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o
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as
w
ell
a
s
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n
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a
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o
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itio
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(
f
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e
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ail
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e
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4
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/
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.
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h
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o
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icate
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w
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g
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atio
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s
:[
3
]
W
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er
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s
.
F
o
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o
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an
,
to
p
alliate
th
e
s
u
cc
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io
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s
o
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n
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y
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a
y
s
.
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e
r
ea
s
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n
t
h
en
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n
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.
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h
e
n
ee
d
f
o
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ac
ity
is
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h
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s
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y
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wh
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u
t
as
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e
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it
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d
b
y
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ld
an
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o
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h
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to
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in
th
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s
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a
m
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e
.
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e
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tu
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l
ca
p
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it
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r
eq
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f
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e
Ah
7
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0
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4
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S
hort
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ter
m st
or
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g
e
DC
B
us
AC
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us
L
o
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t
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er
y
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t
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v
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ic
f
ield
PV
DC/DC
DC/DC
AC/DC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mo
d
elin
g
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n
d
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la
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P
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F
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W
(
S
a
la
h
E
d
d
i
n
e
Ma
n
ko
u
r
)
3273
2
.
1
.
Descript
io
n o
f
t
he
m
o
de
l o
f
a
ph
o
t
o
v
o
lt
a
ic
ce
ll :
T
h
e
m
at
h
e
m
atica
l
m
o
d
el
o
f
t
h
e
p
h
o
to
v
o
ltaic
g
en
er
ato
r
is
b
ased
o
n
th
e
o
n
e
-
d
io
d
e
eq
u
iv
al
en
t
cir
cu
i
t
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
T
h
e
r
elati
o
n
s
h
ip
b
et
w
ee
n
th
e
cu
r
r
en
t
I
an
d
th
e
v
o
lta
g
e
U
o
f
th
e
eq
u
i
v
alen
t
cir
cu
it
ca
n
b
e
f
o
u
n
d
b
y
eq
u
ati
n
g
t
h
e
li
g
h
t
cu
r
r
en
t
I
L
,
d
io
d
e
c
u
r
r
en
t
I
D
,
an
d
s
h
u
n
t
cu
r
r
e
n
t
I
sh
to
t
h
e
o
p
er
atio
n
cu
r
r
en
t
I
,
p
r
esen
ted
b
y
E
q
u
atio
n
5
.
Fig
u
r
e
2
.
C
ir
cu
it i
s
eq
u
i
v
alen
t f
o
r
a
m
o
d
el
to
a
d
io
d
e
o
f
a
g
en
er
ato
r
s
tate
m
en
t
T
h
e
j
u
n
ctio
n
f
o
r
m
i
n
g
t
h
e
b
as
is
o
f
th
e
s
o
lar
ce
ll
is
a
d
io
d
e,
w
h
e
n
ill
u
m
i
n
ated
ap
p
ea
r
s
in
th
e
d
io
d
e
p
h
o
to
cu
r
r
en
t
I
L
(
A
)
w
h
ic
h
d
ep
en
d
s
o
n
th
e
a
m
o
u
n
t
o
f
in
cid
en
t
lig
h
t
(
W
/
m
2
)
.
I
n
d
ee
d
,
th
e
eq
u
iv
ale
n
t
elec
tr
ica
l
cir
cu
it
o
f
t
h
e
s
o
lar
ce
l
l
is
b
as
ed
o
n
a
d
io
d
e
,
ad
d
in
g
t
w
o
r
esis
to
r
s
to
ac
co
m
m
o
d
ate
in
ter
n
al
lo
s
s
e
s
.
