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Vo
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12
,
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Feb
r
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ar
y
20
22
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p
p
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32
~
40
I
SS
N:
2088
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8
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DOI
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v
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32
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[
1
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-
[
3
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[
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I
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33
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7
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p
er
tu
r
b
in
g
th
e
d
u
t
y
cy
cle
o
f
th
e
lin
k
ed
co
n
v
er
ter
.
T
h
e
I
n
c.
C
is
m
ea
s
u
r
ed
u
tili
zi
n
g
th
e
PV
s
y
s
tem
p
o
wer
d
er
iv
ativ
e
r
esp
ec
tin
g
its
v
o
ltag
e,
wh
ich
m
u
s
t h
av
e
a
n
eq
u
iv
alen
t v
alu
e
o
f
ze
r
o
at
th
e
MPP; n
ev
er
th
eless
,
it
co
u
ld
h
av
e
a
n
eg
ativ
e
v
alu
e
at
th
e
r
ig
h
t
s
id
e
o
f
th
e
MPP,
an
d
a
p
o
s
itiv
e
v
alu
e
at
t
h
e
lef
t.
T
h
e
P&
O
m
o
s
tly
h
as
a
co
m
p
ar
ab
le
id
ea
to
th
e
HC
tech
n
iq
u
e,
it
is
an
iter
ativ
e
tech
n
iq
u
e
f
o
r
MPPT;
w
h
er
e
PV
ch
ar
ac
ter
is
tics
ar
e
m
ea
s
u
r
ed
an
d
th
e
n
th
e
PV
s
y
s
tem
r
esp
ec
tiv
e
o
p
er
atin
g
p
o
in
t is p
er
tu
r
b
e
d
in
o
r
d
er
to
m
ee
t th
e
ch
an
g
e
d
ir
ec
tio
n
.
B
io
lo
g
ically
in
s
p
ir
ed
m
eth
o
d
s
,
wh
ich
ar
e
ca
lled
also
n
o
n
-
tr
ad
itio
n
al
m
eth
o
d
s
h
av
e
g
o
tten
m
o
r
e
an
d
m
o
r
e
atten
tio
n
b
ec
au
s
e
o
f
th
eir
f
aster
an
d
g
u
ar
an
teed
c
o
n
v
er
g
en
ce
to
th
e
MPP.
Salp
s
w
ar
m
o
p
tim
izatio
n
(
SS
O)
alg
o
r
ith
m
,
a
n
t
co
lo
n
y
s
y
s
tem
s
(
AC
S),
f
lash
in
g
f
ir
e
f
ly
alg
o
r
ith
m
(
FA)
,
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
,
alg
o
r
is
m
,
c
u
ck
o
o
s
ea
r
ch
alg
o
r
ith
m
(
C
S)
tech
n
iq
u
es
ar
e
s
o
m
e
o
f
th
e
m
o
s
t
co
m
m
o
n
an
d
th
e
latest
ev
o
lu
tio
n
ar
y
alg
o
r
ith
m
s
(
E
A)
.
T
h
e
B
io
lo
g
ically
in
s
p
ir
ed
m
eth
o
d
s
tak
e
th
e
b
en
e
f
it
o
f
th
e
co
llectiv
e
in
tellig
en
ce
o
f
id
en
tical
in
d
iv
id
u
als
to
in
cr
ea
s
e
th
e
o
p
er
atin
g
ef
f
icien
cy
a
n
d
p
r
o
v
id
es
t
h
e
b
asis
o
f
s
war
m
in
tellig
en
ce
[
9
]
,
[
1
0
]
.
I
n
th
is
wo
r
k
,
two
d
is
tin
ct
MPPT
tech
n
iq
u
es
ar
e
ap
p
lied
f
o
r
t
h
e
s
o
lar
s
y
s
tem
to
tak
e
o
u
t
t
h
e
m
ax
im
u
m
o
b
tain
a
b
le
p
o
wer
a
t
th
e
PV,
u
til
izin
g
th
e
MA
T
L
AB
S
im
u
lin
k
to
o
l.
T
h
er
ef
o
r
e,
th
e
m
ain
o
b
jectiv
e
p
o
in
t
o
f
th
is
wo
r
k
is
th
e
co
m
p
ar
ativ
e
ev
alu
atio
n
o
f
th
e
s
i
m
u
latio
n
r
esu
lts
f
o
r
t
h
e
s
alp
s
war
m
o
p
tim
izatio
n
alg
o
r
ith
m
as
a
n
o
n
-
tr
a
d
itio
n
al
tech
n
iq
u
e,
an
d
t
h
e
P&
O
m
et
h
o
d
as
a
tr
a
d
itio
n
al
tech
n
iq
u
e
.
T
h
e
r
em
ai
n
d
er
o
f
th
is
p
ap
er
is
ar
r
an
g
ed
as
f
o
llo
ws.
T
h
e
m
o
d
elin
g
o
f
th
e
PV
m
o
d
u
le
a
n
d
ar
r
ay
b
ased
o
n
th
e
wo
r
k
p
u
b
lis
h
ed
i
n
[
1
1
]
is
d
is
cu
s
s
ed
in
s
ec
tio
n
t
wo
.
I
n
Sectio
n
th
r
ee
,
th
e
co
n
v
en
tio
n
al
P&
O
m
eth
o
d
is
b
r
ief
ly
p
r
e
s
e
n
t
e
d
.
