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[
1
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,
o
n
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m
ajo
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ch
allen
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th
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o
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[
2
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T
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ets
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v
ar
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n
in
en
v
ir
o
n
m
e
n
tal
co
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d
itio
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s
[
3
]
.
T
h
u
s
,
it
d
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s
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Evaluation Warning : The document was created with Spire.PDF for Python.
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I
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t J Ad
v
Ap
p
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,
Vo
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10
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No
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3
,
Sep
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b
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2
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2
1
:
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ax
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s
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p
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[
4
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-
[
8
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.
T
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tech
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9
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cr
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(
I
C
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[
1
0
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.
T
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k
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Sin
g
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Ma
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[
1
1
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im
p
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P&
O
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r
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wh
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is
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ter
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Kim
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C
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[
1
2
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ar
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s
ig
n
if
ican
tly
an
d
h
ig
h
er
s
y
s
tem
ef
f
icien
cy
h
as
b
ee
n
ac
h
iev
e
d
.
Ho
wev
er
,
th
is
is
ca
p
a
b
le
o
f
tr
ac
k
in
g
MPP
o
n
ly
u
n
d
e
r
u
n
if
o
r
m
co
n
d
itio
n
s
as
i
t
s
h
o
ws
s
lu
g
g
is
h
an
d
p
o
o
r
co
n
v
er
g
en
ce
wh
e
n
th
er
e
is
p
ar
tial
s
h
ad
in
g
.
Similar
ly
,
I
C
alg
o
r
ith
m
f
o
r
MPPT
h
as
b
ee
n
ef
f
ec
tiv
ely
im
p
lem
en
t
ed
b
y
Dh
a
o
u
ad
i
et
a
l.
[
1
3
]
,
wh
e
r
e
s
y
s
tem
tr
an
s
ien
ts
an
d
c
o
n
v
e
r
g
in
g
r
esp
o
n
s
e
h
a
v
e
b
ee
n
an
aly
ze
d
with
g
r
ea
ter
o
s
cillatin
g
f
r
eq
u
en
cies.
T
h
e
p
r
o
p
o
s
ed
tech
n
i
q
u
e
is
s
im
p
le
an
d
ef
f
icien
t
b
u
t
th
e
d
r
awb
ac
k
is
th
at
it
ca
n
n
o
t
b
e
ap
p
lied
i
n
d
y
n
am
ically
ch
a
n
g
in
g
c
o
n
d
it
io
n
s
an
d
also
its
u
s
e
is
lim
ited
to
lo
w
p
o
wer
a
p
p
licatio
n
.
Acc
o
r
d
in
g
to
C
h
au
h
a
n
et
a
l.
[
1
4
]
o
v
er
co
m
es
th
is
lim
itatio
n
to
s
o
m
e
ex
ten
t
wh
er
e
a
m
o
d
if
ied
I
C
alg
o
r
ith
m
h
as
b
e
en
p
r
o
p
o
s
ed
b
y
o
p
tim
izin
g
th
e
co
n
tr
o
ller
g
ain
th
r
o
u
g
h
Gr
e
y
W
o
lf
tech
n
iq
u
e.
Ho
wev
er
,
r
es
u
lts
ar
e
s
atis
f
ac
to
r
y
o
n
l
y
f
o
r
i
n
s
o
latio
n
v
ar
i
atio
n
an
d
th
at
to
o
o
v
er
a
s
m
all
s
ca
le
o
n
ly
,
as
d
y
n
am
ic
ch
an
g
e
o
f
o
t
h
er
p
ar
a
m
eter
s
in
tr
o
d
u
ce
s
a
tr
u
n
ca
ted
er
r
o
r
.
Als
o
,
i
n
clu
s
io
n
o
f
o
p
ti
m
izatio
n
alg
o
r
ith
m
h
as in
cr
ea
s
ed
th
e
co
n
tr
o
ller
co
m
p
lex
ity
s
ig
n
if
ican
tly
.
W
ith
th
e
ev
o
l
u
tio
n
in
in
telli
g
en
ce
tech
n
iq
u
e,
th
e
r
e
h
a
v
e
b
ee
n
a
n
u
m
b
er
o
f
MPPT
alg
o
r
ith
m
s
d
ev
elo
p
e
d
in
r
ec
en
t
y
ea
r
s
o
n
t
h
e
b
asis
o
f
s
o
f
t
co
m
p
u
tin
g
.
A
m
o
n
g
th
ese
ev
o
lu
tio
n
ar
y
tech
n
iq
u
es,
th
e
lik
es
o
f
f
u
zz
y
lo
g
ic
co
n
tr
o
l
(
FLC)
[
1
5
]
,
ar
tific
ial
n
eu
r
al
n
etwo
r
k
(
ANN)
[
1
6
]
,
g
en
etic
al
g
o
r
ith
m
(
GA)
[
1
7
]
,
p
ar
ticl
e
s
war
m
o
p
tim
izatio
n
(
PS
O)
[
1
8
]
ar
e
f
o
u
n
d
to
b
e
ex
p
lo
r
e
d
im
m
en
s
ely
in
th
is
n
ew
er
a
o
f
MPPT.
Acc
o
r
d
in
g
t
o
Nem
o
u
r
s
an
d
C
h
o
wd
h
u
r
y
[
1
9
]
,
a
FLC
b
ased
MPPT
s
ch
em
e
h
as
b
ee
n
im
p
lem
e
n
ted
wh
ich
s
h
o
ws
g
o
o
d
tr
ac
k
in
g
ca
p
ab
ilit
y
f
o
r
lo
ad
v
ar
iatio
n
s
as
well.
T
h
e
m
ain
a
d
v
an
tag
e
o
f
FLC
b
ased
tech
n
i
q
u
es
is
th
e
s
p
ee
d
o
f
tr
ac
k
in
g
as
th
ey
ca
n
r
ed
u
ce
th
e
s
ettlin
g
tim
e.
H
o
wev
er
,
th
e
m
ajo
r
lim
itatio
n
o
f
FLC
is
th
a
t
o
n
ce
af
ter
d
ef
in
i
n
g
th
e
r
u
les
th
ey
ca
n
n
o
t
b
e
m
o
d
i
f
ied
an
d
h
e
n
ce
lar
g
e
am
o
u
n
t
o
f
tr
ain
in
g
is
r
eq
u
ir
e
d
f
o
r
e
f
f
ec
tiv
e
tr
ac
k
in
g
u
n
d
e
r
d
y
n
am
ic
in
s
o
latio
n
a
n
d
o
th
er
co
n
d
itio
n
s
.
He
n
ce
FLC
is
h
a
r
d
ly
u
s
ed
alo
n
e
f
o
r
tr
ac
k
in
g
;
r
a
th
er
its
co
m
b
in
atio
n
with
o
th
er
is
p
r
e
f
er
r
ed
as
h
y
b
r
id
MPPT
alg
o
r
ith
m
[
2
0
]
.
B
u
t
th
en
o
f
co
u
r
s
e
s
y
s
tem
co
m
p
le
x
ity
b
ec
o
m
es
a
m
ajo
r
is
s
u
e.
Ab
ad
i
et
a
l.
[
2
1
]
p
r
o
p
o
s
ed
a
Neu
r
o
-
Fu
zz
y
b
ased
ad
ap
tiv
e
MPPT
alg
o
r
ith
m
w
h
ich
h
as
im
p
r
o
v
e
d
th
e
co
n
v
e
r
s
io
n
ef
f
icien
cy
a
n
d
ca
n
b
e
ef
f
ec
tiv
e
f
o
r
all
co
n
d
itio
n
s
.
B
u
t
th
e
p
r
o
b
lem
ass
o
ciate
d
with
ANN
tech
n
iq
u
e
is
th
at
its
co
m
p
u
tatio
n
al
tim
e
an
d
m
em
o
r
y
r
eq
u
i
r
em
en
t
is
lar
g
e
wh
ich
s
ig
n
i
f
ican
tly
in
cr
ea
s
es
th
e
co
m
p
lex
ity
.
Similar
ly
,
GA
b
a
s
ed
alg
o
r
ith
m
s
wh
ich
a
r
e
m
ai
n
ly
em
p
lo
y
ed
f
o
r
s
to
ch
asti
c
s
ea
r
ch
es,
also
h
av
e
th
e
s
am
e
d
r
awb
ac
k
o
f
lar
g
e
m
em
o
r
y
a
n
d
tr
ain
i
n
g
r
e
q
u
ir
e
m
en
t
b
ec
au
s
e
o
f
h
ig
h
in
iti
al
p
o
p
u
latio
n
.
PS
O
is
an
o
th
er
ev
o
lu
tio
n
a
r
y
tech
n
i
q
u
e
wh
ich
is
g
ain
in
g
m
u
c
h
o
f
t
h
e
atten
tio
n
in
r
ec
en
t
y
ea
r
s
[
2
2
]
.
I
t
is
p
ar
ticu
lar
ly
well
s
u
ited
f
o
r
tr
ac
k
in
g
o
f
g
lo
b
al
m
ax
im
a
u
n
d
er
p
ar
tial
s
h
ad
in
g
ca
s
es
wh
er
e
p
an
els
ar
e
n
o
n
-
u
n
if
o
r
m
l
y
illu
m
in
ated
.
Ho
wev
e
r
,
th
e
af
f
air
o
f
p
ar
am
eter
in
itializatio
n
is
a
d
if
f
icu
lt
task
in
PS
O
b
ased
alg
o
r
ith
m
wh
ich
g
iv
es
r
is
e
to
th
e
r
an
d
o
m
n
ess
in
in
itial
d
u
t
y
cy
cle.
An
o
th
er
d
r
awb
ac
k
o
f
PS
O
tech
n
iq
u
e
is
th
at
with
th
e
in
cr
ea
s
e
in
p
o
p
u
latio
n
s
ize,
co
m
p
u
tatio
n
al
d
i
f
f
icu
lty
also
in
cr
ea
s
es.
