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r
t
cir
cu
it
cu
r
r
en
t/o
p
en
c
ir
cu
it
v
o
lta
g
e
u
n
d
er
d
is
s
i
m
ilar
w
ea
t
h
er
cir
cu
m
s
ta
n
ce
s
[
1
2
]
.
P
er
tu
r
b
an
d
o
b
s
er
v
e
tec
h
n
iq
u
e
i
s
th
e
u
s
u
all
y
u
s
ed
d
u
e
to
i
ts
s
i
m
p
licit
y
,
lo
w
co
s
t
a
n
d
ea
s
e
o
f
i
m
p
le
m
en
tatio
n
[
1
3
]
.
P
er
tu
r
b
an
d
o
b
s
er
v
e
w
o
r
k
s
ef
f
icien
tl
y
u
n
d
er
ch
a
n
g
in
g
wea
th
er
cir
cu
m
s
ta
n
ce
s
w
h
er
e
it
ca
n
r
ea
ch
th
e
er
r
o
r
s
ig
n
al
d
u
e
to
its
p
ar
tin
g
b
et
w
ee
n
th
e
MP
E
tech
n
iq
u
e
t
h
at
co
n
tr
o
ls
t
h
e
r
ef
er
en
ce
s
ig
n
al
an
d
th
e
d
u
t
y
-
c
y
cle
en
s
u
in
g
f
r
o
m
v
ar
y
i
n
g
th
e
r
ef
er
en
ce
s
i
g
n
al.
He
n
ce
,
p
er
tu
r
b
an
d
o
b
s
er
v
e
em
p
lo
y
s
th
e
MP
E
f
o
r
th
e
r
ef
er
en
ce
s
ig
n
al,
w
h
ile
th
e
d
c
to
d
c
co
n
v
er
ter
ca
n
b
e
co
n
tr
o
lled
s
e
p
ar
ately
.
Am
o
n
g
d
i
s
s
i
m
ilar
ar
tific
ial
in
t
ellig
e
n
t c
o
n
tr
o
ller
s
,
F
L
C
is
th
e
s
i
m
p
lest
to
i
n
te
g
r
ate
w
i
th
th
e
s
tr
u
ct
u
r
e.
L
atel
y
,
F
L
C
h
a
s
r
ec
eiv
ed
a
n
in
cr
ea
s
i
n
g
a
tten
tio
n
f
r
o
m
r
ese
ar
ch
er
s
f
o
r
m
o
to
r
d
r
iv
es,
co
n
v
er
ter
co
n
tr
o
l,
an
d
o
th
er
p
r
o
ce
s
s
co
n
tr
o
l
as
it
o
f
f
er
s
b
etter
r
ea
ctio
n
s
th
a
n
o
t
h
er
tr
ad
itio
n
al
co
n
tr
o
ller
s
[
1
4
-
2
0
]
.
T
h
e
in
ac
c
u
r
ac
y
o
f
th
e
w
ea
t
h
er
c
h
an
g
es
th
a
t
ca
n
b
e
r
ef
lecte
d
b
y
p
h
o
to
v
o
ltaic
a
r
r
ay
s
ca
n
b
e
ex
p
o
s
ed
ac
c
u
r
atel
y
u
s
i
n
g
f
u
zz
y
lo
g
ic
b
ased
co
n
tr
o
ller
.
I
n
o
r
d
er
to
t
ak
e
t
h
e
m
er
it
s
o
f
F
L
C
al
g
o
r
it
h
m
,
th
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
tr
ac
k
i
n
g
al
g
o
r
it
h
m
is
in
te
g
r
ated
u
s
i
n
g
f
u
zz
y
b
ase
d
co
n
tr
o
ller
s
o
th
at
th
e
co
m
p
l
ete
co
n
tr
o
l
s
y
s
te
m
ca
n
al
w
a
y
s
d
eliv
er
m
a
x
i
m
u
m
p
o
w
er
tr
an
s
f
er
f
r
o
m
p
h
o
to
v
o
ltaic
p
an
el
to
th
e
co
n
v
er
ter
s
id
e,
in
s
p
ite
o
f
th
e
u
n
p
r
ed
ictab
le
clim
a
te
cir
cu
m
s
ta
n
ce
s
.
T
h
e
p
r
o
b
le
m
o
f
m
o
s
t
o
f
t
h
e
F
L
C
-
b
ased
M
P
E
alg
o
r
ith
m
s
[
1
5
-
1
8
]
is
t
h
a
t
th
e
tr
ac
in
g
p
o
i
n
t
i
s
s
itu
a
ted
a
w
a
y
f
r
o
m
th
e
MP
E
w
h
e
n
th
e
cli
m
ate
co
n
d
itio
n
s
v
ar
iatio
n
.
