I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
9
,
No
.
2
,
A
p
r
il
201
9
,
p
p
.
851
~
8
6
0
I
SS
N:
2088
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v
9
i
2
.
pp
851
-
8
6
0
851
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2
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De
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In
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Be
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In
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ia
2
De
p
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rtme
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o
f
El
e
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ica
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&
El
e
c
tro
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RV
CE
,
Be
n
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a
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Art
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R
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2
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M
a
x
i
m
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
in
g
(M
P
P
T
)
is
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th
e
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ss
e
n
ti
a
l
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o
n
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ll
e
r
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ra
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o
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s
o
f
a
n
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P
h
o
t
o
-
Vo
lt
a
ic
(P
V
)
c
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ll
d
e
sig
n
.
De
v
e
lo
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e
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icie
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P
P
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rtain
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th
a
t
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lt
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ig
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to
e
n
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a
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e
r
f
o
r
m
o
f
c
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m
p
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tatio
n
a
l
m
o
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e
l.
He
n
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e
,
th
is
p
a
p
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a
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a
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d
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o
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o
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u
e
n
tl
y
u
se
d
it
e
ra
ti
v
e
a
p
p
ro
a
c
h
.
T
h
e
p
ro
p
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se
d
m
o
d
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l
is
c
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m
p
lete
l
y
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o
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d
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g
a
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a
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m
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t
tak
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p
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t
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(o
p
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n
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ircu
it
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,
c
u
rre
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t
(sh
o
rt
c
ircu
it
),
a
n
d
m
a
x
p
o
we
r
in
o
r
d
e
r
t
o
o
b
tai
n
t
h
e
p
e
a
k
p
o
w
e
r
to
b
e
e
x
trac
ted
f
ro
m
th
e
P
V
c
e
ll
s.
T
h
e
stu
d
y
o
u
tco
m
e
sh
o
w
s
fa
ste
r
re
sp
o
n
se
ti
m
e
a
n
d
b
e
tt
e
r
f
o
rm
o
f
a
n
a
l
y
sis
o
f
c
u
rre
n
t
-
v
o
lt
a
g
e
-
p
o
w
e
r
f
o
r
g
iv
e
n
sta
te o
f
P
V
c
e
ll
s.
K
ey
w
o
r
d
s
:
B
atter
y
E
n
er
g
y
e
f
f
icie
n
c
y
MP
PT
P
h
o
to
-
v
o
ltaic
So
lar
en
er
g
y
Co
p
y
rig
h
t
©
2
0
1
9
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Yo
g
an
a
n
d
in
i
A
.
P
.
,
Dep
ar
t
m
en
t o
f
E
&
C
,
Sa
m
b
h
ar
a
m
I
n
s
tit
u
te
o
f
T
ec
h
n
o
lo
g
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B
en
g
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ia
.
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m
ail:
y
o
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a
n
an
d
i
n
ip
ar
i@
g
m
a
il.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
Ma
x
i
m
u
m
P
o
w
er
P
o
in
t
T
r
ac
k
in
g
(
MP
PT
)
is
co
n
s
id
er
ed
as
a
p
r
o
ce
s
s
th
at
is
r
esp
o
n
s
ib
le
f
o
r
o
b
tain
in
g
in
f
o
r
m
atio
n
ab
o
u
t t
h
e
h
ig
h
es
t
u
s
a
g
e
o
f
p
o
w
er
i
n
a
co
n
tr
o
ller
d
esig
n
[
1
]
,
[
2
]
.
Ho
w
e
v
er
,
it i
s
s
tr
o
n
g
l
y
co
r
r
elate
d
w
it
h
P
h
o
to
-
Vo
ltaic
(
P
V)
m
o
d
u
le
s
y
s
te
m
s
u
b
j
ec
ted
to
s
p
e
ci
f
ic
s
et
o
f
e
n
v
ir
o
n
m
en
tal
a
n
d
o
p
er
atin
g
co
n
d
itio
n
s
.
I
n
th
is
m
ec
h
an
i
s
m
,
th
e
co
n
tr
ib
u
tio
n
o
f
b
o
th
c
u
r
r
en
t a
n
d
v
o
lta
g
e
is
h
i
g
h
l
y
es
s
en
tia
l i
n
o
r
d
er
to
g
en
er
ate
h
i
g
h
e
s
t
p
o
w
er
th
at
is
also
r
ep
r
esen
ted
as
p
ea
k
p
o
in
t
o
f
p
o
w
er
[
3
]
,
[
4
]
.
Ho
w
e
v
er
,
g
en
er
all
y
th
er
e
i
s
h
i
g
h
er
d
eg
r
ee
o
f
s
tab
ilit
y
p
r
o
b
lem
s
as
s
o
ciate
d
th
e
p
o
w
er
in
P
V
ce
lls
a
s
s
o
lar
r
ad
iatio
n
f
l
u
ct
u
ates
v
er
y
o
f
ten
a
n
d
i
s
h
ig
h
l
y
d
ep
en
d
en
t
o
n
v
ar
io
u
s
e
x
ter
n
a
l
p
ar
a
m
eter
s
e.
g
.
te
m
p
er
atu
r
e
o
f
s
o
lar
ce
ll
[
5
]
.
T
h
e
co
r
e
r
o
le
o
f
MP
PT
ap
p
r
o
ac
h
is
to
m
a
k
e
th
e
P
V
ce
ll
w
o
r
k
u
n
d
er
th
e
s
i
g
n
i
f
ica
n
t
s
ca
le
o
f
v
o
ltag
e
t
h
at
co
r
r
esp
o
n
d
s
to
th
e
h
ig
h
es
t
d
eg
r
ee
o
f
p
o
w
er
p
o
in
t
[
6
]
.
T
h
is
o
p
er
ati
o
n
b
asicall
y
a
s
s
i
s
ts
i
n
ex
tr
ac
ti
n
g
h
i
g
h
e
s
t
lev
e
l
o
f
r
esid
u
al
p
o
w
er
r
ig
h
t
f
r
o
m
th
e
P
V
ce
lls
.