S
e
c
t
i
o
n
f
o
u
r
d
e
s
c
r
i
b
e
s
t
h
e
o
v
e
r
v
i
e
w
o
f
t
h
e
S
S
O
a
n
d
h
o
w
i
t
i
s
u
t
i
l
i
z
e
d
t
o
t
r
a
c
k
t
h
e
M
P
P
.
S
e
c
t
i
o
n
f
i
v
e
c
o
m
p
a
r
e
s
t
h
e
r
e
s
u
l
t
s
g
o
t
t
e
n
u
s
i
n
g
t
h
e
p
r
o
p
o
s
e
d
S
S
O
a
n
d
P
&
O
m
e
t
h
o
d
s
.
F
i
n
a
l
l
y
,
t
h
e
c
o
n
c
l
u
s
i
o
n
i
s
p
r
o
p
o
s
e
d
in
th
e
l
ast s
ec
tio
n
.
2.
M
O
DE
L
I
NG
OF
T
H
E
P
V
A
RRAY
T
h
e
cir
cu
it
o
f
t
h
e
id
ea
l
s
o
lar
ce
ll
co
m
p
r
is
es
a
s
o
u
r
ce
o
f
cu
r
r
en
t
th
at
p
ar
ad
ig
m
s
th
e
s
u
n
-
b
ase
d
ir
r
ad
ian
ce
,
a
p
a
r
allel
d
io
d
e
p
a
r
ad
ig
m
th
e
p
-
n
ju
n
ctio
n
,
as
p
r
esen
ted
in
Fig
u
r
e
1
[
1
2
]
.
At
th
e
p
o
in
t
wh
e
n
th
e
s
u
n
-
p
o
wer
e
d
ce
lls
ar
e
ex
p
o
s
ed
to
s
u
n
lig
h
t,
th
e
g
en
e
r
ated
cu
r
r
en
t
v
ar
ies
with
t
h
e
s
u
n
lig
h
t
-
b
ased
ir
r
ad
ian
ce
.
T
h
e
r
esis
tan
ce
co
n
n
ec
ted
in
p
ar
allel
an
d
th
e
r
esis
tan
ce
co
n
n
ec
ted
in
s
er
ies
is
ad
d
ed
to
th
e
m
o
d
el
to
r
ep
r
esen
t
th
e
lo
s
s
es [
1
3
]
,
[
1
4
]
.
Fig
u
r
e
1
.
A
s
in
g
le
d
io
d
e
m
o
d
e
l so
lar
ce
ll e
q
u
iv
alen
t
T
h
e
o
u
tp
u
t c
u
r
r
en
t o
f
th
e
PV c
o
u
ld
b
e
g
o
tten
f
r
o
m
Kir
ch
h
o
f
f
’
s
law
as p
r
esen
ted
in
[
1
5
]
.
I
pv
=I
ph
−
I
d
−
I
sh
(
1
)
W
h
er
e
I
pv
r
ep
r
esen
ts
th
e
ce
ll c
u
r
r
en
t,
I
ph
is
th
e
p
h
o
t
o
cu
r
r
en
t,
I
d
is
th
e
d
io
d
e
c
u
r
r
en
t,
I
sh
is
th
e
p
ar
allel
cu
r
r
e
n
t
.
I
d
=I
o
[
e
V
+
I
.
VT
−
1
]
(
2
)
I
0
is
s
a
tu
r
atio
n
cu
r
r
en
t,
R
s
is
s
er
ial
r
esis
tan
ce
,
V
T
is
th
e
th
er
m
al
v
o
ltag
e,
q
is
th
e
elec
tr
o
n
ch
ar
g
e
(
1
.
6
*
10
-
19
)
,
T
c
is
ac
tu
al
ce
ll tem
p
er
atu
r
e
.
V
T
=
nK
T
c
q
(
3)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
12
,
No
.
1
,
Feb
r
u
ar
y
20
22
:
32
-
40
34
I
ph
=
G
(
ℎ
,
+
μ
.
Δ
T
)
(
4
)
W
h
er
e
G
is
th
e
ir
r
a
d
ian
ce
,
G
ref
is
th
e
s
tan
d
ar
d
test
co
n
d
iti
o
n
(
STC)
ir
r
a
d
ian
ce
(
1
0
0
0
W
.
m
-
2
)
,
I
ph,
ref
is
th
e
p
h
o
to
c
u
r
r
en
t
at
STC,
μ
sc
is
th
e
co
ef
f
icien
t
te
m
p
er
atu
r
e
o
f
s
h
o
r
t
cir
c
u
it
cu
r
r
e
n
t
an
d
Δ
T
(
T
c
–
T
c,
ref
)
wh
er
e
th
e
ce
ll tem
p
er
atu
r
e
at
STC is
T
c,
r
ef
.
I
ph
d
ep
en
d
s
o
n
tem
p
er
atu
r
e
a
n
d
ir
r
a
d
ian
ce
.
ℎ
=
V
+
Rs
∗
I
ℎ
(
5
)
W
h
er
e
R
sh
is
th
e
eq
u
iv
alen
t c
ir
cu
it sh
u
n
t r
esis
tan
ce
.
T
h
e
PV
s
y
s
tem
f
in
al
eq
u
atio
n
is
m
ea
s
u
r
ed
u
s
in
g
(
6
)
.
I
pv
=
G
(
ℎ
,
+
μ
.
Δ
T
)
−
I
o
[
e
V
+
I
.
