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[
4
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6
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2793
T
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1
5
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o
l
s
y
s
te
m
.
Nik
o
lic
et
a
l.
[
1
7
]
an
d
L
ar
b
es
et
a
l.
[
1
8
]
a
p
p
lied
th
e
b
ee
co
lo
n
y
o
p
tim
izatio
n
an
d
g
en
etics
alg
o
r
ith
m
,
r
esp
e
ctiv
ely
,
to
tu
n
e
th
e
f
u
zz
y
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
,
d
em
o
n
s
tr
atin
g
im
p
r
o
v
ed
FLC
p
er
f
o
r
m
an
ce
in
MPPT
ap
p
lic
atio
n
s
.
B
u
ild
in
g
o
n
th
is
,
th
e
p
ar
ticle
s
war
m
o
p
ti
m
izatio
n
(
PS
O)
alg
o
r
ith
m
o
f
f
er
s
an
o
th
e
r
p
o
we
r
f
u
l
o
p
tim
izatio
n
tech
n
iq
u
e,
p
r
o
v
id
i
n
g
s
ig
n
if
ican
t im
p
r
o
v
e
m
en
ts
f
o
r
o
p
tim
izin
g
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
in
FLC.
As
h
ig
h
lig
h
ted
b
y
Ma
r
in
i
an
d
W
alcz
ak
[
1
9
]
,
in
s
p
ir
ed
b
y
th
e
b
eh
av
io
r
o
f
ce
r
tain
g
r
o
u
p
-
liv
in
g
an
im
als,
s
u
ch
as
f
is
h
an
d
b
ir
d
s
,
th
e
PS
O
alg
o
r
ith
m
u
tili
ze
s
a
s
war
m
o
f
in
d
iv
id
u
als
to
r
ea
ch
th
e
o
p
tim
a
l
s
o
lu
tio
n
.
T
h
ey
p
er
f
o
r
m
elem
e
n
tar
y
task
s
an
d
in
ter
ac
t w
ith
o
n
e
an
o
th
e
r
lo
ca
lly
,
a
n
d
with
th
eir
en
v
ir
o
n
m
en
t,
all
with
o
u
t
ce
n
tr
al
c
o
n
tr
o
l.
T
h
e
g
lo
b
al
b
e
h
av
io
r
o
f
th
e
g
r
o
u
p
r
esu
lts
f
r
o
m
t
h
ese
lo
ca
l
in
te
r
ac
tio
n
s
an
d
a
u
to
-
o
r
g
an
izatio
n
.
E
v
en
t
h
o
u
g
h
th
e
ag
en
ts
m
ay
b
e
lim
ited
in
th
ei
r
ca
p
ab
ilit
ies,
th
eir
ef
f
ec
tiv
en
ess
in
r
ea
ch
in
g
th
e
u
ltima
te
o
b
jectiv
e
o
f
p
r
o
b
lem
-
s
o
lv
in
g
is
g
u
ar
a
n
teed
b
y
th
e
ir
ab
ilit
y
to
s
h
ar
e
in
f
o
r
m
atio
n
an
d
in
ter
ac
t
with
ea
ch
o
th
er
[
1
9
]
.
C
h
en
g
et
a
l.
[
2
0
]
f
o
llo
wed
a
s
im
ilar
a
p
p
r
o
ac
h
to
th
is
s
tu
d
y
,
wh
e
r
e
th
ey
f
o
c
u
s
ed
o
n
o
p
tim
izin
g
a
f
u
zz
y
-
lo
g
ic
-
b
as
ed
MPPT
alg
o
r
ith
m
u
s
in
g
th
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
tech
n
iq
u
e.
T
h
ey
ap
p
lied
a
s
y
m
m
etr
ical
F
L
C
s
tr
u
ctu
r
e,
wh
ich
was
later
o
p
tim
ized
in
to
an
asy
m
m
etr
ic
al
FLC,
ac
h
iev
in
g
a
m
ax
im
u
m
ef
f
icien
cy
o
f
9
9
.
1
9
%.
Par
d
esh
i
an
d
Patil
[
2
1
]
,
ad
ju
s
t
ed
th
e
ar
tific
ial
n
eu
r
al
n
etwo
r
k
(
ANN)
f
r
am
ewo
r
k
u
s
in
g
th
e
PS
O
f
o
r
p
h
o
to
v
o
ltaic
s
o
lar
s
y
s
tem
s
.
T
h
ey
co
n
d
u
cted
co
m
p
ar
ativ
e
s
im
u
latio
n
s
b
etwe
en
th
e
PS
O
-
b
ased
ANN,
FLC,
an
d
th
e
P&
O
m
eth
o
d
u
s
in
g
r
ea
l
-
tim
e
d
ata
u
n
d
e
r
d
if
f
er
en
t
clim
atic
co
n
d
itio
n
s
.
T
h
e
r
esu
l
ts
r
ev
ea
l
th
at
th
eir
s
u
g
g
ested
ap
p
r
o
ac
h
ac
h
iev
ed
th
e
g
r
ea
test
lev
els
o
f
ef
f
icie
n
cy
,
with
a
v
al
u
e
o
f
9
9
.
6
%
in
clea
r
co
n
d
itio
n
s
.
Ku
m
ar
et
a
l.