R
S
is
t
h
e
s
er
ies
r
esi
s
ta
n
ce
w
h
ich
tak
e
s
ac
co
u
n
t
o
f
t
h
e
o
h
m
ic
lo
s
s
e
s
o
f
th
e
m
ater
ial,
o
f
th
e
m
eta
ll
izatio
n
a
n
d
m
e
tal
/
s
e
m
i
co
n
d
u
cto
r
,
a
r
esis
to
r
R
P
is
cu
r
r
en
t
leak
a
g
e
f
r
o
m
p
ar
asit
ic
cu
r
r
en
ts
b
et
w
ee
n
t
h
e
to
p
an
d
b
o
tto
m
o
f
t
h
e
ce
ll,
b
y
t
h
e
ed
g
e
a
n
d
in
p
ar
ticu
l
ar
w
it
h
i
n
th
e
m
ater
ial
b
y
ir
r
eg
u
lar
i
ties
o
r
i
m
p
u
r
ities
(R
P
<<
R
S
).
A
p
p
l
y
i
n
g
Kir
ch
h
o
f
f
'
s
la
w
,
t
h
e
o
u
tp
u
t c
u
r
r
en
t
o
f
th
e
ce
l
l
is
g
iv
e
n
b
y
t
h
e
f
o
llo
w
in
g
r
elatio
n
s
h
ip
[
4
]
:
D
L
I
I
I
(
5
)
R
s
h
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s
U
a
k
T
IR
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q
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s
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1
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p
0
(
6
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w
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c
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r
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(
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)
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Ref
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(
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at
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r
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t
(
A
)
,
k
B
o
ltz
m
a
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n
'
s
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ta
n
t
(
1
.
3
8
0
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6
E
+
2
3
J
/K)
,
q
e
lectr
o
n
ch
ar
g
e
(
1
.
6
0
2
1
8
E
+1
9
C
)
,
T
C
tem
p
er
atu
r
e
ce
ll
(
K)
,
a
is
t
h
e
d
io
d
e
id
ea
lit
y
f
ac
to
r
,
I
t
d
ep
en
d
s
o
n
r
ec
o
m
b
in
atio
n
m
ec
h
a
n
is
m
s
i
n
t
h
e
s
p
ac
e
ch
ar
g
e
zo
n
e.
I
n
th
e
id
ea
l
ca
s
e,
R
s
te
n
d
s
to
war
d
s
0
an
d
R
s
h
to
i
n
f
in
it
y
.
An
d
in
t
h
e
r
ea
l
ca
s
e,
t
h
ese
r
esis
to
r
s
p
r
o
v
id
e
an
ass
es
s
m
en
t o
f
th
ei
m
p
er
f
ec
tio
n
s
o
f
th
e
d
io
d
e.
Fo
r
th
e
d
esig
n
o
f
o
u
r
p
h
o
to
v
o
ltaic
p
o
w
er
s
y
s
te
m
1
3
k
w
,
th
i
s
f
ield
co
n
s
is
t
s
o
f
p
h
o
to
v
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m
o
d
u
les
1
8
0
W
(
1
3
m
o
d
u
le
s
i
n
p
ar
allel
0
6
m
o
d
u
le
s
in
s
er
ies).
T
ab
le
1
p
r
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ts
t
h
e
ch
ar
ac
ter
is
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ic
o
f
s
elec
ted
P
an
el
T
ab
le
1.
E
lectr
ic
ch
ar
ac
ter
is
tics
o
f
a
p
h
o
to
v
o
ltaic
p
an
el
-
B
lu
e
So
lar
1
8
0
W
[
5
]
W
e
ca
r
r
ied
o
u
t
s
i
m
u
latio
n
,
t
o
leav
e
s
ta
n
d
ar
d
p
ar
am
e
ter
s
m
o
d
u
le
S
HE
L
L
SP
1
8
0
.
T
h
e
f
o
llo
w
i
ng
F
ig
u
r
e
3
an
d
F
i
g
u
r
e
4
p
r
ese
n
t
th
e
c
h
ar
ac
ter
is
t
ics
o
f
a
p
h
o
to
v
o
ltaic
m
o
d
u
le
f
ield
:o
n
e
tr
ac
ed
th
e
v
ar
iatio
n
o
f
th
e
cu
r
r
en
t
co
m
p
ar
ed
to
th
e
ten
s
io
n
f
o
r
s
ev
er
al
in
ten
s
itie
s
o
f
s
o
lar
ir
r
ad
iatio
n
.