Rs
VT
−
1
]−
V
+
Rs
∗
I
ℎ
(
6
)
T
h
is
eq
u
iv
alen
t
cir
c
u
it
g
iv
en
b
ef
o
r
e
is
f
o
r
a
s
in
g
le
ce
ll
an
d
th
er
ef
o
r
e
an
ad
j
u
s
tm
en
t
is
r
eq
u
ir
ed
f
o
r
n
u
m
b
e
r
o
f
p
ar
allel
ce
lls
(
N
p
)
an
d
n
u
m
b
er
o
f
s
er
ies ce
lls
(
N
s
)
.
T
h
er
ef
o
r
e,
th
e
ar
r
ay
cu
r
r
e
n
t is
m
ea
s
u
r
ed
u
s
in
g
(
7
)
[
1
1
]
.
I
pv=
I
ph
-
N
p
I
o
[
e
(
+
)
-
1
]
−
+
ℎ
(
7
)
3.
CO
NVEN
T
I
O
NA
L
P
&O
M
E
T
H
O
D
T
h
is
is
th
e
m
o
s
t
g
en
er
ally
u
s
ed
m
eth
o
d
f
o
r
MPPT.
I
n
th
is
al
g
o
r
ith
m
,
t
h
e
co
n
t
r
o
ller
ad
j
u
s
ts
th
e
ar
r
ay
v
o
ltag
e.
T
h
ese
ar
r
ay
v
o
ltag
es
ar
e
in
itially
s
et
wi
th
s
o
m
e
v
alu
es.
I
t
s
tar
ts
w
ith
s
o
m
e
th
r
esh
o
ld
v
alu
e
at
th
e
f
ir
s
t
iter
atio
n
an
d
g
o
es
o
n
in
c
r
ea
s
in
g
u
n
til
t
h
e
p
o
we
r
s
tar
ts
d
ec
r
ea
s
in
g
[
1
6
]
,
[
1
7
]
.
I
f
th
e
p
o
we
r
i
n
c
r
e
a
s
e
s
,
t
h
e
n
t
h
e
a
p
p
r
o
a
c
h
i
s
i
n
t
h
e
r
i
g
h
t
d
i
r
e
c
t
i
o
n
i
.
e
.
t
o
w
a
r
d
s
M
P
P
.
I
f
p
o
w
e
r
s
t
a
r
t
s
d
e
c
r
e
a
s
i
n
g
,
t
h
e
n
t
h
e
s
e
t
p
o
i
n
t
i
s
m
o
v
i
n
g
a
w
a
y
f
r
o
m
M
P
P
.
T
h
e
r
e
f
o
r
e
,
t
h
e
v
o
l
t
a
g
e
v
a
l
u
e
m
u
s
t
b
e
d
e
c
r
e
m
e
n
t
e
d
.
F
i
g
u
r
e
2
i
l
l
u
s
t
r
a
t
e
s
t
h
e
f
l
o
w
c
h
a
r
t
o
f
th
e
P&
O
alg
o
r
ith
m
.
Fig
u
r
e
2
.
P&
O
alg
o
r
ith
m
f
l
o
wch
ar
t
[
5
]
4.
SSO
-
B
AS
E
D
M
P
P
T
Salp
s
ar
e
m
ar
in
e
o
r
g
a
n
is
m
s
.
T
h
eir
s
h
ap
e
is
lik
e
a
b
ar
r
el
-
s
h
ap
e
wi
th
a
tr
an
s
p
ar
en
t
b
o
d
y
a
s
d
is
p
lay
ed
in
Fig
u
r
e
3
.
T
h
eir
m
o
v
em
e
n
t
is
d
o
n
e
b
y
jet
ac
tio
n
th
r
u
s
tin
g
o
f
wate
r
.
T
h
e
y
tak
e
s
h
ap
e
o
f
s
p
ir
al
-
lik
e
ch
ain
s
,
as
ap
p
ea
r
ed
in
Fig
u
r
e
3
f
o
r
f
o
o
d
r
ec
o
n
n
aiss
an
ce
an
d
b
etter
s
u
s
tain
ab
ilit
y
.
SS
O
is
p
r
esen
te
d
f
ir
s
tly
in
[
1
8
]
f
o
r
o
p
tim
izatio
n
o
b
jectiv
es.
Salp
ch
ain
s
co
m
p
r
is
e
o
f
a
lead
er
a
n
d
ad
h
er
en
ts
.
T
h
e
lead
er
d
r
i
v
es
th
e
m
o
tio
n
,
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
mp
a
r
is
o
n
b
etw
ee
n
P
&
O
a
n
d
S
S
O
tech
n
iq
u
es b
a
s
ed
…
(
M
o
h
a
med
Hu
s
s
ein
Mo
h
a
med
y
A
li
)
35
th
e
ad
h
er
e
n
ts
u
p
g
r
a
d
e
th
eir
l
o
ca
tio
n
s
ac
co
r
d
i
n
g
ly
.
T
h
e
m
o
tio
n
o
f
th
e
s
alp
s
war
m
is
f
o
r
in
v
esti
g
atio
n
a
n
d
ex
p
lo
itatio
n
[
1
9
]
.
Sin
ce
b
o
th
ar
e
h
ap
p
ed
i
n
n
-
d
im
en
s
io
n
al
s
p
ac
e
f
o
llo
win
g
th
e
lead
e
r
,
a
p
o
is
e
b
etwe
en
th
e
ad
h
er
en
ts
a
n
d
lead
er
is
ess
en
tial
f
o
r
th
e
ch
ec
k
in
g
o
f
s
ea
r
ch
s
p
ac
e
r
ap
id
ly
an
d
ex
p
lo
itatio
n
in
a
lo
ca
lized
ar
ea
f
o
r
b
etter
f
o
o
d
co
n
s
u
m
in
g
.
