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i
n
atio
n
an
d
te
m
p
er
atu
r
e:
(
1
)
Or
I
p
v
,
n
i
s
t
h
e
n
o
m
i
n
al
c
u
r
r
en
t
(
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iv
e
n
u
n
d
er
n
o
m
i
n
al
co
n
d
itio
n
s
:
T
=
2
5
°
C
a
n
d
G
=
1
0
0
0
W
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m
2
)
,
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is
t
h
e
Sh
o
r
t
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cir
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it
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r
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n
t
/
te
m
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atu
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e
f
f
icien
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Δ
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=
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n
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d
T
n
ar
e
th
e
c
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r
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a
n
d
n
o
m
i
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te
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er
atu
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e
R
esp
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ti
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el
y
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G
an
d
G
n
ar
e
t
h
e
c
u
r
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en
t
a
n
d
n
o
m
i
n
al
ill
u
m
in
atio
n
.
T
h
e
cu
r
r
en
t
in
t
h
e
d
io
d
e
is
g
iv
e
n
b
y
:
(
2
)
W
ith
I
0
th
e
s
at
u
r
atio
n
c
u
r
r
en
t
o
f
th
e
d
io
d
e:
(
3
)
I
s
c,
n
i
s
t
h
e
n
o
m
i
n
al
s
h
o
r
t
-
cir
cu
it
c
u
r
r
en
t,
Vo
c,
n
is
th
e
n
o
m
i
n
al
o
p
en
-
cir
c
u
it
v
o
lta
g
e.
KV
i
s
t
h
e
o
p
e
n
cir
cu
it
v
o
ltag
e
/ te
m
p
er
at
u
r
e
c
o
ef
f
icie
n
t,
a
i
s
a
co
n
s
ta
n
t o
f
th
e
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io
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e,
Vt
is
th
e
t
h
er
m
al
v
o
lt
ag
e
o
f
t
h
e
p
a
n
el:
Vt
=N
s
k
T
/q
,
w
h
er
e
N
s
i
s
t
h
e
n
u
m
b
er
o
f
ce
lls
co
n
n
ec
ted
in
s
e
r
ies,
k
is
B
o
ltz
m
a
n
n
's
co
n
s
ta
n
t,
q
is
th
e
ch
ar
g
e
o
f
th
e
elec
tr
o
n
.
R
s
is
t
h
e
s
er
ie
s
r
e
s
is
ta
n
ce
o
f
th
e
ce
ll (
d
ep
en
d
s
o
n
t
h
e
m
ate
r
ial
u
s
ed
to
co
n
s
tr
u
c
t th
e
ce
ll,
its
e
f
f
ec
t
is
m
o
r
e
i
m
p
o
r
tan
t
i
n
th
e
v
o
lta
g
e
s
o
u
r
ce
o
p
er
atin
g
r
eg
io
n
)
.
R
p
is
th
e
p
ar
allel
r
esis
to
r
,
its
ef
f
ec
t
is
g
r
ea
ter
in
t
h
e
cu
r
r
en
t
s
o
u
r
ce
o
p
er
atin
g
r
e
g
io
n
)
.
I
n
g
e
n
er
al,
t
h
e
v
al
u
e
s
o
f
t
h
e
r
esis
to
r
s
ar
e
n
o
t
g
iv
e
n
b
y
t
h
e
co
n
s
tr
u
cto
r
an
d
m
u
s
t b
e
d
eter
m
i
n
ed
b
y
i
ter
ativ
e
alg
o
r
ith
m
s
[
3
]
.
2
.
2
.
M
o
del o
f
a
ph
o
t
o
v
o
l
t
a
ic
f
iled
A
p
h
o
to
v
o
ltaic
f
ie
ld
w
i
th
Np
p
p
an
el
in
p
ar
allel
an
d
Ns
s
p
an
e
l in
s
er
ies i
s
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
T
h
e
o
u
tp
u
t c
u
r
r
en
t i
s
th
e
n
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
A
p
p
lica
tio
n
a
n
d
C
o
mp
a
r
is
o
n
B
etw
ee
n
th
e
C
o
n
ve
n
tio
n
a
l Me
th
o
d
s
a
n
d
P
S
O
Meth
o
d
…
(
B
en
n
is
Gh
ita
)
633
(
4
)
T
h
e
f
o
llo
w
i
n
g
tab
le
g
iv
e
s
th
e
p
ar
am
eter
s
o
f
th
e
p
h
o
to
v
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ltaic
p
an
el
u
s
ed
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h
e
f
o
llo
w
i
n
g
p
ar
ag
r
ap
h
s
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I
s
cn
is
th
e
n
o
m
in
al
s
h
o
r
t
-
cir
c
u
it
c
u
r
r
en
t
at
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
ST
C
)
(
2
5
°
C
an
d
1
0
0
0
W
/
m
²)
,
I
p
v
n
i
s
th
e
n
o
m
i
n
al
cu
r
r
en
t
o
f
th
e
p
a
n
el
Ns
i
s
th
e
n
u
m
b
er
o
f
ce
lls
(
in
s
er
ies)
f
o
r
ea
ch
p
an
el,
a
i
s
a
co
n
s
ta
n
t
o
f
th
e
d
io
d
e,
Np
p
is
th
e
n
u
m
b
er
o
f
m
o
d
u
les
co
n
n
ec
ted
in
p
ar
all
el,
Nss
i
s
t
h
e
n
u
m
b
er
o
f
co
n
n
ec
ted
m
o
d
u
les
I
n
s
er
ies
.
T
ab
le
1
.
P
V
P
an
el
Settin
g
s
.
Pa
r
a
m
e
t
e
r
V
a
l
u
e
I
scn
5
.
9
6
I
p
v
n
6
.
1
0
V
o
c
n
6
4
.
2
Ns
96
a
1
.
3
9
7
7
Ki
0
.
0
6
5
%
/
°
C
Kv
0
.
0
8
0
V
/
°
C
N
p
p
3
N
ss
5
Fig
u
r
e
3
.