T
h
e
ea
s
iest
w
a
y
to
u
n
d
er
s
ta
n
d
th
e
o
p
er
atio
n
al
f
l
o
w
o
f
MP
P
T
is
-
1
)
co
m
p
u
te
t
h
e
o
u
tp
u
t
o
f
P
V
ce
ll,
2
)
p
er
f
o
r
m
an
d
a
n
al
y
s
is
w
it
h
th
e
v
o
lta
g
e
as
s
o
ciate
d
w
ith
b
atter
,
3
)
d
eter
m
i
n
e
t
h
e
o
p
tim
al
p
o
w
er
t
h
at
i
s
ca
p
ab
le
o
f
g
en
er
atin
g
p
o
w
er
b
y
P
V
ce
ll
f
o
r
th
e
p
u
r
p
o
s
e
o
f
b
atter
y
ch
ar
g
in
g
,
4
)
p
er
f
o
r
m
co
n
v
er
s
io
n
to
th
e
o
p
tim
a
l
v
o
lta
g
e
i
n
o
r
d
er
to
o
b
tain
th
e
h
i
g
h
est
a
m
o
u
n
t
o
f
cu
r
r
en
t
th
at
ar
e
d
r
a
w
n
to
t
h
e
b
atter
y
u
n
it
[
7
]
.
T
h
is
p
r
o
ce
s
s
ca
n
also
ac
t
as
a
s
o
u
r
ce
o
f
o
r
ig
in
atio
n
o
f
en
e
r
g
y
s
u
p
p
l
y
f
o
r
DC
lo
ad
s
.
I
t
h
as
b
ee
n
f
o
u
n
d
th
at
cli
m
atic
co
n
d
itio
n
a
n
d
h
ig
h
l
y
d
is
ch
ar
g
ed
b
atter
y
s
tate
ar
e
t
h
e
ad
v
er
s
e
co
n
d
itio
n
th
at
n
e
g
ati
v
el
y
af
f
ec
t
s
MP
PT
.
An
ef
f
icie
n
t
d
esi
g
n
o
f
t
h
e
co
n
tr
o
ller
ca
n
b
e
ac
h
iev
ed
u
s
in
g
MP
P
T
th
at
ar
e
ch
ar
ac
ter
ized
b
y
f
o
llo
w
i
n
g
:
i)
co
n
tr
o
ller
s
y
s
te
m
f
o
r
MP
PT
ass
is
t
s
i
n
r
ec
tify
i
n
g
t
h
e
f
l
u
ctu
atio
n
o
cc
u
r
r
ed
in
v
o
l
ta
g
e
an
d
cu
r
r
en
t o
cc
u
r
r
i
n
g
i
n
s
o
lar
ce
lls
esp
ec
iall
y
,
i
i)
it
ca
n
p
er
f
o
r
m
ex
tr
ac
tio
n
o
f
t
h
e
h
ig
h
e
s
t
lev
e
l
o
f
p
o
w
er
i
n
o
r
d
er
to
en
s
u
r
e
b
etter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il
201
9
:
8
5
1
-
8
6
0
852
o
p
er
atio
n
o
f
v
o
ltag
e
r
eq
u
ir
ed
f
o
r
ef
f
icie
n
t D
C
-
DC
co
n
tr
o
ller
s
y
s
te
m
,
i
ii)
it p
er
m
it
s
t
h
e
u
s
er
to
m
ak
e
u
s
e
o
f
P
V
ce
ll
s
as
s
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ciate
d
w
i
th
m
a
x
i
m
u
m
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tp
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er
atin
g
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h
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atter
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n
i
t,
iv
)
it
is
also
clai
m
ed
to
m
in
i
m
ize
th
e
co
m
p
le
x
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y
a
s
s
o
ciate
d
w
it
h
t
h
e
s
y
s
te
m
th
at
n
o
r
m
all
y
s
u
r
f
ac
e
s
d
u
r
in
g
h
i
g
h
er
p
ea
k
lo
ad
s
.
v
)
i
t
also
al
lo
w
s
to
b
e
u
s
ed
f
o
r
m
u
ltip
le
n
u
m
b
er
o
f
s
o
u
r
ce
s
o
f
e
n
er
g
y
a
s
e
f
f
icie
n
t
co
n
tr
o
llin
g
o
f
DC
-
D
C
co
n
v
e
r
ter
ca
n
b
e
ca
r
r
ied
o
u
t
m
o
r
e
ef
f
icie
n
tl
y
,
v
i)
t
h
e
ap
p
licab
ilit
y
o
f
t
h
e
MP
PT
co
n
tr
o
ller
s
y
s
te
m
i
s
m
o
r
e
to
w
ar
d
s
r
en
e
w
ab
le
r
eso
u
r
ce
s
[
8
]
-
[
1
0
]
.
A
n
ef
f
ec
ti
v
e
d
esig
n
o
f
MP
PT
c
o
n
tr
o
ller
s
y
s
te
m
h
as
m
a
n
y
cla
u
s
e
s
to
b
e
ch
ec
k
ed
f
o
r
as
i)
co
m
p
u
t
in
g
th
e
n
o
r
m
al
v
o
ltag
e
o
f
b
atter
y
th
at
is
r
eq
u
ir
ed
f
o
r
ch
ar
g
i
n
g
th
e
co
n
tr
o
ller
an
d
li
k
e
w
i
s
e
p
er
f
o
r
m
s
elec
t
io
n
o
f
s
u
ch
v
o
lta
g
e,
ii)
s
elec
tio
n
o
f
ap
p
r
o
p
r
iate
cu
r
r
en
t
f
o
r
ch
ar
g
i
n
g
,
iii)
e
n
s
u
r
e
t
h
at
th
e
h
ig
h
e
s
t
c
h
ar
g
i
n
g
c
u
r
r
en
t
is
u
n
d
er
th
e
li
m
it
s
o
f
s
tan
d
ar
d
s
i
m
p
o
s
ed
o
n
o
p
er
atin
g
P
V
ce
lls
,
etc.
