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s
i
f
i
e
d
as
f
o
l
l
o
w
s
:
C
o
n
v
e
n
t
i
o
n
a
l
m
e
t
h
o
d
s
s
u
c
h
a
s
i
n
c
r
e
m
e
n
t
a
l
c
o
n
d
u
c
t
i
o
n
(
I
C
)
,
p
e
r
t
u
r
b
a
n
d
o
b
s
e
r
v
e
d
(
P
O
)
,
h
i
l
l
c
l
i
m
b
i
n
g
(
H
C
)
,
a
n
d
t
h
e
i
m
p
r
o
v
e
d
v
e
r
s
i
o
n
s
o
f
t
h
e
m
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
2
9
9
9
-
3
0
1
0
3000
S
o
f
t
c
o
m
p
u
t
i
n
g
m
et
h
o
d
s
i
n
c
l
u
d
i
n
g
a
r
t
i
f
i
ci
a
l
n
e
u
r
a
l
n
et
w
o
r
k
s
(
A
N
N
)
,
f
u
z
z
y
l
o
g
i
c
c
o
n
t
r
o
l
(
FLC
)
,
a
n
d
e
v
o
l
u
t
i
o
n
a
r
y
a
l
g
o
r
i
t
h
m
s
(
E
A
)
;
a
n
a
l
y
ti
c
a
l
m
et
h
o
d
s
s
u
c
h
as
g
o
l
d
e
n
s
ec
t
i
o
n
o
p
t
i
m
i
z
a
ti
o
n
a
n
d
e
x
t
r
e
m
u
m
s
e
a
r
c
h
i
n
g
;
a
n
d
f
e
e
d
b
a
c
k
c
o
n
t
r
o
l
u
s
i
n
g
d
P
/
d
V
o
r
d
P
/
d
I
.
W
e
ca
n
also
class
if
y
MPPT
c
o
n
tr
o
l
m
eth
o
d
s
in
to
d
ir
ec
t
M
PP
T
co
n
tr
o
l
an
d
in
d
i
r
ec
t
MP
PT
co
n
tr
o
l.
A
co
n
tr
o
ller
th
at
m
ax
im
izes
p
o
wer
co
n
v
er
s
io
n
b
y
d
ir
ec
tly
m
o
d
if
y
in
g
th
e
d
u
ty
r
atio
is
a
d
ir
ec
t
MPP
T
co
n
tr
o
l.
Sev
er
al
ar
ticles
o
n
d
ir
ec
t
MPPT
co
n
tr
o
l
m
et
h
o
d
h
av
e
b
ee
n
p
u
b
lis
h
ed
i
.
e.
p
e
r
tu
r
b
an
d
o
b
s
er
v
e
(
PO
)
[
4,
5
]
,
m
o
d
if
ied
PO
[
6]
,
I
C
[
4,
5,
7,
8
]
,
in
cr
e
m
en
tal
r
esis
tan
ce
(
I
R
)
[
9]
,
cu
c
k
o
o
s
ea
r
ch
alg
o
r
ith
m
(
C
SA)
[
1
0
]
,
I
C
M
with
f
u
zz
y
l
o
g
ic
[
11]
,
FLC
[
12
-
2
0
]
,
a
d
ap
tiv
e
FLC
b
ased
o
n
two
la
y
er
s
FLC
[
21]
,
FL
C
u
s
in
g
au
to
s
ca
lin
g
v
ar
iab
le
s
tep
-
s
ize
[
22]
,
an
d
co
n
s
tan
t
PID
co
n
tr
o
l
[
15,
1
6
]
.
Gen
etic
alg
o
r
ith
m
(
GA)
is
u
s
ed
to
o
p
tim
ize
co
n
s
tan
t
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
(
PI
)
c
o
n
tr
o
l
[
23]
,
An
t
co
lo
n
y
alg
o
r
ith
m
(
AC
O)
is
u
tili
ze
d
f
o
r
o
p
ti
m
izin
g
co
n
s
tan
t
PI
co
n
tr
o
l
[
24]
,
g
r
ad
ie
n
t
d
escen
d
m
eth
o
d
is
ad
o
p
ted
f
o
r
PID
co
n
tr
o
l
o
p
tim
izatio
n
[
2
5
]
,
FLC
is
u
s
ed
f
o
r
ad
a
p
tiv
e
PID
co
n
tr
o
l
[
2
6
,
2
7
]
,
ad
a
p
tiv
e
s
ca
lin
g
f
ac
to
r
is
u
s
ed
f
o
r
f
u
zz
y
g
ain
s
ch
ed
u
lin
g
(
FGS)
PID
co
n
tr
o
l
[
2
8
]
,
an
d
B
ig
B
an
g
-
B
ig
C
r
u
n
ch
(
B
B
-
B
C
)
al
g
o
r
ith
m
is
u
s
e
d
to
tu
n
e
a
f
u
zz
y
PID
co
n
tr
o
ller
[
2
9
]
.
I
n
an
in
d
ir
ec
t M
PP
T
co
n
tr
o
l
an
ex
ter
n
al
c
o
n
tr
o
ller
s
en
d
s
a
r
ef
er
en
ce
c
o
m
m
an
d
s
ig
n
al
to
an
in
ter
n
al
co
n
tr
o
ller
.
Fo
r
th
e
ex
ter
n
al
co
n
t
r
o
ller
,
v
ar
io
u
s
m
eth
o
d
s
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
i.e
.
d
P/d
V
f
ee
d
b
ac
k
co
n
tr
o
l
[
30
-
3
2
]
,
m
o
d
i
f
ied
PO
[
3
3
,
3
4
]
,
a
n
d
PO
with
FLC
[
35]
.
