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MPPT
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d
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ac
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id
1.
I
NT
RO
D
UCT
I
O
N
So
lar
en
er
g
y
is
an
a
b
u
n
d
an
t
an
d
s
u
s
tain
ab
le
r
e
n
ewa
b
le
r
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s
o
u
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ce
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m
ak
i
n
g
it
a
v
ital
alte
r
n
ativ
e
to
d
ep
letin
g
f
o
s
s
il
f
u
els
[
1
]
.
I
ts
u
tili
za
tio
n
th
r
o
u
g
h
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
p
r
o
d
u
ce
s
n
o
ca
r
b
o
n
em
is
s
io
n
s
,
th
u
s
co
n
tr
ib
u
tin
g
to
t
h
e
m
itig
atio
n
o
f
clim
ate
ch
a
n
g
e
a
n
d
air
p
o
ll
u
tio
n
[
2
]
,
[
3
]
.
Un
s
tab
le
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
,
in
clu
d
in
g
f
l
u
ctu
atio
n
in
s
o
lar
ir
r
ad
ian
ce
an
d
tem
p
er
atu
r
e,
ca
n
s
er
io
u
s
ly
im
p
ed
e
th
e
ef
f
icien
cy
o
f
PV
s
y
s
tem
s
[
4
]
.
T
h
er
ef
o
r
e,
it
is
cr
u
cial
t
o
d
ev
el
o
p
m
eth
o
d
s
t
h
at
ca
n
m
ax
im
ize
p
o
wer
o
u
tp
u
t
f
r
o
m
PV
ev
en
u
n
d
er
u
n
p
r
e
d
ictab
le
o
p
e
r
atin
g
en
v
ir
o
n
m
en
ts
.
T
o
o
v
er
c
o
m
e
th
is
ch
allen
g
e,
t
h
e
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
a
ck
in
g
(
MPPT)
alg
o
r
ith
m
is
ess
en
tial
f
o
r
en
s
u
r
in
g
t
h
at
PV
s
y
s
tem
alwa
y
s
o
p
er
ate
at
th
eir
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
[
5
]
-
[
7
]
.
T
h
r
ee
m
ain
class
es
o
f
MPPT
alg
o
r
ith
m
s
ex
is
t:
co
n
v
en
tio
n
al
[
8
]
,
[
9
]
,
in
tellig
en
t
[
1
0
]
-
[
1
2
]
,
an
d
o
p
tim
izatio
n
[
1
3
]
,
[
1
4
]
.
T
h
e
p
er
tu
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b
an
d
o
b
s
er
v
e
(
P&
O)
a
n
d
in
cr
e
m
en
tal
co
n
d
u
cta
n
ce
(
I
NC
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alg
o
r
ith
m
s
ar
e
p
o
p
u
lar
ch
o
ices
d
u
e
to
th
eir
d
ir
ec
t
n
atu
r
e,
ea
s
e
o
f
u
s
e,
an
d
m
in
i
m
al
co
m
p
u
tatio
n
al
r
eq
u
ir
em
e
n
ts
[
1
5
]
,
[
1
6
]
.
Nev
er
t
h
eless
,
th
ese
m
eth
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d
s
ex
h
ib
it
n
o
tab
le
wea
k
n
ess
es,
in
clu
d
in
g
s
lo
w
co
n
v
er
g
en
ce
a
n
d
c
o
n
s
i
d
er
ab
le
p
o
we
r
f
lu
ctu
atio
n
s
n
ea
r
th
e
MPP,
wh
ich
m
ay
co
m
p
r
o
m
is
e
th
e
s
y
s
tem
’
s
ef
f
icien
cy
in
d
y
n
am
ic
wea
th
e
r
co
n
d
iti
o
n
s
[
7
]
,
[
1
7
]
.
On
th
e
o
th
er
h
an
d
,
th
e
u
s
e
o
f
in
tellig
en
t
tech
n
i
q
u
es
in
MPPT
in
cr
ea
s
es
co
m
p
le
x
ity
,
wh
ic
h
lead
s
to
h
i
g
h
er
co
s
ts
[
1
8
]
,
d
a
ta
s
ca
r
city
,
an
d
th
e
ch
allen
g
e
o
f
alg
o
r
ith
m
f
in
e
-
tu
n
in
g
[
1
9
]
.
Op
tim
izatio
n
tech
n
iq
u
es
also
p
r
esen
t
n
u
m
er
o
u
s
ch
allen
g
es
s
u
ch
as
p
ar
am
eter
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itializatio
n
,
p
ar
a
m
eter
tu
n
in
g
,
an
d
th
e
n
u
m
b
er
o
f
iter
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n
s
[
2
0
]
.
T
h
e
r
e
f
o
r
e
,
t
h
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s
p
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x
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m
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s
.
A
n
i
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n
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I
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Dec
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20
25
:
2757
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r
i
m
e
n
t
a
l
t
e
s
t
i
n
g
i
n
r
e
a
l
c
o
n
d
i
t
i
o
n
s
,
c
o
m
p
a
r
i
n
g
i
ts
p
o
w
e
r
o
u
t
p
u
t
w
i
t
h
P
&
O
a
n
d
I
N
C
al
g
o
r
i
t
h
m
s
.
2.
Q
UANTI
T
A
T
I
V
E
F
O
RM
U
L
AT
I
O
N
O
F
P
H
O
T
O
VO
L
T
AIC
Fig
u
r
e
1
d
is
p
lay
s
th
e
co
n
f
ig
u
r
atio
n
o
f
th
e
PV
ce
ll
eq
u
iv
alen
t
cir
cu
it
em
p
lo
y
in
g
a
s
in
g
le
d
io
d
e
co
m
m
o
n
l
y
u
s
ed
to
p
e
r
f
o
r
m
ch
a
r
ac
ter
is
tic
an
aly
s
is
.
Ma
th
em
atica
lly
,
th
e
PV
m
o
d
u
le
in
Fig
u
r
e
1
ca
n
b
e
m
o
d
elle
d
u
s
in
g
(
1
)
-
(
4
)
[
2
1
]
,
[
2
2
]
.
ℎ
=
[
+
(
−
298
)
∗
]
(
1
)
ℎ
is
th
e
p
h
o
to
cu
r
r
en
t,
is
th
e
s
h
o
r
t
-
cir
cu
it
cu
r
r
en
t
o
f
th
e
PV
m
o
d
u
le
at
a
tem
p
er
at
u
r
e
o
f
2
5
°
C
an
d
s
o
lar
r
ad
iatio
n
h
as
in
ten
s
ity
o
f
ap
p
r
o
x
im
ately
1
0
0
0
W
/m
2
,
is
t
h
e
tem
p
er
atu
r
e
co
ef
f
icien
t
o
f
cu
r
r
en
t,
is
th
e
tem
p
er
atu
r
e
o
f
th
e
PV m
o
d
u
le
wh
en
o
p
er
atin
g
(
K)
,
s
o
lar
r
ad
iatio
n
v
alu
e
wh
en
o
p
er
atin
g
(
W
/m
2
)
,
an
d
is
s
o
lar
r
ad
iatio
n
v
al
u
e
o
f
th
e
s
tan
d
ar
d
PV m
o
d
u
le
(
W
/m
2
)
.
=
[
(
)
−
1
]
(
2
)
T
h
e
v
ar
iab
le
d
ef
in
e
t
h
e
m
o
d
u
le’
s
r
ev
er
s
e
leak
ag
e
p
a
r
am
eter
,
q
is
th
e
elec
tr
o
n
ch
ar
g
e
(
1
.
6
×
10
-
19
K)
,
is
th
e
m
o
d
u
le
o
p
en
cir
c
u
it
v
o
lt
ag
e,
is
th
e
to
tal
n
u
m
b
er
o
f
s
er
ies
ce
lls
,
A
s
th
e
id
ea
lity
f
ac
to
r
,
a
n
d
K
is
B
o
ltzm
an
n
'
s
co
n
s
tan
t (
1
.
3
8
×
10
-
23
J
/K)
.
0
=
[
]
3
[
{
1
−
1
}
]
(
3
)
0
r
ep
r
esen
ts
th
e
s
atu
r
atio
n
cu
r
r
e
n
t
v
alu
e
o
f
th
e
PV
m
o
d
u
le,
is
th
e
tem
p
er
atu
r
e
r
ef
e
r
en
ce
(
2
9
8
K)
,
an
d
is
th
e
b
an
d
g
ap
v
alu
e
o
f
s
ilico
n
(
1
.
1
eV)
.
