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Driv
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t
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J
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12
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.
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,
Dec
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2
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p
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24
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P
h
o
t
o
v
o
lt
a
ic
(
P
V
)
p
a
n
e
ls
h
a
v
e
d
r
a
w
b
a
c
k
o
f
h
a
v
in
g
th
e
ir
p
e
a
k
p
o
we
r
re
d
u
c
e
d
w
h
e
n
c
lo
u
d
s
o
r
sh
a
d
e
a
re
p
re
se
n
t
.
F
u
rt
h
e
rm
o
re
,
it
is
o
n
ly
a
v
a
il
a
b
le
w
h
il
e
th
e
su
n
sh
in
e
.
Ne
a
rb
y
stru
c
tu
re
s,
p
lan
ts,
b
ird
d
ro
p
p
i
n
g
s,
a
n
d
o
t
h
e
r
o
b
sta
c
les
sh
a
d
e
o
p
e
ra
ti
n
g
p
h
o
t
o
v
o
lt
a
ic
(
P
V
)
d
e
v
ice
s,
e
ffe
c
ti
v
e
l
y
r
e
d
u
c
in
g
th
e
in
c
i
d
e
n
t
so
lar
ra
d
iatio
n
p
ro
d
u
c
e
d
b
y
th
e
m
o
d
u
les
.
W
h
e
n
th
e
se
P
V
p
a
n
e
ls
a
re
e
x
p
o
se
d
to
p
a
rti
a
l
s
h
a
d
in
g
,
th
e
ir
p
o
w
e
r
e
fficie
n
c
y
is
re
d
u
c
e
d
.
A
n
e
u
ra
l
n
e
tw
o
rk
w
it
h
a
k
in
d
o
f
a
rti
f
icia
l
n
e
u
ra
l
n
e
tw
o
rk
is
u
se
d
in
t
h
e
su
g
g
e
st
e
d
h
y
b
rid
m
e
th
o
d
(A
NN
).
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h
e
k
e
y
f
o
c
u
s
o
f
th
is
a
rti
c
le
is
to
u
se
e
n
v
iro
n
m
e
n
tal
e
ff
e
c
ts
d
e
p
e
n
d
e
n
t
o
n
p
a
rti
a
l
s
h
a
d
i
n
g
to
g
e
t
th
e
m
a
x
i
m
u
m
p
e
r
f
o
r
m
a
n
c
e
f
r
o
m
a
so
lar
s
y
ste
m
.
T
h
e
su
g
g
e
ste
d
h
y
b
rid
so
lu
ti
o
n
is
tes
ted
i
n
t
h
e
M
A
TL
A
B
/S
im
u
li
n
k
w
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in
g
p
latf
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m
u
sin
g
p
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ti
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t
c
a
se
s,
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n
d
th
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f
f
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c
y
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c
o
m
p
a
re
d
to
o
th
e
r
a
p
p
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o
a
c
h
e
s.
A
d
d
it
io
n
a
l
ly
,
th
e
b
e
st
o
p
ti
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n
s
f
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th
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su
g
g
e
ste
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n
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d
p
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w
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r
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x
a
m
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d
.
K
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w
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s
:
P
ar
tial sh
ad
in
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P
h
o
to
v
o
ltaic
P
V
ch
ar
ac
ter
is
tics
S
o
lar
en
er
g
y
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
:
Had
i Fak
h
ir
Has
h
i
m
Mid
d
le
T
ec
h
n
ical
U
n
i
v
er
s
it
y
,
T
ec
h
n
ical
I
n
s
tr
u
cto
r
s
T
r
ain
in
g
I
n
s
tit
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te
B
ag
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d
ad
,
I
r
aq
E
m
ail: d
r
.
ad
n
an
@
m
t
u
.
ed
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
Ov
er
t
h
e
la
s
t
te
n
y
ea
r
s
,
t
h
e
g
l
o
b
al
s
o
lar
P
V
m
ar
k
et
is
ex
p
a
n
d
in
g
s
ig
n
i
f
ica
n
tl
y
,
a
n
d
it
n
o
w
p
la
y
s
an
ess
e
n
tial
p
ar
t
in
r
en
e
w
ab
le
en
er
g
y
i
m
p
le
m
en
tatio
n
s
,
p
ar
ticu
lar
l
y
i
n
r
esid
en
tial,
ag
r
ic
u
lt
u
r
al,
an
d
in
d
u
s
tr
ial
s
etti
n
g
s
[
1
]
.
B
ec
au
s
e
o
f
en
v
ir
o
n
m
e
n
tal
is
s
u
e
s
,
g
r
ee
n
en
er
g
y
r
eso
u
r
ce
s
h
av
e
r
ec
en
t
l
y
r
ec
eiv
ed
a
lo
t
o
f
f
o
cu
s
.