Her
e
it
is
im
p
o
r
tan
t
to
n
o
te
th
at
p
ar
tial
s
h
ad
in
g
h
as
s
ev
er
al
ill
ef
f
ec
ts
o
n
PV
s
y
s
tem
p
er
f
o
r
m
an
ce
as
it
lead
s
to
co
n
s
id
er
ab
le
am
o
u
n
t
o
f
p
o
wer
l
o
s
s
an
d
m
ay
e
v
en
ca
u
s
e
d
am
a
g
e
to
p
an
els
[
2
3
]
,
[
2
4
]
.
T
h
e
r
ef
o
r
e,
to
d
esig
n
a
s
im
p
le
an
d
ef
f
e
ctiv
e
alg
o
r
ith
m
f
o
r
m
in
im
izin
g
th
e
c
o
n
s
eq
u
en
ce
s
o
f
p
ar
tial
s
h
ad
i
n
g
co
n
tin
u
es
to
b
e
an
o
t
h
er
ch
allen
g
in
g
asp
ec
t
in
th
e
f
ield
o
f
MPPT,
ev
en
th
o
u
g
h
th
e
r
e
h
av
e
b
ee
n
m
a
n
y
p
r
o
p
o
s
ed
wo
r
k
.
T
h
u
s
in
v
iew
o
f
d
etailed
an
aly
s
is
o
f
MPPT
alg
o
r
ith
m
s
as
d
is
cu
s
s
ed
ab
o
v
e,
it
is
o
b
s
er
v
ed
th
at
th
er
e
ex
is
ts
a
n
u
m
b
er
o
f
tech
n
i
q
u
e
s
wh
ich
p
er
f
o
r
m
s
atis
f
ac
to
r
ily
in
u
n
if
o
r
m
co
n
d
itio
n
s
with
s
tead
y
v
ar
iatio
n
s
i
n
en
v
ir
o
n
m
en
tal
p
a
r
am
eter
s
.
H
o
wev
er
,
t
h
er
e
a
r
e
two
m
ajo
r
an
d
co
m
m
o
n
d
r
awb
ac
k
s
ass
o
ciate
d
with
th
ese
m
eth
o
d
s
wh
ich
n
ee
d
to
b
e
a
d
d
r
ess
ed
f
o
r
ef
f
ic
ien
t
an
d
r
elia
b
le
PV
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
e
f
ir
s
t
is
th
at
t
h
ey
f
ail
to
r
esp
o
n
d
e
f
f
ec
tiv
ely
wh
en
th
er
e
is
d
y
n
a
m
ic
ch
an
g
e
i
n
th
e
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
I
t
m
ea
n
s
th
at
th
eir
o
p
er
atin
g
p
o
in
t
d
r
if
ts
awa
y
f
r
o
m
MPP
wh
en
th
e
c
o
n
d
it
io
n
s
ar
e
v
ar
ied
r
a
p
id
ly
.
Seco
n
d
ly
,
th
ey
s
h
o
w
in
ca
p
ab
ilit
y
to
g
u
a
r
an
tee
t
h
e
s
u
cc
ess
f
u
l
tr
ac
k
in
g
o
f
g
lo
b
al
MPP
in
ca
s
e
o
f
th
e
p
ar
tial
s
h
a
d
in
g
o
r
n
o
n
-
u
n
if
o
r
m
s
o
lar
ir
r
ad
ian
ce
.
Mo
tiv
ated
b
y
th
e
ab
o
v
e
d
ef
icien
cies
o
f
ex
is
tin
g
MPPT
tech
n
iq
u
es,
t
h
is
r
esear
ch
wo
r
k
p
r
o
p
o
s
es
a
s
im
p
lifie
d
a
n
d
e
n
h
an
ce
d
m
o
d
el
-
b
ased
(
MB)
MPPT
alg
o
r
ith
m
.
Her
e,
th
e
d
is
tin
ct
f
ea
tu
r
e
o
f
p
r
o
p
o
s
ed
MB
alg
o
r
ith
m
is
th
at
it
wo
r
k
s
ef
f
ec
tiv
ely
n
o
t
o
n
ly
i
n
d
y
n
am
ic
co
n
d
itio
n
s
wh
er
e
in
s
o
latio
n
o
r
tem
p
er
atu
r
e
v
ar
ies
r
ap
id
l
y
a
n
d
co
n
tin
u
o
u
s
ly
,
r
ath
e
r
it
h
as
ad
d
itio
n
al
ca
p
a
b
ilit
y
o
f
t
r
ac
k
in
g
t
h
e
MPP
ac
cu
r
ately
in
p
ar
tial
s
h
ad
in
g
c
o
n
d
itio
n
s
also
.
B
ased
o
n
th
e
n
ew
g
o
v
er
n
i
n
g
eq
u
atio
n
s
an
d
p
r
ec
is
ed
esti
m
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2
2
5
2
-
8
8
1
4
E
n
h
a
n
ce
d
mo
d
el
b
a
s
ed
a
l
g
o
r
ith
m
to
r
ein
fo
r
ce
P
V
s
ystem
w
it
h
d
yn
a
mic
MPP
T c
a
p
a
b
ilit
y
(
Md
.
E
h
tesh
a
m
)
263
tech
n
iq
u
e,
th
is
p
a
p
er
h
as
m
o
d
if
ied
th
e
MB
ap
p
r
o
ac
h
to
d
ev
elo
p
an
en
h
an
ce
d
ca
p
ab
ilit
y
o
f
MPPT
in
d
y
n
am
ic
co
n
d
itio
n
s
.
R
ath
er
th
an
g
o
in
g
f
o
r
h
e
u
r
is
tic
s
ea
r
ch
o
f
MPP
as
f
o
llo
wed
b
y
tr
ad
itio
n
al
tech
n
iq
u
es,
th
e
p
r
o
p
o
s
ed
MB
alg
o
r
ith
m
u
tili
ze
s
th
e
m
a
th
em
atica
l
m
o
d
elin
g
an
d
h
e
n
c
e
p
r
e
-
d
eter
m
in
es
th
e
MPP
an
aly
tically
.
T
h
u
s
th
e
p
r
o
p
o
s
ed
MB
alg
o
r
ith
m
e
n
s
u
r
es
ef
f
icien
t
o
p
er
ati
o
n
o
f
PV
s
y
s
tem
m
ain
tai
n
in
g
s
tab
le
an
d
r
eliab
le
s
u
p
p
l
y
i
n
th
e
d
y
n
a
m
ic
wo
r
k
in
g
co
n
d
itio
n
s
.
2.
SYST
E
M
M
O
D
E
L
I
NG
F
O
R
P
RO
P
O
SE
D
M
B
AL
G
O
R
I
T
H
M
T
h
er
e
ar
e
two
m
ai
n
asp
ec
ts
in
v
o
lv
ed
in
ac
c
o
m
p
lis
h
in
g
m
o
d
el
b
ased
MPPT
alg
o
r
ith
m
wh
i
ch
in
d
u
ce
s
th
e
d
is
tin
g
u
is
h
ed
tr
ac
k
in
g
f
ea
tu
r
e.
First
o
f
all
it
im
p
lies
th
e
task
o
f
ac
cu
r
ate
m
o
d
elin
g
o
f
PV
p
an
el.
Sev
e
r
al
m
o
d
els
f
o
r
th
e
PV
p
an
el
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
liter
atu
r
e
w
h
er
e
s
in
g
le
d
i
o
d
e
a
n
d
two
d
io
d
e
m
o
d
el
ar
e
f
o
u
n
d
to
b
e
m
o
s
t
co
m
m
o
n
o
n
es
[
2
5
]
-
[
2
7
]
.
Sin
g
le
d
io
d
e
m
o
d
el
s
h
o
wn
in
Fig
u
r
e
1
is
f
o
u
n
d
to
b
e
th
e
m
o
s
t
s
u
itab
le
o
n
e,
o
f
f
er
i
n
g
s
im
p
licity
with
en
o
u
g
h
ac
c
u
r
ac
y
an
d
h
e
n
ce
i
t
h
as
b
ee
n
ap
p
lied
h
er
e
w
h
ile
m
o
d
elin
g
th
e
PV
cir
cu
it.
A
r
ep
lace
m
en
t
tr
ac
k
i
s
cr
ea
ted
b
y
th
e
p
ar
allel
c
o
n
n
ec
ted
d
io
d
e
(
b
y
p
ass
d
io
d
e)
wh
ich
p
r
ev
en
ts
th
e
d
am
ag
in
g
ef
f
ec
ts
o
f
h
o
t
-
s
p
o
ts
.
On
th
e
b
asis
o
f
eq
u
iv
alen
t
cir
cu
it
th
e
ex
p
r
ess
io
n
f
o
r
o
u
t
p
u
t
cu
r
r
en
t
ca
n
b
e
s
im
p
ly
g
iv
en
as
(
1
)
.
I
=
I
ph
−
I
D
−
I
sh
(
1
)
No
w,
ap
p
ly
in
g
th
eo
r
y
o
f
s
em
ico
n
d
u
ct
o
r
s
m
o
d
if
ie
d
ex
p
r
ess
io
n
ca
n
b
e
g
iv
en
as
(
2
)
.
I
=
I
ph
−
I
o
(
e
xp
(
+
)
−
1
)
−
+
ℎ
(
2
)
W
h
er
e,
I
o
is
th
e
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
e
n
t,
is
th
e
id
ea
lity
f
ac
to
r
a
n
d
is
th
e
th
er
m
a
l
v
o
ltag
e.
Her
e
f
o
r
r
estrictin
g
th
e
p
an
el
o
p
e
r
atio
n
ar
o
u
n
d
MPP,
c
h
ar
ac
ter
is
tic
m
atch
in
g
is
p
er
f
o
r
m
ed
b
y
t
u
n
in
g
th
e
th
er
m
al
v
o
ltag
e
f
r
o
m
tim
e
to
tim
e
wit
h
th
e
s
er
ie
s
r
esis
tan
ce
(
R
s
)
.
T
h
e
r
elev
a
n
cy
o
f
s
h
u
n
t
r
esis
tan
ce
ca
n
b
e
i
g
n
o
r
e
d
as
it
h
ar
d
ly
im
p
ac
ts
th
e
b
eh
av
io
u
r
f
o
r
MPP
r
eg
io
n
.