On
th
e
o
th
er
h
an
d
,
th
e
o
th
e
r
n
o
tices
t
h
at
t
h
e
cu
r
r
en
t
i
s
d
ir
ec
tl
y
p
r
o
p
o
r
tio
n
al
to
th
e
r
ad
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n
o
n
th
e
s
e
lev
el
s
o
f
ill
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m
i
n
at
io
n
.
T
h
e
ten
s
io
n
i
s
n
o
t v
er
y
d
e
g
r
ad
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w
h
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n
t
h
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li
g
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t d
r
o
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.
p
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t
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t
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p
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9
0
V
0
5
.
5
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A
3
6
.
0
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V
0
5
.
0
1
A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
2
0
1
7
:
3
2
7
1
–
3
2
8
1
3274
Fig
u
r
e
3
.
C
u
r
v
e
s
ch
ar
ac
ter
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s
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o
f
a
s
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lar
f
ield
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f
1
3
k
w
(
B
lu
e
So
lar
1
8
0
W
)
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n
f
lu
e
n
ce
o
f
th
e
s
u
n
n
in
g
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co
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s
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n
t te
m
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at
u
r
e
(
2
5
°C
)
Fig
u
r
e
4
.
C
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r
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e
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o
f
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o
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f
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lar
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ield
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f
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3
k
w
(
B
lu
e
So
lar
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8
0
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)
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n
f
lu
e
n
ce
o
f
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h
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n
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n
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s
tan
t
te
m
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er
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r
e
(
2
5
°C
)
T
h
e
F
ig
u
r
e
5
a
n
d
F
i
g
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r
e
6
r
e
p
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t
c
h
ar
ac
ter
is
tic
s
I
-
V
a
n
d
P
-
V
o
f
t
h
e
p
h
o
to
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o
lta
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e
n
er
ato
r
f
o
r
r
esp
ec
tiv
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y
,
a
v
ar
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d
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(
1
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/m
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)
.
W
e
n
o
tic
e
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h
at
t
h
e
s
ite
o
f
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e
p
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o
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m
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-
V
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.
Fig
u
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e
5
.
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ter
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h
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ate
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ated
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r
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t o
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ter
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ac
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to
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ized
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tp
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t
2
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3
.
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nv
er
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er
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T
h
e
lo
ad
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A
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c
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r
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ter
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r
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th
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e
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t
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e
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ter
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u
ll
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atel
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th
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e
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h
e
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u
tp
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t
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s
es
d
r
a
m
atica
ll
y
.
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h
i
s
m
o
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el
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s
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ated
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y
Fig
u
r
e
8
[
7
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.
Fig
u
r
e
8
.
E
v
o
lu
tio
n
o
f
th
e
o
u
t
p
u
t o
f
th
e
i
n
v
er
ter
ac
co
r
d
in
g
t
o
s
tan
d
ar
d
ized
o
u
tp
u
t
3.
M
P
P
T
AL
G
O
RI
T
H
M
S
I
n
o
r
d
er
to
o
p
er
ate
a
P
V
s
y
s
te
m
w
it
h
i
n
it
s
MP
P
,
w
h
ate
v
er
t
h
e
ir
r
ad
ian
ce
an
d
ce
l
l
t
e
m
p
er
atu
r
e
v
ar
iatio
n
s
,
a
MP
P
T
m
et
h
o
d
i
s
n
ee
d
ed
to
f
i
n
d
a
n
d
m
a
in
ta
i
n
t
h
e
p
ea
k
p
o
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er
.