Mo
r
eo
v
er
,
t
h
e
MP
E
tr
ac
k
i
n
g
co
n
tr
o
l
d
ep
en
d
in
g
o
n
d
u
t
y
-
c
y
cle
v
ar
i
atio
n
s
ca
u
s
e
s
n
eg
lig
e
n
ce
i
n
p
o
w
er
co
n
v
er
ter
er
r
o
r
s
ig
n
al
c
o
n
tr
o
ller
.
T
h
o
u
g
h
,
th
er
e
is
a
n
es
s
en
t
ial
to
co
n
tr
o
l
th
e
d
u
t
y
c
y
cle
o
f
t
h
e
c
h
ar
g
e
co
n
v
er
ter
an
d
to
tr
ac
e
th
e
MP
E
d
ep
en
d
in
g
o
n
r
ef
er
en
ce
s
i
g
n
al,
n
o
t
d
u
t
y
c
y
cle
[
1
6
-
2
0
]
.
T
h
is
p
ap
er
p
r
esen
ts
a
n
e
w
f
u
zz
y
lo
g
ic
co
n
tr
o
l
-
b
ased
i
m
p
r
o
v
ed
P
&
O
tech
n
iq
u
e
f
o
r
MP
E
s
tan
d
alo
n
e
p
h
o
to
v
o
lta
ic
s
y
s
te
m
.
T
h
e
d
esig
n
ed
MP
E
tr
ac
k
in
g
i
s
ca
p
ab
le
o
f
ex
p
lo
itin
g
t
h
e
m
er
its
o
f
th
e
p
e
r
tu
r
b
an
d
o
b
s
er
v
e
m
et
h
o
d
an
d
er
ad
icate
s
its
p
r
o
b
le
m
s
.
T
h
e
MP
E
is
an
al
y
ze
d
b
y
co
n
v
er
ti
n
g
t
h
e
i
m
p
r
o
v
ed
P
&
O
alg
o
r
ith
m
in
to
3
7
f
u
zz
y
r
u
le
s
af
ter
th
e
co
n
tr
o
ller
t
w
o
i
n
p
u
t
s
an
d
s
in
g
le
o
u
tp
u
t
h
av
e
b
ee
n
d
i
v
id
ed
to
s
e
v
en
f
u
zz
y
s
u
b
s
ets.
A
s
th
e
d
esig
n
ed
tech
n
iq
u
e
al
w
a
y
s
tr
a
n
s
f
er
s
e
x
tr
e
m
e
p
o
w
er
f
r
o
m
p
h
o
to
v
o
ltaic
ar
r
a
y
s
,
i
t
en
h
a
n
c
es
th
e
n
u
m
b
er
o
f
p
h
o
to
v
o
ltai
c
m
o
d
u
le
s
.
T
h
e
d
esig
n
ed
s
y
s
t
e
m
i
s
in
s
ti
g
ated
i
n
r
ea
l
-
ti
m
e
u
s
i
n
g
m
icr
o
co
n
tr
o
lle
r
b
o
ar
d
.
2.
I
M
P
RO
VE
D
P
E
RT
URB
A
T
I
O
N
AND
O
B
SE
RV
AT
I
O
N
M
E
T
H
O
D
T
h
e
co
n
v
e
n
tio
n
al
P
er
tu
r
b
atio
n
a
n
d
Ob
s
er
v
atio
n
(
P
&
O)
al
g
o
r
ith
m
i
s
w
o
r
k
in
g
o
n
t
h
e
s
u
b
s
eq
u
e
n
t
p
r
in
cip
le:
i
f
t
h
e
v
o
ltag
e
o
r
cu
r
r
en
t
o
f
t
h
e
p
h
o
to
v
o
ltaic
ar
r
a
y
i
s
p
er
tu
r
b
ed
in
a
p
ar
ticu
la
r
d
ir
ec
tio
n
an
d
t
h
e
p
h
o
to
v
o
ltaic
p
o
w
er
r
is
es,
th
i
s
m
ea
n
s
th
a
t
th
e
f
u
n
ctio
n
i
n
g
p
o
in
t
h
a
s
tr
ac
ed
to
w
ar
d
th
e
p
ea
k
p
o
w
er
an
d
,
h
e
n
ce
,
th
e
f
u
n
ctio
n
in
g
v
o
lta
g
e
o
r
cu
r
r
en
t
m
u
s
t b
e
p
er
tu
r
b
ed
in
th
e
s
i
m
ilar
d
ir
ec
tio
n
.
E
ls
e,
i
f
th
e
p
o
w
er
r
ed
u
ctio
n
s
,
th
e
f
u
n
ctio
n
i
n
g
p
o
in
t
h
a
s
p
r
o
g
r
es
s
ed
a
w
a
y
f
r
o
m
t
h
e
p
ea
k
p
o
w
e
r
an
d
,
s
o
,
t
h
e
r
o
u
te
o
f
t
h
e
f
u
n
ctio
n
in
g
v
o
lta
g
e
o
r
cu
r
r
en
t p
er
tu
r
b
atio
n
m
u
s
t b
e
i
n
v
er
ted
[
1
7
,
2
1
]
.