C
o
n
f
ig
u
r
i
n
g
t
h
e
P
V
S
y
s
te
m
.
3.
P
ho
t
o
v
o
lt
a
ic
F
ield Co
ntr
o
l
A
p
h
o
to
v
o
ltaic
f
ie
ld
is
th
e
co
m
b
in
at
io
n
o
f
s
ev
er
al
P
V
p
an
els
co
n
n
ec
ted
in
s
er
ie
s
an
d
p
ar
allel,
th
e
s
lig
h
te
s
t d
ef
ec
t o
n
o
n
e
o
f
th
e
p
an
els ca
n
ca
u
s
e
th
e
p
er
f
o
r
m
an
ce
d
eg
r
ad
atio
n
o
f
th
e
e
n
tire
P
V
f
ield
[
4
-
7
]
.
T
h
at
is
w
h
y
r
esear
c
h
h
as
p
r
o
p
o
s
ed
an
ar
ch
itect
u
r
e
o
r
a
co
n
tr
o
ller
is
p
lace
d
at
ea
ch
s
et
o
f
s
m
all
n
u
m
b
er
ed
p
an
el
s
i
n
o
r
d
er
to
m
a
n
a
g
e
t
h
e
P
V
f
ield
d
ec
e
n
t
r
all
y
.
De
s
p
ite
t
h
e
e
f
f
ec
ti
v
en
e
s
s
o
f
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
,
th
e
to
tal
co
s
t
o
f
s
u
c
h
a
n
i
n
s
talla
tio
n
b
ec
o
m
e
s
u
n
a
f
f
o
r
d
ab
le.
R
ea
s
o
n
o
n
e
co
n
s
id
e
r
s
in
th
i
s
w
o
r
k
th
e
ar
ch
itect
u
r
e
o
r
a
s
in
g
le
co
n
tr
o
l
m
u
s
t
m
an
a
g
e
t
h
e
w
h
o
le
f
ield
P
V.
3
.
1
Co
nfig
uring
t
he
Co
ntr
o
ller
A
D
C
/ D
C
b
o
o
s
ter
co
n
v
er
ter
is
u
s
ed
to
o
b
tain
an
o
u
tp
u
t
v
o
l
tag
e
h
ig
h
er
t
h
an
t
h
at
p
r
o
v
id
ed
b
y
th
e
P
V
f
ield
.
T
h
e
P
V
s
y
s
te
m
s
t
u
d
ied
is
illu
s
tr
ated
in
F
ig
u
r
e
3
.
C
o
n
tr
o
ller
p
ar
am
eter
s
ar
e
g
i
v
e
n
in
T
ab
le
2
.
T
ab
le
2
.
C
o
n
tr
o
ller
Settin
g
s
.
a
C
o
m
p
o
n
e
n
t
v
a
l
u
e
C
i
n
1
µ
F
L
0
.
0
0
5
µ
H
C
o
u
t
2
4
0
0
0
µ
F
RL
1
0
0
Ω
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.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
631
–
640
634
Fig
u
r
e
4
.
C
h
ar
ac
ter
is
t
ic
C
u
r
v
e
o
f
a
P
V
P
an
el.
3
.
2
Co
ntr
o
l A
lg
o
rit
h
m
s
1.
P
&
O
alg
o
r
ith
m
:
Sev
er
al
al
g
o
r
ith
m
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
th
e
liter
at
u
r
e
to
ex
tr
ac
t
th
e
m
a
x
i
m
u
m
p
o
w
er
f
r
o
m
P
V
in
s
ta
llatio
n
s
.
T
h
e
s
i
m
p
le
s
t
a
n
d
f
aste
s
t
co
m
p
u
tatio
n
al
t
i
m
e
alg
o
r
it
h
m
i
s
t
h
e
P
&
O
(
P
er
tu
r
b
&
Ob
s
er
v
e)
alg
o
r
ith
m
w
h
ic
h
is
b
ased
o
n
th
e
d
is
t
u
r
b
an
ce
o
f
t
h
e
r
ef
er
en
ce
c
u
r
r
en
t
to
v
i
s
u
a
lize
t
h
e
d
ir
ec
tio
n
o
f
p
o
w
er
p
r
o
g
r
ess
io
n
.
Fi
g
u
r
e
4
ill
u
s
tr
at
es
t
h
e
p
r
in
cip
le
o
f
t
h
is
co
n
tr
o
l,
th
e
o
b
j
ec
tiv
e
i
s
to
r
ea
ch
th
e
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t (
MP
P)
in
a
m
in
i
m
u
m
o
f
ti
m
e[
1
-
2
]
.
T
h
e
f
lo
w
ch
ar
t
o
f
th
e
'
P
&
O
'
c
o
m
m
a
n
d
i
s
g
i
v
en
in
Fi
g
u
r
e
5
.
T
h
e
o
p
tim
izatio
n
alg
o
r
it
h
m
r
e
q
u
ir
es
t
h
e
p
r
esen
ce
o
f
a
v
o
lta
g
e
an
d
a
cu
r
r
en
t sen
s
o
r
to
b
e
ab
le
to
id
en
tify
th
e
d
ir
ec
tio
n
i
n
w
h
ich
t
h
e
p
o
w
er
ev
o
lv
e
s
.
Fig
u
r
e
5
.
Flo
w
c
h
ar
t o
f
t
h
e
P
&
O
o
p
t
i
m
izat
io
n
al
g
o
r
ith
m
.
2.
Fu
zz
y
L
o
g
ic
Fu
zz
y
lo
g
ic
a
s
s
er
ts
it
s
el
f
as
a
n
o
p
er
atio
n
al
tech
n
iq
u
e.
Used
alo
n
g
s
id
e
o
t
h
er
tec
h
n
iq
u
es
f
o
r
ad
v
an
ce
d
co
n
tr
o
l,
it
m
a
k
es
a
d
is
cr
ee
t
en
tr
an
ce
b
u
t
p
o
p
u
lar
i
n
i
n
d
u
s
tr
ia
l
co
n
tr
o
l
au
to
m
atio
n
.