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h
i
s
s
tr
ateg
y
ai
m
s
to
f
in
d
t
h
e
v
o
ltag
e
o
r
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r
r
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t
o
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w
h
ic
h
t
h
e
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V
s
y
s
te
m
p
r
o
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id
es
t
h
e
m
ax
i
m
u
m
o
u
tp
u
t
p
o
w
er
.
I
n
t
h
is
w
o
r
k
w
e
w
ill
w
o
r
k
w
it
h
2
m
et
h
o
d
s
:
[
8
]
3
.
1
.
T
he
pert
ur
b a
nd
o
bs
er
v
e
m
e
t
ho
d (
P
&O
)
T
h
e
P
er
tu
r
b
an
d
Ob
s
er
v
e
(
P
&
O)
m
et
h
o
d
is
o
n
e
o
f
t
h
e
m
o
s
t
co
m
m
o
n
l
y
u
s
ed
m
et
h
o
d
s
in
p
r
ac
tice.
T
h
e
P
&
O
alg
o
r
ith
m
s
o
p
er
ate
b
y
p
er
io
d
ically
p
er
tu
r
b
in
g
,
i.e
.
in
cr
e
m
e
n
ti
n
g
o
r
d
ec
r
em
en
ti
n
g
,
th
e
ar
r
ay
ter
m
in
al
v
o
ltag
e
a
n
d
co
m
p
ar
in
g
th
e
P
V
o
u
tp
u
t
p
o
w
er
w
it
h
th
a
t
o
f
th
e
p
r
ev
io
u
s
p
er
tu
r
b
atio
n
c
y
c
le.
I
f
th
e
P
V
ar
r
ay
o
p
er
atin
g
v
o
lta
g
e
c
h
an
g
es
an
d
p
o
w
er
in
cr
ea
s
e
s
,
th
e
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n
tr
o
l s
y
s
te
m
m
o
v
e
s
t
h
e
P
V
ar
r
ay
o
p
e
r
atin
g
p
o
i
n
t i
n
th
a
t
d
ir
ec
tio
n
.
Oth
er
w
is
e
th
e
o
p
er
atin
g
p
o
in
t
is
m
o
v
ed
i
n
t
h
e
o
p
p
o
s
ite
d
ir
ec
tio
n
.
T
h
e
o
p
er
atin
g
v
o
lta
g
e
o
f
t
h
e
P
V
s
y
s
te
m
is
p
er
tu
r
b
ed
b
y
a
s
m
all
in
cr
e
m
e
n
t o
f
V,
an
d
t
h
is
r
es
u
l
tin
g
ch
a
n
g
e
in
P
.
I
f
P
is
p
o
s
iti
v
e,
th
e
p
er
tu
r
b
atio
n
o
f
th
e
o
p
er
atin
g
v
o
ltag
e
n
e
ed
s
to
b
e
in
th
e
s
a
m
e
d
ir
ec
tio
n
o
f
th
e
i
n
cr
e
m
e
n
t.
O
n
t
h
e
co
n
tr
ar
y
,
if
P
is
n
e
g
ati
v
e,
th
e
o
b
tain
ed
s
y
s
te
m
o
p
er
atin
g
p
o
in
t
m
o
v
es
a
w
a
y
f
r
o
m
th
e
MP
PT
an
d
th
e
o
p
er
atin
g
v
o
lta
g
e
n
ee
d
s
to
m
o
v
e
i
n
th
e
o
p
p
o
s
ite
d
ir
ec
tio
n
o
f
t
h
e
in
cr
e
m
e
n
t.
A
co
m
m
o
n
s
h
o
r
tco
m
in
g
o
f
t
h
is
m
eth
o
d
i
s
t
h
at
th
e
ar
r
a
y
ter
m
in
a
l
v
o
ltag
e
i
s
p
er
tu
r
b
ed
ev
er
y
M
P
PT
cy
cle.
