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.
3, S
ep 2019,
pp.
1
2
6
3
~1
2
6
9
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1263-1269
1263
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
Development of PV array con
f
ig
uration under differen
t partial
shadi
n
g condition
Moh
a
mm
ad
S
yah
ir
B
i
n
Ish
ak,
R
a
h
m
at
u
l
Hid
a
yah
S
a
l
i
m
in
,
Ismail Mu
s
irin,
Z
u
lk
iff
l
i
Abdul Ha
m
id
Facul
t
y o
f
E
l
e
ct
r
i
cal
Engi
n
eer
ing
,
U
niversiti T
e
knol
ogi MARA
,
M
alay
si
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Sep
2
7
,
2
018
Re
vise
d Jan
1
7
, 2019
Ac
ce
p
t
ed
M
ar 4
, 2
0
19
Th
is
p
a
p
er
i
nv
es
ti
ga
t
e
s
t
h
e
perf
orm
a
n
ces
o
f
d
i
ff
erent
p
hot
ov
olt
aic
(PV)
a
rray
un
der
sev
e
ral
sh
adin
g
con
d
i
t
i
on.
F
o
u
r
types
o
f
p
ho
to
v
o
lta
i
c
a
rr
ay
conf
igurat
i
o
n
s
c
he
m
e
w
hi
c
h
a
re
‘
Se
ri
es’
(S),
S
eries
-
Parallel
’
(
SP),
Tota
l
-
Cr
oss
-
Ti
e
d
’
(TCT
),
a
nd
‘
B
r
i
d
ge-Link’
(
BL
)
array
topol
ogie
s
were
te
ste
d
b
y
a
p
p
l
y
i
n
g
a
6
x6
P
V
a
rra
y
un
de
r
6
di
ffe
r
e
n
t
sh
a
d
in
g
sc
e
nari
os
.
Th
e
m
o
d
e
l
i
n
g
i
s
d
e
vel
oped
us
in
g
M
a
tlab/S
i
m
u
lin
k
.
The
perf
orm
a
nc
es
a
nd
o
u
t
pu
t
ch
aract
eris
ti
c
s
o
f
phot
ov
olt
a
ic
a
rray
are
com
p
ared
a
n
d
anal
yzed
.
S
y
s
t
e
m
e
n
g
i
n
ee
r
can
u
se
t
h
e
d
et
ail
e
d
ch
aracteri
s
ti
cs
o
f
diff
e
r
e
nt
a
rra
y
c
o
nfigu
r
a
t
io
n
to
a
p
p
ro
xima
te
t
he
o
u
t
c
o
me
p
owe
r
a
n
d
pic
k
t
he
b
e
s
t
c
o
nfigu
r
a
t
io
n
o
f
t
h
e
s
yste
m
b
y
c
on
c
e
r
nin
g
t
h
e
c
u
rre
nt
n
a
t
ura
l
c
ondition
to
enh
a
nc
e t
h
e o
v
erall
e
ffici
ency
.
K
eyw
ord
s
:
A
rra
y c
onfi
gur
ati
o
n
Br
idge
-
lin
k
Pa
rti
a
l sha
d
in
g
PV
a
rray
To
tal-cr
oss-
tie
d
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:
Mo
ham
m
a
d
S
ya
hir b
i
n I
s
ha
k,
Fa
cult
y
o
f
E
l
e
c
t
rica
l
En
gine
erin
g,
Un
iv
e
r
sit
i
Tekn
o
lo
gi
M
A
R
A,
40
4
50 S
h
a
h
A
l
a
m
,
Ma
la
ysi
a
.
Em
ail:
sya
h
i
r
is
ha
k
261
@
g
m
a
i
l
.c
om
1.
I
N
TR
OD
U
C
TI
O
N
Gro
w
i
n
g
i
n
t
e
r
e
st
o
f
re
n
e
wab
l
e
en
ergy
s
ou
rce
s
a
nd
s
ola
r
p
h
o
t
o
vol
ta
i
c
(
PV
)
has
bec
o
me
m
ore
si
g
n
i
f
i
c
a
n
t
t
o
g
en
e
r
a
t
e
cl
e
a
n
e
n
ergy
[1
-4
].
H
o
w
ev
e
r
i
t
ha
v
e
s
o
m
e
d
i
s
ad
v
a
nt
a
g
es
w
h
i
ch
a
re
l
o
w
e
n
e
rgy
c
o
nv
e
r
si
on
p
e
r
f
o
rma
n
ce
,
hi
gh
i
n
i
t
i
a
l
co
st
o
f
pu
rc
h
a
si
ng
t
h
e
s
ol
a
r
s
yst
e
m
i
t
s
el
f
,
a
nd
d
e
p
e
n
d
e
n
c
e
of
p
o
w
e
r
ou
tpu
t
o
n
w
e
a
t
her
or
a
tmos
pher
i
c
c
ond
it
i
o
n
[5-
7
].
T
he
o
utp
u
ts
o
f
P
V
d
ev
ic
es
a
re
n
on-l
i
ne
ar
d
u
e
t
o
its
depe
n
d
e
n
c
y
t
o
t
h
e
en
v
i
ro
nm
enta
l c
o
nd
it
io
ns
such
as solar
i
rradi
a
n
ce
an
d t
e
mpe
r
ature
[8]
.
The
r
e
a
r
e
num
erous
e
lem
e
nts
t
h
a
t
m
ake
c
o
ntr
i
bu
t
i
o
n
s
to
t
h
e
r
edu
ct
i
on
of
o
u
t
pu
t
e
l
ectr
i
ci
ty
f
rom
P
V
arr
a
ys.
O
n
e
of
t
he
m
a
i
n
rea
s
ons
t
ha
t
c
o
ntr
i
bute
t
h
e
l
o
ss
o
f
out
p
u
t
po
we
r
i
s
p
a
r
t
i
al
s
h
a
di
ng
[
9
]
.
In
l
arge
P
V
i
n
s
t
all
a
tio
n
,
t
he
p
art
i
a
l
sh
a
d
ing
wi
ll
r
e
d
u
c
e
th
e
e
f
f
i
ci
en
cy
o
f
t
h
e
o
v
e
r
a
l
l
s
y
s
t
e
m
.
I
t
is
i
m
p
r
a
c
t
i
c
a
l
t
o
k
e
e
p
a
w
a
y
from
t
h
e
p
ar
tia
l
sha
d
ing
o
f
t
h
e
a
rr
ay
i
n
a
l
l
w
e
a
t
he
r
c
o
n
d
it
io
ns
a
nd
s
e
a
s
on
s
[10
]
.
Th
e
ou
tpu
t
o
f
PV
m
o
dul
e
alw
a
ys
d
e
p
e
n
d
s
on
t
h
e
so
lar
i
rra
diance
a
nd
te
mpe
r
ature
.
T
he
s
o
l
ar
e
ner
g
y
ca
n
be
c
ha
ng
e
t
o
e
l
e
c
t
rica
l
e
n
erg
y
by us
i
n
g P
V
cell
,
m
odu
le or
ar
ray.