T
h
is
cr
ea
tes p
o
is
e
b
etwe
en
th
e
m
o
tio
n
o
f
th
e
lead
er
an
d
its
ad
h
er
en
ts
[
2
0
]
,
[
2
1
]
.
Fig
u
r
e
3
.
A
s
in
g
le
s
alp
a
n
d
a
s
alp
ch
ain
T
h
e
o
b
jectiv
e
o
f
a
h
e
u
r
is
tic
alg
o
r
ith
m
in
MPPT
is
to
f
in
d
MPP
with
th
e
m
o
s
t
lim
ited
ti
m
e
in
its
tr
an
s
ien
t
s
tate
an
d
r
ed
u
ce
t
h
e
s
tead
y
-
s
tate
o
s
cillatio
n
s
ar
o
u
n
d
MPP
to
d
im
in
is
h
p
o
wer
lo
s
s
.
SS
O
is
p
er
f
o
r
m
ed
f
o
r
MPPT
o
p
tim
izatio
n
,
c
o
n
s
i
d
er
in
g
th
ese
two
c
h
ar
ac
ter
is
tics
.
T
h
e
d
u
ty
c
y
cle
is
r
e
g
ar
d
e
d
as
th
e
s
ea
r
ch
s
p
ac
e
in
o
u
r
d
esig
n
,
wh
ich
h
as
a
r
an
g
e
o
f
[
0
,
1
]
.
T
h
e
s
alp
lead
er
lo
ca
tio
n
is
co
n
n
ec
ted
with
th
e
o
u
tp
u
t
d
u
ty
c
y
cle.
T
h
e
p
o
p
u
latio
n
is
s
tar
ted
h
ap
h
az
ar
d
ly
in
th
e
s
ea
r
ch
s
p
ac
e
.
E
v
er
y
s
alp
is
a
p
r
o
b
a
b
le
s
o
lu
tio
n
.
T
h
e
n
ea
r
est
s
alp
to
th
e
f
o
o
d
lo
ca
tio
n
is
ass
ig
n
ed
to
lead
er
s
h
ip
[
2
2
]
.
4
.
1
.
M
a
t
hem
a
t
ica
l e
qu
a
t
io
n f
o
r
t
he
s
a
lp cha
in
T
h
e
m
o
d
el
f
o
r
th
e
s
alp
ch
ai
n
is
p
r
esen
ted
b
y
[
2
3
]
-
[
2
5
]
an
d
th
is
m
o
d
el
is
u
tili
ze
d
f
o
r
p
r
o
b
lem
o
p
tim
izatio
n
.
T
wo
g
r
o
u
p
s
o
f
p
o
p
u
latio
n
s
u
ch
as
f
o
llo
wer
s
an
d
lead
er
ar
e
u
s
ed
to
r
ep
r
es
en
t
th
is
m
o
d
el.
T
h
e
f
o
r
war
d
-
f
ac
in
g
s
alp
is
ca
lled
a
lead
er
,
an
d
th
e
o
th
e
r
s
alp
s
in
th
e
ch
ain
ar
e
th
e
f
o
llo
we
r
s
.
T
h
e
s
alp
p
o
s
itio
n
is
well
d
ef
in
ed
as
n
-
d
im
e
n
s
io
n
al
s
ea
r
ch
s
p
ac
e,
a
n
d
n
r
e
p
r
esen
t
s
th
e
v
ar
iab
les
n
u
m
b
er
.
T
wo
-
d
im
en
s
io
n
al
m
atr
ix
is
u
s
ed
to
s
to
r
e
th
e
s
alp
p
o
s
iti
o
n
.
T
h
e
s
war
m
g
o
al
is
s
u
p
p
o
s
ed
to
b
e
th
e
s
o
u
r
ce
o
f
f
o
o
d
in
th
e
s
ea
r
ch
s
p
ac
e.
T
h
e
p
o
s
itio
n
o
f
th
e
lead
e
r
is
u
p
d
ated
as in
8
.
1
=
{
+
1
(
(
−
)
2
+
)
3
≥
0
+
1
(
(
−
)
2
+
)
3
<
0
(
8
)
W
h
er
e
th
e
lo
ca
tio
n
o
f
lea
d
er
i
n
th
e
j
th
d
im
e
n
s
io
n
is
n
a
m
ed
a
s
X
j
1
,
th
e
s
o
u
r
c
e
o
f
f
o
o
d
is
d
e
n
o
te
d
as
F
j
,
u
b
j
a
n
d
Ib
j
r
e
p
r
esen
t
th
e
u
p
p
e
r
an
d
lo
wer
b
o
u
n
d
,
r
esp
ec
tiv
ely
,
th
e
r
an
d
o
m
n
u
m
b
er
s
ar
e
C
1
,
C
2
,
an
d
C
3
.
Fro
m
(
8
)
,
i
t
was
s
ee
n
th
at
th
e
lead
er
lo
ca
t
io
n
is
r
ef
r
esh
ed
im
p
u
tin
g
to
th
e
s
o
u
r
ce
o
f
f
o
o
d
.
T
h
e
r
an
d
o
m
n
u
m
b
er
,
C
1
is
a
s
ig
n
if
ican
t
co
ef
f
icie
n
t
in
t
h
e
S
SO
alg
o
r
ith
m
,
a
n
d
th
is
co
ef
f
ic
ien
t
d
et
er
m
in
es
th
e
ex
p
lo
itatio
n
an
d
ex
p
lo
r
atio
n
.