Fo
r
th
e
in
n
er
lo
o
p
c
o
n
tr
o
ller
,
s
ev
er
al
co
n
tr
o
ller
s
h
av
e
b
ee
n
p
u
b
l
is
h
ed
i.e
.
p
r
o
p
o
r
tio
n
al
(
P)
[
30,
3
1
]
,
p
r
o
p
o
r
tio
n
al
in
teg
r
al
(
PI)
[
33
-
3
7
]
,
th
e
r
o
o
t
-
lo
cu
s
tech
n
iq
u
e
b
ased
PID
co
n
tr
o
ller
[
3
8
]
,
f
u
zz
y
lo
g
ic
b
ased
ad
ap
tiv
e
PID
co
n
tr
o
ller
[
39]
,
ad
ap
tiv
e
MPPT
u
s
in
g
au
to
-
tu
n
in
g
[
4
0
]
,
an
d
c
o
n
s
tan
t
co
n
tr
o
ller
b
ased
o
n
Yo
u
la
p
ar
am
eter
izatio
n
[
41
]
.
So
m
e
ar
ticles
h
av
e
ca
r
r
ied
o
u
t
co
m
p
ar
is
o
n
s
b
etwe
en
th
e
d
ir
ec
t
PID
co
n
tr
o
l,
th
e
d
ir
ec
t
FLC,
an
d
th
e
d
ir
ec
t
ad
a
p
tiv
e
PID
co
n
tr
o
l
b
ased
o
n
f
u
zz
y
l
o
g
ic.
T
h
ey
c
o
n
clu
d
e
d
th
at
d
ir
ec
t
FLC
is
b
e
tter
th
an
th
e
d
ir
ec
t
PID
co
n
tr
o
l
[
1
5
,
1
6
]
.
T
h
e
d
ir
e
ct
ad
ap
tiv
e
P
I
D
Fu
zz
y
co
n
tr
o
l
ler
p
r
o
v
id
es
b
etter
p
e
r
f
o
r
m
an
c
e
th
an
PO
m
eth
o
d
[
2
7
]
,
th
e
FGS
PID
co
n
tr
o
l
with
th
e
ad
ap
tiv
e
s
ca
lin
g
f
ac
to
r
g
iv
es
b
etter
p
er
f
o
r
m
an
ce
th
an
PO
m
eth
o
d
an
d
co
n
s
tan
t
PID
co
n
tr
o
ller
[
2
8
]
.
I
t
is
im
p
o
r
tan
t
to
n
o
te
t
h
at
th
o
s
e
d
ir
ec
t
ad
ap
tiv
e
PID
co
n
tr
o
l
m
e
th
o
d
s
in
co
r
p
o
r
ated
two
f
u
zz
y
in
p
u
t
v
ar
ia
b
les
wh
ich
y
ield
a
lar
g
e
n
u
m
b
er
o
f
f
u
z
zy
r
u
les:
7
5
r
u
les
in
[
2
7
]
,
an
d
m
an
y
m
o
r
e
r
u
les
in
[
2
8
]
.
A
d
d
itio
n
ally
,
t
h
e
ab
o
v
e
d
ir
ec
t
ad
ap
tiv
e
PID
co
n
tr
o
l
-
b
a
s
ed
MPPT
m
eth
o
d
s
wer
e
o
n
ly
ev
alu
ated
th
r
o
u
g
h
co
m
p
u
ter
s
im
u
latio
n
s
an
d
we
r
e
n
o
t
v
alid
ated
th
r
o
u
g
h
e
x
p
e
r
im
en
tal
s
tu
d
ies.
I
n
th
e
in
d
i
r
ec
t
MPPT
co
n
tr
o
l,
a
f
u
zz
y
ad
a
p
tiv
e
PID
c
o
n
tr
o
ll
er
is
u
s
ed
i
n
th
e
in
ter
n
al
lo
o
p
wh
ile
th
e
ex
ter
n
al
lo
o
p
u
s
es
a
d
y
n
a
m
ic
s
et
-
p
o
i
n
t
ad
ju
s
tm
en
t
m
ec
h
an
is
m
[
3
9
]
.
T
h
e
au
th
o
r
s
co
n
clu
d
ed
th
at
th
e
co
n
tr
o
ller
p
r
o
d
u
ce
d
b
etter
tr
ac
k
in
g
ef
f
icien
c
y
as
co
m
p
ar
ed
to
PO,
in
c
r
em
en
tal
c
o
n
d
u
cta
n
ce
(
IC
)
with
PI
r
eg
u
lato
r
,
FLC,
NN,
an
d
ANFI
S.
Ho
wev
er
,
th
is
in
d
ir
ec
t
f
u
zz
y
ad
ap
tiv
e
PID
c
o
n
tr
o
ller
n
ee
d
s
3
s
en
s
o
r
s
i.e
.
c
u
r
r
e
n
t
s
en
s
o
r
,
tem
p
er
atu
r
e
s
en
s
o
r
,
an
d
a
s
o
lar
r
a
d
iatio
n
s
en
s
o
r
.
Mo
r
eo
v
er
,
th
e
f
u
zz
y
lo
g
ic
in
v
o
lv
es a
s
m
u
c
h
as
1
4
7
r
u
les.
T
h
e
o
b
jectiv
e
o
f
th
is
p
a
p
er
is
t
o
d
esig
n
an
MPPT
c
o
n
tr
o
l
wh
i
ch
g
iv
es
r
o
b
u
s
tn
ess
p
er
f
o
r
m
an
ce
ag
ain
s
t
DC
lin
k
v
o
ltag
e
d
is
tu
r
b
an
ce
,
g
o
o
d
r
e
g
u
latio
n
p
e
r
f
o
r
m
an
ce
,
an
d
s
atis
f
ac
to
r
y
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
u
n
d
er
r
ap
id
s
o
lar
r
ad
iatio
n
ch
a
n
g
es.
A
n
e
w
MPPT
co
n
tr
o
l
m
eth
o
d
f
o
r
a
PV
p
an
el
is
p
r
o
p
o
s
ed
b
ased
o
n
in
d
ir
ec
t
MPPT
co
n
tr
o
l
to
p
o
lo
g
y
.
T
h
e
c
o
n
tr
o
ll
er
o
n
ly
n
ee
d
s
2
s
en
s
o
r
s
an
d
a
s
less
a
s
1
0
f
u
zz
y
lo
g
ic
r
u
les.