T
h
er
ef
o
r
e,
w
h
e
n
t
h
e
MP
P
is
r
ea
ch
ed
,
th
e
o
u
tp
u
t
p
o
w
er
o
s
cillate
s
ar
o
u
n
d
th
e
m
ax
i
m
u
m
,
r
esu
l
tin
g
in
a
p
o
w
er
lo
s
s
in
t
h
e
P
V
s
y
s
te
m
.
F
u
r
t
h
er
m
o
r
e,
it
s
o
m
et
i
m
es
f
ail
s
to
f
i
n
d
th
e
MP
P
u
n
d
e
r
th
e
co
n
ti
n
u
o
u
s
l
y
i
n
cr
ea
s
i
n
g
o
r
d
ec
r
ea
s
in
g
ir
r
ad
iatio
n
co
n
d
itio
n
s
.
T
h
e
lo
g
ic
o
f
th
is
al
g
o
r
ith
m
a
n
d
th
e
f
lo
w
c
h
ar
t a
r
e
ex
p
lai
n
ed
in
Fig
u
r
e
9
[
9
]
.
0
0
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1
0
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2
0
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3
0
.
4
0
.
5
0
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6
0
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7
0
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0
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4
0
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5
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.
6
0
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7
0
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9
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P
s
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nom
R
e
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e
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l
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ur
2
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o
m
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97
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.
0
1
0
0
10
3
3
0
10
18
10
17
m
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mo
d
elin
g
a
n
d
S
imu
la
tio
n
o
f
a
P
h
o
to
vo
lta
ic
F
ield
fo
r
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K
W
(
S
a
la
h
E
d
d
i
n
e
Ma
n
ko
u
r
)
3277
Fig
u
r
e
9
.
P
&
O
m
et
h
o
d
f
lo
w
ch
ar
t
3
.
2
.
I
ncre
m
e
nta
l c
o
nd
uct
a
nce
M
et
ho
d
T
h
e
I
n
cr
e
m
e
n
tal
C
o
n
d
u
ctan
ce
(
I
NC
-
C
ON)
alg
o
r
it
h
m
i
s
b
as
ed
o
n
t
h
e
o
b
s
er
v
at
io
n
t
h
at
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
s
(
1
2
)
an
d
(
1
3
)
h
o
ld
f
o
r
th
e
MPP
.
T
h
e
p
r
in
cip
le
o
f
th
is
m
et
h
o
d
is
to
j
u
d
g
e
w
h
et
h
er
th
e
s
y
s
te
m
w
o
r
k
at
MP
P
o
r
w
o
r
k
at
t
h
e
le
f
t o
r
th
e
r
ig
h
t [
9
]
.
0
)
(
V
I
V
I
dV
dI
V
I
dV
IV
d
dV
dP
(
1
2
)
V
I
V
I
(
1
3
)
T
h
er
ef
o
r
e,
b
y
a
n
al
y
zi
n
g
th
e
d
er
iv
ativ
e,
o
n
e
ca
n
te
s
t
w
h
et
h
er
t
h
e
P
V
g
e
n
er
ato
r
is
o
p
er
atin
g
at
its
MP
P
o
r
f
ar
f
r
o
m
it
u
s
i
n
g
eq
u
at
io
n
s
f
o
llo
w
in
g
.
0
dV
dp
f
o
r
V<
V
MPP
(
1
4
)
0
dV
dp
f
o
r
V
=
V
MPP
(
1
5
)
0
dV
dp
f
o
r
V>
V
MPP
(
1
6
)
T
h
e
MPP
ca
n
th
u
s
b
e
tr
ac
k
ed
b
y
co
m
p
ar
in
g
t
h
e
i
n
s
ta
n
ta
n
eo
u
s
co
n
d
u
cta
n
ce
(
I
/V)
to
th
e
i
n
cr
e
m
en
ta
l
co
n
d
u
ctan
ce
(
∆I
/
∆V
)
.