As s
h
o
wn
in
(
9
)
m
ea
s
u
r
es th
e
co
ef
f
icien
t,
C
1
.
C
1
=2
−
(
4
)
2
(
9
)
W
h
er
e
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
is
L
,
th
e
ex
is
tin
g
iter
atio
n
is
I
.
T
h
e
co
ef
f
icien
ts
(
C
2
an
d
C
3
)
ar
e
p
r
o
d
u
ce
d
in
a
r
an
d
o
m
way
b
et
wee
n
[
0
,
1
]
.
T
h
e
ad
h
e
r
en
ts
lo
c
atio
n
is
r
ef
r
esh
ed
as in
(
10
).
=
1
2
at
2
+V
o
t
(
1
0
)
W
h
er
e
th
e
ad
h
er
en
ts
lo
ca
tio
n
in
th
e
j
th
d
im
en
s
io
n
is
n
am
ed
as
,
i ≥
2
,
th
e
in
itial
q
u
ick
n
ess
is
V
o
,
a=
V
final
/V
o
,
an
d
V=
X
-
X
o
/t.
Ass
u
m
e
V
o
=0
,
a
tim
e
in
o
p
tim
izatio
n
is
d
en
o
ted
as
an
iter
atio
n
an
d
i
n
c
o
n
s
i
s
t
e
n
c
y
b
e
t
w
e
e
n
t
h
e
i
t
e
r
a
t
i
o
n
e
q
u
a
l
t
o
1
.
E
q
u
a
t
i
o
n
(
1
0
)
i
s
m
o
d
i
f
i
e
d
a
s
(
1
1
)
.
A
s
s
h
o
w
n
i
n
(
8
)
-
(
1
1
)
a
r
e
u
t
i
l
i
z
e
d
t
o
m
o
d
e
l
a
n
d
s
i
m
u
l
a
t
e
th
e
s
alp
ch
ain
s
.
=0
.
5
(
+
−
1
)
(
11)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
12
,
No
.
1
,
Feb
r
u
ar
y
20
22
:
32
-
40
36
4
.
2.
Sa
lp s
wa
rm
o
ptim
iza
t
io
n (
S
SO
)
a
lg
o
rit
hm
a
pp
lica
t
io
n t
o
M
P
P
T
T
h
e
m
ain
g
o
al
o
f
th
is
tech
n
iq
u
e
is
to
lo
ca
te
th
e
MPP.
I
n
th
e
ch
ain
o
f
s
alp
p
ar
ad
i
g
m
,
th
e
ad
h
er
en
ts
f
o
llo
w
th
e
lead
er
to
t
h
e
s
o
u
r
ce
o
f
f
o
o
d
[
2
6
]
.
I
f
t
h
e
MPP
s
u
b
s
titu
tes
th
e
s
o
u
r
ce
o
f
f
o
o
d
,
th
e
c
h
ain
o
f
s
alp
tr
an
s
f
er
s
to
th
e
MPP.
T
h
e
b
e
tter
s
o
lu
tio
n
is
th
e
MP
P,
an
d
th
e
ch
ain
o
f
s
alp
f
lo
ws
th
e
s
o
u
r
ce
o
f
f
o
o
d
.
T
h
e
f
lo
wch
ar
t
f
o
r
th
e
u
tili
ze
d
SS
O
tech
n
iq
u
e
is
p
r
esen
ted
in
Fi
g
u
r
e
4
.
T
h
e
s
tag
es
f
o
r
th
e
u
tili
ze
d
SS
O
tech
n
iq
u
e
ar
e
lis
ted
:
Stag
e
1
:
I
n
itialize
th
e
lo
ca
tio
n
o
f
th
e
s
alp
s
with
s
p
ac
e
o
f
s
ea
r
ch
s
o
m
ewh
er
e
i
n
th
e
r
a
n
g
e
o
f
3
5
%
an
d
8
5
%
o
f
d
u
ty
r
atio
f
o
r
t
h
e
d
c
-
d
c
co
n
v
er
ter
.
Stag
e
2
:
At
ev
er
y
s
alp
lo
ca
tio
n
,
th
e
p
o
wer
o
u
tp
u
t
o
f
PV
is
m
ax
im
ized
with
th
e
ch
an
g
in
g
o
f
th
e
d
u
ty
c
y
cle
o
f
th
e
co
n
v
e
r
ter
an
d
o
b
tain
s
th
e
PV p
o
wer
o
u
tp
u
t.
Stag
e
3
: T
h
e
s
alp
lo
ca
tio
n
is
ch
an
g
ed
as f
o
llo
ws:
T
h
e
o
b
jecti
v
e
f
u
n
ctio
n
f
o
r
th
e
g
iv
en
is
s
u
e
is
g
iv
en
in
(
12
).
P(
)
P(
−
1
)
(
12
)
W
h
er
e
th
e
p
o
wer
o
u
tp
u
t
o
f
th
e
PV
is
P,
th
e
d
u
ty
cy
cle
is
d
,
I
is
th
e
iter
atio
n
n
u
m
b
er
a
n
d
n
is
th
e
c
h
ain
s
lap
s
n
u
m
b
er
.
T
h
e
d
u
ty
c
y
cle
is
r
ep
r
esen
ted
u
s
in
g
(
13
).
D
n
(
l
+1
)
=D
n
(L)
-
C
1
(
13
)
Stag
e
4
: Rep
ea
t stag
es 3
an
d
4
till
th
e
co
n
v
er
g
en
ce
of
all
s
alp
s
.