P
er
tu
r
b
an
d
o
b
s
er
v
e
f
u
n
ctio
n
s
b
y
v
ar
y
i
n
g
th
e
p
o
w
er
co
n
v
er
t
er
v
o
ltag
e
r
e
f
er
en
ce
s
i
g
n
al
o
r
d
u
t
y
-
c
y
cle
an
d
d
etec
tin
g
its
i
m
p
ac
t
o
n
t
h
e
o
u
tp
u
t
p
o
w
er
[
1
8
]
.
T
h
e
p
er
t
u
r
b
atio
n
an
d
o
b
s
er
v
atio
n
is
t
h
e
m
o
s
t
u
s
u
all
y
u
s
ed
s
y
s
te
m
b
ec
au
s
e
o
f
its
ea
s
e
o
f
i
m
p
le
m
en
ta
tio
n
,
s
i
m
p
licit
y
a
n
d
lo
w
co
s
t.
B
u
t,
it
f
l
u
ctu
ates
ar
o
u
n
d
th
e
f
u
n
ctio
n
i
n
g
p
o
in
t
w
h
ich
ca
u
s
es
lo
s
s
es
i
n
th
e
p
o
w
er
,
an
d
th
e
f
u
n
ct
io
n
i
n
g
p
o
in
t
tr
ac
es
a
w
a
y
f
r
o
m
t
h
e
p
ea
k
p
o
w
er
p
o
in
t
w
h
ic
h
lo
s
e
s
th
e
w
a
y
d
u
r
i
n
g
f
as
t
w
ea
th
er
(
r
ad
ian
ce
)
ch
a
n
g
e
s
.
Du
e
to
t
h
e
p
r
o
b
lem
s
th
e
s
w
i
n
g
ar
o
u
n
d
to
th
is
p
ea
k
p
o
in
t
[
1
9
]
.
Fig
u
r
e
1
illu
s
tr
atio
n
s
t
h
e
b
eh
av
io
r
o
f
th
e
p
h
o
to
v
o
ltaic
p
o
w
er
u
s
i
n
g
t
h
e
tr
ad
itio
n
al
P
&
O
MP
E
tech
n
iq
u
e.
T
h
e
p
h
o
to
v
o
lta
ic
o
u
tp
u
t
p
o
w
er
i
s
i
m
p
o
s
ed
to
tr
a
ck
to
w
ar
d
th
e
MP
E
p
o
in
t.
Af
ter
attain
m
e
n
t
t
h
e
b
est
p
o
in
t,
th
e
p
h
o
to
v
o
ltaic
o
u
tp
u
t
p
o
w
er
f
l
u
ct
u
ates
ar
o
u
n
d
th
e
p
o
in
t.
A
t
t
h
e
p
er
io
d
0
.
3
3
s
ec
o
n
d
s
,
th
e
r
ad
iatio
n
r
ed
u
ce
d
; so
,
p
o
w
er
d
ev
iates
f
r
o
m
t
h
e
b
est v
a
lu
e
d
u
e
to
th
e
p
r
o
b
lem
af
o
r
e
m
en
t
io
n
ed
.
T
h
e
co
n
v
en
tio
n
al
P
&
O
alg
o
r
ith
m
m
a
y
e
x
h
ib
it
er
r
atic
b
eh
av
io
r
in
f
ast
v
ar
y
i
n
g
atm
o
s
p
h
er
i
c
cir
cu
m
s
ta
n
ce
s
as
a
r
es
u
lt
o
f
m
o
v
i
n
g
clo
u
d
s
.
T
h
is
li
m
itatio
n
ca
n
b
e
i
llu
m
i
n
ated
u
s
in
g
F
ig
u
r
e
2
w
it
h
a
t
w
o
v
o
ltag
e
v
er
s
u
s
p
o
w
er
cu
r
v
es
w
it
h
ch
a
n
g
i
n
g
r
ad
ian
ce
[
2
0
]
.
Ass
u
m
e
th
at
t
h
e
f
u
n
c
tio
n
i
n
g
p
o
in
t
is
at
th
e
p
o
in
t
„
A‟
a
n
d
is
f
lu
ct
u
ati
n
g
ar
o
u
n
d
th
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
an
d
a
p
er
tu
r
b
atio
n
w
il
l
m
o
v
e
s
t
h
e
f
u
n
c
tio
n
i
n
g
p
o
in
t
to
w
ar
d
th
e
p
o
in
t
„
B
‟
.
Ne
v
er
t
h
eles
s
,
if
t
h
e
r
ad
ian
ce
r
i
s
es
r
ap
id
ly
to
cu
r
v
e
P
2
p
o
w
er
c
u
r
v
e
w
i
th
i
n
s
in
g
le
s
a
m
p
li
n
g
p
er
io
d
,
th
e
f
u
n
c
ti
o
n
in
g
p
o
in
t
w
il
l
r
ea
ll
y
m
o
v
es
f
r
o
m
t
h
e
p
o
in
t
„
A‟
to
w
ar
d
t
h
e
p
o
in
t
„
C
‟
.