S
e
ve
ral
re
se
archer
s
ha
ve
s
t
u
di
e
d
t
he
c
onse
que
nces
a
nd
e
x
p
l
o
r
ed
t
h
e
r
e
m
e
dies
o
f
pa
rt
ia
l
sha
d
i
n
g
o
n
PV
s
ystem
s
.
O
n
e
of
t
h
e
b
est
so
lu
ti
o
n
s
i
n
t
h
i
s
d
i
rec
tio
n
is
P
V
a
r
r
ay
c
onfiguration.
D
i
f
f
e
r
e
nt
P
V
ar
ray
con
f
ig
ura
tio
ns
t
ha
t
ha
ve
b
e
e
n
p
ro
p
o
sed
i
n
t
he
l
i
t
era
t
ur
e
ar
e:
S
e
r
ies
(S
),
P
a
r
allel
(P
),
S
er
i
e
s-Parallel
(SP)
,
To
tal-
Cross-
Tie
d
(
TCT
)
,
Brid
ge-Li
n
ked
(BL)
a
n
d
H
on
ey-C
om
b
(
H
C)
.
I
n
[11-1
3
],
a
M
A
TLA
B-
base
d
mo
d
e
li
n
g
a
nd
si
mul
a
t
i
on
s
c
h
e
m
e
s
u
it
a
b
le
f
o
r
s
tu
dyi
ng
t
h
e
p
e
r
fo
r
m
a
nce
o
f
t
he
m
a
x
imum
o
u
t
pu
t
power
gene
r
ate
d
.
I
n
a
norm
a
l
c
ond
i
t
i
on,
pow
er
–
v
olta
ge
(
P
-
V
)
a
nd
curr
ent
–
v
o
lt
ag
e
(I-V
)
c
u
r
v
e
w
i
l
l
on
l
y
h
a
v
e
on
e
pea
k
v
al
ue,
w
h
er
eas
u
n
d
e
r
p
ar
t
i
a
l
s
ha
d
i
n
g
c
on
d
iti
on
(P
SC)
the
c
urve
w
il
l
be
m
ul
ti
pl
e
pe
aks.
T
here
fore,
the
des
i
g
n
er
h
as
t
o
c
h
o
o
se
t
he
r
ig
ht
o
r
s
u
ita
b
l
e
val
u
e
a
n
d
use
the
ma
xim
u
m
pow
er
p
oi
n
t
t
rac
k
i
n
g
(MP
P
T)
to
t
ra
ck
t
he
m
aximum
p
o
w
er
[
14
-
1
5].
MP
P
T
i
s
lar
g
ely
a
dc-
d
c
con
v
e
r
t
e
r
w
h
i
c
h
m
a
k
e
s
u
s
e
o
f
a
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
126
3
– 1
269
1
264
alg
o
ri
t
h
m
to
d
eterm
i
ne
t
he
m
aximum
p
o
w
e
r
poi
n
t
(
M
P
P)
o
f
the
P
-
V
a
n
d
I
-
V
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
i
n
v
a
r
y
i
n
g
env
i
ro
nm
en
tal
si
tua
t
i
o
n
[1
6-1
7
].
In
[1
8],
gener
a
li
z
e
d
M
A
T
L
A
B
M-c
ode
h
as
b
ee
n
de
v
e
l
ope
d
to
s
ui
t
w
i
th
a
ny
r
e
qui
red
array
si
z
e
,
con
f
ig
ura
tio
n,
s
ha
din
g
p
a
tter
n
s
a
n
d
n
u
mbe
r
o
f
b
ypa
ss
d
i
o
d
es.
Mo
de
li
n
g
a
nd
c
o
m
p
ar
i
s
o
n
o
f
th
e
pe
rform
anc
e
of
d
i
ffe
re
nt
P
V
array
c
onfi
gur
at
ions
u
n
d
e
r
v
ari
ous
P
S
C
s
i
s
p
re
s
en
ted
[1
9].
The
pe
rfor
ma
n
c
e
of
e
xis
tin
g
a
n
d
some
p
rop
o
se
d
so
lar
P
V
a
rr
ay
c
on
fi
gur
at
ions
i
s
i
nve
st
i
g
ate
d
c
om
pr
e
h
en
si
ve
ly
i
n
[20].
In
[
21],
a
fu
ll
in
ves
tiga
t
io
n
of
o
nl
y
T
o
ta
l-Cross-T
i
e
d
(
TCT)
c
o
n
fig
u
rat
i
o
n
u
n
d
e
r
P
S
C
is
d
one
n
e
g
l
e
c
t
i
n
g
ot
her
con
f
ig
ura
tio
ns.
Interc
on
ne
ct
i
o
ns
w
h
o
se
p
e
r
form
ance
l
ies
in
b
e
t
w
ee
n
SP
a
n
d
TC
T
i
n
t
e
rc
onn
e
c
t
i
on
s
are
pro
pose
d
i
n
[22]
t
o
cr
eat
e
a
c
l
ear
c
o
rre
l
a
tion
be
tw
ee
n
nu
m
b
er
a
nd
l
oc
a
tio
n
of
s
ha
de
d
m
o
d
u
l
e
s
,
in
t
e
rco
n
n
e
c
t
i
o
n
s a
n
d m
a
xim
u
m
po
w
e
r
obt
a
i
ne
d
In
[
2
3
]
,
re
c
o
nfi
g
u
r
ati
o
n
of
a
rra
y
h
as
b
een
m
a
d
e
by
w
ay
o
f
c
onv
e
rti
n
g
con
n
ec
t
i
o
n
o
f
all
m
odu
les
o
n
the
arr
a
y.
T
he
p
ro
pose
d
c
i
r
cu
it
w
h
ich
is
a
c
ombi
na
ti
o
n
o
f
a
b
u
c
k
–
b
o
o
s
t
c
o
n
v
e
r
t
e
r
a
n
d
t
h
e
s
w
i
t
c
h
e
d
-
c
a
p
a
c
i
t
o
r
(BBS
C)
c
i
r
cu
it
s,
e
qua
li
zes
t
he
vol
ta
ge
o
f
P
V
m
odu
les
a
n
d
p
r
e
v
en
ts
b
y
p
a
s
s
d
i
ode
s
from
b
ypa
ssi
n
g
t
he
s
had
e
d
modu
les
in
a
s
tri
ng
[2
4].
The
a
u
t
hor
i
n
[
25]
i
s
pro
pos
e
d
b
y
us
i
ng
Binary
S
earch
Algorithm
(BSA
)
to
deter
m
i
n
e
th
e
m
a
xim
u
m
pow
er
point
(
MP
P
)
in ph
o
t
o
v
o
l
t
a
i
c
(P
V)
s
y
ste
m
un
d
er
p
artia
l s
h
ade
d
c
ond
i
t
ions.