I
ts
p
er
f
o
r
m
a
n
ce
is
co
m
p
ar
ed
to
a
d
ir
ec
t
FLC.
Fu
r
th
er
m
o
r
e
,
th
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
p
r
o
p
o
s
ed
MPPT
co
n
tr
o
l
m
eth
o
d
is
v
er
if
ie
d
th
r
o
u
g
h
ex
p
er
im
en
ts
u
n
d
er
n
atu
r
al
clim
ate
co
n
d
itio
n
s
with
r
e
al
s
o
lar
r
ad
iatio
n
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws
;
s
ec
tio
n
1
is
th
e
in
tr
o
d
u
ctio
n
.
Sectio
n
2
d
escr
ib
es
th
e
r
esear
ch
m
eth
o
d
in
clu
d
in
g
m
o
d
elin
g
o
f
th
e
PV
m
o
d
u
le,
m
o
d
elin
g
o
f
t
h
e
PV
b
o
o
s
t
co
n
v
er
ter
,
p
r
ev
io
u
s
s
tu
d
ies
o
n
MPPT
u
s
in
g
f
u
zz
y
lo
g
ic
an
d
PID
co
n
t
r
o
l,
an
d
th
e
p
r
o
p
o
s
ed
f
u
zz
y
ad
ap
tiv
e
PI
MPPT
co
n
tr
o
l.
Secti
o
n
3
p
r
esen
ts
r
esu
lts
an
d
an
aly
s
is
.
Fin
ally
,
th
e
c
o
n
c
lu
s
io
n
is
d
r
awn
in
s
ec
tio
n
4.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
M
o
delin
g
o
f
t
he
P
V
m
o
du
le
R
elatio
n
s
h
ip
b
etwe
en
cu
r
r
e
n
t
an
d
v
o
lta
g
e
o
f
a
PV m
o
d
u
le
is
g
iv
en
b
elo
w
[
42
-
4
4
]
.
=
−
{
[
(
+
)
]
−
1
}
−
+
(
1
)
=
(
2
)
T
h
e
PV
m
o
d
u
le
g
en
e
r
ates
cu
r
r
en
t
I
an
d
v
o
ltag
e
V
.
I
L
is
lig
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[
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s
e
d
o
n
f
u
z
z
y
l
o
g
i
c
[
2
7
]
.
I
t
i
s
t
e
r
m
e
d
a
s
d
i
r
e
c
t
M
P
P
T
a
d
a
p
t
i
v
e
P
I
D
-
F
L
C
.
T
h
e
s
i
m
u
l
a
t
i
o
n
r
e
s
u
l
t
s
i
n
d
i
c
a
t
e
d
t
h
a
t
t
h
e
c
o
n
t
r
o
l
l
e
r
c
o
u
l
d
t
r
a
c
k
t
h
e
M
P
P
b
e
t
t
e
r
t
h
a
n
t
h
e
w
e
l
l
-
k
n
o
w
n
P
O
m
e
t
h
o
d
[
2
7
]
.
Fig
u
r
e
3
.
Dir
ec
t M
PP
T
ad
ap
ti
v
e
PID
-
FLC
[
27]
T
h
e
PID
co
n
tr
o
ller
ca
lcu
late
s
th
e
d
u
ty
r
atio
u
s
in
g
t
h
e
er
r
o
r
s
ig
n
al
d
P/d
V.
T
h
e
PID
c
o
n
tr
o
ller
’
s
p
ar
am
eter
v
alu
es
ar
e
au
to
-
t
u
n
e
d
u
s
in
g
f
u
zz
y
lo
g
ic.
T
h
e
f
u
zz
y
lo
g
ic
u
s
es
two
f
u
zz
y
in
p
u
t
v
ar
iab
les
i.e
.
th
e
e
r
r
o
r
s
ig
n
al
d
P/d
V
an
d
its
r
ate
o
f
c
h
an
g
e.
E
ac
h
f
u
zz
y
in
p
u
t
an
d
o
u
tp
u
t
v
ar
iab
les
ar
e
d
i
v
id
ed
i
n
to
f
iv
e
f
u
zz
y
s
ets.
Ho
wev
er
,
ex
p
lan
atio
n
r
eg
ar
d
i
n
g
m
em
b
er
s
h
ip
f
u
n
ctio
n
,
f
u
z
zy
in
p
u
t
an
d
o
u
tp
u
t
v
ar
ia
b
les,
f
u
zz
if
icatio
n
,
an
d
d
ef
u
zz
if
icatio
n
m
eth
o
d
s
c
o
u
ld
n
o
t b
e
f
o
u
n
d
[
2
7
]
.
No
ex
p
er
i
m
en
t r
esu
lt wa
s
r
ep
o
r
ted
.
An
in
d
ir
ec
t
MPPT
ad
ap
tiv
e
P
I
D
co
n
tr
o
l
u
s
in
g
f
u
zz
y
lo
g
ic
was
p
u
b
lis
h
ed
co
n
s
is
tin
g
o
f
an
ad
ap
tiv
e
PID
cu
r
r
en
t
c
o
n
tr
o
ller
a
n
d
a
s
et
p
o
in
t
tr
ac
k
e
r
[
3
9
]
.
I
t
is
n
am
ed
as
in
d
ir
ec
t
MPPT
ad
ap
tiv
e
PI
D
-
FLC.
T
h
e
MPPT
m
eth
o
d
g
i
v
es
lar
g
er
ef
f
icien
c
y
wh
en
co
m
p
a
r
ed
to
PO,
I
NC
,
f
u
zz
y
lo
g
ic,
a
n
d
ANFI
S
u
n
d
er
f
ast
s
o
lar
ir
r
ad
ia
n
ce
ch
an
g
es
[
3
9
]
.
T
h
e
s
etp
o
in
t
tr
ac
k
er
ca
lcu
lates
th
e
cu
r
r
e
n
t
s
et
p
o
in
t
u
s
in
g
s
o
lar
ir
r
ad
ia
n
c
e
,
th
e
PV
m
o
d
u
le
tem
p
er
atu
r
e,
an
d
d
atash
ee
t
f
r
o
m
th
e
m
an
u
f
ac
tu
r
e
r
.