T
h
is
d
if
f
ic
u
lt
o
cc
u
r
s
b
ec
au
s
e
th
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
tr
a
ck
in
g
ca
n
n
o
t
r
ec
o
g
n
ize
th
a
t
p
o
w
er
in
cr
e
m
en
t
is
th
e
r
esu
l
t
o
f
th
e
r
is
i
n
g
r
ad
iatio
n
an
d
s
i
m
p
l
y
ass
u
m
es
t
h
at
it
is
th
e
r
esu
lt
o
f
m
o
v
i
n
g
t
h
e
f
u
n
ct
io
n
in
g
p
o
in
t
to
th
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t.
I
f
th
e
r
ad
ian
ce
is
s
till
r
ap
id
l
y
r
is
i
n
g
,
th
e
MP
E
co
n
ti
n
u
in
g
to
p
er
t
u
r
b
to
th
e
r
ig
h
t
a
g
ai
n
an
d
th
e
f
u
n
ctio
n
i
n
g
p
o
in
t
co
n
tin
u
es
to
d
ev
iate
f
r
o
m
t
h
e
r
ea
l
MP
E
u
n
til
th
e
s
o
lar
ir
r
ad
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n
alter
atio
n
s
lo
w
s
.
T
h
is
co
n
d
itio
n
ca
n
o
cc
u
r
o
n
th
e
p
ar
tl
y
clo
u
d
y
d
a
y
s
,
an
d
th
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
ex
tr
ac
ti
n
g
is
m
o
s
t
p
r
o
b
lem
atic
b
ec
au
s
e
o
f
t
h
e
f
r
e
q
u
en
t
m
o
v
e
m
e
n
t o
f
t
h
e
m
a
x
i
m
u
m
p
o
w
er
ex
tr
ac
ti
n
g
p
o
in
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
n
t
J
R
ob
&
A
u
to
m
,
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
9
:
2
6
–
3
5
28
T
h
e
Div
er
g
e
n
ce
o
f
th
e
co
n
v
e
n
tio
n
al
P
&
O
f
r
o
m
t
h
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
u
n
d
er
r
ap
id
l
y
v
ar
y
i
n
g
at
m
o
s
p
h
er
ic
cir
c
u
m
s
ta
n
ce
s
t
h
at
w
as
d
e
f
i
n
ed
in
t
h
e
p
r
ev
io
u
s
s
ec
tio
n
ca
n
b
e
s
o
l
v
e
d
b
y
u
tili
zi
n
g
t
h
e
p
h
o
to
v
o
ltaic
v
o
lta
g
e
-
c
u
r
r
en
t
cu
r
v
e.
A
s
s
h
o
w
n
i
n
th
is
cu
r
v
e,
in
f
i
x
ed
r
ad
iatio
n
,
w
h
e
n
th
e
v
o
ltag
e
d
ec
r
ea
s
es
(
in
cr
ea
s
es),
t
h
e
cu
r
r
en
t
is
i
n
cr
ea
s
es
(
d
ec
r
ea
s
es).
Usi
n
g
th
is
s
i
m
p
le
s
tati
s
tic,
ca
n
b
e
r
eso
l
v
ed
th
e
Di
v
er
g
e
n
ce
f
r
o
m
t
h
e
r
ea
l
MP
E
in
r
ap
id
l
y
v
ar
y
i
n
g
at
m
o
s
p
h
er
ic
s
it
u
ati
o
n
s
,
as
f
o
llo
w
.
I
f
t
h
e
i
n
cr
ea
s
es
v
o
lta
g
e
an
d
t
h
e
in
cr
ea
s
es
in
s
ta
n
tan
eo
u
s
l
y
i
n
cr
ea
s
e
an
d
t
h
e
cu
r
r
e
n
t
i
n
cr
ea
s
e
s
to
o
,
th
e
al
g
o
r
ith
m
r
ea
lizes
t
h
at
it
i
s
i
n
r
ap
id
l
y
v
ar
y
i
n
g
at
m
o
s
p
h
er
ic
s
i
tu
atio
n
s
an
d
d
ec
r
ea
s
es
t
h
e
v
o
lta
g
e,
in
s
tead
,
it
i
n
cr
ea
s
e
s
.
W
h
en
t
h
e
v
o
lta
g
e
a
n
d
th
e
p
o
w
er
ar
e
in
cr
ea
s
i
n
g
s
i
m
u
l
ta
n
eo
u
s
l
y
a
n
d
th
e
c
u
r
r
en
t
i
s
d
ec
r
ea
s
in
g
,
alg
o
r
it
h
m
is
i
n
f
i
x
ed
ir
r
ad
iatio
n
an
d
in
cr
ea
s
es
t
h
e
v
o
ltag
e.
