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19
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R
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2
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a
s t
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s,
b
u
il
d
in
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lo
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s.
A s
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m
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p
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s
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d
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p
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u
p
p
li
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b
y
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so
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m
b
a
se
d
o
n
P
V
p
a
n
e
ls.
T
h
e
p
u
rp
o
se
o
f
th
is
st
u
d
y
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t
o
m
o
d
e
l
a
n
d
sim
u
late
p
h
o
t
o
v
o
lt
a
ic
m
o
d
u
les
b
a
se
d
o
n
a
n
id
e
a
l
si
n
g
le
a
n
d
d
o
u
b
le
d
io
d
e
.
Afte
r
th
a
t,
we
will
sim
u
late
fiv
e
c
o
n
fig
u
ra
ti
o
n
s
f
o
rm
e
d
b
y
n
in
e
p
h
o
to
v
o
lt
a
ic
so
lar
p
a
n
e
ls
:
se
ries
(S
),
p
a
ra
ll
e
l
(P
),
se
ries
-
p
a
ra
ll
e
l
(S
P
),
b
rid
g
e
-
l
in
k
(BL),
a
n
d
to
tal
-
c
ro
ss
-
ti
e
d
(
TCT
)
u
n
d
e
r
u
n
ifo
rm
a
n
d
n
o
n
-
u
n
if
o
rm
c
a
se
s
(c
e
n
ter,
d
iag
o
n
a
l,
a
n
d
fra
m
e
).
T
h
e
se
fiv
e
P
V
so
lar
c
o
n
fi
g
u
ra
ti
o
n
s
a
re
c
o
m
p
a
re
d
in
term
s
o
f
s
h
o
rt
c
ircu
it
c
u
rre
n
ts
(
IS
C),
o
p
e
n
c
ircu
i
t
v
o
l
tag
e
s
(V
OC),
p
e
a
k
p
o
we
rs
(P
M
P
),
th
e
v
o
lt
a
g
e
a
n
d
c
u
rre
n
t
v
a
lu
e
s
c
o
rre
sp
o
n
d
i
n
g
to
m
a
x
imu
m
p
o
we
r
(VM
P
,
IM
P
)
,
m
ism
a
tch
p
o
we
r
lo
ss
(
M
P
L),
fil
l
fa
c
to
r
(F
F
),
e
fficie
n
c
y
ra
ti
o
(ER)
,
a
n
d
o
v
e
ra
ll
m
a
x
imu
m
p
o
we
r
(OMP
).
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e
six
P
V
c
o
n
fi
g
u
ra
ti
o
n
s
a
re
sim
u
late
d
,
c
o
n
si
d
e
rin
g
t
h
e
p
a
r
a
m
e
ters
o
f
th
e
S
TM
6
-
4
0
/3
6
P
V m
o
d
u
le.
K
ey
w
o
r
d
s
:
Do
u
b
le
d
io
d
es
E
f
f
icien
cy
r
atio
Fil
l f
ac
to
r
I
d
ea
l d
io
d
e
Mism
atch
p
o
wer
lo
s
s
Par
tial sh
ad
in
g
Sin
g
le
d
io
d
e
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mo
h
cin
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Ab
o
u
y
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k
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u
b
L
ab
o
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ato
r
y
o
f
E
n
g
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n
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in
g
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Sy
s
tem
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d
Ap
p
licatio
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s
,
Sid
i M
o
h
am
ed
B
en
Ab
d
ellah
Un
iv
er
s
ity
Fez,
Mo
r
o
cc
o
E
m
ail:
m
o
h
cin
e.
a
b
o
u
y
aa
k
o
u
b
@
u
s
m
b
a.
ac
.
m
a
1.
I
NT
RO
D
UCT
I
O
N
So
lar
en
er
g
y
is
am
o
n
g
th
e
m
o
s
t
wid
ely
u
s
ed
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
in
th
e
wo
r
ld
an
d
p
ar
ticu
lar
ly
in
Mo
r
o
cc
o
.
Utilizin
g
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
s
u
c
h
as
s
o
lar
an
d
win
d
p
o
wer
,
wh
ic
h
p
r
im
ar
ily
f
o
cu
s
o
n
d
ec
r
ea
s
in
g
g
r
ee
n
h
o
u
s
e
g
as
em
is
s
io
n
s
,
is
cr
u
cial
f
o
r
m
o
v
in
g
to
war
d
s
s
u
s
tain
ab
le
en
er
g
y
s
o
lu
tio
n
s
[
1
]
.
On
e
o
f
th
e
ad
v
an
tag
es
o
f
PV
s
y
s
tem
s
is
th
at
th
ey
r
eq
u
ir
e
m
in
im
al
m
ain
ten
an
ce
f
o
r
p
r
o
d
u
cin
g
elec
tr
ical
en
er
g
y
[
2
]
.
T
h
e
s
o
lar
p
h
o
t
o
v
o
ltaic
s
y
s
tem
s
ar
e
s
en
s
itiv
e
to
m
an
y
f
ac
to
r
s
,
in
clu
d
in
g
s
o
lar
ir
r
ad
ian
c
e,
tem
p
er
atu
r
e,
a
n
d
ag
in
g
[
3
]
,
[
4
]
.
L
o
o
k
in
g
to
war
d
s
,
th
e
r
esear
ch
[
5
]
an
aly
ze
s
t
h
e
ef
f
ec
t
o
f
tem
p
er
atu
r
e
an
d
d
u
s
t
o
n
s
o
lar
e
n
er
g
y
p
r
o
d
u
ctio
n
in
Mo
r
o
cc
o
.
I
t a
ls
o
ev
alu
ates th
e
q
u
ality
o
f
g
r
o
u
n
d
wate
r
u
s
ed
f
o
r
m
ain
tain
in
g
p
h
o
to
v
o
ltaic
p
a
n
els.
T
h
e
f
in
d
i
n
g
s
r
ev
ea
l
a
2
0
%
r
e
d
u
ctio
n
in
en
er
g
y
p
r
o
d
u
ctio
n
at
4
5
°C
,
alth
o
u
g
h
th
e
wate
r
is
g
en
er
ally
s
u
itab
le
.
T
h
e
o
u
tp
u
t
o
f
p
h
o
to
v
o
ltaic
p
an
els
is
s
ig
n
if
ican
tly
af
f
ec
ted
b
y
d
u
s
t,
wh
ich
r
ed
u
ce
s
ef
f
icien
cy
an
d
p
o
we
r
g
en
er
atio
n
as
its
ac
cu
m
u
latio
n
in
cr
ea
s
es.
T
h
e
s
tu
d
y
[
6
]
an
al
y
ze
s
th
e
im
p
ac
t
o
f
d
u
s
t
o
n
PV
p
an
el
p
e
r
f
o
r
m
an
ce
an
d
p
r
o
p
o
s
es
an
ef
f
ec
tiv
e
c
lean
in
g
s
y
s
tem
th
at
n
o
t
o
n
l
y
r
em
o
v
es
d
u
s
t
b
u
t
also
h
e
lp
s
m
ain
tain
lo
wer
tem
p
er
atu
r
es o
n
th
e
p
an
els.
C
lo
u
d
s
,
tr
ee
s
,
p
o
les,
b
u
ild
i
n
g
s
,
a
n
d
o
th
er
o
b
jects c
an
s
h
ad
e
s
o
m
e
ce
lls
o
r
m
o
d
u
les
in
a
PV a
r
r
ay
d
u
r
in
g
p
ar
tial sh
ad
in
g
co
n
d
itio
n
s
[
7
]
.
Du
e
to
th
e
s
h
ad
in
g
ef
f
ec
t,
t
h
e
ef
f
icien
cy
o
f
p
h
o
to
v
o
ltaic
s
y
s
tem
s
d
ec
r
ea
s
es
;
s
ev
er
al
s
o
lu
t
io
n
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
o
v
er
co
m
e
th
is
p
r
o
b
lem
,
s
u
ch
as
th
e
to
p
o
lo
g
y
o
f
th
e
p
h
o
to
v
o
ltaic
n
etw
o
r
k
an
d
m
ax
im
u
m
p
o
wer
p
o
in
t te
ch
n
i
q
u
es (
MPPT)
[
8
]
-
[
1
0
]
.
T
h
e
PV sy
s
tem
ar
ch
itectu
r
e
is
o
n
e
o
f
th
e
m
o
s
t e
f
f
ec
tiv
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s
o
lu
tio
n
s
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
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8
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9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
19
49
-
1
9
6
1
1950
s
ig
n
if
ican
tly
r
ed
u
ce
p
o
wer
l
o
s
s
es
d
u
e
to
th
e
s
h
ad
in
g
e
f
f
ec
t
[
1
1
]
-
[
1
4
]
.