A
s
p
ec
if
ic
f
ac
to
r
is
also
n
ee
d
ed
[
4
6
]
.
T
h
e
PID
co
n
t
r
o
ller
g
ets
cu
r
r
en
t
r
ef
e
r
en
ce
f
r
o
m
th
e
s
etp
o
in
t
tr
ac
k
er
an
d
s
en
d
s
d
u
ty
r
atio
to
th
e
s
witch
in
g
d
r
iv
er
.
T
h
e
f
u
zz
y
lo
g
ic
tu
n
es
th
e
PID
co
n
tr
o
ller
’
s
g
a
in
v
alu
es
in
a
r
ea
l
tim
e
m
an
n
er
.
T
h
e
f
u
zz
y
lo
g
ic
u
s
es
two
in
p
u
ts
th
o
s
e
ar
e
th
e
cu
r
r
en
t
e
r
r
o
r
s
ig
n
al
an
d
it
s
r
ate
o
f
ch
an
g
e
.
E
ac
h
f
u
zz
y
i
n
p
u
t
an
d
o
u
tp
u
t
v
ar
iab
les
ar
e
d
iv
id
ed
in
to
s
ev
en
f
u
zz
y
s
ets.
I
ts
f
u
zz
y
r
u
le
b
ase
i
n
v
o
lv
es
1
4
7
r
u
les.
T
h
e
r
e
q
u
ir
e
m
en
t
o
f
th
e
m
en
tio
n
ed
th
r
ee
s
en
s
o
r
s
an
d
th
e
q
u
ite
am
o
u
n
t
o
f
f
u
zz
y
r
u
les m
ig
h
t p
r
o
h
ib
it th
e
m
et
h
o
d
t
o
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e
im
p
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T
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p
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tr
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A
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a
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co
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l fo
r
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V
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(
S
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3003
2
.
4
.
T
he
pro
po
s
ed
f
uzzy
a
da
ptiv
e
P
I
M
P
P
T
co
ntr
o
l
T
h
is
p
ap
er
p
r
o
p
o
s
es
a
n
ew
MP
PT
m
eth
o
d
wh
ich
in
co
r
p
o
r
ates
an
in
ter
n
al
PI
co
n
tr
o
ller
an
d
a
n
ex
ter
n
al
ad
ap
tiv
e
PI
co
n
tr
o
ller
wh
ic
h
i
s
au
to
-
tu
n
ed
b
y
an
FLC.
T
h
e
ad
v
an
tag
es
o
f
th
is
MPPT
m
eth
o
d
ar
e
two
f
o
l
d
s
:
it
o
n
ly
r
e
q
u
ir
es
two
s
en
s
o
r
s
f
o
r
v
o
ltag
e
an
d
cu
r
r
en
t
m
ea
s
u
r
em
en
ts
;
th
e
FLC
o
n
ly
n
ee
d
s
o
n
e
f
u
zz
y
in
p
u
t
an
d
1
0
f
u
zz
y
r
u
les.
Mo
r
eo
v
er
,
th
is
in
d
ir
ec
t
MPPT
to
p
o
lo
g
y
ca
n
en
h
an
ce
r
o
b
u
s
tn
ess
ag
ain
s
t
DC
l
in
k
v
o
ltag
e
d
is
tu
r
b
an
ce
wh
ile
m
ain
tain
i
n
g
a
g
o
o
d
tr
ac
k
in
g
r
esp
o
n
s
e
to
w
ar
d
s
f
ast
s
o
lar
r
ad
iatio
n
c
h
an
g
es.
Fig
u
r
e
4
s
h
o
ws
a
b
lo
ck
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
MPPT
co
n
tr
o
l.
Fig
u
r
e
4
.
T
h
e
p
r
o
p
o
s
ed
i
n
d
ir
e
ct
MPPT
co
n
t
r
o
l
b
ased
o
n
ad
a
p
tiv
e
PI
co
n
tr
o
l
u
s
in
g
f
u
zz
y
l
o
g
ic
T
h
e
in
ter
n
al
PI
co
n
tr
o
ller
is
u
s
ed
to
r
eg
u
late
th
e
PV
v
o
ltag
e
s
o
th
at
it
tr
ac
k
s
t
h
e
r
e
f
er
en
ce
.
T
h
e
r
ef
er
e
n
ce
is
g
en
er
ated
b
y
t
h
e
ex
ter
n
al
ad
a
p
tiv
e
PI
co
n
tr
o
l
ler
in
s
u
ch
a
way
s
o
th
at
=
b
ein
g
ze
r
o
.
is
g
iv
en
b
y
t
h
e
ex
ter
n
al
ad
ap
ti
v
e
PI
co
n
tr
o
ller
in
(
1
2
)
.
(
)
=
−
(
)
−
∫
(
)
0
(
1
2
)
I
n
itial
v
alu
es
o
f
th
e
ad
a
p
tiv
e
PI
co
n
tr
o
ller
’
s
g
ain
s
ar
e
(
,
)
.
T
h
e
co
n
tr
o
ller
p
a
r
am
eter
s
v
alu
es
(
,
)
ar
e
au
to
tu
n
e
d
b
y
f
u
zz
y
l
o
g
ic
as f
o
llo
ws
;
=
+
∆
(
1
3
)
=
+
∆
(
1
4
)
T
h
e
FLC
o
n
ly
u
s
es
th
e
er
r
o
r
s
ig
n
al
as
th
e
in
p
u
t
an
d
ca
lcu
lat
es
th
e
f
u
zz
y
o
u
tp
u
t
v
ar
iab
les
∆
an
d
∆
.