B
ec
au
s
e
o
f
th
e
ad
v
a
n
ce
m
e
n
t
o
f
p
h
o
to
v
o
ltaic
(
P
V)
f
ab
r
icatio
n
tech
n
o
lo
g
ies,
p
h
o
to
v
o
ltaic
s
(
P
Vs)
h
as
g
ain
ed
a
lo
t
o
f
atten
tio
n
a
m
o
n
g
r
en
e
w
ab
le
en
er
g
y
s
o
u
r
ce
s
[
2
]
.
PV
m
o
d
u
les
ar
e
m
ad
e
u
p
o
f
P
V
ce
ll
s
th
at
ar
e
elec
tr
icall
y
li
n
k
ed
.
T
h
e
m
ai
n
is
s
u
e
w
it
h
P
V
is
t
h
at
it
lo
s
es
en
er
g
y
p
r
o
d
u
ctio
n
d
u
e
to
v
ar
iatio
n
s
in
s
o
lar
li
g
h
t,
p
ar
tial
s
h
ad
i
n
g
,
o
r
ien
tatio
n
,
p
o
llen
,
an
d
b
ir
d
d
r
o
p
lets
[
3
]
.
A
s
a
r
esu
lt,
it
is
cr
itical
to
em
p
lo
y
s
tr
ateg
ies
t
h
at
in
cr
ea
s
e
th
e
P
V
s
y
s
te
m
's
e
n
er
g
y
co
n
s
u
m
p
tio
n
.
T
o
m
ee
t
t
h
e
lo
ad
d
e
m
an
d
,
th
e
P
V
m
o
d
u
le
s
h
a
v
e
a
c
o
n
n
ec
tio
n
in
s
er
ies
an
d
/o
r
p
ar
allel
[
4
]
.
P
V
m
o
d
u
l
es
h
a
v
e
t
h
e
ad
v
a
n
ta
g
e
o
f
b
ei
n
g
ex
tr
e
m
el
y
s
ca
lab
le,
an
d
w
it
h
p
r
o
p
er
s
izin
g
,
t
h
e
y
ca
n
b
e
ass
u
m
ed
to
h
a
v
e
s
u
f
f
ic
i
en
t p
o
w
er
f
o
r
a
lar
g
e
r
an
g
e
o
f
lo
ad
s
[
5
]
.
P
V
m
o
d
u
les
h
a
v
e
ev
o
l
v
ed
in
t
o
s
tab
le
an
d
d
ep
en
d
ab
le
p
o
w
e
r
s
o
u
r
ce
s
w
it
h
a
2
0
-
to
3
0
-
y
ea
r
lif
esp
an
.
No
r
m
a
l
test
co
n
d
itio
n
s
(
NT
C
)
ar
e
u
s
ed
to
r
ate
th
eir
ef
f
icien
c
y
(
i.e
.
,
T
em
p
.
=
3
0
0
K,
th
e
s
o
lar
ir
r
ad
ian
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=
1
k
W
/
m
2
,
i
n
ad
d
itio
n
to
Air
Ma
s
s
1
.
5
)
.
T
h
e
d
if
f
er
en
ce
b
et
w
ee
n
r
ea
l
-
w
o
r
ld
o
p
er
atio
n
al
co
n
d
itio
n
s
b
es
id
es
ST
C
r
atin
g
s
ca
u
s
es
a
d
if
f
er
en
ce
in
p
r
ed
icted
P
V
o
u
tp
u
t.
T
h
e
co
m
b
in
ed
id
en
tific
atio
n
an
d
d
iag
n
o
s
is
o
f
o
p
en
cir
cu
it,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
0
8
8
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8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
2
4
35
–
24
4
2
2436
d
ec
ay
,
a
s
w
ell
a
s
p
ar
tial
s
h
ad
i
n
g
h
a
s
b
ee
n
s
u
g
g
ested
b
y
s
o
m
e
r
esear
c
h
er
s
[
6
]
,
[
7
]
,
w
h
er
e
v
er
th
e
P
V
c
u
r
v
e
o
f
m
o
d
u
le
'
s
c
u
r
r
en
t
-
v
o
ltag
e
co
n
s
id
er
s
a
s
ig
n
if
ican
t i
n
d
ex
to
cla
s
s
i
f
y
t
h
e
o
u
tp
u
t o
f
P
V
m
o
d
u
le
s
.
Ma
n
y
d
e
v
elo
p
m
e
n
ts
h
av
e
o
c
cu
r
r
ed
as
a
r
esu
lt
o
f
t
h
e
g
r
o
w
i
n
g
p
o
p
u
lar
it
y
o
f
P
V
-
b
as
ed
en
er
g
y
,
allo
w
i
n
g
it
to
i
m
p
r
o
v
e
i
ts
e
f
f
icien
c
y
w
h
ile
also
lo
w
er
in
g
i
ts
co
s
t.
Si
n
g
le
-
cr
y
s
tal
lin
e
s
ili
co
n
-
b
ased
P
V
ce
ll
s
also
h
a
v
e
a
2
8
p
er
ce
n
t
h
i
g
h
er
p
er
f
o
r
m
a
n
ce
t
h
an
k
s
to
r
ec
en
t
ad
v
a
n
ce
s
i
n
s
ilico
n
m
an
u
f
ac
t
u
r
in
g
[
8
]
.
