In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
4, D
e
c
e
m
ber
201
9,
pp.
1914~
19
22
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1914-1922
1
9
14
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
A model for predicting photo
voltai
c modul
e p
erfo
r
man
ces
Na
dia
Bo
ua
z
i
z
1
,
A
r
ezk
i
B
e
nf
di
l
a
2
,
A
h
cene Lak
h
l
ef
3
1
D
e
p
a
rtem
en
t of El
ectri
c
a
l E
n
g
i
n
eeri
n
g
,
U
niv
e
rsity
of T
izi-O
u
zo
u
,
Al
g
e
ri
a
2,
3
Dep
a
rt
em
e
n
t
of
A
utom
ati
c
s,
U
ni
ve
rsit
y
of
Tizi-Ouzou, Algeria
1
, 2
, 3
M
i
c
r
o
and
Nan
o
el
ectron
i
cs
Research
Gro
up,
F
acult
y
o
f
Electri
cal
E
ng
in
eeri
n
g
and
Com
p
u
t
er S
cien
c
e
s
,
U
n
i
v
ersi
ty M
oulo
u
d
M
a
m
m
eri
, A
lgeri
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Mar
4
,
201
9
Re
vise
d A
p
r
14,
201
9
Ac
ce
p
t
ed
J
un
2
4
,
2
019
Th
e
pres
ent
p
a
p
e
r
d
e
als
wit
h
t
h
e
d
ev
elo
p
m
e
n
t
o
f
a
simu
la
t
i
o
n
m
o
de
l
for
pred
ict
i
ng
t
he
p
erf
o
rman
ces
o
f
a
s
o
l
a
r
p
h
o
t
ov
oltai
c
(
P
V
)
syst
e
m
o
perati
ng
under
current
m
eteorologi
c
a
l
co
nditions
a
t
the
site
l
ocati
on.
T
he
p
rop
o
s
e
d
m
o
d
e
l
is
b
as
ed
o
n
th
e
cel
l
equi
val
e
nt
c
ircu
it
i
nc
ludi
ng
a
pho
to
curren
t
s
ou
rce,
a
di
od
e,
a
s
eries
and
shu
n
t
resistan
ces.
M
a
t
h
em
ati
cal
e
xp
ress
io
ns
d
evel
op
ed
f
o
r
m
o
d
e
li
ng
t
h
e
P
V
g
e
n
er
ato
r
p
erf
o
rm
ances
a
r
e
b
as
ed
o
n
curr
ent
-v
ol
ta
ge
chara
c
t
e
ri
stic
o
f
th
e
co
ns
id
ere
d
m
odu
les.
T
he
d
evelo
p
ed
m
o
d
el
a
ll
o
w
s
t
h
e
pred
ict
i
on
o
f
PV
cell
(m
o
dule
)
b
ehav
io
r
u
n
d
e
r
d
i
ff
erent
physi
c
a
l
and
env
i
ro
nm
ent
a
l
p
a
ram
e
t
e
rs
.
Th
e
mo
del
can
b
e
ext
e
nded
to
e
x
t
ra
ct
ph
ysic
a
l
param
e
ters
f
o
r
a
g
iv
e
n
s
olar
P
V
mo
dule
as
a
f
unctio
n
o
f
t
emp
e
ra
ture
a
nd
so
lar
irradi
a
t
i
on.
A
t
ypical
2
60
W
solar
pan
e
l
devel
o
p
e
d
by
LG
Company
was
us
ed
f
o
r
m
od
el
e
valu
ati
o
n
us
in
g
N
e
wt
o
n
-Rap
hs
on
a
pp
roach
u
n
d
er
M
A
TLAB
en
viro
nm
en
t
in
o
rder
t
o
an
aly
z
e
i
t
s
b
e
hav
i
o
r
u
nd
er
a
c
t
ua
l
operati
ng
conditions
.
C
o
mparison
of
o
ur
r
esul
t
s
w
i
t
h
dat
a
t
aken
f
r
o
m
t
h
e
m
a
nu
f
a
ct
urer’s
d
atash
eet
s
ho
ws
g
o
o
d
a
greem
ent
and
co
nf
i
r
ms
t
he
val
i
dity
o
f
ou
r
mo
del
.
H
ence,
t
he
p
ro
po
se
d
ap
proa
ch
can
b
e
an
a
lt
ernati
v
e
t
o
e
x
tra
c
t
diff
erent
param
e
ters
o
f
an
y
P
V
m
od
ul
e
to
s
t
u
d
y
a
n
d
p
redi
ct its
p
e
rfor
m
a
nc
e
s
.
K
eyw
ord
s
:
Co
nv
ersi
on
e
f
f
i
c
i
e
n
c
y
Elec
tric
a
l
par
am
eter
s
I-V charact
eristi
c
s
M
o
d
e
li
ng
Phot
o
v
o
lta
ic
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Arezki Benfdila,
M
i
c
r
o a
nd N
a
n
o
elec
tro
n
i
cs
R
e
s
e
a
rc
h G
r
oup
,
Fa
cult
y
o
f
E
l
e
c
t
rica
l
En
gine
erin
g
an
d C
o
mp
uter
S
cience
s,
U
n
i
v
ersi
ty
M
o
u
lo
ud
M
a
mm
e
r
i
,
Tiz
i
-
O
u
zo
u,
A
lgeria.
Em
ail:
ben
f
di
l
a
@um
m
to.dz
;
a
be
n
f
di
l
@
ic
t
p
.
i
t
1.
I
N
TR
OD
U
C
TI
O
N
Our
env
i
ro
nm
ent
is
f
ac
i
n
g
si
gnif
i
c
a
n
t
cha
lle
n
g
e
s
i
n
the
pr
esen
t
a
nd
f
utu
r
e
d
e
cad
e
s
a
s
en
e
r
gy
con
s
um
pt
io
n
is
e
xpe
c
t
ed
t
o
gl
o
b
al
ly
d
ou
b
l
e
duri
ng
the
fi
rst
hal
f
of
t
his
cent
u
ry
[
1]
.
D
u
e
to
i
nc
rea
s
in
g
o
il
sup
p
l
i
es
c
o
n
s
t
r
a
in
s,
t
he
w
orl
d
i
s
urged
to
s
e
a
rc
h
for
a
lter
n
a
t
i
ve
e
ner
g
y
s
ource
s.
T
he
ref
o
r
e
,
a
bet
t
e
r
s
ol
u
tio
n
w
o
u
l
d
be
t
he
i
nve
st
i
g
at
ion
i
n
R
enew
a
b
le
E
ner
g
y
S
ourc
e
s
(RES
)
[2
-
4
]
m
a
i
n
l
y
,
s
o
l
a
r
e
n
e
r
g
y
.
S
o
l
a
r
a
n
d
o
t
h
e
r
form
s
of
r
en
e
w
able
e
ner
g
i
e
s
a
r
e
see
n
a
s
pr
act
ica
l
a
n
d
clea
n
so
l
ut
io
n
t
o
m
ee
t
ou
r
pla
n
e
t
’
s
g
ro
w
i
n
g
env
i
ro
nm
en
tal
a
n
d
e
n
er
g
y
c
ha
lle
nge
s.
I
n
fac
t
,
th
e
dem
a
nd
for
so
lar
ener
gy
i
s
b
ec
o
m
ing
mor
e
a
n
d
m
ore
incre
a
s
i
ng
a
n
d
i
t
s
c
o
n
s
um
p
t
i
o
n
more
a
nd
mor
e
g
e
n
era
l
i
z
ed.
The
i
nve
st
i
g
at
i
o
n
s
o
n
s
o
l
a
r
ener
gy
pro
d
u
ct
i
on,
ut
iliz
a
t
i
on
a
n
d
con
v
ersi
on
a
r
e
r
e
gular
ly
i
n
c
r
easin
g
t
o
c
ove
r
m
o
re
f
iel
d
s
in
t
he
purp
o
s
e
of
d
e
s
i
g
ni
n
g
a
n
d
implem
e
n
t
i
ng
so
lar
and e
l
ec
trica
l
en
e
rgy c
o
n
v
e
r
ter
s
o
f
hig
h
e
r
p
er
form
anc
e
s a
nd effic
i
enc
y
[
5].
The
m
o
st
c
om
m
on
pri
n
ci
p
l
e
w
i
de
l
y
k
n
o
w
n
i
n
s
o
lar
ene
r
g
y
c
o
n
v
ersi
on
is
t
he
p
h
o
to
v
o
l
t
a
i
c
cell
base
d
on
a
p-
n
j
unc
t
i
on
a
s
a
p
h
o
t
o
dio
d
e,
i
.
e
.
,
i
t
ge
ne
rates
a
v
o
lta
ge
acr
oss
i
t
s
te
rm
inal
w
he
n
a
li
g
h
t
bea
m
i
s
i
n
ci
de
nt
on
t
h
e
dev
i
ce
j
unc
t
i
o
n
a
rea
[6
].