E
ac
h
f
u
zz
y
in
p
u
t
an
d
o
u
tp
u
t
v
ar
ia
b
les
ar
e
d
i
v
id
ed
in
to
f
iv
e
f
u
zz
y
s
ets,
v
iz.
n
eg
ativ
e
b
i
g
(
NB
)
,
n
eg
ativ
e
s
m
all
(
NS)
,
ze
r
o
(
Z
)
,
p
o
s
itiv
e
s
m
all
(
PS
)
,
a
n
d
p
o
s
itiv
e
b
ig
(
PB
)
.
A
t
o
tal
n
u
m
b
er
o
f
o
n
ly
1
0
r
u
les
ar
e
n
ec
ess
ar
y
as sh
o
wn
in
T
ab
le
1
.
T
h
is
r
ed
u
ce
s
th
e
co
m
p
u
tatio
n
b
u
r
d
e
n
s
o
th
at
it
is
m
o
r
e
im
p
lem
en
tab
le
as
co
m
p
ar
ed
to
th
e
p
r
ev
io
u
s
ly
p
u
b
lis
h
ed
m
eth
o
d
s
d
escr
ib
ed
in
th
e
p
r
ev
io
u
s
s
ec
tio
n
.
T
ab
le
1
.
R
u
le
b
ase
f
o
r
th
e
f
u
z
zy
o
u
p
u
t v
ar
ia
b
les
O
u
t
p
u
t
I
n
p
u
t
:
Er
r
o
r
(
)
NB
NS
Z
PS
PB
∆
NB
NS
Z
PS
PB
∆
NB
NS
Z
PS
PB
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
T
h
e
p
r
o
p
o
s
ed
MPPT
m
eth
o
d
h
as
b
ee
n
im
p
lem
en
ted
in
to
co
m
p
u
ter
s
im
u
latio
n
as
well
as
ex
p
er
im
en
ts
.
T
h
r
o
u
g
h
co
m
p
u
ter
s
im
u
latio
n
s
,
its
p
er
f
o
r
m
an
ce
is
co
m
p
a
r
ed
with
th
e
d
ir
ec
t
FLC
to
ev
alu
ate
r
o
b
u
s
tn
ess
p
er
f
o
r
m
an
ce
a
g
ain
s
t
DC
lin
k
v
o
ltag
e
d
is
tu
r
b
an
ce
an
d
tr
ac
k
i
n
g
p
er
f
o
r
m
an
ce
to
war
d
s
s
o
lar
ir
r
ad
ian
ce
s
tep
-
lik
e
ch
an
g
es
as
well
as
s
tead
y
-
s
tate
co
n
d
itio
n
s
.
T
h
en
,
its
ef
f
ec
t
iv
en
ess
is
v
alid
ated
th
r
o
u
g
h
ex
p
er
im
en
ts
u
n
d
er
n
atu
r
al
clim
ate
co
n
d
itio
n
s
with
r
ea
l so
lar
r
a
d
iatio
n
.
3
.
1
.
Sim
ula
t
i
o
n
C
o
m
p
u
ter
s
im
u
latio
n
is
co
n
d
u
cted
u
s
in
g
a
p
h
y
s
ical
m
o
d
el
r
ep
r
esen
ted
in
Simu
lin
k
®
.
T
h
e
PV
m
o
d
el
is
b
u
ilt
u
s
in
g
S
-
f
u
n
ctio
n
,
th
e
c
o
n
v
er
ter
is
b
u
ilt
u
s
in
g
Simu
lin
k
m
o
d
el
c
o
m
p
o
n
en
ts
,
an
d
a
d
is
cr
ete
tim
e
co
n
tr
o
ller
is
d
esig
n
ed
.
So
lar
ir
r
ad
ian
ce
is
v
ar
ied
an
d
th
e
p
r
o
d
u
ce
d
PV
p
o
wer
is
ev
alu
ated
.
Fo
r
p
er
f
o
r
m
an
ce
co
m
p
ar
is
o
n
s
tu
d
y
,
a
d
ir
ec
t
MPPT
FLC
h
as
also
b
ee
n
d
esig
n
e
d
u
s
in
g
er
r
o
r
s
ig
n
al
e
an
d
its
r
ate
o
f
ch
an
g
e
d
e
as f
u
zz
y
in
p
u
t
PV
M
o
d
u
l
e
DC
-
D
C
Boo
s
t
C
on
v
er
t
er
P
W
M
I
n
t
e
r
n
a
l
P
I
C
o
n
t
r
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ese
e
x
p
er
im
e
n
t
r
esu
lts
v
alid
ate
th
at
p
r
o
p
o
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ed
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n
tr
o
l
ef
f
ec
tiv
ely
p
r
o
v
id
e
g
o
o
d
r
e
g
u
l
atio
n
an
d
r
o
b
u
s
tn
ess
p
er
f
o
r
m
a
n
ce
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
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o
m
p
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t E
l Co
n
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o
l
A
r
o
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u
s
t m
a
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m
p
o
w
er p
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t tra
ck
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p
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d
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ller
b
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…
(
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l
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3007
(
a)
(
b
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Fig
u
r
e
11
.
E
x
p
e
r
im
en
t r
esu
lts
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s
in
g
PI
co
n
tr
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ller
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a)
PV p
a
n
el
p
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(
b
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P
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V
c
u
r
v
e
(
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(
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Fig
u
r
e
12
.
E
x
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e
r
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en
t r
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s
in
g
ad
ap
tiv
e
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L
FC
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a)
PV p
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el
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wer
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b
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P
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V
cu
r
v
e
I
n
ex
p
er
im
e
n
t
3
,
th
e
tr
ac
k
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g
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er
f
o
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m
a
n
ce
o
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e
ad
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tiv
e
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ated
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y
m
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u
all
y
o
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g
an
d
clo
s
in
g
th
e
PV
p
an
el
u
n
d
er
s
o
lar
ir
r
ad
ian
ce
o
f
7
0
8
(
W
/m
2
)
.
C
lo
s
in
g
th
e
PV
p
an
el
s
u
r
f
ac
e
with
a
th
ick
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r
to
n
s
h
u
ts
o
f
f
th
e
s
o
lar
r
ad
iat
io
n
in
to
th
e
p
an
el.