J
h
a
[
1
5
]
d
is
cu
s
s
es
a
g
en
er
alize
d
m
o
d
elin
g
o
f
p
h
o
t
o
v
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ltaic
m
o
d
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les
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d
ar
r
ay
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n
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ig
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s
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n
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s
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m
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f
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r
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d
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im
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late
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m
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with
MA
T
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.
I
n
th
e
liter
atu
r
e
[
1
6
]
,
th
e
f
o
cu
s
is
o
n
m
o
d
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g
a
n
d
ass
es
s
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f
o
r
m
an
ce
o
f
d
if
f
er
en
t
p
h
o
to
v
o
ltaic
(
PV)
ar
r
ay
co
n
f
ig
u
r
atio
n
s
u
n
d
e
r
v
ar
i
o
u
s
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
(
PS
C
)
to
im
p
r
o
v
e
ef
f
icien
cy
an
d
r
e
d
u
ce
m
is
m
atch
lo
s
s
es.
T
h
e
s
tu
d
y
ex
am
in
es
co
n
f
ig
u
r
atio
n
s
s
u
ch
as
s
er
ies
(
S)
,
p
ar
allel
(
P)
,
s
er
ies
-
p
ar
allel
(
SP)
,
to
tal
-
cr
o
s
s
-
tied
(
T
C
T)
,
b
r
id
g
e
-
lin
k
ed
(
B
L
)
,
an
d
h
o
n
e
y
-
co
m
b
(
HC
)
u
s
in
g
a
6
×
4
PV
ar
r
ay
a
n
d
th
e
b
is
h
o
p
m
o
d
el
f
o
r
d
etai
led
s
im
u
latio
n
.
T
h
e
f
in
d
in
g
s
d
em
o
n
s
tr
ate
th
at
th
e
T
C
T
co
n
f
ig
u
r
atio
n
ty
p
ically
y
ield
s
th
e
b
est
p
er
f
o
r
m
a
n
ce
a
cr
o
s
s
m
o
s
t
s
h
ad
in
g
s
ce
n
ar
i
o
s
,
p
r
o
v
id
in
g
v
al
u
ab
le
g
u
id
an
ce
f
o
r
s
elec
tin
g
o
p
tim
al
PV
ar
r
ay
s
etu
p
s
.
Kar
ee
m
et
a
l.
[
1
7
]
a
d
d
r
ess
th
e
ch
all
en
g
e
o
f
im
p
r
o
v
i
n
g
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
ef
f
icien
cy
b
y
in
tr
o
d
u
cin
g
a
m
o
d
if
ied
s
er
ies
-
p
ar
allel
(
MSP)
co
n
f
ig
u
r
atio
n
an
d
co
m
p
ar
in
g
it
with
f
o
u
r
o
th
er
s
etu
p
s
:
SP
,
T
C
T
,
B
L
,
an
d
HC
.
Usi
n
g
a
3
×3
s
o
lar
ar
r
ay
,
t
h
e
s
tu
d
y
s
im
u
lates
v
ar
io
u
s
p
ar
tial
s
h
ad
i
n
g
co
n
d
itio
n
s
in
MA
T
L
AB
/Si
m
u
lin
k
.
T
h
e
r
esu
lts
in
d
icate
th
at
MSP
p
er
f
o
r
m
s
b
est
u
n
d
er
b
o
th
e
v
en
an
d
u
n
ev
en
r
o
w
s
h
a
d
in
g
,
wh
ile
T
C
T
e
x
ce
ls
in
v
er
t
ical
u
n
ev
e
n
s
h
a
d
in
g
,
an
d
b
o
th
T
C
T
an
d
MSP
ar
e
ef
f
ec
tiv
e
f
o
r
d
iag
o
n
al
s
h
ad
in
g
.
Pen
d
em
an
d
Mik
k
ili
[
1
8
]
ta
ck
le
th
e
is
s
u
e
o
f
en
h
an
cin
g
en
er
g
y
ef
f
icien
cy
in
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
im
p
ac
ted
b
y
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
(
PS
C
)
,
wh
ich
r
esu
lt
in
p
o
wer
m
is
m
atch
es
b
etwe
en
m
o
d
u
les.
T
h
ey
m
o
d
e
l
an
d
s
im
u
late
th
e
p
er
f
o
r
m
an
c
e
o
f
s
ev
er
al
5
×5
PV
ar
r
ay
co
n
f
ig
u
r
atio
n
s
,
S,
SP
,
B
L
,
an
d
HC
,
ac
r
o
s
s
v
a
r
io
u
s
s
h
ad
in
g
s
ce
n
ar
io
s
.
T
h
e
e
v
alu
atio
n
in
clu
d
es
k
ey
p
er
f
o
r
m
an
ce
m
etr
ics
s
u
ch
as
g
lo
b
al
m
ax
im
u
m
p
o
wer
p
o
in
t
(
GM
PP
)
,
m
is
m
atch
lo
s
s
es,
an
d
e
f
f
icien
cy
,
u
s
in
g
KYOCERA
-
KC
2
0
0
GT
PV
m
o
d
u
les
in
MA
T
L
AB
/Si
m
u
lin
k
.
Usi
n
g
a
3
×
3
PV
ar
r
a
y
b
a
s
ed
o
n
a
s
in
g
le
d
io
d
e,
th
e
au
th
o
r
s
an
aly
ze
d
th
e
p
er
f
o
r
m
an
ce
o
f
S,
P,
SP
,
T
C
T
,
an
d
B
L
co
n
f
ig
u
r
atio
n
s
in
s
h
ad
in
g
s
itu
atio
n
s
.
T
h
e
b
e
s
t
p
er
f
o
r
m
an
ce
was
ac
h
iev
ed
with
th
e
T
C
T
co
n
f
ig
u
r
atio
n
[
1
9
]
.
Desp
ite
p
r
ev
io
u
s
s
tu
d
ies,
th
ey
d
id
n
o
t
co
m
p
ar
e
th
e
s
h
a
d
in
g
ef
f
ec
t
o
n
t
h
r
ee
ty
p
es
o
f
p
h
o
to
v
o
ltaic
ce
ll
m
o
d
elin
g
:
m
o
d
elin
g
b
ased
o
n
an
id
ea
l
d
io
d
e,
m
o
d
elin
g
b
ased
o
n
a
s
in
g
le
d
io
d
e
,
an
d
m
o
d
elin
g
b
ased
o
n
two
d
io
d
es.
T
h
is
co
m
p
ar
ativ
e
an
aly
s
is
is
ess
en
tial
as
ea
ch
m
o
d
el
b
eh
av
es
d
if
f
er
e
n
tly
u
n
d
er
v
a
r
y
in
g
s
h
ad
in
g
co
n
d
itio
n
s
.
Un
d
e
r
s
tan
d
in
g
t
h
ese
d
if
f
er
en
ce
s
ca
n
lead
t
o
b
etter
o
p
tim
izatio
n
o
f
p
h
o
to
v
o
ltaic
s
y
s
tem
s
,
en
h
an
cin
g
th
eir
o
v
er
all
ef
f
ici
en
cy
an
d
p
e
r
f
o
r
m
an
ce
.
B
y
ev
alu
atin
g
th
e
s
h
ad
in
g
im
p
ac
t
a
cr
o
s
s
th
ese
m
o
d
els,
we
ca
n
id
en
tif
y
th
e
m
o
s
t
ef
f
ec
tiv
e
ap
p
r
o
ac
h
f
o
r
r
ea
l
-
wo
r
l
d
ap
p
licatio
n
s
.
I
n
th
is
p
a
p
er
,
we
in
v
esti
g
ate
th
e
ef
f
ec
t o
f
s
h
ad
in
g
o
n
PV c
ells
u
s
in
g
th
r
ee
d
if
f
e
r
en
t m
o
d
els:
th
e
f
ir
s
t b
ased
o
n
a
lo
s
s
less
id
ea
l d
io
d
e,
th
e
s
ec
o
n
d
b
ased
o
n
a
s
in
g
le
d
io
d
e
with
r
esis
to
r
s
,
an
d
th
e
th
ir
d
b
ased
o
n
two
d
io
d
es with
r
esis
to
r
s
.
2.
M
E
T
H
O
D
T
h
is
s
ec
tio
n
d
escr
ib
es
th
e
m
et
h
o
d
u
s
ed
to
ev
alu
ate
th
e
e
f
f
ec
t
o
f
s
h
a
d
in
g
o
n
s
o
lar
p
a
n
els.
T
h
is
s
tu
d
y
ass
es
s
es
th
e
im
p
ac
t
o
f
s
h
ad
in
g
b
y
m
o
d
elin
g
a
3
×
3
p
h
o
to
v
o
ltaic
ar
r
ay
b
ased
o
n
t
h
r
ee
ty
p
es
o
f
p
h
o
to
v
o
ltaic
ce
lls
:
an
id
ea
l
s
in
g
le
d
io
d
e,
a
s
in
g
le
d
io
d
e
with
r
esis
to
r
s
,
an
d
d
o
u
b
le
d
io
d
es.