Fu
r
t
h
er
m
o
r
e,
s
ev
er
al
s
o
p
h
is
tic
ated
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
m
o
n
ito
r
in
g
alg
o
r
it
h
m
s
ar
e
n
o
w
av
ailab
le,
allo
w
in
g
f
o
r
g
r
ea
ter
en
er
g
y
h
ar
v
est
in
g
f
r
o
m
a
P
V
p
an
el.
Desp
ite
th
e
s
e
ad
v
an
ce
m
e
n
ts
i
n
s
o
lar
en
er
g
y
p
r
o
ce
s
s
i
n
g
,
P
V
m
o
d
u
les
a
ls
o
u
s
e
a
f
ix
ed
to
p
o
lo
g
y
b
ased
o
n
s
er
ie
s
-
p
ar
allel
(
SP
)
[
9
]
,
[
1
0
]
.
P
h
o
to
v
o
ltaic
(
P
V)
d
ev
ices
ar
e
in
ch
ar
g
e
o
f
m
a
k
in
g
co
n
v
er
s
io
n
o
f
s
o
lar
e
n
er
g
y
in
to
elec
tr
ical
en
er
g
y
.
Su
c
h
d
e
v
ices
ar
e
m
ad
e
u
p
o
f
m
u
ltip
l
e
in
te
g
r
ated
P
V
ce
lls
f
o
r
m
in
g
a
p
ac
k
ag
e
th
at
p
r
o
v
id
es
s
u
f
f
i
cien
t
s
ec
u
r
it
y
f
o
r
th
e
ce
lls
wh
ile
also
p
r
o
v
id
in
g
v
alu
e
s
o
f
v
o
ltag
e
a
n
d
elec
tr
ic
cu
r
r
en
t
w
h
ich
m
a
y
b
e
u
tili
ze
d
in
o
p
er
atio
n
[
1
1
]
.
As
a
n
alter
n
ati
v
e
to
t
h
e
SP
-
b
ased
P
V
m
o
d
u
le
w
it
h
b
y
p
as
s
d
io
d
e,
a
P
V
m
o
d
u
le
w
i
th
co
m
p
le
m
e
n
tar
y
m
etal
o
x
id
e
s
e
m
ico
n
d
u
cto
r
(
C
MO
S)
s
w
itc
h
es
h
as
r
ec
en
tl
y
b
ee
n
p
r
o
p
o
s
ed
[
1
2
]
.
P
V
m
o
d
u
les
w
it
h
s
w
itc
h
es
h
av
e
b
ee
n
s
ee
n
in
e
x
p
er
i
m
e
n
ts
to
b
e
m
o
r
e
p
r
ep
a
r
ed
to
d
e
al
w
it
h
p
ar
tial
s
h
ad
i
n
g
,
d
is
to
r
tio
n
p
r
o
b
lem
s
,
an
d
u
n
s
tab
le
s
itu
a
tio
n
s
.
F
u
r
th
er
m
o
r
e,
s
i
m
i
lar
P
V
m
o
d
u
les
ca
n
b
e
r
estru
ct
u
r
ed
in
r
ea
l
ti
m
e
(
i.e
.
,
th
e
n
u
m
b
er
o
f
P
V
ce
lls
attac
h
ed
in
s
er
ies
v
er
s
u
s
p
ar
allel
ch
an
g
es),
allo
w
i
n
g
f
o
r
th
e
cr
ea
tio
n
o
f
a
p
o
w
er
is
lan
d
.
Fo
r
i
m
p
r
o
v
in
g
t
h
e
e
f
f
icien
c
y
o
f
th
e
q
u
est
f
o
r
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t,
s
o
m
e
b
r
illi
a
n
t
tr
ai
n
in
g
-
b
ased
alg
o
r
ith
m
s
li
k
e
ar
ti
f
icial
n
e
u
r
al
n
et
w
o
r
k
s
(
A
N
Ns)
o
r
f
u
zz
y
lo
g
ic
w
er
e
cr
ea
ted
.
S
m
ar
t
co
n
tr
o
ller
s
,
i
n
clu
d
i
n
g
th
e
f
u
zz
y
lo
g
ic
s
y
s
te
m
,
o
u
tp
er
f
o
r
m
e
d
p
er
tu
r
b
&
o
b
s
er
v
e
(
P&
O
)
co
n
tr
o
ller
s
in
s
o
m
e
ca
s
es
[
1
3
]
.
Fu
r
th
er
m
o
r
e,
co
m
p
ar
ed
to
th
e
P
&
O
ap
p
r
o
a
ch
,
th
e
n
e
u
r
o
-
f
u
zz
y
h
y
b
r
id
in
t
ellig
e
n
t
co
n
tr
o
l
s
ch
e
m
e
s
h
o
w
s
ce
r
tain
ad
v
an
tag
e
s
[
1
4
]
.