=
∗
ℎ
−
∗
[
{
∗
(
+
∗
)
}
−
1
]
(
4
)
Me
an
wh
ile,
an
d
ar
e
th
e
v
o
lta
g
e
an
d
cu
r
r
en
t
o
f
PV
m
o
d
u
le
o
u
tp
u
t,
r
ep
r
esen
ts
th
e
n
u
m
b
e
r
o
f
p
ar
allel
-
co
n
n
ec
ted
ce
lls
,
an
d
is
th
e
s
er
ies r
esis
tan
ce
v
alu
e.
Fig
u
r
e
1
.
Sin
g
le
d
io
d
e
e
q
u
iv
al
en
t c
ir
cu
it u
s
ed
f
o
r
m
o
d
elin
g
t
h
e
PV c
ell
Ma
n
y
f
ac
t
o
r
s
in
f
l
u
en
ce
th
e
p
r
o
d
u
ctio
n
o
f
elec
tr
icity
th
r
o
u
g
h
s
o
lar
p
an
els
s
u
ch
as
s
o
lar
r
ad
iatio
n
,
tem
p
er
atu
r
e,
win
d
s
p
ee
d
,
air
h
u
m
id
ity
,
s
h
ad
o
w
ef
f
ec
ts
,
a
n
d
p
an
el
clea
n
lin
ess
(
d
u
s
t
an
d
o
th
e
r
d
eb
r
is
o
n
th
e
s
o
lar
p
an
el'
s
s
u
r
f
ac
e)
[
2
3
]
,
[
2
4
]
.
T
h
e
(
5
)
ca
n
b
e
u
s
ed
as a
th
eo
r
eti
ca
l b
asis
in
ca
lcu
latin
g
th
e
ele
ctr
icity
g
en
er
ated
b
y
s
o
lar
p
an
els
[
2
5
]
.
=
[
1
+
(
−
)
]
(
5
)
is
PV
o
u
tp
u
t
(
k
W
)
,
is
th
e
s
o
lar
p
an
el’
s
elec
tr
ical
p
o
wer
at
ST
C
(
k
W
)
,
is
th
e
am
o
u
n
t
o
f
s
o
lar
r
ad
iatio
n
r
ec
eiv
ed
b
y
s
o
lar
p
a
n
els
(
W
/m
2)
,
is
t
h
e
s
tan
d
ar
d
s
o
lar
r
a
d
iatio
n
in
ten
s
ity
(
W
/m
2
)
,
is
th
e
p
o
we
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
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i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
n
h
a
n
ce
d
in
cremen
ta
l c
o
n
d
u
cta
n
ce
MPP
T me
th
o
d
fo
r
ma
xi
miz
in
g
p
h
o
to
vo
lta
ic
p
o
w
er
…
(
A
s
n
il
A
s
n
il
)
2759
co
ef
f
icien
t w
ith
r
esp
ec
t to
tem
p
er
atu
r
e,
is
th
e
tem
p
er
atu
r
e
o
f
th
e
s
o
lar
p
an
el
wh
en
o
p
er
ati
n
g
(
°
C
)
,
d
an
is
th
e
n
o
r
m
al
tem
p
e
r
atu
r
e
(
2
5
°
C
)
.
ca
n
also
b
e
ca
lcu
lated
u
s
in
g
(
6
)
.
=
+
(
6
)
is
air
tem
p
er
atu
r
e
an
d
is
a
s
o
lar
co
n
s
tan
t.
Fu
r
th
e
r
m
o
r
e
,
(
6
)
m
ay
b
e
e
x
p
r
ess
ed
as (
7
)
.
=
(
+
−
+
)
(
7
)
3.
DC
-
DC
B
O
O
S
T
CO
NVER
T
E
R
A
DC
-
DC
b
o
o
s
t
co
n
v
e
r
ter
s
er
v
es
as
a
v
ital
c
o
m
p
o
n
en
t
with
in
a
PV
s
y
s
tem
,
p
r
im
ar
ily
to
e
lev
ate
th
e
o
u
tp
u
t
v
o
ltag
e
.
I
ts
cir
cu
it
is
illu
s
tr
ated
in
Fig
u
r
e
2
.
T
h
e
(
8
)
–
(
1
1
)
[
2
6
]
,
[
2
7
]
is
em
p
lo
y
ed
to
ascer
tain
th
e
p
ar
am
eter
v
al
u
es o
f
th
e
b
o
o
s
t
co
n
v
er
ter
,
as illu
s
tr
ated
in
Fig
u
r
e
2
.
=
1
1
−
(
8
)
1
≥
8
2
0
.
01
(
9
)
2
≥
0
.
02
(
1
0
)
=
(
1
−
2
)
(
1
1
)
B
y
em
p
lo
y
in
g
(
8
)
to
(
1
1
)
,
th
e
p
ar
am
eter
s
o
f
th
e
b
o
o
s
t
co
n
v
e
r
ter
u
s
ed
in
t
h
e
d
esig
n
e
d
PV
s
y
s
tem
ca
n
b
e
ac
q
u
ir
e
d
as illu
s
tr
ated
in
T
ab
le
1
.
Fig
u
r
e
2
.
B
o
o
s
t c
o
n
v
er
ter
ci
r
c
u
it
T
ab
le
1
.
C
alcu
lated
p
a
r
am
eter
s
f
o
r
b
o
o
s
t c
o
n
v
er
ter
No
C
o
m
p
o
n
e
n
t
V
a
l
u
e
1
L
2
.
2
mH
2
C
1
1
0
0
u
F
3
C
2
1
0
0
uF
4
F
7
,
8
1
2
H
z
5
R
1
3
5
O
h
m
6
D
0
.
7
4.
M
E
T
H
O
D
A
p
r
o
p
o
s
ed
h
y
b
r
id
MPPT
s
y
s
tem
,
wh
ich
is
d
esig
n
ed
to
m
ax
im
ize
p
o
wer
g
en
er
atio
n
i
n
ch
a
n
g
in
g
en
v
ir
o
n
m
en
ts
,
is
th
o
r
o
u
g
h
l
y
d
escr
ib
ed
in
ter
m
s
o
f
its
d
esig
n
an
d
im
p
lem
e
n
tatio
n
in
th
is
s
ec
tio
n
.
4
.
1
.
M
a
x
i
m
um
po
wer
po
int
t
ra
ck
ing
a
lg
o
rit
hm
T
h
is
r
esear
ch
p
r
o
p
o
s
ed
a
n
o
v
e
l
h
y
b
r
id
MPPT
alg
o
r
ith
m
th
at
in
tellig
en
tly
co
m
b
in
es
th
e
c
o
n
v
en
tio
n
al
I
NC
m
eth
o
d
with
an
en
h
a
n
ce
d
I
NC
d
ev
elo
p
ed
u
s
in
g
VSS co
n
ce
p
t.
T
h
e
s
elec
tio
n
o
f
t
h
e
o
p
er
atin
g
alg
o
r
ith
m
is
d
eter
m
in
ed
b
y
th
e
s
o
lar
i
r
r
ad
ia
n
ce
v
alu
e.
Sh
o
u
ld
th
e
i
n
s
o
latio
n
b
e
g
r
ea
te
r
th
an
5
0
0
W
/m
2
,
th
e
MPPT
alg
o
r
ith
m
o
p
er
ates
u
s
in
g
th
e
VSS
co
n
ce
p
t,
as
o
u
tlin
ed
in
(
1
2
)
[
2
8
]
,
[
2
9
]
.
T
h
is
ap
p
r
o
ac
h
allo
ws
f
o
r
an
a
d
ap
tiv
e
ad
ju
s
tm
en
t
o
f
th
e
s
tep
s
ize
to
ac
h
iev
e
f
ast co
n
v
er
g
en
ce
to
t
h
e
MPP u
n
d
e
r
h
ig
h
i
r
r
ad
ian
ce
c
o
n
d
itio
n
s
.
=
∗
|
|
(
1
2
)
W
h
e
r
e
S
t
e
p
i
s
t
h
e
a
d
j
u
s
t
m
e
n
t
s
t
e
p
s
i
z
e
,
N
i
s
t
h
e
s
c
a
l
i
n
g
f
a
c
t
o
r
a
n
d
dP
i
s
t
h
e
c
h
a
n
g
e
i
n
t
h
e
P
V
s
y
s
t
e
m
’
s
p
o
w
e
r
o
u
t
p
u
t
.
T
h
e
u
s
e
o
f
(
1
2
)
e
n
s
u
r
e
s
t
h
a
t
t
h
e
s
t
e
p
s
i
z
e
b
e
c
o
m
e
s
l
a
r
g
e
r
w
h
e
n
t
h
e
s
y
s
t
e
m
i
s
f
a
r
f
r
o
m
t
h
e
M
P
P
a
n
d
s
h
r
i
n
k
s
a
s
i
t
a
p
p
r
o
a
c
h
e
s
t
h
e
M
P
P
,
t
h
e
r
e
b
y
r
e
d
u
c
i
n
g
p
o
w
e
r
o
s
c
i
l
l
a
t
i
o
n
a
n
d
a
c
c
e
l
e
r
a
t
i
n
g
c
o
n
v
e
r
g
e
n
c
e
.