Fig
u
r
e
1
illu
s
tr
ates
th
e
s
im
u
latio
n
m
o
d
el
o
f
th
e
3
x
3
p
h
o
to
v
o
ltaic
ar
r
ay
i
n
MA
T
L
AB
/Si
m
u
lin
k
.
Simu
latio
n
s
ar
e
co
n
d
u
cted
u
n
d
er
u
n
if
o
r
m
is
o
latio
n
an
d
th
r
ee
s
h
ad
in
g
s
ce
n
ar
io
s
(
ce
n
ter
,
d
ia
g
o
n
al,
an
d
f
r
am
e)
t
o
an
aly
ze
th
ei
r
ef
f
ec
ts
.
Fig
u
r
e
1
.
PV a
r
r
a
y
3
×
3
s
im
u
latio
n
in
MA
T
L
AB
/Si
m
u
lin
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
va
lu
a
tin
g
s
h
a
d
in
g
effec
ts
o
n
p
h
o
to
v
o
lta
ic
mo
d
u
les:
Ma
th
e
ma
tica
l
…
(
Mo
h
cin
e
A
b
o
u
y
a
a
ko
u
b
)
1951
Fiv
e
p
an
el
co
n
f
ig
u
r
atio
n
s
,
S,
P,
SP
,
T
C
T
,
an
d
B
L
,
ar
e
ex
a
m
in
ed
to
d
eter
m
in
e
wh
ich
p
er
f
o
r
m
s
b
est
u
n
d
er
s
h
a
d
in
g
.
Key
m
etr
ics,
i
n
clu
d
in
g
s
h
o
r
t
-
cir
c
u
it
cu
r
r
e
n
t
(
I
SC
)
,
o
p
en
-
cir
cu
it
v
o
ltag
e
(
VOC),
p
ea
k
p
o
wer
(
PMP)
,
m
is
m
atch
p
o
wer
lo
s
s
(
MPL
)
,
f
ill
f
ac
to
r
(
FF
)
,
ef
f
i
cien
cy
r
atio
(
E
R
)
,
an
d
o
v
er
al
l
m
ax
im
u
m
p
o
wer
(
OM
P),
ar
e
an
aly
ze
d
u
s
in
g
th
e
STM
6
-
4
0
/3
6
m
o
d
u
le.
T
h
e
f
in
d
in
g
s
p
r
o
v
id
e
v
alu
ab
le
in
s
i
g
h
ts
f
o
r
im
p
r
o
v
in
g
s
o
lar
en
er
g
y
p
r
o
d
u
ctio
n
an
d
o
p
tim
izin
g
s
y
s
tem
d
esig
n
.
T
h
e
p
h
o
to
v
o
ltaic
m
o
d
u
le
p
ar
a
m
eter
s
u
s
ed
in
th
is
ar
ticle
ar
e
b
ased
o
n
th
e
wo
r
k
c
ited
in
[
2
0
]
.
T
ab
le
1
p
r
o
v
id
es
all
th
e
n
ec
ess
ar
y
p
ar
am
eter
s
o
f
STM
6
-
4
0
/3
6
.
T
ab
le
1
.
STM
6
-
4
0
PV m
o
d
u
le
s
p
ec
if
icatio
n
P
a
r
a
me
t
e
r
s
I
d
e
a
l
s
i
n
g
l
e
d
i
o
d
e
S
i
n
g
l
e
d
i
o
d
e
D
o
u
b
l
e
d
i
o
d
e
V
o
l
t
a
g
e
a
t
ma
x
i
m
u
m
p
o
w
e
r
(
V
mp
)
1
8
V
1
8
V
1
8
V
C
u
r
r
e
n
t
a
t
ma
x
i
mu
m
p
o
w
e
r
(
I
mp
)
2
.
2
3
A
2
.
2
3
A
2
.
2
3
A
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
(
V
oc
)
2
1
.
6
V
2
1
.
6
V
2
1
.
6
V
R
a
t
e
d
p
o
w
e
r
(
W
)
4
0
W
4
0
W
4
0
W
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
(
I
sc
)
2
.
3
6
A
2
.
3
6
A
2
.
3
6
A
To
t
a
l
n
u
m
b
e
r
o
f
c
e
l
l
s
i
n
seri
e
s (N
S
)
36
36
36
To
t
a
l
n
u
m
b
e
r
o
f
c
e
l
l
s
i
n
p
a
r
a
l
l
e
l
(
N
P
)
1
1
1
I
d
e
a
l
i
t
y
f
a
c
t
o
r
o
f
t
h
e
d
i
o
d
e
(
n
)
1
.
5
3
2
8
1
.
5
3
2
8
n
1
=
1
.
5
8
1
8
n
2
=
1
.
5
4
4
5
S
h
u
n
t
r
e
si
st
a
n
c
e
(
R
sh
)
-
1
5
.
8
5
5
Ω
5
9
7
.
2
9
Ω
S
e
r
i
e
s r
e
si
s
t
a
n
c
e
(
R
s)
-
2
.
9
3
0
9
mΩ
1
1
.
0
1
mΩ
3.
M
AT
H
E
M
AT
I
CA
L
E
Q
U
I
V
AL
E
NT
M
O
DE
L
I
NG
O
F
P
V
M
O
DUL
E
T
h
e
liter
atu
r
e
s
u
g
g
ests
s
ev
er
al
eq
u
iv
alen
t
m
o
d
els
f
o
r
PV
ce
lls
[
2
1
]
,
[
2
2
]
.
I
n
th
is
wo
r
k
,
we
h
av
e
s
tu
d
ied
th
r
ee
eq
u
i
v
alen
t
m
o
d
els:
th
e
id
ea
l
d
i
o
d
e
(
I
D)
,
th
e
s
in
g
le
d
io
d
e
(
SD)
,
an
d
th
e
d
o
u
b
le
d
io
d
e
(
DD)
m
o
d
el.
Fig
u
r
e
2
s
h
o
ws
th
e
th
r
ee
m
o
d
els
s
tu
d
ied
in
th
is
p
ap
er
:
th
e
id
ea
l
d
i
o
d
e
m
o
d
el
Fig
u
r
e
2
(
a
)
,
th
e
s
in
g
le
-
d
io
d
e
m
o
d
el
Fig
u
r
e
2
(
b
)
,
an
d
t
h
e
d
o
u
b
le
-
d
io
d
e
m
o
d
el
Fig
u
r
e
2
(
c)
.
3
.
1
.
I
dea
l
-
dio
de
P
V
mo
du
le
I
n
o
r
d
er
to
s
tu
d
y
th
e
elec
tr
ical
b
eh
av
io
r
o
f
a
p
h
o
t
o
v
o
ltaic
c
ell
in
th
e
f
ac
e
o
f
n
u
m
er
o
u
s
p
h
en
o
m
e
n
a
s
u
ch
as
s
h
ad
in
g
,
th
e
ce
ll
ca
n
b
e
m
o
d
elled
b
y
a
s
im
p
lifie
d
m
o
d
el
b
ased
o
n
a
s
in
g
le
p
h
o
t
o
g
en
er
ated
cu
r
r
e
n
t
I
ph_Cell
an
d
o
n
e
d
io
d
e
.
T
h
e
eq
u
iv
alen
t
m
o
d
el
o
f
t
h
is
ce
ll
is
p
r
esen
ted
in
Fig
u
r
e
2
(
a)
.
T
h
e
cu
r
r
en
t
p
r
o
d
u
ce
d
b
y
a
PV c
ell
I
ph_Cell
is
as (
1
)
.
ℎ
_
=
0
[
−
(
−
)
]
(
1
)
T
h
e
o
u
tp
u
t
cu
r
r
en
t o
f
th
e
PV
c
ell
is
as (
2
)
.
_
=
ℎ
_
−
0
[
(
_
.
.
)
−
1
]
(
2
)
PV c
ell
s
atu
r
atio
n
cu
r
r
en
t is d
escr
ib
ed
b
y
(
3
)
.
0
=
(
(
.
.
.
)
−
1
)
.
[
]
3
(
−
0
(
1
−
1
)
)
(
3
)
T
h
e
PV
m
o
d
u
le
eq
u
iv
ale
n
t
cir
cu
it
b
ased
o
n
an
id
ea
l
d
io
d
e
c
ell
is
s
h
o
wn
in
Fig
u
r
e
3
(
a)
.
T
h
e
cu
r
r
e
n
t
o
u
t
p
u
t
o
f
th
is
PV is as (
4
)
.
=
.
ℎ
_
−
.
0
[
(
.
.
.
.