V
ref
i
s
t
h
e
r
ef
er
e
n
ce
v
o
lta
g
e
at
w
h
ich
th
e
P
V
ar
r
ay
is
f
o
r
ce
d
to
o
p
er
ate.
On
ce
t
h
e
MP
P
is
r
ea
ch
ed
,
t
h
e
o
p
er
atio
n
o
f
t
h
e
P
V
ar
r
ay
i
s
m
ai
n
tai
n
ed
at
t
h
is
p
o
in
t
u
n
les
s
a
c
h
an
g
e
i
n
∆I
is
n
o
ted
,
i
n
d
icati
n
g
a
ch
an
g
e
i
n
at
m
o
s
p
h
er
ic
co
n
d
itio
n
s
a
n
d
th
e
MP
P
.
T
h
e
m
ai
n
ad
v
a
n
tag
e
s
o
f
t
h
e
I
NC
-
C
O
N
alg
o
r
ith
m
ar
e
t
h
e
s
tar
t
S
a
m
p
le V
(n
),
I(n
)
d
P
=
P
(n
)
-
P
(n
-
1
)
d
V
=
V
(n
)
-
V
(
n
-
1)
d
P
=
0
Vr
ef
=V
r
ef
-
dV
R
etu
r
n
Y
ES
Y
ES
d
V
<
0
d
V
>
0
Vr
ef
=V
r
ef
+d
V
Vr
ef
=V
r
ef
+d
V
Vr
ef
=V
r
ef
-
dV
Y
ES
Y
ES
NO
NO
NO
dP
>0
NO
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
2
0
1
7
:
3
2
7
1
–
3
2
8
1
3278
f
i
n
e
co
n
tr
o
l
t
h
e
s
y
s
te
m
o
b
tai
n
s
,
a
n
d
its
h
i
g
h
s
tab
ilit
y
u
n
d
er
r
ap
id
ly
c
h
an
g
i
n
g
at
m
o
s
p
h
e
r
ic
co
n
d
itio
n
s
.
T
h
e
f
lo
w
ch
ar
t o
f
th
i
s
m
e
th
o
d
is
as
s
h
o
w
n
in
F
ig
u
r
e
1
0
.
Fig
u
r
e
1
0
.
I
n
cr
em
e
n
tal
co
n
d
u
c
tan
ce
m
et
h
o
d
f
lo
w
c
h
ar
t
4.
CO
M
P
L
E
T
E
SY
ST
E
M
Fig
u
r
e
11
p
r
esen
ts
th
e
co
m
p
le
te
s
y
s
te
m
w
h
ich
m
ak
e
s
it
p
o
s
s
ib
le
to
ca
lc
u
late
t
h
e
p
o
in
t
s
o
f
o
p
er
atio
n
o
f
ea
ch
co
m
p
o
n
e
n
t
d
u
r
i
n
g
o
n
e
d
ay
co
m
p
lete
(
n
o
t
o
f
ti
m
e
1
0
m
i
n
u
te
s
)
.
T
h
is
m
o
d
el
is
m
ad
e
u
p
m
a
n
y
al
g
eb
r
aic
lo
o
p
s
:
T
h
e
s
y
s
te
m
is
co
n
tr
o
lled
in
p
o
w
er
.
T
h
e
elec
tr
ic
m
o
d
el
b
ein
g
th
e
ten
s
io
n
ac
co
r
d
in
g
t
o
th
e
i
n
ten
s
it
y
,
t
h
e
p
o
in
t
o
f
o
p
er
atio
n
m
u
s
t
b
e
r
e
q
u
ir
ed
to
o
b
tain
th
e
r
eq
u
ir
ed
p
o
w
er
.
T
h
e
o
th
er
lo
o
p
s
alg
eb
r
aic
ar
e
th
at
o
f
t
h
e
MP
U.
