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o
n
e
o
r
m
o
r
e
s
o
lar
p
an
els,
an
in
v
er
ter
,
a
n
d
o
t
h
er
elec
t
r
ical
an
d
m
ec
h
a
n
ical
co
m
p
o
n
e
n
ts
.
T
h
ese
elem
en
ts
wo
r
k
to
g
eth
e
r
to
ca
p
tu
r
e
s
o
lar
en
er
g
y
an
d
g
en
er
ate
elec
tr
i
city
,
illu
s
tr
atin
g
th
e
f
u
n
d
am
e
n
tal
o
p
er
atio
n
o
f
a
p
h
o
to
v
o
ltaic
s
y
s
tem
[
7
]
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
a
PV
s
y
s
tem
is
in
f
lu
en
ce
d
b
y
its
u
n
iq
u
e
ch
ar
a
cter
is
tic,
k
n
o
wn
as
th
e
m
ax
im
u
m
p
o
we
r
p
o
in
t
(
M
PP
)
,
wh
ich
v
ar
ies
with
ex
ter
n
al
f
ac
to
r
s
s
u
ch
as
ir
r
ad
iatio
n
an
d
tem
p
er
atu
r
e
[
8
]
.
A
k
ey
f
u
n
cti
o
n
o
f
PV
s
y
s
tem
s
is
to
ef
f
icien
tly
a
n
d
r
ap
id
ly
e
x
tr
ac
t
th
e
m
ax
im
u
m
av
aila
b
le
s
o
lar
en
e
r
g
y
u
n
d
er
v
ar
y
in
g
en
v
ir
o
n
m
e
n
tal
co
n
d
iti
o
n
s
,
a
p
r
o
ce
s
s
k
n
o
wn
as m
a
x
im
u
m
p
o
wer
p
o
i
n
t tr
ac
k
in
g
(
M
PP
T
)
[
9
]
,
[
1
0
]
.
Ov
er
th
e
y
ea
r
s
,
n
u
m
er
o
u
s
MPPT
alg
o
r
ith
m
s
h
av
e
b
ee
n
d
e
v
e
lo
p
ed
t
o
o
p
tim
ize
p
o
wer
tr
ac
k
in
g
in
PV
s
y
s
tem
s
,
in
clu
d
in
g
p
e
r
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
,
in
c
r
em
en
ta
l
co
n
d
u
cta
n
ce
(
I
NC
)
,
f
u
zz
y
lo
g
ic
co
n
t
r
o
l
(
FLC)
[
1
1
]
–
[
1
3
]
an
d
a
d
ap
tiv
e
f
r
ac
tio
n
al
o
r
d
er
PID
(
A
-
FOPID)
co
n
tr
o
ller
s
[
1
4
]
.
C
o
n
v
en
tio
n
al
m
e
th
o
d
s
s
u
ch
as
P&
O
an
d
I
NC
ar
e
wid
el
y
u
s
ed
d
u
e
t
o
th
eir
s
im
p
licity
a
n
d
ea
s
e
o
f
i
m
p
lem
en
tatio
n
.
T
h
e
P&
O
m
et
h
o
d
p
er
tu
r
b
s
th
e
PV
ar
r
ay
v
o
ltag
e
o
r
cu
r
r
e
n
t
to
tr
ac
k
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
,
wh
ile
I
N
C
d
eter
m
in
es
t
h
e
MPP
b
y
an
aly
zin
g
th
e
s
lo
p
e
o
f
th
e
PV
p
o
wer
cu
r
v
e
[
1
5
]
,
[
1
6
]
.
Ho
wev
er
,
th
ese
m
eth
o
d
s
f
ac
e
s
ig
n
if
ican
t
ch
all
en
g
es
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
(
PS
C
s
)
,
wh
er
e
th
e
p
o
wer
-
v
o
ltag
e
(P
-
V)
cu
r
v
e
co
n
tain
s
m
u
ltip
le
p
ea
k
s
,
in
clu
d
in
g
a
g
lo
b
al
m
ax
im
u
m
p
o
wer
p
o
in
t
(
GM
PP
)
an
d
s
ev
er
al
lo
ca
l
m
a
x
im
u
m
p
o
wer
p
o
in
ts
(
L
MPPs
)
.
T
h
is
o
f
ten
ca
u
s
es
P&
O
an
d
I
NC
to
b
ec
o
m
e
tr
ap
p
e
d
at
lo
ca
l
m
ax
im
a,
lead
in
g
to
p
o
wer
lo
s
s
es.
I
n
co
n
tr
ast,
FLC
o
f
f
er
s
g
r
ea
ter
ad
a
p
tab
ilit
y
th
r
o
u
g
h
r
u
le
-
b
ase
d
s
y
s
tem
s
,
an
d
A
-
FOPID
d
em
o
n
s
tr
ates
im
p
r
o
v
ed
tr
ac
k
in
g
ac
cu
r
ac
y
an
d
r
esp
o
n
s
e
s
p
ee
d
.
T
h
e
p
r
o
p
o
s
ed
asy
m
m
et
r
ical
FL
C
ap
p
r
o
ac
h
b
u
ild
s
u
p
o
n
th
ese
ad
v
a
n
ce
m
en
ts
b
y
b
al
an
cin
g
ad
a
p
tab
ilit
y
,
s
im
p
licity
,
an
d
f
lex
ib
ilit
y
,
m
ak
in
g
it
h
ig
h
ly
s
u
itab
le
f
o
r
r
ea
l
-
wo
r
ld
PV
s
y
s
tem
s
u
n
d
er
PS
C
s
.
Ad
d
r
ess
in
g
th
e
ch
allen
g
es
p
o
s
ed
b
y
PS
C
s
r
eq
u
ir
es
r
o
b
u
s
t
alg
o
r
ith
m
s
ca
p
ab
l
e
o
f
ac
cu
r
ately
d
is
ti
n
g
u
is
h
in
g
GM
PP
f
r
o
m
L
MPPs
u
n
d
er
v
ar
y
i
n
g
s
h
ad
in
g
s
ce
n
ar
i
o
s
[
1
7
]
.
FLC
alg
o
r
ith
m
is
an
o
t
h
er
wid
e
ly
u
s
ed
a
p
p
r
o
ac
h
f
o
r
t
r
ac
k
in
g
t
h
e
m
ax
im
u
m
p
o
wer
p
o
in
t
i
n
P
V
s
y
s
tem
s
,
p
ar
ticu
lar
ly
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
T
h
e
f
u
zz
y
c
o
n
tr
o
l
s
tr
ateg
y
ca
n
ef
f
ec
tiv
ely
a
d
d
r
ess
th
e
in
h
er
e
n
t
f
laws
in
PV
s
y
s
tem
s
b
y
d
y
n
am
ically
ad
ju
s
tin
g
to
v
a
r
iatio
n
s
in
o
p
er
atin
g
c
o
n
d
itio
n
s
[
1
8
]
,
[
1
9
]
.
On
e
o
f
th
e
k
e
y
ad
v
an
tag
es
o
f
f
u
zz
y
th
eo
r
y
is
its
ab
ilit
y
to
h
an
d
le
u
n
ce
r
tai
n
ties
an
d
in
ac
cu
r
ac
ies
r
elate
d
to
MPP
d
etec
tio
n
,
wh
ich
o
f
ten
a
r
is
e
f
r
o
m
f
lu
ctu
a
tio
n
s
in
s
o
lar
ir
r
a
d
ian
ce
an
d
lo
ad
ch
a
n
g
es
[
2
0
]
,
[
2
1
]
.
Ad
d
itio
n
ally
,
th
e
f
lex
i
b
ilit
y
o
f
f
u
zz
y
lo
g
ic
allo
ws
f
o
r
th
e
d
ev
elo
p
m
en
t
o
f
r
u
le
-
b
ased
s
y
s
tem
s
th
at
ca
n
a
d
ap
t
t
o
a
w
id
e
r
an
g
e
o
f
in
p
u
t
co
n
d
itio
n
s
,
en
s
u
r
in
g
m
o
r
e
r
eli
ab
le
an
d
ef
f
icien
t
MPP
tr
ac
k
in
g
in
co
m
p
lex
en
v
ir
o
n
m
en
ts
.
T
h
e
FLC
s
y
s
tem
u
s
e
s
two
in
p
u
t
v
ar
iab
les
an
d
o
n
e
o
u
tp
u
t
v
a
r
iab
le,
with
th
e
co
n
tr
o
l
p
r
o
ce
s
s
d
iv
id
ed
in
to
t
h
r
ee
s
tag
es:
f
u
zz
if
icatio
n
,
f
u
zz
y
in
f
er
en
ce
,
a
n
d
d
ef
u
zz
if
i
ca
tio
n
.
T
h
is
s
tu
d
y
aim
s
to
d
ev
elo
p
an
im
p
r
o
v
e
d
MPPT
alg
o
r
ith
m
th
at
lev
er
ag
es
asy
m
m
etr
ical
FLC
t
o
en
h
an
ce
tr
ac
k
in
g
p
e
r
f
o
r
m
an
ce
u
n
d
er
P
SC
s
.