)
−
1
]
(
4
)
W
h
e
r
e
:
I
p
h
_
Ce
l
l
:
p
h
o
t
o
g
e
n
e
r
at
e
d
c
u
r
r
e
n
t
o
f
PV
c
el
l
,
I
sh
:
c
u
r
r
e
n
t
t
h
r
o
u
g
h
p
a
r
a
l
l
e
l r
e
s
i
s
t
o
r
,
R
sh
:
p
a
r
a
l
l
e
l
r
e
s
is
t
o
r
,
R
s
:
s
e
r
i
es
r
es
is
t
o
r
,
V
PV
_
C
el
l
:
o
u
t
p
u
t
v
o
l
t
a
g
e
o
f
PV
c
el
l
,
I
P
V
_
Ce
l
l
:
o
u
tp
u
t
c
u
r
r
e
n
t
o
f
PV
c
el
l
,
I
sc
:
s
h
o
r
t
c
i
r
c
u
it
c
u
r
r
e
n
t
,
I
r
:
s
o
l
a
r
i
r
r
a
d
i
a
ti
o
n
o
f
PV
c
el
l
,
I
r0
:
r
e
f
e
r
e
n
c
e
s
o
l
a
r
i
r
r
a
d
i
a
ti
o
n
(
I
r0
=
1000
W
/
m
2
),
I
rs
:
r
e
v
e
r
s
e
s
a
t
u
r
a
t
i
o
n
c
u
r
r
e
n
t
o
f
d
i
o
d
e
,
I
0
:
s
a
t
u
r
a
t
i
o
n
c
u
r
r
e
n
t
o
f
P
V
c
e
l
l
,
K
i
:
c
o
e
f
f
i
c
i
e
n
t
o
f
c
e
ll
c
u
r
r
e
n
t
(
K
i
=
0
.
0
0
2
)
,
T:
P
V
c
e
l
l
t
e
m
p
e
r
a
t
u
r
e
,
T
r
:
P
V
c
e
ll
r
e
f
e
r
e
n
c
e
t
e
m
p
e
r
a
t
u
r
e
(
T
r
=
2
9
8
K
)
,
n
:
q
u
a
l
i
t
y
f
a
c
t
o
r
t
h
e
d
i
o
d
e
,
E
g0
:
g
a
p
e
n
e
r
g
y
(
E
g0
=
1
.
1
e
V
)
,
k
:
c
o
n
s
t
a
n
t
o
f
B
o
l
t
z
m
a
n
n
(
k
=
1
.
3
8
0
5
×
1
0
−
2
3
J
/K
)
,
N
s
:
n
u
m
b
e
r
o
f
c
e
l
l
s
i
n
s
e
r
i
e
s
,
N
p
:
n
u
m
b
e
r
o
f
c
e
l
ls
i
n
p
a
r
a
l
le
l
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
19
49
-
1
9
6
1
1952
3
.
2
.
Sin
g
le
dio
de
P
V
m
o
du
le
PV c
ells
wi
th
a
s
in
g
le
d
io
d
e
e
q
u
iv
alen
t m
o
d
el
h
av
e
a
cu
r
r
e
n
t so
u
r
ce
I
ph_Cell
,
an
an
tip
ar
allel
d
io
d
e
(
D)
,
s
er
ies
r
esis
tan
ce
(
R
s
)
,
an
d
a
p
ar
allel
s
h
u
n
t
r
esis
tan
ce
(
R
sh
)
.
Fig
u
r
e
2
(
b
)
illu
s
tr
ates
th
is
eq
u
iv
alen
t
m
o
d
el
o
f
a
PV c
ell.
P
V
m
o
d
u
le
eq
u
iv
alen
t c
ir
cu
it sh
o
wn
in
Fig
u
r
e
3
(
b
)
.
T
h
e
cu
r
r
en
t o
u
tp
u
t o
f
th
e
PV m
o
d
u
le
in
th
is
ca
s
e
is
as (
5
)
.
=
.
ℎ
_
−
ℎ
−
.
0
[
(
(
.
.
+
.
)
.
.
.
.
)
−
1
]
(
5
)
T
h
e
s
h
u
n
t r
esis
to
r
cu
r
r
en
t
I
sh
i
s
d
ef
in
ed
b
y
(
6
)
.
ℎ
=
.
_
+
_
ℎ
(
6
)
Par
tial
s
h
ad
in
g
ca
u
s
es
r
ev
er
s
e
b
ias
in
s
h
ad
e
d
m
o
d
u
les,
in
c
r
ea
s
in
g
h
ea
t
an
d
r
is
k
in
g
d
a
m
a
g
e
[
2
3
]
.
T
o
a
d
d
r
ess
th
is
ch
allen
g
e,
we
will
u
s
e
an
ti
-
r
etu
r
n
s
em
ico
n
d
u
cto
r
d
io
d
es
with
an
ti
-
p
ar
allel
d
io
d
e
p
r
o
tectio
n
f
o
r
ea
ch
m
o
d
u
le.
MA
T
L
AB
/Si
m
u
lin
k
m
o
d
el
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
el
is
p
r
esen
ted
in
Fig
u
r
e
4
,
wh
ich
is
b
ased
o
n
o
n
e
d
io
d
e
ce
ll
.
3
.
3
.
Do
ub
le
dio
des
P
V
m
o
d
ule
T
h
e
d
o
u
b
le
d
io
d
e
m
o
d
el
p
r
o
v
i
d
es
a
m
o
r
e
p
r
ec
is
e
an
d
d
etailed
r
ep
r
esen
tatio
n
o
f
th
e
b
e
h
av
i
o
r
o
f
s
o
lar
ce
lls
co
m
p
ar
ed
t
o
th
e
s
in
g
le
d
io
d
e
m
o
d
el.
Fig
u
r
e
2
(
c
)
s
h
o
w
s
th
e
eq
u
iv
ale
n
t
cir
cu
it
r
e
p
r
es
en
tatio
n
o
f
th
is
PV
ce
ll.
I
n
th
e
ca
s
e
o
f
an
eq
u
iv
ale
n
t m
o
d
el
with
two
d
io
d
es,
th
e
cu
r
r
en
t su
p
p
lied
b
y
th
e
PV m
o
d
u
le
is
as (
7
)
.
=
.
ℎ
−
ℎ
−
.
01
[
(
(
.
.
+
.
)
.
.
1
.
.
)
−
1
]
−
.
02
[
(
(
.
.
+
.
)
.
.
2
.
.
)
−
1
]
(
7
)
T
h
e
ex
p
r
ess
io
n
o
f
th
e
two
s
atu
r
atio
n
cu
r
r
en
ts
I
01
an
d
I
02
is
ex
p
r
ess
ed
as (
8
)
.
01
=
1
[
]
3
[
0
1
(
1
−
1
)
]
,
02
=
2
[
]
3
[
0
2
(
1
−
1
)
]
(
8
)
(
a)
(
b
)
(
c)
Fig
u
r
e
2
.
E
q
u
iv
alen
t c
ir
c
u
it
:
(
a)
id
ea
l
d
io
d
e
m
o
d
el,
(
b
)
s
in
g
l
e
d
io
d
e
m
o
d
el,
a
n
d
(
c
)
d
o
u
b
le
d
io
d
e
m
o
d
el
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
va
lu
a
tin
g
s
h
a
d
in
g
effec
ts
o
n
p
h
o
to
v
o
lta
ic
mo
d
u
les:
Ma
th
e
ma
tica
l
…
(
Mo
h
cin
e
A
b
o
u
y
a
a
ko
u
b
)
1953
(
a)
(
b
)
Fig
u
r
e
3
.
PV m
o
d
u
le
eq
u
iv
ale
n
t c
ir
cu
it b
ased
:
(
a)
o
n
a
n
id
ea
l d
io
d
e
ce
ll
an
d
(
b
)
o
n
a
s
in
g
le
d
io
d
e
ce
ll
(
a)
(
b
)
Fig
u
r
e
4
.
MA
T
L
AB
/Si
m
u
lin
k
m
o
d
el
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
el
:
(
a)
im
p
lem
en
tatio
n
o
f
t
h
e
p
h
o
to
v
o
ltaic
s
y
s
tem
as a
s
u
b
s
y
s
tem
in
clu
d
in
g
v
o
lta
g
e,
cu
r
r
en
t,
a
n
d
p
o
wer
m
ea
s
u
r
em
en
ts
u
s
in
g
MA
T
L
A
B
/Si
m
u
lin
k
;
an
d
(
b
)
d
etailed
v
iew
o
f
th
e
s
o
lar
p
an
el
m
o
d
el
b
ased
o
n
a
s
in
g
le
-
d
io
d
e
eq
u
iv
alen
t c
ir
c
u
it
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
19
49
-
1
9
6
1
1954
4.