Fu
zz
y
c
o
n
tr
o
ller
is
d
iv
id
ed
in
to
th
r
ee
s
tep
s
ill
u
s
tr
ated
in
F
ig
u
r
e
6.
Fig
u
r
e
6
.
Step
s
o
f
f
u
zz
y
co
n
tr
o
l
Fig
u
r
e
7
.
Nu
m
er
ic
r
es
u
lt o
b
tai
n
ed
b
y
in
f
er
en
ce
b
lo
ck
f
o
r
E
=0
an
d
Δ
E
=0
.
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
A
p
p
lica
tio
n
a
n
d
C
o
mp
a
r
is
o
n
B
etw
ee
n
th
e
C
o
n
ve
n
tio
n
a
l Me
th
o
d
s
a
n
d
P
S
O
Meth
o
d
…
(
B
en
n
is
Gh
ita
)
635
F
uzzica
t
io
n:
T
h
is
s
ec
tio
n
tr
an
s
f
o
r
m
s
i
n
p
u
ts
in
to
f
u
zz
y
v
ar
iab
les.
T
h
e
in
p
u
t
s
ar
e
tr
a
n
s
f
o
r
m
ed
in
t
o
lin
g
u
i
s
tic
v
ar
iab
les
d
escr
ib
ed
b
y
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
.
T
h
ese
f
u
n
ctio
n
s
ca
n
tak
e
m
a
n
y
f
o
r
m
s
:
tr
ia
n
g
u
lar
,
tr
ap
ez
o
id
al,
b
ell
o
r
o
th
er
.
T
h
i
s
f
u
zz
y
co
n
tr
o
ller
u
s
e
s
tr
ap
ez
o
id
a
l
an
d
tr
ian
g
u
lar
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
.
T
h
e
in
p
u
t
an
d
o
u
tp
u
t
v
ar
iab
les
w
i
l
l
b
e
tr
an
s
f
o
r
m
ed
to
t
h
e
f
o
llo
win
g
li
n
g
u
i
s
tic
v
ar
iab
les:
1
.
N
G:
Gr
an
d
n
eg
at
iv
e,
2
.
NM
:
Mid
d
le
n
eg
ati
v
e,
3
.
N:
Neg
ati
v
e,
4
.
Z
E
:
Z
er
o
,
5
.
P
:
P
o
s
itiv
e,
6
.
P
M:
Mid
d
le
p
o
s
itiv
e,
7
.
P
G:
Gr
a
n
d
p
o
s
itiv
e.
I
nte
rf
er
ence
:
I
t
g
iv
es
t
h
e
r
el
atio
n
s
h
ip
b
et
w
ee
n
in
p
u
t
an
d
o
u
tp
u
t
v
ar
iab
les
in
la
n
g
u
a
g
e
f
o
r
m
.
T
h
er
e
ar
e
s
ev
er
al
m
et
h
o
d
s
o
f
i
n
f
er
en
ce
:
M
AX
-
MI
N,
M
A
X
-
P
R
O
D
an
d
SUM
-
P
R
OD.
E
ac
h
m
eth
o
d
tak
e
s
it
s
o
w
n
o
p
er
ato
r
s
an
d
ea
ch
r
u
le
h
as t
h
e
f
o
llo
w
in
g
f
o
r
m
:
I
f
(
Co
nd
it
io
n),
T
hen (
Co
nclu
s
io
n)
T
h
e
m
eth
o
d
u
s
ed
b
y
th
i
s
f
u
z
z
y
co
n
tr
o
ller
i
s
t
h
e
M
A
X
-
MI
N
m
et
h
o
d
.
I
n
t
h
is
m
e
th
o
d
t
h
e
o
p
er
ato
r
s
A
N
D,
OR
an
d
T
h
en
ar
e
r
ep
r
esen
ted
b
y
th
e
MI
N
a
n
d
MA
X.
Def
uzzif
ica
t
io
n:
Du
r
in
g
t
h
is
s
tep
,
th
e
r
esu
lt
p
r
o
v
id
ed
b
y
th
e
f
u
zz
y
i
n
f
er
en
ce
o
u
tp
u
t
d
D
i
s
co
n
v
er
ted
to
r
ea
l
v
alu
e
o
r
n
u
m
er
ical
v
al
u
e.
W
e
d
is
tin
g
u
is
h
s
e
v
er
al
m
eth
o
d
s
o
f
d
ef
u
zz
i
f
icatio
n
:
th
e
m
ax
i
m
u
m
m
et
h
o
d
,
th
e
w
ei
g
h
ted
av
er
a
g
e
m
et
h
o
d
,
s
i
m
p
li
f
ied
m
et
h
o
d
o
f
ce
n
t
r
o
id
,
th
e
ce
n
tr
o
id
m
eth
o
d
a
n
d
o
th
er
s
.
T
h
e
u
s
ed
m
et
h
o
d
b
y
t
h
e
u
s
ed
f
u
zz
y
co
n
tr
o
ller
is
t
h
e
ce
n
tr
o
id
m
et
h
o
d
.
T
h
is
m
et
h
o
d
w
ill
t
h
en
co
n
v
er
t
th
e
r
es
u
lt
o
f
th
e
f
u
zz
y
o
u
tp
u
t
v
ar
iab
le
d
D
to
th
e
d
u
t
y
r
atio
v
ar
iatio
n
s
th
at
w
il
l
b
e
ac
ce
p
tab
le
b
y
th
e
co
n
v
er
ter
.
T
h
e
ce
n
tr
o
id
m
et
h
o
d
ca
lcu
lates t
h
e
ce
n
ter
o
f
g
r
a
v
it
y
o
f
t
h
e
f
u
zz
y
s
u
r
f
ac
e
o
b
tain
ed
b
y
t
h
e
in
f
er
e
n
ce
b
lo
ck
(
f
i
g
u
r
e
7
)
.