Fu
r
th
er
m
o
r
e,
ce
r
tain
ar
ti
f
icial
n
e
u
r
al
n
e
t
w
o
r
k
tr
ai
n
i
n
g
m
et
h
o
d
s
h
a
v
e
b
ee
n
estab
li
s
h
ed
s
o
th
at
to
s
p
ee
d
u
p
th
e
q
u
e
s
t
f
o
r
th
e
p
o
in
t o
f
m
ax
i
m
u
m
s
tr
en
g
t
h
.
P
&
O,
o
r
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t sear
ch
in
g
,
m
a
y
b
e
u
tili
ze
d
to
p
r
ac
tice
a
n
eu
r
al
n
et
w
o
r
k
,
r
esu
lti
n
g
i
n
an
o
p
ti
m
u
m
in
cr
ea
s
i
n
g
o
r
r
ed
u
cin
g
d
u
t
y
r
atio
in
th
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
o
r
ien
tati
o
n
[
1
5
]
.
Ma
n
y
P
V
in
s
tallat
io
n
s
w
er
e
u
s
in
g
MP
PT
c
o
n
tr
o
llin
g
,
w
h
ic
h
m
e
an
s
t
h
at
t
h
e
o
u
tp
u
t
en
er
g
y
v
ar
ies
w
it
h
v
ar
iatio
n
s
in
ir
r
ad
ian
ce
s
tr
en
g
t
h
as
w
ell
as
o
th
er
e
n
v
ir
o
n
m
e
n
tal
co
n
d
it
io
n
s
.
F
u
r
th
er
m
o
r
e,
v
ar
iatio
n
s
in
o
u
tp
u
t e
n
er
g
y
ca
n
b
e
ca
u
s
ed
b
y
elec
tr
ical
r
es
tr
i
ctio
n
s
a
n
d
P
V
s
y
s
te
m
p
o
w
er
.
2.
P
V
SYST
E
M
M
O
DE
L
L
I
NG
T
h
e
P
V
eq
u
iv
alen
t
cir
c
u
it
wh
en
li
g
h
t
is
ir
r
ad
iated
ca
n
b
e
r
ep
r
esen
ted
in
Fig
u
r
e
1
.
T
h
e
s
h
u
n
t
r
esis
ta
n
ce
R
s
h
d
en
o
tes
f
o
r
th
e
leak
ag
e
r
esis
ta
n
ce
ch
ar
ac
ter
ized
b
y
a
co
n
s
tan
t
r
esi
s
tan
ce
,
th
at
is
f
ar
o
f
f
th
e
id
ea
l
d
io
d
e
ch
ar
ac
ter
is
tics
[
1
6
]
.
Me
an
w
h
ile
t
h
e
P
V
v
o
ltag
e
a
n
d
cu
r
r
en
t
r
elatio
n
s
h
i
p
co
n
s
id
er
s
s
tr
ict
l
y
n
o
n
li
n
ea
r
,
s
o
t
h
at
P
V
m
o
d
eli
n
g
co
u
ld
b
e
p
r
esen
ted
f
o
r
p
er
f
o
r
m
i
n
g
a
co
m
p
lete
s
ch
e
m
e
s
i
m
u
lat
io
n
s
o
a
s
to
ac
cu
r
ate
s
y
s
te
m
ac
h
iev
e
m
e
n
t
ch
ar
ac
ter
is
tic
s
.
Fig
u
r
e
1
.
T
h
e
eq
u
iv
alen
t c
ir
c
u
it o
f
th
e
P
V
m
o
d
u
le
I
n
an
ar
r
a
y
o
f
P
V,
t
h
e
s
er
ie
s
an
d
p
ar
allel
ce
ll
s
n
u
m
b
er
g
i
v
es
a
c
h
ar
ac
ter
is
tics
o
f
a
n
o
p
en
cir
cu
it
v
o
ltag
e
i
n
ad
d
itio
n
to
s
h
o
r
t c
ir
cu
it c
u
r
r
e
n
t a
s
s
h
o
w
n
in
:
V
OC
=
N
s
V
oc
I
SC
=
(
1
)
P
ar
tial
s
h
ad
in
g
,
in
w
h
ic
h
t
h
e
p
h
o
to
-
g
e
n
er
ated
cu
r
r
en
t
o
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s
h
ad
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lls
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ec
r
ea
s
es
as
o
p
p
o
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t
o
u
n
s
h
ad
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ie
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co
n
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l
ls
,
is
o
n
e
o
f
t
h
e
m
ai
n
ch
a
llen
g
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f
o
r
P
V
m
o
d
u
les.
T
h
e
s
h
a
d
ed
P
V
ce
lls
w
o
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ld
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e
r
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er
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h
o
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t
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r
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n
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t
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all
y
d
estru
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iv
e
r
e
v
er
s
e
b
r
ea
k
d
o
w
n
v
o
lta
g
e
a
n
d
h
o
ts
p
o
ts
lo
s
s
.