T
h
e
m
ea
s
u
r
ed
PV
p
o
we
r
is
p
lo
tted
i
n
F
ig
u
r
e
13
.
T
h
ese
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lts
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em
o
n
s
tr
ate
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at
th
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n
tr
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ller
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n
tr
ac
k
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en
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o
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ir
r
ad
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g
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lly
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r
o
m
7
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d
ec
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ea
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s
t z
er
o
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d
th
en
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n
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ea
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ac
k
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8
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W
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).
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ee
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er
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y
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es
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u
r
e
1
3
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ed
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p
o
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e
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r
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e
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r
e
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3
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atis
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to
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y
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f
r
o
m
Fig
u
r
e
1
3
(
a)
t
h
e
PV
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an
el
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co
n
tr
o
l
r
esp
o
n
s
es
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n
s
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ten
tly
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d
s
s
o
lar
ir
r
a
d
ian
ce
f
ast
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ep
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ted
ly
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n
d
ly
,
f
r
o
m
Fig
u
r
e
1
3
(
b
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th
e
PV
p
o
wer
r
is
es
f
astl
y
f
r
o
m
2
.
8
5
W
at
tim
e
1
4
.
2
2
s
to
its
MPP
o
f
2
2
W
at
tim
e
1
4
.
4
2
s
.
T
h
u
s
,
th
e
av
er
ag
e
s
p
ee
d
o
f
th
e
PV
p
o
wer
tr
ac
k
i
n
g
is
9
5
.
7
5
W
/s
.
T
h
ese
ex
p
e
r
im
en
tal
r
esu
lts
v
alid
ate
th
e
s
a
tis
f
ac
to
r
y
tr
ac
k
i
n
g
p
er
f
o
r
m
an
ce
o
f
th
e
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r
o
p
o
s
ed
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n
tr
o
l
m
eth
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d
.
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h
is
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ch
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p
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d
ed
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t
o
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ar
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eter
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alu
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o
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izatio
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o
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e
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ter
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al
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n
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o
ller
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d
th
e
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ter
n
al
ad
ap
ti
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e
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o
f
th
e
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r
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o
s
ed
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n
tr
o
l
m
eth
o
d
in
o
r
d
e
r
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o
b
tain
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ett
er
p
er
f
o
r
m
an
ce
o
f
b
o
th
p
er
f
o
r
m
an
ce
in
d
icato
r
s
.
(
a)
(
b
)
Fig
u
r
e
1
3
.
T
r
ac
k
in
g
p
e
r
f
o
r
m
a
n
ce
o
f
th
e
PV p
o
wer
: (
a)
tr
ac
k
in
g
r
ep
etitio
n
,
(
b
)
clo
s
ed
u
p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
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n
C
o
m
p
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t E
l Co
n
tr
o
l
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Vo
l.
18
,
No
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6
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Dec
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r
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4.
CO
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f
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5
W
/
s
.
ACK
NO
WL
E
DG
M
E
N
T
S
T
h
e
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th
o
r
s
co
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th
is
r
esear
ch
at
th
e
I
n
d
o
n
esian
I
n
s
titu
te
o
f
Scien
ce
s
(
L
I
PI)
,
B
an
d
u
n
g
-
I
n
d
o
n
esia.
T
h
is
r
esear
ch
was
also
f
in
an
cially
s
u
p
p
o
r
ted
b
y
th
e
Min
is
tr
y
o
f
E
n
er
g
y
an
d
Min
er
al
R
eso
u
r
ce
s
o
f
th
e
R
ep
u
b
lic
o
f
I
n
d
o
n
esia
(
K
E
SDM)
an
d
U
n
iv
er
s
iti
T
ek
n
o
lo
g
i
Ma
lay
s
ia
(
UT
M)
.
T
h
e
a
u
th
o
r
s
d
eliv
er
th
ei
r
g
r
atitu
d
e
to
th
ese
th
r
ee
in
s
titu
tio
n
s
.
RE
F
E
R
E
NC
E
S
[1
]
T.
Esra
m
a
n
d
P
.
L.
C
h
a
p
m
a
n
,
“
C
o
m
p
a
riso
n
o
f
p
h
o
t
o
v
o
lt
a
ic
a
rra
y
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
te
c
h
n
iq
u
e
s,”
IEE
E
T
ra
n
s.
En
e
rg
y
C
o
n
v
e
rs
.
,
v
o
l.
2
2
,
n
o
.
2
,
p
p
.
4
3
9
-
4
4
9
,
2
0
0
7
.
[2
]
K.
Ish
a
q
u
e
a
n
d
Z
.
S
a
lam
,
"
A
re
v
iew
o
f
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
in
g
tec
h
n
i
q
u
e
s
o
f
P
V
sy
ste
m
fo
r
u
n
ifo
r
m
in
so
lati
o
n
a
n
d
p
a
rti
a
l
sh
a
d
in
g
c
o
n
d
i
ti
o
n
,
"
Re
n
e
wa
b
le
a
n
d
S
u
s
ta
in
a
b
le
E
n
e
rg
y
Rev
iews
,
El
se
v
ier
,
v
o
l.
1
9
,
p
p
.
4
7
5
-
4
8
8
,
2
0
1
3
.
[3
]
M
.
Ke
rm
a
d
i
a
n
d
E.
M
.
Be
rk
o
u
k
,
“
Artifi
c
ial
in
telli
g
e
n
c
e
-
b
a
se
d
m
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
i
n
g
c
o
n
tr
o
ll
e
rs
f
o
r
P
h
o
t
o
v
o
lt
a
ic sy
ste
m
s: Co
m
p
a
ra
ti
v
e
stu
d
y
,
”
Re
n
e
w.
S
u
sta
i
n
.
E
n
e
rg
y
Rev
.
,
v
o
l
.
6
9
,
p
p
.
3
6
9
-
3
8
6
,
2
0
1
7
.
[4
]
K
.
I
s
h
a
q
u
e
,
Z
.
S
a
l
a
m
,
a
n
d
G
.