Stag
e
5
:
W
h
en
th
e
tech
n
iq
u
e
f
in
d
s
th
e
MPP.
C
h
an
g
e
th
e
s
al
p
s
d
ep
en
d
e
n
t
o
n
th
e
u
p
p
er
an
d
lo
wer
lim
its
o
f
th
e
d
u
ty
cy
cle.
T
h
e
f
lo
wch
a
r
t
o
f
t
h
e
u
tili
ze
d
MPPT
m
eth
o
d
b
eg
in
s
wit
h
th
e
esti
m
ated
MPP
b
y
all
o
ca
tin
g
th
e
h
ap
h
az
ar
d
lo
ca
tio
n
f
o
r
th
e
n
u
m
er
o
u
s
s
alp
s
.
T
h
is
b
est
v
alu
e
f
in
d
s
th
e
f
itn
ess
,
d
ec
id
es
th
e
b
est
s
u
itab
le
s
alp
,
an
d
th
e
l
o
ca
tio
n
o
f
th
e
o
p
tim
u
m
co
n
v
e
n
ien
t
s
alp
is
d
o
le
d
o
u
t
as
a
s
o
u
r
ce
o
f
f
o
o
d
.
T
h
e
v
ar
ia
b
le
F
is
tr
ac
k
ed
b
y
th
e
m
u
ltit
u
d
e
o
f
s
alp
s
.
T
h
e
C
1
co
ef
f
icien
t
is
r
ef
r
esh
ed
u
tili
zin
g
(
9
).
At
ea
ch
d
im
e
n
s
io
n
,
th
e
lo
ca
tio
n
o
f
th
e
s
alp
lead
er
is
r
e
f
r
esh
ed
as
in
(
8
)
,
a
n
d
th
e
a
d
h
er
e
n
t
s
alp
lo
c
atio
n
is
r
ef
r
esh
ed
as
i
n
(
10
)
.
I
n
th
e
ev
en
t
th
at
th
e
s
alp
lo
ca
tio
n
is
o
u
t o
f
s
ea
r
ch
s
p
ac
e,
it will r
etu
r
n
to
th
e
lim
its
.
Fig
u
r
e
4
.
Flo
wch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
SS
O
MPPT
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
mp
a
r
is
o
n
b
etw
ee
n
P
&
O
a
n
d
S
S
O
tech
n
iq
u
es b
a
s
ed
…
(
M
o
h
a
med
Hu
s
s
ein
Mo
h
a
med
y
A
li
)
37
T
h
e
s
tag
es
ar
e
r
eiter
ated
till
t
h
e
co
n
v
er
g
en
ce
n
o
r
m
s
ar
e
m
et
[
2
7
]
.
T
h
e
s
o
u
r
ce
o
f
f
o
o
d
is
r
ef
r
esh
ed
o
win
g
to
t
h
at
s
alp
s
is
p
r
o
b
a
b
ly
g
o
in
g
to
d
ec
id
e
t
h
e
o
p
tim
al
s
o
lu
tio
n
b
y
u
tili
zin
g
a
n
d
in
v
esti
g
atio
n
ar
o
u
n
d
th
e
s
p
ac
e
o
f
s
ea
r
ch
.
T
h
e
s
war
m
tr
an
s
f
er
s
to
th
e
MPP
.
T
h
e
p
o
s
itio
n
o
f
lead
er
s
alp
is
th
e
co
n
v
er
t
er
d
u
ty
r
atio
.
5.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
5
.
1.
Sy
s
t
em
des
cr
iptio
n
Sig
n
if
ican
t
p
o
wer
p
ar
ts
ass
o
ciate
d
with
th
e
o
f
f
-
g
r
id
PV
s
y
s
tem
lik
e
PV,
E
SDs
,
an
d
MPPT
wer
e
d
esig
n
ed
u
tili
zin
g
MA
T
L
AB
/Si
m
u
lin
k
.
T
h
e
m
ain
PV
s
y
s
te
m
s
tr
u
ctu
r
e
is
g
i
v
en
i
n
Fig
u
r
e
5
.
T
h
e
s
y
s
tem
was
s
ized
b
y
d
ec
id
in
g
th
e
l
o
ad
d
e
m
an
d
.
T
h
er
ea
f
ter
,
th
e
PV
m
o
d
u
les,
b
atter
y
,
a
n
d
SC
s
izin
g
wer
e
ca
r
r
ied
o
u
t
to
f
u
lf
ill th
e
lo
ad
n
ee
d
[
2
6
]
.
Ov
er
all
s
y
s
tem
co
n
f
ig
u
r
ati
on
Fig
u
r
e
5
.
B
lo
ck
d
iag
r
am
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
with
b
at
ter
y
-
SC
en
er
g
y
s
to
r
a
g
e
d
e
v
ices
T
h
e
m
ain
p
ar
ts
in
th
e
d
iag
r
a
m
s
h
o
wn
b
ef
o
r
e
ar
e
th
e
PV
m
o
d
u
les,
s
tep
u
p
,
b
i
-
d
ir
ec
tio
n
al
co
n
v
e
r
ter
,
an
d
MPPT.
PV
m
o
d
u
les
c
o
n
n
ec
ted
with
th
e
s
tep
u
p
c
o
n
v
e
r
ter
g
en
e
r
ate
a
DC
p
o
wer
[
2
8
]
.