I
f
th
e
a
m
b
ie
n
t
te
m
p
er
atu
r
e
r
is
es,
th
e
P
V
m
o
d
u
les
'
o
p
en
-
c
ir
cu
it
v
o
lta
g
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Vo
c
d
ec
r
ea
s
es
lin
ea
r
l
y
(
an
d
d
ep
en
d
in
g
o
n
t
h
e
te
m
p
er
atu
r
e
co
ef
f
icien
t
o
f
Vo
c)
,
w
h
il
e
th
e
s
h
o
r
t
-
cir
cu
it
cu
r
r
en
t
I
s
c
r
is
es
li
n
ea
r
l
y
a
s
th
e
in
cid
en
t
s
o
lar
ir
r
ad
ian
ce
r
is
es
[
1
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
P
o
w
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&
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2
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8
8
-
8
694
I
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Ha
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2437
T
h
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ch
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ter
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I
-
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d
P
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f
th
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P
V
ca
n
b
e
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b
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a
s
[
1
8
]
:
ℎ
=
+
(
−
)
(
2
)
=
[
e
xp
(
(
+
)
−
1
]
(
3
)
=
[
]
.
e
xp
(
(
1
−
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I
n
(
3
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is
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ti
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e
w
it
h
co
n
s
ta
n
t
ir
r
ad
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lev
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it
h
s
p
ec
if
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atin
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ce
ll
te
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atu
r
e
T
c
.
T
h
e
ch
ar
ac
ter
is
tics
o
f
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a
n
d
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V
w
ith
n
u
m
er
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s
le
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ad
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n
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y
t
h
e
s
id
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f
co
n
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t
te
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er
at
u
r
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a
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ie
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y
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eter
m
i
n
i
n
g
th
e
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cu
r
r
en
t
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g
e,
i
n
ad
d
itio
n
to
p
o
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er
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n
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e
s
ee
n
in
Fi
g
u
r
e
2
.
T
h
e
P
V
ce
ll c
h
ar
ac
ter
is
tic
cu
r
r
en
t
ca
n
b
e
r
ef
o
r
m
u
lated
as
:
=
ℎ
−
ℎ
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+
ℎ
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(
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w
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ℎ
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io
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ess
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=
(
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(
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(
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O
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r
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m
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d
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h
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m
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le,
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r
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g
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ter
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ad
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in
p
ar
allel
s
tr
in
g
s
w
i
th
i
n
t
h
e
s
a
m
e
ar
r
ay
[
1
9
]
.
Fig
u
r
e
2
.
T
h
e
ch
ar
ac
ter
is
tics
o
f
v
o
lta
g
e
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cu
r
r
en
t
an
d
p
o
w
er
-
c
u
r
r
en
t
w
it
h
m
an
y
ir
r
ad
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n
le
v
els at
co
n
s
ta
n
t
te
m
p
er
atu
r
e
As
s
ee
n
f
r
o
m
F
i
g
u
r
e
1
,
th
e
ir
r
ad
ian
ce
as
w
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as
te
m
p
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r
e
h
as
a
ch
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r
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ay
,
s
o
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a
t
cu
r
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en
t,
v
o
lta
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e,
an
d
p
o
w
er
also
ch
an
g
e
f
o
r
co
n
s
eq
u
e
n
ce
s
.
Fig
u
r
e
2
d
em
o
n
s
tr
ate
t
h
e
I
-
V
an
d
P
-
V
w
it
h
ir
r
ad
ian
ce
d
if
f
er
en
ce
s
,
r
esp
ec
tiv
el
y
.
Fo
r
ac
q
u
ir
in
g
th
e
p
r
ef
er
r
ed
v
alu
es
o
f
cu
r
r
en
t
an
d
v
o
ltag
e
w
it
h
i
n
P
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
2
4
35
–
24
4
2
2438
m
o
d
u
le,
s
er
ies
o
r
p
ar
allel
P
V
ce
lls
ca
n
b
e
co
n
f
ig
u
r
ed
.
So
lar
ce
ll
co
n
s
id
er
s
f
o
r
P
N
j
u
n
ctio
n
f
o
r
m
at
io
n
th
at
e
m
p
lo
y
s
t
h
e
s
u
n
lig
h
t to
cr
ea
te
p
h
o
to
cu
r
r
en
t th
e
n
r
u
n
as a
d
io
d
e
w
ith
i
n
t
h
e
s
h
ad
o
w
s
o
r
d
ar
k
n
e
s
s
[
2
0
]
.
T
h
e
b
y
p
ass
d
io
d
e
ap
p
r
o
ac
h
h
as
b
ee
n
s
elec
ted
p
r
i
m
ar
il
y
e
m
p
lo
y
ed
in
co
m
m
er
cial
d
e
v
ices
.
W
h
ile
it
ac
co
m
p
li
s
h
es
f
o
r
s
u
f
f
icie
n
tl
y
h
an
d
le
t
h
e
h
o
t
s
p
o
ts
p
h
e
n
o
m
en
o
n
b
esid
es
r
eser
v
atio
n
th
e
m
o
d
u
les
lif
e,
h
er
e
th
er
e
is
s
till
a
s
u
b
s
ta
n
tia
l
m
at
t
er
co
n
ce
r
n
in
g
t
h
e
P
-
V
c
u
r
v
e
d
ef
o
r
m
atio
n
.