E
x
is
tin
g
s
y
s
te
m
s
h
o
w
s
t
h
at
t
h
er
e
ar
e
v
ar
io
u
s
f
o
r
m
s
o
f
class
i
f
icat
io
n
o
f
co
n
tr
o
ller
d
esig
n
s
tr
ateg
y
e.
g
.
i)
in
cr
e
m
en
tal
c
o
n
d
u
ctan
ce
,
ii)
p
er
t
u
r
b
an
d
o
b
s
er
v
e,
iii)
co
n
s
ta
n
t
v
o
lta
g
e,
iv
)
c
u
r
r
en
t
s
w
ee
p
.
A
t
p
r
ese
n
t,
th
er
e
i
s
v
ar
io
u
s
r
esear
ch
w
o
r
k
s
b
ei
n
g
ca
r
r
ied
o
u
t
to
w
ar
d
s
d
ev
e
lo
p
in
g
MP
P
T
f
o
r
d
esig
n
in
g
a
n
ef
f
icien
t
co
n
tr
o
ller
s
y
s
te
m
[
1
1
]
.
I
n
s
p
ite
o
f
a
s
s
o
ciate
d
b
en
ef
its
o
f
e
x
i
s
ti
n
g
ap
p
r
o
ac
h
es,
t
h
er
e
ar
e
n
o
n
-
av
ai
lab
ilit
y
o
f
a
n
y
f
o
r
m
o
f
b
en
ch
m
ar
k
ed
m
o
d
els
to
e
n
s
u
r
e
th
e
b
est
p
er
f
o
r
m
an
ce
o
f
M
P
PT.
T
h
is
lead
s
to
m
o
tiv
a
te
th
a
t
th
er
e
i
s
an
i
m
m
en
s
e
n
ee
d
to
p
er
f
o
r
m
a
d
ed
icate
r
esear
ch
w
o
r
k
to
w
ar
d
d
ev
elo
p
in
g
a
n
ef
f
icie
n
t
MP
PT
-
b
ased
m
o
d
el
f
o
r
d
e
v
elo
p
in
g
an
ef
f
icie
n
t
co
n
tr
o
ll
er
s
y
s
te
m
ap
p
licab
le
in
r
ea
l
-
li
f
e
co
n
d
itio
n
s
.
T
h
er
ef
o
r
e,
th
e
co
n
tr
ib
u
tio
n
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
te
m
is
to
in
tr
o
d
u
ce
o
n
e
s
u
c
h
s
i
m
p
li
s
tic
co
m
p
u
tatio
n
a
l
m
o
d
el
to
ad
d
r
ess
s
u
c
h
p
r
o
b
lem
s
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
e
m
p
h
asize
s
o
n
o
f
f
er
i
n
g
a
co
s
t
ef
f
ec
ti
v
e
c
o
m
p
u
tatio
n
al
m
o
d
el
th
at
ca
n
p
er
f
o
r
m
a
p
r
ec
is
e
i
d
en
tific
atio
n
o
f
MP
P
T
s
tate
co
n
s
id
er
in
g
P
V
ce
lls
u
n
d
er
v
ar
iab
le
co
n
d
itio
n
s
o
f
d
if
f
er
en
t
co
n
s
tr
ain
ts
.
Sectio
n
1
.
1
d
is
cu
s
s
es
ab
o
u
t
th
e
ex
i
s
tin
g
liter
at
u
r
es
w
h
er
e
d
if
f
er
en
t
tech
n
iq
u
e
s
ar
e
d
is
cu
s
s
ed
f
o
r
d
etec
tio
n
s
ch
e
m
es
u
s
ed
i
n
M
P
P
T
s
ch
e
m
e
f
o
llo
w
ed
b
y
d
i
s
cu
s
s
io
n
o
f
r
e
s
ea
r
ch
p
r
o
b
le
m
s
i
n
Sectio
n
1
.
2
an
d
p
r
o
p
o
s
ed
s
o
lu
tio
n
in
1
.
3
.
Sectio
n
2
d
is
c
u
s
s
es
ab
o
u
t
alg
o
r
it
h
m
i
m
p
le
m
e
n
tatio
n
f
o
llo
w
ed
b
y
d
is
cu
s
s
io
n
o
f
r
esu
l
t a
n
al
y
s
i
s
i
n
Sectio
n
3
.
Fin
all
y
,
t
h
e
co
n
cl
u
s
iv
e
r
e
m
ar
k
s
ar
e
p
r
o
v
id
ed
in
S
ec
tio
n
4
.
1
.
1
.
B
a
ck
g
ro
un
d
T
h
is
s
ec
tio
n
is
a
co
n
ti
n
u
a
tio
n
o
f
o
u
r
p
r
io
r
ex
p
lo
r
atio
n
to
war
d
s
ef
f
ec
tiv
e
MP
PT
tech
n
iq
u
es
w
h
er
e
f
u
r
t
h
er
u
p
d
ated
in
f
o
r
m
atio
n
i
s
ad
d
ed
o
n
th
e
to
p
o
f
it
[
1
2
]
.
E
x
is
t
in
g
l
iter
atu
r
es
h
a
v
e
b
ee
n
r
ec
o
r
d
ed
to
f
in
d
t
h
e
i
m
p
o
r
tan
ce
o
f
ac
cu
r
a
c
y
to
w
ar
d
s
MPPT
as
r
e
p
o
r
ted
b
y
th
e
w
o
r
k
o
f
Ah
m
ed
an
d
Sala
m
[
1
3
]
.
Stu
d
y
o
f
MP
PT
h
as a
ls
o
b
ee
n
ca
r
r
ied
o
u
t to
w
a
r
d
s
d
esig
n
i
n
g
in
v
er
ter
f
o
r
en
h
an
cin
g
c
u
r
r
en
t
q
u
ali
t
y
.
T
h
i
s
f
a
ct
w
as d
i
s
cu
s
s
ed
b
y
A
za
r
i
et
a
l.
[
1
4
]
;
h
o
w
e
v
er
,
th
e
s
tu
d
y
lack
s
e
f
f
ic
ien
c
y
i
n
i
n
v
er
ter
d
esig
n
.
C
ap
o
r
al
et
a
l.