I
n
t
h
i
s
pa
pe
r,
6
d
i
f
fere
n
t
s
ha
di
ng
ca
se
s
tu
d
i
es
o
n
6
by
6
P
V
ar
ray,
t
he
p
erform
ance
o
f
Series
(
S)
,
S
e
ries-P
a
r
a
l
l
e
l
(SP
)
,
Tot
a
l-
Cr
oss-
T
i
e
d
(
T
C
T),
and
Bri
dge-L
in
k
(
B
L
)
c
o
n
f
igur
a
tio
ns
w
e
r
e
anal
yze
d
.
M
a
t
l
a
b/
Si
mu
lin
k
i
s
u
se
d
a
s
a
s
i
m
ul
a
t
i
on
to
ol
s
to
c
o
n
st
ru
ct
a
l
l
P
V
a
rr
ay
c
on
f
i
g
u
ra
tio
ns
u
nder
di
ffere
n
t
sha
d
i
n
g
ca
se
s.
T
he
c
om
par
i
s
ons
o
f
t
h
e
per
f
orm
a
nc
es
o
f
p
hot
ov
o
l
t
a
i
c
a
rra
y
co
n
f
i
g
ura
t
i
on
i
n
t
er
ms
o
f
ou
t
put
pow
er
w
er
e
ma
de.
2.
RESEARCH
M
ETH
O
D
2.1.
St
r
u
ctu
red of th
e
ph
otovo
lta
i
c ar
ra
y
A
n
a
l
y
s
i
s
a
n
d
c
o
m
p
a
r
i
s
o
n
s
o
f
t
h
e
o
u
t
p
u
t
c
h
a
r
a
c
t
e
r
i
s
t
i
c
o
f
P
V
a
r
r
ay
w
i
t
h
S
,
S
P,
T
CT
a
nd
BL
con
f
ig
ura
tio
ns
w
e
r
e
m
a
de
i
n
this
s
t
u
d
y
.
The
arr
a
y
c
o
n
s
is
ts
o
f
3
6
ph
ot
o
v
o
l
tai
c
m
o
d
u
l
es
i
n
a
6
x
6
ar
ray
arr
a
ngem
e
nt
a
nd
a
P
V
m
od
ul
e
si
m
u
la
ti
on
m
odel.
F
ig
ur
e
1
sh
ow
s
t
h
e
bloc
k
dia
g
ram
s
o
f
t
h
e
ph
o
t
o
v
o
l
t
a
i
c
modu
le
s
imu
l
a
t
i
o
n
m
o
del.
T
he
m
ax
imum
p
o
w
er
p
o
i
n
t
,
P
ma
x
,
open-c
i
r
c
u
it
v
o
l
t
a
ge,V
OC
,
short-circuit
c
u
rrent
I
SC
,
vol
ta
ge
a
t
t
h
e
m
a
xim
u
m
poi
n
t
,
V
mp
a
nd
c
u
rre
nt
a
t
t
h
e
m
a
xim
u
m
poi
n
t
,
I
mp
.
A
ll
of
t
he
p
ara
m
e
t
ers
me
ntio
ne
d a
b
o
v
e
ar
e give
n
un
der
S
t
anda
rd T
e
s
t
Con
d
i
t
i
on
s (
S
TC)
i
n
t
h
e
ma
n
uf
act
u
r
er’s d
at
ash
e
e
t
.
The
v
a
r
i
a
n
t
is
j
u
s
t
i
fie
d
b
y
a
p
pl
y
i
n
g
p
ar
am
eters
of
S
unP
ow
e
r
S
P
R
-X
20-2
50-
BLK
so
la
r
pa
ne
l
fr
om
data
shee
t. P
a
r
am
eters
of solar
PV
m
odu
l
e
a
re
s
how
n
i
n
Tab
le
I
.
F
i
g
u
re
1
. P
V
M
odul
e
s
i
mu
l
a
t
i
o
n
mo
d
e
l
i
n
M
at
l
a
b/
Si
mu
lin
k
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Dev
e
l
op
me
nt
o
f
PV a
rra
y
c
onf
i
g
u
r
a
t
i
o
n
unde
r d
i
f
f
erent
pa
rt
i
a
l
sha
d
in
g
…
(Mo
h
a
mma
d
Sy
a
h
i
r
Bin
Ish
a
k
)
1
265
Ta
b
l
e 1.
The
PV
Mod
u
le
pa
r
am
eter
V
a
ri
a
b
le
s
Pa
r
a
m
e
t
e
r
V
alue
Pm
a
x
Ma
xi
m
u
m
powe
r
250
W
Im
pp
M
a
x
i
m
u
m
powe
r
point
c
urre
nt
5
.
84
A
Vm
pp
Ma
xi
m
u
m
powe
r
point
volt
a
ge
42.
8
V
I
s
c
Short
c
i
r
c
uit c
u
rrent
50.
9
V
Voc
O
p
e
n
c
ir
c
u
it
vol
t
a
ge
50.
9
V
K
p
T
em
p
e
r
a
ture
c
o
e
ffic
i
e
n
t of P
m
p
p
-0
.30% / °C
Kv
T
e
m
p
e
r
a
tu
re
c
o
e
ff
ic
i
e
n
t
o
f
Vo
c
-
1
25
.6
mV /
°
C
K
i
T
em
p
e
r
a
ture
c
o
e
ff
ic
i
e
nt
of
Isc
3.5 m
A
/
°
C
N
s
N
u
m
be
r of
s
e
r
ie
s
c
e
l
l
72
2.2.
I-V
and
P-V
c
h
arac
ter
i
stic
s
of p
h
o
t
ovolt
a
i
c
arr
ay u
n
d
e
r
i
d
en
tic
al i
llu
m
i
n
a
t
i
on
Th
e
e
ffi
ci
en
cy
a
n
d
ma
xi
mu
m
o
u
tp
ut
p
o
w
e
r
o
f
PV
m
o
d
u
l
e
c
an
b
e
aff
e
c
t
e
d
by
t
h
e
c
h
a
ngi
ng
o
f
so
l
a
r
irra
d
i
a
n
ce
va
lu
e
and
tem
p
er
a
t
ure.
T
he
t
e
m
pe
rature
t
h
a
t
rec
e
ive
d
b
y
t
h
e
solar
pa
ne
l
is
i
n
v
erse
ly
p
r
o
por
t
i
o
n
al
to
t
he
g
e
n
era
t
ed
o
u
t
p
u
t
p
ow
er
.
For
sola
r
i
rradia
n
ce,
it
h
a
s
a
l
m
os
t
li
ne
a
r
e
ffec
t
on
c
u
rrent
a
nd
p
o
w
e
r
a
nd
marginal
e
f
f
ect
o
n
vo
ltage.
The
C
u
r
r
ent-Voltage
(I-V)
and
P
o
wer
-V
olt
a
ge
(
P
-
V)
c
ha
rac
t
e
r
istic
s
of
P
V
m
odu
le
r
un
ni
n
g
a
t
sam
e
t
em
per
a
t
u
re
o
f
25
°
C
a
n
d
d
i
f
fere
n
t
of
i
rra
diance
v
a
l
ue
a
r
e
g
i
v
e
n
i
n
F
i
g
u
r
e
2
and
F
i
g
u
re
3
.
F
i
gure
2.