[
9
]
4
AP
P
L
I
CA
T
I
O
N
O
F
P
SO
O
N
M
P
P
T
T
o
illu
s
tr
ate
t
h
e
ap
p
licatio
n
o
f
th
e
P
SO a
lg
o
r
ith
m
i
n
tr
ac
k
i
n
g
th
e
MP
P
u
s
in
g
th
e
i
m
p
r
o
v
ed
t
ec
h
n
iq
u
e
)
(
)
(
2
2
1
1
1
k
id
k
b
e
s
t
k
k
id
k
b
e
s
t
k
k
id
k
id
x
G
r
c
x
P
r
c
v
v
d
d
1
1
k
id
k
id
k
id
v
x
x
(
5
)
th
e
p
ar
ticle
p
o
s
itio
n
x
i
is
ad
j
u
s
ted
w
h
er
e
th
e
v
elo
cit
y
co
m
p
o
n
en
t
v
i
r
ep
r
esen
ts
t
h
e
s
tep
s
i
ze
,
w
is
th
e
i
n
er
tia
w
ei
g
h
t,
C
1
an
d
C
2
ar
e
th
e
ac
ce
ler
atio
n
co
ef
f
ic
ien
t
s
,
r
1
,
r
2
ϵ
U(
0
,
1
)
,
P
b
esti
is
th
e
p
er
s
o
n
al
b
est
p
o
s
itio
n
o
f
p
ar
ticle
,
an
d
Gb
esti
is
th
e
b
est
p
o
s
itio
n
o
f
th
e
p
ar
ticle
s
i
n
t
h
e
e
n
tire
p
o
p
u
latio
n
.
I
f
p
o
s
iti
o
n
is
d
e
f
i
n
ed
as
t
h
e
ac
tu
al
d
u
t
y
c
y
c
le
w
h
i
le
v
elo
cit
y
s
h
o
w
s
t
h
e
p
er
tu
r
b
atio
n
in
t
h
e
p
r
esen
t d
u
t
y
c
y
cle,
t
h
en
ca
n
b
e
r
ew
r
it
ten
:
)
(
)
(
2
2
1
1
1
k
id
k
b
e
s
t
k
k
id
k
b
e
s
t
k
k
id
k
id
d
G
r
c
d
P
r
c
d
d
1
k
id
k
id
k
id
d
d
(
6
)
I
n
th
e
ca
s
e
o
f
P
SO,
r
esu
lti
n
g
p
er
tu
r
b
atio
n
in
t
h
e
p
r
esen
t
d
u
t
y
c
y
cle
d
ep
en
d
s
o
n
P
b
esti
a
n
d
Gb
est.
I
f
I
f
th
e
p
r
esen
t
d
u
t
y
c
y
cle
(
D)
is
f
ar
f
r
o
m
t
h
ese
t
w
o
d
u
t
y
c
y
cl
es,
th
e
r
esu
lti
n
g
c
h
an
g
e
i
n
th
e
d
u
t
y
c
y
cle
w
ill
also
b
e
lar
g
e,
an
d
v
ice
v
er
s
a.
I
n
th
e
last
,
th
e
p
er
tu
r
b
atio
n
in
th
e
D
is
al
w
a
y
s
f
ix
ed
b
u
t
i
n
P
SO
it
v
ar
ies
ac
co
r
d
in
g
to
th
e
p
o
s
itio
n
o
f
t
h
e
p
ar
ticles.
W
ith
p
r
o
p
er
ch
o
ice
o
f
co
n
tr
o
l
p
ar
a
m
eter
s
,
a
s
u
itab
le
Ma
x
i
m
u
m
p
o
w
er
p
o
i
n
t
tr
ac
k
in
g
co
n
tr
o
ller
u
s
i
n
g
P
SO
ca
n
b
e
ea
s
il
y
d
esi
g
n
ed
.
4
.
1
M
P
P
T
f
o
r
s
ing
le
pea
k
First a
s
o
lu
tio
n
v
ec
to
r
o
f
d
u
t
y
c
y
cles
w
i
th
Np
p
ar
ticles is
d
et
er
m
in
ed
,
i.e
:
dg
=
[
d1,d2,d3,...,di]
i=1,2,3,...,N
(
7
)
w
h
er
e
d
g
is
t
h
e
d
u
t
y
c
y
cle
o
f
t
h
e
DC
-
D
C
co
n
v
er
to
r
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
is
d
ef
i
n
ed
as:
)
(
)
(
1
k
i
k
i
d
P
d
P
(
8
)
)
(
k
i
d
P
is
th
e
p
o
w
er
f
o
r
p
ar
ticle
i a
t iter
atio
n
k
,
h
a
v
i
n
g
a
d
u
t
y
c
y
cle.
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.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
631
–
640
636
Fig
u
r
e
8
.
P
SO p
ar
ticle
m
o
v
e
m
en
ts
i
n
s
ea
r
c
h
in
g
f
o
r
th
e
MP
P
Fig
u
r
e
9
.
MP
PT
tr
ac
k
in
g
b
y
P
SO d
u
r
in
g
p
ar
tial
s
h
ad
i
n
g
T
h
e
s
ea
r
ch
p
r
o
ce
s
s
b
eg
in
s
to
tr
an
s
m
it
s
th
r
ee
d
u
t
y
c
y
cles
d
i
(
i=
1
,
2
,
3
)
to
th
e
p
o
w
er
co
n
v
er
ter
.
I
n
f
i
g
u
r
e
8
,
d
u
t
y
c
y
cle
s
d
1
,
d
2
,
a
n
d
d
3
ar
e
in
d
icate
d
,
w
ith
tr
ia
n
g
u
lar
,
cir
cu
lar
,
an
d
s
q
u
ar
e
p
o
in
ts
,
r
esp
ec
ti
v
el
y
.
i
n
th
e
f
ir
s
t
iter
atio
n
,
T
h
ese
d
u
t
y
c
y
cles
s
er
v
ed
as
t
h
e
P
b
esti
.