D
e
s
igner
s
o
f
ele
c
t
rica
l
co
n
v
er
te
r
s
a
r
e
i
n
t
e
r
e
s
te
d
i
n
m
o
d
e
li
n
g
P
V
c
e
ll
/
m
o
d
u
l
e
s
f
o
r st
u
dyi
ng
t
he
e
l
e
ct
ri
c
a
l
c
onv
e
r
t
e
rs
i
n
c
lud
i
n
g
a
PV sy
s
t
e
m
.
T
his ne
e
d
s t
o
k
now
h
ow
to
mode
l
the
P
V
d
e
v
i
c
e
fe
ed
i
n
g
t
h
e
co
nve
r
t
er.
The
PV
m
odu
les
sh
o
w
a
n
o
n
l
i
n
e
a
r
I
-V
c
ha
r
ac
t
e
ristic
w
i
t
h
a
numb
e
r
of
p
a
r
am
ete
r
s
th
a
t
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
m
ode
l
f
o
r pr
edic
t
i
ng p
h
o
to
v
o
lt
aic m
o
du
l
e
perf
orm
a
nce
s
(Na
d
ia Bo
u
a
zi
z)
1
915
n
e
ed
b
e
adju
s
t
e
d
d
u
r
ing
ex
pe
ri
men
t
a
l
d
a
t
a
a
n
al
y
s
i
s
o
f
prac
t
i
c
al
m
o
d
u
l
es.
Mat
h
em
at
i
cal
m
o
d
el
i
n
g
of
P
V
ce
l
l
/m
od
ule
is
i
mpor
ta
n
t
t
o
sim
u
late
t
h
e
P
V
sys
t
em
a
n
d
its
c
om
p
on
e
n
t
s
.
D
i
ffere
n
t
me
th
ods
f
or
m
ode
l
i
ng
ph
o
t
o
vol
ta
i
c
(
PV
)
cell/mo
d
u
l
es
h
a
v
e
bee
n
d
e
v
el
o
p
ed
a
nd
e
x
p
l
ored
ea
rli
e
r.
T
he
i
r
m
ain
d
i
ffe
renc
e
resides
es
sen
tia
l
l
y
i
n
t
he
e
le
ct
ric
e
q
u
i
va
l
e
n
t
c
i
r
c
u
i
t
o
f
t
h
e
stud
ie
d
P
V
cell,
t
he
ir
con
v
er
ge
nce
,
a
nd
c
om
p
l
e
x
i
t
y.
T
y
p
i
cal
l
y
,
Tow
n
se
n
d
[
7,
8
]
m
ode
l
i
s
one
o
f
th
e
m
ode
ls
d
e
v
e
l
o
p
e
d
for
eva
l
ua
tin
g
t
h
e
para
me
t
e
rs
o
f
t
h
e
e
q
ui
va
le
nt
e
lectr
i
c
circ
u
i
t
of
t
he
c
e
ll.
H
ow
e
v
er,
Ro
ha
n.
S
.
K
o
lkarn
i
a
nd
a
l
pro
pose
d
i
n
the
i
r
w
o
r
k
a
n
o
t
h
er
m
et
ho
d
for
m
o
de
lin
g
the
so
lar
p
h
o
t
ovo
lta
ic
m
od
u
l
e
us
i
n
g
s
y
stem
ide
n
tif
i
c
at
i
on
[9]
.
H
ow
eve
r
,
Tar
a
k
S
a
lm
i
a
nd
a
l
h
a
v
e
pr
opos
e
d
a
M
at
la
b/S
i
m
u
lin
k
mo
de
l
of
P
V
c
e
ll
b
ase
d
o
n
ma
them
at
i
c
al e
qua
t
i
ons
u
si
ng
S
i
muli
n
k
B
l
o
k
s
[
10].
Za
id
H
esse
in
A
l
i
e
t
a
l
[
1
1
]
e
x
p
o
se
d
a
Simu
lat
i
o
n
mo
de
l
o
f
s
ola
r
P
V
c
e
l
l
an
d
he
nc
e
P
V
p
a
n
e
l
u
sin
g
nume
r
ica
l
a
ppr
oach
c
on
si
der
a
in
g
o
n
ly
t
he
e
f
f
ec
t
of
e
x
t
erna
l
pa
r
am
eter
s
(
t
e
m
pe
rature
a
n
d
s
o
l
a
r
i
rra
di
a
n
ce)
i
n
w
e
ster
n
Ira
q.
T
he
M
at
l
a
b
m
a
th
m
o
d
e
l
i
n
g
is
i
mp
le
me
nt
e
d
u
s
i
n
g
c
l
i
m
a
te
a
nd
p
h
y
s
i
c
a
l
p
ar
am
ete
r
s
wi
th
mode
l
i
ng
e
qua
ti
o
n
s
[
11,
12].
N
e
w
t
o
n
-
R
a
p
hson
itera
ti
o
n
num
er
i
c
al
m
e
t
hod
has
bee
n
a
pp
lied
to
e
xtra
c
t
t
he
val
u
e
o
f
c
ur
ren
t
f
or
e
ve
ry
w
or
ki
n
g
v
ol
ta
ge
t
o
fin
d
P
-
V
cur
v
es
u
n
d
er
t
he
e
ffec
t
o
f
tem
p
er
a
t
ure
a
n
d
irra
dia
tio
n
of
A
nb
ar
p
rov
i
nc
e
Wes
t
I
raq
[
11,
13].
I
n
t
hi
s
w
o
rk,
w
e
d
em
onstra
t
e
the
b
e
ha
v
i
or
a
n
d
f
unc
t
i
on
i
n
g
o
f
a
P
V
d
ev
i
c
e
by
e
xp
l
o
ri
ng
i
t
s
b
a
s
i
c
equa
t
i
o
n
s,
m
odel
i
ng
a
nd
s
i
mula
t
i
n
g
t
he
2
6
0
S
1
C-G
2
P
V
Mo
du
le
u
si
n
g
N
ew
t
on-
Ra
phs
on
a
l
g
o
ri
t
h
m
t
o
s
o
l
ve
the
non
li
nea
r
I-V
c
ha
rac
t
e
r
is
tic
u
nder
Ma
tl
a
b
e
n
v
iro
n
m
e
n
t
.
Th
is
i
s
a
c
h
ie
v
e
d
b
y
f
oc
us
in
g
o
n
b
ot
h
t
h
e
stud
y
o
f
exter
n
al
p
a
r
am
eter
s
ef
fec
t
s
(te
m
per
a
ture
a
n
d
i
r
r
adia
nc
e)
o
n
t
h
e
e
vo
l
u
t
i
on o
f
P
V
device
s
pe
r
f
orm
a
nc
es
a
s
w
e
l
l
a
s
t
ho
s
e
o
f
t
h
e
i
n
t
e
rn
al
p
a
r
amet
ers
(se
r
i
e
s
re
si
st
a
n
ce
a
n
d
p
a
ra
lle
l
one
).
C
om
pariso
n
o
f
t
h
e
o
b
t
a
i
ne
d
da
t
a
w
i
t
h
t
h
at
of
man
u
f
act
u
r
e
r
’s
d
a
t
a
s
he
et
sho
ws g
ood
ag
r
e
e
men
t
a
nd
c
o
n
fi
rm
s the
val
i
di
t
y
of
o
u
r m
odel.
2.
PHOTOVOLT
A
I
C
G
E
N
ERATO
R
2.1.
Mod
e
lin
g
th
e
p
h
otovo
ltaic
c
e
ll
A
so
l
a
r
mo
dule
i
s
d
e
f
i
n
ed
a
s
t
h
e
in
di
v
i
du
a
l
p
i
e
c
e
of
e
quip
m
en
t
t
h
at
e
nc
om
passes
num
er
ous
s
ola
r
ce
l
l
s
c
o
n
n
e
c
t
e
d
i
n
pa
ra
lle
l
or
i
n
se
rie
s
[
1
4
]
.
I
n
or
der
to
s
i
m
u
late
t
he
r
ea
l
b
e
hav
i
or
o
f
a
ph
o
t
o
v
o
lta
i
c
c
e
l
l,
a
n
equ
i
vale
n
t
e
lec
t
r
i
c
c
i
r
c
u
i
t
m
o
del
i
s
n
ee
ded.
S
e
v
era
l
m
ode
l
s
a
re
p
ro
p
o
se
d
in
l
i
t
era
t
ur
e
su
c
h
a
s
t
h
e
si
n
g
l
e
d
i
ode
mode
l
[1
5]
w
h
i
ch
i
s
der
i
ve
d
fr
om
s
i
m
p
l
ific
ati
o
ns
i
n
t
h
e
t
w
o
d
i
o
de
m
odel
[
1
6
]
.
A
singl
e
e
q
u
i
v
a
l
e
nt
c
i
r
cui
t
mode
l
for
a
PV
c
e
l
l
c
o
nsis
t
s
o
f
a
rea
l
d
iode
i
n
para
lle
l
w
i
th
a
n
ide
a
l
d
irec
t
c
u
rr
ent
source
a
s
pr
e
s
en
ted
in Fig
ure
1.