T
h
e
n
o
v
elty
o
f
th
is
r
esear
ch
lies
in
th
e
im
p
lem
en
tatio
n
o
f
asy
m
m
etr
ical
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
an
d
tailo
r
ed
f
u
zz
y
r
u
le
s
ets,
wh
ich
im
p
r
o
v
e
tr
ac
k
i
n
g
ac
cu
r
ac
y
,
s
tab
ilit
y
,
an
d
ef
f
icien
cy
in
d
y
n
am
ically
ch
an
g
in
g
en
v
i
r
o
n
m
en
tal
co
n
d
itio
n
s
.
Un
lik
e
co
n
v
en
tio
n
al
f
u
zz
y
lo
g
ic
m
et
h
o
d
s
,
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
is
s
p
ec
if
ically
d
esig
n
ed
to
ad
a
p
t
to
th
e
c
o
m
p
lex
a
n
d
n
o
n
-
lin
ea
r
c
h
ar
ac
ter
is
tics
o
f
PV
s
y
s
tem
s
u
n
d
er
PS
C
s
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
is
p
ap
er
is
as
f
o
llo
ws:
Sect
io
n
2
p
r
o
v
id
es
an
o
v
er
v
iew
o
f
th
e
PV
s
y
s
tem
an
d
its
co
m
p
o
n
en
ts
.
Sectio
n
3
in
tr
o
d
u
ce
s
th
e
p
r
o
p
o
s
ed
asy
m
m
e
tr
ical
FLC
a
lg
o
r
ith
m
.
Sectio
n
4
d
is
cu
s
s
es
th
e
MA
T
L
AB
/S
im
u
lin
k
s
im
u
latio
n
r
esu
lts
,
an
d
Sectio
n
5
co
n
cl
u
d
es th
e
p
ap
er
.
2.
DE
SCR
I
P
T
I
O
N
O
F
T
H
E
P
H
O
T
O
VO
L
T
A
I
C
SY
ST
E
M
2
.
1
.
P
ho
t
o
v
o
lt
a
ic
(
P
V)
s
y
s
t
em
Fig
u
r
e
1
illu
s
tr
ates
th
e
b
lo
ck
d
iag
r
am
o
f
a
PV
s
y
s
tem
with
a
n
MPPT
co
n
tr
o
ller
.
T
h
e
s
y
s
tem
em
p
lo
y
s
an
MPPT
co
n
tr
o
ller
b
ased
o
n
asy
m
m
etr
ical
f
u
zz
y
lo
g
ic
c
o
n
t
r
o
l
(
AFLC),
wh
ich
p
r
o
ce
s
s
es
v
o
ltag
e
an
d
cu
r
r
en
t
in
p
u
ts
f
r
o
m
th
e
PV
p
a
n
el
to
a
d
ju
s
t
th
e
d
u
ty
cy
cle
ac
c
o
r
d
in
g
ly
.
T
h
e
d
ir
ec
t
cu
r
r
e
n
t
(
DC
)
-
to
-
d
ir
ec
t
cu
r
r
en
t
(
DC
)
co
n
v
er
ter
s
er
v
es
to
r
eg
u
late
t
h
e
DC
o
u
tp
u
t,
e
n
s
u
r
in
g
it
ca
n
b
e
ad
ju
s
ted
f
o
r
m
a
x
im
u
m
p
o
wer
ex
tr
ac
tio
n
[
2
2
]
.
T
h
e
AFLC a
lg
o
r
ith
m
in
v
o
lv
es th
r
ee
m
ain
p
r
o
ce
s
s
es: f
u
zz
if
icatio
n
,
in
f
er
e
n
ce
,
an
d
d
ef
u
zz
if
i
ca
tio
n
.
2
.
2
.
P
ho
t
o
v
o
lt
a
ic
c
ell
Fig
u
r
e
2
d
e
p
icts
a
cir
cu
it
m
o
d
e
l
o
f
a
s
o
lar
PV
ce
ll,
wh
ic
h
s
er
v
es
as
an
elec
tr
ical
t
r
an
s
d
u
ce
r
to
tr
an
s
f
o
r
m
p
h
o
to
n
en
e
r
g
y
f
r
o
m
lig
h
t
i
n
to
elec
tr
ical
en
e
r
g
y
.
A
c
u
r
r
e
n
t
s
o
u
r
ce
,
r
esis
to
r
s
,
an
d
a
d
io
d
e
m
ak
e
u
p
t
h
e
cir
c
u
it.
T
h
is
m
o
d
el
is
id
en
tifie
d
as
th
e
s
in
g
le
d
io
d
e
m
o
d
el
co
m
p
r
is
es
o
f
s
er
ies
r
esis
tan
ce
(
)
an
d
p
ar
allel
r
esis
tan
ce
(
)
.
I
d
ea
lly
,
an
d
ar
e
n
eg
lig
ib
le
,
b
u
t
in
p
r
ac
tice,
t
h
ese
r
esis
tan
ce
s
ca
n
n
o
t
b
e
ig
n
o
r
ed
,
as
th
ey
af
f
ec
t
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
6
4
2
-
2
6
5
4
2644
ef
f
icien
cy
o
f
th
e
s
o
lar
PV
ce
ll
[
2
3
]
.
So
lar
PV
ce
lls
ar
e
attac
h
ed
in
s
er
ies
o
r
p
ar
allel
co
m
b
i
n
atio
n
s
to
f
o
r
m
PV
m
o
d
u
les,
wh
ich
ar
e
th
e
n
lin
k
e
d
to
cr
ea
te
PV a
r
r
ay
s
with
th
e
r
eq
u
ir
ed
o
u
tp
u
t.
T
h
e
s
o
lar
PV
ce
ll's
o
u
tp
u
t c
an
b
e
d
er
iv
ed
u
s
in
g
Kir
ch
h
o
f
f
’
s
L
a
w:
(
)
=
ℎ
−
−
(
1
)
(
)
=
ℎ
−
∗
[
e
x
p
(
(
(
)
+
(
)
∗
)
)
−
1
]
−
(
)
+
(
)
ℎ
(
2
)
wh
ile
th
e
o
u
tp
u
t c
u
r
r
e
n
t f
o
r
th
e
PV a
r
r
ay
is
g
iv
en
as
=
.
ℎ
−
.
∗
[
e
xp
(
(
+
∗
(
/
)
)
)
−
1
]
−
/
+
/
(
/
)
(
/
)
(
3
)
Her
e,
d
en
o
tes
th
e
o
u
tp
u
t
cu
r
r
en
t,
wh
ile
r
ep
r
esen
ts
th
e
v
o
lta
g
e
o
f
t
h
e
PV
ar
r
ay
.
is
th
e
d
io
d
e’
s
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t,
r
ef
er
s
to
th
e
n
u
m
b
er
o
f
ce
lls
co
n
n
ec
t
ed
in
s
er
ies,
a
n
d
is
th
e
n
u
m
b
er
o
f
p
ar
allel
ce
lls
.
r
ep
r
esen
ts
th
e
elem
en
tar
y
ch
ar
g
e
with
a
v
alu
e
o
f
1
.
6
0
2
×
10
-
19
,
is
th
e
id
ea
lity
f
ac
to
r
,
is
B
o
ltzm
an
n
’
s
co
n
s
tan
t (
1
.
3
8
×
10
-
23
J
)
,
an
d
d
en
o
tes th
e
ac
tu
al
tem
p
er
atu
r
e.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
P
V
s
y
s
tem
Fig
u
r
e
2
.
E
q
u
iv
alen
t c
ir
c
u
it o
f
PV
ce
ll
2
.
3
.
P
V
s
y
s
t
e
m
s
un
der
pa
rt
ia
l sh
a
din
g
co
nd
it
io
ns
I
n
lar
g
e
PV
s
y
s
tem
s
,
s
o
lar
p
an
els
ar
e
ty
p
ically
co
n
n
ec
ted
i
n
s
er
ies
to
in
cr
ea
s
e
th
e
s
tr
in
g
v
o
ltag
e
o
r
in
p
ar
allel
to
b
o
o
s
t
o
u
tp
u
t
p
o
wer
[
2
4
]
.
Du
e
t
o
th
e
ex
ten
s
iv
e
ex
te
r
io
r
ar
ea
o
f
PV
m
o
d
u
les,
th
ey
ar
e
o
f
ten
u
n
co
v
e
r
ed
to
v
ar
y
in
g
s
o
lar
ir
r
ad
ian
ce
,
w
h
ich
is
a
m
ajo
r
ca
u
s
e
o
f
p
o
we
r
lo
s
s
es
in
P
V
s
y
s
tem
s
.
I
n
a
s
t
r
in
g
o
f
PV
m
o
d
u
les,
wh
en
in
d
iv
id
u
al
p
a
n
els ex
h
ib
i
t d
if
f
er
en
t sh
o
r
t
-
cir
c
u
it c
u
r
r
en
t
s
,
th
e
m
o
d
u
le
with
a
lo
wer
cu
r
r
en
t th
an
th
e
s
tr
in
g
cu
r
r
en
t w
ill ex
p
er
ien
ce
r
ev
er
s
e
v
o
ltag
e
a
n
d
b
eg
in
to
a
b
s
o
r
b
en
er
g
y
f
r
o
m
th
e
o
th
er
m
o
d
u
le
s
[
2
5
]
.
T
h
is
ca
n
lead
to
s
ig
n
if
ican
t
p
o
wer
d
is
s
ip
atio
n
in
th
e
f
o
r
m
o
f
h
ea
t,
p
o
ten
tia
lly
ca
u
s
in
g
p
er
m
an
en
t
d
estru
c
tio
n
to
th
e
af
f
ec
ted
PV
p
an
els.