Am
o
n
g
t
h
ese,
d
2
is
t
h
e
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est
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at
o
f
f
er
th
e
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t
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n
e
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e,
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s
ill
u
s
tr
ated
b
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u
r
e
8
(
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.
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r
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g
t
h
e
n
ex
t
iter
atio
n
,
th
e
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n
g
v
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y
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o
n
l
y
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u
e
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e
Gb
est
ter
m
.
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h
e
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P
b
esti
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(
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o
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h
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a
ze
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v
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d
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n
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ed
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A
s
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lt,
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ar
ticle
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t
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ec
t
in
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e
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lo
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atio
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r
o
ce
s
s
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c
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F
ig
u
r
e
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b
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,
t
o
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s
u
r
e
t
h
e
c
h
a
n
g
e
i
n
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it
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e
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s
v
al
u
e.
F
ig
u
r
e
8
(
c)
p
r
esen
t
th
e
p
ar
ticles
m
o
v
e
m
e
n
t
i
n
t
h
e
th
ir
d
iter
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n
.
D
u
e
to
t
h
e
f
ac
t
th
at
all
t
h
e
D
in
th
e
p
r
ev
io
u
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iter
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n
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ain
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b
etter
f
i
tn
e
s
s
v
alu
e,
t
h
e
v
elo
cit
y
d
ir
ec
tio
n
o
f
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h
ese
p
ar
ticles
r
e
m
ai
n
s
u
n
ch
an
g
ed
a
n
d
s
u
b
s
eq
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e
n
tl
y
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e
y
m
o
v
e
to
w
ar
d
Gb
est
alo
n
g
th
e
s
a
m
e
d
ir
ec
tio
n
.
I
n
t
h
is
iter
atio
n
,
al
l
d
u
t
y
c
y
cles
(
d
i,i=
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2
,
3
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ar
r
iv
e
at
Ma
x
i
m
u
m
P
o
w
er
P
o
in
t
w
it
h
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lo
w
v
al
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e
o
f
v
elo
cit
y
.
I
n
th
e
s
u
b
s
eq
u
e
n
t
iter
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n
,
d
u
e
to
v
er
y
lo
w
v
elo
cit
y
,
t
h
e
v
alu
e
o
f
th
e
D
i
s
ap
p
r
o
ac
h
in
g
a
co
n
s
ta
n
t.
w
h
er
ef
o
r
e,
th
e
o
p
er
atin
g
p
o
i
n
t
w
i
l
l
b
e
k
ee
p
ed
an
d
t
h
e
o
s
cillatio
n
ar
o
u
n
d
t
h
e
MP
P
d
i
m
in
is
h
es.
4
.
2
M
P
P
T
f
o
r
m
ulti
-
pea
ks
W
h
en
t
h
e
p
h
o
to
v
o
ltaic
ar
r
ay
is
o
p
er
atin
g
in
a
u
n
if
o
r
m
s
o
lar
in
s
o
latio
n
,
t
h
e
r
es
u
lti
n
g
P
−V
ch
ar
ac
ter
is
tic
c
u
r
v
e
o
f
t
h
e
ar
r
ay
e
x
h
ib
its
a
s
i
n
g
le
m
a
x
i
m
u
m
p
o
w
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ar
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ized
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ar
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ter
ized
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r
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h
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d
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t
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n
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m
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ce
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ased
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d
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4
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g
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co
r
r
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tly
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t
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er
y
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h
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t
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s
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eter
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ates th
e
e
f
f
icie
n
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y
o
f
th
e
P
V
s
y
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te
m
[
5
-
8
]
.
Fig
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r
e
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MPPT
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ac
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I
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P
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w
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Dr
i
S
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s
t
I
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N:
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p
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lica
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B
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637
On
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icts
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e
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r
ac
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f
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ticles.
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th
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t
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5
RE
SU
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Fig
u
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s
h
o
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SIM
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g
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r
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1
1
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Diag
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r
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1
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P
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m
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n
d
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ty
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n
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ter
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g
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r
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en
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m
m
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n
d
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n
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Fig
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1
3
.
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ith
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Fig
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1
4
.
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I
SS
N
:
2
0
8
8
-
8
694
I
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t J
P
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w
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lec
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Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
631
–
640
638
Fig
u
r
e
1
5
.
T
h
e
m
ax
i
m
u
m
tr
ac
k
ed
p
o
w
er
o
f
th
e
P
V
m
o
d
el
u
s
i
n
g
P
SO a
lg
o
r
it
h
m
Fig
u
r
e
1
6
.
P
SO,
P
&
O
an
d
f
u
z
z
y
lo
g
ic
r
es
u
lt
s
in
tr
ac
k
in
g
t
h
e
MP
P
Fig
u
r
e
1
4
s
h
o
w
s
th
e
v
ar
iat
io
n
o
f
p
o
w
er
o
f
th
e
SP
as
a
f
u
n
cti
o
n
o
f
ti
m
e.
W
e
o
b
s
er
v
e
th
e
ef
f
ec
t
o
f
th
e
ap
p
lied
P
SO
alg
o
r
ith
m
o
n
th
e
m
a
x
i
m
u
m
p
o
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er
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o
in
t,
o
n
ce
th
e
m
ax
i
m
u
m
p
o
w
er
is
r
ea
ch
ed
th
e
s
y
s
te
m
s
tab
ilized
at
th
is
v
al
u
e
w
it
h
a
n
o
s
cillat
io
n
ap
p
r
o
x
i
m
a
tel
y
e
q
u
al
to
8
W
.
W
e
w
ill
co
m
p
ar
e
th
e
o
b
tain
ed
r
es
u
lt
s
o
f
th
e
P
SO a
lg
o
r
it
h
m
w
i
t
h
th
e
alg
o
r
ith
m
"
P
&
O"
an
d
th
e
alg
o
r
ith
m
b
ased
o
n
f
u
zz
y
lo
g
ic.
