,
a
n
d
Ya
n
Ch
e
n
,
“
Ac
ti
v
e
p
o
we
r
c
o
n
tro
l
t
o
m
it
ig
a
te
v
o
lt
a
g
e
a
n
d
fre
q
u
e
n
c
y
d
e
v
iati
o
n
s f
o
r
t
h
e
sm
a
rt
g
ri
d
u
si
n
g
sm
a
rt
P
V i
n
v
e
rters
,
”
Ap
p
li
e
d
E
n
e
rg
y
,
v
o
l.
2
5
8
,
p
p
.
1
1
4
0
0
0
,
2
0
2
0
.
[1
9
]
I.
Kim
,
a
n
d
R.
G
.
Ha
rley
,
“
Ex
a
m
in
a
ti
o
n
o
f
th
e
e
ffe
c
t
o
f
t
h
e
re
a
c
ti
v
e
p
o
we
r
c
o
n
tr
o
l
o
f
p
h
o
t
o
v
o
lt
a
ic
sy
ste
m
s
o
n
e
lec
tri
c
p
o
we
r
g
rid
s
a
n
d
t
h
e
d
e
v
e
lo
p
m
e
n
t
o
f
a
v
o
lt
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g
e
-
re
g
u
la
ti
o
n
m
e
th
o
d
t
h
a
t
c
o
n
si
d
e
rs
fe
e
d
e
r
imp
e
d
a
n
c
e
se
n
siti
v
it
y
,
”
El
e
c
tric P
o
we
r
S
y
ste
ms
Res
e
a
rc
h
,
v
o
l
.
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8
0
,
p
p
.
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3
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0
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o
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/
j.
e
p
sr.
2
0
1
9
.
1
0
6
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3
0
.
[2
0
]
B.
Lek
o
u
a
g
h
e
t
,
A.
Bo
u
k
a
b
o
u
,
N
.
Lo
u
rc
i,
a
n
d
K.
Be
d
ri
n
e
,
“
Co
n
t
ro
l
o
f
P
V
g
ri
d
c
o
n
n
e
c
ted
s
y
ste
m
s
u
sin
g
M
P
C
tec
h
n
iq
u
e
a
n
d
d
iffere
n
t
in
v
e
rter
c
o
n
fig
u
ra
ti
o
n
m
o
d
e
ls,”
El
e
c
tric
Po
we
r
S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
1
5
4
,
p
p
.
2
8
7
-
2
9
8
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6
/
j.
e
p
sr.
2
0
1
7
.
0
8
.
0
2
7
[2
1
]
P
.
Na
jafi,
A.
H.
Vik
i,
a
n
d
M
.
S
h
a
h
p
a
ra
sti,
“
No
v
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l
sp
a
c
e
v
e
c
to
r
-
b
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se
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c
o
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with
d
c
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lan
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in
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c
a
p
a
b
il
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y
f
o
r
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tch
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v
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in
b
ip
o
lar
h
y
b
ri
d
m
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ri
d
,
”
S
u
st
a
in
a
b
le
E
n
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id
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n
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.
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5
6
.
[2
2
]
J.
P
.
Ro
se
ly
n
e
t
a
l
.
,
“
De
sig
n
a
n
d
imp
lem
e
n
tatio
n
o
f
fu
z
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y
l
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a
se
d
m
o
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ifi
e
d
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ti
v
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p
o
we
r
c
o
n
tro
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o
f
in
v
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f
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lo
w
v
o
lt
a
g
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rid
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th
ro
u
g
h
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n
h
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n
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e
m
e
n
t
in
g
r
id
c
o
n
n
e
c
ted
so
lar
P
V
s
y
ste
m
,
”
Co
n
tr
o
l
E
n
g
in
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rin
g
Pra
c
ti
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e
,
v
o
l.
1
0
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,
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p
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4
4
9
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o
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.
c
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g
p
ra
c
.
2
0
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0
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1
0
4
4
9
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
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694
I
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t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2492
–
2
5
0
0
2500
[2
3
]
S
.
F
.
Zare
i,
H.
M
o
k
h
tari,
M
.
A.
G
h
a
se
m
i,
S
.
P
e
y
g
h
a
m
i,
P
.
Da
v
a
ri,
a
n
d
F
.
Blaa
b
jerg
,
“
DC
-
li
n
k
lo
o
p
b
a
n
d
wi
d
t
h
se
lec
ti
o
n
stra
teg
y
fo
r
g
r
id
-
c
o
n
n
e
c
ted
in
v
e
rters
c
o
n
sid
e
ri
n
g
p
o
we
r
q
u
a
li
ty
re
q
u
irem
e
n
ts,”
El
e
c
trica
l
Po
we
r
a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
1
1
9
,
p
p
.
1
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8
7
9
,
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0
2
0
,
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0
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ij
e
p
e
s.
2
0
2
0
.
1
0
5
8
7
9
.
[2
4
]
G
.
G
a
n
e
s
a
n
,
M
.
K.
M
ish
ra
,
K.
Ja
y
a
p
ra
k
a
sh
,
a
n
d
P
.
J.
S
u
re
sh
b
a
b
u
,
“
S
imu
lati
o
n
S
tu
d
y
o
f
Hy
s
tere
sis
Cu
rre
n
t
Co
n
tr
o
ll
e
d
S
in
g
le
-
P
h
a
se
In
v
e
rters
fo
r
P
h
o
to
V
o
lt
a
ic
S
y
ste
m
s
with
R
e
d
u
c
e
d
Ha
rm
o
n
ics
lev
e
l,
”
In
ter
n
a
ti
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