M
O
DE
L
I
NG
AN
D
SI
M
U
L
AT
I
O
N
O
F
P
V
ARRA
Y
S
I
n
th
is
s
ec
tio
n
,
we
h
av
e
cr
ea
te
d
f
o
u
r
p
h
o
t
o
v
o
ltaic
ar
r
ay
c
o
n
f
ig
u
r
atio
n
s
in
MA
T
L
AB
/Si
m
u
lin
k
b
ased
o
n
an
id
ea
l
d
io
d
e
(
I
D)
,
s
in
g
le
d
io
d
e
(
SD)
,
an
d
d
o
u
b
le
d
i
o
d
e
(
DD)
PV
ce
ll.
T
h
ese
co
n
f
ig
u
r
atio
n
s
ar
e
s
u
b
jecte
d
to
f
o
u
r
ty
p
es
o
f
ir
r
ad
iatio
n
s
:
u
n
if
o
r
m
an
d
n
o
n
-
u
n
i
f
o
r
m
.
T
h
e
b
est
co
n
f
ig
u
r
atio
n
a
m
o
n
g
th
e
f
o
u
r
is
ch
o
s
en
b
y
co
m
p
ar
in
g
s
ev
er
al
cr
iter
ia.
4
.
1
.
P
V
a
rr
a
y
co
nfig
ura
t
io
n
3
×
3
I
n
th
e
p
r
esen
t
wo
r
k
,
f
if
teen
P
V
ar
r
ay
ty
p
es
ar
e
m
o
d
elled
a
n
d
s
tu
d
ied
in
MA
T
L
AB
/
S
im
u
lin
k
;
ea
ch
ar
r
ay
co
n
s
is
ts
o
f
n
in
e
p
h
o
to
v
o
ltaic
p
an
els
.
T
h
r
ee
elec
tr
ical
p
an
el
m
o
d
els
ar
e
u
s
ed
:
I
D,
SD
,
an
d
DD.
Fo
u
r
PV
f
ield
co
n
f
ig
u
r
atio
n
s
ar
e
ev
al
u
ated
:
s
er
ies
f
ield
(
S),
p
ar
allel
f
ield
(
P),
s
er
ies
-
p
a
r
allel
f
iel
d
(
SP
)
,
b
r
id
g
e
-
lin
k
f
ield
(
B
L
)
,
an
d
to
tal
-
cr
o
s
s
-
tied
f
ield
(
T
C
T
)
.
-
Ser
ies
co
n
f
ig
u
r
atio
n
(
S):
T
h
e
o
u
tp
u
t
cu
r
r
en
t
o
f
th
e
p
h
o
to
v
o
ltaic
ar
r
ay
in
th
is
co
n
f
ig
u
r
atio
n
is
eq
u
al
to
th
e
cu
r
r
en
t
p
ass
in
g
th
r
o
u
g
h
ea
ch
PV
m
o
d
u
le
[
2
4
]
,
[
2
5
]
.
T
h
e
n
in
e
v
o
lts
f
r
o
m
ea
ch
m
o
d
u
le
ad
d
u
p
to
t
h
e
o
u
tp
u
t
v
o
ltag
e.
T
h
is
co
n
f
ig
u
r
a
tio
n
is
s
h
o
wn
in
Fig
u
r
e
5
(
a)
.
-
Par
allel
co
n
f
ig
u
r
atio
n
(
P):
Nin
e
PV
m
o
d
u
les
wo
u
ld
b
e
lin
k
ed
in
p
ar
allel
in
th
is
co
n
f
ig
u
r
atio
n
.
On
e
PV
m
o
d
u
le'
s
v
o
ltag
e
is
eq
u
al
to
t
h
e
o
u
tp
u
t
v
o
ltag
e,
an
d
th
e
to
t
al
o
f
th
e
n
in
e
cu
r
r
e
n
ts
p
ass
in
g
th
r
o
u
g
h
ea
c
h
m
o
d
u
le
is
eq
u
al
t
o
th
e
o
u
tp
u
t
cu
r
r
en
t [
2
6
]
.
I
n
Fig
u
r
e
5
(
b
)
,
t
h
is
co
n
f
ig
u
r
atio
n
is
d
is
p
lay
ed
.
-
Ser
ies
-
pa
r
allel
co
n
f
ig
u
r
atio
n
(
SP
)
:
T
h
e
to
tal
o
u
t
p
u
t
v
o
ltag
e
an
d
cu
r
r
en
t
o
f
a
PV
m
o
d
u
le
a
r
e
eq
u
al
t
o
th
e
s
u
m
o
f
th
e
v
o
ltag
e
a
n
d
cu
r
r
en
t
o
f
th
e
th
r
ee
m
o
d
u
les
[
2
4
]
,
[
2
5
]
.
T
h
is
PV a
r
r
ay
is
s
h
o
wn
i
n
Fig
u
r
e
5
(
c)
.
-
B
r
id
g
e
-
li
n
k
co
n
f
ig
u
r
atio
n
(
B
L
)
:
T
h
e
c
o
m
b
in
atio
n
o
f
f
o
u
r
m
o
d
u
les
in
a
r
ec
tifie
r
b
r
id
g
e
g
iv
es
th
is
co
n
f
ig
u
r
atio
n
[
2
4
]
,
[
2
5
]
.
T
h
is
co
n
f
ig
u
r
atio
n
is
g
iv
e
n
in
Fig
u
r
e
5
(
d
)
.
-
T
o
tal
-
cr
o
s
s
-
tied
co
n
f
ig
u
r
atio
n
(
T
C
T
)
:
T
h
e
co
n
n
ec
tio
n
s
ar
e
estab
lis
h
ed
b
etwe
en
all
n
in
e
PV
m
o
d
u
les
as
s
h
o
wn
in
Fig
u
r
e
5
(
e)
[
2
4
]
,
[
2
5
]
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
Fig
u
r
e
5
.
PV c
o
n
f
ig
u
r
atio
n
:
(
a
)
p
ar
allel,
(
b
)
s
er
ies,
(
c)
s
er
ies
-
p
ar
allel,
(
d
)
b
r
id
g
e
-
lin
k
,
a
n
d
(
e)
to
tal
-
cr
o
s
s
-
tied
4
.
2
.
Sh
a
din
g
m
o
del c
o
nfig
ura
t
io
ns
T
h
e
f
iv
e
PV c
o
n
f
ig
u
r
atio
n
s
(
S,
P,
SP
,
B
L
,
T
C
T
)
ar
e
b
ein
g
test
ed
an
d
s
im
u
lated
u
n
d
er
p
ar
ti
al
s
h
ad
in
g
ef
f
ec
t.
Fo
u
r
ca
s
es
will
b
e
s
im
u
lated
an
d
an
aly
ze
d
to
an
aly
z
e
th
e
s
h
ad
in
g
ef
f
ec
t.
T
h
e
f
o
ll
o
win
g
f
ig
u
r
e
s
h
o
ws
th
e
u
n
if
o
r
m
ca
s
e
an
d
th
r
ee
p
ar
tial sh
ad
in
g
s
ce
n
ar
io
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
va
lu
a
tin
g
s
h
a
d
in
g
effec
ts
o
n
p
h
o
to
v
o
lta
ic
mo
d
u
les:
Ma
th
e
ma
tica
l
…
(
Mo
h
cin
e
A
b
o
u
y
a
a
ko
u
b
)
1955
-
U
n
i
f
o
r
m
c
o
n
d
i
t
i
o
n
(
c
a
s
e
1
)
:
A
ll
m
o
d
u
l
e
s
h
a
v
e
a
n
i
n
s
o
l
a
ti
o
n
o
f
1
0
0
0
W
/
m
2
.
Fi
g
u
r
e
6
(
a
)
i
l
l
u
s
t
r
a
t
e
s
t
h
i
s
ca
s
e
.
-
C
en
ter
s
h
ad
in
g
co
n
d
itio
n
(
ca
s
e
2
)
: PV5
in
th
e
ce
n
ter
is
s
u
b
j
ec
ted
to
2
0
0
W
/m
2
.
T
h
er
e
is
also
an
is
o
latio
n
o
f
1
0
0
0
W
/m
2
o
n
t
h
e
o
th
e
r
m
o
d
u
les.
T
h
is
ca
s
e
is
s
h
o
wn
in
Fig
u
r
e
6
(
b
)
.
-
Diag
o
n
al
s
h
ad
in
g
co
n
d
itio
n
(
c
ase
3
)
:
A
PV1
m
o
d
u
le
h
as
an
in
s
o
latio
n
o
f
2
0
0
W
/m
2
,
a
PV
5
m
o
d
u
le
h
as
an
in
s
o
latio
n
o
f
4
0
0
W
/m
2
an
d
a
PV9
m
o
d
u
le
h
as a
n
in
s
o
latio
n
o
f
6
0
0
W
/m
2
.