Hen
c
e
th
e
MP
E
tr
ac
k
i
n
g
al
g
o
r
ith
m
a
v
o
id
s
d
i
f
f
er
e
n
t
f
r
o
m
th
e
ac
tu
a
l
MP
E
.
T
h
e
im
p
r
o
v
ed
P
&
O
al
g
o
r
ith
m
f
lo
w
ch
ar
t i
s
o
f
f
er
ed
in
Fi
g
u
r
e
3.
Fig
u
r
e
1
.
P
h
o
to
v
o
ltaic
o
u
tp
u
t
p
o
w
er
o
f
t
h
e
co
n
v
e
n
tio
n
al
P
&
O
ap
p
r
o
ac
h
Fig
u
r
e
2
.
Var
ian
ce
o
f
co
n
v
en
t
i
o
n
al
P
&
O
f
r
o
m
MP
E
as sh
o
w
n
i
n
Fig
u
r
e
3
.
I
m
p
r
o
v
ed
P
&
O
alg
o
r
ith
m
f
lo
w
ch
ar
t a
s
s
h
o
w
n
i
n
[
2
]
3.
SUG
G
E
S
T
E
D
NO
VE
L
F
U
Z
Z
Y
SYS
T
E
M
T
h
e
ch
an
g
e
o
f
v
o
lta
g
e
o
u
tp
u
t
f
ed
to
t
h
e
b
atter
y
a
n
d
co
n
v
er
t
in
to
AC
b
y
u
s
i
n
g
i
n
v
er
ter
is
t
h
e
p
r
i
m
ar
y
o
p
er
atio
n
o
f
th
e
D
C
to
D
C
b
o
o
s
t
co
n
v
er
ter
.
I
n
t
h
i
s
p
r
o
ce
s
s
d
u
t
y
-
c
y
cle
le
v
el
d
ec
r
ea
s
es
o
r
i
n
cr
ea
s
es
d
ep
en
d
i
n
g
o
n
th
e
m
ax
i
m
u
m
p
o
w
er
.
I
n
a
d
d
itio
n
,
th
e
co
n
tr
o
l
ler
v
ar
iati
o
n
s
th
e
v
o
lta
g
e
lev
el
o
f
o
u
tp
u
t
b
y
c
h
an
g
i
n
g
t
h
e
d
u
t
y
-
c
y
cle
o
f
th
e
P
W
M
s
ig
n
al
,
w
h
ich
tr
ac
es
t
h
e
r
ef
er
e
n
ce
s
i
g
n
al.
A
tr
ia
n
g
u
lar
r
ef
er
e
n
ce
s
i
g
n
al
i
s
li
k
en
ed
w
it
h
th
e
o
u
tp
u
t
s
i
g
n
al
o
f
f
u
zz
y
v
o
l
tag
e
r
ef
er
e
n
ce
to
p
r
o
d
u
ce
a
s
u
p
p
o
s
ed
l
y
ze
r
o
er
r
o
r
s
ig
n
al
.
T
h
e
f
u
zz
y
r
u
les
ar
e
d
er
iv
ed
f
r
o
m
i
m
p
r
o
v
ed
p
er
tu
r
b
an
d
o
b
s
er
v
e
m
et
h
o
d
.
T
h
is
r
ef
er
en
ce
s
i
g
n
al
i
s
ad
ap
tiv
e,
v
ar
y
i
n
g
it
s
s
h
ap
e
ac
co
r
d
in
g
to
cli
m
atic
s
it
u
atio
n
s
.
T
h
e
b
o
o
s
t c
o
n
v
er
ter
f
ee
d
th
e
b
atter
y
lo
ad
w
it
h
th
e
m
o
s
t s
u
itab
le
p
o
w
er
.
T
h
e
p
r
o
p
o
s
ed
en
tire
b
lo
c
k
d
ia
g
r
a
m
Fi
g
u
r
e
4
i
s
s
h
o
w
s
o
f
b
o
o
s
t
d
c
to
d
c
co
n
v
er
ter
to
g
eth
e
r
w
it
h
th
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
tr
ac
k
i
n
g
a
n
d
th
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
.
T
h
e
cr
ea
tio
n
o
f
FLC
w
a
s
d
o
n
e
u
s
i
n
g
Ma
m
d
a
n
i
tech
n
iq
u
e.
T
h
e
d
esig
n
o
f
th
e
r
u
les,
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
w
il
l
b
e
d
etailed
in
t
h
e
n
e
x
t
s
ec
tio
n
s
.
T
h
e
P
u
ls
e
W
id
th
Mo
d
u
latio
n
P
W
M)
ch
an
g
e
s
its
d
u
t
y
-
c
y
cle
ac
co
r
d
in
g
t
o
th
e
co
n
tr
o
l sig
n
al.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
MPP
T u
s
in
g
n
o
ve
l F
LC
b
a
s
ed
MPO
fo
r
p
h
o
to
vo
lta
ic
s
ystem
(
R.
A
r
u
lmu
r
u
g
a
n
)
29
4.