C
o
n
v
e
r
s
e
l
y
,
i
f
t
h
e
s
o
l
a
r
i
r
r
a
d
i
a
n
c
e
v
a
l
u
e
i
s
l
e
s
s
t
h
a
n
5
0
0
W
/
m
2
,
t
h
e
c
o
n
v
e
n
t
i
o
n
a
l
I
N
C
a
l
g
o
r
i
t
h
m
w
i
l
l
o
p
e
r
a
t
e
.
T
h
i
s
c
h
o
i
c
e
i
s
b
a
s
e
d
o
n
t
h
e
r
o
b
u
s
t
n
e
s
s
a
n
d
c
o
r
r
e
c
t
n
e
s
s
o
f
t
h
e
c
o
n
v
e
n
t
i
o
n
a
l
I
N
C
m
e
t
h
o
d
u
n
d
e
r
l
o
w
i
r
r
a
d
i
a
n
c
e
c
o
n
d
i
t
i
o
n
s
.
T
h
is
s
witch
in
g
m
ec
h
an
is
m
b
ased
o
n
th
e
5
0
0
W
/m
2
th
r
esh
o
ld
is
a
k
ey
a
d
v
an
tag
e
th
at
d
is
tin
g
u
is
h
es
th
is
ap
p
r
o
ac
h
f
r
o
m
o
th
e
r
ad
a
p
tiv
e
m
eth
o
d
s
.
T
h
is
co
m
b
in
atio
n
ai
m
s
to
ac
h
ie
v
e
a
b
alan
ce
b
etwe
en
f
ast c
o
n
v
er
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ig
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d
itio
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r
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p
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o
n
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itio
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Fo
r
a
cl
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n
d
er
s
tan
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i
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g
o
f
th
e
alg
o
r
ith
m
’
s
im
p
lem
en
tatio
n
,
r
ef
er
t
o
t
h
e
f
lo
wch
ar
t i
n
Fig
u
r
e
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2757
-
2
7
6
7
2760
Fig
u
r
e
3
.
T
h
e
p
r
o
p
o
s
ed
MPPT
alg
o
r
ith
m
4
.
2
.
Sy
s
t
em
a
nd
ex
perim
ent
a
l pa
ra
m
et
er
s
des
cr
iptio
n
T
h
e
ex
p
er
im
en
tal
m
eth
o
d
o
lo
g
y
em
p
lo
y
e
d
to
e
v
alu
ate
th
e
M
PP
T
s
y
s
tem
’
s
p
er
f
o
r
m
an
ce
is
d
etailed
in
Fig
u
r
e
4
,
wh
ich
illu
s
tr
ates
its
m
ain
co
m
p
o
n
en
ts
.
T
h
e
s
y
s
tem
is
p
o
wer
ed
b
y
th
r
ee
Gr
ee
n
tek
MSP
-
1
0
0
W
PV
m
o
d
u
les,
ea
c
h
with
a
ca
p
ac
ity
o
f
1
0
0
W
p
,
wh
ich
co
n
v
er
t
s
o
la
r
en
er
g
y
in
to
elec
tr
ical
p
o
wer
.
A
p
o
wer
co
n
v
er
ter
,
s
p
ec
if
ically
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
,
is
a
cr
itical
p
ar
t
o
f
th
is
en
er
g
y
co
n
v
er
s
io
n
s
y
s
tem
,
u
s
ed
to
i
n
cr
ea
s
e
th
e
v
o
ltag
e
f
r
o
m
th
e
PV
m
o
d
u
les.
T
h
e
co
n
v
er
ter
is
co
n
tr
o
lled
b
y
a
m
icr
o
co
n
tr
o
ller
th
at
g
en
er
ates
an
8
-
b
it
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
s
ig
n
al.
T
h
is
p
r
o
v
id
es
2
5
6
d
is
ti
n
c
t
d
u
ty
c
y
cle
lev
els,
en
ab
li
n
g
p
r
ec
is
e
v
o
ltag
e
ad
ju
s
tm
en
ts
to
tr
ac
k
th
e
MPP.
Fig
u
r
e
4
.
T
h
e
d
esig
n
e
d
PV sy
s
tem
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
6
9
4
E
n
h
a
n
ce
d
in
cremen
ta
l c
o
n
d
u
cta
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MPP
T me
th
o
d
fo
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(
A
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A
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2761
Fu
n
ctio
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in
g
as
th
e
s
y
s
tem
’
s
co
r
e
in
tellig
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o
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ith
m
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n
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tan
tly
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s
er
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th
e
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o
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le’
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tp
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t v
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(
V
pv
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,
cu
r
r
en
t
(
I
pv
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,
an
d
ir
r
ad
ian
ce
(
G
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.
Usi
n
g
th
i
s
d
ata,
th
e
alg
o
r
ith
m
ca
lcu
lates th
e
o
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tim
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u
t
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cy
cle.
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t
is
im
p
o
r
tan
t
to
n
o
te
th
at
th
e
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n
tr
o
l
f
r
e
q
u
en
cy
an
d
s
am
p
lin
g
tim
e
ar
e
im
p
lem
en
ted
with
d
elay
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)
co
m
m
a
n
d
s
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e
m
ic
r
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co
n
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d
e
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esu
ltin
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a
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ar
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s
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lin
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te
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v
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l.
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it
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th
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th
e
im
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en
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em
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e
f
f
ec
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atin
g
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e
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e
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itio
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r
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n
v
er
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th
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o
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ith
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n
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ig
n
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to
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r
o
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u
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ig
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f
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ain
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o
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th
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n
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e
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ter
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o
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u
s
tain
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y
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tem
’
s
ef
f
icien
cy
,
th
e
f
u
n
d
a
m
en
tal
r
o
le
o
f
th
e
MPPT
alg
o
r
ith
m
is
to
m
ain
tain
th
e
PV
m
o
d
u
le’
s
o
p
er
atio
n
at
its
MPP,
th
er
eb
y
s
u
s
tain
in
g
th
e
s
y
s
tem
’
s
ef
f
icien
cy
.
T
h
e
s
ig
n
al
g
en
er
ated
b
y
th
e
alg
o
r
ith
m
d
i
r
ec
tly
co
n
tr
o
ls
th
e
p
o
wer
co
n
v
er
ter
’
s
d
u
t
y
cy
cle
to
ac
h
iev
e
th
is
o
b
jectiv
e.
T
h
e
co
n
v
er
ter
’
s
p
ar
am
eter
s
wer
e
c
alcu
lated
b
y
a
p
p
ly
in
g
(
8
)
to
(
1
1
)
an
d
ar
e
p
r
esen
ted
in
T
a
b
le
1
.
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
PV
s
y
s
tem
co
n
s
tr
u
cted
f
o
r
th
is
r
esear
c
h
,
as
illu
s
tr
at
ed
in
Fig
u
r
es
5
a
n
d
6
,
is
a
p
h
y
s
ical
im
p
lem
en
tatio
n
o
f
th
e
m
et
h
o
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g
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d
escr
ib
ed
in
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h
e
p
r
e
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io
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ec
tio
n
.
Fig
u
r
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5
s
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o
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e
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er
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o
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o
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e
ex
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im
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tal
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y
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clu
d
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e
PV
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o
d
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les
u
s
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eir
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h
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ical
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n
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ig
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r
atio
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Me
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ile,
Fig
u
r
e
6
d
is
p
lay
s
th
e
MPPT
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n
tr
o
l
s
y
s
tem
u
tili
zin
g
a
DC
-
D
C
b
o
o
s
t
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n
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ter
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ased
o
n
an
Ar
d
u
in
o
Un
o
m
icr
o
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n
tr
o
ller
.
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o
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llect
ex
p
er
im
en
tal
d
ata
f
r
o
m
all
s
e
n
s
o
r
s
an
d
m
o
n
ito
r
th
e
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tr
i
ca
l
p
ar
am
eter
s
,
th
is
r
esear
ch
u
tili
ze
d
p
ar
allax
d
ata
ac
q
u
is
itio
n
(
PLX
-
DAQ)
,
wh
ic
h
en
ab
le
d
r
ea
l
-
tim
e
d
ata
o
b
s
er
v
atio
n
in
Mic
r
o
s
o
f
t
E
x
ce
l
f
o
r
m
at
o
n
a
p
er
s
o
n
al
c
o
m
p
u
ter
(
PC
)
.
T
h
e
s
y
s
tem
u
n
d
er
wen
t
a
th
r
ee
-
d
a
y
test
in
g
p
er
io
d
to
ev
alu
ate
its
ef
f
ec
tiv
en
ess
u
n
d
er
v
ar
io
u
s
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
,
with
Fig
u
r
es 7
-
9
p
r
esen
tin
g
th
e
test
r
esu
lt.