The
t
w
o
par
a
m
e
ter
s
u
sed
t
o
m
ode
l
an
d
cha
r
ac
terize
a
P
V
cell
a
r
e
:
t
h
e
op
en
c
ircui
t
v
o
ltag
e
(
)
and
the
s
h
o
r
t
c
i
r
c
ui
t
c
u
rre
n
t
(
).
T
he
i
s
the
ma
xim
u
m
v
o
lta
ge
w
hi
c
h
a
s
ola
r
cell
can
p
r
o
v
i
de
a
t
ze
ro
curr
ent.
The
i
s
the m
a
xim
u
m
curr
ent
which
a
sola
r c
e
ll ca
n prov
i
d
e
at z
ero
vo
l
t
ag
e
.
F
i
gure
1.
Ide
al P
V c
e
ll m
ode
l circ
u
i
t
d
i
a
g
ram
The
o
u
tp
ut c
ur
re
n
t
f
rom
the
PV
c
e
l
l
can
b
e fou
n
d
us
i
ng
t
h
e fo
ll
ow
in
g e
qua
tio
n
(
1
)
O
n
the
o
ther
h
and,
w
e
have
1
.
(
2
)
a
t
t
h
e
ref
e
re
n
c
e
t
e
mp
e
r
at
ure
(
is
f
o
u
n
d
on
the
datas
h
ee
t
,
a
nd
r
e
f
e
r
s
t
o
t
h
e
t
e
m
p
e
r
a
t
u
r
e
c
o
eff
i
ci
ent
o
f
i
n
pe
rce
n
t
c
h
a
nge
p
e
r
d
egre
e
.
T
he
m
easureme
n
ts
a
re
don
e
un
de
r
the
sta
ndar
d
i
r
r
adia
nc
e
of
1
000
W
/
m
2
a
n
d
r
e
f
e
r
e
n
c
e
t
e
m
p
e
r
a
t
u
r
e
o
f
2
5
°
C
.
T
h
e
p
h
o
t
o
n
g
e
n
e
r
a
t
e
d
c
u
r
r
e
nt
a
lso
va
rie
s
w
i
t
h
re
spe
c
t
to
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 : 1
9
1
4
–
19
22
1
916
irrad
i
a
n
ce
.
The
assu
m
p
tion
s
that
≈
i
s
ge
ne
rall
y
use
d
s
i
n
c
e
t
he
s
er
i
e
s
r
e
sista
n
ce
(
)
i
s
lo
w
and
the
p
a
rall
el
res
i
s
t
a
n
c
e
is a
very
h
igh.
This le
a
d
s
us t
o the
fol
l
o
w
i
n
g
e
xpre
ssi
o
n
∗
1
.
(3)
:
Irr
adiati
o
n
at
t
e
mpe
r
at
ure
,
:
Re
fere
nce
irra
di
a
n
ce
ta
ke
n
equa
ls t
o
sta
nda
rd irr
adianc
e o
f
1
000
W/m
2
,
Re
fere
nce
tem
p
era
t
ur
e e
qual
s
to 2
5
°
C
,
A
nd (
)
i
s
th
e
shu
nt
e
d
c
u
r
rent
t
hro
u
gh
the
i
n
tr
insic
di
ode
.
U
s
i
ng
S
hoc
k
l
e
y
’
s
d
io
d
e
m
odel,
t
he d
i
ode
c
urr
e
n
t
c
an be
w
ritte
n
.
.
.
/
1
(
4
)
:
D
i
o
d
e
q
u
a
l
i
t
y
f
a
c
t
o
r
(
i
t
i
s
b
e
t
w
e
e
n
1
a
n
d
5
)
,
:
Bo
ltzm
a
nn’s
co
ns
ta
nt
(
1.38
1.
10
-23
J
/
K
)
,
:
Ju
nc
tio
n
tem
p
era
t
ur
e in
K
elv
i
n
,
:
Cha
r
ge
o
f t
h
e
elec
tron (1.
6
02.1
0
-1
9
Coulo
m
b
),
V
:
V
o
lta
g
e
pr
o
v
i
d
e
d
by s
o
lar
cel
l
.
i
s
the d
i
o
d
e
satura
ti
o
n
c
urrent,
it depe
n
d
s
al
so i
n tem
p
er
at
ur
e
as it is e
xpr
essed
i
n
re
l
a
tio
n
(5)
.
.
.
.
.
.
/
.
(
5
)
: S
hort-cir
c
u
i
t
curr
ent o
f
t
he c
ell at
t
e
m
pe
rat
u
re
T
c
,
:
Ener
gy
of
t
he
ga
p
(
1.16
eV
f
or
S
ili
c
on).
: O
pe
n circ
ui
t
vo
lta
ge a
t
tem
p
era
t
ur
e T
c
,
: Refere
n
ce
t
e
mpe
r
at
ure
e
qua
ls
t
o 25
°
C
:
S
im
il
a
r
to
qua
lit
y fac
t
or,
it i
s
ta
k
e
n
e
qu
a
l
t
o
.
S
e
ve
ral
c
e
l
l
s
c
o
n
n
ec
te
d
in
s
e
r
ies
form
t
he
P
V
m
odule
an
d
a
co
ll
ec
ti
on
of
P
V
m
odu
le
s
c
o
ns
t
i
t
u
te
a
P
V
p
a
n
el,
an
d
fi
nal
l
y
,
the
c
o
l
l
e
c
t
ion
of
a
g
i
v
e
n
n
um
ber
of
p
ane
ls
f
or
m
s
t
he
a
rr
ay.
The
pra
c
tica
l
c
urrent
vo
lta
ge
I-V
c
hara
cter
i
s
t
i
c
o
f
a
p
r
actica
l
m
o
d
u
l
e
req
u
ire
s
t
he
i
ncl
u
s
i
on
o
f
t
he
p
ara
m
e
t
e
r
s
(
)
a
n
d
(
)
w
h
ic
h m
a
ke
s the
mode
l
mor
e
a
cc
urate
as r
e
p
re
sen
t
ed i
n
F
i
gure
2.
F
i
gure
2.
S
i
n
g
l
e
di
o
d
e
P
V
c
ell
m
o
d
e
l circ
u
i
t
di
a
g
ram
If
w
e
cons
ider
∞
,
w
e
subst
i
tu
t
e
the
(
2), (3), (
4
),
(
5)
a
nd
(1) w
e
ge
t:
I
I
1
a
.
T
–T
.
..
.
.e
x
p
.
/
.
.
e
x
p
q.
.
.
.
1
(6)
Tak
i
n
g
i
nt
o co
ns
idera
t
ion
t
h
e
tw
o pa
ram
e
te
rs
a
nd
(6) becom
es as
f
o
llow:
I
.I
.
1
a
.
T
–T
.
.
.
.
.e
x
p
.
.
.e
x
p
q
.
.
.
.
1
∗
(7)
Th
e
s
e
ri
e
s
r
es
i
s
t
a
n
c
e
(
)
a
ccount
s
for
the
los
s
e
s
rela
t
e
d
t
o
t
h
e
c
onne
c
t
io
n
o
f
t
he
cel
l
s
in
s
e
r
ie
s
,
t
h
e
resista
n
ce
o
f
t
h
e
se
mico
n
duc
t
o
r
ma
terial
a
nd
tha
t
o
f
m
e
ta
l
grid
w
h
e
r
e
a
s
t
h
e
p
a
r
a
l
l
e
l
o
n
e
(
)
a
c
c
oun
ts
f
or
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
m
ode
l
f
o
r pr
edic
t
i
ng p
h
o
to
v
o
lt
aic m
o
du
l
e
perf
orm
a
nce
s
(Na
d
ia Bo
u
a
zi
z)
1
917
the
losses
as
s
o
cia
t
e
d
t
o
lea
k
a
g
e
c
u
rr
en
t
thr
o
u
g
h
a
p
ar
alle
l
r
e
s
ist
a
nc
e
pat
h
t
o
t
h
e
dev
i
c
e
.
It
b
com
e
s
con
s
i
d
era
b
l
e
f
or
l
a
r
ge
n
um
be
r
of
p
ar
al
lel
c
e
l
l
s
.
These
two
p
a
ra
me
t
e
rs
c
o
u
l
d
be
o
b
t
ai
ne
d
expe
r
i
me
nt
a
lly
f
r
o
m
the
I-V
c
ur
ve
[
16,
17].
This
m
e
t
hod
is
b
a
s
e
d
on
t
h
e
fa
c
t
t
h
a
t
,
the
se
r
i
es
r
e
s
is
t
a
nce
im
pac
t
s
si
gn
i
f
ica
n
tl
y
the
I-
V
c
u
rve
sl
ope
a
t
near
b
y
po
i
nt
,
0
a
nd
t
he pa
r
al
l
e
l one
a
t
t
h
e
p
o
i
n
t
0
,
,
s
o
w
e
ca
n
w
r
i
t
e
(
8
)
(
9
)
W
e
have to der
iv
e (
6
) to ge
t
(
) expression
.
.
.
.
.
.
.
.