I-V
C
hara
cteris
t
i
cs
of
si
m
u
la
te
d
arr
a
y w
ith di
f
fer
e
nt
i
rra
di
an
ce
v
a
l
u
e
F
i
gure
3.
P
-
V
C
hara
cter
i
s
t
i
cs
of simula
te
d
arr
a
y w
i
th di
f
fer
e
nt
irradi
a
n
ce
value
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
126
3
– 1
269
1
266
2.3.
PV
a
rray
con
f
ig
u
r
at
ion
P
V
M
od
ul
e
is
d
e
v
e
l
ope
d
by
j
o
in
in
g
se
ve
ral
P
V
cell
in
to
o
ne
u
n
i
t
.
N
o
rm
all
y
,
a
P
V
m
odu
l
e
c
ons
is
t
s
of
36
c
e
l
l
s
t
hat
con
n
ec
te
d
in
s
e
r
ies
co
nfig
ura
t
i
o
n,
how
e
v
e
r
o
t
h
e
r
c
o
nnec
t
i
on
a
r
e
als
o
f
ea
sible.
F
ig
ure
4
show
s
the
c
o
nnec
tio
n
of
t
he
P
V
M
o
du
le
i
n
S
e
ries,
S
e
rie
s
-
P
arallel,
T
ot
a
l
-cr
o
ss-
tie
d
an
d
Bri
d
ge
-l
i
n
k
w
i
t
h
3
6
P
V
c
e
lls
use
d
in
the
simula
t
i
o
n
.
F
i
gure
4.
S
c
h
em
atic d
ia
gram
of 3
6
P
V a
rra
y
s
(
6
x 6)
i
n
d
i
ffer
e
n
t c
o
n
f
igur
a
tio
n
2.4.
Mod
e
ll
i
n
g of
p
ar
tia
l
s
h
a
d
i
n
g
e
ffec
t
s
Thi
s
s
t
u
dy
f
o
c
used
t
o
i
n
v
e
st
ig
at
e
an
d
i
d
en
tif
y
t
h
e
p
erf
o
rman
c
e
s
o
f
d
i
ss
i
m
il
a
r
it
y
o
f
a
r
r
a
y
con
f
ig
ura
tio
n
un
der
se
vera
l
s
h
ad
i
ng
c
o
nd
i
tion
or
s
c
e
nari
o.
T
her
e
are
6
d
i
ffere
n
t
s
h
ad
i
n
g
pat
t
erns
w
hic
h
t
h
e
y
are
r
e
pre
s
e
n
t
e
d
a
s
t
he
p
a
ssa
ge
o
f
a
c
l
ou
d
over
the
P
V
a
rra
y.
T
h
e
r
e
are
3
dif
f
e
re
nt
i
rra
d
i
a
n
c
e
v
a
l
u
e
in
e
ach
pat
t
ern
w
h
ic
h
are
1000
W/m2,
50
0
W/m2,
and
20
0
W/m
2
t
o
repre
s
en
t
t
h
e
fu
l
l
y
ill
um
ina
t
i
on
c
o
n
d
i
t
i
o
n
,
hal
f
clea
r c
l
o
u
d
an
d
most dim
ness
of
c
l
o
ud foc
u
s.
The
shad
i
n
g
s
ce
nar
i
o
can
b
e de
scri
bed
ac
c
o
rdi
ng t
o
:
First
S
h
ad
in
g S
c
e
n
ario
:
The
val
u
e of s
ola
r
i
rr
adianc
e tha
t
s
et
f
o
r
4 mod
u
l
es t
ha
t loca
te
d at le
f
t
b
o
t
t
o
m of
the
a
rra
y
a
r
e
200
W/m
2
w
h
i
l
e
12
m
o
d
u
le
s
tha
t
i
rr
ad
iate
d
w
i
t
h
5
0
0
W/m
2
a
n
d
r
em
aini
ng
20
mod
u
l
es
fu
l
l
y re
cei
ved
l
i
g
h
t
w
it
h 10
0
0
W
/m2.
S
e
cond
S
ha
d
i
n
g
S
ce
nari
o:
T
h
e
v
a
l
ue
o
f
s
o
l
a
r
irra
di
a
n
ce
t
h
a
t
se
t
f
o
r
t
w
o
r
o
w
a
t
t
h
e
b
o
t
t
o
m
o
f
t
h
e
a
r
r
a
y
are
20
0 W/m2.
Th
is
h
a
s
c
ove
r
e
d 12
m
o
d
u
l
e
s
w
hi
le tw
o
row
s at
t
he
mid
d
l
e of
t
he ar
r
ay are
p
a
r
t
l
y s
h
a
d
e
d
w
ith
5
0
0
W/m
2 a
nd re
ma
i
n
in
g tw
o
row
s
a
t
the to
p o
f
the
a
rr
ay a
r
e
f
u
lly irradi
a
t
e
d
with 1000 W
/
m
2.
Thi
r
d
Sh
adi
ng
Sc
en
a
r
i
o
:
Th
e
v
a
lu
e
o
f
s
ol
a
r
i
rrad
i
an
c
e
t
h
a
t
s
et
for
tw
o
c
o
l
u
m
n
s
a
t
t
h
e
r
ig
ht
s
ide
of
t
h
e
arr
a
y
is
2
0
0
W
/m
2.
T
hi
s
h
a
s
c
o
vere
d
12
m
odu
l
e
s
w
h
i
l
e
tw
o
c
o
lumn
s
at
t
he
m
id
dle
of
t
he
a
r
r
ay
a
re
part
ly
s
h
a
de
d w
i
t
h
50
0
W/m2 a
nd
rem
ain
i
n
g
tw
o
c
o
l
um
ns
a
t t
h
e l
e
ft
s
i
d
e
o
f
the
ar
r
ay ar
e
f
ull
y
ir
r
adia
t
e
d
w
ith
1
0
0
0
W/
m
2.
F
ourt
h
S
had
i
n
g
S
ce
nari
o:
T
h
e
v
al
ue
o
f
s
o
l
a
r
irra
di
a
n
ce
t
h
at
s
e
t
f
or
t
w
o
r
ow
s
at
t
he
t
op
o
f
t
he
a
r
r
ay
a
r
e
20
0
W/m
2
.
T
h
is
h
a
s
c
o
v
er
ed
12
mo
du
les
w
h
i
l
e
tw
o
row
s
a
t
the
m
i
d
d
l
e
of
t
he
a
rra
y
a
r
e
pa
rtl
y
s
hade
d
w
ith
5
0
0
W/m
2 a
nd re
ma
i
n
in
g tw
o
row
s
a
t
the bo
t
t
om
o
f
th
e
array
a
r
e
f
u
l
ly
i
r
r
a
d
i
a
t
e
d
w
i
th
1
000
W
/
m
2
.