[
1
5
]
h
av
e
p
r
esen
ted
a
s
tu
d
y
w
h
er
e
en
h
an
ce
d
P
V
s
y
s
te
m
h
a
s
b
ee
n
d
ev
elo
p
ed
t
o
o
f
f
er
b
etter
p
r
ed
ictiv
e
s
ch
e
m
e.
A
d
o
p
tio
n
o
f
ap
p
r
o
x
im
a
tio
n
t
h
eo
r
y
h
as b
ee
n
s
ee
n
i
n
t
h
e
w
o
r
k
o
f
G
h
ase
m
i
e
t a
l.
[
1
6
]
w
i
th
m
o
r
e
f
o
c
u
s
o
n
s
p
ee
d
o
f
o
b
tain
i
n
g
MP
PT
co
n
s
id
er
in
g
p
ar
tial
s
h
ad
ed
co
n
d
itio
n
.
Si
m
ilar
ap
p
r
o
ac
h
o
f
m
o
d
elin
g
w
as
al
s
o
s
ee
n
in
t
h
e
w
o
r
k
o
f
J
ey
ap
r
ab
h
a
an
d
Sel
v
a
k
u
m
ar
[
1
7
]
w
h
er
e
f
l
y
b
ac
k
co
n
v
er
ter
i
s
u
til
ized
.
J
ian
g
et
a
l.
[
1
8
]
h
av
e
w
o
r
k
ed
to
w
ar
d
s
en
h
a
n
ci
n
g
t
h
e
tr
ac
k
i
n
g
p
er
f
o
r
m
an
ce
o
f
MP
P
T
u
s
in
g
s
i
m
u
latio
n
-
b
ased
s
t
u
d
y
.
A
ca
s
e
s
tu
d
y
o
f
r
elu
cta
n
ce
m
o
to
r
w
as
co
n
s
id
er
ed
f
o
r
i
n
v
esti
g
ati
n
g
t
h
e
MP
P
T
p
e
r
f
o
r
m
an
ce
i
n
w
ater
p
u
m
p
i
n
g
m
o
to
r
b
y
Ko
r
eb
o
in
a
et
a
l.
[
1
9
]
.
T
h
e
s
tu
d
y
h
a
s
e
m
p
h
a
s
ized
o
n
lo
w
er
p
ea
k
s
o
f
p
h
a
s
es
w
it
h
h
i
g
h
l
y
co
n
tr
o
lled
n
o
is
e
lev
el.
Ku
m
ar
et
a
l.
[
2
0
]
,
[
2
1
]
h
av
e
u
s
ed
m
ac
h
in
e
lear
n
i
n
g
ap
p
r
o
ac
h
f
o
r
d
ev
elo
p
in
g
co
n
tr
o
ller
w
it
h
ef
f
icie
n
t
MP
PT
as
w
e
ll
as
th
e
a
u
t
h
o
r
s
h
a
v
e
al
s
o
w
o
r
k
ed
o
n
ex
tr
ac
tio
n
o
f
p
o
w
er
ef
f
icie
n
tl
y
.
L
as
h
ee
n
et
a
l.
[
2
2
]
h
av
e
w
o
r
k
ed
o
n
in
co
r
p
o
r
atin
g
ad
ap
tiv
it
y
i
n
o
b
tain
i
n
g
MP
P
T
u
s
in
g
r
e
f
e
r
en
ce
v
o
ltag
e
s
y
s
te
m
.
L
eic
h
t
et
a
l.
[
2
3
]
h
av
e
d
ev
elo
p
ed
an
o
p
tim
ized
m
o
d
el
f
o
r
co
n
tr
o
llin
g
MP
PT
w
it
h
h
ig
h
e
s
t
d
eg
r
ee
o
f
e
f
f
icie
n
c
y
co
n
s
id
er
in
g
h
ar
v
e
s
ter
d
esig
n
o
f
v
ib
r
atio
n
e
n
er
g
y
.
Ad
o
p
tio
n
o
f
s
w
a
m
i
n
tell
i
g
e
n
ce
w
a
s
s
ee
n
i
n
s
t
u
d
y
o
f
L
i
u
et
a
l
.
[
2
4
]
f
o
r
en
s
u
r
i
n
g
b
etter
s
tab
ilit
y
o
n
th
e
MP
PT
o
u
tco
m
e
s
.
Stu
d
y
to
w
ar
d
s
en
er
g
y
h
ar
v
e
s
to
r
w
a
s
also
f
o
u
n
d
to
b
e
ad
o
p
ted
b
y
L
iu
et
a
l.
[
2
5
]
in
o
r
d
er
to
o
b
tain
b
etter
v
alu
e
o
f
MP
P
T
f
o
llo
w
ed
b
y
r
e
m
o
v
a
l
o
f
a
n
y
d
ep
en
d
en
cies
o
n
ca
p
ac
ito
r
s
to
r
ag
e.
A
P
ar
a
m
eter
ized
-
b
ase
d
m
o
d
el
w
a
s
ad
o
p
ted
in
th
e
w
o
r
k
o
f
Mia
o
et
a
l.
[
2
6
]
co
n
s
id
er
in
g
s
i
n
g
le
s
tep
o
f
d
eter
m
in
at
io
n
o
f
MP
P
T
f
o
llo
w
ed
b
y
u
s
i
n
g
m
u
lt
ip
le
p
ar
a
m
eter
m
o
d
els.
Ho
w
e
v
er
,
t
h
e
s
y
s
te
m
i
s
h
i
g
h
l
y
r
ec
u
r
s
iv
e
i
n
it
s
o
p
er
atio
n
.
P
en
g
et
a
l.
[
2
7
]
h
a
v
e
p
r
ese
n
ted
an
o
th
er
u
n
iq
u
e
m
o
d
el
o
f
MP
P
T
co
n
s
id
er
in
g
s
i
m
ilar
co
n
d
itio
n
o
f
p
ar
tiall
y
s
h
ad
ed
co
n
d
itio
n
.