(10)
Th
is
m
ode
l
gi
ve
s
a
be
t
t
er
p
r
ecis
i
o
n
f
or
m
a
ny
m
o
d
u
l
e
s.
T
he
m
ode
l
e
x
p
r
e
ssi
o
n
r
e
s
u
lts
f
rom
sim
p
li
fic
a
tio
ns
ob
ta
ine
d
i
n
t
h
e
t
w
o
d
i
o
d
e
mode
l
d
i
agra
m
prese
n
t
e
d
i
n
[
16,
1
8,
1
9].
C
e
ll
s
co
n
n
e
c
te
d
in
s
er
i
e
s
i
n
cr
ease
t
h
e
ou
tpu
t
v
ol
t
a
ge
w
here
as
c
e
lls
c
on
nec
t
e
d
i
n
par
a
l
l
el
p
ro
v
i
de
h
i
g
h
er
c
urre
nt
s
va
l
u
e
s
,
so
i
f
our
m
o
d
u
l
e
i
s
com
p
o
s
ed o
f
N
cell
s
the
n
I
I
∗N
a
nd
I
I
∗N
Th
e
cu
rrent
vol
t
a
g
e
c
h
a
ra
c
t
eri
s
t
i
c
o
f
t
h
e
PV
m
o
d
u
l
e
i
s
a
no
n
li
n
e
a
r
e
qu
a
t
ion
;
i
t
shou
ld
b
e
solv
ed
us
i
n
g
di
ffere
n
t
m
e
t
h
o
d
s.
I
n
this
w
or
k,
w
e
have
c
h
o
s
e
n
the
N
e
w
t
o
n-
Ra
ph
so
n
m
e
th
o
d
f
or
i
t
s
q
u
i
c
k
con
v
er
ge
nce
re
spo
n
se
a
s
ind
i
c
a
t
ed i
n
li
tera
tur
e
[
16,
20].
3.
NEWTON-RAPHSON
M
E
T
H
OD
I
n
t
h
i
s
s
e
c
t
i
o
n
,
i
t
i
s
e
x
p
l
a
i
n
e
d
t
h
e
r
e
s
u
l
t
s
o
f
r
e
s
e
a
r
c
h
a
n
d
a
t
t
he
s
a
m
e
t
i
m
e
i
s
gi
ven
th
e
com
p
rehe
nsive
d
i
scus
sio
n
.
Re
su
lts
c
an
b
e
pr
esen
ted
i
n
f
i
g
u
r
e
s
,
graphs,
ta
b
l
es
a
nd
o
the
r
s
t
h
at
m
ake
t
h
e
r
e
a
d
er
un
dersta
n
d
easil
y [2,
5]. The
di
s
cuss
io
n
can
b
e
ma
de in
se
v
e
ra
l
sub-cha
p
t
e
rs.
N
e
w
t
on-
Rap
h
s
on a
l
gor
ithm
c
o
n
s
is
ts
i
n
x
x
(11)
: is the der
i
va
tive
of
the f
unc
tion
f
x
0
:
i
s
the fu
nc
t
i
o
n
t
o
be
s
ol
ve
d,
x
:
i
s th
e
p
r
e
s
en
t
i
t
erat
ion
, an
d
x
:
i
s
t
h
e
n
e
x
t
i
t
e
r
a
t
i
o
n
The
n
our e
qua
t
i
o
n
t
o
so
l
v
e
w
o
ul
d be
f
I
I
II
exp
q
∗
∗
∗∗
1
.
0
(12)
The
su
bs
ti
tut
i
o
n of
(
12)
i
n
(11
)
w
e
get
.
.
.
.
.
1
.
ℎ
.
.
.
.
.
.
.
.
.
(13)
4.
RESULT
S
A
N
D
DISCU
SSIO
N
I
n
t
hi
s
sec
t
i
o
n,
t
h
e
d
isc
u
ssi
on
s
of
t
he
r
e
s
ul
ts
o
b
t
a
i
ne
d
i
n
t
h
i
s
w
o
r
k
a
r
e
d
i
v
i
d
e
d
i
n
t
o
f
i
v
e
p
a
r
t
s
.
T
h
i
s
i
s
bec
a
u
s
e
the
pr
op
o
s
e
d
m
od
el
h
as
b
e
e
n
i
m
p
l
e
m
ented
a
n
d
s
i
m
u
late
d
u
n
d
er
v
ari
ous
o
pe
rat
i
ng
c
o
nd
iti
o
n
s
s
u
ch
a
s
varie
d
t
em
per
a
t
u
r
e
s,
v
arie
d
i
r
ra
d
i
an
ce
s,
v
a
r
yi
ng
s
eri
e
s
resi
st
a
nc
es
v
a
l
ue
s
an
d
l
a
st
v
aryi
n
g
t
he
p
ara
llel
resista
n
ce
s
v
a
l
u
es.
A
c
o
mpa
r
ison
of
o
bta
i
ne
d
r
e
su
l
t
s
w
i
t
h
t
hos
e
t
a
k
e
n
f
r
o
m
t
h
e
m
a
n
u
f
a
c
t
u
r
e
r
’
s
d
a
t
a
s
h
e
e
t
h
a
s
bee
n
m
ade.
A
ccor
d
in
g
ear
lie
r
w
o
r
k
s
pre
s
e
n
ted
in
liter
a
t
u
r
e
,
the
pur
pose
of
a
d
j
ust
i
ng
t
h
e
ma
them
at
i
c
al
I
-V
c
u
rv
e
at
t
h
e
t
h
r
e
e
p
erc
e
pt
ib
l
e
p
oi
n
t
s
wa
s
su
cc
es
sfu
l
ly
a
ch
iev
e
d
.
T
h
e
elec
t
r
i
c
al
p
ara
m
e
t
e
r
s
of
L
G
2
6
0
S
1
C
-G2
P
V
m
od
ule
da
t
a
a
re give
n
i
n
Tab
l
e
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 : 1
9
1
4
–
19
22
1
918
Ta
b
l
e
1.
LG
26
0 S
1
C-
G
2
P
V
modu
le
s
pec
i
fi
ca
tio
ns
unde
r stan
da
rd te
s
t
co
nd
iti
o
n
s
(1kW/
m
2
,
A
m
1
.5
,
T
=
25
°C
)
V
a
r
i
a
b
l
e
Va
lu
e
Ma
xi
m
u
m
Powe
r (W)
P
MA
X
260
V
o
l
t
ag
e
at
m
a
x
p
o
w
e
r
(
V)
V
MP
P
30,
1
Cu
r
r
e
n
t
at
m
a
x
p
o
w
er
(
A
)
I
MP
P
8,
64
Op
en
-
c
i
r
cu
it
v
o
l
t
a
g
e
(
V
)
V
OC
37,
3
Short
-
c
i
rc
uit
c
u
rr
e
n
t (A
I
SC
8,
94
4.1.
Imp
a
ct
o
f irradiation
S
i
m
u
l
a
t
i
o
n
s
a
r
e
m
a
d
e
a
t
c
o
n
s
t
a
n
t
t
e
m
p
e
r
a
t
u
r
e
o
f
2
5
°
C
f
o
r
v
a
r
i
o
u
s
irr
a
d
i
a
tio
ns
:
(2
00,
4
0
0
,
6
00,
8
0
0
a
n
d
100
0
W/
m
2
),
t
he
C
urr
e
n
t
V
ol
t
a
ge
a
n
d
P
ow
e
r
V
olta
ge
c
urve
s
ob
ta
in
e
d
a
re
s
h
ow
n
i
n
F
i
gure
4.
F
rom
t
h
e
resul
t
s
s
how
n
in
F
ig
ur
e
4,
i
t
is
o
b
v
i
o
u
s
t
h
at
t
h
e
c
ur
ren
t
m
od
u
l
e
is
d
ire
c
t
l
y
pr
op
ort
i
ona
l
to
i
rrad
i
a
n
ce
a
s
t
h
e
ph
o
t
o
c
u
rre
n
t
i
s
direc
t
l
y
p
ro
por
ti
o
n
al
t
o
irr
a
dia
n
c
e
a
n
d
d
e
m
on
s
trate
d
i
n
(
3
)
.
I
t
ca
n
be
n
o
t
i
c
ed
t
hat
as
irra
d
i
a
n
ce
va
lu
e
d
e
cr
eases,
short-circ
u
it
cur
r
ent
dec
r
ea
se
s
pro
port
i
ona
ll
y.
D
ecr
easing
irradia
n
ce
a
l
so
r
e
duce
s
the
o
p
en
c
irc
u
it
v
o
l
t
a
ge
(
V
oc
),
b
ut
f
ol
lo
wing
a
l
og
a
r
ith
mi
c
re
l
a
tio
ns
hip
l
e
ad
ing
re
l
a
t
i
v
e
l
y
t
o
a
m
o
d
e
s
t
c
h
a
n
g
e
at
(
V
oc
).