Fig
u
r
e
5
.
T
h
e
b
u
ilt PV sy
s
tem
u
s
ed
in
th
is
r
esear
ch
(
a)
(
b
)
Fig
u
r
e
6
.
T
h
e
h
ar
d
war
e
s
y
s
tem
:
(
a)
a
b
o
o
s
t c
o
n
v
er
ter
an
d
(
b
)
h
ar
d
war
e
co
n
n
ec
ted
to
a
co
m
p
u
ter
f
o
r
m
ea
s
u
r
em
en
t m
o
n
ito
r
in
g
5
.
1
.
Da
ily
perf
o
rm
a
nce
a
na
ly
s
is
Ov
e
r
a
t
h
r
ee
-
d
a
y
p
e
r
i
o
d
,
t
h
e
th
r
e
e
MPP
T
a
lg
o
r
it
h
m
s
w
er
e
s
u
b
je
ct
ed
t
o
tes
ti
n
g
t
o
d
et
er
m
i
n
e
th
ei
r
p
e
r
f
o
r
m
a
n
c
e,
w
it
h
e
ac
h
d
a
y
h
av
i
n
g
d
i
f
f
er
e
n
t
s
o
la
r
r
a
d
ia
ti
o
n
c
o
n
d
iti
o
n
s
.
T
h
e
o
u
t
p
u
t
d
at
a
f
r
o
m
e
ac
h
al
g
o
r
it
h
m
was
d
i
r
e
ctl
y
c
o
m
p
ar
e
d
t
o
ass
es
s
its
e
f
f
ec
ti
v
e
n
ess
.
F
i
g
u
r
e
7
p
r
e
s
en
ts
t
h
e
co
m
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le
te
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ile
o
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est
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o
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u
c
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th
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ir
s
t
d
a
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,
w
h
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ch
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u
r
r
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t
a
n
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tr
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r
.
As
d
ep
i
cte
d
in
Fi
g
u
r
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7
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a
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,
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e
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o
la
r
r
a
d
ia
ti
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n
p
att
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o
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e
d
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ch
in
g
its
p
e
ak
at
m
id
d
ay
a
n
d
t
h
e
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2757
-
2
7
6
7
2762
d
e
cr
ea
s
i
n
g
.
I
n
t
h
es
e
s
it
u
a
ti
o
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ed
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r
o
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c
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t
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h
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NC
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o
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t
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n
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g
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r
e
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(
b
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.
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a
r
l
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s
h
o
w
n
in
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ig
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r
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c
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,
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t
p
u
t
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u
r
r
en
t
was
m
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r
e
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m
i
n
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t
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s
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g
th
e
p
r
o
p
o
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g
o
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e
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n
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h
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g
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l
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ct
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a
ti
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o
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r
r
e
d
,
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o
ll
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d
b
y
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h
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I
N
C
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n
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P
&
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al
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s
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e
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ic
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w
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er
ate
d
,
s
h
o
w
n
in
Fig
u
r
e
7
(
d
),
was
m
o
s
t
s
i
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n
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f
ic
an
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i
n
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y
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te
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d
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NC
a
n
d
P
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.
(
a)
(
b
)
(
c)
(
d
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Fig
u
r
e
7
.
T
h
e
s
y
s
tem
test
r
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lts
o
n
th
e
f
ir
s
t d
ay
:
(
a)
ir
r
a
d
ian
ce
,
(
b
)
PV o
u
tp
u
t v
o
ltag
e,
(
c
)
PV o
u
tp
u
t c
u
r
r
en
t,
an
d
(
d
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p
o
we
r
g
en
e
r
ated
T
h
e
test
r
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p
r
o
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ile
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o
r
th
e
s
ec
o
n
d
d
a
y
ca
n
b
e
s
ee
n
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n
Fig
u
r
e
8
,
T
h
e
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
,
p
ar
ticu
lar
ly
th
e
s
o
lar
r
ad
iatio
n
in
ten
s
ity
as
d
ep
icted
in
Fig
u
r
e
8
(
a)
,
s
lig
h
tly
in
cr
ea
s
ed
co
m
p
a
r
ed
to
th
e
f
ir
s
t
d
ay
.
T
h
is
p
h
en
o
m
en
o
n
was
ca
u
s
ed
b
y
h
ig
h
er
tem
p
er
atu
r
es
an
d
t
h
e
p
r
esen
ce
o
f
cl
o
u
d
s
t
h
at
b
l
o
ck
ed
s
u
n
lig
h
t
f
r
o
m
r
ea
ch
in
g
th
e
s
u
r
f
ac
e
o
f
th
e
s
o
lar
p
an
els.
Un
d
e
r
th
ese
co
n
d
itio
n
s
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
d
em
o
n
s
tr
ates
a
s
u
p
er
io
r
ab
ilit
y
to
tr
ac
k
th
e
MPP,
y
ield
in
g
h
ig
h
er
v
o
ltag
e
an
d
cu
r
r
en
t
v
alu
es
co
m
p
ar
e
d
to
th
e
I
NC
an
d
P&
O
alg
o
r
ith
m
s
,
as
s
h
o
wn
in
Fig
u
r
es
8
(
b
)
an
d
8
(
c)
.
T
h
is
p
r
o
v
es
th
e
ef
f
ec
tiv
en
ess
o
f
t
h
e
VSS
m
o
d
e
i
n
o
p
ti
m
izin
g
p
o
wer
u
n
d
er
h
ig
h
r
ad
iatio
n
co
n
d
itio
n
s
.
T
h
e
co
n
d
itio
n
s
o
n
th
e
s
ec
o
n
d
d
ay
r
esu
lted
in
lo
wer
elec
tr
ical
p
o
wer
g
en
er
atio
n
co
m
p
ar
ed
to
th
e
f
ir
s
t
d
ay
;
h
o
w
ev
er
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
till
p
r
o
d
u
ce
d
g
r
ea
ter
p
o
wer
th
a
n
th
e
I
NC
an
d
P&
O
al
g
o
r
ith
m
s
,
as d
is
p
lay
ed
i
n
Fig
u
r
e
8
(
d
)
.
T
h
e
m
o
s
t
s
ig
n
if
ican
t
test
was
co
n
d
u
cte
d
o
n
t
h
e
th
ir
d
d
ay
,
w
h
er
e
Fig
u
r
e
9
(
a)
s
h
o
ws
d
r
asti
c
an
d
r
ap
i
d
f
lu
ctu
atio
n
s
in
s
o
lar
r
a
d
iatio
n
d
u
e
to
th
ick
cl
o
u
d
s
an
d
lig
h
t
r
ai
n
in
th
e
af
te
r
n
o
o
n
.
Alth
o
u
g
h
t
h
er
e
was
a
co
n
s
is
ten
t
in
cr
ea
s
e
in
r
ad
iatio
n
at
th
e
b
eg
in
n
in
g
,
th
e
r
ad
iatio
n
lev
el
s
tar
ted
to
d
ec
lin
e
in
th
e
af
ter
n
o
o
n
d
u
e
to
clo
u
d
f
o
r
m
atio
n
.
T
h
is
ch
an
g
e
was
also
ac
co
m
p
an
ied
b
y
an
in
cr
ea
s
e
in
win
d
s
p
ee
d
,
wh
ich
ca
u
s
ed
a
d
r
o
p
i
n
tem
p
er
atu
r
e,
in
d
ir
ec
tly
af
f
ec
ti
n
g
th
e
p
o
wer
o
u
tp
u
t.
T
h
ese
c
o
n
d
itio
n
s
also
d
ir
ec
tly
im
p
ac
t
ed
o
n
th
e
r
esu
ltin
g
v
o
ltag
e.
As
s
h
o
wn
in
Fig
u
r
e
9
(
b
)
,
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
m
ain
tain
ed
a
s
tab
le
v
o
ltag
e
f
r
o
m
th
e
b
e
g
in
n
in
g
o
f
th
e
test
,
wh
ile
th
e
I
N
C
an
d
P
&
O
alg
o
r
ith
m
s
ex
h
ib
ited
f
lu
ct
u
atio
n
s
.
Ho
wev
er
,
af
ter
th
e
r
a
d
iatio
n
d
r
o
p
p
ed
,
th
e
o
u
tp
u
t
v
o
ltag
e
e
x
p
er
ien
ce
d
s
ig
n
if
ican
t
f
lu
ctu
atio
n
s
u
n
til
th
e
en
d
o
f
th
e
test
.
I
n
co
n
tr
ast,
th
e
o
u
tp
u
t
cu
r
r
e
n
t
d
is
p
lay
ed
in
Fig
u
r
e
9
(
c)
r
e
m
ain
ed
q
u
ite
s
tab
le,
h
o
v
er
in
g
b
etwe
en
1
an
d
1
.