La
u
ss
,
“
T
h
e
p
e
r
f
o
r
m
a
n
c
e
o
f
p
e
r
t
u
r
b
a
n
d
o
b
s
e
r
v
e
a
n
d
i
n
c
r
e
m
e
n
t
a
l
c
o
n
d
u
c
t
a
n
c
e
m
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
m
e
t
h
o
d
u
n
d
e
r
d
y
n
a
m
i
c
w
e
a
t
h
e
r
c
o
n
d
i
t
i
o
n
s
,
”
A
p
p
l
.
E
n
e
r
g
y
,
v
o
l
.
1
1
9
,
p
p
.
2
2
8
-
2
3
6
,
2
0
1
4
.
[5
]
K.
Ish
a
q
u
e
a
n
d
Z
.
S
a
lam
,
“
Dy
n
a
m
ic
e
fficie
n
c
y
o
f
d
irec
t
c
o
n
tro
l
b
a
se
d
m
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
e
rs,”
Pro
c
.
-
In
t
.
Co
n
f.
In
tell
.
S
y
st.
M
o
d
e
l.
S
imu
la
ti
o
n
,
IS
M
S
,
v
o
l.
2
0
1
5
-
S
e
p
te,
p
p
.
4
2
9
-
4
3
4
,
2
0
1
5
.
[6
]
M
.
N.
S
y
a
h
a
n
d
S
.
S
u
b
i
y
a
n
t
o
,
“
P
e
rfo
rm
a
n
c
e
e
n
h
a
n
c
e
m
e
n
t
o
f
m
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
i
n
g
f
o
r
g
rid
-
c
o
n
n
e
c
te
d
p
h
o
to
v
o
lt
a
ic
sy
ste
m
u
n
d
e
r
v
a
rio
u
s
g
ra
d
ien
t
o
f
irrad
ian
c
e
c
h
a
n
g
e
s,”
T
EL
KOM
NIKA
T
e
lec
o
mm
u
n
ica
ti
o
n
,
C
o
mp
u
ti
n
g
,
El
e
c
tro
n
ics
a
n
d
C
o
n
tro
l,
v
o
l.
1
7
,
n
o
.
4
,
p
p
.
1
9
7
3
-
1
9
8
4
,
2
0
1
9
.
[7
]
F
.
Li
u
,
S
.
Du
a
n
,
F
.
Li
u
,
B.
Li
u
,
a
n
d
Y.
Ka
n
g
,
“
A
v
a
riab
le
ste
p
siz
e
INC
M
P
P
T
m
e
th
o
d
fo
r
P
V
sy
ste
m
s,”
IEE
E
T
ra
n
s.
In
d
.
El
e
c
tro
n
.
,
v
o
l
.
5
5
,
n
o
.
7
,
p
p
.
2
6
2
2
-
2
6
2
8
,
2
0
0
8
.
[8
]
Y.
Zh
o
u
,
F
.
Li
u
,
J.
Yin
,
a
n
d
S
.
Du
a
n
,
“
S
t
u
d
y
o
n
re
a
li
z
in
g
M
P
P
T
b
y
imp
ro
v
e
d
i
n
c
re
m
e
n
tal
c
o
n
d
u
c
ta
n
c
e
m
e
th
o
d
wit
h
v
a
riab
le ste
p
-
siz
e
,
”
2
0
0
8
3
r
d
IEE
E
Co
n
f.
I
n
d
.
El
e
c
tro
n
.
Ap
p
l.
ICIE
A
2
0
0
8
,
p
p
.
5
4
7
-
5
5
0
,
2
0
0
8
.
[9
]
Q.
M
e
i,
M
.
S
h
a
n
,
L.
Li
u
,
a
n
d
J.
M
.
G
u
e
rre
ro
,
“
A
n
o
v
e
l
im
p
ro
v
e
d
v
a
riab
le
ste
p
-
siz
e
in
c
re
m
e
n
tal
-
re
sista
n
c
e
M
P
P
T
m
e
th
o
d
f
o
r
P
V s
y
ste
m
s,”
IEE
E
T
ra
n
s.
I
n
d
.
El
e
c
tro
n
.
,
v
o
l
.
5
8
,
n
o
.
6
,
p
p
.
2
4
2
7
-
2
4
3
4
,
2
0
1
1
.
[1
0
]
J.
Ah
m
e
d
a
n
d
Z.
S
a
lam
,
“
A
so
ft
c
o
m
p
u
ti
n
g
M
P
P
T
fo
r
P
V
sy
st
e
m
b
a
se
d
o
n
Cu
c
k
o
o
S
e
a
rc
h
a
lg
o
rit
h
m
,
”
In
t.
Co
n
f
.
Po
we
r E
n
g
.
E
n
e
rg
y
El
e
c
tr.
Dr
ive
s
,
n
o
.
M
a
y
,
p
p
.
5
5
8
-
5
6
2
,
2
0
1
3
.
[1
1
]
T.
Ra
d
jai,
L.
Ra
h
m
a
n
i,
S
.
M
e
k
h
il
e
f,
a
n
d
J
.
P
.
G
a
u
b
e
rt,
“
Im
p
lem
e
n
tatio
n
o
f
a
m
o
d
ifi
e
d
in
c
re
m
e
n
t
a
l
c
o
n
d
u
c
tan
c
e
M
P
P
T
a
lg
o
rit
h
m
with
d
irec
t
c
o
n
tro
l
b
a
se
d
o
n
a
fu
z
z
y
d
u
t
y
c
y
c
le
c
h
a
n
g
e
e
stim
a
to
r
u
sin
g
d
S
P
ACE,
”
S
o
l.
E
n
e
rg
y
,
v
o
l.
1
1
0
,
p
p
.
3
2
5
-
3
3
7
,
2
0
1
4
.
[1
2
]
M
.
M
.
Alg
a
z
a
r,
H.
Al
-
M
o
n
ier,
H.
A.
El
-
Ha
li
m
,
a
n
d
M
.
E.
E
.
K.