R
e
s
u
l
t
s
i
ll
ustra
t
e
d
i
n
F
i
gure
5
sh
ow
t
ha
t
the
m
o
du
l
e
m
axim
um
p
o
w
e
r
i
s
a
l
s
o
d
i
r
e
c
t
l
y
p
r
o
p
o
r
t
i
o
n
a
l
t
o
irra
d
i
a
n
ce
w
h
i
c
h m
a
ke
s the m
odu
le
a
s be
in
g
more
e
fficie
n
t
w
h
en
ir
radia
n
ce
is im
porta
n
t
.
Figure
4.
I
rra
d
iatio
n
l
e
v
e
l im
p
act
on cur
r
en
t-vo
l
t
age
cur
v
e
s
F
i
gur
e 5.
Irradiat
ion level impa
ct on
power-
vo
ltage cur
v
es
0
5
10
15
20
25
30
35
40
0
1
2
3
4
5
6
7
8
9
10
C
u
r
r
e
n
t
[A
]
Cur
r
ent
V
ol
t
a
g
e
C
ur
v
e
f
or
d
i
f
f
e
r
ent
i
r
r
adi
a
t
i
ons
V
o
l
t
age
[
V
]
1000
W
/
m
2
8
0
0
W
/m
2
6
0
0
W
/m
2
4
0
0
W
/m
2
2
0
0
W
/m
2
T
=
25°C
0
5
10
15
20
25
30
35
40
0
50
10
0
15
0
20
0
25
0
30
0
V
o
l
t
ag
e
[
V
]
P
o
w
e
r
[W
]
P
o
w
e
r
V
o
l
t
a
ge
c
u
r
v
e
f
o
r
di
f
f
e
r
ent
i
r
r
adi
at
i
ons
1
000
W
/
m
2
8
0
0
W
/
m
2
60
0
W
/
m
2
40
0
W
/
m
2
T
=
25°
C
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
m
ode
l
f
o
r pr
edic
t
i
ng p
h
o
to
v
o
lt
aic m
o
du
l
e
perf
orm
a
nce
s
(Na
d
ia Bo
u
a
zi
z)
1
919
4.2.
Imp
a
ct
o
f t
e
m
p
erat
u
re
S
i
mulat
i
o
ns
a
r
e
m
a
d
e
a
t
c
ons
tan
t
i
rra
d
i
a
n
ce
o
f
1
0
00
W/m
2
f
or
v
ar
iou
s
t
e
m
pera
tures:
(
0,
2
5,
5
0
a
n
d
75
°
C
)
,
t
he
C
ur
r
e
nt
V
ol
ta
ge
a
nd
P
ow
er
V
ol
ta
ge
c
urves
ob
t
a
i
n
e
d
a
r
e
pre
s
ente
d
i
n
F
i
gur
e
6
an
d
F
i
gur
e
7.
A
s
ca
n
be
s
een
i
n
F
i
gure
6,
i
ncre
asi
ng
mod
u
l
e
’
s
tem
p
er
ature
de
cre
a
se
s
si
gn
i
f
i
c
a
n
tl
y
t
h
e
o
p
e
n
-c
i
r
cui
t
vo
lt
age
w
h
i
l
e
t
h
e
s
h
o
r
t-
c
ir
cui
t
c
ur
re
nt
i
nc
rea
s
e
s
o
n
l
y
sl
i
ght
ly.
I
n
F
i
gure
8,
it
ca
n
a
l
so
b
e
no
tic
ed
t
hat
w
h
en
t
h
e
t
e
mp
e
r
at
ure
o
f
t
h
e
m
o
dul
e
i
n
c
r
ea
se
s
th
e
po
wer
p
r
o
d
u
ce
d
d
ecr
ea
ses,
a
ffec
ti
n
g
n
ega
t
iv
el
y
th
e
mo
d
u
l
e
e
ffi
ci
en
c
y
.
The
e
f
fe
c
t
o
f
t
e
m
p
er
ature
ap
pe
ars
in
t
he
d
e
c
re
ase
of
t
he
ope
n
c
ircu
it
v
o
l
t
a
g
e
va
l
u
e.
W
e
co
nc
lu
de
t
h
at
m
axi
m
um
p
o
w
er
g
e
n
era
t
e
d
b
y
th
e
PV
g
en
e
r
at
o
r
d
e
p
en
d
s
s
t
r
o
n
g
l
y
o
n
the
so
l
a
r
irra
di
a
tio
n
a
n
d
tem
p
era
t
ur
e
w
h
i
c
h
m
e
a
n
s tha
t
t
he
s
olar
m
od
ule
ge
ne
rates
a
ma
xim
um
p
o
w
e
r
only
for
ce
rtai
n
va
lue
o
f
c
urrent
and
corre
sp
ond
in
g v
o
l
t
a
g
e
.
F
i
gure
6.
Tempe
rat
u
re
i
mpa
c
t on
curre
n
t
-v
o
l
ta
ge
c
urves
F
i
gure
7.
T
empera
t
u
r
e
i
m
p
ac
t
on p
o
w
e
r-vo
l
tage
c
ur
ve
s
4.3.
Imp
a
ct
o
f ser
i
es r
esist
a
nc
e
F
i
gure
8
a
n
d
F
i
gure
9
sh
o
w
t
he
s
im
ula
t
i
o
n
r
e
su
lts
o
f
c
u
r
r
ent-v
o
lta
ge
a
nd
p
ow
e
r-vo
l
t
a
ge
c
urves
ob
ta
ine
d
u
n
d
e
r
t
he
s
am
e
S
t
andar
d
T
es
t
C
o
n
d
i
t
i
ons
o
f
t
e
mpe
r
at
ure
a
n
d
i
rrad
i
ation
f
o
r
different
s
eries
resistance values
(
).
A
s
s
e
e
n
i
n
F
i
g
u
r
e
8
,
t
h
e
s
e
r
i
e
s
r
e
s
i
s
t
a
n
c
e
o
f
t
h
e
m
o
d
u
l
e
h
a
s
a
no
ti
ceab
l
e
i
mp
a
c
t
of
t
h
e
c
u
r
re
n
t
-
vo
lta
ge
c
urve
s
l
ope
i
n
t
h
e
r
e
gi
o
n
w
he
re
t
he
c
e
ll
opera
te
s
a
s
a
v
o
lta
g
e
g
e
n
er
at
or.
Inte
gr
at
i
n
g
t
h
e
series
resista
n
ce
e
ffe
ct
i
n
the
PV
e
qu
i
v
ale
n
t
circ
u
it
re
sul
t
s
in
a
v
ol
t
a
g
e
d
e
c
re
ase
a
t
a
ny
g
iv
en
c
u
r
re
n
t
.
Th
e
in
cre
a
se
i
n
t
h
e
s
e
r
i
e
s
r
e
s
i
s
t
a
n
c
e
v
a
l
u
e
h
a
s
a
n
e
g
a
t
i
v
e
i
m
p
a
c
t
o
n
t
h
e
m
a
x
i
m
um
powe
r
g
ener
a
t
ed
a
n
d
h
enc
e
,
the
efficie
n
c
y
d
ecr
ease
s
as
i
l
l
u
s
t
r
a
ted
in
F
ig
ure
9.
0
5
10
15
20
25
30
35
40
45
0
1
2
3
4
5
6
7
8
9
10
Vo
l
t
a
g
e
[V
]
Curr
e
n
t
V
o
l
t
a
ge
c
u
rv
e
f
o
r
di
f
f
erent
t
e
m
perat
ures
C
u
r
r
en
t
[A
]
T
=
75°
C
T
=
5
0
°
C
T
=
2
5
°
C
T
=
0
°
C
I
rradi
at
i
o
n
=
1
000
W
/
m
2
0
5
10
15
20
25
30
35
40
45
0
50
100
150
200
250
300
V
o
l
t
age
[
V
]
P
o
w
e
r
[W
]
P
o
w
e
r
V
o
l
t
age
c
u
r
v
e
f
o
r
di
f
f
e
ren
t
t
em
per
at
ures
T=
0
°
C
T
=
25°
C
T
=
50°
C
T
=
75°
C
I
r
r
adi
a
t
i
on
=
1
000
W
/
m
2
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 : 1
9
1
4
–
19
22
1
920
F
i
gure
8.
S
e
r
i
e
s re
si
stanc
e
i
m
p
ac
t
o
n
cur
ren
t
-vo
lta
ge
c
urve
s
Figure
9.
S
eries Resis
t
a
n
ce
Im
p
ac
t Powe
r-V
o
l
t
age
Curve
s
4.4.
Imp
a
ct
o
f s
h
un
t
resistance
S
i
mulat
i
o
ns
a
re
m
ade
for
S
t
a
ndar
d
T
e
s
t
Con
d
iti
on
s
o
f
t
e
m
pe
ratur
e
an
d
irra
dia
t
i
o
n
(
T
=25
°
C
an
d
G
=
10
00
W
/
m
2
).
T
he
e
qu
i
v
al
e
n
t
el
ec
tric
c
ircui
t
o
f
a
si
ngle
d
i
o
d
e
m
ode
l
con
s
i
d
e
r
e
d
i
n
t
h
i
s
w
o
r
k
i
s
t
h
e
o
n
e
prese
n
t
e
d i
n
F
i
gur
e 2
co
nsi
d
e
r
in
g
8
,9
00
6
.