T
h
u
s
all
th
e
f
ac
to
r
s
af
f
ec
tin
g
ac
cu
r
ac
y
o
f
PV
m
o
d
el
h
av
e
b
ee
n
tak
en
ca
r
e
an
d
th
ese
s
et
a
b
en
ch
m
a
r
k
f
o
r
g
o
v
er
n
in
g
t
h
e
PV
ch
ar
ac
ter
is
tics
u
n
d
er
d
y
n
a
m
ic
co
n
d
itio
n
s
.
Fig
u
r
e
1
.
E
q
u
iv
alen
t sin
g
le
d
i
o
d
e
PV c
ir
cu
it
No
w,
th
e
n
e
x
t
asp
ec
t
o
f
MB
alg
o
r
ith
m
wh
ic
h
p
lay
s
a
v
ital
r
o
le
f
o
r
d
y
n
am
ic
tr
ac
k
in
g
is
to
esti
m
ate
th
e
p
ar
a
m
eter
s
p
r
ec
is
ely
.
Gen
er
ally
,
p
a
n
el
s
p
ec
if
icatio
n
s
ar
e
d
e
clar
ed
b
y
th
e
m
an
u
f
ac
tu
r
er
as
g
iv
en
in
T
a
b
le
1
in
d
icatin
g
v
o
ltag
e
an
d
cu
r
r
en
t
r
atin
g
s
f
o
r
v
er
tices
lik
e
o
p
e
n
cir
cu
it,
s
h
o
r
t
cir
c
u
it
an
d
MP
P.
T
h
u
s
PV
m
o
d
el
ca
n
b
e
d
ef
i
n
ed
u
tili
zin
g
r
ated
v
alu
es
f
r
o
m
d
atash
ee
t
f
o
r
Sta
n
d
ar
d
T
est
C
o
n
d
itio
n
s
(
STC:
I
n
s
o
latio
n
S=
1
0
0
0
W
/m
2
,
T
em
p
er
atu
r
e
T
=
2
5
o
C
)
.
B
u
t
d
esig
n
in
g
th
e
m
o
d
el
u
s
in
g
s
p
ec
if
ied
d
ata
m
ay
lea
d
to
ce
r
tain
in
ac
cu
r
ac
y
d
u
e
to
d
is
p
er
s
io
n
o
f
th
e
m
an
u
f
ac
tu
r
in
g
s
ch
em
e
an
d
u
n
u
s
ed
r
ated
v
alu
es.
T
h
u
s
to
o
b
tai
n
a
h
ig
h
ly
p
r
ec
is
ed
m
o
d
el,
h
er
e
in
MB
alg
o
r
ith
m
all
th
e
en
v
ir
o
n
m
en
tal
p
ar
a
m
eter
s
ar
e
m
ea
s
u
r
ed
p
r
e
cisely
with
th
e
h
elp
o
f
p
y
r
an
o
m
eter
an
d
h
u
m
id
ity
s
en
s
o
r
as
s
h
o
wn
in
th
e
n
e
x
t
s
ec
tio
n
.
T
h
en
ac
c
o
r
d
i
n
g
ly
PV
p
a
n
el
p
ar
am
eter
s
ar
e
esti
m
ated
s
o
as
to
g
et
a
h
ig
h
ly
ac
cu
r
ate
tu
n
in
g
with
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
T
h
is
p
r
e
d
ictiv
e
ap
p
r
o
ac
h
lead
s
to
p
r
ed
ictio
n
o
f
er
r
o
r
i
n
ad
v
a
n
ce
to
s
witch
in
g
s
ig
n
als
f
ed
to
co
n
v
er
te
r
an
d
th
u
s
allo
ws
f
ast
ju
m
p
in
th
e
ar
r
ay
v
o
ltag
e
f
o
r
r
ap
id
ly
v
ar
y
in
g
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
T
h
e
r
ef
o
r
e,
r
ath
er
th
an
g
o
i
n
g
f
o
r
h
eu
r
is
tic
s
ea
r
ch
o
f
MPP
as
f
o
llo
wed
b
y
co
m
m
o
n
tech
n
iq
u
es,
th
e
p
r
o
p
o
s
ed
MB
alg
o
r
ith
m
u
tili
ze
s
th
e
p
r
ec
is
ed
m
o
d
elin
g
an
d
esti
m
atio
n
wh
ich
en
ab
les
it
to
p
r
e
-
d
ete
r
m
in
e
th
e
MPP
an
aly
tically
.
C
o
n
s
eq
u
en
tly
,
it
ac
h
iev
es
a
s
ig
n
if
ican
t
en
h
an
ce
m
e
n
t in
tr
ac
k
i
n
g
ca
p
a
b
ilit
y
u
n
d
er
d
y
n
am
ic
co
n
d
itio
n
s
r
esu
ltin
g
i
n
to
h
i
g
h
ac
cu
r
ac
y
an
d
ef
f
icien
cy
.
Fin
ally
f
o
r
s
u
cc
ess
f
u
l
im
p
lem
en
tatio
n
o
f
MB
alg
o
r
ith
m
s
o
m
e
m
ath
em
atica
l
o
p
er
atio
n
s
ar
e
ca
r
r
ied
o
u
t w
h
ich
ch
a
r
ac
ter
izes th
e
PV p
an
el
ac
cu
r
ately
in
t
h
e
r
eg
i
o
n
o
f
MPP.
On
ce
th
e
o
p
er
atin
g
v
o
ltag
e
a
n
d
cu
r
r
en
t
f
o
r
MPP
is
o
b
tain
e
d
th
en
th
e
o
u
tp
u
t
p
o
wer
is
d
if
f
er
e
n
tiated
an
d
eq
u
ated
to
ze
r
o
as
ex
p
r
e
s
s
ed
b
y
(
3
)
an
d
(
4
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
261
–
2
7
0
264
I
m
p
o
s
itio
n
o
f
t
h
ese
s
et
o
f
eq
u
atio
n
s
lead
s
to
f
in
e
tu
n
in
g
o
f
p
an
el
an
d
b
o
u
n
d
s
th
e
s
y
s
tem
to
o
p
er
ate
at
its
MPP
u
n
d
er
all
s
o
r
t
o
f
d
y
n
am
ic
c
o
n
d
itio
n
s
.
=
+
(
1
−
mp
sc
)
−
(
3
)
(
VI
)
dI
|
I=
I
mp
=
mp
+
mp
mp
-
I
sc
−
mp
=
0
(
4
)
3.
H
ARDWA
R
E
P
L
A
T
F
O
RM
F
O
R
M
B
M
P
P
T
ANA
L
YS
I
S
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
d
escr
ip
tio
n
o
f
h
ar
d
war
e
s
etu
p
alo
n
g
with
all
its
co
m
p
o
n
en
ts
th
at
p
r
o
v
id
ed
a
p
latf
o
r
m
f
o
r
ex
p
er
im
en
tal
an
a
ly
s
is
o
f
MB
alg
o
r
ith
m
.
PV
p
an
els
o
f
2
KW
r
atin
g
wer
e
ex
p
lo
r
ed
f
o
r
th
is
wo
r
k
wh
ich
co
n
s
is
ts
o
f
ten
p
o
l
y
cr
y
s
tallin
e
m
o
d
u
les,
f
i
v
e
m
o
n
o
cr
y
s
tallin
e
an
d
f
iv
e
th
in
f
ilm
m
o
d
u
les
ea
ch
o
f
1
0
0
W
r
atin
g
.
A
p
ictu
r
e
o
f
i
n
s
talled
p
an
el
is
s
h
o
wn
b
y
Fig
u
r
e
2
wh
er
ea
s
th
e
p
an
el
s
p
ec
if
icatio
n
s
h
av
e
b
ee
n
s
u
m
m
ar
ized
in
T
ab
le
1
as
d
is
cu
s
s
ed
ea
r
lier
,
cr
u
x
o
f
MB
alg
o
r
ith
m
is
th
e
o
p
tim
u
m
esti
m
atio
n
o
f
PV
m
o
d
e
l
p
ar
am
eter
s
as
a
f
u
n
ctio
n
o
f
th
eir
d
ep
e
n
d
en
c
y
o
n
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
.
T
h
er
e
b
y
,
v
ar
i
atio
n
s
in
f
ac
to
r
s
lik
e
s
o
lar
in
s
o
latio
n
,
h
u
m
id
ity
a
n
d
win
d
s
p
ee
d
h
av
e
b
ee
n
tr
ied
to
b
e
m
ea
s
u
r
ed
with
u
tm
o
s
t
ac
cu
r
ac
y
.
Py
r
a
n
o
m
ete
r
h
as b
ee
n
u
s
ed
h
e
r
e
to
p
r
ec
is
ely
m
ea
s
u
r
e
th
e
s
o
lar
in
s
o
latio
n
.
I
t is a
s
en
s
o
r
th
at
m
ea
s
u
r
es f
lu
x
d
en
s
ity
o
r
g
lo
b
al
r
ad
iatio
n
an
d
b
ea
r
s
alm
o
s
t
a
lin
ea
r
r
elatio
n
with
th
e
f
r
eq
u
en
cy
b
an
d
o
f
t
o
tal
s
o
lar
r
a
d
iatio
n
.
I
t
ca
n
also
m
ea
s
u
r
e
th
e
d
if
f
u
s
e
r
a
d
iatio
n
f
o
r
wh
ich
p
y
r
an
o
m
ete
r
is
s
h
ad
ed
with
a
d
is
k
p
lace
d
f
o
r
p
r
ev
en
tin
g
th
e
d
ir
ec
t
in
cid
en
ce
o
f
b
ea
m
.
Similar
ly
,
a
h
u
m
id
ity
s
en
s
o
r
h
as
b
ee
n
a
ls
o
u
s
ed
to
g
iv
e
t
h
e
m
ea
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r
e
o
f
wate
r
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o
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r
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e
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o
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e.