T
h
ese
m
is
m
atch
ed
co
n
d
itio
n
s
,
p
a
r
ticu
lar
ly
r
esu
lt
in
g
f
r
o
m
s
o
lar
ir
r
ad
ian
ce
f
lu
ct
u
atio
n
s
,
em
p
h
asize
th
e
im
p
o
r
tan
ce
o
f
M
PP
T
f
o
r
e
n
s
u
r
in
g
o
p
tim
al
p
er
f
o
r
m
a
n
ce
co
n
tr
o
l.
I
n
Fig
u
r
e
3
,
th
e
PV
s
y
s
tem
is
d
is
p
lay
ed
with
p
ar
t
ial
s
h
ad
e
an
d
u
n
if
o
r
m
illu
m
in
atio
n
.
Fig
u
r
es
3
(
a)
an
d
3
(
b
)
s
h
o
w
th
e
o
p
er
atio
n
o
f
a
PV
ar
r
ay
c
o
m
p
r
is
in
g
o
f
th
r
ee
PV
m
o
d
u
les
attac
h
ed
in
p
ar
allel
with
b
y
p
ass
d
io
d
es.
Un
d
er
u
n
if
o
r
m
i
r
r
ad
iatio
n
,
th
e
b
y
p
ass
d
io
d
es
d
o
n
o
t
co
n
d
u
ct
a
n
d
h
a
v
e
n
o
im
p
ac
t
o
n
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
PV
ar
r
a
y
.
Ho
wev
er
,
d
u
r
in
g
PS
C
s
,
th
e
b
y
p
ass
d
io
d
es
ac
tiv
ate,
allo
win
g
cu
r
r
en
t
to
b
y
p
ass
th
e
s
h
ad
ed
ce
lls
.
W
ith
o
u
t
b
y
p
ass
d
io
d
es,
th
e
o
u
tp
u
t
p
o
wer
wo
u
ld
d
r
o
p
s
ig
n
if
ica
n
tly
.
T
h
e
r
ef
o
r
e,
t
o
m
ain
tain
DC
-
D
C
C
o
n
v
e
r
t
e
r
M
P
P
T
C
o
n
t
r
o
l
l
e
r
(
A
sy
mm
e
t
r
i
c
a
l
F
u
z
z
y
Lo
g
i
c
C
o
n
t
r
o
l
)
Lo
a
d
D
u
t
y
c
y
c
l
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
mp
a
r
a
tive
a
s
s
ess
men
t o
f a
n
imp
r
o
ve
d
a
s
ymm
etri
ca
l fu
z
z
y
lo
g
ic
…
(
A
th
ir
a
h
B
a
tr
is
yia
K
a
ma
l A
r
iffi
n
)
2645
h
ig
h
er
o
u
tp
u
t
p
o
wer
u
n
d
er
PS
C
s
,
b
y
p
ass
d
io
d
es
m
u
s
t
co
n
tin
u
ally
b
e
lin
k
ed
in
p
a
r
allel
with
a
s
et
o
f
PV
ce
ll
s
in
th
e
PV
m
o
d
u
les.
I
n
Fig
u
r
e
3
(
c)
,
th
e
P
-
V
cu
r
v
e
o
f
th
e
PV
ar
r
ay
d
is
p
lay
s
s
ev
er
al
L
MPPs
an
d
o
n
e
g
lo
b
al
m
ax
im
u
m
p
o
we
r
p
o
in
t
(
GM
PP
)
u
n
d
er
PS
C
s
.
Hen
ce
,
it
is
cr
it
ical
to
d
is
tin
g
u
is
h
b
etwe
en
th
e
GM
PP
an
d
L
MPP
s
.
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
PV G
en
er
ato
r
(
a)
u
n
d
er
u
n
i
f
o
r
m
i
r
r
ad
iatio
n
,
(
b
)
u
n
d
er
PS
C
s
an
d
(
c)
P
-
V
cu
r
v
e
u
n
d
er
u
n
if
o
r
m
ir
r
ad
iatio
n
an
d
PS
C
s
A
b
o
o
s
t
co
n
v
e
r
ter
is
a
DC
-
to
-
DC
co
n
v
er
ter
th
at
lo
wer
s
cu
r
r
en
t
f
r
o
m
th
e
s
u
p
p
ly
to
t
h
e
o
u
t
p
u
t
(
lo
ad
)
an
d
r
aises
v
o
ltag
e.
Fig
u
r
e
4
p
r
esen
ts
th
e
s
ch
em
atic
d
iag
r
am
o
f
a
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
.
T
h
e
in
s
u
lated
-
g
ate
b
ip
o
lar
tr
an
s
is
to
r
(
I
GB
T
)
s
wit
ch
,
in
d
u
cto
r
,
s
h
u
n
t
ca
p
ac
ito
r
,
an
d
d
io
d
e
ar
e
c
o
m
p
o
n
en
ts
o
f
th
e
b
o
o
s
t
co
n
v
e
r
ter
.
T
h
e
v
alu
es f
o
r
in
d
u
ctan
ce
,
ca
p
ac
itan
ce
,
d
u
ty
r
atio
,
an
d
r
esis
tiv
e
lo
ad
ca
n
b
e
ascer
tain
ed
as
(
4
)
-
(
7
)
.
=
/
∗
(
/
−
/
)
(
∆
/
)
(
4
)
=
1
−
(
/
/
)
(
5
)
=
(
/
∆
)
(
6
)
=
(
1
−
)
2
(
7
)
H
e
r
e
,
/
r
e
p
r
e
s
e
n
ts
t
h
e
o
u
t
p
u
t
v
o
lt
a
g
e
,
i
s
t
h
e
d
u
t
y
r
at
i
o
,
∆
i
s
t
h
e
r
ip
p
l
e
i
n
o
u
t
p
u
t
c
u
r
r
e
n
t
,
w
h
i
c
h
is
1
0
%
o
f
t
h
e
i
n
p
u
t
c
u
r
r
e
n
t
,
d
e
n
o
t
e
s
t
h
e
s
w
it
ch
i
n
g
f
r
e
q
u
e
n
c
y
,
∆
i
n
d
i
c
a
t
e
s
t
h
e
r
ip
p
l
e
i
n
p
e
a
k
v
o
l
t
a
g
e
,
i
s
t
h
e
a
v
e
r
a
g
e
o
u
t
p
u
t
c
u
r
r
e
n
t
c
o
n
s
i
d
e
r
e
d
as
3
%
o
f
t
h
e
o
u
t
p
u
t
v
o
l
t
a
g
e
,
/
i
s
t
h
e
i
n
p
u
t
v
o
l
t
a
g
e
,
a
n
d
r
e
f
e
r
s
t
o
t
h
e
i
n
p
u
t
r
e
s
is
t
a
n
c
e
.
Fig
u
r
e
4
.
Sch
em
atic
d
iag
r
am
o
f
DC
-
DC
b
o
o
s
t c
o
n
v
er
te
r
3.
P
RO
P
O
SE
D
ASY
M
M
E
T
RI
CAL F
UZ
Z
Y
L
O
G
I
C
CO
N
T
RO
L
-
B
AS
E
D
M
P
P
T
AL
G
O
RIT
H
M
3
.
1
.
Co
nv
ent
i
o
na
l P
&O
I
n
th
is
s
tu
d
y
,
th
e
c
o
n
v
e
n
tio
n
al
P&
O
m
eth
o
d
is
a
d
o
p
ted
as
a
b
en
ch
m
ar
k
to
c
o
m
p
ar
e
with
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
T
h
e
P&
O
alg
o
r
ith
m
is
ex
ten
s
iv
ely
em
p
lo
y
e
d
f
o
r
MPPT
in
p
h
o
t
o
v
o
ltaic
s
y
s
tem
s
b
ec
au
s
e
it
is
s
tr
aig
h
tf
o
r
war
d
a
n
d
s
im
p
le
to
u
s
e.
T
h
e
alg
o
r
it
h
m
o
p
e
r
ates
b
y
p
er
io
d
ically
p
er
tu
r
b
in
g
(
ad
ju
s
tin
g
)
th
e
o
p
er
atin
g
v
o
ltag
e
o
f
th
e
PV
s
y
s
tem
an
d
o
b
s
er
v
in
g
th
e
r
esu
ltin
g
ch
a
n
g
es
in
p
o
wer
o
u
tp
u
t
[
1
6
]
.
I
n
itially
,
th
e
s
y
s
tem
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
6
4
2
-
2
6
5
4
2646
m
ea
s
u
r
es
th
e
v
o
ltag
e
(
V)
an
d
cu
r
r
en
t
(
I
)
f
r
o
m
th
e
PV
ar
r
a
y
t
o
co
m
p
u
te
p
o
wer
(
P).
A
s
m
all
p
er
tu
r
b
atio
n
is
th
en
in
tr
o
d
u
ce
d
to
th
e
v
o
ltag
e,
eith
er
in
cr
ea
s
in
g
o
r
d
ec
r
ea
s
in
g
it.
T
o
d
eter
m
in
e
th
e
u
p
d
ate
d
p
o
wer
af
ter
th
e
d
is
tu
r
b
an
ce
,
t
h
e
n
ew
v
o
ltag
e
an
d
cu
r
r
en
t
ar
e
m
ea
s
u
r
ed
.