F
i
ft
h
S
h
a
d
i
n
g
S
c
enar
i
o
:
T
h
e
val
u
e
of
s
o
l
a
r
i
rra
di
a
n
ce
t
h
a
t
s
e
t
f
o
r
4
mo
du
l
e
s
at
t
h
e
m
idd
l
e
of
t
h
e
a
rra
y
a
r
e
2
0
0
W/
m2
w
h
i
l
e
1
2
modul
es
a
re
p
art
l
y
s
h
a
d
e
d
wi
th
5
00
W
/
m
2
a
n
d
r
e
m
a
i
ni
n
g
20
mo
du
les
rec
e
i
v
e
d
lig
ht w
ith 1
0
0
0
W/m2.
S
i
xt
h
S
h
a
d
ing
S
cena
r
io
:
The
val
u
e
o
f
s
ola
r
i
rra
di
a
n
ce
tha
t
s
e
t
f
o
r
4
m
odu
l
e
s
at
t
he
m
idd
l
e
o
f
t
h
e
a
r
r
ay
a
r
e
1
000
W
/
m
2
whil
e
1
2
m
od
ul
e
s
a
re
p
a
r
t
l
y
sh
ade
d
w
i
t
h
5
00
W/
m
2
a
n
d
re
ma
i
n
i
n
g 20
modu
les
rec
e
i
v
ed
lig
ht w
ith 2
0
0
W
/m2.
3.
RESULT
S
A
N
D
ANALY
S
IS
The
s
i
mu
lat
i
o
n
a
r
e
exe
c
u
t
e
d
by
u
s
i
ng
M
atla
b
/
S
i
m
u
l
i
n
k
so
ftw
a
re.
Al
l
th
e
co
nfi
g
u
r
at
ion
s
n
a
m
e
l
y
Se
ries,
S
e
rie
s
-Par
allel,
T
o
t
al-
C
ross-T
i
ed,
a
n
d
Bri
d
ge-
L
ink
ar
e
com
p
ar
ed
i
n
ter
m
o
f
t
h
eir
disa
pea
r
anc
e
o
u
t
put
pow
er
u
n
d
er
p
art
i
al
s
ha
d
i
n
g
c
o
n
d
it
io
n
(
P
S
C
).
T
he
c
o
m
pariso
n
i
s
an
al
y
zed
b
y
ba
se
d
o
n
t
h
e
di
ff
ere
n
t
irra
d
i
a
n
ce
va
lu
e
and
sh
ad
i
ng
sc
enar
io.
F
i
gur
e
5
show
s
P
o
w
e
r-V
ol
tage
c
ha
r
acter
i
s
t
i
cs
o
f
t
h
e
m
e
nt
io
ne
d
arr
a
y
con
f
ig
ura
tio
n u
nde
r 6
part
ia
l sha
d
ing
sc
e
n
ar
ios.
(a)
S
eri
e
s
(b)Series-Paral
l
e
l
(
c) Tota
l
-C
ross
-
T
i
e
d
(d)B
ri
dge-Link
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
De
v
e
l
o
p
m
e
n
t
of
PV
a
r
r
a
y co
nf
igu
r
a
t
io
n
under
d
i
f
f
e
r
e
n
t
pa
rt
ial
sha
d
i
n
g
…
(Mo
h
a
m
m
a
d
Sy
a
h
i
r
Bin
I
s
h
a
k)
1
267
B
a
se
d
o
n
T
a
b
le
2
,
t
h
e
m
a
xi
mum
out
pu
t
p
o
w
e
r
in
t
he
case
shad
i
ng
sce
n
a
r
i
o
1
,
5,
a
nd
6
for
TC
T
i
s
hi
g
h
er
c
om
par
e
d
w
i
t
h
t
he
o
t
h
er
t
hr
ee
o
f
P
V
a
rr
ay
c
onf
i
gur
at
io
n
.
M
ea
n
w
hi
l
e
,
ba
sed
o
n
T
ab
le
I
V
,
V
a
nd
V
I
show
t
he
m
ax
i
m
um
outp
u
t
p
o
w
e
r
i
n
t
h
e
c
a
s
e
sha
d
i
n
g
2,
3
,
and
4
f
or
T
CT,
B
L
a
n
d
S
P
pr
oduce
d
t
h
e
s
am
e
m
a
xim
u
m
ou
t
p
ut
pow
er
i
f
c
o
m
p
ar
ed
w
i
t
h
S
c
o
n
f
ig
ur
at
io
n
t
h
at
p
r
o
d
u
c
ed
l
ea
st
ou
t
pu
t
powe
r
.
Tab
l
e
2.
M
a
x
im
um
outp
u
t
p
o
w
er
f
or
s
hadin
g
s
ce
nar
i
o
1-
6
C
onf
igu
r
a
t
ion
Sc
e
n
ar
i
o
1
S
en
a
r
i
o
4
Pm
a
x
(
W)
N
u
m
be
r
of
p
ea
ks
P
m
a
x
(
W
)
Nu
m
b
e
r
o
f
pea
k
s
Se
r
i
e
s
480,
53
1,
3
3
0
3
2355,
2
038,
3
3
0
3
Se
ri
e
s
-
P
a
r
a
l
l
e
l
2957,
4
407,
5193
3
2877,
3
183,
1
983
3
T
o
ta
l-
C
r
oss-
T
i
e
d
2878,
4
202,
5470
3
2877,
3
183,
1
983
3
B
r
idge
-
L
ink
2900,
4
302,
5310
3
2877,
3
183,
1
983
3
C
onf
igu
r
a
t
ion
Sc
e
n
ar
i
o
2
S
cen
a
r
io
5
Pm
a
x
(
W)
N
u
m
be
r
of
p
ea
ks
P
m
a
x
(
W
)
Nu
m
b
e
r
o
f
pea
k
s
Se
r
i
e
s
480,
53
0,
3
3
0
3
1500
1
Se
ri
e
s
-
P
a
r
a
l
l
e
l
2877,
3
183,
1983
3
2957,
4
407,
5
193
3
T
o
ta
l-
C
r
oss-
T
i
e
d
2877,
3
183,
1983
3
2878,
4
202,
5
470
3
B
r
idge
-
L
ink
2877,
3
183,
1983
3
2878,
4
267,
5
382
3
C
onf
igu
r
a
t
ion
Sc
e
n
ar
i
o
3
S
cen
a
r
i
o
6
Pm
a
x
(
W)
N
u
m
be
r
of
p
ea
ks
P
m
a
x
(
W
)
Nu
m
b
e
r
o
f
pea
k
s
Se
r
i
e
s
1500
1
1155,
1
343,
2
8
6
3
Se
ri
e
s
-
P
a
r
a
l
l
e
l
5036
1
1685,
2
441,
1
817
3
T
o
ta
l-
C
r
oss-
T
i
e
d
5036
1
1610,
2
477,
1
946
3
B
r
idge
-
L
ink
5036
1
1635,
2
436,
1
937
3
F
i
gur
e
5.