10
Oh
m.
F
i
gure
11
a
nd
F
ig
ure
1
2
s
ho
w
the
simu
la
t
i
on
re
sults
o
f
c
u
rrent-
v
o
lta
ge
a
nd
p
ow
er
-vo
lta
ge
c
ur
ves
c
h
ara
c
t
e
ri
st
i
c
f
o
und
u
nd
e
r
t
he
s
ame
st
an
d
a
r
d
t
est
c
ondi
tion
s
o
f
t
em
per
a
ture
a
nd
i
rradia
t
ion
an
d
fo
r
dif
f
e
re
nt
val
u
es
o
f
para
lle
l
re
sis
t
a
n
ce
(
.
F
i
gure
10
sh
ow
s
tha
t
t
he
p
ara
l
le
l
re
sista
n
ce
o
f
the
m
o
d
u
le
h
a
s
a
gr
eat
impa
ct o
n t
h
e
cur
r
ent-v
o
lta
ge
c
urve
sl
ope i
n
the
re
gion
w
h
ere
t
he
c
e
ll ope
ra
te
s
as a
c
urre
n
t
g
ener
at
or.
The
inc
r
ea
se
i
n
t
h
e
p
a
ra
ll
e
l
r
e
s
i
s
tanc
e
va
lue
ca
uses
t
he
i
nc
r
e
a
se
i
n
the
va
l
u
e
o
f
t
he
m
a
x
im
um
pow
e
r
gene
ra
ted
s
o
t
he
e
f
f
ic
ie
ncy
r
i
se
s
a
s
d
e
m
ons
tra
t
e
d
i
n
t
h
e
F
i
gur
e
1
1
.
T
h
e
s
h
u
n
t
r
e
s
i
s
t
a
n
c
e
s
e
r
v
e
s
a
s
a
l
t
e
r
n
a
t
i
v
e
pat
h
s
f
o
r
t
h
e
fr
e
e
c
a
rrier
s
pro
duce
d
b
y
s
o
la
r
r
a
dia
t
i
o
n.
A
h
i
g
h
e
r
s
hu
nt
r
es
ist
a
n
c
e
me
an
s
th
a
t
a
l
arg
e
a
mo
unt
o
f
the
s
e
c
a
rrie
r
s
c
o
n
t
ri
b
u
t
e
t
o
ge
nera
te
p
ow
er
w
here
as
a
l
ow
e
r
s
hu
nt
r
esista
nc
e
i
n
d
i
ca
tes
l
a
r
g
e
losse
s
,
affec
tin
g
ma
inly
t
he
s
l
o
p
e
o
f
t
h
e
I–V
cur
v
e
o
n
t
he
p
r
oxim
ity
o
f
t
h
e
sh
ort
c
irc
u
it
re
gio
n
[
2
1
,
22]
.
The
c
e
l
l
e
ffic
i
e
nc
y
is
a
f
f
e
c
t
ed
b
e
c
a
us
e
sh
u
n
t
s
r
ed
uce
t
h
e
Fi
ll
F
ac
to
r
(FF)
a
n
d
t
h
e
Op
e
n
Ci
r
c
ui
t
V
o
l
t
age
(V
oc
).
T
his
e
ffe
ct
b
e
c
om
es
mor
e
p
rom
i
na
nt
u
nder
l
o
w
l
i
gh
t
c
o
n
d
i
t
i
ons [2
3
].
A
l
ow
s
h
u
n
t
r
es
ista
nce ca
n
lea
d
t
o
ho
t
-
spo
t
s
i
n
r
eve
r
s
e
cells,
espec
i
al
ly
w
hen
t
h
e
p
o
w
e
r
dis
s
ipa
t
i
on oc
c
u
rs
i
n
a
sm
all a
r
ea [2
4].
0
5
10
15
20
25
30
35
40
0
1
2
3
4
5
6
7
8
9
10
Vo
l
t
a
g
e
[
V
]
C
u
r
r
e
n
t [
A
]
I
m
pac
t
of
s
e
r
i
e
s
res
i
s
t
anc
e
v
al
ue
o
n
t
h
e
c
u
rr
ent
v
o
l
t
age
c
u
r
v
e
T
e
m
p
e
r
at
ure
=
2
5
°C
a
n
d
I
r
r
a
di
a
n
c
e
=
1
000
W
/
m
2
R
s
=
9
e
-
0
0
4
O
h
m
R
s
=
9
e
-
0
0
3
O
h
m
R
s
=
2
e
-
0
0
2
O
h
m
R
s
=
3
e
-
0
0
2
O
h
m
0
5
10
15
20
25
30
35
40
0
50
10
0
15
0
20
0
25
0
30
0
V
o
l
t
age
[
V
]
P
o
w
e
r
[W
]
I
n
f
l
ue
nc
e
of
s
er
i
e
s
r
e
s
i
s
t
anc
e
on
t
h
e
P
o
w
e
r
V
o
l
t
age
c
u
r
v
e
s
R
s
=
9
e
-
4
O
h
m
R
s
=
9
e
-
3
O
h
m
R
s
=
3
e
-
2
O
h
m
T
e
m
p
er
a
t
u
r
e
=
2
5
°C
,
I
r
r
a
di
an
c
e
=
1
000
W
/
m
2
R
s
=
2
e
-
2
O
h
m
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
m
ode
l
f
o
r pr
edic
t
i
ng p
h
o
to
v
o
lt
aic m
o
du
l
e
perf
orm
a
nce
s
(Na
d
ia Bo
u
a
zi
z)
1
921
F
i
gure
1
0
.
P
a
r
a
lle
l r
e
sistanc
e
i
m
p
ac
t
on c
u
rre
nt-
v
o
lt
ag
e
cu
rv
e
s
F
i
gur
e 1
1
.
P
a
rall
e
l
r
esis
tance
i
m
pact on
p
o
w
e
r-
vo
lta
ge c
ur
ves
4.5.
C
o
mp
aris
on
o
f
r
e
su
lts
with
th
e
r
esults ta
k
e
n
from
man
u
fac
t
ur
er
’
s
d
a
tasheet
an
d
previous
wor
k
s mod
e
l
lin
g
A
com
p
ar
i
s
o
n
b
e
t
w
e
e
n
c
a
l
c
u
la
t
e
d
a
n
d
ex
pe
r
i
me
nt
a
l
v
a
l
ues
of
t
he
co
ns
id
ere
d
P
V
m
odu
l
e
i
s
m
a
de
.
The
o
b
t
a
ine
d
re
s
ults a
re
p
rese
nt
e
d
i
n F
i
gur
e 12.
Res
u
l
t
s
prese
n
t
e
d
in
F
i
g
ur
e
12
s
how
s
co
ns
is
t
e
nc
ies
be
t
w
een
e
x
p
e
r
i
m
e
n
t
al
a
nd
pr
e
d
ic
t
e
d
r
e
sul
t
s.
I
t
com
e
s
o
u
t
e
v
i
d
en
t
t
h
at
t
he
c
alcu
la
te
d
resu
l
t
s
are
i
n
g
o
od
agre
e
m
e
nt
w
i
t
h
the
e
x
per
i
m
e
nta
l
d
a
t
a
pr
ov
i
d
ed
b
y
the
m
a
n
u
fa
c
t
ur
er
i
n
da
tas
h
ee
t
.
A
cc
ording
t
o
pr
ev
i
o
us
w
or
k
s
p
res
e
n
te
d
i
n
l
i
t
era
t
ure
[1
0,
11,
15],
t
h
e
p
u
r
pose
of
a
djus
t
i
n
g
t
h
e
m
athem
a
ti
ca
l
I-
V
cur
v
e
a
t
t
he
t
hr
ee
perc
ept
i
bl
e
p
o
in
ts
(
S
hort
C
i
rc
u
it
C
u
rre
nt,
O
p
e
n
C
irc
u
it
V
o
l
t
a
g
e
an
d M
a
xim
u
m
P
o
w
e
r) w
as
s
uc
cessful
l
y
a
chi
e
ve
d.
F
i
gure
1
2
.
Exp
e
rim
e
nta
l
a
nd
ca
lcu
l
a
t
e
d
I
-V curve
s
o
f
the
L
G
26
0
S
1
C
-
G
2 P
V
modu
le
u
nder
st
a
ndard
t
e
s
t
c
o
n
d
iti
on
s (
25°C,
1
0
00 W/m
2
and AM
1
.5)
5.
CO
NC
L
U
S
I
O
N
The
re
pr
esen
ts
w
ork
a
c
h
ie
ve
d
a
c
o
n
t
ri
bu
t
i
on
to
t
he
p
re
dic
t
i
o
n
o
f
ph
o
t
o
vol
ta
ic
d
e
v
ice
p
e
rfor
ma
nces
wh
i
c
h
co
nst
i
t
u
t
e
a
v
e
r
y
i
m
p
o
rt
ant
st
ep
i
n
the
st
ud
y
of
a
ny
P
V
s
yst
e
m.