T
h
is
asp
ec
t
ca
n
b
e
s
ee
n
w
it
h
F
ig
u
r
e
3
,
th
at
ex
p
lain
h
o
w
t
h
e
en
er
g
y
r
ec
o
v
er
y
i
s
p
r
o
v
id
in
g
b
y
t
h
e
m
a
n
n
er
ca
n
b
e
p
er
ce
iv
ed
,
alo
n
g
w
it
h
P
-
V
cu
r
v
e
d
is
to
r
tio
n
.
Fu
r
t
h
er
m
o
r
e,
a
n
o
b
s
er
v
an
ce
as
a
r
e
s
u
l
t
o
f
t
h
e
p
o
w
er
c
u
r
v
e
d
i
s
to
r
tio
n
,
co
n
v
e
n
tio
n
al
MP
PT
tech
n
iq
u
es
li
k
e
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P
&
O)
an
d
in
cr
e
m
en
t
al
co
n
d
u
ctan
ce
(
I
n
c
C
o
n
)
co
n
s
id
er
in
ac
ti
v
e
an
d
p
ass
iv
e
[
2
1
]
,
th
e
y
ca
n
al
s
o
d
ef
i
n
itel
y
g
et
m
is
s
i
n
g
in
a
n
y
o
f
d
if
f
er
e
n
t
lo
ca
l
m
a
x
i
m
u
m
p
o
wer
p
o
in
ts
(
L
MP
P
s
)
,
th
er
ef
o
r
e
n
ec
e
s
s
it
y
f
o
r
m
o
r
e
ap
p
licab
le
ap
p
r
o
ac
h
es
is
d
ir
ec
t th
is
p
r
o
b
le
m
.
Fig
u
r
e
3
.
P
V,
V
-
I
,
an
d
V
-
P
ch
ar
ac
ter
is
tics
u
n
d
er
p
ar
tial sh
ad
in
g
Sh
ad
i
n
g
h
a
s
a
d
etr
im
e
n
tal
a
f
f
ec
t
o
n
s
o
lar
P
V
s
y
s
te
m
p
er
f
o
r
m
an
ce
v
ia
lo
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er
i
n
g
p
o
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er
o
u
tp
u
t
a
n
d
p
r
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d
u
cin
g
ir
r
ep
ar
ab
le
d
am
a
g
e
to
P
V
m
o
d
u
le
s
th
r
o
u
g
h
th
e
h
o
ts
p
o
ts
cr
ea
tio
n
.
I
t
'
s
ea
s
y
to
ass
u
m
e
t
h
at
t
h
e
r
ed
u
ctio
n
i
n
p
o
w
er
o
u
tp
u
t
i
s
e
q
u
iv
ale
n
t
to
th
e
ar
ea
o
f
s
h
ad
e
d
m
o
d
u
le,
a
n
d
t
h
at
co
u
ld
b
e
a
cc
u
r
ate
f
o
r
a
s
i
n
g
le
s
h
ad
ed
ce
ll.
Sh
ad
i
n
g
ca
n
b
e
ap
p
lied
to
a
s
in
g
le
m
o
d
u
le
c
ell,
a
w
h
o
le
m
o
d
u
le,
o
r
an
ar
r
ay
.
S
h
ad
in
g
s
ar
e
d
iv
id
ed
in
to
t
w
o
ca
teg
o
r
ies:
1)
o
b
j
ec
tiv
e
s
h
ad
in
g
,
w
h
ich
is
p
r
o
d
u
ce
d
b
y
s
it
u
atio
n
s
f
u
r
th
er
th
an
h
u
m
a
n
co
n
tr
o
l
th
at
d
i
m
i
n
i
s
h
t
h
e
s
u
n
'
s
to
tal
i
n
ten
s
it
y
,
s
u
c
h
as
clo
u
d
co
v
er
,
h
az
e,
f
o
g
,
o
r
h
ea
v
y
p
o
llu
tio
n
;
an
d
2
)
s
u
b
j
ec
tiv
e
s
h
ad
i
n
g
,
w
h
ic
h
is
ca
u
s
ed
b
y
ite
m
s
b
lo
ck
i
n
g
i
n
co
m
in
g
s
o
lar
en
er
g
y
an
d
r
es
u
lti
n
g
i
n
s
h
ad
o
w
s
.
D
y
n
a
m
ic
s
h
ad
i
n
g
i
s
g
e
n
er
ated
b
y
th
i
n
g
s
th
at
ca
s
t
s
h
ad
o
w
s
d
ep
en
d
en
t
o
n
th
e
an
g
l
e
o
f
t
h
e
li
g
h
t,
w
h
e
r
ea
s
s
tatic
s
h
ad
e
is
g
en
er
ated
b
y
b
lo
ck
i
n
g
th
i
n
g
s
s
u
ch
a
s
b
ir
d
d
r
o
p
p
in
g
s
,
ac
cu
m
u
lated
d
ir
t,
leaf
d
r
o
p
p
in
g
s
,
a
n
d
s
o
o
n
.