P
-
V
c
har
a
cter
is
t
i
c
s
o
f
4
d
i
f
f
e
r
e
nt
p
ho
tov
o
lta
ic
a
r
r
a
y
c
on
f
i
gur
at
i
ons
i
n
6
di
ff
er
e
n
t
scena
r
i
o
S
cen
ario
1
S
cenario
4
S
cen
ario
2
S
cenario
5
S
cen
ario
3
S
cenario
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
126
3
– 1
269
1
268
F
r
om
t
he
r
esul
t,
it
sh
ow
s
the
To
t
a
l-
Cr
oss-
Tie
d
s
e
t
tin
g
has
show
n
t
h
e
gre
a
tes
t
p
erf
o
rmance
i
n
e
v
e
r
y
part
ial
s
h
a
d
i
n
g
sce
n
ari
o
a
n
d
i
t
c
a
n
be
c
o
n
s
i
d
e
re
d
tha
t
e
ve
n
th
o
ug
h
its
p
a
tte
rn
i
s
c
o
mp
le
x
,
it
i
s
b
e
n
e
f
icia
l
w
i
t
h
t
h
e
p
r
e
s
en
ce
o
f e
x
t
r
a-c
o
mp
li
c
a
t
e
d
sh
adin
g
sce
n
ario
i
n
ac
tu
al
su
rr
oun
di
n
g
s or
p
rac
t
i
c
a
l
sta
te.
4.
CONCL
U
S
ION
I
n
t
he
s
tu
d
y
,
a
simu
la
ti
on
te
chn
i
que
i
s
u
s
ed
f
or
a
na
l
y
z
i
n
g
P
V
m
odu
le
s
w
i
t
h
f
o
u
r
di
ffe
re
nt
o
f
ph
o
t
o
v
o
l
t
a
i
c
a
rra
y
conf
igur
a
tio
n
w
h
i
c
h
ar
e
S
e
rie
s
,
S
e
ri
es-
P
ar
al
l
e
l
,
T
o
t
a
l
-C
ro
ss-Ti
e
d
a
nd
B
ri
dg
e-Li
nk
c
o
nfi
g
u
r
at
i
o
n
s
r
e
s
p
e
c
t
iv
e
l
y
by
u
sin
g
M
a
t
l
a
b
/
S
i
m
ul
in
k
so
ft
wa
re
.
The
a
s
se
ssm
e
n
t
o
f
fo
ur
c
on
nec
t
ion
con
f
ig
ura
tio
ns ha
s
b
ee
n
d
one
thr
ou
g
h
u
s
i
n
g
36 P
V
modu
le
s and ev
a
l
uat
i
n
g
i
n
te
rms of the
ir
m
axim
um ou
t
pu
t
pow
er
f
or
f
o
u
r
con
f
ig
ura
tio
n
schem
e
s.
T
he
e
ffec
t
o
f
p
ar
tia
l
s
h
a
d
i
ng
to
t
h
e
P
V
m
odu
les
on
t
h
e
S
e
rie
s
,
S
e
r
i
es-
P
a
rallel,
T
o
t
a
l
-Cross-Tie
d
a
nd
Bri
d
ge-
L
in
k
co
n
f
i
g
ura
tio
ns
a
l
s
o
ha
ve
b
ee
n
i
nve
st
i
g
a
t
ed
unde
r
6
d
i
ffe
r
en
t
sha
d
i
n
g
sc
e
n
ar
i
o
s.
R
ef
err
i
n
g
t
o
these
results,
T
otal-Cr
o
ss-Tied
c
on
fi
g
u
ra
t
i
o
n
t
he
h
ighe
st
m
ax
im
um
o
u
t
p
u
t
pow
er
e
ven
t
h
o
u
g
h
un
de
r
part
ial
s
h
ad
i
n
g
c
o
nd
iti
o
n
s
c
o
mpa
r
ed
t
o
ot
her
c
o
n
f
i
g
ur
atio
ns.
A
s
a
r
esul
t,
P
V
a
rra
y
confi
gura
t
i
o
n
str
o
n
g
l
y
a
ffe
c
t
i
n
g
th
e
e
f
fic
i
e
n
c
y
o
f
P
V
a
r
r
a
y.
T
he
r
esul
t
tha
t
o
ffer
or
p
rov
i
de
i
s
ver
y
bene
f
i
cia
l
a
nd
trus
tw
ort
h
y
de
ta
ils
o
n
t
h
e
per
f
orm
a
nc
es
o
f
a
rra
y
c
onf
i
g
ur
at
ion
i
n
d
iffere
n
t
s
ha
di
n
g
s
i
t
u
at
ion
or
scena
r
i
o
.
A
ll
the
inf
o
rm
atio
n
c
a
n
be
u
se
d
t
o
e
n
h
a
n
c
e
w
h
o
le
e
ffi
ci
e
n
cy
o
f
t
h
e
ph
ot
o
vol
t
a
i
c
s
y
s
t
e
m
du
ri
n
g
des
i
g
n
t
he
s
ys
t
e
m
.
ACKNOW
LEDG
E
MEN
T
S
The
a
u
thor
s
w
o
u
l
d
l
i
ke
t
o
ackn
o
w
l
e
dge
t
he
I
n
s
t
i
t
ute
of
R
esea
rch
M
an
ag
e
m
e
n
t
an
d
Inn
o
v
a
t
i
o
n
(IRMI),
U
i
T
M
S
h
ah
A
lam
,
S
elangor,
M
alay
si
a
fo
r
t
h
e
fi
n
a
n
c
i
a
l
su
pp
ort
o
f
t
hi
s
re
se
a
r
c
h
.
Th
i
s
r
es
earch
i
s
sup
por
t
e
d
b
y
R
esea
rch
Man
a
gem
e
nt
a
n
d
I
nno
va
ti
on
(I
RMI)
,
U
i
TM
w
i
t
h
p
r
o
j
e
c
t
c
o
d
e
:
6
0
0
-
I
R
M
I
/
M
Y
R
A
5/
3/
BES
T
A
R
I
(02
7
/
201
7)
.
REFE
RENCES
[1]
L.
F
.
L.
V
i
l
l
a
,
D.
P
icaul
t
,
B.
R
aiso
n,
S
.
Bacha,
a
nd
A
.
L
a
bo
nne
,
“Ma
x
im
iz
in
g
th
e
po
we
r
ou
tp
u
t
o
f
pa
rt
ia
l
l
y
sh
a
d
e
d
ph
ot
ovo
lt
aic
p
l
a
n
ts
t
h
r
ou
gh
optim
izati
o
n
of
t
h
e
i
n
t
erco
nnect
io
n
s am
ong
i
ts
m
od
ule
s
,
”
IE
EE
J.
P
hotovo
l
t
a
i
c
s
,
vol
.
2,
no
.
2
,
pp
.
1
5
4
–163,
2
0
1
2
.
[2]
H.
S
.
S
a
hu
an
d
S.
K
.
N
ayak
,
“
P
ower enh
anc
e
m
e
nt
of
partiall
y sh
a
d
e
d
PV
array
by
u
s
i
n
g
a
nov
el
a
ppro
ach f
o
r
sh
a
de
di
sper
sion,”
20
1
4
IEEE Inn
o
v.
S
m
art Grid T
echn
o
l
.
- Asi
a
, IS
G
T
ASIA 2
01
4, p
p
.