A
d
o
p
tio
n
o
f
m
ac
h
i
n
e
lear
n
i
n
g
-
b
a
s
ed
ap
p
r
o
ac
h
w
as
also
r
ep
o
r
ted
in
th
e
w
o
r
k
o
f
R
ed
d
y
a
n
d
Su
d
h
a
k
ar
[
2
8
]
w
h
er
e
n
eu
r
al
n
et
w
o
r
k
h
as
b
ee
n
i
m
p
le
m
e
n
ted
f
o
r
o
p
ti
m
izi
n
g
o
u
tco
m
e
s
.
A
n
o
n
-
li
n
ea
r
-
b
ased
ap
p
r
o
ac
h
o
f
co
m
p
u
tin
g
MP
PT
w
a
s
s
ee
n
in
t
h
e
w
o
r
k
o
f
T
ah
er
i
an
d
T
ah
er
i
[
2
9
]
co
n
s
id
er
in
g
a
m
o
d
el
w
i
th
t
w
o
d
io
d
es.
Stu
d
y
to
w
ar
d
s
i
n
v
e
s
ti
g
ati
n
g
e
f
f
ec
ti
v
en
e
s
s
o
f
s
tep
-
s
ized
b
ased
ap
p
r
o
ac
h
es
o
f
o
p
ti
m
izatio
n
w
a
s
s
ee
n
i
n
t
h
e
w
o
r
k
o
f
T
an
g
et
a
l.
[
3
0
]
as
w
ell
as
T
h
an
g
a
v
el
u
et
a
l.
[
3
1
]
.
T
h
e
in
v
e
s
ti
g
atio
n
w
as
ca
r
r
ied
o
u
t
co
n
s
id
er
in
g
p
er
f
o
r
m
a
n
ce
o
f
s
tead
y
-
s
tate.
W
a
n
g
e
t
a
l.
[
3
2
]
h
av
e
en
h
a
n
ce
s
th
e
m
ec
h
a
n
i
s
m
o
f
p
r
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ce
s
s
i
n
g
p
o
w
er
in
P
V
ce
ll
in
o
r
d
er
to
o
b
tain
b
etter
co
n
tr
o
llin
g
m
e
ch
an
i
s
m
o
f
MP
PT
.
A
p
ar
t
f
r
o
m
th
i
s
,
t
h
e
s
tu
d
y
al
s
o
e
m
p
h
a
s
ized
o
n
ac
h
ie
v
i
n
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b
etter
ac
cu
r
ac
y
o
f
it
u
s
i
n
g
d
i
f
f
er
en
tial
p
r
o
ce
s
s
in
g
o
f
p
o
w
er
tech
n
iq
u
e.
T
h
e
s
u
d
y
i
s
d
o
n
e
b
y
P
u
r
w
a
h
y
u
d
i
et
a
l.
[
3
3
]
"
s
elf
co
n
s
tr
u
ctin
g
n
eu
r
a
l
n
etw
o
r
k
(
S
C
N
N
)
"
tech
n
u
q
e
e
m
p
lo
y
ed
to
e
n
h
a
n
c
e
th
e
ac
c
u
r
ac
y
o
f
th
e
elec
tr
n
i
ca
l
ch
ar
ac
ter
is
t
ics
i
n
to
th
e
s
o
lar
P
V
ce
ll
m
o
d
el.
Si
m
i
lar
l
y
P
r
ad
h
an
an
d
P
an
d
a
[
3
4
]
th
is
r
ev
ie
w
s
t
u
d
y
f
o
cu
s
ed
o
n
r
ea
l
ti
m
e
e
x
p
er
i
m
e
n
t
to
e
x
a
m
i
n
e
t
h
e
r
es
u
lt
o
f
d
if
f
er
e
n
ts
f
ac
to
r
s
l
ik
e
ir
r
ad
ian
ce
,
h
ea
t,
an
d
a
n
g
le
o
f
t
ilt,
s
o
il
in
g
,
d
ar
k
n
e
s
s
o
v
er
t
h
e
p
o
w
er
o
u
tco
m
e
o
f
th
e
p
v
-
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
-
8708
A
co
s
t e
ffective
co
mp
u
ta
tio
n
a
l
d
esig
n
o
f m
a
ximu
m
p
o
w
er p
o
in
t
tr
a
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(
Yo
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i A
.
P
.
)
853
m
o
d
u
le.
B
y
Ma
n
k
o
u
r
e
t
a
l.
[
3
5
]
d
em
o
n
s
tar
ted
m
o
d
eli
n
g
o
f
a
s
ta
n
d
alo
n
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e
n
er
g
y
s
y
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te
m
w
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h
i
s
f
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v
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P
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ltaic
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g
y
tec
h
n
iq
u
e
s
.
T
h
e
n
e
x
t
s
ec
tio
n
b
r
ief
l
y
d
is
c
u
s
s
es
ab
o
u
t
p
r
o
b
le
m
s
i
d
en
tifie
d
as
m
aj
o
r
r
ese
ar
ch
is
s
u
e
s
ass
o
ciate
d
w
it
h
MP
PT
in
P
V
ce
lls
.
1
.
2
.
T
he
p
ro
ble
m
T
h
e
s
ig
n
i
f
ica
n
t r
esear
c
h
p
r
o
b
l
e
m
s
ar
e
as
f
o
llo
w
s
:
a.
No
n
e
o
f
ex
is
ti
n
g
tec
h
n
iq
u
e
s
ar
e
e
v
er
as
s
ess
ed
f
o
r
o
f
f
er
in
g
co
m
p
u
ta
tio
n
all
y
e
f
f
ic
ien
c
y
f
r
o
m
i
ts
p
er
f
o
r
m
a
n
ce
a
n
al
y
s
is
.
b.
E
x
is
ti
n
g
ap
p
r
o
ac
h
es
i
n
co
r
p
o
r
ates
m
o
r
e
n
u
m
b
er
o
f
e
x
ter
n
al
p
ar
a
m
eter
i
n
o
r
d
er
to
o
b
tain
b
etter
o
u
tp
u
t
o
f
MP
PT
,
w
h
ic
h
is
e
x
p
en
s
i
v
e
in
r
ea
l
-
li
f
e
ap
p
licatio
n
d
esi
g
n
.
c.