I
t
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r
elate
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with
th
e
tem
p
er
atu
r
e
in
t
h
e
s
en
s
e
th
at
v
ap
o
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r
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t
o
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ter
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ictu
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e
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f
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as b
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Fig
u
r
e
3
.
T
ab
le
1
.
Sp
ec
if
icatio
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o
f
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ac
tical
2
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els in
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talled
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.
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o
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P
a
r
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me
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p
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V
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l
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e
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To
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e
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Ph
o
to
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ltaic
p
an
els
POL
Y
CR
YST
ALLI
NE
M
O
NO
CR
YST
ALLI
NE
TH
IN
FILM
Fig
u
r
e
2
.
PV p
a
n
els in
s
talled
o
n
r
o
o
f
-
to
p
(
a)
(
b
)
Fig
u
r
e
3
.
I
n
s
talled
m
ea
s
u
r
in
g
d
ev
ices
:
(
a)
p
y
r
an
o
m
eter
an
d
(
b
)
h
u
m
id
ity
s
en
s
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2
2
5
2
-
8
8
1
4
E
n
h
a
n
ce
d
mo
d
el
b
a
s
ed
a
l
g
o
r
ith
m
to
r
ein
fo
r
ce
P
V
s
ystem
w
it
h
d
yn
a
mic
MPP
T c
a
p
a
b
ilit
y
(
Md
.
E
h
tesh
a
m
)
265
Fu
r
th
er
,
it
h
as
to
b
e
n
o
te
d
h
er
e
th
at
an
y
k
in
d
o
f
m
o
n
ito
r
in
g
s
ch
em
e
u
tili
zin
g
s
en
s
o
r
m
o
n
ito
r
in
g
r
eq
u
ir
es
a
d
ata
c
o
llectio
n
s
y
s
tem
.
Fo
r
th
is
p
u
r
p
o
s
e
a
p
o
r
tab
l
e
C
R
1
0
0
0
d
ata
lo
g
g
er
was
in
s
talled
wh
ich
k
ee
p
s
r
ec
o
r
d
in
g
all
th
e
m
ea
s
u
r
ed
v
a
lu
es
o
f
p
ar
a
m
eter
s
as
well
as
co
r
r
esp
o
n
d
in
g
v
ar
iatio
n
s
in
p
an
el
ch
ar
ac
ter
is
tics
.
T
h
is
d
ata
l
o
g
g
er
was
s
y
n
c
h
r
o
n
is
ed
with
a
d
is
p
lay
b
o
a
r
d
s
etu
p
in
s
id
e
th
e
lab
an
d
at
t
h
e
s
a
m
e
tim
e
it
was
also
co
n
n
ec
ted
to
a
co
m
p
u
ter
.
Hen
ce
th
e
in
s
tan
tan
e
o
u
s
v
alu
es
o
f
cu
r
r
e
n
t,
v
o
ltag
e
a
n
d
p
o
wer
wer
e
av
ailab
le
i
n
th
e
d
is
p
lay
b
o
ar
d
wh
er
ea
s
a
co
n
ti
n
u
o
u
s
r
ec
o
r
d
o
f
th
e
s
am
e
was
s
to
r
ed
in
th
e
s
y
s
tem
.
Fig
u
r
e
4
s
h
o
ws
a
p
ictu
r
e
o
f
d
ata
lo
g
g
er
in
s
talled
o
n
r
o
o
f
-
to
p
an
d
th
e
co
r
r
esp
o
n
d
in
g
d
is
p
lay
p
an
el
is
s
h
o
wn
in
Fig
u
r
e
5
.
Fig
u
r
e
4
.
C
R
1
0
0
0
d
ata
lo
g
g
er
Fig
u
r
e
5
.
Dis
p
lay
b
o
ar
d
s
etu
p
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Hav
in
g
esti
m
ated
all
t
h
e
p
a
r
am
eter
s
p
r
ec
is
ely
with
t
h
eir
d
ep
en
d
e
n
cy
estab
lis
h
ed
o
n
th
e
wo
r
k
in
g
co
n
d
itio
n
s
,
th
is
s
ec
tio
n
n
o
w
p
r
esen
ts
th
e
d
etailed
p
er
f
o
r
m
an
ce
an
al
y
s
is
o
f
MB
alg
o
r
ith
m
.
Her
e
th
e
ef
f
ec
tiv
en
ess
o
f
p
r
o
p
o
s
ed
al
g
o
r
ith
m
is
ev
alu
ated
f
o
r
r
a
p
id
v
ar
iatio
n
s
o
f
all
s
o
r
ts
o
f
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
in
clu
d
in
g
p
ar
tial
s
h
ad
in
g
o
v
er
th
eir
f
u
ll
p
r
ac
tical
r
an
g
e.
First
th
e
MB
alg
o
r
ith
m
is
test
ed
i
n
MA
T
L
AB
/S
im
u
lin
k
p
latf
o
r
m
wh
er
e
s
im
u
lated
r
esu
lts
o
f
t
r
ac
k
ed
MPP
f
o
r
d
y
n
am
ic
i
n
s
o
latio
n
,
tem
p
er
at
u
r
e
an
d
s
h
ad
in
g
ar
e
p
r
esen
ted
.
T
h
en
th
e
r
ea
l
tim
e
p
er
f
o
r
m
a
n
ce
i
s
an
aly
s
ed
wh
er
e
e
x
p
er
im
e
n
tal
r
esu
lts
h
av
e
b
ee
n
d
is
cu
s
s
ed
.
Fin
ally
co
m
p
ar
is
o
n
s
o
f
b
o
th
th
e
r
esu
lts
h
av
e
b
ee
n
ca
r
r
ied
o
u
t
to
v
alid
ate
th
e
ef
f
ec
tiv
en
ess
o
f
p
r
o
p
o
s
ed
MB a
lg
o
r
ith
m
.
4
.
1
.
Sim
ula
t
io
n
re
s
ults
Simu
lin
k
m
o
d
el
h
as
b
ee
n
s
tr
ictly
d
esig
n
ed
o
n
th
e
b
asis
o
f
m
ath
em
atica
l
eq
u
atio
n
s
ch
ar
ac
t
er
izin
g
th
e
MB
alg
o
r
ith
m
as
d
is
cu
s
s
ed
ea
r
lier
.
First
th
e
p
h
o
to
cu
r
r
en
t
(
I
p
h
)
is
ev
alu
ated
as
a
f
u
n
ctio
n
o
f
s
o
lar
r
a
d
iatio
n
,
th
en
af
ter
p
r
o
p
er
co
m
p
u
tatio
n
o
f
r
ev
e
r
s
e
s
atu
r
atio
n
cu
r
r
e
n
t
(
I
o
)
an
d
th
er
m
al
v
o
ltag
e
(
Vt)
d
io
d
e
cu
r
r
e
n
t
is
o
b
tain
ed
as
s
h
o
wn
b
y
b
u
ild
in
g
b
lo
c
k
s
in
Fig
u
r
e
6
.
Her
e
it
ca
n
b
e
s
ee
n
t
h
at
d
io
d
e
cu
r
r
e
n
t
h
as
ex
p
o
n
e
n
tial
d
ep
en
d
e
n
cy
o
n
th
e
r
m
al
v
o
ltag
e.
T
h
er
ea
f
ter
th
e
s
u
m
m
atio
n
o
f
d
io
d
e
c
u
r
r
e
n
t
an
d
s
h
u
n
t
c
u
r
r
en
t
is
s
u
b
tr
ac
te
d
f
r
o
m
p
h
o
to
cu
r
r
en
t
to
r
esu
lt
in
to
th
e
p
an
el
o
u
tp
u
t
cu
r
r
en
t
as
illu
s
tr
ated
b
y
th
e
b
lo
ck
s
in
Fig
u
r
e
7
.
T
h
u
s
o
n
ce
th
e
tu
n
ed
v
alu
es
f
o
r
cu
r
r
e
n
t
a
n
d
v
alu
es
ar
e
esti
m
ated
f
o
r
M
PP
o
p
er
atio
n
,
th
ese
ar
e
ex
p
o
r
ted
to
wo
r
k
s
p
ac
e
f
o
r
p
r
o
ce
s
s
in
g
m
ax
im
u
m
p
o
wer
o
u
tp
u
t a
s
s
h
o
wn
in
Fig
u
r
e
8
.
No
w
b
ef
o
r
e
g
o
in
g
f
o
r
d
y
n
am
ic
v
ar
iatio
n
s
in
o
p
er
atin
g
c
o
n
d
itio
n
s
,
f
ir
s
t
o
f
all
th
e
ch
ar
ac
t
er
is
tic
f
o
r
PV
p
o
wer
is
a
n
aly
ze
d
at
s
tan
d
ar
d
test
co
n
d
itio
n
(
STC).
T
h
is
s
ets
a
b
en
ch
m
a
r
k
f
o
r
th
e
r
e
s
t
o
f
e
v
alu
atio
n
an
d
also
r
atif
ies
h
ig
h
er
tr
ac
k
i
n
g
ef
f
icien
cy
o
f
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
Fig
u
r
e
9
s
h
o
ws
th
e
PV
cu
r
v
e
o
b
tain
e
d
at
STC
wh
er
e
it
ca
n
b
e
o
b
s
er
v
e
d
th
a
t
MPP
is
s
u
cc
es
s
f
u
lly
tr
ac
k
ed
ar
o
u
n
d
a
v
o
ltag
e
o
f
1
9
0
V
with
an
ac
h
iev
e
d
m
ax
im
u
m
p
o
wer
o
f
1
9
2
0
W
.
T
h
u
s
MB
alg
o
r
ith
m
is
n
o
t
o
n
ly
ef
f
ec
t
iv
e
f
o
r
d
y
n
am
ic
co
n
d
itio
n
s
b
u
t
it
is
also
ca
p
ab
le
o
f
y
ield
in
g
a
h
ig
h
er
tr
ac
k
in
g
ef
f
icien
cy
.