4
9
8
–
5
0
3
,
2
01
4.
[3]
As
if,
M
u
h
a
m
m
a
d,
a
nd
T
ariq
M
uneer.
"Energ
y
su
pp
ly
,
its
dem
a
nd
a
n
d
s
e
cu
rit
y
i
s
s
u
e
s
f
o
r
dev
e
lo
pe
d
an
d
em
e
r
g
i
n
g
econ
o
m
i
es
."
Renewabl
e
an
d
Susta
in
ab
le E
n
erg
y
Revi
ews
, vo
l
. 11
,
n
o. 7
,
p
p
. 13
8
8
-
1
41
3, 2
00
7.
[4]
W
a
n
g
,
Y
-
J.,
and
P
-
C.
H
s
u
.
"
A
nal
y
tical
m
o
d
elli
ng
of
p
arti
a
l
s
had
in
g
a
n
d
d
i
ffe
r
e
n
t
o
r
ie
nta
t
ion
of
p
ho
to
v
o
l
t
a
i
c
mo
du
le
s
.
"
IET Renewabl
e Pow
e
r Generati
on
,
vo
l.
4
,
no.
3
,
2
7
2
-282,
2
0
1
0
.
[5]
M
ä
ki
,
An
s
s
i,
a
n
d
S
epp
o
V
alk
ealah
ti.
"P
ower
l
osses
i
n
l
on
g
strin
g
and
p
a
rallel
-
con
n
ected
s
hort
s
t
ri
ngs
o
f
seri
es-
connected
s
ilicon-based
p
hotovolt
a
i
c
modules
due
t
o
partial
sha
di
ng
c
on
diti
on
s."
IE
EE Tr
ans
ac
t
i
o
n
s
on
E
n
er
gy
Conversi
on,
vo
l.
2
7, pp
.
1
, 17
3
-1
83
, 20
1
2
.
[6]
Ish
a
qu
e
,
K
ashif
,
a
nd
Zai
n
al
S
alam.
"A
r
evi
e
w
o
f
m
ax
im
u
m
p
o
w
er
p
o
i
nt
t
racki
n
g
tech
ni
qu
es
o
f
P
V
s
y
s
te
m
f
o
r
uni
f
or
m
ins
o
lation
and
pa
r
tia
l
shading
condi
t
ion
.
"
Ren
e
w
abl
e a
n
d
S
u
s
t
ain
abl
e
Ener
gy
Revi
ews,
vo
l.
19,
p
p
.4
75
-48
8
, 2
01
3.
[7]
M
a
,
T
a
o
,
H
o
n
g
x
i
n
g
Y
a
n
g
,
a
n
d
L
i
n
L
u
.
"
D
e
v
e
l
o
p
m
e
n
t
o
f
a
m
o
d
e
l
t
o
s
i
m
u
l
a
te
t
h
e
p
erf
o
rm
an
ce
c
haracteri
s
t
i
cs
o
f
crys
talline sili
con phot
ovolt
a
ic
modules/st
r
ings/ar
r
ays
.
"
So
la
r E
n
e
r
gy
, vo
l
.
10
0
, p
p
. 31
-
41
G
,
2
01
4
.
[8]
Y.-J.
W
a
ng
and
P
.
-C.
Hs
u
,
“
A
n
al
ytical
m
odelli
n
g
o
f
p
arti
al
s
had
ing
and
different
o
ri
e
n
tatio
n
o
f
p
h
o
t
ovolt
a
ic
mo
du
le
s
,
”
IET
Ren
e
wabl
e Po
wer G
e
ner
a
tion
,
vo
l. 4
, n
o.
3,
p
. 2
72
,
2
0
1
0
.
[9]
S
.
B
an
a
and
R. P.
S
a
ini,
“
Ex
perim
e
n
t
al
i
n
v
esti
gati
on
o
n
p
o
w
e
r
o
utpu
t
o
f
d
if
fe
re
nt
p
h
o
tov
o
ltaic
a
r
r
ay
c
onf
i
gurati
o
n
s
un
der u
n
if
orm and
p
a
rt
ia
l
sh
ad
i
n
g
scen
arios
,
”
En
e
r
gy
,
v
ol.
1
2
7
,
p
p
.
4
38–
45
3,
2017.
[10]
K.
Ş
.
Parl
ak,
“
P
V
array
re
co
nf
igurat
io
n
me
t
h
o
d
u
n
d
er
p
arti
al
s
h
a
d
ing
conditions,”
In
t. J.
Elec
t
r
. Power Energy
Sys
t
.
,
vol.
63,
pp.
7
13–
72
1,
2
0
14.
[11]
M
o
h
a
mm
ad
nej
a
d,
S
hah
r
am,
Ali
K
h
al
a
f
i,
a
nd
S
.
M
o
rteza
Ah
mad
i
.
"M
a
th
em
at
ical
a
n
a
ly
si
s
of
t
o
t
a
l
-cross
-tied
ph
ot
ovo
lt
aic
arra
y
u
n
d
e
r
part
ial
s
h
adi
n
g
co
nd
i
t
ion
an
d
its
c
om
p
aris
on
w
ith
oth
e
r
con
f
ig
ura
t
ions.
"
So
lar
E
n
er
gy,
vo
l.
133
,
5
0
1
-
511,
2
01
6.
[12]
M
a
gh
ami
,
M
oham
m
ad
R
ez
a,
e
t
al.
"P
ow
er
l
o
s
s
du
e
to
s
oiling
on
s
o
la
r
pa
n
e
l:
A
r
e
v
i
e
w
,
"
Re
ne
wa
ble
a
n
d
Su
st
a
i
n
a
b
l
e E
n
e
r
gy
R
eviews,
vol.
59
,
pp
.
1
3
0
7
-1
3
1
6
,
2
016
.
[13]
M
.
G
.
Vil
l
al
va
,
J.
R
.
G
azol
i
,
and
E.
R
up
pert
F
il
ho,
“
M
o
deli
ng
a
n
d
c
i
r
cui
t
-bas
ed
s
im
ula
t
io
n
o
f
p
hoto
v
o
lta
i
c
a
rray
s
,
”
20
09
Br
a
z
ili
a
n
Po
wer E
l
ectro
n. Co
nf
.
COB
E
P
2009
,
p
p
.
1
24
4–1
2
5
4,
200
9.
[14]
S
i
l
v
est
r
e,
S
an
ti
a
g
o
,
A
lf
red
o
B
oron
at,
and
A.
C
h
o
uder.
"
S
t
u
dy
o
f
b
y
p
ass
d
i
odes
co
nfi
g
u
r
a
tio
n
o
n
P
V
m
o
du
l
e
s.
"
Applied Energy
,
v
o
l
.
8
6
,
n
o
.
9
,
1632
-16
4
0
,
2
0
0
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Dev
e
l
op
me
nt
o
f
PV a
rra
y
c
onf
i
g
u
r
a
t
i
o
n
unde
r d
i
f
f
erent
pa
rt
i
a
l
sha
d
in
g
…
(Mo
h
a
mma
d
Sy
a
h
i
r
Bin
Ish
a
k
)
1
269
[15]
T
e
y
,
K
o
k
S
o
o
n
,
a
n
d
S
a
a
d
M
e
k
h
i
l
e
f
.