T
h
e
n
ew
p
o
wer
an
d
th
e
p
r
i
o
r
v
alu
e
ar
e
c
o
m
p
a
r
ed
b
y
th
e
alg
o
r
ith
m
.
T
h
e
p
er
tu
r
b
atio
n
p
er
s
is
ts
in
th
e
s
am
e
d
ir
ec
ti
o
n
f
o
r
th
e
s
u
b
s
eq
u
en
t
cy
cle
i
f
th
e
p
o
wer
is
in
c
r
ea
s
ed
.
On
th
e
o
th
er
h
a
n
d
,
th
e
d
ir
ec
ti
o
n
o
f
d
is
tu
r
b
an
ce
is
r
ev
er
s
ed
i
f
th
e
p
o
wer
d
r
o
p
s
.
T
h
is
o
p
er
at
io
n
o
f
p
e
r
tu
r
b
atio
n
an
d
o
b
s
er
v
atio
n
is
r
ep
ea
ted
,
with
th
e
alg
o
r
ith
m
iter
ativ
ely
ad
ju
s
tin
g
th
e
v
o
ltag
e
to
lo
ca
te
an
d
m
ain
tain
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t.
Alth
o
u
g
h
ef
f
ec
tiv
e,
th
e
P&
O
alg
o
r
i
th
m
m
ay
ca
u
s
e
f
lu
ctu
atio
n
s
a
r
o
u
n
d
th
e
MPP
an
d
ca
n
b
e
s
lo
w
t
o
ad
a
p
t to
en
v
ir
o
n
m
en
tal
ch
an
g
es.
3
.
2
.
Co
nv
ent
i
o
na
l F
L
C
a
lg
o
rit
hm
T
h
e
FLC
alg
o
r
ith
m
is
a
n
in
telli
g
en
t
co
n
tr
o
l
s
y
s
tem
th
at
u
s
es
f
u
zz
y
lo
g
ic
p
r
in
cip
les
to
r
eg
u
late
co
m
p
le
x
s
y
s
tem
s
,
in
clu
d
in
g
MPPT
in
p
h
o
to
v
o
ltaic
s
y
s
tem
s
.
W
ith
in
th
e
f
r
am
ewo
r
k
o
f
t
r
ac
k
in
g
th
e
G
MPP
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
FLC
p
r
o
v
id
es
a
f
lex
ib
le
ap
p
r
o
ac
h
f
o
r
ad
ju
s
tin
g
s
y
s
tem
p
ar
am
eter
s
b
ased
o
n
im
p
r
ec
is
e
in
p
u
ts
.
I
t
u
tili
ze
s
lin
g
u
is
tic
v
ar
iab
les,
f
u
zz
y
r
u
les,
a
n
d
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
to
m
o
d
el
s
y
s
tem
b
eh
av
io
r
an
d
m
ak
e
d
ec
is
io
n
s
u
n
d
er
u
n
ce
r
tai
n
co
n
d
itio
n
s
.
Ho
wev
er
,
co
n
v
e
n
tio
n
al
FLC
m
ay
s
tr
u
g
g
le
to
d
is
ti
n
g
u
is
h
b
etwe
en
lo
ca
l
MPPs
an
d
th
e
g
lo
b
al
MPPs
d
u
r
in
g
p
ar
tial
s
h
ad
in
g
c
o
n
d
i
tio
n
s
,
lead
in
g
to
s
u
b
o
p
tim
al
tr
a
ck
in
g
,
o
s
cillatio
n
s
,
an
d
ef
f
icien
c
y
lo
s
s
es.
T
o
ad
d
r
ess
th
ese
is
s
u
es,
th
e
d
esig
n
o
f
f
u
zz
y
l
o
g
ic
m
em
b
er
s
h
ip
f
u
n
c
tio
n
s
an
d
r
u
les
was
ad
ap
ted
f
r
o
m
m
eth
o
d
o
lo
g
ies
o
u
tlin
ed
b
y
[
2
0
]
,
[
2
6
]
,
wi
th
m
o
d
if
icatio
n
s
to
in
co
r
p
o
r
ate
asy
m
m
etr
ical
ch
ar
ac
ter
is
tics
f
o
r
im
p
r
o
v
ed
a
d
ap
tab
ilit
y
u
n
d
er
PS
C
s
.
3
.
3
.
P
r
o
po
s
ed
a
s
y
mm
et
rica
l
F
L
C
-
ba
s
ed
a
lg
o
rit
hm
I
n
th
e
co
n
v
en
ti
o
n
al
FLC
alg
o
r
ith
m
,
th
e
m
em
b
er
s
h
i
p
f
u
n
c
tio
n
s
(
MFs)
ar
e
d
esig
n
ed
s
y
m
m
etr
ically
ar
o
u
n
d
th
e
ze
r
o
o
r
n
eu
tr
al
p
o
in
t
o
f
th
e
in
p
u
t
v
ar
ia
b
les.
W
h
ile
d
esig
n
in
g
MFs
is
r
elativ
ely
s
tr
aig
h
tf
o
r
war
d
,
in
v
o
lv
in
g
th
e
u
n
if
o
r
m
d
e
f
in
itio
n
o
f
th
e
s
h
ap
e
an
d
s
p
r
ea
d
o
f
t
h
e
f
u
n
ctio
n
s
,
th
er
e
ar
e
ce
r
tain
lim
itatio
n
s
,
s
u
ch
as
u
n
if
o
r
m
s
en
s
itiv
ity
an
d
r
ed
u
c
ed
ad
ap
tab
ilit
y
.
C
o
n
v
en
tio
n
al
FLC
with
s
y
m
m
etr
ical
MF
s
m
ay
n
o
t
p
er
f
o
r
m
o
p
tim
ally
in
PV
s
y
s
tem
s
with
h
ig
h
ly
n
o
n
-
lin
ea
r
ch
ar
ac
ter
is
tics
,
as
it
s
tr
u
g
g
les
to
ad
ap
t
to
q
u
ick
l
y
alter
in
g
co
n
d
itio
n
s
,
p
a
r
ticu
lar
ly
u
n
d
er
p
ar
tial sh
ad
in
g
.
T
o
ad
d
r
ess
th
e
lim
itatio
n
s
o
f
co
n
v
en
tio
n
al
FLC,
an
im
p
r
o
v
ed
AFLC
i
s
p
r
o
p
o
s
ed
in
th
is
p
ap
er
.
T
h
e
AFLC
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
ar
e
d
esig
n
ed
asy
m
m
etr
ically
to
p
r
o
v
i
d
e
d
if
f
er
e
n
t
lev
els
o
f
s
en
s
itiv
ity
an
d
ad
ap
tab
ilit
y
u
n
d
er
p
a
r
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
Fo
r
th
e
f
u
zz
y
v
ar
iab
les,
th
e
asy
m
m
etr
ic
d
is
tr
ib
u
tio
n
o
f
in
p
u
t
an
d
o
u
tp
u
t
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
ex
h
ib
it
b
o
th
d
i
v
er
g
en
t
an
d
co
n
v
er
g
en
t
f
o
r
m
s
o
f
asy
m
m
et
r
y
.
T
h
e
p
ar
a
m
eter
s
wer
e
ad
ju
s
ted
to
b
alan
ce
th
e
s
en
s
iti
v
ity
an
d
r
o
b
u
s
tn
ess
o
f
th
e
alg
o
r
ith
m
,
allo
win
g
it
to
co
n
v
e
r
g
e
to
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t w
ith
r
ed
u
ce
d
o
s
cillatio
n
s
.
T
h
e
b
lo
ck
d
iag
r
am
f
o
r
th
e
asy
m
m
etr
ical
FLC
-
b
ased
co
n
tr
o
l
alg
o
r
ith
m
is
d
is
p
lay
ed
in
Fig
u
r
e
5
a
n
d
illu
s
tr
ates
i
ts
f
lo
w.
T
h
e
s
y
s
tem
h
as
two
m
ain
in
p
u
ts
,
o
u
tp
u
t
v
o
ltag
e
/
an
d
o
u
tp
u
t
cu
r
r
en
t
/
,
wh
i
ch
u
n
d
er
g
o
in
itial
p
r
o
ce
s
s
in
g
th
r
o
u
g
h
m
u
l
tip
licatio
n
an
d
s
u
b
tr
ac
tio
n
o
p
er
atio
n
s
.
T
h
ese
p
r
o
ce
s
s
ed
in
p
u
ts
ar
e
th
e
n
u
s
ed
to
ca
lcu
late
th
e
“e
r
r
o
r
”
an
d
“c
h
a
n
g
e
o
f
er
r
o
r
.
”
T
h
e
asy
m
m
etr
i
ca
l
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
co
n
s
is
ts
o
f
th
r
ee
s
tag
es:
f
u
zz
if
icatio
n
,
a
n
i
n
f
e
r
en
ce
e
n
g
in
e,
an
d
d
ef
u
zz
if
icatio
n
.
T
h
e
f
i
n
al
o
u
tp
u
t
o
f
th
e
p
r
o
ce
s
s
is
th
e
d
u
ty
r
atio
,
a
c
r
itical
p
ar
am
eter
f
o
r
co
n
tr
o
llin
g
t
h
e
DC
-
DC
co
n
v
er
ter
in
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
to
o
p
tim
ize
p
e
r
f
o
r
m
an
ce
.
Fig
u
r
e
5
.