No
w
th
e
r
esp
o
n
s
e
i
n
PV
c
h
a
r
ac
ter
is
tic
is
tr
ac
k
ed
f
o
r
th
e
d
y
n
am
ic
wo
r
k
i
n
g
co
n
d
itio
n
s
,
b
y
r
ap
i
d
ly
v
ar
y
in
g
d
if
f
er
en
t
p
ar
am
eter
s
o
n
e
b
y
o
n
e.
First
th
e
in
s
o
latio
n
is
v
a
r
ied
d
y
n
am
ically
o
v
e
r
th
e
f
u
ll
s
ca
le
f
r
o
m
1
0
0
W
/m
2
to
1
0
0
0
W
/m
2
k
ee
p
in
g
t
h
e
tem
p
e
r
atu
r
e
co
n
s
tan
t
at
2
5
º
C
.
T
h
er
ef
o
r
e,
PV
ch
ar
ac
ter
is
tics
also
k
ee
p
o
n
ch
a
n
g
in
g
d
y
n
am
ically
an
d
co
r
r
esp
o
n
d
in
g
to
ea
ch
ch
ar
ac
t
er
is
tic
g
lo
b
al
MPP
is
tr
ac
k
ed
ef
f
ec
tiv
ely
.
T
h
u
s
a
lar
g
e
n
u
m
b
er
o
f
ch
a
r
ac
ter
is
tics
ar
e
o
b
tain
ed
w
h
er
e
MPP
is
tr
ac
k
ed
s
ep
ar
ately
f
o
r
d
y
n
am
ic
v
ar
iatio
n
s
o
f
in
s
o
latio
n
f
r
o
m
1
0
0
t
o
2
0
0
to
3
0
0
an
d
s
o
o
n
.
As it is n
o
t p
o
s
s
ib
le
h
er
e
to
s
h
o
w
all
th
e
ch
ar
ac
ter
is
tics
an
d
MPP
tr
ac
k
ed
f
o
r
co
r
r
esp
o
n
d
i
n
g
in
s
o
latio
n
,
h
en
ce
as a
s
am
p
le
v
alu
e
o
n
e
s
u
ch
ch
a
r
ac
ter
is
tic
o
b
tain
ed
at
in
s
o
latio
n
o
f
6
0
0
W
/m
2
is
s
h
o
wn
in
Fig
u
r
e
1
0
.
I
t
ca
n
b
e
o
b
s
er
v
ed
h
e
r
e
th
at
MPP
n
o
w
o
cc
u
r
s
ar
o
u
n
d
a
v
o
ltag
e
o
f
1
8
5
V
with
tr
ac
k
ed
m
ax
i
m
u
m
p
o
wer
o
f
1
0
9
0
W
,
wh
ich
is
o
b
v
io
u
s
ly
m
u
ch
less
th
an
th
at
o
b
tain
e
d
at
STC
d
u
e
to
th
e
r
ed
u
ce
d
i
n
s
o
latio
n
.
Nex
t,
we
k
ee
p
th
e
in
s
o
latio
n
c
o
n
s
tan
t
at
1
0
0
0
W
/m
2
an
d
v
ar
y
th
e
tem
p
er
atu
r
e
o
v
er
th
e
s
ca
le
f
r
o
m
1
2
º
C
to
4
5
º
C
.
Ag
ain
MPP
is
s
u
cc
ess
f
u
lly
tr
ac
k
ed
with
th
is
r
ap
id
v
ar
iatio
n
in
tem
p
er
atu
r
e
w
h
er
e
g
lo
b
al
m
a
x
im
a
also
v
ar
ie
s
d
y
n
am
ically
.
O
n
e
s
u
ch
ch
ar
ac
te
r
is
tic
o
b
tain
ed
at
a
tem
p
er
atu
r
e
o
f
1
5
º
C
,
is
s
h
o
wn
in
Fig
u
r
e
1
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
261
–
2
7
0
266
Fin
ally
ef
f
ec
tiv
en
ess
o
f
MB
alg
o
r
ith
m
f
o
r
tr
ac
k
in
g
MPP
u
n
d
er
th
e
d
y
n
am
ic
v
ar
iatio
n
s
in
p
ar
tial
s
h
ad
in
g
is
an
aly
ze
d
b
y
ca
lib
r
a
tin
g
in
s
o
latio
n
with
p
er
ce
n
tag
e
s
h
ad
in
g
.
As
s
h
o
wn
in
Fig
u
r
e
1
2
MPP
is
tr
ac
k
ed
s
u
cc
ess
f
u
lly
f
o
r
d
y
n
am
ic
in
cr
e
ase
in
s
h
ad
in
g
p
er
ce
n
tag
e
in
s
tep
s
o
f
1
0
%.
I
n
ter
esti
n
g
ly
,
h
e
r
e
th
er
e
is
n
o
t m
u
ch
v
ar
iatio
n
in
t
h
e
p
a
n
el
v
o
ltag
e
till
we
g
o
b
ey
o
n
d
7
0
%
o
f
s
h
a
d
in
g
b
u
t
th
e
c
u
r
r
e
n
t
v
ar
iatio
n
is
f
o
u
n
d
to
b
e
m
u
ch
s
ig
n
if
ican
t.
E
v
e
n
t
h
e
cu
r
r
en
t
b
ec
o
m
es
n
eg
ativ
e
if
s
h
ad
in
g
g
o
es
to
th
e
lim
it
o
f
1
0
0
%
b
ec
au
s
e
o
f
r
ev
e
r
s
e
s
atu
r
atio
n
im
p
ac
t.
(
a)
(
b
)
Fig
u
r
e
6
.
B
lo
ck
s
f
o
r
s
im
u
latin
g
:
(
a)
p
h
o
to
c
u
r
r
en
t
a
n
d
(
b
)
d
io
d
e
cu
r
r
e
n
t
Fig
u
r
e
7
.
Mo
d
elin
g
o
f
p
a
n
el
o
u
tp
u
t c
u
r
r
en
t
Fig
u
r
e
8
.
Simu
lated
b
lo
ck
s
f
o
r
esti
m
atin
g
p
o
wer
o
u
tp
u
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2
2
5
2
-
8
8
1
4
E
n
h
a
n
ce
d
mo
d
el
b
a
s
ed
a
l
g
o
r
ith
m
to
r
ein
fo
r
ce
P
V
s
ystem
w
it
h
d
yn
a
mic
MPP
T c
a
p
a
b
ilit
y
(
Md
.
E
h
tesh
a
m
)
267
Fig
u
r
e
9
.
PV c
h
ar
ac
te
r
is
tic
o
b
tain
ed
at
STC
Fig
u
r
e
1
0
.
PV c
h
ar
ac
ter
is
tic
at
an
in
s
o
latio
n
o
f
6
0
0
W
/m
2
(
T
=
2
5
o
C)
Fig
u
r
e
1
1
.
PV
ch
ar
ac
ter
is
tic
at
T
em
p
er
atu
r
e
o
f
1
5
o
C
(
S=
1
0
0
0
W
/m
2
)
Fig
u
r
e
1
2
.
MPP tr
ac
k
ed
f
o
r
d
y
n
am
ic
% sh
ad
in
g
4
.
2
.
E
x
perim
ent
a
l
a
na
ly
s
is
All
th
e
s
im
u
lated
r
esu
lts
f
o
r
tr
ac
k
ed
MPP
u
n
d
er
d
y
n
a
m
ic
co
n
d
itio
n
s
wer
e
v
er
if
ied
ex
p
e
r
im
en
tally
t
o
v
alid
ate
th
e
ef
f
ec
tiv
e
n
ess
o
f
MB
alg
o
r
ith
m
.
As
d
is
cu
s
s
ed
ea
r
lier
,
v
ar
iatio
n
s
in
th
e
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
wer
e
p
r
ac
tically
m
o
n
ito
r
e
d
with
th
e
h
elp
o
f
in
s
t
alled
s
en
s
o
r
s
an
d
c
o
r
r
esp
o
n
d
in
g
ly
th
e
esti
m
ated
d
ata
i.
e
v
ar
iatio
n
s
in
cu
r
r
e
n
t,
v
o
ltag
e
a
n
d
p
o
wer
at
tr
ac
k
ed
MPP we
r
e
r
ec
o
r
d
ed
t
h
r
o
u
g
h
d
ata
lo
g
g
e
r
C
R
1
0
0
0
.
Fu
r
th
er
,
th
ese
r
ea
d
in
g
s
wer
e
also
m
o
n
ito
r
ed
in
th
e
d
is
p
lay
p
a
n
el
s
h
o
wn
in
Fig
u
r
e
5
an
d
s
to
r
ed
i
n
c
o
m
p
u
ter
as
well.
As
d
o
n
e
in
th
e
ca
s
e
o
f
s
im
u
lat
ed
r
esu
lts
,
h
er
e
also
we
s
tar
t
with
f
ir
s
t
tr
ac
k
in
g
th
e
MPP
at
ST
C
an
d
th
e
co
r
r
esp
o
n
d
in
g
r
ea
d
in
g
s
ar
e
g
i
v
en
in
T
ab
le
2
.
T
h
en
th
e
e
x
p
er
im
en
tal
r
esu
lts
f
o
r
tr
ac
k
ed
MPP
f
o
r
d
y
n
am
i
c
v
ar
iatio
n
s
in
en
v
ir
o
n
m
en
tal
c
o
n
d
it
io
n
s
a
r
e
s
u
m
m
a
r
ized
o
n
e
b
y
o
n
e
in
T
ab
u
lar
f
o
r
m
w
h
er
e
ap
ar
t
f
r
o
m
th
e
m
ax
im
u
m
p
o
wer
o
u
tp
u
t,
th
e
v
alu
es
o
f
cu
r
r
en
t
a
n
d
v
o
ltag
e
r
ea
d
in
g
s
at
MPP
h
a
v
e
also
b
ee
n
s
p
ec
if
ied
.