Usag
e
o
f
P
V
ar
r
a
y
a
n
d
its
s
i
m
p
lif
ied
o
p
ti
m
izatio
n
tech
n
iq
u
e
is
v
er
y
f
e
w
to
f
i
n
d
i
n
e
x
is
tin
g
s
y
s
te
m
w
h
er
e
th
e
d
ep
en
d
en
cie
s
ar
e
m
o
r
e
f
o
r
iter
ativ
e
m
ac
h
i
n
e
lear
n
in
g
ap
p
r
o
ac
h
es.
d.
L
es
s
er
ex
te
n
t
o
f
s
i
m
p
lifie
d
m
ath
e
m
atica
l
m
o
d
eli
n
g
ex
is
t
s
w
h
ic
h
r
ed
u
ce
s
t
h
e
s
co
p
e
o
f
i
m
p
le
m
e
n
tat
io
n
o
f
th
e
co
s
t e
f
f
ec
t
iv
e
m
o
d
el
f
o
r
r
ea
ch
in
g
MP
P
T
.
T
h
e
s
tate
m
e
n
t
o
f
s
i
g
n
if
ican
t
p
r
o
b
lem
id
en
t
if
ied
f
o
r
p
r
o
p
o
s
ed
s
y
s
te
m
is
―
Dev
elo
p
in
g
a
co
s
t
effec
tive
co
mp
u
ta
tio
n
a
l
mo
d
el
w
h
ere
a
s
imp
li
s
tic
a
p
p
r
o
a
ch
o
f
en
h
a
n
cin
g
th
e
MPP
T
p
o
s
itio
n
s
ca
n
b
e
o
b
ta
in
ed
w
ith
fa
s
ter r
e
s
p
o
n
s
e
time
in
P
V
-
ce
l
ls
is
q
u
ite
ch
a
llen
g
in
g
.
‖
1
.
3
.
P
r
o
po
s
ed
s
o
lutio
n
T
h
e
p
r
in
cip
le
ai
m
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
s
te
m
i
s
to
d
esig
n
a
n
d
d
ev
elo
p
a
v
er
y
s
i
m
p
le
m
o
d
el
o
f
DC
-
D
C
co
n
v
er
ter
u
s
i
n
g
P
V
ce
ll
t
h
at
ca
n
b
e
u
s
ed
f
o
r
a
s
s
es
s
i
n
g
it
s
MP
PT
.
I
n
o
r
d
er
to
ev
alu
a
te
th
e
p
r
o
p
o
s
ed
ai
m
,
it
is
es
s
en
t
ial
t
h
at
all
th
e
co
m
p
o
n
en
ts
b
e
n
u
m
er
icall
y
d
es
ig
n
ed
an
d
is
s
u
b
j
ec
ted
to
h
i
g
h
er
d
eg
r
ee
o
f
f
lex
ib
ilit
y
in
o
r
d
er
to
ch
ec
k
th
e
b
est
p
er
f
o
r
m
a
n
ce
o
f
p
r
o
p
o
s
ed
s
y
s
te
m
.
T
h
er
ef
o
r
e,
th
e
p
r
o
p
o
s
ed
s
y
s
te
m
ad
o
p
ts
an
a
l
y
t
ical
r
esear
ch
m
et
h
o
d
o
lo
g
y
t
h
at
r
etain
s
t
h
e
ca
p
ab
ilit
y
o
f
b
o
th
e
m
p
ir
ical
ev
al
u
atio
n
a
s
w
el
l
as
m
at
h
e
m
atica
l
m
o
d
eli
n
g
.
T
h
e
an
al
y
tical
s
c
h
e
m
e
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
s
te
m
i
s
s
h
o
w
ca
s
ed
in
F
ig
u
r
e
1
.
P
V
m
o
d
e
l
S
o
l
a
r
R
a
d
i
a
t
i
o
n
T
e
m
p
e
r
a
t
u
r
e
A
n
a
l
y
s
i
s
V
o
l
t
a
g
e
,
o
p
e
n
c
i
r
c
u
i
t
C
u
r
r
e
n
t
,
s
h
o
r
t
c
i
r
c
u
i
t
V
o
l
t
a
g
e
-
C
u
r
r
e
n
t
(
m
a
x
P
o
w
e
r
)
M
a
x
P
o
w
e
r
M
P
P
T
A
l
g
o
r
i
t
h
m
f
o
r
C
o
m
p
u
t
i
n
g
C
u
r
r
e
n
t
a
n
d
P
o
w
e
r
o
f
D
C
-
D
C
C
o
n
v
e
r
t
e
r
o
f
P
V
M
o
d
u
l
e
I
V
,
P
V
c
u
r
v
e
A
n
a
l
y
s
i
s
Fig
u
r
e
1
.
An
al
y
tical
s
c
h
e
m
e
o
f
p
r
o
p
s
o
ed
s
ch
e
m
e
Fig
u
r
e
1
h
i
g
h
l
ig
h
ts
t
h
e
s
i
m
p
li
s
tic
v
ie
w
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el
th
at
u
n
d
er
tak
e
s
4
d
i
f
f
er
e
n
t
t
y
p
es
o
f
in
p
u
t
i.e
.
v
o
lta
g
e
co
r
r
esp
o
n
d
in
g
to
o
p
en
cir
cu
it,
c
u
r
r
en
t
c
o
r
r
esp
o
n
d
in
g
to
clo
s
e
cir
c
u
it,
b
o
th
cu
r
r
en
t
a
n
d
v
o
ltag
e
co
r
r
esp
o
n
d
in
g
to
m
ax
i
m
u
m
p
o
w
er
a
n
d
m
a
x
i
m
u
m
p
o
w
er
o
f
t
h
e
P
V
ce
lls
.
T
h
e
p
r
o
p
o
s
ed
s
y
s
te
m
also
in
tr
o
d
u
ce
s
a
n
al
g
o
r
ith
m
t
h
at
ass
is
ts
i
n
n
u
m
er
icall
y
as
w
e
l
l
as
g
r
ap
h
ica
ll
y
e
x
p
lo
r
in
g
t
h
e
MP
PT
w
h
er
e
th
e
an
al
y
s
is
i
s
ca
r
r
ied
o
u
t
co
n
s
id
er
in
g
t
h
e
tes
t c
ase
s
o
f
b
o
th
s
o
la
r
r
ad
iatio
n
an
d
te
m
p
er
at
u
r
e.