T
he
s
im
p
lic
it
y
of
a
s
in
gle
d
i
ode
m
ode
l
w
ith
t
h
e
t
ec
h
n
ique
o
f
a
d
jus
t
in
g
the
pa
ram
e
te
r
s
a
nd
the
imp
r
ovem
en
ts
p
ro
pos
ed
i
n
th
is
p
ape
r
c
an
m
ake
t
h
is
mode
l
an
a
lt
e
r
nat
i
v
e
to
o
l
f
or
d
es
i
gners
w
h
o
a
r
e
i
n
ne
e
d
o
f
a
si
m
p
le
a
n
d
e
ffec
ti
ve
m
o
d
e
l
f
or
s
im
ul
a
tin
g
PV
dev
i
ce
s
ass
o
c
i
ated
t
o
p
o
wer
co
nv
erter
s
.
So,
t
h
e
m
o
de
li
ng
sim
u
l
a
t
i
on
b
y
Ma
tla
b
is
h
elfu
l
for
P
V
s
ys
t
e
ms
des
i
g
n
ers
du
e
t
o
the
s
impl
ic
ity,
e
ffe
ct
ive
n
es
s,
acc
urac
y a
n
d
ea
sy
t
o use
sim
u
lat
i
on
a
nd
m
odel
i
ng m
e
t
h
od.
Th
e
p
r
op
ose
d
m
o
d
e
l
wa
s
u
s
e
d
t
o
st
udy
t
he
i
mp
act
o
f
seri
e
s
a
nd
p
ar
a
l
l
e
l
re
sis
t
ance
s
as
w
el
l
as
tem
p
era
t
ur
e
a
n
d
irra
dia
t
i
o
n
o
n
t
h
e
d
e
v
e
l
op
me
nt
o
f
pho
to
vo
l
t
a
i
c
d
e
vi
ce
p
e
rf
o
r
man
c
e
s
i
n
t
e
rms
o
f
r
el
ia
b
ilit
y
a
n
d
ef
fi
c
i
en
cy
. Fu
r
t
h
ermo
re
,
si
mul
a
t
i
o
n
re
sul
t
s
s
ho
w a
n
exc
el
l
e
n
t
agre
e
m
e
nt w
it
h t
h
e e
x
pe
rime
nta
l
d
a
t
a t
a
ke
n
direc
t
l
y
from
t
h
e
ma
nufac
tur
e
r
da
tas
h
eet.
F
i
na
ly
o
ur
c
o
n
t
r
i
b
u
t
i
o
n
c
o
u
l
d
c
o
n
s
t
i
t
u
t
e
a
f
i
r
s
t
s
t
e
p
t
o
b
u
i
l
d
u
p
a
fu
l
l
solar
P
V
p
o
w
e
r
elec
t
r
on
ic
c
o
nve
rs
io
n s
y
ste
m
i
n
deve
lop
i
ng
a g
r
id
con
n
e
ct
ed
a
p
p
li
ca
t
i
on
.
0
5
10
15
20
25
30
35
40
0
1
2
3
4
5
6
7
8
9
10
V
o
l
t
age
[
V
]
I
m
pac
t
o
f
S
hunt
r
es
i
s
t
a
nc
e
on
c
ur
r
ent
v
ol
t
age
c
u
r
v
e
Cu
r
r
e
n
t
[A
]
T
e
m
p
e
r
a
t
u
r
e
= 2
5
°
C
, I
r
r
a
d
i
a
t
i
o
n
=
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pac
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Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 : 1
9
1
4
–
19
22
1
922
REFE
RENCES
[1]
R.
F
o
s
ter
,
M
ad
jid
G
hasmi,
a
nd
A
lma
C
o
ta,
S
o
l
a
r energ
y
: renewa
bl
e
en
erg
y
a
n
d
the en
viro
n
m
ent
.
Ta
ylo
r
a
nd
F
r
anci
s
G
r
o
up,
201
0.
[2]
Ab
delk
ader
M
ez
o
u
ari,
R
.
Elgo
u
ri
,
M.
A
lareq
i
,
K.
M
ateu
r,
H
.
Da
h
o
u,
a
n
d
L
.
Hlo
u
,
“A
N
e
w
P
ho
to
vo
lta
i
c
B
l
o
c
ks
M
u
t
u
ali
zati
on
Sy
stem
f
or
M
icro
-G
rid
s
Using
a
n
A
r
du
ino
Bo
ard
and
L
abvi
ew,
”
I
nt
ern
a
tion
a
l
Jo
ur
nal
of Po
wer
El
ectro
n
i
cs
a
n
d
Dr
ive S
y
s
t
em
(
I
JPEDS)
,
V
o
l
.
9
,
No
.
1
,
pp.
9
8-104,
M
arch
2
018
.
[3]
M
u
ru
ganan
t
h
a
m
B,
G
nan
a
das
s
R
,
an
d
P
a
d
hy
N
P
.,
“
Cha
l
len
g
e
s
w
ith
r
en
ewab
le
e
nerg
y
s
o
u
r
c
e
s
a
nd
s
to
rage
i
n
pract
ical
d
is
tri
buti
on systems
,
”
Renewab
l
e a
n
d
Su
st
a
i
nab
le Ener
gy
R
eviews
,
vol.
73,
p
p
.
1
25
-134
,
201
7.
[4]
Ko
dan
d
a
R.
a
nd
M
an
nam
V.
,
“O
perati
on
a
nd
Co
nt
ro
l
of
G
rid
Conn
ec
t
e
d
Hy
br
i
d
A
C
/
D
C
M
ic
r
o
g
r
id
s
u
s
in
g
R
E
S
,
”
Int
e
rna
t
i
o
n
a
l
Jo
u
r
n
a
l of Po
wer
E
l
ectr
onics an
d
D
r
i
ve Systems
(
I
JPE
D
S)
,
V
ol
5
,
No
2
,
p
p
.
1
9
5
-202,
2
0
1
4
.
[5]
N.
B
ouazi
z,
A
.
Benf
d
i
la,
and
A.
l
akh
l
ef
,
“
C
o
n
t
r
ib
ut
ion
t
o
t
he
P
redi
cti
o
n
o
f
P
h
o
tov
o
lt
a
i
c
M
o
du
le
P
erf
o
rm
an
ces,”
IEEE, 17th Internati
o
na
l
Conf
erence on
Power El
ectronics
and
Motion Cont
rol (PE
M
C
)
,
V
a
rna/Bu
lg
ari
a
,
pp
.
1
168
-11
7
3
, 2
5-30
S
ept
e
m
b
e
r
2
016
.
[6]
A.
B
en
f
d
ila,
“
I
n
v
est
i
g
a
tio
n
o
n
M
OS
S
yst
e
m
App
l
i
catio
n
i
n
P
hoto
v
o
l
t
a
ic
cell
En
gi
neerin
g,”
W
o
r
l
d Co
n
f
erence
o
n
Ph
ysics a
nd
Susta
in
ab
le
D
evelop
men
t
, W
C
PS
D
,
ICC,
Durb
an-S
outh
Afri
ca
,
3
1st
Octo
ber
-
2
n
d
No
v
e
m
b
er
2
0
05.
[7]
T.
U
.
Townsend,
“A
M
ethod
f
o
r
Es
ti
ma
ting
th
e
L
o
ng
T
e
r
m
Pe
r
f
o
r
ma
n
ce
of
D
i
r
ect
-Cou
pled
P
h
o
to
v
o
lt
a
i
c
S
y
st
ems,”
M
S
Th
e
si
s,
S
ola
r
E
nerg
y L
a
bo
ra
t
o
ry
,
U
n
i
v
ersity
of
W
i
s
c
on
sin
,
M
a
diso
n
, 1
98
9.
[8]
W
.
L
.
D
e
S
o
t
o
,
“
I
m
p
r
o
v
e
m
e
n
t
a
n
d
V
a
l
i
d
a
t
i
o
n
o
f
a
M
o
d
e
l
f
o
r
P
h
o
t
o
v
o
l
t
a
ic
A
rray
P
erf
o
rm
ance,”
M
S
T
h
e
si
s
,
S
olar
En
ergy
Labo
ratory
U
ni
versity
o
f
Wis
c
on
si
n-M
a
diso
n,
200
4
.
[9]
Roh
a
n.
S
.
K
ulkarni
an
d
Dh
an
anj
a
y
B.
T
alan
ge,
“
M
od
eli
ng
o
f
s
ol
ar
p
h
o
t
ov
ol
ta
i
c
m
o
dule
usi
n
g
s
y
s
t
e
m
identi
f
i
cation,”
7
t
h
In
ter
natio
n
a
l co
nfer
ences
on p
o
wer
s
y
st
em
(
I
CPS)
,
colle
ge o
f
En
gi
neerin
g Pu
ne,
In
dia
,
p
p
. 78
2
-
78
4,
De
c
e
m
be
r 2
1
-2
3, 2
01
7.