2
A.
T
h
ese
d
y
n
am
ic
co
n
d
itio
n
s
ef
f
ec
tiv
ely
test
ed
th
e
co
n
v
er
g
en
ce
s
p
ee
d
an
d
r
o
b
u
s
tn
ess
o
f
ea
c
h
alg
o
r
ith
m
.
As
s
ee
n
in
Fi
g
u
r
e
9
(
d
)
,
th
e
P&
O
an
d
I
NC
alg
o
r
ith
m
s
ex
p
e
r
ien
ce
d
s
ig
n
if
ican
t
d
if
f
icu
lty
i
n
tr
ac
k
in
g
th
e
MPP
d
u
r
in
g
r
ap
id
f
lu
ctu
atio
n
s
,
wh
ich
was
ev
id
en
t
f
r
o
m
s
ev
er
e
p
o
wer
o
s
cillatio
n
s
an
d
a
s
h
ar
p
d
ec
r
ea
s
e
in
ef
f
icien
c
y
.
C
o
n
v
er
s
ely
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
was
co
n
s
is
ten
tly
ab
le
to
tr
ac
k
t
h
e
MPP
ch
an
g
es
q
u
ick
ly
,
d
em
o
n
s
tr
atin
g
its
ad
ap
tiv
e
ca
p
ab
ilit
y
an
d
ef
f
ec
tiv
en
ess
in
th
e
m
o
s
t c
h
all
en
g
in
g
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
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
6
9
4
E
n
h
a
n
ce
d
in
cremen
ta
l c
o
n
d
u
cta
n
ce
MPP
T me
th
o
d
fo
r
ma
xi
miz
in
g
p
h
o
to
vo
lta
ic
p
o
w
er
…
(
A
s
n
il
A
s
n
il
)
2763
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
8
.
T
h
e
s
y
s
tem
test
r
esu
lts
o
n
th
e
s
ec
o
n
d
d
ay
:
(
a
)
ir
r
a
d
ian
ce
,
(
b
)
PV o
u
tp
u
t
v
o
ltag
e,
(
c)
PV o
u
tp
u
t c
u
r
r
e
n
t,
an
d
(
d
)
p
o
wer
g
e
n
er
ated
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
9
.
T
h
e
s
y
s
tem
test
r
esu
lts
o
n
th
e
th
ir
d
d
ay
:
(
a
)
ir
r
a
d
ian
ce
,
(
b
)
PV o
u
tp
u
t v
o
ltag
e,
(
c)
PV o
u
tp
u
t c
u
r
r
e
n
t,
an
d
(
d
)
p
o
wer
g
e
n
er
ated
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2757
-
2
7
6
7
2764
5
.
2
.
Sta
t
is
t
ica
l a
na
ly
s
is
a
nd
k
ey
f
ind
ing
s
Af
ter
an
aly
zin
g
t
h
e
q
u
alitativ
e
p
er
f
o
r
m
an
ce
f
r
o
m
t
h
e
f
ig
u
r
es,
a
q
u
an
titativ
e
ev
al
u
atio
n
was
co
n
d
u
cte
d
to
p
r
o
v
i
d
e
s
tr
o
n
g
s
tatis
tical
ev
id
en
ce
.
T
h
is
an
aly
s
is
in
clu
d
es
a
co
m
p
ar
is
o
n
o
f
th
e
a
v
e
r
ag
e
an
d
s
tatis
tical
d
is
p
er
s
io
n
o
f
th
e
p
o
wer
o
u
t
p
u
t
f
r
o
m
ea
c
h
alg
o
r
i
th
m
d
u
r
in
g
th
e
test
in
g
p
er
io
d
.
Fig
u
r
e
1
0
illu
s
tr
ates
th
e
co
m
p
ar
is
o
n
o
f
th
e
a
v
er
ag
e
d
ai
ly
elec
tr
ical
g
en
er
ated
.
T
o
p
r
o
v
id
e
a
m
o
r
e
ac
c
u
r
ate
d
e
p
ictio
n
o
f
t
h
e
r
eliab
ilit
y
an
d
co
n
s
is
ten
cy
o
f
ea
ch
alg
o
r
ith
m
,
t
h
e
s
tan
d
ar
d
d
ev
iatio
n
(
)
o
f
th
e
p
o
wer
o
u
tp
u
t
d
ata
was
ca
lcu
lated
.
T
h
e
m
ain
o
b
jectiv
e
o
f
th
is
ca
lcu
latio
n
is
to
m
ea
s
u
r
e
th
e
m
ag
n
itu
d
e
o
f
d
ata
f
lu
ctu
atio
n
o
f
d
is
p
er
s
io
n
ar
o
u
n
d
its
m
ea
n
v
alu
e.
A
lo
wer
s
tan
d
a
r
d
d
e
v
iatio
n
in
d
icate
s
th
at
th
e
p
o
wer
o
u
tp
u
t
is
m
o
r
e
s
tab
le
an
d
co
n
s
is
ten
t,
wh
ich
is
a
k
ey
in
d
icato
r
o
f
ef
f
ec
tiv
e
MPPT
p
er
f
o
r
m
an
ce
,
esp
ec
ially
u
n
d
er
f
lu
ct
u
atin
g
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
T
h
is
ca
lcu
latio
n
u
s
es
th
e
s
am
p
le
s
tan
d
ar
d
d
ev
iatio
n
f
o
r
m
u
la,
wh
ich
is
m
o
r
e
ap
p
r
o
p
r
iate
f
o
r
lim
ited
d
ata,
with
(
1
3
)
[
3
0
]
.
=
√
∑
(
−
̅
)
2
−
1
(
1
3
)
W
h
e
r
e
̅
i
s
t
h
e
m
e
a
n
i
n
g
o
f
t
h
e
d
a
t
a
,
i
s
,
e
ac
h
i
n
d
i
v
i
d
u
a
l
d
at
a
v
al
u
e
,
i
s
t
h
e
t
o
t
a
l
c
o
u
n
t
o
f
d
a
t
a
p
o
i
n
t
s
.
T
a
b
le
2
p
r
o
v
i
d
e
s
a
s
u
m
m
a
r
y
o
f
t
h
e
k
e
y
s
t
a
ti
s
t
i
c
al
d
a
t
a
o
f
t
h
e
p
o
w
e
r
o
u
t
p
u
t
f
o
r
e
a
c
h
a
l
g
o
r
i
t
h
m
d
u
r
i
n
g
th
e
t
e
s
ti
n
g
p
e
r
i
o
d
.
As
s
h
o
wn
in
T
ab
le
2
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
g
en
er
ated
th
e
h
ig
h
est
av
er
ag
e
p
o
wer
(
2
1
.
3
7
W
)
,
o
u
tp
er
f
o
r
m
in
g
b
o
th
I
NC
(
1
7
.
9
9
W
)
an
d
P&
O
(
1
5
.
3
0
W
)
.
T
h
e
s
tan
d
ar
d
d
e
v
iatio
n
o
f
th
e
I
NC
alg
o
r
ith
m
is
s
lig
h
tl
y
lo
wer
th
an
th
at
o
f
t
h
e
P&
O
al
g
o
r
ith
m
a
n
d
th
e
p
r
o
p
o
s
ed
al
g
o
r
ith
m
.
T
h
is
r
ef
lects th
e
c
h
ar
ac
t
er
is
tics
o
f
tr
ad
e
-
o
f
f
b
etwe
en
s
tab
ilit
y
an
d
t
0
r
ac
k
in
g
s
p
ee
d
.
T
h
e
I
NC
alg
o
r
ith
m
u
s
es
a
f
ix
ed
an
d
r
elativ
ely
s
m
all
s
tep
s
ize,
m
in
im
izes
p
o
wer
f
lu
ctu
atio
n
s
wh
en
n
ea
r
th
e
MPP,
th
u
s
y
ield
in
g
h
ig
h
co
n
s
is
ten
cy
.
C
o
n
v
er
s
ely
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
with
its
VSS m
o
d
e,
a
g
g
r
ess
iv
e
ly
ad
ju
s
ts
its
s
tep
s
ize
to
tr
ac
k
r
ap
id
c
h
an
g
es i
n
r
a
d
iatio
n
.
W
h
ile
th
is
r
esu
lts
in
a
s
ig
n
if
ican
tly
h
ig
h
e
r
av
er
a
g
e
p
o
wer
an
d
b
etter
o
v
e
r
all
ef
f
icie
n
cy
,
th
is
ag
g
r
ess
iv
e
tr
ac
k
in
g
p
r
o
ce
s
s
ca
u
s
es
m
in
o
r
f
lu
ctu
atio
n
s
,
wh
ich
ar
e
r
ef
lect
ed
in
th
e
s
lig
h
tly
h
ig
h
er
s
tan
d
ar
d
d
ev
iatio
n
v
alu
e.