T
h
e
f
i
n
al
o
u
tco
m
e
o
f
th
e
p
r
o
p
o
s
ed
s
tu
d
y
is
a
s
s
es
s
ed
w
it
h
r
esp
ec
t
to
th
e
c
u
r
r
en
t
-
v
o
lta
g
e
an
d
p
o
w
er
-
v
o
ltag
e
cu
r
v
e.
T
h
e
s
t
u
d
y
co
n
s
id
er
s
P
V
ce
ll
to
b
e
o
r
ig
in
atio
n
p
o
in
t
o
f
e
n
er
g
y
w
h
ile
a
DC
-
DC
co
n
tr
o
ller
is
u
til
ized
f
o
r
r
ec
tify
in
g
t
h
e
id
en
ti
f
ied
f
l
u
ctu
a
tio
n
ex
p
lo
r
e
d
in
b
o
th
v
o
ltag
e
an
d
cu
r
r
e
n
t
ch
ar
ec
ter
is
t
ics
o
f
f
er
ed
b
y
g
iv
e
n
s
o
lar
ce
lls
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il
201
9
:
8
5
1
-
8
6
0
854
T
h
e
co
n
tr
ib
u
tio
n
o
f
th
e
ab
o
v
e
s
h
o
w
n
d
e
s
i
g
n
is
t
h
at
it
s
ig
n
i
f
ican
tl
y
a
s
s
i
s
ts
i
n
i
o
b
tain
in
g
th
e
h
ig
h
est
v
a
lu
e
o
f
p
o
w
er
as
w
ell
as
it
in
s
is
ts
t
h
e
P
V
ce
ll
f
o
r
w
o
r
k
i
n
g
w
it
h
a
n
allo
ca
ted
v
o
lta
g
e
t
h
at
i
s
v
e
r
y
m
u
c
h
clo
s
er
to
h
ig
h
e
s
t v
al
u
e
o
f
t
h
e
p
o
w
er
f
o
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th
e
p
u
r
p
o
s
e
o
f
d
r
a
w
i
n
g
h
i
g
h
es
t p
o
w
er
.
2.
AL
G
O
RI
T
H
M
I
M
P
L
E
M
E
NT
A
T
I
O
N
T
h
e
alg
o
r
ith
m
i
s
i
n
tr
o
d
u
ce
d
in
o
r
d
er
to
b
etter
u
n
d
er
s
tan
d
th
e
f
lo
w
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
s
te
m
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e
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o
r
ass
es
s
i
n
g
t
h
e
MP
P
T
o
f
p
r
o
p
o
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ed
s
y
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te
m
.
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h
e
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m
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lete
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n
al
y
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i
s
o
f
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h
as
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ee
n
ca
r
r
ied
o
u
t
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n
s
id
er
in
g
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o
th
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o
lar
r
ad
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n
an
d
te
m
p
e
r
atu
r
e
f
ac
to
r
.
Fig
u
r
e
3
an
d
Fig
u
r
e
4
h
ig
h
li
g
h
t
s
th
e
C
u
r
r
e
n
t
-
Vo
ltag
e
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u
r
v
e
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d
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o
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er
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Vo
lta
g
e
cu
r
v
e,
w
h
er
e
th
e
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p
o
s
itio
n
s
o
f
5
ca
r
d
in
alit
ies o
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o
lar
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ad
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n
h
a
s
b
ee
n
test
i
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.
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n
o
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m
al
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o
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n
to
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en
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s
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o
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th
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t
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r
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t
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ac
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m
i
n
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izes
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h
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e
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n
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o
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o
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ce
lls
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n
I
V
c
u
r
v
e
a
t
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5
o
C
(
Fig
u
r
e
3
)
w
h
ile
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o
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er
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s
es
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h
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e
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n
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l
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e
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ac
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u
n
til
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h
e
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it
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s
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o
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n
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e
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eg
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ad
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ter
th
at.
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r
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it
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m
p
ar
is
o
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et
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ee
n
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o
th
th
e
g
r
ap
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ical
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a
l
y
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is
w
il
l
s
h
o
w
t
h
e
s
i
m
ilar
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n
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e
n
ce
p
o
i
n
t
(
w
h
ich
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s
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clo
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er
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r
o
x
i
m
ir
y
o
f
2
0
V
o
f
P
V
ce
ll)
.
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h
e
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p
o
in
ts
ar
e
h
i
g
h
li
g
h
ted
in
Fi
g
u
r
e
4
.
E
x
ac
tl
y
,
s
i
m
ilar
i
n
ter
p
r
etatio
n
ca
n
b
e
f
o
u
n
d
f
o
r
Fi
g
u
r
e
5
an
d
Fig
u
r
e
6
.
Ho
w
e
v
er
,
th
e
tr
en
d
s
o
f
b
o
th
p
o
w
er
a
n
d
v
o
lta
g
e
ar
e
s
lig
h
tl
y
d
if
f
er
en
t
f
o
r
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o
th
th
e
t
w
o
f
o
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m
s
o
f
a
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al
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s
i.e
.
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o
lar
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d
te
m
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e
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h
e
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r
b
o
th
cu
r
r
en
t
an
d
p
o
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er
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o
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al
y
z
in
g
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o
lar
f
ac
to
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is
q
u
ite
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is
tin
ct
w
it
h
r
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ec
t
to
d
i
f
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er
e
n
t
ca
r
d
in
al
it
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o
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s
o
lar
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.
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w
ev
er
,
t
h
i
s
i
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t
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cu
r
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is
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n
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,
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.
Fig
u
r
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3
.
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ter
is
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at
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An
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m
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h
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atel
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o
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el
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s
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e
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s
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y
Ka
k
o
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o
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et
a
l.
[
3
6
]
an
d
Ned
u
m
g
att
et
a
l.
[
3
7
]
.