[10]
Zai
d
H
u
s
sei
n
A
li,
A
b
dullah
K
h
alid
A
hm
ed,
and
Am
er
T
ay
es
S
ae
ed
,
“Modeling
S
o
lar
M
o
dules
Pe
rf
or
mance
Under
Tem
p
erat
ure
an
d
S
o
l
a
r
Rad
i
ati
o
n
of
W
estern
Ira
q
,
”
Int
e
rna
t
i
o
n
a
l
Jo
ur
na
l of
Po
we
r
El
ectro
n
i
cs and D
r
i
ve
S
y
st
em
(I
J
P
E
D
S
)
, Vol. 9, N
o
.
4
, p
p
.
18
4
2
-
185
0,
Decem
b
e
r 2
0
1
8
.
[11]
TA
RAK
S
a
lm
i
,
M
ou
ni
r
Bo
uzg
u
en
da,
Ad
el
G
as
tel
i
,
an
d
Ah
m
e
d
M
a
sm
ou
d
i
,
“
Ma
tl
ab
/S
i
m
u
link
B
a
sed
Model
i
ng
o
f
Sol
a
r
Photovol
taic
c
e
l
l,
”
Int
e
rnat
io
na
l
Jo
ur
nal
of
Ren
e
wab
l
e Ener
gy
Res
e
arch
,
Vol.
2
,
No
.
2,
p
p
.
2
13
-218
,
Decem
ber
201
2.
[12]
Ka
rte
e
k
G
u
m
mi
a
n
d
M
e
h
di
F
e
r
do
ws,
“Do
u
b
l
e
-In
pu
t
DC–DC
Powe
r
Ele
c
t
r
on
ic
C
o
n
v
e
rt
ers
f
o
r
E
l
ect
ric-Dri
v
e
Ve
hic
l
e
s
—Top
o
l
o
g
y
Exp
l
o
r
a
t
io
n
a
n
d
Sy
nthe
sis
Usin
g
a
Sing
le
-P
ole
T
ri
p
l
e-Throw
Switch,”
IE
EE
T
r
ans
ac
t
i
o
n
s
on
Ind
u
s
t
r
i
a
l
El
ectron
i
cs
, v
ol
.
5
7
, n
o. 2,
Feb
r
uary
2
0
1
0
.
[13]
As
hish
K
um
ar
S
i
n
g
h
al
a
n
d
R
ake
s
h
N
a
rvey
,
"P
S
I
M
an
d
M
A
T
L
A
B
B
ased
S
i
m
u
latio
n
of
P
V
Array
f
o
r
E
nhan
ce
t
h
e
Pe
rfo
r
ma
n
c
e
by
U
sing
M
P
P
T
Al
go
rith
m"
,
Int
e
rnat
ion
a
l
Jou
r
nal o
f
Electrica
l E
n
g
i
neer
in
g (
I
EEE)
,
Vo
l.
4
,
No
.
5
,
pp
.
5
11-5
2
0
,
2
0
1
1.
[14]
Jey
r
aj
S
el
varaj
a
n
d
N
a
srud
in
A
.
Rah
i
m
,
“
Mu
ltil
e
v
el
I
nv
erter
Fo
r
G
rid
-
Co
nn
ected
P
V
S
y
s
t
e
m
E
m
p
lo
yi
ng
Digital
P
I
Controller,
”
I
E
EE
Tran
sa
c
t
ion
s
On In
du
s
t
r
i
a
l
Ele
c
t
ro
nic
s
, v
ol
.
5
6
,
n
o
.
1,
p
p.
14
9
-
1
5
8
, 20
0
9
.
[15]
Ahm
e
d
A.
E
l
T
a
yya
n
,
“
P
V
s
y
s
t
em
b
ehavior
based
on
dat
a
sheet
,”
Jour
na
l of
Electr
o
n
D
evices
,
Vo
l
.
9
,
p
p
.3
35
-34
1
, 2
01
1.
[16]
B.
A
lsayid,
“Model
i
ng
a
nd
S
im
u
l
ation
of
P
hot
ovolt
a
ic
C
ell/Mod
ul
e/A
rray
with
T
wo
D
i
ode
M
od
el,
”
International
Jou
r
n
a
l
o
f
Co
m
p
ut
er Tech
no
lo
gy a
nd
El
e
c
t
r
o
n
i
c
s
E
n
g
i
neer
in
g
, Vo
l
.
1,
no
.
3
,
Ju
ne
2
01
2.
[17]
D.
B
onk
ou
ng
ou,
Z
.
Kaolaga,
a
nd
D
.
Njom
o,
“
M
o
delin
g
an
d
S
i
mu
la
t
i
on
o
f
P
h
otov
o
lta
ic
M
o
d
u
l
e
Co
nside
r
in
g
Sing
l
e
-
D
iode
E
q
u
ival
ent
c
i
rcuit
Model
in
M
atla
b,”
Int
e
rn
a
t
i
o
n
a
l Jou
r
na
l of
E
m
e
r
gin
g
T
ech
no
logy an
d A
d
van
c
e
d
En
gi
neeri
n
g
,
Vo
l. 3
, n
o.
3,
March
20
13
.
[18]
H.
B
ou
rdou
cen and
A.
G
as
tli
,
“
A
n
al
ytical
M
odel
i
n
g
a
n
d
S
im
u
l
ati
o
n
of
P
hotov
o
l
tai
c
P
anel
s
an
d
A
rrays
”,
Jo
ur
nal
o
f
En
gi
neeri
ng Resear
ch
, Vo
l
.
4,
N
o. 1,
pp
75
-
81
, 2
0
0
7
.
[19]
A.
N
.
Celi
k
and
N.
A
ci
kg
oz,
“M
o
d
elin
g
an
d
exp
e
ri
m
e
nt
al
V
erifi
c
a
t
i
o
n
o
f
The
Op
era
t
in
g
Current
o
f
M
o
n
o
-
Crys
tallin
e
P
h
o
t
o
v
o
lta
i
c
M
od
ul
e
s
U
si
ng
F
our
a
nd
F
ive
P
a
ram
e
t
e
rs
M
o
d
els
,
”
Ap
plie
d Ene
r
gy
,
V
o
l.
84,
n
o.
1
,
p
p
. 1-1
5
, 2
00
7.
[20]
Er.
M
o
h
a
mm
ad
O
m
a
ir
a
nd
E
r.
P
rati
bha
T
iwa
r
i
.
,
“S
im
ulation
and
P
e
rf
orman
ce
A
n
aly
s
i
s
o
f
Th
ree
P
h
ase
P
h
o
t
ov
o
l
ta
i
c
A
rray
B
as
ed
I
n
v
e
r
ter,
”
Int
e
rn
ational
Jo
ur
nal
o
f
Scien
ce,
E
n
g
i
n
e
e
r
in
g
an
d T
ech
nol
og
y R
e
sear
ch
Applications
,
Vo
l. 3
, n
o.
9,
Sep
t
e
m
b
e
r 20
1
4
.
[21]
A.
H
adj
Arab
,
F
.
C
h
e
n
l
o,
a
nd
M
.
B
en
ghan
e
m
,
“
Loss
-o
f
-
Load
P
ro
bab
ili
t
y
of
P
h
o
t
ovolt
a
ic
W
ater
P
u
m
p
i
ng
Sy
ste
m
s
,
”
So
lar E
n
erg
y
,
v
o
l
.
7
6
, p
p.
7
1
3–7
23
,
2
0
0
4
.
[22]
Cristia
no
S
a
b
oia
Rusc
he
l,
F
a
b
ia
no
P
e
r
in
G
a
s
pa
rin,
E
u
r
id
e
s
R
a
m
o
s
C
os
ta,
and
A
rno
K
r
enzin
g
er,
“
A
s
s
essm
ent
o
f
P
V
m
o
d
u
les
s
hunt
r
e
s
istan
ce
dep
e
nd
en
ce
on
s
o
l
ar
i
rradi
a
nce,
”
E
L
SEVIE
R
,
Solar Ene
r
gy,
vol.
1
3
3
,
p
p
.
3
5-4
3
,
20
16.
[23]
Breit
e
ns
t
e
in,
O.,
Rak
o
ton
i
ai
n
a
,
J.P.
,
A
l
R
ifai,
M
.
H.
,
and
W
e
rn
e
r
M
.,
“S
hu
n
t
t
y
p
e
crys
tal
lin
e
sil
i
co
n
so
lar
cells.
P
r
og
.
P
h
o
t
o
volt
a
i
c
s,
”
Res., A
p
p
l
.
,
v
o
l
. 12
,
p
p
. 5
29
–5
38
, 20
0
4
.
[24]
P
.
G
ru
no
w
,
S
.
Lu
s
t
,
D.
S
aut
e
r,
V
.
H
o
ffm
an,
C.
B
enek
in
g,
B
.
L
i
tz
en
bu
rger,
and
L.
P
odlo
w
s
k
i
,
19t
h Eu
ro
pea
n
Ph
ot
ovo
l
taic S
o
lar
En
ergy Conf
e
r
en
ce,
Pa
ri
s
,
p
p
.
21
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