3.
P
ARTI
A
L
SH
AD
I
N
G
CO
NDIT
I
O
N
O
N
T
H
E
P
E
RF
O
RM
ANCE
O
F
P
H
O
T
O
VO
L
T
AIC
SYST
E
M
S
E
n
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
,
alo
n
g
w
it
h
in
s
tal
lat
io
n
an
g
le
s
,
h
av
e
an
i
m
p
ac
t
o
n
th
e
s
o
lar
s
y
s
te
m
'
s
p
er
f
o
r
m
a
n
ce
s
a
n
d
ef
f
icie
n
cies
.
T
h
e
s
u
g
g
ested
tech
n
iq
u
e
ev
alu
a
tes
th
e
s
y
s
te
m
's
p
er
f
o
r
m
an
ce
u
s
i
n
g
p
ar
tial
s
h
ad
i
n
g
.
D
u
e
to
t
h
e
e
x
is
te
n
ce
o
f
i
m
p
ed
i
m
en
ts
i
n
t
h
e
p
r
o
x
i
m
i
t
y
o
f
P
V
s
y
s
te
m
s
d
ep
lo
y
ed
i
n
an
u
r
b
a
n
co
n
te
x
t,
it
is
n
o
r
m
a
l
f
o
r
t
h
e
in
s
tallat
io
n
to
ex
p
er
ien
ce
s
o
m
e
s
h
ad
in
g
[
2
2
]
,
[
2
3
]
.
T
h
e
in
f
l
u
en
ce
o
f
s
h
ad
in
g
w
ill
a
ls
o
b
e
d
eter
m
in
ed
b
y
a
n
u
m
b
er
o
f
p
ar
am
eter
s
,
in
c
lu
d
i
n
g
th
e
k
in
d
o
f
P
V
m
o
d
u
le,
b
y
p
ass
d
io
d
e
s
etu
p
,
s
tr
in
g
co
n
f
i
g
u
r
atio
n
,
an
d
th
e
f
o
r
m
o
f
th
e
s
h
ad
o
w
.
T
h
e
p
o
w
er
lo
s
s
co
u
ld
b
e
co
r
r
esp
o
n
d
in
g
l
y
g
r
ea
t
w
h
e
n
co
m
p
ar
ed
to
th
e
s
h
ad
in
g
ar
ea
in
t
h
e
p
ar
tial sh
ad
i
n
g
s
it
u
atio
n
o
f
t
h
e
m
o
d
u
l
e,
an
d
th
er
e
w
ill b
e
lo
s
s
o
w
i
n
g
to
th
e
in
co
n
s
is
ten
t
o
f
elec
tr
ical
c
u
r
r
en
t
a
m
o
n
g
th
e
s
a
m
e
s
tr
i
n
g
m
o
d
u
les,
a
s
w
el
l
as
a
lo
s
s
f
o
r
th
e
e
lectr
ical
v
o
ltag
e
m
is
m
atc
h
i
n
g
in
p
ar
allel
s
tr
i
n
g
s
f
o
u
n
d
ed
in
t
h
e
id
en
tical
ar
r
a
y
s
,
in
ad
d
itio
n
to
th
e
en
er
g
y
lo
s
s
e
s
o
w
in
g
to
s
h
ad
i
n
g
[
2
4
]
.
W
ith
th
e
p
u
r
p
o
s
e
o
f
m
in
i
m
izi
n
g
t
h
e
ef
f
ec
t
o
n
s
h
ad
i
n
g
’
s
p
o
w
er
g
e
n
er
atio
n
i
n
P
V
s
y
s
te
m
,
a
p
r
o
p
o
s
ed
m
o
d
u
le
h
as
b
y
p
ass
d
i
o
d
es
th
a
t,
o
n
ce
p
o
lar
ized
,
r
ed
ir
ec
t
th
e
cu
r
r
en
t
a
w
a
y
f
r
o
m
th
a
t
s
u
b
s
tr
i
n
g
.
W
h
en
t
h
e
ce
ll
's
elec
tr
ical
cu
r
r
en
t
is
lo
w
er
ed
b
y
s
h
ad
in
g
,
s
o
th
at
it
i
s
co
n
v
en
i
en
t
w
it
h
t
h
e
s
u
b
s
tr
in
g
c
u
r
r
en
t,
th
e
n
t
h
e
ce
ll
n
ee
d
s
to
b
e
r
ev
er
s
ely
p
o
lar
ized
to
a
ct
lik
e
a
ch
ar
g
e.
S
u
c
h
b
y
p
as
s
d
io
d
e
w
h
en
p
o
lar
ized
at
a
co
n
d
itio
n
o
f
s
u
b
s
tr
i
n
g
to
tal
v
o
ltag
e
s
ta
n
d
s
less
t
h
a
n
ze
r
o
,
f
o
r
cin
g
th
e
ce
ll
to
r
u
n
n
ea
r
to
th
e
v
o
ltag
e
[
2
5
]
,
[
2
6
]
.