T
h
e
im
p
ac
t
o
f
d
y
n
am
ic
v
ar
iatio
n
o
f
th
e
r
ad
iatio
n
in
ten
s
ity
o
n
M
PP
T
ca
p
ab
ilit
y
h
as b
ee
n
i
n
v
es
tig
ated
f
o
r
th
e
r
an
g
e
o
f
in
s
o
latio
n
in
b
etwe
en
1
0
0
W
/m
2
to
1
0
0
0
W
/m
2
an
d
th
e
co
r
r
esp
o
n
d
in
g
r
ea
d
i
n
g
s
ar
e
s
u
m
m
ar
ized
i
n
T
ab
le
3
.
T
ab
le
2
.
E
x
p
er
im
en
tal
PV c
h
a
r
ac
ter
is
tic
at
STC
V
o
l
t
a
g
e
(
V
)
C
u
r
r
e
n
t
(
A
)
P
o
w
e
r
(
W
)
50
1
1
.
1
8
1
5
8
4
.
3
1
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0
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7
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8
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1
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.
9
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7
1
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2
.
5
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5
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3
.
0
1
5
7
9
5
.
4
2
3
0
0
.
3
3
1
1
7
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
261
–
2
7
0
268
T
ab
le
3
.
MPP tr
ac
k
ed
f
o
r
d
y
n
am
ic
in
s
o
latio
n
I
n
so
l
a
t
i
o
n
(
W
/
m
2
)
I
m
(A)
V
m
(V)
M
P
P
(
W
)
1
0
0
1
.
4
0
1
1
5
9
.
2
1
0
7
.
6
2
2
0
0
2
.
7
2
9
1
6
3
.
4
2
6
7
.
3
2
3
0
0
3
.
4
1
3
1
7
1
.
3
4
5
9
.
1
3
4
0
0
4
.
3
4
5
1
7
9
.
5
6
7
5
.
3
9
5
0
0
5
.
1
3
6
1
8
1
.
7
8
3
8
.
1
2
6
0
0
6
.
7
1
1
1
8
5
.
1
1
0
8
8
.
3
1
7
0
0
7
.
3
2
6
1
8
7
.
5
1
3
1
4
.
5
2
8
0
0
9
.
4
3
2
1
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9
.
4
1
5
1
4
.
8
1
9
0
0
1
0
.
7
5
9
1
9
0
.
7
1
7
1
4
.
3
7
1
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3
1
9
1
.
5
1
9
0
8
.
6
8
Similar
ly
,
th
e
MB
alg
o
r
ith
m
is
test
ed
f
o
r
m
o
s
t
ty
p
ical
o
p
e
r
atin
g
c
o
n
d
itio
n
wh
er
e
p
a
r
tial
s
h
ad
in
g
co
n
d
itio
n
s
a
r
e
r
a
p
id
ly
v
ar
ied
.
I
t
is
f
o
u
n
d
th
at
t
h
e
MB
alg
o
r
ith
m
ca
n
ef
f
ec
ti
v
ely
tr
ac
k
MPP f
o
r
r
ap
id
v
ar
iatio
n
s
o
f
s
h
ad
in
g
also
f
o
r
wh
ich
t
h
e
tr
ac
k
ed
v
alu
es
ar
e
s
u
m
m
a
r
ized
b
elo
w
in
T
ab
le
4.
Her
e,
cu
r
r
en
t
also
v
ar
ies
s
ig
n
if
ican
tly
an
d
e
v
en
b
ec
o
m
e
s
n
eg
ativ
e
f
o
r
f
u
lly
s
h
a
d
ed
p
a
n
els b
ec
au
s
e
o
f
r
e
v
er
s
e
s
atu
r
at
io
n
.
T
ab
le
4
.
MPP tr
ac
k
ed
f
o
r
d
y
n
am
ic
p
ar
tial sh
ad
in
g
S
h
a
d
i
n
g
(
%)
M
P
P
(
W
)
V
m
(V)
I
m
(A)
0
1
9
2
3
.
9
6
2
2
9
.
8
9
1
1
.
1
8
10
1
7
3
1
.
6
1
2
2
9
.
3
5
1
0
.
0
3
20
1
5
1
7
.
1
2
2
2
5
.
1
6
9
.
1
5
30
1
3
0
4
.
2
3
2
2
1
.
8
7
7
.
9
7
40
1
0
9
3
.
7
8
2
1
3
.
0
2
6
.
8
3
50
8
8
5
.
7
5
2
1
6
.
2
9
5
.
6
9
60
6
8
0
.
4
7
2
1
1
.
3
4
4
.
5
5
70
4
7
9
.
5
7
2
0
4
.
1
3
3
.
4
1
80
2
8
5
.
4
5
1
8
9
.
5
2
.
2
7
90
9
7
.
7
2
1
2
3
.
2
9
1
.
1
3
1
0
0
0
.
2
9
0
-
0
.
1
7
T
h
e
ex
p
e
r
im
en
tally
m
ea
s
u
r
ed
r
ea
d
in
g
s
f
o
r
tr
ac
k
ed
MPP
ar
e
th
en
f
in
ally
co
m
p
ar
e
d
o
n
e
b
y
o
n
e
with
th
o
s
e
p
r
ed
icted
b
y
th
e
s
im
u
lated
m
o
d
el
o
f
p
r
o
p
o
s
ed
tech
n
iq
u
e
b
y
p
lo
ttin
g
th
em
o
n
s
am
e
g
r
ap
h
s
.
C
lear
ly
,
th
e
r
esu
lts
s
h
o
w
a
v
e
r
y
clo
s
e
r
esem
b
lan
ce
b
etwe
en
m
ea
s
u
r
ed
an
d
p
r
ed
icted
b
eh
a
v
io
r
s
o
f
p
r
o
p
o
s
ed
MPPT
tech
n
iq
u
e
a
n
d
th
u
s
v
alid
ates
its
ef
f
ec
tiv
en
ess
u
n
d
er
d
y
n
a
m
ic
co
n
d
itio
n
s
.
First
th
e
co
m
p
ar
is
o
n
o
f
p
o
wer
o
u
tp
u
t
ch
a
r
ac
ter
is
tics
o
b
tain
ed
at
STC
is
s
h
o
wn
in
Fig
u
r
e
1
3
.
I
t
ca
n
b
e
s
ee
n
th
at
MB
alg
o
r
ith
m
is
n
o
t
o
n
l
y
ca
p
ab
le
o
f
tr
ac
k
in
g
MPP
in
d
y
n
am
ic
co
n
d
itio
n
s
b
u
t
at
th
e
s
am
e
tim
e
it
also
g
iv
es
o
u
t
a
h
ig
h
tr
ac
k
i
n
g
ef
f
icien
cy
.
T
h
e
n
th
e
co
m
p
ar
a
tiv
e
r
esu
lt
o
f
MPP
tr
ac
k
ed
f
o
r
d
y
n
am
ic
v
ar
iatio
n
s
in
th
e
i
n
s
o
latio
n
h
as
b
ee
n
p
lo
tted
in
Fig
u
r
e
1
4
an
d
f
i
n
ally
r
esu
lts
ar
e
co
m
p
ar
ed
a
n
d
p
lo
tte
d
f
o
r
th
e
m
o
s
t
ty
p
i
ca
l
o
n
e
i.e
p
ar
tial
s
h
ad
in
g
.
ca
s
e.
Fig
u
r
e
1
3
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PV p
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MPP tr
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Evaluation Warning : The document was created with Spire.PDF for Python.
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269
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ased
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ct
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ith
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tain
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h
e
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ea
l
tim
e
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alu
es.
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ally
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o
th
th
e
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e
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atch
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ely
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a
s
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ee
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if
ied
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o
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ith
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y
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ly
in
d
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n
am
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c
co
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itio
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s
w
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n
s
o
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o
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tem
p
er
atu
r
e
v
ar
ies
r
ap
i
d
ly
a
n
d
co
n
tin
u
o
u
s
ly
,
b
u
t
it
h
as
ad
d
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tio
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al
ca
p
a
b
ilit
y
o
f
tr
ac
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th
e
MPP a
cc
u
r
ately
in
p
ar
tial sh
ad
in
g
co
n
d
itio
n
s
also
.
RE
F
E
R
E
NC
E
S
[1
]
D.
De
lg
a
d
o
,
M
.
Ca
rv
a
lh
o
a
n
d
R.
Ch
a
c
a
rteg
u
i,
“
P
h
o
to
v
o
lt
a
ic
S
o
lar
En
e
rg
y
in
t
h
e
e
c
o
n
o
m
ic
o
p
ti
m
iza
ti
o
n
o
f
e
n
e
rg
y
su
p
p
l
y
a
n
d
c
o
n
v
e
rsio
n
,
”
I
ET
Ren
e
wa
b
le
Po
we
r
Ge
n
e
ra
ti
o
n
,
v
o
l
.
1
2
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o
.
1
1
,
p
p
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.
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0
4
9
/
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-
rp
g
.
2
0
1
8
.
0
0
9
0
.
[2
]
K.
Din
g
,
X.
B
ian
,
H.
Li
u
a
n
d
T
.
P
e
n
g
,
“
A
M
ATLAB
-
S
imu
li
n
k
-
Ba
s
e
d
P
V
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o
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o
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l
a
n
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Its
Ap
p
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ti
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n
U
n
d
e
r
Co
n
d
it
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s
o
f
No
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u
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if
o
rm
Irra
d
i
a
n
c
e
,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
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o
n
En
e
rg
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v
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rs
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o
l.
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o
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0
9
/T
EC.
2
0
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2
.
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2
1
6
5
2
9
.
[3
]
S
.
K.
Ko
ll
ima
ll
a
a
n
d
M
.
K.
M
ish
r
a
,
“
A No
v
e
l
Ad
a
p
ti
v
e
P
&
O M
P
P
T
Alg
o
rit
h
m
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u
d
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e
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Ch
a
n
g
e
s in
t
h
e
Irra
d
ian
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,
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in
IEE
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ra
n
sa
c
ti
o
n
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o
n
E
n
e
rg
y
Co
n
v
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2
9
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/
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C.
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4
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2
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9
3
.
[4
]
D.
Ve
rm
a
,
S
.
Ne
m
a
,
A.M
.
S
h
a
n
d
il
y
a
a
n
d
S
.
K.