I
M
P
RO
VE
D
P
&O
B
ASE
D
NE
W
F
U
Z
Z
Y
L
O
G
I
C
B
AS
E
D
M
E
T
H
O
D
I
n
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
d
esi
g
n
,
o
n
e
s
h
o
u
ld
d
etec
t
t
h
e
f
o
r
e
m
o
s
t
co
n
tr
o
l
v
ar
iab
les
a
n
d
r
eg
u
la
te
t
h
e
s
ets
t
h
at
d
e
f
in
e
th
e
v
al
u
es
o
f
in
d
iv
id
u
all
y
li
n
g
u
is
tic
v
ar
iab
le.
T
h
e
i
m
p
r
o
v
ed
P
er
tu
r
b
an
d
Ob
s
er
v
e
(
P
&
O)
s
ea
r
ch
i
n
g
al
g
o
r
ith
m
is
ca
lc
u
l
ated
to
attain
th
e
m
er
i
ts
o
f
c
o
n
v
e
n
tio
n
al
P
&
O
s
i
m
p
lici
t
y
a
n
d
er
ad
icate
all
af
o
r
e
m
e
n
tio
n
ed
d
is
ad
v
a
n
ta
g
e
s
.
T
h
e
ch
an
g
e
i
n
p
h
o
to
v
o
lta
i
c
o
u
tp
u
t
v
o
lta
g
e
an
d
t
h
e
ch
a
n
g
e
i
n
p
h
o
to
v
o
ltaic
ar
r
ay
o
u
tp
u
t
p
o
w
er
ar
e
t
h
e
t
wo
in
p
u
t
o
f
t
h
e
m
o
d
i
f
ied
F
L
C
ap
p
r
o
ac
h
.
T
h
e
in
cr
e
m
e
n
t
o
f
t
h
e
r
ef
er
e
n
ce
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
F
L
C
w
h
er
e
f
ed
in
to
d
is
cr
ete
P
I
co
n
tr
o
ller
th
r
o
u
g
h
P
u
ls
e
W
id
t
h
Mo
d
u
la
tio
n
(
P
W
M
)
co
n
tr
o
l b
o
x
to
p
r
o
d
u
ce
th
e
p
u
ls
e.
T
h
e
t
w
o
in
p
u
t
s
an
d
s
i
n
g
le
o
u
tp
u
t
o
f
t
h
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
ar
e
g
iv
en
i
n
th
e
eq
u
atio
n
s
f
r
o
m
(
1
)
to
(
3
)
.
(
1
)
(
2
)
(
3
)
T
h
e
m
er
its
o
f
t
h
is
i
m
p
r
o
v
ed
in
p
er
t
u
r
b
an
d
o
b
s
er
v
e
i
s
t
h
a
t
th
e
o
u
tp
u
t
o
f
t
h
e
f
u
zz
y
b
as
ed
co
n
tr
o
l
ch
an
g
es
th
e
r
e
f
er
en
ce
v
o
lta
g
e
o
n
l
y
.
He
n
ce
,
t
h
e
d
u
t
y
c
y
cle
o
f
th
e
DC
to
DC
b
o
o
s
t
co
n
v
e
r
ter
ca
n
f
u
r
t
h
er
b
e
r
eg
u
lated
u
s
i
n
g
s
p
ec
i
f
ic
co
n
tr
o
ller
.
Mo
r
e
o
v
er
,
th
e
b
o
o
s
t
co
n
v
er
ter
co
n
tr
o
ller
en
s
u
r
es
t
h
a
t
th
e
p
h
o
to
v
o
ltaic
o
u
tp
u
t
p
o
w
er
d
o
es
n
o
t
d
e
v
iate
f
r
o
m
t
h
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
d
u
r
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n
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ch
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n
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in
g
w
ea
t
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er
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itu
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tio
n
s
o
r
v
ar
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le
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ad
.
(
a)
(
b
)
(
c)
Fig
u
r
e
4
.
(
a)
p
r
o
p
o
s
ed
o
v
er
all
s
etu
p
o
f
t
h
e
P
V
s
y
s
te
m
(
b
)
Su
b
s
y
s
te
m
o
f
t
h
e
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u
zz
y
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g
ic
co
n
tr
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ller
(
c)
DC
to
DC
B
o
o
s
t c
o
n
v
er
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
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4856
I
n
t
J
R
ob
&
A
u
to
m
,
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
9
:
2
6
–
3
5
30
T
h
e
v
ar
iab
les
o
f
t
h
e
in
p
u
t
f
u
z
z
y
lo
g
ic
ar
e
d
i
v
id
ed
i
n
to
s
e
v
e
n
f
u
zz
y
s
u
b
s
ets
w
h
ic
h
ar
e:
n
e
g
ati
v
e
b
i
g
(
NB
)
,
n
eg
ati
v
e
m
ed
i
u
m
(
NM
)
,
n
eg
at
iv
e
s
m
all
(
NS)
,
ze
r
o
(
Z
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o
s
iti
v
e
s
m
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P
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it
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v
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m
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M)
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itiv
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ig
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P
B
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h
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s
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n
f
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u
b
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ets
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t
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o
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les,
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th
e
ze
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ip
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l
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ak
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en
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t
y
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n
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e.