Fig
u
r
e
1
5
s
h
o
w
s
a
co
m
p
ar
is
o
n
b
et
w
ee
n
th
e
o
b
tain
ed
p
o
w
er
o
f
th
e
SP
o
f
P
SO,
P
&
O
an
d
f
u
zz
y
lo
g
ic
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o
r
ith
m
s
.
Fro
m
th
e
r
es
u
lt
s
o
b
tain
ed
in
f
ig
u
r
e
1
5
w
e
ca
n
d
ed
u
ce
th
at
o
n
ce
t
h
e
m
a
x
i
m
u
m
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o
wer
p
o
in
t
is
r
ea
ch
ed
,
th
e
s
y
s
te
m
s
s
tar
ts
o
s
cillatin
g
w
i
th
a
v
alu
e
o
f
2
0
0
W
u
s
i
n
g
P
&
O
al
g
o
r
ith
m
a
n
d
5
0
W
u
s
in
g
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
;
h
o
w
e
v
er
t
h
is
o
s
cillatio
n
d
ec
r
ea
s
es
to
8
W
u
s
i
n
g
P
SO.
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e
ca
n
d
ed
u
ce
t
h
at
i
n
tr
ac
k
i
n
g
t
h
e
MP
P
o
f
th
e
SP
,
P
SO p
r
o
v
id
es
h
ig
h
ac
c
u
r
ac
y
m
o
r
e
t
h
an
t
h
e
P
&
O
a
n
d
f
u
zz
y
lo
g
ic.
5
.
2
M
P
P
T
f
o
r
m
ulti
-
pea
ks
T
h
e
r
o
le
o
f
P
SO
b
lo
ck
is
to
lead
th
e
s
y
s
te
m
to
th
e
MP
P
G
(
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
g
l
o
b
al)
w
ith
m
ar
g
i
n
o
f
a
s
m
a
ll
er
r
o
r
,
an
d
th
en
s
tab
ilize
s
th
e
s
y
s
te
m
at
th
e
m
ax
i
m
u
m
.
Fi
g
u
r
e
1
1
s
h
o
w
s
th
e
d
ia
g
r
a
m
o
f
co
m
p
lete
s
y
s
te
m
.
W
e
w
il
l
d
o
a
co
m
p
ar
is
o
n
b
et
w
ee
n
t
h
e
r
es
u
lts
g
o
n
e
u
s
i
n
g
th
e
P
SO
al
g
o
r
ith
m
,
a
n
d
th
e
r
es
u
lt
s
o
b
tain
ed
f
r
o
m
t
h
e
n
eu
r
al
-
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
.
I
n
t
h
is
s
ec
tio
n
,
w
e
p
r
ese
n
t
t
w
o
d
i
f
f
er
en
t
s
i
m
u
latio
n
s
.
I
n
s
o
latio
n
v
al
u
es o
f
t
h
e
t
w
o
s
i
m
u
latio
n
s
w
ill b
e
g
i
v
e
n
b
elo
w
.
SI
M
UL
AT
I
O
N
1
:
Fig
u
r
e
4
-
1
3
s
h
o
w
s
t
h
e
c
h
ar
ac
ter
is
tic
c
u
r
v
e
o
f
P
V
s
y
s
te
m
u
n
d
er
th
e
f
o
llo
w
in
g
i
n
s
o
latio
n
:
E
1
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,
E
2
an
d
E
3
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W
/m
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Fig
u
r
e
1
7
.
P
-
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ch
ar
ac
ter
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o
f
th
e
f
ir
s
t s
i
m
u
lat
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Fig
u
r
e
1
8
.
VP
V
o
f
th
e
f
ir
s
t s
i
m
u
latio
n
co
m
p
ar
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at
o
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r
o
m
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r
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n
d
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u
zz
y
lo
g
ic
co
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
A
p
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lica
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tio
n
a
l Me
th
o
d
s
a
n
d
P
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O
Meth
o
d
…
(
B
en
n
is
Gh
ita
)
639
Fig
u
r
e
1
9
.
PP
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o
f
th
e
f
ir
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m
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m
p
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o
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r
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m
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d
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u
r
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PP
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th
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m
u
latio
n
co
m
p
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r
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u
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M
UL
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N
2
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u
r
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4
-
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s
h
o
w
s
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ter
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1
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2
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3
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u
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1
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u
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2
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o
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n
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m
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(b
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Fig
u
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e
2
3
.
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a)
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s
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o
n
d
s
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m
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la
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m
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d
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l,
(
b
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P
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f
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m
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m
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Du
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to
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n
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f
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r
m
s
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lar
in
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o
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n
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t
h
e
r
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lti
n
g
P
-
V
ch
ar
a
cter
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tic
cu
r
v
e
o
f
th
e
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ex
h
ib
its
m
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l
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p
ea
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s
h
o
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n
i
n
f
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g
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r
es
1
6
an
d
2
0
.
Fig
u
r
es
1
7
,
1
8
,
2
1
,
an
d
2
2
s
h
o
w
th
e
v
o
ltag
e
a
n
d
th
e
p
o
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er
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el
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th
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al
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i
th
m
co
m
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tain
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r
o
m
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e
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n
d
ed
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ce
f
r
o
m
t
h
e
s
e
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lt
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th
a
t
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v
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s
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e
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ller
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o
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t
40
V
in
b
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th
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i
m
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n
s
,
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it
i
s
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o
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ith
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t
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m
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12
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d
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r
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n
m
ak
e
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h
e
s
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m
e
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ed
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ctio
n
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th
e
P
P
V
.
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n
g
n
eu
r
al
-
f
u
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y
lo
g
ic
co
n
tr
o
ller
,
th
e
p
o
w
er
o
s
cillatio
n
f
r
o
m
t
h
e
tr
ac
k
ed
m
a
x
i
m
u
m
p
o
w
er
p
o
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n
t
i
s
8
0
0
0
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th
e
f
ir
s
t
s
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n
d
4
0
0
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th
e
s
ec
o
n
d
,
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h
er
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u
s
in
g
t
h
e
P
SO
alg
o
r
ith
m
it
i
s
300
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th
e
f
ir
s
t
s
i
m
u
latio
n
an
d
2
0
0
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in
th
e
s
ec
o
n
d
.