B
lo
ck
d
iag
r
am
o
f
th
e
asy
m
m
etr
ical
FLC
-
b
ased
alg
o
r
ith
m
3
.
3
.
1
.
F
uzzif
ica
t
io
n
T
h
e
f
u
zz
if
icatio
n
p
r
o
ce
s
s
in
v
o
l
v
es
tr
an
s
f
o
r
m
in
g
n
u
m
er
ical
in
p
u
t
v
ar
iab
les
in
to
d
eg
r
ee
s
o
f
m
em
b
er
s
h
ip
in
co
r
r
esp
o
n
d
in
g
f
u
zz
y
s
ets.
T
h
e
ef
f
ec
tiv
en
ess
o
f
th
is
p
r
o
ce
s
s
lar
g
ely
d
ep
e
n
d
s
o
n
th
e
d
esig
n
an
d
ch
ar
ac
ter
is
tics
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
mp
a
r
a
tive
a
s
s
ess
men
t o
f a
n
imp
r
o
ve
d
a
s
ymm
etri
ca
l fu
z
z
y
lo
g
ic
…
(
A
th
ir
a
h
B
a
tr
is
yia
K
a
ma
l A
r
iffi
n
)
2647
o
f
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
.
T
wo
in
p
u
t
v
ar
iab
les
ar
e
p
r
e
s
en
t:
er
r
o
r
(
)
an
d
c
h
an
g
e
o
f
e
r
r
o
r
(
∆
)
,
b
o
th
s
am
p
led
at
th
e
in
s
tan
t
.
I
n
r
eg
a
r
d
to
th
e
v
o
ltag
e
an
d
c
u
r
r
en
t
d
etec
ted
,
th
e
p
o
wer
is
co
m
p
u
te
d
.
T
h
e
v
ar
ia
b
les
an
d
∆
ar
e
d
er
iv
e
d
as
(
8
)
a
n
d
(
9
)
.
(
)
=
(
)
−
(
−
1
)
/
(
)
−
/
(
−
1
)
(
8
)
∆
(
)
=
(
)
−
(
−
1
)
(
9
)
wh
er
e
/
is
th
e
p
o
wer
o
u
tp
u
t a
n
d
/
is
th
e
cu
r
r
e
n
t o
u
t
p
u
t o
f
th
e
PV sy
s
tem
.
T
h
e
f
lo
wc
h
ar
t
o
f
th
e
o
v
er
all
s
y
s
tem
is
p
r
esen
ted
in
Fig
u
r
e
6
.
T
h
e
p
r
o
ce
s
s
in
itiates
b
y
s
ettin
g
th
e
in
itial
v
alu
e
o
f
th
e
d
u
ty
r
atio
b
ased
o
n
th
e
s
y
s
tem
p
ar
am
eter
s
.
I
t
t
h
en
m
ea
s
u
r
es
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
o
f
th
e
PV
s
y
s
tem
.
Usi
n
g
th
ese
m
ea
s
u
r
ed
v
alu
es,
th
e
p
o
wer
o
f
th
e
P
V
s
y
s
tem
is
ca
lcu
lated
.
Nex
t,
th
e
MPPT
alg
o
r
ith
m
co
m
p
u
tes th
e
er
r
o
r
(
)
an
d
c
h
an
g
e
o
f
e
r
r
o
r
(
∆
)
b
ased
o
n
th
e
p
r
esen
t a
n
d
p
r
ev
io
u
s
p
o
wer
an
d
cu
r
r
en
t v
alu
es.
T
h
ese
v
alu
es
ar
e
th
en
in
p
u
t
in
to
th
e
AFLC
-
b
ased
alg
o
r
ith
m
an
d
u
n
d
er
g
o
f
u
zz
if
icatio
n
u
s
in
g
asy
m
m
et
r
ical
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
.
T
h
e
f
u
zz
if
ied
v
alu
es
a
r
e
p
r
o
ce
s
s
ed
th
r
o
u
g
h
t
h
e
in
f
er
en
ce
m
et
h
o
d
,
wh
ich
u
tili
ze
p
r
ed
ef
in
e
d
f
u
zz
y
s
ets
an
d
r
u
le
s
.
T
h
e
o
u
t
p
u
t
f
r
o
m
t
h
e
in
f
e
r
en
ce
m
eth
o
d
is
th
en
d
e
f
u
zz
if
ied
to
p
r
o
d
u
ce
a
cr
is
p
v
alu
e
f
o
r
th
e
ch
an
g
e
in
d
u
ty
r
a
tio
(
)
.
T
h
e
n
ew
d
u
ty
r
atio
is
ca
lc
u
lated
an
d
f
ed
b
ac
k
in
to
th
e
b
eg
in
n
in
g
o
f
th
e
p
r
o
ce
s
s
,
wh
er
e
it is
u
s
ed
to
ad
j
u
s
t th
e
o
p
er
atin
g
p
o
i
n
t o
f
th
e
PV sy
s
tem
.
Fig
u
r
e
6
.
Flo
wch
ar
t
o
f
AL
FC
-
b
ased
alg
o
r
ith
m
A
k
ey
id
ea
in
f
u
zz
y
lo
g
ic
ar
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
,
wh
ich
s
p
ec
if
y
h
o
w
ev
er
y
s
in
g
le
p
o
in
t
in
th
e
i
n
p
u
t
s
p
ac
e
is
ass
ig
n
ed
to
a
m
em
b
e
r
s
h
ip
q
u
an
tity
b
etwe
en
0
a
n
d
1
.
T
h
ese
v
alu
es
r
ep
r
esen
t
th
e
d
eg
r
ee
to
wh
ic
h
a
n
in
p
u
t f
its
to
a
s
p
ec
if
ic
f
u
zz
y
s
e
t.
I
n
th
e
p
r
o
p
o
s
ed
s
y
s
tem
,
b
o
t
h
th
e
in
p
u
t a
n
d
o
u
tp
u
t f
u
zz
y
s
ets co
m
p
r
is
e
o
f
f
iv
e
tr
ian
g
u
lar
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
.
T
h
e
f
u
zz
y
in
p
u
t
an
d
o
u
tp
u
t
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
u
tili
ze
d
to
tr
ac
k
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
u
n
d
er
p
ar
tially
co
v
e
r
ed
s
itu
atio
n
s
h
av
e
an
asy
m
m
etr
ical
d
is
tr
ib
u
tio
n
,
as
s
h
o
wn
in
Fig
u
r
e
7
.
Fig
u
r
e
7
(
a)
p
r
esen
t
s
th
e
asy
m
m
etr
ical
in
p
u
t
v
ar
i
ab
le,
er
r
o
r
,
wh
er
e
th
e
m
e
m
b
e
r
s
h
ip
f
u
n
ctio
n
s
ar
e
d
iv
id
ed
in
to
f
iv
e
f
u
zz
y
s
ets:
Neg
ativ
e
B
ig
(
NB
)
,
Neg
ativ
e
Sm
all
(
NS)
,
Z
er
o
(
Z
O)
,
Po
s
itiv
e
Sm
all
(
PS
)
,
an
d
Po
s
itiv
e
B
ig
(
P
B
)
.
Fig
u
r
e
7
(
b
)
d
ep
icts
th
e
in
p
u
t
v
a
r
ia
b
le,
c
h
an
g
e
o
f
er
r
o
r
,
wh
ich
in
f
lu
en
ce
s
th
e
co
n
tr
o
ller
’
s
d
ec
is
io
n
-
m
ak
in
g
p
r
o
ce
s
s
.
Fin
ally
,
Fig
u
r
e
7
(
c
)
s
h
o
ws
th
e
o
u
tp
u
t
v
ar
iab
le,
d
u
ty
r
atio
,
wh
ich
d
eter
m
i
n
es
th
e
ad
ju
s
tm
en
t
ap
p
lied
to
th
e
s
y
s
tem
.
T
h
e
in
p
u
t
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
ar
e
n
ar
r
o
wer
n
ea
r
th
e
ze
r
o
-
er
r
o
r
p
o
i
n
t
to
en
h
an
ce
s
en
s
itiv
ity
ar
o
u
n
d
t
h
e
MPP.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
6
4
2
-
2
6
5
4
2648
(
a)
(
b
)
(
c)
Fig
u
r
e
7
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
o
f
AFLC a
lg
o
r
ith
m
f
o
r
(
a)
A
s
y
m
m
etr
ical
in
p
u
t v
a
r
iab
le,
er
r
o
r
(
)
,
(
b
)
I
n
p
u
t
v
ar
iab
le,
ch
a
n
g
e
o
f
er
r
o
r
(
∆
)
,
an
d
(
c)
Ou
tp
u
t
v
ar
iab
le,
d
u
ty
r
atio
(
)
3
.
3
.
2
.
I
nfe
re
nce
T
h
e
in
f
er
en
ce
m
et
h
o
d
in
AFL
C
is
th
e
p
r
o
ce
s
s
o
f
m
ap
p
i
n
g
f
u
zz
if
ied
in
p
u
ts
to
f
u
zz
if
ied
o
u
tp
u
ts
u
s
in
g
a
r
u
le
b
ase.
T
h
e
r
u
le
b
ase
co
n
s
is
ts
o
f
ca
r
ef
u
lly
cr
af
ted
r
u
les
th
at
co
n
s
id
er
th
e
asy
m
m
etr
ical
r
elatio
n
s
h
ip
s
b
etwe
en
in
p
u
t
an
d
o
u
tp
u
t
v
a
r
i
ab
les
to
o
p
tim
ize
p
o
wer
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
.