Da
sh
,
“
M
a
x
i
m
u
m
p
o
we
r
p
o
in
t
trac
k
in
g
(
M
P
P
T)
tec
h
n
i
q
u
e
s:
Re
c
a
p
it
u
latio
n
in
s
o
lar
p
h
o
t
o
v
o
lt
a
ic
sy
ste
m
s
,
”
Ren
e
wa
b
le
a
n
d
S
u
st
a
in
a
b
le
E
n
e
rg
y
Rev
iews
,
v
o
l.
5
4
,
p
p
.
1
0
1
8
-
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0
3
4
,
F
e
b
.
2
0
1
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,
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i:
1
0
.
1
0
1
6
/
j.
rse
r.
2
0
1
5
.
1
0
.
0
6
8
.
[5
]
D.
Qu
a
n
,
M
.
M
a
o
,
P
.
D
u
a
n
,
a
n
d
B.
Hu
,
“
An
in
telli
g
e
n
t
a
l
g
o
rit
h
m
f
o
r
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
in
g
in
p
h
o
to
v
o
lt
a
ic
s
y
ste
m
u
n
d
e
r
p
a
rti
a
l
sh
a
d
in
g
c
o
n
d
i
ti
o
n
s
,
”
T
ra
n
sa
c
ti
o
n
s
o
f
th
e
In
st
it
u
te
o
f
M
e
a
su
re
me
n
t
a
n
d
Co
n
tro
l
,
v
o
l.
3
9
,
n
o
.
2
,
p
p
.
2
4
4
-
2
5
6
,
M
a
r.
2
0
1
5
,
d
o
i:
1
0
.
1
1
7
7
/
0
1
4
2
3
3
1
2
1
5
6
0
6
5
1
4
.
[6
]
M
.
Ra
k
h
sh
a
n
,
N.
Va
fa
m
a
n
d
,
M
.
Kh
o
o
b
a
n
a
n
d
F
.
Blaa
b
jer
g
,
“
M
a
x
imu
m
P
o
we
r
P
o
in
t
Trac
k
in
g
Co
n
tr
o
l
o
f
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
s:
A
P
o
ly
n
o
m
ial
F
u
z
z
y
M
o
d
e
l
-
Ba
se
d
A
p
p
r
o
a
c
h
,
”
i
n
IE
EE
J
o
u
rn
a
l
o
f
Eme
rg
i
n
g
a
n
d
S
e
lec
ted
T
o
p
ics
i
n
P
o
we
r E
lec
tro
n
ics
,
v
o
l.
6
,
n
o
.
1
,
p
p
.
2
9
2
-
2
9
9
,
M
a
rc
h
2
0
1
8
,
d
o
i:
1
0
.
1
1
0
9
/JES
T
P
E.
2
0
1
7
.
2
7
0
8
8
1
5
.
[7
]
S
.
Li
,
“
Li
n
e
a
r
e
q
u
i
v
a
len
t
m
o
d
e
ls
a
t
th
e
m
a
x
imu
m
p
o
we
r
p
o
in
t
b
a
se
d
o
n
v
a
riab
le
we
a
th
e
r
p
a
ra
m
e
ters
fo
r
p
h
o
to
v
o
lt
a
ic ce
ll
,
”
A
p
p
li
e
d
E
n
e
rg
y
,
v
o
l
.
1
8
2
,
p
p
.
9
4
-
1
0
4
,
2
0
1
6
,
d
o
i:
1
0
.
1
0
1
6
/j
.
a
p
e
n
e
r
g
y
.
2
0
1
6
.
0
8
.
0
9
7
.
[8
]
T.
H.
Ka
wa
n
a
n
d
X.
Wu
,
“
M
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
u
si
n
g
a
v
a
riab
le
a
n
tec
e
d
e
n
t
f
u
z
z
y
l
o
g
ic
c
o
n
tro
ll
e
r
,
”
S
o
l
a
r E
n
e
rg
y
,
v
o
l.
1
3
7
,
p
p
.
1
8
9
-
2
0
0
,
2
0
1
6
,
d
o
i:
1
0
.
1
0
1
6
/j
.
s
o
len
e
r.
2
0
1
6
.
0
8
.
0
0
8
.
[9
]
A.
M
o
h
a
p
a
tra,
B.
Na
y
a
k
a
n
d
C.
S
a
ip
ra
k
a
sh
,
“
Ad
a
p
ti
v
e
P
e
rtu
r
b
&
Ob
se
rv
e
M
P
P
T
f
o
r
P
V S
y
ste
m
with
Ex
p
e
rime
n
tal
Va
li
d
a
ti
o
n
,
”
2
0
1
9
IEE
E
In
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
S
u
sta
i
n
a
b
l
e
En
e
rg
y
T
e
c
h
n
o
l
o
g
ies
a
n
d
S
y
ste
ms
(ICS
ET
S
)
,
2
0
1
9
,
p
p
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2
5
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CS
ET
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.
2
0
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9
.
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7
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4
8
1
9
.
[1
0
]
S
.
M
a
rh
ra
o
u
i,
A
.
Ab
b
o
u
,
N.
E
l
Hic
h
a
m
i,
S
.
E.
Rh
a
il
i
a
n
d
M
.
R.
Tu
r,
“
G
rid
-
Co
n
n
e
c
ted
P
V
Us
in
g
S
l
id
i
n
g
M
o
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se
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re
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tal
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e
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VSC,
”
2
0
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9
8
t
h
In
ter
n
a
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
261
–
2
7
0
270
[1
1
]
S
.
Th
a
k
ra
n
,
J.
S
in
g
h
,
R.
G
a
rg
a
n
d
P
.
M
a
h
a
jan
,
“
Im
p
lem
e
n
tatio
n
o
f
P
&
O
Alg
o
rit
h
m
fo
r
M
P
P
T
in
S
P
V
S
y
ste
m
,
”
2
0
1
8
In
ter
n
a
ti
o
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a
l
C
o
n
fer
e
n
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e
o
n
Po
we
r
En
e
rg
y
,
E
n
v
iro
n
me
n
t
a
n
d
In
telli
g
e
n
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Co
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tro
l
(P
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0
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,
p
p
.
2
4
2
-
2
4
5
,
d
o
i:
1
0
.
1
1
0
9
/P
E
EIC.
2
0
1
8
.
8
6
6
5
5
8
8
.
[1
2
]
J.
Kim
a
n
d
H.
Ch
a
,
“
A
No
v
e
l
Va
riab
le
S
tep
siz
e
d
M
P
P
T
Co
n
tr
o
l
b
a
se
d
o
n
P
&
O
M
e
t
h
o
d
f
o
r
P
h
o
to
v
o
lt
a
ic
S
y
ste
m
,
”
2
0
1
9
2
2
n
d
In
ter
n
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
El
e
c
trica
l
M
a
c
h
i
n
e
s
a
n
d
S
y
ste
ms
(ICEM
S
)
,
2
0
1
9
,
p
p
.
1
-
5
,
d
o
i:
1
0
.
1
1
0
9
/IC
EM
S
.
2
0
1
9
.
8
9
2
1
5
7
1
.
[1
3
]
G
.
Dh
a
o
u
a
d
i,
O.
Dja
m
e
l,
S
.
Yo
u
c
e
f
a
n
d
C.
S
a
lah
,
“
Im
p
lem
e
n
ta
ti
o
n
o
f
I
n
c
re
m
e
n
tal
Co
n
d
u
c
tan
c
e
Ba
se
d
M
P
P
T
Alg
o
rit
h
m
fo
r
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
,
”
2
0
1
9
4
t
h
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Po
we
r
El
e
c
tro
n
ics
a
n
d
th
e
ir
Ap
p
li
c
a
ti
o
n
s (ICP
E
A)
,
2
0
1
9
,
p
p
.
1
-
5
,
d
o
i:
1
0
.
1
1
0
9
/IC
P
EA1
.
2
0
1
9
.
8
9
1
1
1
8
6
.
[1
4
]
U.
Ch
a
u
h
a
n
,
A.
Ra
n
i,
V.
si
n
g
h
a
n
d
B.
Ku
m
a
r,
“
A
M
o
d
ifi
e
d
I
n
c
re
m
e
n
tal
Co
n
d
u
c
tan
c
e
M
a
x
imu
m
P
o
we
r
P
o
in
t
Tec
h
n
iq
u
e
fo
r
S
tan
d
a
lo
n
e
P
V
S
y
ste
m
,
”
2
0
2
0
7
t
h
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
S
ig
n
a
l
Pr
o
c
e
ss
in
g
a
n
d
In
te
g
ra
te
d
Ne
two
rk
s
(S
PIN)
,
2
0
2
0
,
p
p
.
6
1
-
6
4
,
d
o
i:
1
0
.
1
1
0
9
/
S
P
IN4
8
9
3
4
.
2
0
2
0
.
9
0
7
1
1
5
6
.
[1
5
]
H.
Re
z
k
,
M
.
Al
y
,
M
.
Al
-
Dh
a
ifal
lah
a
n
d
M
.
S
h
o
y
a
m
a
,
"
De
sig
n
a
n
d
Ha
r
d
wa
re
Im
p
lem
e
n
tatio
n
o
f
Ne
w
Ad
a
p
ti
v
e
F
u
z
z
y
L
o
g
ic
-
Ba
se
d
M
P
P
T
C
o
n
tr
o
l
M
e
t
h
o
d
fo
r
P
h
o
t
o
v
o
lt
a
ic
Ap
p
l
ica
ti
o
n
s,"
in
IEE
E
Acc
e
ss
,
v
o
l.
7
,
p
p
.
1
0
6
4
2
7
-
1
0
6
4
3
8
,
2
0
1
9
,
d
o
i:
1
0
.
1
1
0
9
/ACC
ES
S
.
2
0
1
9
.
2
9
3
2
6
9
4
.
[1
6
]
M
.