A
1
0
0
0
W
/m
2
in
s
u
latio
n
is
p
r
o
v
id
e
d
b
y
th
e
o
t
h
er
m
o
d
u
les
.
Fig
u
r
e
6
(
c
)
d
e
p
icts
th
is
ca
s
e.
-
Fra
m
e
s
h
ad
in
g
co
n
d
itio
n
(
ca
s
e
4
)
:
PV1
,
PV4
an
d
PV9
r
ec
eiv
es
2
0
0
W
/m
2
o
f
s
o
lar
in
s
o
latio
n
,
PV6
r
ec
eiv
es
4
0
0
W
/m
2
,
PV2
an
d
PV8
r
ec
eiv
es
6
0
0
W
/m
2
,
a
PV
3
an
d
PV7
r
ec
eiv
es
8
0
0
W
/m
2
.
PV5
m
o
d
u
le
h
as so
lar
in
s
o
latio
n
o
f
1
0
0
0
W
/m
2
.
Fig
u
r
e
6
(
d
)
g
i
v
es th
is
ca
s
e.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
6
.
Sh
a
d
in
g
m
o
d
el
co
n
f
i
g
u
r
atio
n
s
:
(
a)
u
n
if
o
r
m
ca
s
e,
(
b
)
ce
n
ter
,
(
c
)
d
iag
o
n
al,
a
n
d
(
d
)
f
r
am
e
s
h
ad
in
g
ca
s
e
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
E
x
am
in
in
g
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
f
o
llo
win
g
PV
ar
r
ay
to
p
o
lo
g
ies:
S,
P,
S
P,
B
L
,
an
d
T
C
T
u
n
d
er
a
r
an
g
e
o
f
p
ar
tial
s
h
ad
in
g
s
ce
n
a
r
io
s
,
in
clu
d
in
g
f
r
am
e,
d
ia
g
o
n
a
l,
u
n
if
o
r
m
,
an
d
ce
n
te
r
s
h
ad
in
g
,
is
th
e
aim
o
f
th
is
s
ec
tio
n
.
T
o
d
o
t
h
is
,
we
will
u
s
e
MA
T
L
AB
/S
im
u
lin
k
to
s
im
u
late
th
e
f
iv
e
co
n
f
ig
u
r
atio
n
s
(
S,
P,
SP
,
B
L
,
an
d
T
C
T
)
an
d
ass
ess
th
e
im
p
ac
t
o
f
p
ar
tial
s
h
ad
e
in
f
o
u
r
s
h
ad
i
n
g
s
ce
n
ar
io
s
.
T
h
e
e
v
alu
atio
n
o
f
t
h
e
ef
f
e
ct
o
f
p
ar
tial
s
h
ad
in
g
(
f
o
u
r
ca
s
es)
o
n
p
h
o
t
o
v
o
ltaic
m
o
d
u
les
b
ased
o
n
a
n
id
ea
l
d
io
d
e
(
I
D)
,
s
in
g
le
d
io
d
e
(
SD)
an
d
d
o
u
b
le
d
io
d
es
(
DD)
is
co
n
d
u
cte
d
b
y
p
lo
ttin
g
th
e
cu
r
r
e
n
t
an
d
p
o
we
r
cu
r
v
es
s
im
u
lated
o
n
MA
T
L
AB
/Si
m
u
lin
k
,
an
d
co
n
tr
asti
n
g
th
e
v
alu
es
o
f
:
s
h
o
r
t
cir
cu
it
c
u
r
r
e
n
ts
(
I
SC
)
,
o
p
en
cir
cu
it
v
o
ltag
es
(
VOC),
p
ea
k
p
o
wer
s
(
PMP)
,
m
is
m
atch
p
o
wer
lo
s
s
(
MPL
)
,
f
ill
f
ac
to
r
(
FF
)
,
ef
f
icien
cy
r
ati
o
(
E
R
)
an
d
o
v
e
r
all
m
ax
im
u
m
p
o
wer
(
OM
P).
Peak
p
o
wer
PMP
r
ef
er
s
to
th
e
m
a
x
im
u
m
am
o
u
n
t
o
f
en
er
g
y
g
e
n
er
ated
b
y
a
PV
ar
r
ay
.
T
h
is
v
alu
e
in
d
icate
s
th
e
ef
f
icien
cy
an
d
ca
p
ac
ity
o
f
th
e
PV
s
y
s
tem
to
p
r
o
d
u
ce
en
er
g
y
.
I
n
th
e
f
o
llo
win
g
ex
p
r
ess
io
n
,
m
is
m
atch
p
o
we
r
lo
s
s
(
MPL
)
is
ex
p
r
ess
ed
as a
p
er
ce
n
tag
e:
=
_
0
−
_
_
0
.
100
(
9
)
T
h
e
e
f
f
icien
cy
r
atio
(
E
R
)
is
d
e
f
in
ed
b
y
(
1
0
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
19
49
-
1
9
6
1
1956
=
_
_
0
.
100
(
1
0
)
Ov
er
all
m
ax
im
u
m
p
o
wer
(
OM
P)
is
g
iv
en
b
y
(
1
1
)
.
=
_
.
100
(
11)
P
MP_i0
is
th
e
m
ax
im
u
m
p
o
wer
p
r
o
v
id
e
d
b
y
co
n
f
ig
u
r
atio
n
S(
i=0
)
,
P(
i=1
)
,
SP
(
i=2
)
,
B
L
(
i=3
)
o
r
T
C
T
(
i=4
)
u
n
d
e
r
u
n
if
o
r
m
co
n
d
itio
n
.
P
MP_ij
r
ep
r
esen
ts
th
e
m
ax
im
u
m
p
o
wer
g
en
er
ated
b
y
th
e
c
o
n
f
ig
u
r
at
io
n
S(
i=0
)
,
P(
i=1
)
,
SP(
i=2
)
,
B
L
(
i=3
)
,
T
C
T
(
i=4
)
in
th
e
s
ce
n
ar
io
:
Un
if
o
r
m
(
j=0
)
,
C
en
ter
(
j=1
)
,
Diag
o
n
al
(
j=2
)
an
d
Fra
m
e
(
j=3
)
.
P
MP
is
th
e
m
ax
im
u
m
p
o
wer
a
m
o
n
g
t
h
e
f
o
u
r
co
n
f
ig
u
r
atio
n
s
t
ested
in
th
e
s
am
e
s
h
ad
in
g
.
Fill
f
ac
to
r
(
FF
)
is
ca
lcu
lated
as
th
e
q
u
o
tien
t
o
f
t
h
e
m
ax
i
m
u
m
o
u
tp
u
t
p
o
wer
(
V
MP
×I
MP
)
an
d
th
e
p
r
o
d
u
ct
o
f
o
p
en
cir
cu
it
v
o
ltag
e
an
d
s
h
o
r
t
cir
cu
it
cu
r
r
en
t
(
V
oc
×I
sc
)
.
Fil
l
Facto
r
i
s
ex
p
r
ess
ed
in
(
12
)
as
a
p
er
ce
n
tag
e:
(
%
)
=
.
.
.
100
(
1
2
)
V
MP
an
d
I
MP
ar
e
r
esp
ec
tiv
ely
t
h
e
v
o
ltag
e
a
n
d
c
u
r
r
en
t c
o
r
r
esp
o
n
d
in
g
to
th
e
m
ax
im
u
m
p
o
we
r
.
B
ased
o
n
th
e
s
im
u
latio
n
r
esu
lts
in
Fig
u
r
es
7
a
n
d
8
,
it
ca
n
b
e
o
b
s
er
v
e
d
t
h
at
th
e
two
-
d
io
d
e
m
o
d
el
p
r
o
v
id
es
h
i
g
h
er
s
h
o
r
t
-
cir
cu
it
v
o
ltag
es
th
an
th
o
s
e
p
r
o
v
id
e
d
b
y
th
e
s
in
g
le
-
d
io
d
e
m
o
d
el.
Su
b
s
eq
u
en
tly
,
we
h
av
e
d
etailed
ea
ch
s
h
ad
in
g
ca
s
e
an
d
its
ef
f
ec
t o
n
ea
ch
m
o
d
el.
-
Un
i
f
o
r
m
co
n
d
iti
o
n
(
c
ase
1
)
: U
n
d
e
r
th
ese
i
r
r
a
d
ia
ti
o
n
co
n
d
it
io
n
s
,
1
0
0
0
W
/m
²,
t
h
er
e
a
r
e
n
o
m
u
lt
ip
le
m
ax
im
a
p
o
we
r
p
o
in
ts
;
t
h
e
f
o
u
r
PV
ar
r
ay
co
n
f
i
g
u
r
ati
o
n
s
p
r
es
e
n
t
a
s
i
n
g
le
m
a
x
i
m
u
m
p
o
we
r
p
o
in
t.