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n
s
u
m
m
ar
y
,
th
e
test
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esu
lts
co
n
f
ir
m
t
h
at
th
e
d
e
v
elo
p
ed
alg
o
r
ith
m
s
u
cc
ess
f
u
lly
im
p
r
o
v
es
th
e
elec
tr
ical
p
o
wer
g
e
n
er
atio
n
.
Fig
u
r
e
1
0
.
T
h
e
a
v
er
ag
e
elec
tr
i
ca
l p
o
wer
g
e
n
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ated
d
u
r
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th
e
test
T
ab
le
2
.
Statis
tical
an
aly
s
is
o
f
alg
o
r
ith
m
p
e
r
f
o
r
m
an
ce
No
A
l
g
o
r
i
t
h
m
A
v
e
r
a
g
e
p
o
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e
r
(W)
S
t
a
n
d
a
r
d
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v
i
a
t
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n
(
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0
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.
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9
0
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9
7
3
P
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o
p
o
se
d
2
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.
3
7
1
.
7
2
6.
CO
NCLU
SI
O
N
T
h
is
r
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ch
d
is
cu
s
s
es
th
e
d
ev
elo
p
m
en
t
o
f
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MPPT
alg
o
r
ith
m
aim
ed
at
en
h
an
cin
g
elec
tr
ical
p
o
wer
f
r
o
m
a
PV sy
s
tem
.
T
o
e
v
alu
at
e
its
ef
f
ec
tiv
en
ess
,
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
alg
o
r
ith
m
was e
x
p
er
i
m
en
tally
test
ed
a
n
d
co
m
p
ar
ed
a
g
ain
s
t
two
co
n
v
en
t
io
n
al
alg
o
r
ith
m
s
,
n
am
el
y
I
NC
an
d
P&
O.
T
h
e
test
s
wer
e
co
n
d
u
cted
o
v
er
a
th
r
ee
-
d
ay
p
er
i
o
d
u
n
d
er
v
ar
y
i
n
g
clim
atic
co
n
d
itio
n
s
in
a
f
iled
s
ettin
g
.
B
ased
o
n
th
e
e
x
p
er
im
e
n
tal
r
esu
lts
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
was
f
o
u
n
d
to
s
ig
n
if
ican
tly
in
cr
ea
s
e
t
h
e
p
o
wer
g
e
n
er
atio
n
ca
p
ac
ity
.
T
h
e
h
y
b
r
id
alg
o
r
ith
m
p
r
o
d
u
ce
d
th
e
h
ig
h
est
a
v
er
ag
e
p
o
wer
o
f
2
1
.
3
7
W
,
r
ep
r
esen
tin
g
a
s
ig
n
i
f
ican
t
in
cr
ea
s
e
o
f
1
8
.
7
9
%
co
m
p
ar
ed
to
th
e
I
NC
alg
o
r
ith
m
an
d
3
9
.
6
7
%
co
m
p
a
r
ed
to
th
e
P&
O
alg
o
r
ith
m
.
T
h
is
im
p
r
o
v
em
en
t
is
cr
u
cial,
esp
ec
ially
in
d
y
n
am
ic
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
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lec
&
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t
I
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2088
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8
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n
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2765
en
v
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itio
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ay
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ap
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iatio
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ail
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o
tr
ac
k
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MPP
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Sp
ec
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ically
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t
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e
co
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ib
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tio
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s
o
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is
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esear
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h
ig
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ly
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ield
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o
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ed
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ir
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t
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ter
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ich
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k
ey
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in
o
p
tim
izin
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o
wer
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o
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v
ar
i
o
u
s
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lar
-
p
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ed
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tr
ical
d
r
iv
e
s
y
s
tem
s
an
d
h
y
b
r
id
s
y
s
tem
s
.
T
h
e
p
r
o
v
en
in
cr
ea
s
e
in
p
o
we
r
o
u
t
p
u
t
will
al
s
o
en
h
an
ce
en
er
g
y
av
ailab
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f
o
r
b
atter
y
ch
a
r
g
i
n
g
an
d
s
u
p
p
o
r
t
m
o
r
e
r
eliab
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teg
r
atio
n
in
to
s
m
ar
t
g
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id
s
.
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ite
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ex
ce
llen
t
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o
r
m
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ce
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h
e
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r
o
p
o
s
ed
m
et
h
o
d
s
till
h
as
lim
itatio
n
s
,
s
u
ch
a
s
its
r
elian
ce
o
n
s
o
lar
r
ad
iatio
n
lev
els
to
d
et
er
m
in
e
th
e
alg
o
r
ith
m
’
s
s
elec
tio
n
p
r
o
c
ess
.
T
h
er
ef
o
r
e,
th
is
r
esear
ch
c
an
b
e
e
x
ten
d
ed
in
th
e
f
u
tu
r
e.
F
u
r
th
er
d
ev
elo
p
m
en
t
m
ay
in
clu
d
e
i
n
teg
r
atin
g
th
is
alg
o
r
ith
m
with
Ar
tific
ial
I
n
tellig
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ce
(
AI
)
-
b
ased
m
eth
o
d
s
,
s
u
ch
as
n
eu
r
al
n
etwo
r
k
,
to
im
p
r
o
v
e
its
ac
cu
r
ac
y
an
d
a
d
ap
tab
ilit
y
.
Ad
d
itio
n
ally
,
its
ap
p
licatio
n
ca
n
b
e
ex
p
an
d
e
d
to
g
r
id
-
tied
PV sy
s
tem
o
r
h
y
b
r
id
en
er
g
y
s
y
s
tem
s
.
T
o
ass
es
s
th
e
alg
o
r
ith
m
’
s
p
er
f
o
r
m
an
ce
in
m
o
r
e
in
t
r
icate
en
v
ir
o
n
m
en
tal
s
ce
n
ar
io
s
,
Har
d
war
e
-
in
-
th
e
-
lo
o
p
(
HI
L
)
v
alid
atio
n
ca
n
also
b
e
u
tili
ze
d
.
ACK
NO
WL
E
DG
M
E
N
T
S
T
h
e
au
th
o
r
wo
u
ld
lik
e
t
o
ex
p
r
ess
th
e
d
ir
ec
to
r
ate
o
f
r
esear
c
h
,
tech
n
o
l
o
g
y
,
a
n
d
c
o
m
m
u
n
ity
s
er
v
ice.
Dir
ec
to
r
ate
g
en
e
r
al
o
f
h
i
g
h
er
e
d
u
ca
tio
n
,
r
esear
ch
,
an
d
tech
n
o
lo
g
y
.
Mi
n
is
tr
y
o
f
ed
u
ca
tio
n
,
c
u
ltu
r
e,
r
esear
ch
a
n
d
tech
n
o
lo
g
y
in
d
o
ct
o
r
al
d
is
s
er
tatio
n
r
esear
ch
s
ch
em
a.
Pr
o
jec
t
n
u
m
b
e
r
0
4
1
/E5
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2
.
0
0
.
PL/2
0
2
4
with
f
is
ca
l
y
ea
r
2
0
2
4
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
is
r
esear
ch
was
f
u
n
d
e
d
b
y
th
e
d
ir
ec
to
r
ate
o
f
r
esear
ch
,
tech
n
o
l
o
g
y
,
an
d
co
m
m
u
n
it
y
s
er
v
ice.
Dir
ec
to
r
ate
g
en
er
al
o
f
h
ig
h
er
e
d
u
ca
tio
n
,
r
esear
ch
,
an
d
tech
n
o
lo
g
y
.
Min
is
tr
y
o
f
ed
u
ca
ti
o
n
,
cu
ltu
r
e,
r
esear
ch
,
a
n
d
tech
n
o
lo
g
y
in
d
o
ct
o
r
al
d
is
s
er
tatio
n
r
esear
ch
s
ch
em
a.
Pr
o
jec
t
n
u
m
b
e
r
0
4
1
/E5
/PG.0
2
.
0
0
.
PL/2
0
2
4
with
f
is
ca
l
y
ea
r
2
0
2
4
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
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M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
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Vi
Su
P
Fu
Asn
il
Asn
il
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
R
ef
d
in
al
Naz
ir
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Kr
is
m
ad
in
ata
Kr
is
m
ad
in
ata
✓
✓
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✓
✓
✓
✓
✓
✓
Mu
h
am
m
ad
Nasir
✓
✓
✓
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✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
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g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
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d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
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O
:
W
r
i
t
i
n
g
-
O
r
i
g
i
n
a
l
D
r
a
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t
E
:
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r
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t
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g
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R
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t
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p
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v
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P
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Fu
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T
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A
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E
NT
Au
th
o
r
s
s
tate
n
o
co
n
f
lict o
f
in
t
er
est.