T
h
e
p
o
wer
s
tr
ea
m
s
in
to
th
e
DC
b
u
s
ar
e
th
en
u
tili
ze
d
b
y
th
e
l
o
ad
o
r
s
to
r
ed
in
a
b
atter
y
an
d
is
u
p
h
el
d
ad
d
i
tio
n
ally
b
y
SC
.
b
i
-
d
ir
ec
tio
n
al
c
o
n
v
e
r
ter
s
f
o
r
b
atter
ies
an
d
SC
ar
e
u
tili
ze
d
to
ad
ju
s
t
th
e
p
o
wer
p
r
o
v
id
ed
f
r
o
m
(
to
)
S
C
an
d
b
atter
ies d
ep
en
d
in
g
o
n
th
e
lo
a
d
r
eq
u
i
r
em
en
ts
.
5
.
2
.
Sim
ula
t
io
n o
f
t
he
pro
po
s
ed
P
V
s
y
s
t
em
T
h
e
d
esig
n
o
f
th
e
s
y
s
tem
am
alg
am
atio
n
as
p
e
r
th
e
attr
ib
u
t
es
o
f
th
e
s
ch
e
m
e
ap
p
ea
r
ed
in
Fig
u
r
e
6
,
wh
ich
co
m
p
r
is
es
o
f
th
e
m
o
d
el
o
f
s
o
lar
PV
an
d
E
SDs
ass
o
ciate
d
wit
h
th
e
DC
b
u
s
m
ad
e
u
tili
zin
g
th
e
MA
T
L
AB
/S
im
u
lin
k
.
T
o
ev
al
u
ate
th
e
ef
f
ec
tiv
en
ess
an
d
co
m
p
ar
e
th
e
two
u
tili
ze
d
alg
o
r
it
h
m
s
,
P&
O
an
d
SS
O
-
b
ased
MPPT,
s
im
u
latio
n
s
tu
d
ies
wer
e
p
er
f
o
r
m
e
d
.
T
h
e
d
u
t
y
cy
cle
o
f
t
h
e
u
s
ed
b
o
o
s
t
co
n
v
er
ter
is
co
m
p
u
ted
u
s
in
g
th
e
a
p
p
lied
MPPT
tech
n
iq
u
es
with
Simu
lin
k
,
an
d
th
e
PW
M
s
ig
n
al
is
g
en
er
ated
.
T
h
e
s
im
u
latio
n
r
esu
lt
f
o
r
b
o
th
th
e
tr
a
d
itio
n
al
m
eth
o
d
(
P&
O)
an
d
n
o
n
-
tr
ad
itio
n
al
m
eth
o
d
(
SS
O)
ar
e
p
r
esen
ted
in
t
h
e
n
ex
t Fig
u
r
e
.
T
h
e
tr
ac
k
in
g
wav
ef
o
r
m
s
d
eter
m
in
ed
b
y
u
t
i
l
i
z
i
n
g
S
S
O
a
n
d
P
&
O
a
l
g
o
r
i
t
h
m
s
a
r
e
p
r
e
s
e
n
t
e
d
i
n
F
i
g
u
r
e
7
.
T
h
e
MPPTs
tr
ac
k
in
g
d
ata
f
o
r
ir
r
ad
iatio
n
2
0
0
w/m
2
ar
e
s
u
m
m
ar
ized
in
T
ab
le
1
.
T
h
e
s
u
g
g
ested
PV
-
B
atter
y
-
SC
s
y
s
tem
ad
o
p
ts
a
DC
b
u
s
co
n
s
tr
u
ctio
n
t
h
at
is
m
ad
e
o
u
t
o
f
P
V
m
o
d
u
les,
b
atter
ies,
a
SC
,
a
s
t
e
p
u
p
c
o
n
v
e
r
t
e
r
,
a
Bi
-
d
i
r
e
c
t
i
o
n
a
l
c
o
n
v
e
r
t
e
r
,
a
n
d
t
h
e
l
o
a
d
.
I
n
t
h
e
s
u
g
g
e
s
t
e
d
s
y
s
t
e
m
,
t
h
e
D
C
b
u
s
v
o
l
t
a
g
e
i
s
s
e
t
V
b
u
s
,
a
n
d
t
h
e
m
o
d
u
l
e
s
o
f
P
V
a
r
e
a
s
s
o
c
i
a
t
e
d
w
i
t
h
t
h
e
D
C
b
u
s
u
t
i
l
i
z
i
n
g
t
h
e
s
t
e
p
u
p
c
o
n
v
e
r
t
e
r
,
w
h
i
c
h
a
t
t
a
i
n
s
t
h
e
P
V
m
o
d
u
l
e
s
MPPT
co
n
tr
o
l.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
u
tili
ze
d
SS
O
ca
n
r
ea
ch
MPP
f
aster
th
an
P&
O;
I
n
d
ee
d
,
th
e
o
s
cillatio
n
s
in
th
e
p
h
o
t
o
v
o
ltaic
p
o
wer
ar
e
n
o
ticea
b
ly
id
en
tifie
d
in
th
e
s
tea
d
y
s
tate
with
th
e
P&
O
b
ased
MPPT
co
m
p
ar
ed
to
th
e
SS
O
ap
p
r
o
ac
h
,
s
in
ce
th
e
d
u
ty
cy
cle
o
s
cillates
ar
o
u
n
d
t
h
e
MPP.