T
h
is
p
r
o
ce
s
s
in
v
o
lv
es
ap
p
ly
in
g
f
u
zz
y
r
u
les to
th
e
in
p
u
t m
em
b
er
s
h
ip
v
alu
es to
d
er
iv
e
an
o
u
tp
u
t f
u
zz
y
s
et,
wh
ich
is
th
e
n
d
e
f
u
zz
ied
to
p
r
o
d
u
ce
a
cr
is
p
co
n
tr
o
l
ac
tio
n
.
T
h
e
f
u
zz
y
in
f
er
en
ce
s
y
s
tem
ca
n
u
s
e
eith
er
th
e
Ma
m
d
an
i
o
r
T
ak
ag
i
-
Su
g
en
o
m
eth
o
d
s
,
as
b
o
th
ca
n
in
co
r
p
o
r
ate
s
y
m
m
etr
ical
o
r
asy
m
m
etr
ical
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
[
1
1
]
.
I
n
th
e
co
n
tex
t
o
f
AFLC
f
o
r
MPP tr
ac
k
in
g
,
th
e
Ma
m
d
a
n
i t
ec
h
n
iq
u
e
is
em
p
l
o
y
ed
b
ec
au
s
e
it is
s
im
p
le
to
u
tili
ze
.
C
r
ea
tin
g
a
r
u
le
b
ase
as
a
k
i
n
d
o
f
a
m
atr
ix
is
an
e
f
f
ec
tiv
e
wa
y
to
s
y
s
tem
atica
lly
d
eter
m
in
e
t
h
e
co
n
tr
o
l
ac
tio
n
s
r
eq
u
ir
e
d
to
tr
ac
k
th
e
MPP
in
a
p
h
o
t
o
v
o
ltaic
s
y
s
tem
,
esp
ec
ially
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
T
h
e
m
ain
g
o
al
is
to
g
et
th
e
o
p
er
ati
n
g
p
o
in
t
n
ea
r
e
r
th
e
MPP
with
m
in
im
al
f
lu
ctu
atio
n
s
b
y
a
p
p
r
o
p
r
iately
ad
j
u
s
tin
g
th
e
d
u
ty
r
atio
o
f
th
e
DC
-
DC
co
n
v
er
ter
.
T
ab
le
1
s
h
o
ws
th
e
f
u
zz
y
r
u
le
b
ase
f
o
r
co
m
p
u
tin
g
t
h
e
o
u
tp
u
t
v
ar
ia
b
le
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
.
T
h
e
r
u
le
s
ar
e
o
r
g
an
ized
i
n
a
m
atr
ix
f
o
r
m
at
wh
er
e
r
o
ws
r
ep
r
ese
n
t
th
e
er
r
o
r
a
n
d
co
lu
m
n
s
r
ep
r
esen
t
d
if
f
er
e
n
t
v
alu
es
o
f
t
h
e
ch
an
g
e
in
e
r
r
o
r
.
T
h
e
f
u
zz
y
r
u
le
b
ase
co
n
s
is
ts
o
f
2
5
r
u
les,
d
ef
in
ed
b
ased
o
n
ex
p
er
t
k
n
o
wled
g
e
an
d
s
im
u
latio
n
r
esu
lts
.
Fo
r
ex
am
p
le,
if
th
e
er
r
o
r
(
)
is
'
Po
s
i
tiv
e
Sm
all
'
an
d
th
e
ch
an
g
e
o
f
er
r
o
r
(
∆
)
is
'
Po
s
i
tiv
e
B
ig
’
,
th
e
o
u
tp
u
t
d
u
ty
r
atio
(
)
is
ad
ju
s
ted
to
'
Z
er
o
'
.
T
h
e
asy
m
m
etr
ical
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
wer
e
d
esig
n
e
d
to
b
e
n
ar
r
o
wer
a
r
o
u
n
d
ze
r
o
-
er
r
o
r
p
o
in
ts
f
o
r
h
i
g
h
er
s
en
s
itiv
ity
,
with
v
alu
es
r
an
g
in
g
f
r
o
m
-
0
.
1
t
o
0
.
1
.
Ad
d
itio
n
ally
,
a
3
D
g
r
a
p
h
ca
lled
a
s
u
r
f
ac
e
v
i
ewe
r
s
h
o
ws th
ese
r
u
les as illu
s
tr
a
ted
in
Fig
u
r
e
8
.
T
ab
le
1
.
Fu
zz
y
r
u
le
b
ase
E
∆
E
NB
NS
ZO
PS
PB
NB
ZO
ZO
NB
NB
NB
NS
ZO
ZO
NS
NS
NS
ZO
NS
ZO
ZO
ZO
PS
PS
PS
PS
PS
ZO
ZO
PB
PB
PB
PB
ZO
ZO
3
.
3
.
3
.
Def
uzzif
ica
t
io
n
Def
u
zz
if
icatio
n
in
AFLC
i
s
em
p
lo
y
ed
to
tr
an
s
f
o
r
m
th
e
f
u
zz
y
o
u
tp
u
t
v
alu
es
attain
ed
f
r
o
m
th
e
in
f
er
en
ce
m
eth
o
d
b
ac
k
in
to
c
r
is
p
o
u
t
p
u
t
v
alu
es
f
o
r
p
r
ac
tical
im
p
lem
en
tatio
n
in
th
e
PV
co
n
tr
o
l
s
y
s
tem
.
T
h
e
p
r
o
ce
s
s
in
v
o
lv
es c
alcu
latin
g
a
cr
is
p
o
u
tp
u
t v
alu
e
b
ased
o
n
th
e
f
u
zz
y
o
u
tp
u
t m
e
m
b
er
s
h
ip
d
eg
r
e
es a
n
d
th
e
asy
m
m
etr
ical
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
mp
a
r
a
tive
a
s
s
ess
men
t o
f a
n
imp
r
o
ve
d
a
s
ymm
etri
ca
l fu
z
z
y
lo
g
ic
…
(
A
th
ir
a
h
B
a
tr
is
yia
K
a
ma
l A
r
iffi
n
)
2649
d
is
tr
ib
u
tio
n
o
f
th
e
o
u
tp
u
t
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
.
Def
u
zz
if
i
ca
tio
n
ca
n
b
e
p
er
f
o
r
m
ed
u
s
in
g
th
e
ce
n
ter
o
f
ar
ea
,
k
n
o
wn
as
th
e
ce
n
tr
o
id
m
et
h
o
d
.
I
n
th
is
s
tu
d
y
,
t
h
e
ce
n
tr
o
i
d
m
e
th
o
d
is
em
p
lo
y
ed
f
o
r
th
e
d
ef
u
zz
if
icatio
n
p
r
o
ce
s
s
,
an
d
it is
r
ep
r
esen
ted
b
y
th
e
(
1
0
)
.
=
∑
(
)
=
1
∑
(
)
=
1
(
1
0
)
w
h
er
e
is
th
e
ac
tiv
atio
n
d
e
g
r
e
e
o
f
r
u
le
′
′
,
is
th
e
ce
n
tr
e
o
f
th
e
m
ax
im
u
m
-
m
in
im
u
m
c
o
m
p
o
s
itio
n
o
f
th
e
o
u
tp
u
t m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
an
d
is
th
e
o
u
tp
u
t w
h
ich
is
d
u
t
y
cy
cle.
Fig
u
r
e
8
.
3
D
Dim
en
s
io
n
s
o
f
f
u
zz
y
r
u
le
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
A
ND
DIS
C
USS
I
O
N
T
h
e
p
r
o
p
o
s
ed
Asy
m
m
etr
ic
al
FLC
-
b
ased
MPPT
alg
o
r
ith
m
was
b
u
ilt
an
d
s
im
u
lated
in
MA
T
L
AB
/S
im
u
lin
k
s
o
f
twar
e
in
a
clo
s
ed
-
lo
o
p
co
n
f
ig
u
r
atio
n
to
ev
alu
ate
its
s
tab
ilit
y
an
d
p
er
f
o
r
m
a
n
ce
u
n
d
er
s
tan
d
ar
d
test
co
n
d
itio
n
s
a
n
d
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
Fig
u
r
e
9
s
h
o
ws
th
e
PV
s
y
s
tem
w
ith
a
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
a
n
d
th
e
p
r
o
p
o
s
ed
M
PP
T
co
n
tr
o
ller
u
n
d
er
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
STC).
T
h
e
P
V
m
o
d
u
les
u
s
ed
in
th
is
s
tu
d
y
ar
e
1
So
ltech
1
STH
-
215
-
P,
with
a
m
ax
im
u
m
p
o
we
r
o
f
2
1
3
.
1
5
W
,
co
n
s
is
tin
g
o
f
1
s
er
ies
m
o
d
u
le
an
d
1
p
ar
allel
s
tr
in
g
.
I
n
th
is
s
tu
d
y
,
all
th
r
ee
PV
m
o
d
u
les
in
th
e
p
r
o
p
o
s
ed
AFLC
-
b
ased
alg
o
r
ith
m
ar
e
c
o
n
n
ec
te
d
in
s
er
ies
an
d
ex
p
o
s
ed
to
d
if
f
er
e
n
t
ir
r
ad
iatio
n
le
v
els
with
v
ar
io
u
s
s
h
ad
in
g
p
atter
n
s
.