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h
e
Me
m
b
er
s
h
i
p
Fu
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tio
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s
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MF)
o
f
t
h
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u
tp
u
t
v
ar
iab
les
ar
e
n
i
n
e
-
ter
m
f
u
zz
y
s
ets
w
i
th
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lass
ical
tr
ian
g
u
lar
a
n
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tr
ap
ez
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p
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B
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ig
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NB
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at
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m
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u
m
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NM
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n
eg
a
t
iv
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s
m
all
(
N
S),
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r
o
(
Z
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,
p
o
s
itiv
e
s
m
all
(
P
S),
p
o
s
itiv
e
m
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i
u
m
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M)
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e
g
ati
v
e
v
er
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L
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m
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d
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ig
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B
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h
e
f
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zz
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h
n
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e
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d
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itio
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eth
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s
ed
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t
h
e
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er
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ce
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ter
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of
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p
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s
ed
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th
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ef
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zz
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f
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t
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th
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b
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et
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en
ce
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g
e
t
h
at
ch
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g
es to
r
ea
l n
u
m
b
er
s
as o
f
f
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ed
in
(
4
)
.
∑
∑
(
4
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W
h
er
e
Vr
ef
is
t
h
e
F
L
C
o
u
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t
a
n
d
Vr
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i
s
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m
i
m
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e
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o
f
i
m
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v
ed
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e
r
tu
r
b
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d
o
b
s
er
v
e
tech
n
iq
u
e.
T
h
e
f
u
zz
i
f
icatio
n
o
f
t
h
e
P
&
O
tech
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iq
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e
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i
t
h
t
h
e
r
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F
ig
u
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et
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o
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t
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d
t
w
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ts
e
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o
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ed
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Fig
u
r
e
6
d
ep
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o
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e
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eh
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io
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th
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n
tr
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ic
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n
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r
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t
h
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s
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t
f
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u
ct
u
a
tio
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o
n
ce
it
attain
s
th
e
MP
P;
th
is
ze
r
o
–
MF
is
co
n
s
id
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an
o
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tak
i
n
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e
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v
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g
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l
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ct
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ter
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ith
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zz
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m
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ip
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T
h
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tr
ian
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lar
f
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MF
f
o
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n
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g
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r
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7
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r
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8
r
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Fig
u
r
e
5
.
Fu
zz
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f
icatio
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o
f
th
e
i
m
p
r
o
v
ed
p
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tu
r
b
an
d
o
b
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er
v
e
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
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u
to
m
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N:
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u
r
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7
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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8
9
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4856
I
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&
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1
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r
ch
2
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9
:
2
6
–
3
5
32
5.
SI
M
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AT
I
O
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th
e
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e
n
ce
lo
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ased
MPPT
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2
2
]
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33
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RE
F
E
R
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NC
E
S
[1
]
A
h
m
a
d
H.
El
Kh
a
teb
,
e
t
a
l,
“
Fu
zz
y
lo
g
ic
c
o
n
tro
l
a
p
p
r
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h
o
f
a
ma
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o
we
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o
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t
e
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l
o
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in
g
S
EP
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o
n
v
e
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r
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r
sta
n
d
a
l
o
n
e
p
h
o
t
o
v
o
lt
a
ic
sy
ste
m
,
”
P
ro
c
e
e
d
in
g
o
f
th
e
3
rd
In
tern
a
ti
o
n
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l
Co
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re
n
c
e
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n
S
u
sta
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le
F
u
tu
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o
r
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u
m
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S
e
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rit
y
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p
.
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3
6
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o
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0
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n
v
.
2
0
1
3
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0
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6
8
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2
0
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3
.
[2
]
A
li
A
k
b
a
r
G
h
a
ss
a
m
i,
e
t
a
l
.
,
“
A
h
ig
h
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o
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n
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e
m
a
x
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m
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m
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in
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k
e
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f
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V
sy
ste
m
s
,
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e
c
trica
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Po
we
r
a
n
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E
n
e
rg
y
S
y
ste
ms
,
v
o
l.
5
3
,
p
p
.
2
3
7
–
2
4
3
,
2
0
1
3
.
[3
]
A
ru
l
m
u
ru
g
a
n
,
R,
“
C
o
m
p
a
ra
ti
v
e
e
v
a
lu
a
ti
o
n
o
f
n
e
w
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L
C
c
o
n
tro
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ler
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se
d
M
P
P
T
f
o
r
a
DC
to
DC
b
u
c
k
-
b
o
o
st
z
e
ta
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o
n
v
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rter
,
”
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S
EA
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n
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ti
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we
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ste
ms
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l.
1
1
,
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p
.