No
u
r
Ali
,
“
Im
p
ro
v
e
d
De
sig
n
o
f
Artifi
c
ial
Ne
u
ra
l
Ne
two
rk
fo
r
M
P
P
T
o
f
G
rid
-
Co
n
n
e
c
ted
P
V
S
y
ste
m
s,
”
2
0
1
8
T
we
n
ti
e
th
I
n
ter
n
a
ti
o
n
a
l
M
i
d
d
l
e
Ea
st
Po
we
r
S
y
ste
ms
Co
n
f
e
re
n
c
e
(M
EP
CON)
,
2
0
1
8
,
p
p
.
9
7
-
1
0
2
,
d
o
i
:
1
0
.
1
1
0
9
/
M
EP
CON
.
2
0
1
8
.
8
6
3
5
2
0
2
.
[1
7
]
C.
Lee
,
H.
Ts
o
u
,
T.
Ch
o
u
a
n
d
K.
Wen
g
,
“
Ap
p
li
c
a
ti
o
n
o
f
th
e
h
y
b
ri
d
tag
u
c
h
i
g
e
n
e
ti
c
a
lg
o
rit
h
m
t
o
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
o
f
p
h
o
t
o
v
o
lt
a
ic
sy
s
tem
,
”
2
0
1
8
IE
EE
I
n
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
A
p
p
l
ied
S
y
ste
m
In
v
e
n
ti
o
n
(ICA
S
I)
,
2
0
1
8
,
p
p
.
2
3
1
-
2
3
4
,
d
o
i:
1
0
.
1
1
0
9
/I
CASI.
2
0
1
8
.
8
3
9
4
5
7
5
.
[1
8
]
O.
Kırc
ıo
ğ
l
u
,
M
.
Ün
lü
a
n
d
S
.
Ça
m
u
r,
“
Th
e
P
S
O
Ba
se
d
G
lo
b
a
l
M
a
x
imu
m
P
o
we
r
P
o
in
t
Trac
k
e
r,
”
2
0
1
9
1
1
t
h
In
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
El
e
c
tro
n
ics
,
Co
m
p
u
ter
s
a
n
d
Arti
fi
c
ia
l
I
n
telli
g
e
n
c
e
(ECA
I)
,
2
0
1
9
,
p
p
.
1
-
4
,
d
o
i:
1
0
.
1
1
0
9
/
ECAI4
6
8
7
9
.
2
0
1
9
.
9
0
4
1
9
2
6
.
[1
9
]
J.
A.
Ne
m
o
u
rs
a
n
d
S
.
Ch
o
wd
h
u
ry
,
“
P
e
rfo
rm
a
n
c
e
An
a
ly
sis
o
f
F
u
z
z
y
L
o
g
ic
M
a
x
imu
m
P
o
we
r
P
o
in
t
Trac
k
i
n
g
S
c
h
e
m
e
fo
r
S
o
lar
P
V
S
y
ste
m
Un
d
e
r
Va
ry
in
g
L
o
a
d
a
n
d
At
m
o
sp
h
e
ric
Co
n
d
it
io
n
s,
”
2
0
1
9
I
EE
E
PE
S
/IA
S
Po
we
rAfrica
,
2
0
1
9
,
p
p
.
1
3
4
-
1
3
9
,
d
o
i:
1
0
.
1
1
0
9
/P
o
we
rAfri
c
a
.
2
0
1
9
.
8
9
2
8
8
9
5
.
[2
0
]
K.
Ba
tain
e
h
,
“
Im
p
ro
v
e
d
h
y
b
ri
d
a
lg
o
rit
h
m
s
-
b
a
se
d
M
P
P
T
a
lg
o
ri
th
m
fo
r
P
V
sy
ste
m
o
p
e
ra
ti
n
g
u
n
d
e
r
se
v
e
re
we
a
th
e
r
c
o
n
d
i
ti
o
n
s,”
IET
Po
we
r E
lec
tro
n
i
c
s
,
v
o
l.
1
2
,
n
o
.
4
,
p
p
.
7
0
3
-
7
1
1
,
2
0
1
9
,
d
o
i:
1
0
.
1
0
4
9
/i
e
t
-
p
e
l.
2
0
1
8
.
5
6
5
1
.
[2
1
]
I.
Ab
a
d
i,
C.
Im
ro
n
,
M
a
rd
li
j
a
h
,
R.
D.
No
riy
a
ti
,
“
Im
p
lem
e
n
tatio
n
o
f
M
a
x
imu
m
P
o
we
r
P
o
in
t
Tr
a
c
k
in
g
(M
P
P
T)
Tec
h
n
iq
u
e
o
n
S
o
lar
Trac
k
i
n
g
S
y
ste
m
Ba
s
e
d
o
n
Ad
a
p
t
iv
e
Ne
u
ro
-
F
u
z
z
y
In
fe
re
n
c
e
S
y
ste
m
(AN
F
IS
),
”
E3
S
W
e
b
o
f
Co
n
fer
e
n
c
e
s
,
v
o
l.
4
3
,
p
.
0
1
0
1
4
,
2
0
1
8
,
d
o
i:
1
0
.
1
0
5
1
/e3
sc
o
n
f
/2
0
1
8
4
3
0
1
0
1
4
.
[2
2
]
A.
Be
l
tran
,
C.
Hu
g
h
e
s
a
n
d
S
.
D
a
s,
“
Im
p
ro
v
e
d
M
a
x
imu
m
P
o
we
r
P
o
i
n
t
Trac
k
in
g
o
f
P
a
rti
a
ll
y
S
h
a
d
e
d
P
V
Arra
y
s
Us
in
g
P
a
rti
c
le
S
wa
rm
Op
ti
m
iza
ti
o
n
wit
h
Z
o
n
e
I
n
it
ializa
ti
o
n
,
”
2
0
1
9
IEE
E
4
6
th
P
h
o
to
v
o
l
ta
ic
S
p
e
c
ia
l
ists
Co
n
fer
e
n
c
e
(PV
S
C)
,
2
0
1
9
,
p
p
.
0
6
6
3
-
0
6
6
7
,
d
o
i:
1
0
.
1
1
0
9
/P
VSC
4
0
7
5
3
.
2
0
1
9
.
8
9
8
0
4
6
9
.
[2
3
]
K.
Lap
p
a
lai
n
e
n
a
n
d
S
.
Va
lk
e
a
lah
ti
,
“
F
lu
c
t
u
a
ti
o
n
o
f
P
V
Arra
y
G
lo
b
a
l
M
a
x
imu
m
P
o
we
r
P
o
i
n
t
Vo
lt
a
g
e
Du
r
in
g
Irra
d
ian
c
e
Tran
siti
o
n
s
c
a
u
se
d
b
y
Clo
u
d
s,”
IET
Ren
e
w
a
b
le
P
o
we
r
Ge
n
e
ra
ti
o
n
,
v
o
l.
1
3
,
n
o
.
1
5
,
p
p
.
2
8
6
4
-
2
8
7
0
,
2
0
1
9
,
d
o
i:
1
0
.
1
0
4
9
/i
e
t
-
rp
g
.
2
0
1
9
.
0
0
8
5
.
[2
4
]
A.
Al
M
a
n
su
r
a
n
d
M
.
R
.
Am
in
,
“
P
e
rfo
rm
a
n
c
e
In
v
e
sti
g
a
ti
o
n
o
f
Diffe
re
n
t
P
V
Arra
y
Co
n
f
ig
u
ra
ti
o
n
s
a
t
P
a
rti
a
l
S
h
a
d
i
n
g
Co
n
d
it
io
n
fo
r
M
a
x
imu
m
P
o
we
r
O
u
tp
u
t,
”
2
0
1
9
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
S
u
sta
i
n
a
b
le
T
e
c
h
n
o
l
o
g
ies
f
o
r
In
d
u
stry
4
.
0
(S
T
I)
,
2
0
1
9
,
p
p
.
1
-
5
,
d
o
i:
1
0
.
1
1
0
9
/S
TI
4
7
6
7
3
.
2
0
1
9
.
9
0
6
7
9
9
8
.
[2
5
]
B.
C.
Ba
b
u
a
n
d
S
.
G
u
rjar,
“
A
N
o
v
e
l
S
imp
li
fied
Two
-
Di
o
d
e
M
o
d
e
l
o
f
P
h
o
to
v
o
l
taic
(P
V)
M
o
d
u
le,
”
i
n
IEE
E
J
o
u
rn
a
l
o
f
P
h
o
t
o
v
o
lt
a
ics
,
v
o
l.
4
,
n
o
.
4
,
p
p
.
1
1
5
6
-
1
1
6
1
,
Ju
l
y
2
0
1
4
,
d
o
i:
1
0
.
1
1
0
9
/JP
HO
TOV.
2
0
1
4
.
2
3
1
6
3
7
1
.
[2
6
]
H.
K.
M
e
h
ta,
H.
Wark
e
,
K.
K
u
k
a
d
iy
a
a
n
d
A.
K.
P
a
n
c
h
a
l,
“
Ac
c
u
ra
t
e
Ex
p
re
ss
io
n
s f
o
r
S
i
n
g
le
-
Di
o
d
e
-
M
o
d
e
l
S
o
lar Cell
P
a
ra
m
e
teriz
a
ti
o
n
,
”
in
IEE
E
J
o
u
rn
a
l
o
f
Ph
o
to
v
o
lt
a
ics
,
v
o
l.
9
,
n
o
.
3
,
p
p
.
8
0
3
-
8
1
0
,
M
a
y
2
0
1
9
,
d
o
i:
1
0
.
1
1
0
9
/JP
HO
TOV.
2
0
1
9
.
2
8
9
6
2
6
4
.
[2
7
]
A.
Ortiz
-
Co
n
d
e
,
D
.
Lu
g
o
-
M
u
ñ
o
z
a
n
d
F
.
J.
G
a
rc
ía
-
S
á
n
c
h
e
z
,
“
An
Ex
p
li
c
it
M
u
lt
iex
p
o
n
e
n
ti
a
l
M
o
d
e
l
a
s
a
n
Altern
a
ti
v
e
to
Trad
it
io
n
a
l
S
o
lar
Ce
ll
M
o
d
e
ls
with
S
e
ries
a
n
d
S
h
u
n
t
Re
sista
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