T
ab
le
2
s
h
o
ws
th
e
g
lo
b
al
an
d
lo
ca
l
m
ax
im
u
m
p
o
wer
p
o
in
ts
o
f
t
h
e
PV
s
y
s
tem
u
n
d
er
d
if
f
er
en
t
s
h
ad
in
g
p
atter
n
s
.
T
h
e
f
o
llo
win
g
ca
s
es
ar
e
co
n
s
id
er
ed
,
with
s
o
lar
i
r
r
ad
ian
ce
v
ar
y
i
n
g
as
s
p
ec
if
ie
d
f
o
r
ea
c
h
ca
s
e
an
d
th
e
tem
p
er
atu
r
e
r
e
m
ain
in
g
c
o
n
s
tan
t
a
t
2
5
°C
:
a.
C
ase
1
: A
ll PV
m
o
d
u
les ar
e
u
n
d
er
s
tan
d
ar
d
test
co
n
d
itio
n
s
,
with
s
o
lar
ir
r
ad
ian
ce
at
1
,
0
0
0
W
/m
2
.
b.
C
ase
2
: PV
Mo
d
u
le
1
is
ex
p
o
s
ed
to
1
,
000
W
/m
2
,
Mo
d
u
le
2
to
7
5
0
W
/m
2
an
d
Mo
d
u
le
3
t
o
5
0
0
W
/m
2
.
c.
C
ase
3
: PV
Mo
d
u
le
1
is
ex
p
o
s
ed
to
5
0
0
W
/m
2
,
Mo
d
u
le
2
to
4
0
0
W
/m
2
an
d
M
o
d
u
le
3
to
7
0
0
W
/m
2
.
Fig
u
r
e
9
.
C
ir
cu
it si
m
u
latio
n
o
f
p
r
o
p
o
s
ed
AFLC
-
b
ased
MPPT
u
n
d
er
s
tan
d
ar
d
test
co
n
d
itio
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
6
4
2
-
2
6
5
4
2650
T
ab
le
2
.
Po
wer
at
GM
PP
an
d
L
MPP u
n
d
er
v
ar
i
o
u
s
ir
r
ad
iatio
n
s
C
a
se
1
C
a
se
2
C
a
se
3
P
GMPP
(W)
2
1
3
.
1
5
2
1
3
.
1
5
1
5
0
.
7
9
P
L
M
P
P
(W)
-
1
6
1
.
3
3
;
1
0
7
.
9
9
1
0
7
.
9
9
;
8
6
.
2
7
4
.
1
.
All P
V
m
o
du
les a
re
un
d
er
s
t
a
nd
a
rd
t
est
co
nd
it
io
ns
,
wit
h so
la
r
irra
dia
nce
a
t
1
0
0
0
W/m
2
Fig
u
r
e
1
0
illu
s
tr
ates
th
e
o
b
tain
ed
g
r
ap
h
f
r
o
m
th
e
s
im
u
latio
n
o
f
PV
v
o
ltag
e,
PV
cu
r
r
en
t
an
d
PV
p
o
wer
o
f
th
e
p
r
o
p
o
s
ed
AFLC
-
b
ased
alg
o
r
ith
m
u
n
d
er
C
ase
1
s
tan
d
ar
d
test
co
n
d
itio
n
s
r
esp
ec
tiv
ely
.
T
h
e
MPPT
co
n
tr
o
ller
d
em
o
n
s
tr
ates
ex
ce
p
tio
n
al
p
er
f
o
r
m
an
ce
u
n
d
er
u
n
if
o
r
m
ir
r
ad
ian
c
e
o
f
1
,
000
W
/m
2
.
T
h
e
v
o
ltag
e
g
r
a
p
h
in
Fig
u
r
e
1
0
(
a)
s
h
o
ws
a
s
tab
l
e
r
esp
o
n
s
e
af
ter
a
b
r
ief
p
er
io
d
.
T
h
e
PV
v
o
ltag
e
s
tar
ts
clo
s
e
to
0
V
an
d
q
u
ick
ly
r
is
es
to
ar
o
u
n
d
1
0
0
V
in
a
v
e
r
y
s
h
o
r
t
tim
e
(
a
p
p
r
o
x
im
ately
0
.
0
1
s
ec
o
n
d
s
)
.
Af
ter
th
at,
it
r
em
ain
s
s
tab
le
at
its
m
ax
im
u
m
lev
el
wit
h
o
u
t
an
y
s
ig
n
if
ican
t
f
lu
ctu
atio
n
s
.
T
h
is
in
d
icate
s
th
at
th
e
PV
s
y
s
tem
is
o
p
er
atin
g
at
its
m
ax
im
u
m
v
o
ltag
e
an
d
b
ec
o
m
es
s
tab
le
af
ter
th
e
in
itial
tr
an
s
itio
n
p
h
ase.
As
s
h
o
wn
in
Fig
u
r
e
1
0
(
b
)
,
th
e
PV
cu
r
r
en
t
ex
h
ib
its
a
s
im
ilar
tr
an
s
ien
t
r
esp
o
n
s
e,
s
tar
tin
g
ar
o
u
n
d
0
A
an
d
in
cr
ea
s
in
g
to
a
s
tab
le
lev
el
o
f
ap
p
r
o
x
im
ately
5
A
af
ter
0
.
0
1
s
ec
o
n
d
s
.
T
h
e
cu
r
r
en
t
th
en
r
e
m
ain
s
s
tab
le
th
r
o
u
g
h
o
u
t
th
e
s
im
u
latio
n
,
in
d
icatin
g
th
at
th
e
s
y
s
tem
h
as
r
ea
ch
e
d
th
e
s
tead
y
cu
r
r
en
t
r
e
q
u
ir
ed
f
o
r
m
ax
im
u
m
en
er
g
y
o
u
t
p
u
t.
T
h
e
p
o
wer
o
u
tp
u
t
in
itially
in
cr
ea
s
es
an
d
s
tab
ilizes
at
ar
o
u
n
d
4
8
0
W
af
ter
a
s
h
o
r
t
p
er
io
d
,
as
s
ee
n
in
Fig
u
r
e
1
0
(
c)
.
Af
t
er
0
.
0
1
s
ec
o
n
d
s
,
th
e
p
o
wer
o
u
tp
u
t
r
em
ain
s
c
o
n
s
is
ten
t,
in
d
icatin
g
th
at
t
h
e
s
y
s
tem
h
as
r
ea
ch
ed
t
h
e
MPP.
T
h
is
s
im
u
latio
n
d
em
o
n
s
tr
ates
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
AFL
C
-
b
ased
MPPT
alg
o
r
ith
m
u
s
ed
to
en
s
u
r
e
t
h
at
th
e
PV
s
y
s
tem
o
p
er
ates
at
th
e
m
ax
im
u
m
p
o
wer
lev
el
.
T
h
e
ac
h
iev
em
en
t
o
f
a
m
ax
im
u
m
p
o
w
er
o
f
ar
o
u
n
d
4
8
0
W
s
h
o
ws
th
at
th
e
s
y
s
tem
o
p
e
r
ates
ef
f
icien
tly
u
n
d
e
r
s
tan
d
ar
d
test
co
n
d
itio
n
s
,
with
v
o
ltag
e
an
d
c
u
r
r
en
t
alig
n
ed
with
th
e
PV
r
eq
u
ir
em
en
ts
to
p
r
o
d
u
ce
o
p
tim
al
p
o
wer
o
u
tp
u
t.
(
a)
(
b
)
(
c)
Fig
u
r
e
1
0
.
Simu
lated
g
r
a
p
h
o
f
(
a)
PV
v
o
ltag
e,
(
b
)
PV
c
u
r
r
en
t
,
(
c)
PV
p
o
wer
o
f
PV sy
s
tem
u
n
d
er
s
tan
d
ar
d
test
co
n
d
itio
n
s
4
.
2
.
Co
m
pa
riso
n o
f
pro
po
s
e
d
AF
L
C
-
ba
s
e
d a
lg
o
rit
hm
wi
t
h c
o
nv
ent
io
na
l
P
&O
T
h
e
r
esu
lts
alig
n
with
th
e
s
tu
d
y
'
s
o
b
jectiv
e
o
f
en
h
an
cin
g
MPPT
p
er
f
o
r
m
an
ce
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
d
em
o
n
s
tr
atin
g
t
h
e
s
u
p
er
io
r
ity
o
f
th
e
p
r
o
p
o
s
ed
AFLC
alg
o
r
ith
m
o
v
e
r
th
e
co
n
v
en
t
io
n
al
P&
O
m
et
h
o
d
in
ter
m
s
o
f
ac
cu
r
ac
y
a
n
d
a
d
ap
t
ab
ilit
y
.
T
h
is
s
tu
d
y
f
o
c
u
s
es o
n
a
d
ir
ec
t c
o
m
p
ar
is
o
n
b
etwe
en
t
h
e
AFLC a
n
d
P&
O
m
eth
o
d
s
,
wh
ich
ar
e
wid
ely
u
s
ed
in
MPPT
ap
p
licatio
n
s
.