T
h
e
u
s
e
o
f
th
e
P&
O
MPPT
tech
n
iq
u
e
co
n
tin
u
o
u
s
ly
ch
an
g
es
th
e
d
u
t
y
cy
cle
v
alu
e
to
allo
w
th
e
MPPT;
as
a
r
esu
lt,
th
e
s
y
s
tem
c
o
n
tin
u
es
o
s
cillatin
g
r
o
u
n
d
th
is
p
o
in
t a
s
s
h
o
wn
in
F
ig
u
r
e
7
,
wh
ich
ca
u
s
es p
o
wer
lo
s
s
in
th
e
PV sy
s
tem
f
o
r
in
cr
e
asin
g
r
u
n
n
i
n
g
tim
e.
Mo
r
eo
v
er
,
at
a
s
tead
y
s
tate,
t
h
e
P&
O
s
u
r
r
o
u
n
d
s
th
e
MPPT,
n
ev
er
th
eless
th
e
SS
O
s
til
l
o
n
tr
ac
k
f
o
r
th
e
MPP
with
th
e
lo
west
f
lu
ctu
atio
n
as
s
h
o
wn
i
n
Fig
u
r
e
7
.
T
h
is
is
s
h
o
w
ad
d
itio
n
al
b
e
n
ef
it f
o
r
th
e
u
s
e
o
f
SS
O.
T
h
e
o
s
cillatio
n
f
o
r
th
e
SS
O
tech
n
iq
u
e
is
r
e
g
ar
d
e
d
as
n
eg
lig
i
b
le
u
n
lik
e
P&
O
at
a
s
tead
y
s
tate
th
at
p
r
o
m
p
ts
a
s
u
p
er
io
r
MPPT
ef
f
icien
cy
.
I
t
co
u
ld
b
e
s
ee
n
th
at
in
th
e
f
ir
s
t,
th
e
SS
O
co
n
s
u
m
es
a
h
ig
h
p
o
wer
b
ec
au
s
e
o
f
o
s
cillatio
n
as
th
is
tech
n
i
q
u
e
b
eg
in
s
with
ch
ec
k
in
g
f
o
r
r
an
d
o
m
d
u
ty
cy
cle
s
am
p
les.
No
twith
s
tan
d
in
g
,
th
is
o
s
cillatio
n
co
u
ld
b
e
i
g
n
o
r
ed
as
th
e
p
ar
ticles co
n
v
e
r
g
e
m
o
r
e
a
n
d
m
o
r
e
to
th
e
MPP
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
12
,
No
.
1
,
Feb
r
u
ar
y
20
22
:
32
-
40
38
Fig
u
r
e
6
.
C
o
m
p
lete
Simu
lin
k
m
o
d
el
o
f
s
tan
d
alo
n
e
PV b
atter
y
SC
s
y
s
tem
Fig
u
r
e
7
.
Po
wer
,
v
o
ltag
e,
an
d
cu
r
r
en
t
v
ar
iatio
n
o
f
th
e
PV sy
s
tem
th
r
o
u
g
h
MPPT
u
s
in
g
SS
O
an
d
P&
O
tech
n
iq
u
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
mp
a
r
is
o
n
b
etw
ee
n
P
&
O
a
n
d
S
S
O
tech
n
iq
u
es b
a
s
ed
…
(
M
o
h
a
med
Hu
s
s
ein
Mo
h
a
med
y
A
li
)
39
T
ab
le
1
.
Per
f
o
r
m
an
ce
co
m
p
a
r
is
o
n
o
f
P&
O
an
d
SS
O
m
eth
o
d
s
Tr
a
c
k
i
n
g
met
h
o
d
s
P
o
w
e
r
(
W
)
V
o
l
t
a
g
e
(
V
)
C
u
r
r
e
n
t
(
A
)
Tr
a
c
k
i
n
g
sp
e
e
d
(
sec
o
n
d
s)
M
a
x
i
m
u
m
p
o
w
e
r
f
r
o
m
P
-
V
c
u
r
v
e
(
w
a
t
t
s)
%
Tr
a
c
k
i
n
g
e
f
f
i
c
i
e
n
c
y
P
&O
8
2
2
.
5
1
4
5
.
5
5
.
6
5
2
1.
34
8
4
9
.
5
9
6
.
8
SSO
8
4
3
.
5
1
3
9
.
7
5
6
.
0
3
6
0.
72
9
9
.
3
6.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
p
r
esen
ts
a
s
im
u
lat
io
n
co
m
p
ar
is
o
n
b
etwe
en
two
d
if
f
er
e
n
t
MPPT
tech
n
iq
u
es
o
f
th
e
PV
s
y
s
tem
ap
p
ly
in
g
SS
O
an
d
P
&
O
alg
o
r
ith
m
s
,
in
ter
m
s
o
f
th
eir
co
n
v
er
g
en
ce
s
p
ee
d
,
tr
ac
k
in
g
ef
f
icien
cy
,
an
d
p
er
f
o
r
m
an
ce
.
Acc
o
r
d
i
n
g
to
t
h
e
s
im
u
latio
n
r
esu
lt
s
,
th
e
SS
O
alg
o
r
ith
m
was
ab
le
t
o
r
ea
ch
MPP
f
aster
th
an
th
e
P&
O
tech
n
iq
u
e.
Fu
r
th
er
m
o
r
e,
it
alm
o
s
t
s
h
o
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ly
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m
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e
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sy
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m
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lar
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ll
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rica
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t
h
in
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m
s
tec
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n
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p
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s.
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h
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c
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P
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M
a
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p
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t
h
ro
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th
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sc
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l
with
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2
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,
p
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istry
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_
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.
c
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m
.
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