Hen
ce
,
p
r
o
p
o
s
ed
s
y
s
te
m
o
f
f
er
s
co
s
t
ef
f
ec
ti
v
e
co
m
p
u
tatio
n
al
m
o
d
el
o
f
MP
PT
ev
alu
atio
n
in
P
V
ce
lls
.
4.
CO
NCLU
SI
O
N
T
h
e
p
r
o
p
o
s
e
d
s
y
s
tem
in
tr
o
d
u
c
es
a
s
im
p
lif
ie
d
m
o
d
el
f
o
r
d
ev
e
lo
p
in
g
a
P
V
ce
ll
in
o
r
d
e
r
to
en
s
u
r
e
b
ett
e
r
s
co
r
e
o
f
M
PP
T
.
T
h
e
p
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p
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s
e
d
s
y
s
tem
u
s
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d
i
o
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e
l
aw
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es
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ce
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d
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o
d
e
w
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s
in
g
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j
u
n
cti
o
n
,
cu
r
r
en
t
,
r
esis
tan
c
e
(
s
e
r
i
es)
,
s
o
la
r
r
a
d
ia
tio
n
,
an
d
t
em
p
er
a
tu
r
e.
T
h
e
p
r
o
p
o
s
ed
s
y
s
em
u
s
es
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o
th
s
o
la
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an
d
t
em
p
er
a
tu
r
e
p
a
r
am
ete
r
as
th
e
c
ase
s
tu
d
y
to
ev
alu
at
e
th
e
M
PP
T
s
c
o
r
e
.
T
h
e
s
tu
d
y
o
u
tc
o
m
e
is
ass
es
s
ed
w
ith
r
es
p
e
ct
t
o
cu
r
r
en
t
-
v
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l
tag
e
an
d
p
o
w
er
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v
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ltag
e
ch
a
r
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cte
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is
tics
.
C
o
n
s
i
d
e
r
in
g
a
s
p
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if
ic
en
v
i
r
o
n
m
en
t
o
f
DC
-
DC
co
n
v
er
te
r
to
p
o
l
o
g
y
,
th
e
s
tu
d
y
o
u
tco
m
e
s
h
o
w
s
th
at
an
ef
f
icien
t a
n
d
f
ast
er
i
d
en
t
if
ica
ti
o
n
o
f
M
PP
T
.
T
h
e
s
tu
d
y
o
u
tco
m
e
w
as
also
f
o
u
n
d
t
o
o
f
f
er
f
aste
r
c
o
m
p
u
tatio
n
al
p
r
o
c
ess
in
g
tim
e
w
ith
r
es
p
e
ct
t
o
ex
is
t
in
g
m
ec
h
n
an
is
m
o
f
MPPT
ev
alu
at
io
n
c
o
n
s
i
d
e
r
in
g
P
V
c
ell
s
.
REFEREN
CES
[1
]
M
d
.
Ra
b
i
u
l
Is
l
a
m
,
F
a
z
Ra
h
m
a
n
,
W
e
i
Xu
,
A
d
v
a
n
c
e
s
i
n
S
o
la
r
P
h
o
t
o
v
o
l
ta
ic
P
o
w
e
r
P
la
n
t
s,
S
p
r
i
n
g
e
r
,
2
0
1
6
[2
]
W
e
id
o
n
g
X
i
a
o
,
P
h
o
t
o
v
o
l
ta
ic
P
o
w
e
r
S
y
ste
m
:
M
o
d
e
l
i
n
g
,
De
sig
n
,
a
n
d
C
o
n
t
r
o
l
,
J
o
h
n
W
i
ley
&
S
o
n
s
,
2
0
1
7
[3
]
A
n
g
è
le
Re
i
n
d
e
r
s
,
P
i
e
r
re
V
e
rl
i
n
d
e
n
,
A
lex
a
n
d
re
F
re
u
n
d
li
c
h
,
P
h
o
t
o
v
o
l
ta
ic
S
o
la
r
E
n
e
rg
y
:
F
r
o
m
F
u
n
d
a
m
e
n
tals
t
o
A
p
p
li
c
a
t
i
o
n
s,
J
o
h
n
W
il
e
y
&
S
o
n
s,
2
0
1
7
[4
]
S
u
n
e
e
l
De
a
m
b
i
,
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
De
sig
n
:
P
r
o
c
e
d
u
re
s
,
T
o
o
l
s a
n
d
A
p
p
l
ica
ti
o
n
s
,
CR
C
P
re
ss
,
2
0
1
6
[5
]
Ca
r
lo
s A
lg
o
r
a
,
Ig
n
a
c
i
o
Re
y
-
S
t
o
l
le
,
Ha
n
d
b
o
o
k
o
n
C
o
n
c
e
n
t
ra
t
o
r
P
h
o
t
o
v
o
l
ta
ic T
e
c
h
n
o
lo
g
y
,
J
o
h
n
W
i
ley
&
S
o
n
s
,
2
0
1
6
[6
]
P
a
n
k
a
j
K
u
m
a
r
,
O
rg
a
n
i
c
S
o
la
r
Ce
ll
s:
De
v
ic
e
P
h
y
s
ics
,
P
r
o
c
e
ss
i
n
g
,
De
g
ra
d
a
t
i
o
n
,
a
n
d
P
r
e
v
e
n
t
i
o
n
,
C
RC
P
re
ss
,
2
0
1
6
[7
]
M
u
h
a
m
m
a
d
H.
Ra
s
h
i
d
,
P
o
w
e
r
E
le
c
tr
o
n
ics
Ha
n
d
b
o
o
k
,
B
u
tt
e
rw
o
r
t
h
-
He
i
n
e
m
a
n
n
,
2
0
1
7
[8
]
B.
G
.
De
v
i
a
n
d
M
.
M
a
h
e
s
h
,
―
A
b
r
ief
su
rv
e
y
o
n
d
if
f
e
re
n
t
m
u
l
t
i
l
e
v
e
l
i
n
v
e
rte
r
t
o
p
o
lo
g
ies
f
o
r
g
r
i
d
-
ti
e
d
s
o
lar
p
h
o
t
o
v
o
l
ta
ic
sy
s
tem
,
‖
2
0
1
7
IE
E
E
I
n
te
rn
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
S
m
a
r
t
E
n
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