T
h
e
asy
m
m
etr
y
in
th
e
AFLC
alg
o
r
ith
m
en
s
u
r
es
h
ig
h
e
r
s
en
s
itiv
ity
n
ea
r
ze
r
o
er
r
o
r
,
en
ab
lin
g
f
aster
an
d
m
o
r
e
ac
c
u
r
at
e
r
esp
o
n
s
es
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
Fo
r
in
s
tan
ce
,
wh
en
th
e
er
r
o
r
(
)
is
'Ne
g
ativ
e
Sm
all'
an
d
th
e
ch
an
g
e
o
f
e
r
r
o
r
(
)
is
'Po
s
itiv
e
B
ig
'
,
th
e
f
u
zz
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
mp
a
r
a
tive
a
s
s
ess
men
t o
f a
n
imp
r
o
ve
d
a
s
ymm
etri
ca
l fu
z
z
y
lo
g
ic
…
(
A
th
ir
a
h
B
a
tr
is
yia
K
a
ma
l A
r
iffi
n
)
2651
in
f
er
en
ce
s
y
s
tem
ad
ju
s
ts
th
e
d
u
ty
r
atio
b
y
a
s
m
all
d
ec
r
e
m
en
t
to
m
ain
tain
o
p
tim
al
p
er
f
o
r
m
an
ce
.
T
h
e
co
m
p
ar
is
o
n
ac
r
o
s
s
th
r
ee
ca
s
es
in
Fig
u
r
e
1
1
h
ig
h
lig
h
ts
th
at
AFLC
co
n
s
is
ten
tly
o
u
tp
er
f
o
r
m
s
P&
O,
d
em
o
n
s
tr
atin
g
f
aste
r
r
esp
o
n
s
e
tim
es,
r
ed
u
ce
d
s
tead
y
-
s
tate
o
s
cill
atio
n
s
,
an
d
g
r
ea
te
r
s
tab
ilit
y
u
n
d
er
v
ar
y
i
n
g
s
h
ad
i
n
g
co
n
d
itio
n
s
.
I
n
Fig
u
r
e
1
1
(
a
)
,
f
o
r
C
ase
1
u
n
d
er
STC,
th
e
AFLC
-
b
ased
alg
o
r
ith
m
ac
h
ie
v
ed
a
m
a
x
im
u
m
v
o
ltag
e
o
f
9
9
.
7
8
V
in
ju
s
t
0
.
0
0
4
s
ec
o
n
d
s
,
wh
er
ea
s
th
e
co
n
v
en
tio
n
al
P&
O
m
eth
o
d
r
e
q
u
ir
e
d
0
.
4
2
s
ec
o
n
d
s
to
r
ea
ch
a
l
o
wer
v
o
ltag
e
o
f
9
2
.
1
0
V.
T
h
ese
r
esu
lts
clea
r
ly
illu
s
tr
ate
th
at
th
e
AF
L
C
m
eth
o
d
s
u
s
tain
s
a
m
o
r
e
s
ta
b
le
v
o
ltag
e
o
u
tp
u
t,
with
a
q
u
ick
er
r
esp
o
n
s
e
an
d
f
ewe
r
o
s
cillatio
n
s
co
m
p
ar
ed
to
P&
O,
wh
ich
ex
p
er
ie
n
ce
s
lar
g
er
f
lu
ctu
ati
o
n
s
.
Fig
u
r
es
1
1
(
b
)
an
d
1
1
(
c)
s
h
o
w
th
e
p
er
f
o
r
m
an
ce
u
n
d
er
p
a
r
tia
l
s
h
ad
in
g
co
n
d
itio
n
s
.
I
n
C
ase
2
as
d
ep
i
cted
in
Fig
u
r
e
1
1
(
b
)
,
th
e
AFLC
-
b
ased
MPPT
alg
o
r
ith
m
r
ea
ch
ed
a
m
ax
im
u
m
v
o
ltag
e
o
f
7
9
.
4
4
V
in
0
.
0
1
7
s
ec
o
n
d
s
,
wh
ile
th
e
co
n
v
en
tio
n
al
P&
O
m
eth
o
d
to
o
k
0
.
9
8
s
ec
o
n
d
s
to
r
ea
ch
2
9
.
8
7
V,
h
ig
h
lig
h
tin
g
AFLC
'
s
ab
ilit
y
to
lo
ca
te
an
d
m
ain
tain
th
e
g
lo
b
al
m
ax
i
m
u
m
p
o
wer
p
o
in
t
d
esp
ite
v
a
r
iatio
n
s
in
ir
r
ad
ian
ce
.
As
d
ep
ict
ed
in
Fig
u
r
e
1
1
(
c)
,
in
C
ase
3
th
e
AFLC
-
b
ased
alg
o
r
ith
m
r
ea
ch
ed
a
m
ax
im
u
m
v
o
ltag
e
o
f
6
4
.
0
2
V
in
ju
s
t
0
.
0
1
s
ec
o
n
d
s
,
co
m
p
a
r
ed
to
th
e
P&
O
m
eth
o
d
,
wh
ich
r
eq
u
i
r
ed
0
.
8
9
s
ec
o
n
d
s
t
o
r
ea
c
h
6
2
.
0
6
V.
Alth
o
u
g
h
t
h
is
s
tu
d
y
f
o
c
u
s
es
o
n
c
o
m
p
ar
in
g
th
e
p
r
o
p
o
s
ed
AFLC
ap
p
r
o
ac
h
with
th
e
co
n
v
en
tio
n
al
P&
O
m
eth
o
d
,
r
ec
en
t
ad
v
a
n
ce
m
en
ts
lik
e
th
e
A
-
FOPID
co
n
tr
o
ller
[
1
4
]
h
av
e
d
e
m
o
n
s
tr
ated
s
ig
n
if
ican
t
im
p
r
o
v
em
e
n
ts
in
MPPT
p
er
f
o
r
m
an
ce
.
C
o
m
p
ar
ed
to
A
-
FOPID,
th
e
AFLC
m
eth
o
d
o
f
f
er
s
a
s
im
p
ler
y
et
r
o
b
u
s
t
alter
n
ativ
e,
p
ar
ticu
lar
ly
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
T
h
e
s
im
p
licity
o
f
AFLC
m
ak
es
i
t
a
m
o
r
e
f
ea
s
ib
le
s
o
lu
tio
n
f
o
r
r
ea
l
-
wo
r
ld
a
p
p
licatio
n
s
,
a
s
it
r
eq
u
ir
es
f
ewe
r
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
.
T
ab
l
e
3
tab
u
lates th
e
s
im
u
latio
n
r
e
s
u
lts
o
f
th
ese
th
r
ee
s
tu
d
ies.
(
a)
(
b
)
(
c)
Fig
u
r
e
1
1
.
C
o
m
p
ar
is
o
n
r
esu
lt o
f
PV V
o
ltag
e
b
etwe
en
th
e
p
r
o
p
o
s
ed
AFLC
-
b
ased
alg
o
r
ith
m
an
d
c
o
n
v
e
n
tio
n
al
P&
O
u
n
d
er
(
a
)
C
ase
1
–
STC,
(
b
)
C
ase
2
–
PS
C
p
atter
n
1
,
a
n
d
(
c)
C
ase
3
–
PS
C
p
atter
n
2
T
ab
le
3
.
C
o
m
p
a
r
is
o
n
o
f
Stead
y
-
s
tate
r
esp
o
n
s
e
b
etwe
en
th
e
p
r
o
p
o
s
ed
AFLC
-
b
ased
alg
o
r
ith
m
an
d
th
e
co
n
v
en
tio
n
al
P&
O
M
P
P
T
T
e
c
h
n
i
q
u
e
s
V
o
l
t
a
g
e
(
V
)
S
t
e
a
d
y
-
S
t
a
t
e
O
s
c
i
l
l
a
t
i
o
n
s
C
a
se
1
C
a
se
2
C
a
se
3
C
o
n
v
e
n
t
i
o
n
a
l
P
&O
9
2
.
1
0
2
9
.
8
7
6
2
.
0
6
S
i
g
n
i
f
i
c
a
n
t
P
r
o
p
o
se
d
A
F
L
C
-
b
a
se
d
a
l
g
o
r
i
t
h
m
9
9
.
7
8
7
9
.
4
4
6
4
.
0
2
M
i
n
i
m
a
l
Simu
latio
n
s
d
em
o
n
s
tr
ated
th
a
t
th
e
AFLC
co
n
tr
o
ller
ac
h
iev
e
d
s
tab
le
o
p
er
atio
n
with
m
in
im
al
s
tead
y
-
s
tate
o
s
cillatio
n
s
an
d
f
aster
s
ettlin
g
tim
es
co
m
p
ar
ed
to
th
e
co
n
v
e
n
tio
n
al
P&
O
m
eth
o
d
.
T
h
e
asy
m
m
etr
ical
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
in
t
h
e
AFLC
d
esig
n
wer
e
cr
itical
in
m
ain
tain
in
g
s
tab
ilit
y
b
y
d
y
n
a
m
ically
ad
ju
s
tin
g
t
h
e
o
u
tp
u
t
b
ased
o
n
er
r
o
r
m
ag
n
it
u
d
e
an
d
d
ir
ec
tio
n
.
Ho
we
v
er
,
th
is
s
tu
d
y
is
lim
ited
to
s
im
u
l
atio
n
s
p
er
f
o
r
m
ed
in
MA
T
L
AB
/S
im
u
lin
k
,
an
d
th
e
r
esu
lts
h
av
e
n
o
t
y
et
b
ee
n
v
alid
ated
th
r
o
u
g
h
h
ar
d
war
e
im
p
lem
en
tatio
n
.
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