Fig
u
r
es
2
0
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d
2
3
s
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o
w
t
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e
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iati
o
n
o
f
th
e
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P
V(
av
er
ag
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u
s
i
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g
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SO
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o
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ith
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n
d
n
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r
al
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f
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zz
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n
tr
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ller
.
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e
ca
n
f
i
g
u
r
e
o
u
t
th
a
t
o
n
ce
th
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
(
3000
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in
f
ir
s
t
s
i
m
u
la
tio
n
,
4900
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in
th
e
s
ec
o
n
d
s
i
m
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lati
o
n
)
is
r
ea
c
h
ed
b
y
t
h
e
P
SO,
it
i
s
s
tab
ilized
a
t
t
h
is
v
al
u
e;
h
o
wev
er
,
w
e
ca
n
s
ee
i
n
n
eu
r
al
-
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
,
o
n
ce
t
h
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
i
s
r
ea
c
h
ed
,
th
e
s
y
s
te
m
‘
s
p
o
w
er
f
all
s
to
a
v
al
u
e
1
00
W
less
th
an
th
e
m
a
x
i
m
u
m
p
o
w
er
.
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.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
631
–
640
640
6
CO
NCLU
SI
O
N
T
h
is
p
ap
er
co
n
tain
s
an
ap
p
r
o
ac
h
o
f
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
tr
ac
k
i
n
g
o
f
p
h
o
to
v
o
ltaic
s
y
s
t
e
m
s
b
a
s
ed
o
n
p
ar
ticle
s
w
ar
m
o
p
ti
m
izatio
n
al
g
o
r
ith
m
.
A
p
ar
ticle
s
w
ar
m
o
p
ti
m
izatio
n
(
P
SO)
w
it
h
t
h
e
ca
p
ab
ilit
y
o
f
d
ir
ec
t
d
u
t
y
c
y
cle
is
u
s
ed
to
tr
ac
k
t
h
e
MP
P
o
f
P
V
s
y
s
te
m
.
A
P
V
s
y
s
te
m
,
d
esig
n
ed
i
n
M
A
T
L
A
B
Si
m
u
li
n
k
w
a
s
u
s
ed
f
o
r
th
e
v
alid
atio
n
,
in
w
h
ich
a
d
c
-
d
c
b
o
o
s
t
co
n
v
er
ter
w
a
s
u
s
e
d
as
a
M
P
P
tr
ac
k
er
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
p
r
o
p
o
s
ed
co
n
tr
o
ller
is
co
m
p
ar
ed
w
it
h
“P
&
O”
an
d
f
u
zz
y
-
lo
g
ic
co
n
tr
o
l
alg
o
r
ith
m
s
.
T
h
e
to
tal
m
ax
i
m
u
m
p
o
w
er
tr
ac
k
i
n
g
u
s
i
n
g
th
e
P
SO
al
g
o
r
ith
m
in
t
h
is
r
ep
o
r
t
g
iv
e
s
a
b
etter
r
esu
lt
th
an
t
h
e
“
P
&
O”
a
n
d
f
u
zz
y
o
n
es
f
o
r
s
in
g
le
-
p
ea
k
MP
PT
,
w
h
ic
h
is
p
r
o
v
ed
b
y
s
i
m
u
latio
n
e
x
p
er
i
m
e
n
ts
i
n
t
h
is
r
ep
o
r
t.
I
n
th
e
ca
s
e
o
f
p
ar
tial
s
h
ad
i
n
g
o
f
P
V
ar
r
ay
t
h
e
o
u
tp
u
t
c
h
ar
a
cter
is
tics
p
r
ese
n
ts
a
n
u
m
b
er
o
f
ex
tr
e
m
e
p
o
in
ts
.
W
ith
th
e
co
n
s
id
er
atio
n
o
f
t
h
e
g
o
o
d
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
P
SO
i
n
m
u
lt
i
-
p
ea
k
f
u
n
ctio
n
o
p
ti
m
izat
io
n
,
g
lo
b
al
o
p
ti
m
izatio
n
,
as
w
ell
a
s
m
u
lti
-
v
ar
iab
le
o
p
ti
m
izatio
n
,
t
h
e
P
SO a
lg
o
r
it
h
m
is
ap
p
l
ied
t
o
th
e
MP
PT
co
n
tr
o
l
alg
o
r
ith
m
.
T
h
e
u
s
ed
P
SO
alg
o
r
ith
m
ca
n
f
a
s
t
a
n
d
ac
cu
r
atel
y
r
ea
lize
th
e
MP
P
T
in
P
V
s
y
s
te
m
s
,
an
d
t
h
is
w
a
s
p
r
o
v
ed
b
y
th
e
s
i
m
u
latio
n
r
e
s
u
lt
s
o
n
M
A
T
L
A
B
co
m
p
ar
e
d
to
th
at
o
b
tain
ed
b
y
th
e
n
eu
r
al
-
f
u
zz
y
co
n
tr
o
l
alg
o
r
ith
m
.
Ho
w
e
v
er
,
t
h
er
e
ar
e
s
t
il
l
m
a
n
y
ar
ea
s
f
o
r
i
m
p
r
o
v
e
m
e
n
t
f
o
r
th
e
P
SO
al
g
o
r
ith
m
to
m
a
k
e
it
ea
s
y
ap
p
licab
le
in
m
an
y
d
o
m
ai
n
s
e
s
p
ec
iall
y
co
n
tr
o
l.
RE
F
E
R
E
NC
E
S
[1
]
Be
n
n
is,
G
.
,
Ka
ri
m
,
M
.
,
&
Lag
ri
o
u
i,
A
.
(2
0
1
5
,
De
c
e
m
b
e
r).