T
h
e
e
f
f
ici
e
n
c
y
r
at
io
is
t
h
e
s
a
m
e
f
o
r
all
c
o
n
f
i
g
u
r
ati
o
n
s
a
n
d
e
q
u
a
ls
1
0
0
%
.
T
h
e
f
ill
f
a
ct
o
r
f
o
r
all
PV
n
et
wo
r
k
c
o
n
f
i
g
u
r
at
io
n
s
h
as
a
g
o
o
d
v
al
u
e
,
r
a
n
g
in
g
b
e
t
wee
n
7
1
%
a
n
d
7
6
%.
T
h
e
b
est
v
al
u
e
o
f
p
e
ak
p
o
w
er
s
is
p
r
o
v
id
ed
b
y
t
h
e
s
er
i
e
s
co
n
f
i
g
u
r
a
ti
o
n
b
as
ed
o
n
a
n
i
d
ea
l
d
io
d
e,
wit
h
t
h
is
p
o
w
er
b
ein
g
3
5
0
W
.
F
i
g
u
r
e
s
7
(
a)
a
n
d
8
(
a
)
p
r
o
v
id
e
d
et
ail
e
d
i
n
f
o
r
m
ati
o
n
o
n
t
h
e
v
ar
i
o
u
s
p
a
r
a
m
e
te
r
s
e
v
a
lu
at
ed
.
T
h
e
SP
,
B
L
,
a
n
d
T
C
T
c
o
n
f
i
g
u
r
ati
o
n
s
h
a
v
e
alm
o
s
t
id
e
n
ti
ca
l
s
h
o
r
t
c
ir
cu
it
cu
r
r
e
n
t
I
SC
v
al
u
es
,
b
u
t
t
h
e
r
e
is
a
s
li
g
h
t
d
i
f
f
er
e
n
ce
i
n
V
OC
,
es
p
e
cia
ll
y
i
n
t
h
e
two
-
d
i
o
d
e
c
o
n
f
i
g
u
r
ati
o
n
.
T
h
e
o
v
e
r
al
l
m
a
x
i
m
u
m
p
o
w
e
r
is
h
i
g
h
,
e
q
u
al
in
g
1
0
0
%
i
n
t
h
e
ca
s
e
o
f
t
h
e
s
er
i
e
s
co
n
f
i
g
u
r
a
ti
o
n
wi
th
a
n
i
d
e
al
d
io
d
e
.
T
h
e
m
is
m
at
ch
p
o
w
er
l
o
s
s
h
as
a
v
er
y
g
o
o
d
v
al
u
e
0
%
f
o
r
al
l
a
r
r
a
y
co
n
f
i
g
u
r
a
ti
o
n
s
.
H
o
we
v
er
,
t
h
e
S
a
n
d
P
c
o
n
f
i
g
u
r
at
io
n
s
,
b
ase
d
o
n
an
i
d
ea
l
d
i
o
d
e
,
wit
h
o
n
e
o
r
two
d
i
o
d
es
,
g
e
n
e
r
a
te
v
o
l
ta
g
es
a
n
d
c
u
r
r
e
n
ts
th
a
t
d
i
f
f
e
r
s
ig
n
i
f
i
ca
n
tl
y
f
r
o
m
t
h
o
s
e
o
f
t
h
e
o
t
h
e
r
co
n
f
i
g
u
r
ati
o
n
s
.
-
C
en
ter
s
h
ad
in
g
co
n
d
itio
n
(
ca
s
e
2
)
:
Acc
o
r
d
in
g
t
o
Fig
u
r
e
s
7
(
b
)
an
d
8
(
b
)
,
d
u
r
in
g
th
e
ce
n
ter
is
o
latio
n
,
th
er
e
ar
e
m
u
ltip
le
m
a
x
im
a
p
o
we
r
p
o
in
ts
.
T
h
e
c
u
r
v
e
in
Fig
u
r
e
7
(
b
)
s
h
o
ws
two
m
ax
im
u
m
p
o
wer
p
o
in
ts
p
r
o
v
id
e
d
b
y
s
tr
u
ct
u
r
es
S,
SP
,
B
L
,
an
d
T
C
T
,
b
u
t
th
e
p
ar
allel
P
co
n
f
ig
u
r
atio
n
p
r
o
v
id
es
a
s
in
g
le
m
ax
im
u
m
p
o
wer
p
o
in
t.
Par
allel
co
n
f
ig
u
r
atio
n
b
ased
o
n
d
o
u
b
le
d
i
o
d
e
s
(
P
DD)
h
as
th
e
lo
we
s
t
Mi
s
m
atch
Po
wer
L
o
s
s
,
1
0
%,
b
u
t
v
er
y
litt
le
o
p
e
n
cir
cu
it
v
o
ltag
e
is
g
e
n
er
ated
.
T
h
e
b
est
v
alu
e
o
f
f
ill
f
ac
to
r
i
s
g
iv
en
b
y
th
e
Par
allel
co
n
f
ig
u
r
atio
n
b
ased
o
n
th
e
id
ea
l
d
io
d
e
(
P
I
D)
7
6
%.
P
I
D,
P
SD
,
an
d
P
DD
y
ield
a
g
o
o
d
v
alu
e
o
f
th
e
ef
f
icien
c
y
r
atio
.
T
h
e
d
is
a
d
v
an
tag
e
o
f
p
ar
allel
c
o
n
f
i
g
u
r
atio
n
is
th
at
it
y
ield
s
a
m
in
im
al
o
p
en
cir
cu
it
v
o
ltag
e
(V
OC
)
.
S
I
D
co
n
f
ig
u
r
atio
n
o
f
f
e
r
s
th
e
b
est
v
alu
e
o
f
o
v
er
all
m
ax
im
u
m
p
o
wer
an
d
th
e
h
ig
h
est
g
lo
b
al
p
ea
k
p
o
wer
v
alu
e.
T
h
e
SP
,
B
L
,
an
d
T
C
T
co
n
f
ig
u
r
atio
n
s
h
av
e
n
ea
r
ly
id
en
tica
l
s
h
o
r
t
cir
cu
it
cu
r
r
en
ts
I
SC
v
alu
es
o
f
7
.
08
A,
b
u
t th
er
e
is
a
s
m
all
d
if
f
e
r
en
ce
in
o
p
en
cir
cu
it v
o
ltag
es.
-
Diag
o
n
al
s
h
ad
in
g
co
n
d
itio
n
(
c
ase
3
)
:
Un
d
er
th
is
s
h
ad
in
g
co
n
d
itio
n
,
Fig
u
r
e
8
(
c
)
s
h
o
ws
th
at
th
e
f
ile
f
ac
to
r
r
ep
r
esen
ts
a
f
a
v
o
r
a
b
le
v
al
u
e
7
8
%
wh
ile
th
e
v
o
ltag
e
p
r
o
d
u
ce
d
is
m
in
im
al
i
n
th
e
P
I
D,
P
S
D,
an
d
P
DD
co
n
f
ig
u
r
atio
n
s
.
T
o
tal
-
cr
o
s
s
-
tied
an
d
p
ar
allel
ar
e
am
o
n
g
th
e
b
est
co
n
f
ig
u
r
atio
n
s
in
t
h
is
s
h
a
d
in
g
s
ce
n
a
r
io
d
u
e
to
th
e
Mism
atch
Po
wer
L
o
s
s
f
ac
to
r
'
s
g
o
o
d
v
alu
e
o
f
ar
o
u
n
d
2
0
%.
T
C
T
I
D
an
d
P
I
D
p
r
o
d
u
ce
f
av
o
r
a
b
le
r
esu
lts
f
o
r
o
v
er
all
m
ax
im
u
m
p
o
wer
an
d
p
ea
k
p
o
wer
:
1
0
0
%
an
d
2
6
4
W
,
r
es
p
ec
tiv
ely
.
T
h
e
Par
allel
co
n
f
ig
u
r
atio
n
p
r
o
v
id
e
s
s
ig
n
if
ican
tly
f
av
o
r
a
b
le
r
esu
l
ts
f
o
r
th
e
ef
f
icien
c
y
r
atio
7
8
%
.
Fig
u
r
e
7
(
c)
p
r
esen
ts
th
at
co
n
f
ig
u
r
atio
n
s
S
I
D
an
d
S
SD
h
av
e
f
o
u
r
m
ax
i
m
u
m
p
o
wer
p
o
in
ts
,
o
n
e
o
f
wh
ich
is
a
g
lo
b
al
p
o
in
t
with
a
v
alu
e
o
f
2
2
0
W
f
o
r
S
I
D
an
d
2
0
2
W
f
o
r
S
SD.
C
o
n
f
ig
u
r
atio
n
S
DD
o
f
f
er
s
th
r
ee
m
ax
im
u
m
p
o
wer
p
o
in
ts
,
in
clu
d
in
g
two
lo
ca
l
m
ax
im
a.