A
t
th
at
p
o
in
t,
in
d
iv
id
u
al
c
u
r
v
e
s
o
f
ea
c
h
s
u
b
s
tr
in
g
b
esid
es
t
h
e
s
tr
in
g
's
s
er
i
es
-
p
ar
allel
ar
r
an
g
e
m
en
t
w
ill
r
esu
lt
in
th
e
c
u
r
r
en
t
v
er
s
u
s
v
o
lta
g
e
c
u
r
v
e
o
f
a
P
V
ar
r
ay
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
p
h
o
to
v
o
lt
aic
s
y
s
te
m
s
is
al
s
o
in
f
l
u
e
n
ce
d
b
y
s
h
ad
o
w
i
n
g
f
r
o
m
n
u
m
er
o
u
s
s
o
u
r
ce
s
s
u
c
h
as
clo
u
d
s
,
tr
ee
s
,
s
u
r
r
o
u
n
d
in
g
s
tr
u
ct
u
r
es,
a
n
d
s
o
o
n
.
A
s
a
r
esu
lt
o
f
t
h
is
p
h
en
o
m
en
o
n
,
th
e
s
u
n
'
s
r
ad
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n
d
o
es
n
o
t
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g
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ates
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[
30
]
.
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k
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o
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ith
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ased
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u
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e
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er
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er
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s
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ased
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ted
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ated
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les
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n
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er
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d
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n
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e
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n
in
F
ig
u
r
e
5
.
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h
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ir
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ad
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o
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t
h
ese
m
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le
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m
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Fig
u
r
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5
(
a)
an
d
5
(
b
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s
h
o
w
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h
e
ir
r
ad
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h
e
g
en
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ated
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m
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te
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r
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n
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er
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s
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n
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e
s
ee
n
in
Fi
g
u
r
e
6
.
Her
e
th
e
o
u
tp
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t
v
o
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e
i
s
p
r
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g
r
ess
i
v
el
y
in
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ea
s
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f
r
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ch
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0
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as o
b
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l
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n
Fig
u
r
e
6
(
a)
in
b
et
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th
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ti
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e
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e
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io
d
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6
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o
u
r
s
w
h
ic
h
r
ep
r
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t
t
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ir
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ay
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ith
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2
4
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o
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u
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6
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r
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w
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o
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s
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ter
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t
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e
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h
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t
h
e
P
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er
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g
o
u
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t
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eth
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n
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e
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in
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u
r
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P
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w
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Vo
l.
12
,
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.
4
,
Dec
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2021
:
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4
35
–
24
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NC
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S
[1
]
B.
M
e
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g
,
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C.
L
o
o
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n
,
a
n
d
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L
.
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se
n
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ta
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ter
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]
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[6
]
M
.
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sa
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z
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n
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.
[7
]
M
.
J.
M
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ti
,
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.
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.
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isa
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,
A
.
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.
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.
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li
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.
V
a
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ss
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h
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,
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n
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.
[8
]
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.
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n
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ti
,
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.
Ha
sa
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,
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.
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A
.
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sin
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y
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[9
]
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.
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.
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.
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0
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M.
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Yo
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2
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3
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4
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6
]
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[1
7
]
F.
Be
lh
a
c
h
a
t
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n
d
C.
L
a
rb
e
s,
“
G
lo
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l
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m
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m
p
o
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sh
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,
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[1
8
]
M
.
Am
in
,
J.
Ba
i
ley
,
C.
Tap
ia
,
a
n
d
V
.
T
h
o
d
im
e
lad
in
e
,
“
Co
m
p
a
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n
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f
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V
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g
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ra
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3
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9
]
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.
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ss
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.
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A
li
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Co
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0
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.
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Nu
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5
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8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
2
4
35
–
24
4
2
2442
[2
1
]
O.
Bin
g
ö
l
a
n
d
B.
Öz
k
a
y
a
,
“
A
n
a
ly
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a
n
d
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o
m
p
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o
f
d
if
f
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n
t
P
V
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d
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s
,
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ar
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rg
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0
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2
]
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.
L
.
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o
y
,
C.
G
.
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k
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d
i
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t
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p
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rti
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in
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n
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lar
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ste
m
w
it
h
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L
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tro
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r
,
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ter
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ti
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J
o
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rn
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we
r
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tro
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.
[2
3
]
M
.
J.
M
n
a
ti
,
A
.
H
a
sa
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,
D.
V
.
B
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z
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lak
o
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,
a
n
d
A
.
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.
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o
ss
c
h
e
,
“
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m
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rt
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o
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h
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to
v
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v
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sy
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m
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si
n
g
lo
ra
tec
h
n
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lo
g
y
.
6
th
Eu
r
,
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n
f.
Ren
.
E
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rg
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.
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.
[2
4
]
S
.
A
.
L
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f
ta,
A
.
H.
A
li
,
M
.
M
.
Ka
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.
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.
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ss
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A
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