DATA AV
AI
L
AB
I
L
I
T
Y
T
h
e
d
ata
th
at
s
u
p
p
o
r
t
th
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
ar
e
av
ailab
le
f
r
o
m
th
e
co
r
r
esp
o
n
d
in
g
au
t
h
o
r
,
[
R
N]
,
u
p
o
n
r
ea
s
o
n
ab
le
r
eq
u
est.
RE
F
E
R
E
NC
E
S
[1
]
J.
Zh
a
n
g
,
“
En
e
rg
y
a
c
c
e
ss
c
h
a
ll
e
n
g
e
a
n
d
t
h
e
ro
le
o
f
f
o
ss
il
f
u
e
ls
in
m
e
e
ti
n
g
e
lec
tri
c
it
y
d
e
m
a
n
d
:
P
r
o
m
o
ti
n
g
re
n
e
wa
b
le
e
n
e
rg
y
c
a
p
a
c
it
y
f
o
r
su
sta
in
a
b
le
d
e
v
e
l
o
p
m
e
n
t
,
”
Ge
o
sc
ien
c
e
Fro
n
ti
e
rs
,
v
o
l.
1
4
,
n
o
.
5
,
p
.
1
0
1
8
7
3
,
2
0
2
4
.
d
o
i:
1
0
.
1
0
1
6
/
j.
g
sf.
2
0
2
4
.
1
0
1
8
7
3
.
[2
]
A.
As
n
il
e
t
a
l.
,
“
P
e
rfo
rm
a
n
c
e
a
n
a
l
y
sis
o
f
a
n
i
n
c
re
m
e
n
tal
c
o
n
d
u
c
tan
c
e
M
P
P
T
a
l
g
o
ri
th
m
f
o
r
p
h
o
to
v
o
lt
a
i
c
sy
ste
m
s
u
n
d
e
r
ra
p
id
irra
d
ian
c
e
c
h
a
n
g
e
s,”
T
EM
J
o
u
rn
a
l
,
v
o
l.
1
3
,
n
o
.
2
,
p
p
.
1
0
8
7
–
1
0
9
4
,
2
0
2
4
,
d
o
i:
1
0
.
1
8
4
2
1
/T
E
M
1
3
2
-
2
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2757
-
2
7
6
7
2766
[3
]
J.
Wan
g
a
n
d
W.
Az
a
m
,
“
Na
tu
ra
l
r
e
so
u
rc
e
sc
a
rc
it
y
,
f
o
ss
il
fu
e
l
e
n
e
rg
y
c
o
n
s
u
m
p
ti
o
n
,
a
n
d
to
tal
g
re
e
n
h
o
u
s
e
g
a
s
e
m
issio
n
s
in
t
o
p
e
m
it
ti
n
g
c
o
u
n
tri
e
s,”
Ge
o
sc
i
e
n
c
e
Fro
n
ti
e
rs
,
v
o
l.
1
5
,
n
o
.
2
,
2
0
2
4
,
d
o
i:
1
0
.
1
0
1
6
/j
.
g
sf.2
0
2
3
.
1
0
1
7
5
7
.
[4
]
M
.
M
.
Ha
sa
n
e
t
a
l
.
,
“
Ha
rn
e
ss
in
g
so
lar
p
o
we
r:
A
re
v
iew
o
f
p
h
o
t
o
v
o
lt
a
ic
in
n
o
v
a
ti
o
n
s,
so
lar
t
h
e
rm
a
l
sy
ste
m
s,
a
n
d
th
e
d
a
wn
o
f
e
n
e
rg
y
sto
ra
g
e
s
o
lu
ti
o
n
s,
”
En
e
rg
ies
,
v
o
l.
1
6
,
n
o
.
1
8
,
2
0
2
3
,
d
o
i:
1
0
.
3
3
9
0
/en
1
6
1
8
6
4
5
6
.
[5
]
M
.
Las
h
e
e
n
a
n
d
M
.
Ab
d
e
l
-
S
a
lam
,
“
M
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
in
g
u
si
n
g
Hi
ll
Cli
m
b
in
g
a
n
d
AN
F
I
S
tec
h
n
i
q
u
e
s
fo
r
P
V
a
p
p
l
ica
ti
o
n
s:
A
re
v
iew
a
n
d
a
n
o
v
e
l
h
y
b
ri
d
a
p
p
r
o
a
c
h
,
”
E
n
e
rg
y
c
o
n
v
e
rs
io
n
a
n
d
ma
n
a
g
e
me
n
t
,
v
o
l.
1
7
1
,
p
p
.
1
0
0
2
–
1
0
1
9
,
2
0
1
8
,
d
o
i:
1
0
.
1
0
1
6
/j
.
e
n
c
o
n
m
a
n
.
2
0
1
8
.
0
6
.
0
0
3
.
[6
]
R.
Ce
li
k
e
l,
M
.
Yilma
z
,
a
n
d
A.
Gu
n
d
o
g
d
u
,
“
Im
p
ro
v
e
d
v
o
lt
a
g
e
sc
a
n
n
i
n
g
a
lg
o
rit
h
m
b
a
se
d
M
P
P
T
a
l
g
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
u
c
ti
o
n
,
”
He
li
y
o
n
,
v
o
l
.
1
0
,
n
o
.
2
0
,
2
0
2
4
,
d
o
i:
1
0
.
1
0
1
6
/j
.
h
e
li
y
o
n
.
2
0
2
4
.
e
3
9
3
8
2
.
[7
]
L.
G
u
a
n
g
h
u
a
e
t
a
l.
,
“
M
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
stra
teg
ies
fo
r
so
lar
p
v
sy
ste
m
s:
A
re
v
iew
o
f
c
u
rre
n
t
m
e
th
o
d
s
a
n
d
fu
tu
re
i
n
n
o
v
a
ti
o
n
s,”
Res
u
lt
s i
n
En
g
i
n
e
e
rin
g
,
p
.
1
0
7
2
2
7
,
2
0
2
5
,
d
o
i:
1
0
.
1
0
1
6
/j
.
r
in
e
n
g
.
2
0
2
5
.
1
0
7
2
2
7
.
[8
]
M
.
L
.
Ka
tch
e
e
t
a
l
.
,
“
A
c
o
m
p
re
h
e
n
siv
e
re
v
iew
o
f
m
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
i
n
g
(M
P
P
T)
tec
h
n
i
q
u
e
s
u
se
d
i
n
s
o
lar
P
V sy
ste
m
s,”
En
e
rg
ies
,
v
o
l.
1
6
,
n
o
.
5
,
p
.
2
2
0
6
,
2
0
2
3
,
d
o
i:
1
0
.
3
3
9
0
/
e
n
1
6
0
5
2
2
0
6
.
[9
]
M
.
H.
Al
i,
M
.
Za
k
a
ria,
a
n
d
S
.
El
-
Taw
a
b
,
“
A
c
o
m
p
re
h
e
n
siv
e
st
u
d
y
o
f
re
c
e
n
t
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
tec
h
n
iq
u
e
s fo
r
p
h
o
to
v
o
lt
a
ic sy
ste
m
s,”
S
c
ien
ti
fi
c
Rep
o
rts
,
v
o
l.
1
5
,
n
o
.
1
,
2
0
2
5
,
d
o
i:
1
0
.
1
0
3
8
/s
4
1
5
9
8
-
0
2
5
-
9
6
2
4
7
-
5.
[1
0
]
D.
M
a
z
u
m
d
a
re
t
e
t
a
l.
,
“
Ov
e
rv
ie
w
o
f
so
lar
p
h
o
t
o
v
o
lt
a
ic
M
P
P
T
m
e
th
o
d
s:
A
sta
te
o
f
th
e
a
rt
o
n
c
o
n
v
e
n
ti
o
n
a
l
a
n
d
a
rti
ficia
l
in
telli
g
e
n
c
e
c
o
n
t
ro
l
t
e
c
h
n
iq
u
e
s,”
In
ter
n
a
ti
o
n
a
l
T
ra
n
sa
c
ti
o
n
s
o
n
El
e
c
trica
l
E
n
e
rg
y
S
y
ste
ms
,
d
o
i
:
1
0
.
1
1
5
5
/
2
0
2
4
/8
3
6
3
3
4
2
.
[1
1
]
M
.
Y.
W
o
rk
u
e
t
a
l
.
,
“
A co
m
p
re
h
e
n
siv
e
re
v
iew
o
f
re
c
e
n
t
m
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
in
g
tec
h
n
iq
u
e
s fo
r
p
h
o
t
o
v
o
lt
a
i
c
sy
ste
m
s u
n
d
e
r
p
a
rti
a
l
sh
a
d
in
g
,
”
S
u
sta
i
n
a
b
il
it
y
,
v
o
l.