2
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4
,
E
-
IS
S
N:
2
2
2
4
-
3
5
0
X
,
2
0
1
6
.
[4
]
M
.
H.
Ra
sh
i
d
,
“
P
o
w
e
r
El
e
c
tro
n
ics
,
Circu
it
s De
v
ice
s an
d
A
p
p
li
c
a
ti
o
n
s,
”
A
c
a
d
e
m
i
c
P
re
ss
,
2
0
0
6
.
[5
]
R.
A
ru
l
m
u
ru
g
a
n
a
n
d
Dr.N.
S
u
t
h
a
n
t
h
irav
a
n
it
h
a
,
“
M
o
d
e
l
a
n
d
d
e
sig
n
o
f
f
u
z
z
y
-
b
a
s
e
d
Ho
p
f
ield
NN
trac
k
in
g
c
o
n
tr
o
ll
e
r
f
o
r
sta
n
d
a
lo
n
e
P
V
a
p
p
l
ica
ti
o
n
s
,
”
El
se
v
ier
-
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
tric
Po
we
r
S
y
ste
ms
Res
e
a
rc
h
(
IJ
EP
ES
),
v
o
l.
1
2
0
,
p
p
.
1
8
4
-
1
9
3
,
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I
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0
.
1
0
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6
/j
.
e
p
sr.
2
0
1
4
.
0
5
.
0
0
7
Im
p
a
c
t
,
2
0
1
5
.
[6
]
N.
M
u
t
o
h
,
M
.
Oh
n
o
,
a
n
d
T
.
In
o
u
e
,
“
A
m
e
th
o
d
f
o
r
M
P
P
T
c
o
n
tro
l
w
h
il
e
se
a
rc
h
in
g
f
o
r
p
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ra
m
e
ter
s
c
o
rre
sp
o
n
d
in
g
t
o
w
e
a
th
e
r
c
o
n
d
it
io
n
s
f
o
r
P
V
g
e
n
e
ra
ti
o
n
sy
st
em
s,
”
IEE
E
tra
n
sa
c
ti
o
n
s
in
d
u
stria
l
e
lec
tro
n
ics
,
v
o
l.
5
3
,
n
o
.
4
,
p
p
.
1
0
5
5
-
1
0
6
5
,
A
u
g
.
2
0
0
6
.
[7
]
R.
A
ru
lm
u
ru
g
a
n
,
e
t
a
l
.
,
“
T
ra
c
k
in
g
o
f
p
h
o
to
v
o
lt
a
ic
p
o
w
e
r
s
y
ste
m
w
it
h
n
e
w
F
u
z
z
y
L
o
g
ic Co
n
tro
l
stra
te
g
y
,
”
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
(
J
EE
)
,
V
o
l
u
m
e
1
4
,
2
0
1
4
-
E
d
it
i
o
n
:
4
,
p
p
.
1
-
1
0
.
IS
S
N
1
5
8
2
-
4
5
9
4
,
2
0
1
4
.
[8
]
A
ru
l
m
u
ru
g
a
n
,
R&
V
e
n
k
a
tes
a
n
,
T
,
“
Re
se
a
rc
h
a
n
d
Ex
p
e
ri
m
e
n
tal
I
m
p
lem
e
n
tatio
n
o
f
a
CV
-
F
OIN
C
A
lg
o
rit
h
m
Us
in
g
M
P
P
T
f
o
r
P
V
P
o
w
e
r
S
y
ste
m
,
”
J
o
u
rn
a
l
o
f
El
e
c
trica
l
E
n
g
i
n
e
e
rin
g
a
n
d
T
e
c
h
n
o
lo
g
y
,
v
o
l.
1
0
,
n
o
.
1
,
p
p
.
3
0
-
4
0
,
2
0
1
5
.
[9
]
B.
N.
A
la
j
m
i,
e
t
a
l
.
,
“
F
u
z
z
y
-
L
o
g
ic
-
Co
n
tro
l
A
p
p
ro
a
c
h
o
f
a
M
o
d
if
ie
d
Hill
-
Cli
m
b
in
g
M
e
th
o
d
f
o
r
M
a
x
m
u
m
P
o
w
e
r
P
o
in
t
in
m
icro
g
rid
sta
n
d
a
lo
n
e
p
h
o
t
o
v
o
lt
a
ic
sy
ste
m
,
”
IEE
E
T
ra
n
s.
Po
we
r
El
e
c
tro
n
ics
,
v
o
l.
2
6
,
n
o
.
4
,
p
p
.
1
0
2
2
-
1
0
3
0
,
2
0
1
1
[1
0
]
R.
A
ru
l
m
u
ru
g
a
n
,
e
t
a
l,
“
Op
ti
m
a
l
De
sig
n
o
f
DC
to
DC Bo
o
st Co
n
v
e
rter
w
it
h
Clo
se
d
L
o
o
p
Co
n
tro
l
P
ID M
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APPENDI
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Evaluation Warning : The document was created with Spire.PDF for Python.