"
M
o
d
i
f
i
e
d
i
n
c
r
e
m
e
n
t
a
l
c
o
n
d
u
c
t
ance
al
gori
t
hm
f
or
p
h
o
t
o
v
o
ltaic
s
ystem
un
de
r
part
ial
shadi
ng
conditions
a
nd
l
oad
vari
at
ion,
"
I
E
E
E
Tr
an
sa
c
tion
s
o
n
I
n
du
st
ri
al E
l
e
c
t
ro
n
i
c
s
.
v
o
l
.
61
,
n
o
.
1
0,
pp
.
5
384
-53
9
2
, 2
014
.
[16]
W
a
ng
,
Jen-Cheng,
e
t
al.
"
A
n
ov
el
m
u
ltipo
i
nt
d
i
r
ect-est
i
m
ation
m
e
t
ho
d
fo
r
the
m
a
x
i
mu
m
p
o
we
r
po
in
t
tra
c
k
in
g
o
f
ph
ot
ovo
lt
aic
mod
u
l
e
s
und
er
p
arti
all
y
s
h
a
ded
i
r
rad
i
atio
n
con
d
iti
on
s."
E
n
erg
y
Co
nf
eren
ce a
nd Exh
i
b
i
tion
(E
N
E
R
G
Y
C
ON
)
, 2012 I
EEE Interna
t
ional. I
EEE,
2012.
[17]
Belh
achat,
F.,
and
C.
L
a
r
b
e
s.
"
M
odel
i
n
g
,
anal
y
s
is
a
n
d
c
o
m
pariso
n
of
s
o
l
ar
p
hoto
vol
ta
i
c
a
rray
co
nfig
urat
ions
u
n
d
er
part
ial shading
c
o
nditions
.
"
Sol
a
r
En
erg
y
,
v
ol.
120,
pp.
3
9
9
-4
18,
20
1
5
.
[18]
P
a
rlak
,
K
o
ray
Şen
e
r.
"
P
V
a
rray
recon
f
igu
r
ati
o
n
m
e
t
hod
u
nd
er
p
ar
ti
a
l
s
h
a
din
g
c
ondi
ti
ons.
"
In
ter
nati
onal Jou
r
n
a
l
o
f
El
ectr
i
cal Po
wer
&
Ener
gy
S
y
s
t
ems
, v
ol
.
6
3
, 7
13
-
7
2
1
, 2
01
4.
[19]
Se
y
e
dm
a
h
mo
ud
i
a
n,
M
oh
a
m
ma
d
m
e
h
di,
e
t
a
l.
"
Si
mula
tio
n
a
n
d
h
a
r
dwa
r
e
i
m
p
lem
e
n
t
ation
of
n
ew
m
axim
u
m
power
po
in
t
track
in
g
tech
ni
qu
e
f
o
r
pa
rti
a
ll
y
s
h
aded
P
V
sy
s
t
em
u
sing
h
y
b
ri
d
DEP
S
O
m
e
th
od.
"
IEEE tran
sa
c
tio
ns
o
n
su
st
a
i
n
able en
erg
y
,
v
o
l
.
6
,
no.
3
,
85
0-8
62,
2
0
1
5
.
[20]
Dad
j
é,
A
b
dou
ram
a
ni
,
e
t
a
l
.
"
Maxi
m
u
m
pow
er
p
oi
nt
t
rack
in
g
m
e
tho
d
s
f
o
r
p
h
o
t
ov
oltai
c
s
y
s
t
e
m
s
o
p
e
ratin
g
under
part
ially
s
haded
or
r
api
d
l
y
v
aria
ble
insola
t
i
on
c
onditions
:
a
r
evi
e
w
paper.
"
In
te
rn
atio
na
l J
o
ur
na
l of
S
u
s
ta
ina
b
l
e
En
gi
neeri
ng,
vo
l
. 9
, n
o.
4,
p
p
.
22
4-2
3
9
, 20
1
6
.
[21]
La
M
an
na,
Dami
ano,
e
t
al.
"Re
c
o
n
fi
gu
rab
l
e
electri
cal
i
ntercon
n
e
c
t
i
o
n
s
t
rategies
f
or
p
h
o
t
o
v
o
ltaic
a
rrays:
A
revi
ew.
"
Ren
e
wabl
e an
d Sus
tain
abl
e
E
n
e
r
g
y
Revi
ews,
v
o
l
. 33
,
p
p
. 4
12
-42
6
, 2
01
4.
[22]
Ka
ra
te
p
e
,
En
gi
n,
M
u
t
lu
B
oz
te
pe
,
a
n
d
M
e
tin
C
ola
k
.
"
D
e
v
e
l
o
p
me
n
t
o
f
a
sui
t
able
m
o
d
el
f
or
c
haract
eri
z
in
g
ph
ot
ovo
lt
aic
array
s
w
it
h
s
h
ad
e
d
s
olar
c
e
l
ls
.
"
So
lar E
n
er
gy,
v
ol.
8
1
,
no.
8
,
97
7-99
2
,
20
0
7
.
[23]
G.
V
elas
co-Q
u
e
s
a
d
a
,
F
.
G
ui
n
j
oan
-
G
i
s
p
ert
,
R
.
Pi
qu
é-L
ó
p
ez,
M
.
Rom
án-Lu
m
breras,
and
A.
C
o
n
es
a-Roca,
“
E
l
ectrical
P
V
array
re
con
f
ig
ura
t
i
o
n
st
rateg
y
f
o
r
e
nerg
y
ex
trac
t
i
on
i
mp
rov
e
m
e
nt
i
n
gri
d
-con
nect
ed
P
V
sy
st
e
m
s,
”
IEEE
Trans. Ind
.
Elect
ron
.
,
vol.
56
,
n
o
.
1
1,
pp.
4
3
1
9
–
4
331
,
2
00
9.
[24]
M
.
T
ahm
a
sbi-F
a
rd,
M
.
T
araf
dar-Hag
h
,
S
.
P
ou
rpay
am,
and
A
.
H
ag
hra
h
,
“
A
Vo
ltag
e
E
qual
i
zer
C
i
r
cui
t
t
o
Red
u
ce
P
a
rti
a
l
S
h
a
d
in
g
Eff
ect i
n
P
h
o
t
ovol
ta
ic
S
trin
g
,
”
I
E
E
E
J. Photovoltaics
, p
p.
1–
8
, 2
01
8.
[25]
H.
e
t
Al
.
,
“
B
i
na
ry
S
earc
h
A
lgorit
h
m
a
s
Ma
ximu
m
P
o
w
e
r
P
o
in
t
Tr
a
c
ki
ng
f
or
P
h
o
tov
o
ltai
c
S
ystem
U
n
d
e
r
P
a
rti
a
l
S
h
ad
ed Co
ndi
ti
o
n
.”
Evaluation Warning : The document was created with Spire.PDF for Python.