1
5
,
n
o
.
1
4
,
p
.
1
1
1
3
2
.
d
o
i:
1
0
.
3
3
9
0
/s
u
1
5
1
4
1
1
1
3
2
.
[1
2
]
A.
T.
Na
se
r
e
t
a
l.
,
“
Im
p
ro
v
e
d
c
o
o
t
o
p
ti
m
ize
r
a
lg
o
ri
th
m
-
b
a
se
d
M
P
P
T
fo
r
P
V
sy
ste
m
s
u
n
d
e
r
c
o
m
p
lex
p
a
rti
a
l
sh
a
d
in
g
c
o
n
d
i
ti
o
n
s
a
n
d
lo
a
d
v
a
riatio
n
,
”
En
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
6
,
n
p
.
1
4
,
2
0
2
4
,
d
o
i
:
1
0
.
1
0
1
6
/
j.
e
c
m
x
.
2
0
2
4
.
1
0
0
5
6
5
.
[1
3
]
N.
P
a
m
u
k
,
“
P
e
rfo
rm
a
n
c
e
a
n
a
ly
sis
o
f
d
iffere
n
t
o
p
t
imiz
a
ti
o
n
a
l
g
o
rit
h
m
s
fo
r
M
P
P
T
c
o
n
tro
l
tec
h
n
i
q
u
e
s u
n
d
e
r
c
o
m
p
lex
p
a
rti
a
l
sh
a
d
i
n
g
c
o
n
d
it
i
o
n
s i
n
P
V sy
ste
m
s,”
En
e
rg
ies
(Ba
se
l)
,
v
o
l.
1
6
,
n
o
.
8
,
2
0
2
3
,
d
o
i:
1
0
.
3
3
9
0
/en
1
6
0
8
3
3
5
8
.
[1
4
]
M
.
H
.
Zafa
r
e
t
a
l.
,
“
A
n
o
v
e
l
m
e
t
a
-
h
e
u
risti
c
o
p
ti
m
iza
ti
o
n
a
l
g
o
ri
th
m
b
a
se
d
M
P
P
T
c
o
n
tro
l
tec
h
n
i
q
u
e
fo
r
P
V
sy
ste
m
s
u
n
d
e
r
c
o
m
p
lex
p
a
rti
a
l
sh
a
d
i
n
g
c
o
n
d
it
io
n
,
”
S
u
st
a
in
a
b
le
En
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
7
,
2
0
2
1
,
d
o
i:
1
0
.
1
0
1
6
/
j.
se
ta.2
0
2
1
.
1
0
1
3
6
7
.
[1
5
]
M
.
S
.
En
d
iz,
G
.
G
ö
k
k
u
ş,
A
.
E
.
C
o
şg
u
n
,
a
n
d
H.
De
m
ir,
“
A
r
e
v
iew
o
f
tra
d
it
i
o
n
a
l
a
n
d
a
d
v
a
n
c
e
d
M
P
P
T
a
p
p
ro
a
c
h
e
s
f
o
r
P
V
sy
ste
m
s
u
n
d
e
r
u
n
ifo
rm
l
y
i
n
so
latio
n
a
n
d
p
a
rti
a
ll
y
sh
a
d
e
d
c
o
n
d
it
io
n
s,”
A
p
p
li
e
d
S
c
ien
c
e
s,
v
o
l.
1
5
,
n
o
.
3
,
p
.
1
0
3
1
,
2
0
2
5
,
d
o
i:
1
0
.
3
3
9
0
/a
p
p
1
5
0
3
1
0
3
1
.
[1
6
]
S
.
A.
S
a
ra
n
g
e
t
a
l
.
,
“
M
a
x
imiz
in
g
so
lar
p
o
we
r
g
e
n
e
ra
ti
o
n
t
h
ro
u
g
h
c
o
n
v
e
n
ti
o
n
a
l
a
n
d
d
i
g
it
a
l
M
P
P
T
tec
h
n
iq
u
e
s:
a
c
o
m
p
a
ra
ti
v
e
a
n
a
ly
sis,”
S
c
ien
ti
fi
c
Rep
o
rts
,
v
o
l
.
1
4
,
n
o
.
1
,
p
.
8
9
4
4
,
2
0
2
4
,
d
o
i:
1
0
.
1
0
3
8
/s4
1
5
9
8
-
0
2
4
-
5
9
7
7
6
-
z.
[1
7
]
B.
Ya
n
g
e
t
a
l
.
,
“
Co
m
p
re
h
e
n
siv
e
o
v
e
rv
iew
o
f
m
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
in
g
a
l
g
o
ri
th
m
s
o
f
P
V
s
y
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
,
”
2
0
2
0
.
d
o
i
:
1
0
.
1
0
1
6
/j
.
jcle
p
ro
.
2
0
2
0
.
1
2
1
9
8
3
.
[1
8
]
R.
B.
Bo
ll
ip
o
,
S
.
M
ik
k
il
i
,
a
n
d
P
.
K.
Bo
n
t
h
a
g
o
rla,
“
Hy
b
rid
,
o
p
ti
m
a
l
,
in
tell
ig
e
n
t
a
n
d
c
las
sic
a
l
P
V
M
P
P
T
tec
h
n
i
q
u
e
s:
A
re
v
iew
,
”
CS
EE
J
o
u
rn
a
l
o
f
Po
we
r
a
n
d
E
n
e
rg
y
S
y
ste
ms
,
v
o
l
.
7
,
n
o
.
1
,
p
p
.
9
–
3
3
,
2
0
2
1
,
d
o
i
:
1
0
.
1
7
7
7
5
/CS
E
EJP
ES
.
2
0
1
9
.
0
2
7
2
0
.
[1
9
]
M
.
Ku
m
a
r
e
t
a
l.
,
“
Co
m
p
re
h
e
n
si
v
e
re
v
iew
o
f
c
o
n
v
e
n
ti
o
n
a
l
a
n
d
e
m
e
rg
in
g
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
in
g
a
lg
o
rit
h
m
s
fo
r
u
n
ifo
rm
ly
a
n
d
p
a
rti
a
ll
y
sh
a
d
e
d
so
lar
p
h
o
t
o
v
o
lt
a
ic
sy
ste
m
s,”
IEE
E
Acc
e
ss
,
v
o
l.
1
1
,
p
p
.
3
1
7
7
8
–
3
1
8
1
2
,
2
0
2
3
,
d
o
i
:
1
0
.
1
1
0
9
/ACCE
S
S
.
2
0
2
3
.
3
2
6
2
5
0
2
.
[2
0
]
M
.
D.
Ve
n
k
a
tab
ra
h
m
a
n
a
id
u
,
R.
T
h
a
m
izh
se
lv
a
n
,
a
n
d
C.
C
h
e
n
g
a
iah
,
“
M
P
P
T
a
l
g
o
rit
h
m
fo
r
s
o
lar
p
o
we
r
sy
ste
m
u
sin
g
a
rti
ficia
l
in
telli
g
e
n
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[2
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.
R.
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[2
2
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B.
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.
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Ku
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.
S
.
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d
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.
Na
g
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Ra
o
,
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teristics
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o
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L.
D.
Ja
th
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t
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l.
,
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v
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[2
4
]
A.
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se
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.
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p
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i,
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M
.
S
.
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lb
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rb
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,
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.
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ro
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N.
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Be
n
ti
,
“
A co
m
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re
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v
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a
l
y
sis o
f
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d
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n
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lar
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l
p
ro
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u
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ti
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n
d
e
ffici
e
n
c
y
th
ro
u
g
h
n
u
m
e
rica
l
m
o
d
e
ls
a
n
d
e
m
o
ti
o
n
a
l
n
e
u
ra
l
n
e
two
r
k
s,”
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c
i
e
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ti
fi
c
Rep
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rts
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[2
5
]
M
.
Zh
a
n
g
,
W.
L
iu
,
a
n
d
W.
Qi,
“
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p
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ra
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n
IOP
Co
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fer
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rie
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.
[2
6
]
A.
As
n
il
,
K.
Krim
a
d
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a
ta,
E.
As
tri
d
,
a
n
d
I.
H
u
sn
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h
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x
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m
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o
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h
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f
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p
h
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t
o
v
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lt
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ic
sy
ste
m
in
v
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riab
le
c
o
n
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it
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o
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sc
,
”
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o
u
rn
a
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E
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ro
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s
S
y
ste
me
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Au
to
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.
[2
7
]
S
.
M
o
ta
h
h
ir
,
A.
El
G
h
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iza
l
A,
S
.
S
e
b
ti
,
a
n
d
A.
De
ro
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ic
h
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IL
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d
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IL
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d
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ts
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r
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P
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T
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m
,
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.
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.
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4
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5
.
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