I
n
d
ee
d
,
at
th
e
m
o
m
e
n
t
T
,
o
n
e
k
n
o
w
s
t
h
e
p
o
w
er
o
f
t
h
e
s
tate
m
e
n
t,
h
is
te
n
s
io
n
a
n
d
t
h
e
p
o
w
er
r
eq
u
es
ted
b
y
t
h
e
lo
ad
.
Si
m
u
li
n
k
is
t
h
e
id
ea
l to
o
l to
s
o
lv
e
th
is
t
y
p
e
o
f
p
r
o
b
lem
[
10
].
Fig
u
r
e
11
.
C
o
m
p
lete
m
o
d
el
o
f
o
u
r
in
s
talla
tio
n
Re
tu
rn
S
a
m
p
le V
(n
),
I(n
)
∆
I=
I(n
)
-
I(n
-
1
)
∆
V
=
V
(
n
)
-
V
(n
-
1)
s
tar
t
V
re
f
=
V
re
f
+
d
V
V
re
f
=
V
re
f
-
dV
V
re
f
=
V
re
f
-
dV
V
re
f
=
V
re
f
+
d
V
∆
I
>
0
∆
I/
∆V
>
-
I
/
V
∆
I/
∆V
=
-
I
/
V
∆
I
=
0
∆V
=0
Y
ES
Y
ES
Y
ES
Y
ES
Y
ES
NO
NO
NO
l
o
a
d
P
ch
a
r
g
e
T
o
W
o
r
ksp
a
c
e
t
T
S
i
g
n
a
l
1
On
d
u
l
e
u
r
DC/A
C
/
Pe
(
W
)
Ps
(
W
)
M
P
U
P
p
v
(
W
)
P
ch
a
r
g
e
(
W
)
P
b
a
tt
e
r
i
e
(
W
)
Es
S
i
g
n
a
l
1
DC
/DC r
e
ce
i
v
e
r
Pe
(
W
)
Ps
(
W
)
DC
/
DC
G
é
n
e
r
a
te
u
r
Pe
(
W
)
Ps
(
W
)
Cl
o
c
b
a
tt
e
r
y
b
a
tt
e
r
y
P
h
o
to
vo
lta
i
c f
i
e
l
d
T
(
°C
)
G
(
W
/
m
2
)
P
g
é
n
(
W
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mo
d
elin
g
a
n
d
S
imu
la
tio
n
o
f
a
P
h
o
to
vo
lta
ic
F
ield
fo
r
1
3
K
W
(
S
a
la
h
E
d
d
i
n
e
Ma
n
ko
u
r
)
3279
4
.
1
.
P
o
w
er
m
a
na
g
e
m
ent
un
it
(
M
P
U)
T
h
e
s
y
s
te
m
is
co
n
tr
o
lled
in
p
o
w
er
,
th
e
m
o
d
el
allo
w
s
to
d
ef
i
n
e
th
e
MP
U,
P
pv
,
P
load
,
P
battery
d
ep
en
d
in
g
o
n
th
e
p
o
w
er
o
u
tp
u
t
o
f
t
h
e
PV
an
d
t
h
at
r
eq
u
ir
ed
b
y
t
h
e
lo
a
d
.
An
al
g
o
r
ith
m
f
o
r
p
o
w
er
m
a
n
ag
e
m
e
n
t
h
as
b
ee
n
d
ev
elo
p
ed
f
o
r
th
e
s
tu
d
ied
s
y
s
te
m
.
E
n
er
g
y
b
ala
n
ce
s
ar
e
alw
a
y
s
m
ad
e
at
th
e
co
m
m
o
n
b
u
s
co
n
n
ec
tin
g
th
e
d
if
f
er
e
n
t
co
m
p
o
n
e
n
t
s
o
f
t
h
e
e
n
er
g
y
s
y
s
te
m
.
T
h
e
p
r
io
r
it
y
is
to
p
r
o
v
id
e
th
e
en
er
g
y
r
eq
u
ir
e
d
b
y
t
h
e
u
s
er
f
r
o
m
th
e
e
n
er
g
y
p
r
o
d
u
ce
d
b
y
th
e
p
h
o
to
v
o
ltaic
f
ie
ld
.