S
a
lem
,
“
M
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
i
n
g
u
sin
g
f
u
z
z
y
lo
g
ic co
n
tr
o
l,
”
I
n
t.
J
.
El
e
c
tr.
Po
w
e
r E
n
e
rg
y
S
y
st
.
,
v
o
l.
3
9
,
n
o
.
1
,
p
p
.
2
1
-
2
8
,
2
0
1
2
.
[1
3
]
R.
Ra
h
m
a
n
i,
M
.
S
e
y
e
d
m
a
h
m
o
u
d
i
a
n
,
S
.
M
e
k
h
il
e
f,
a
n
d
R
.
Yu
so
f
,
“
Im
p
lem
e
n
tatio
n
o
f
fu
z
z
y
l
o
g
ic
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
c
o
n
tr
o
ll
e
r
f
o
r
p
h
o
t
o
v
o
lt
a
ic sy
ste
m
,
”
Am.
J
.
A
p
p
l.
S
c
i
.
,
v
o
l.
1
0
,
n
o
.
3
,
p
p
.
2
0
9
-
2
1
8
,
2
0
1
3
.
[1
4
]
H.
M
a
h
a
m
u
d
u
l,
M
.
S
a
a
d
,
a
n
d
M
.
Ib
ra
h
im
He
n
k
,
“
P
h
o
to
v
o
l
taic
sy
s
tem
m
o
d
e
li
n
g
wit
h
f
u
z
z
y
l
o
g
ic
b
a
se
d
m
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
i
n
g
a
l
g
o
ri
th
m
,
”
In
t.
J
.
Ph
o
to
e
n
e
rg
y
,
v
o
l.
2
0
1
3
,
p
p
.
1
-
1
0
,
2
0
1
3
.
[1
5
]
C.
S
h
a
rm
a
a
n
d
A.
Ja
in
,
“
M
o
d
e
li
n
g
o
f
b
u
c
k
c
o
n
v
e
rter
m
o
d
e
ls
in
M
P
P
T
u
sin
g
P
ID
a
n
d
F
LC,
”
T
EL
KOM
NI
K
A
T
e
lec
o
mm
u
n
ica
ti
o
n
,
Co
m
p
u
t
in
g
,
El
e
c
tro
n
ics
a
n
d
C
o
n
tro
l
,
v
o
l.
1
3
,
n
o
.
4
,
p
p
.
1
2
7
0
-
1
2
8
0
,
2
0
1
5
.
[1
6
]
A.
G
h
e
ib
i,
S
.
M
.
A.
M
o
h
a
m
m
a
d
i,
a
n
d
M
.
M
.
F
a
rsa
n
g
i,
“
C
o
m
p
a
rin
g
P
e
rf
o
rm
a
n
c
e
Of
P
i
d
An
d
F
u
z
z
y
Co
n
tro
ll
e
rs
I
n
Th
e
P
re
se
n
t
Of N
o
ise
F
o
r
A
P
h
o
t
o
v
o
lt
a
ic S
y
ste
m
,
”
J
.
M
a
t
h
.
C
o
mp
u
t.
S
c
i
.
,
v
o
l
.
0
9
,
n
o
.
0
1
,
p
p
.
6
9
-
7
6
,
2
0
1
4
.
[1
7
]
B.
Be
n
d
ib
,
F
.
Krim
,
H.
Be
lmili
,
M
.
F
.
Alm
i,
a
n
d
S
.
B
o
u
lo
u
m
a
,
“
Ad
v
a
n
c
e
d
fu
z
z
y
M
P
P
T
c
o
n
tr
o
ll
e
r
f
o
r
a
sta
n
d
-
a
lo
n
e
P
V sy
ste
m
,
”
En
e
rg
y
Pro
c
e
d
i
a
,
v
o
l.
5
0
,
p
p
.
3
8
3
-
3
9
2
,
2
0
1
4
.
[1
8
]
U.
S
.
Ali,
“
Z
-
so
u
rc
e
DC
-
DC
C
o
n
v
e
rter
wit
h
F
u
z
z
y
L
o
g
ic
M
P
P
T
Co
n
tro
l
f
o
r
P
h
o
to
v
o
lt
a
ic
Ap
p
li
c
a
ti
o
n
s,”
En
e
rg
y
Pro
c
e
d
i
a
,
v
o
l.
9
0
,
n
o
.
De
c
e
m
b
e
r
2
0
1
5
,
p
p
.
1
6
3
-
1
7
0
,
2
0
1
6
.
[1
9
]
C.
L.
Li
u
,
J.
H.
Ch
e
n
,
Y.
H.
Li
u
,
a
n
d
Z.
Z.
Ya
n
g
,
“
An
a
sy
m
m
e
tri
c
a
l
fu
z
z
y
-
lo
g
ic
-
c
o
n
tr
o
l
-
b
a
se
d
M
P
P
T
a
lg
o
rit
h
m
fo
r
p
h
o
to
v
o
lt
a
ic s
y
ste
m
s,”
En
e
rg
ies
,
v
o
l.
7
,
n
o
.
4
,
p
p
.
2
1
7
7
-
2
1
9
3
,
2
0
1
4
.
[2
0
]
Am
iru
ll
a
h
,
A.
Kisw
a
n
t
o
n
o
,
O.
P
e
n
a
n
g
sa
n
g
,
a
n
d
A.
S
o
e
p
ri
jan
to
,
“
Tran
sie
n
t
p
o
we
r
q
u
a
li
t
y
p
e
rfo
r
m
a
n
c
e
o
f
m
u
lt
i
p
h
o
to
v
o
lt
a
ics
u
si
n
g
M
P
P
T
P
a
n
d
O/M
P
P
T
fu
z
z
y
,
”
T
EL
KOM
NIK
A
T
e
le
c
o
mm
u
n
ica
ti
o
n
,
Co
mp
u
ti
n
g
,
El
e
c
tro
n
ics
a
n
d
Co
n
tro
l,
v
o
l.
1
6
,
n
o
.
6
,
p
p
.
2
9
6
7
–
2
9
7
9
,
2
0
1
8
.
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