C
o
n
f
ig
u
r
atio
n
s
B
L
I
D,
B
L
S
D,
an
d
B
L
DD
p
r
o
v
id
e
two
m
ax
im
u
m
p
o
wer
p
o
in
ts
ea
ch
.
T
h
e
co
n
f
ig
u
r
atio
n
s
P
an
d
T
C
T
,
b
ased
o
n
th
e
th
r
ee
m
o
d
el
s
I
D,
SD,
an
d
DD,
p
r
o
d
u
ce
a
s
in
g
le
m
ax
i
m
u
m
p
o
wer
p
o
in
t.
-
Fra
m
e
s
h
ad
in
g
co
n
d
itio
n
(
ca
s
e
4
)
:
Du
r
in
g
th
is
in
s
o
latio
n
,
th
e
p
h
o
to
v
o
ltaic
ar
r
a
y
,
m
a
d
e
u
p
o
f
n
in
e
m
o
d
u
les,
is
af
f
ec
ted
b
y
s
h
ad
in
g
ef
f
ec
ts
o
n
m
o
s
t
o
f
t
h
em
,
with
th
e
n
o
tab
le
e
x
ce
p
tio
n
o
f
th
e
ce
n
t
r
al
m
o
d
u
le,
wh
ic
h
ca
p
tu
r
es
th
e
t
o
tal
ir
r
ad
ian
ce
o
f
1
0
0
0
W
/m
2
.
Par
allel
co
n
f
ig
u
r
atio
n
p
r
o
d
u
ce
s
th
e
lo
west
m
is
m
atch
p
o
wer
lo
s
s
ar
o
u
n
d
4
6
%.
P
I
D
g
iv
es
a
b
est
f
ill
f
ac
to
r
FF
=7
6
%,
b
u
t
m
in
im
a
l
v
o
ltag
e.
T
h
e
p
ar
allel
co
n
f
i
g
u
r
atio
n
b
ased
o
n
o
n
e
d
io
d
e
p
r
o
v
i
d
es
g
o
o
d
v
alu
es
f
o
r
Fil
l
Facto
r
eq
u
al
t
o
FF
=7
6
%,
f
o
r
ef
f
icien
cy
r
atio
eq
u
al
to
E
R
=7
6
%,
f
o
r
o
v
e
r
all
m
ax
im
u
m
p
o
wer
eq
u
al
to
1
2
%,
an
d
f
o
r
p
ea
k
p
o
wer
eq
u
al
to
1
8
0
W
,
b
u
t
th
is
co
n
f
ig
u
r
ati
o
n
P
I
D
o
f
f
er
s
a
m
in
im
al
o
p
e
n
cir
cu
it
v
o
lta
g
e.
Fig
u
r
es
7
(
d
)
an
d
8
(
d
)
s
h
o
w
in
d
etail
th
e
co
m
p
ar
is
o
n
b
etwe
en
th
e
twelv
e
co
n
f
ig
u
r
atio
n
s
s
u
b
jecte
d
to
f
r
am
e
s
h
ad
in
g
co
n
d
itio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
va
lu
a
tin
g
s
h
a
d
in
g
effec
ts
o
n
p
h
o
to
v
o
lta
ic
mo
d
u
les:
Ma
th
e
ma
tica
l
…
(
Mo
h
cin
e
A
b
o
u
y
a
a
ko
u
b
)
1957
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
7
.
P(V
)
a
n
d
I
(
V)
o
f
se
r
ies (
S),
pa
r
allel
(
P),
s
er
ies
-
p
ar
a
llel
(
SP
)
,
b
r
id
g
e
-
lin
k
(
B
L
)
,
to
t
al
-
cr
o
s
s
-
tied
(
T
C
T
)
b
ased
o
n
a
n
id
ea
l d
io
d
e
(
I
D
)
,
s
in
g
le
(
SD)
,
an
d
d
o
u
b
le
-
d
i
o
d
e
(
DD)
u
n
d
er
p
ar
tial sh
ad
in
g
:
(
a)
u
n
if
o
rm
,
(
b
)
c
en
ter
,
(
c)
d
ia
g
o
n
al
,
an
d
(
d
)
f
r
am
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
19
49
-
1
9
6
1
1958
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
8
.
Mism
atch
p
o
wer
lo
s
s
(
MPL
)
,
f
ill f
ac
to
r
(
FF
)
,
ef
f
icien
cy
r
atio
(
E
R
)
,
an
d
o
v
er
all
m
ax
im
u
m
p
o
wer
(
OM
P)
o
f
f
iv
e
PV a
r
r
ay
co
n
f
i
g
u
r
atio
n
s
: S,
P,
SP,
B
L
,
T
C
T
,
b
ased
o
n
a
n
id
ea
l (
I
D
)
,
s
in
g
le
d
io
d
e
(
SD)
,
an
d
d
o
u
b
le
d
io
d
e
(
DD)
u
n
d
e
r
u
n
if
o
r
m
an
d
n
o
n
-
u
n
if
o
r
m
i
r
r
a
d
iatio
n
: (
a)
u
n
if
o
r
m
,
(
b
)
ce
n
ter
,
(
c)
d
iag
o
n
al,
an
d
(
d
)
f
r
a
m
e
6.
CO
NCLU
SI
O
N
I
n
th
is
s
tu
d
y
,
f
iv
e
a
r
r
ay
co
n
f
i
g
u
r
atio
n
s
wer
e
ex
am
in
e
d
:
S,
P,
SP
,
B
L
,
an
d
T
C
T
,
u
n
d
er
u
n
if
o
r
m
a
n
d
th
r
ee
p
ar
tial
s
h
ad
in
g
s
ce
n
ar
io
s
:
ce
n
ter
,
d
iag
o
n
al
,
an
d
f
r
am
e.
T
h
e
f
ir
s
t
s
tep
o
f
o
u
r
wo
r
k
was
to
d
ev
elo
p
in
MA
T
L
AB
/S
im
u
lin
k
a
m
ath
e
m
atica
l
ce
ll
m
o
d
el
b
ased
o
n
th
r
ee
d
if
f
er
en
t
m
o
d
els:
th
e
i
d
ea
l
d
io
d
e,
th
e
o
n
e
-
d
io
d
e
m
o
d
el
with
a
r
esis
to
r
a
n
d
th
e
two
-
d
io
d
e
m
o
d
el.
Nex
t
,
we
cr
ea
ted
,
test
ed
,
s
im
u
late
d
,
an
d
an
aly
ze
d
th
e
f
if
teen
3
x
3
PV
co
n
f
i
g
u
r
atio
n
s
u
n
d
er
f
o
u
r
d
if
f
er
en
t
s
ce
n
ar
io
s
.
T
o
e
v
alu
ate
th
e
ef
f
ec
t
o
f
s
h
ad
in
g
o
n
p
h
o
to
v
o
ltaic
m
o
d
u
les,
we
co
m
p
ar
e
s
ev
e
r
al
p
e
r
f
o
r
m
an
ce
m
etr
ics.
Fro
m
t
h
e
r
esu
lts
o
b
tain
ed
,
in
th
e
ab
s
en
ce
o
f
s
h
ad
in
g
,
th
e
SP
co
n
f
ig
u
r
atio
n
is
am
o
n
g
th
e
b
est
co
n
f
ig
u
r
ati
o
n
s
th
at
y
ield
g
o
o
d
e
v
alu
atio
n
p
ar
am
eter
v
alu
es,
s
p
ec
if
ically
th
e
SP
I
D
co
n
f
ig
u
r
atio
n
.
T
h
e
T
C
T
co
n
f
ig
u
r
atio
n
p
r
o
v
i
d
es
v
alu
es
th
at
ar
e
n
ea
r
l
y
id
en
tical
to
th
o
s
e
o
f
th
e
SP
co
n
f
ig
u
r
atio
n
;
h
o
w
ev
er
,
it
r
eq
u
ir
es
m
o
r
e
ca
b
les.
I
n
o
u
r
ca
s
e,
th
e
T
C
T
co
n
f
ig
u
r
atio
n
r
eq
u
ir
es
1
4
co
n
n
ec
tio
n
ca
b
les
b
etwe
en
th
e
9
PV
s
o
lar
,
wh
ile
th
e
SP
co
n
f
ig
u
r
atio
n
r
eq
u
ir
es
o
n
ly
1
0
c
ab
les
to
co
n
n
ec
t
th
e
9
p
an
els.
T
h
er
ef
o
r
e,
th
e
T
C
T
co
n
f
ig
u
r
atio
n
i
n
cu
r
s
a
co
s
t
th
a
t
is
4
0
%
h
ig
h
er
t
h
an
t
h
at
o
f
th
e
SP
co
n
f
ig
u
r
atio
n
.
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