T
h
e
en
er
g
y
d
eliv
er
ed
to
th
e
u
s
er
is
m
ai
n
l
y
p
h
o
to
v
o
ltaic
p
an
el
s
.
T
h
e
alg
o
r
ith
m
o
f
th
e
e
n
er
g
y
f
l
o
w
f
o
llo
w
s
th
e
s
e
r
u
le
s
:
1.
If
th
e
p
o
w
er
r
eq
u
ir
ed
b
y
t
h
e
lo
ad
is
less
t
h
an
t
h
e
p
o
w
er
av
a
il
ab
le
s
o
lar
:
a.
T
h
e
b
atter
y
is
c
h
ar
g
ed
in
s
ec
u
r
it
y
p
r
io
r
it
y
if
n
ec
es
s
ar
y
.
b.
T
h
e
lo
ad
ca
n
o
n
ly
w
o
r
k
i
f
t
h
e
b
atter
ies
h
av
e
a
h
i
g
h
le
v
el
o
f
c
ar
e.
2.
I
f
t
h
e
ex
ce
s
s
s
o
lar
can
b
e
co
n
s
u
m
ed
eith
er
b
y
b
atter
y
o
r
by
th
e
b
atter
y
,
t
h
e
v
o
ltag
e
o
f
th
e
s
o
lar
f
ield
in
cr
ea
s
es,
t
h
u
s
r
ed
u
ci
n
g
t
h
e
in
ten
s
i
t
y
a
n
d
th
e
p
o
w
er
d
eliv
er
e
d
b
y
th
e
g
en
er
ato
r
r
en
e
w
ab
le
.
T
h
is
m
et
h
o
d
is
illu
s
tr
ated
b
y
Fig
u
r
e
1
2
.
Fig
u
r
e
12.
Sch
e
m
at
ic
MP
U
-
C
alcu
latio
n
o
f
p
o
w
er
of
ea
ch
co
m
p
o
n
e
n
t o
n
t
h
e
bus
5.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S
W
e
ch
o
s
e
to
s
tu
d
y
th
e
s
y
s
te
m
w
h
er
e
it
is
a
u
to
n
o
m
o
u
s
o
v
er
o
n
e
y
ea
r
o
f
o
p
er
atio
n
.
T
h
e
p
o
w
er
o
f
th
e
co
m
p
o
n
e
n
t
s
b
ein
g
f
i
x
ed
,
o
n
e
d
eter
m
in
e
s
th
e
a
v
er
ag
e
ch
ar
g
e
av
ailab
le
an
d
th
e
v
o
lu
m
e
o
f
s
to
r
ag
e
n
ec
ess
ar
y
to
th
e
au
to
n
o
m
y
o
f
th
e
s
t
u
d
ied
s
y
s
te
m
.
W
e
w
ill
ev
al
u
ate
t
h
e
in
f
lu
e
n
ce
o
f
th
e
v
ar
io
u
s
p
ar
a
m
eter
s
o
f
th
e
s
y
s
te
m
in
o
r
d
er
to
d
eter
m
i
n
e
th
e
p
e
r
f
o
r
m
an
ce
o
f
th
e
s
y
s
te
m
.
Se
lecte
d
lo
ca
liz
atio
n
:
Or
an
-
A
l
g
er
ia.
T
h
e
av
er
ag
e
s
u
n
n
in
g
i
s
o
f
5
,
2
k
W
h
/
m
²
p
er
d
ay
in
a
p
lan
i
n
cli
n
ed
w
it
h
4
5
°
(
s
lo
p
e
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
els).
F
i
g
u
r
e
1
3
p
r
esen
t d
escr
ib
es th
e
e
v
o
lu
t
io
n
o
f
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1
2
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1000
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