Op
ti
m
iz
a
ti
o
n
o
f
th
e
p
e
rf
o
r
m
a
n
c
e
o
f
a
p
h
o
t
o
v
o
lt
a
ic
s
y
ste
m
w
it
h
M
P
P
T
c
o
n
tr
o
ll
e
r.
In
2
0
1
5
3
r
d
In
ter
n
a
ti
o
n
a
l
Re
n
e
w
a
b
le
a
n
d
S
u
sta
in
a
b
le
E
n
e
rg
y
Co
n
f
e
r
e
n
c
e
(IRS
EC)
(p
p
.
1
-
6
)
.
IEE
E
[2
]
G
h
it
a
,
B.
,
M
o
h
a
m
m
e
d
,
K.,
A
h
m
e
d
,
L
.
,
Na
d
a
,
Z.
,
N
o
u
r
d
d
i
n
e
,
S
.
,
&
Ay
o
u
b
,
E.
(
2
0
1
6
).
Ortim
iza
ti
o
n
a
n
d
m
o
d
e
li
n
g
o
f
a
g
iv
e
n
P
V
sy
ste
m
h
a
s a sin
g
le p
h
a
se
lo
a
d
.
Jo
u
rn
a
l
o
f
T
h
e
o
re
ti
c
a
l
&
A
p
p
li
e
d
In
f
o
rm
a
ti
o
n
T
e
c
h
n
o
l
o
g
y
,
8
6
(1
).
[3
]
Em
e
r
y
,
K.;
Bu
rd
ick
,
J.;
Ca
i
y
e
m
,
Y.;
Du
n
lav
y
,
D.;
F
ield
,
H.;
Kro
p
o
sk
i,
B.
;
M
o
riarty
,
T
.
;Ott
o
so
n
,
L
.
;
Ru
m
m
e
l,
S
.
;
S
tran
d
,
T
.
;
W
a
n
las
s,
M
.
W
.
;
"
T
e
m
p
e
ra
tu
re
d
e
p
e
n
d
e
n
c
e
o
f
p
h
o
t
o
v
o
lt
a
ic ce
ll
s,
m
o
d
u
l
e
s an
d
sy
ste
m
s
[4
]
Du
rg
a
d
e
v
i.
A
,
A
ru
lse
lv
i.
S
a
n
d
Na
tara
jan
.
S
,
"
S
tu
d
y
a
n
d
im
p
le
m
e
n
ta
ti
o
n
o
f
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
t
ra
c
k
in
g
(M
P
P
T
)
a
lg
o
rit
h
m
f
o
r
p
h
o
t
o
v
o
lt
a
ic
sy
ste
m
s,"
in
El
e
c
tri
c
a
l
En
e
rg
y
S
y
ste
m
s
(ICEE
S
),
2
0
1
1
1
st
In
ter
n
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
,
P
a
g
e
s.
2
4
1
-
2
4
4
.
[5
]
M
.
M
i
y
a
ta
k
e
,
M
.
V
e
e
ra
c
h
a
r
y
,
F
.
T
o
riu
m
i,
N.
F
u
ji
i,
a
n
d
H.
Ko
,
“
M
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
o
f
m
u
lt
ip
le
p
h
o
to
v
o
lt
a
ic arra
y
s:
A
P
S
O ap
p
ro
a
c
h
,
”
2
0
1
1
.
IEE
E
T
ra
n
s.
A
e
ro
sp
.
El
e
c
tro
n
.
S
y
st.,
P
a
g
e
s.
3
6
7
–
3
8
0
,
[6
]
P
a
tel,
H.
a
n
d
A
g
a
r
w
a
l,
V
.
M
a
x
im
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
in
g
S
c
h
e
m
e
f
o
r
P
V
S
y
ste
m
s
Op
e
ra
ti
o
n
Un
d
e
r
P
a
rti
a
ll
y
S
h
a
d
e
d
C
o
n
d
it
i
o
n
s.
IEE
E
T
ra
n
s.
On
In
d
u
strial
El
e
c
tro
n
ics
,
5
5
,
4
,
1
6
8
9
-
1
6
9
8
,
2
0
0
8
.
[7
]
Qu
a
sc
h
n
in
g
,
V
.
a
n
d
Ha
n
i
tsc
h
,
R.
Nu
m
e
ri
c
a
l
si
m
u
latio
n
o
f
c
u
rre
n
t
-
v
o
lt
a
g
e
c
h
a
ra
c
teristics
o
f
p
h
o
to
v
o
lt
a
ic
s
y
ste
m
s
w
it
h
sh
a
d
e
d
so
lar c
e
ll
s.
S
o
lar E
n
e
rg
y
,
5
6
,
6
,
5
1
3
-
5
2
0
,
1
9
9
6
.
[8
]
V
il
lalv
a
,
M
.
G
.
,
Ga
z
o
li
,
J.
R.
a
n
d
F
il
h
o
,
E.
R.
Co
m
p
re
h
e
n
s
iv
e
A
p
p
ro
a
c
h
to
M
o
d
e
li
n
g
a
n
d
S
im
u
latio
n
o
f
P
h
o
t
o
v
o
lt
a
ic A
rra
y
s.
IEE
E
T
ra
n
s.
On
P
o
w
e
r
El
e
c
tro
n
ics
,
2
4
,
1
1
9
8
-
1
2
0
8
,
2
0
0
9
.
[9
]
T
a
f
ti
c
h
t,
T
.
,
&
A
g
b
o
ss
o
u
,
K.
(
2
0
0
4
,
M
a
y
).
De
v
e
lo
p
m
e
n
t
o
f
a
M
P
P
T
m
e
th
o
d
f
o
r
p
h
o
to
v
o
lt
a
ic
sy
ste
m
s.
In
El
e
c
tri
c
a
l
a
n
d
Co
m
p
u
ter E
n
g
in
e
e
rin
g
,
2
0
0
4
.
Ca
n
a
d
ian
C
o
n
f
e
re
n
c
e
o
n
(
V
o
l.
2
,
p
p
.
1
1
2
3
-
1
1
2
6
).
IE
EE
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