[
2
2
]
p
r
o
p
o
s
ed
a
n
o
v
el
h
y
b
r
id
MPPT
ap
p
r
o
a
ch
f
o
r
s
o
lar
PV
s
y
s
tem
s
th
at
co
m
b
in
es
p
ar
ticle
s
war
m
o
p
tim
izatio
n
-
tr
ain
ed
m
ac
h
in
e
lear
n
in
g
with
f
ly
in
g
s
q
u
ir
r
el
s
ea
r
ch
o
p
tim
izatio
n
to
en
h
an
ce
s
y
s
tem
ef
f
icien
cy
.
T
h
e
m
et
h
o
d
was
test
ed
in
MA
T
L
AB
/Si
m
u
lin
k
u
n
d
er
v
ar
io
u
s
e
n
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
,
in
clu
d
in
g
id
ea
l
o
n
es.
T
h
eir
r
esu
lts
,
co
m
p
ar
ed
to
s
ev
er
al
ex
is
tin
g
tech
n
iq
u
es
f
r
o
m
th
e
liter
atu
r
e,
s
h
o
wed
th
at
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
im
p
r
o
v
ed
ef
f
icien
cy
b
y
0
.
7
2
%.
I
n
o
r
d
er
to
m
a
x
im
ize
th
e
en
e
r
g
y
p
r
o
d
u
ctio
n
o
f
PV
p
an
els
an
d
im
p
r
o
v
e
th
eir
e
f
f
icien
cy
,
th
is
p
ap
er
p
r
o
p
o
s
es
to
im
p
r
o
v
e
th
e
FLC
ap
p
r
o
ac
h
b
y
lev
er
ag
in
g
PS
O
to
o
p
tim
ize
th
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
u
p
p
o
r
ts
,
with
th
e
aim
o
f
m
ax
im
izin
g
t
h
e
en
er
g
y
p
r
o
d
u
ctio
n
o
f
PV
p
an
els
an
d
im
p
r
o
v
in
g
th
eir
ef
f
i
cien
cy
.
T
o
ex
a
m
in
e
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
an
d
ascer
tain
its
ef
f
ec
tiv
en
ess
,
th
e
b
eh
av
io
r
o
f
th
e
1
So
ltech
1
STH
-
215
-
P”
PV
m
o
d
u
le
was
s
im
u
lated
in
th
e
MA
T
L
AB
-
Simu
lin
k
en
v
ir
o
n
m
e
n
t
u
n
d
er
id
ea
l
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
o
f
2
5
°C
an
d
1
0
0
0
W
/m
².
T
h
is
en
ab
led
a
c
o
m
p
ar
ativ
e
ev
alu
atio
n
b
etwe
e
n
th
e
p
er
f
o
r
m
an
ce
o
f
c
o
n
v
e
n
tio
n
al
FLC
an
d
th
at
o
f
PS
O
-
o
p
tim
ized
FLC,
wh
er
e
a
n
o
tab
le
im
p
r
o
v
e
m
en
t in
e
f
f
i
cien
cy
was a
ch
iev
ed
.
2.
M
E
T
H
O
D
2
.
1
.
E
x
plo
ring
M
P
P
T
:
“
princip
le
a
nd
des
ig
n
”
Acc
o
r
d
in
g
t
o
th
e
V
-
I
ch
ar
ac
t
er
is
tics
,
th
er
e
is
o
n
e
s
in
g
u
lar
v
o
ltag
e
v
alu
e
th
at
alig
n
s
with
th
e
MPP.
An
y
r
is
e
in
lo
ad
r
esis
tan
ce
lead
s
th
e
PV
m
o
d
u
le
to
f
u
n
ctio
n
at
h
ig
h
er
v
o
ltag
es
th
an
t
h
e
MPP,
r
esu
ltin
g
in
a
d
r
o
p
in
th
e
c
u
r
r
en
t
an
d
v
ice
v
er
s
a
,
as
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
is
in
d
icate
s
th
at
a
d
ir
ec
t
co
n
n
ec
tio
n
b
etwe
en
th
e
PV
p
an
el
an
d
th
e
lo
a
d
m
ay
p
r
ev
en
t
th
e
PV
m
o
d
u
le
f
r
o
m
o
p
er
atin
g
at
its
MPP
,
an
d
it
is
g
o
in
g
to
b
e
f
o
r
ce
d
t
o
o
p
er
ate
at
v
o
ltag
es c
lo
s
er
to
th
e
lo
ad
im
p
e
d
an
ce
[
2
3
]
.
T
o
r
e
a
c
h
t
h
e
M
P
P
,
a
m
a
t
c
h
i
n
g
s
t
a
g
e
DC
-
DC
s
i
n
g
l
e
-
e
n
d
e
d
p
r
i
m
a
r
y
-
i
n
d
u
c
t
o
r
c
o
n
v
e
r
t
e
r
(
S
E
P
I
C
)
c
o
n
v
e
r
t
e
r
w
i
t
h
t
h
e
p
a
r
a
m
e
t
e
r
s
l
i
s
t
e
d
i
n
T
a
b
l
e
1
w
a
s
a
d
d
e
d
t
o
l
i
n
k
t
h
e
P
V
m
o
d
u
l
e
a
n
d
t
h
e
l
o
a
d
,
a
s
i
l
l
u
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
2
.
T
h
i
s
e
n
s
u
r
e
s
t
h
e
m
at
c
h
b
e
t
w
e
e
n
t
h
e
l
o
a
d
r
e
s
is
t
a
n
ce
a
n
d
t
h
e
i
m
p
e
d
a
n
c
e
s
e
e
n
b
y
th
e
P
V
m
o
d
u
l
e
.
A
n
M
P
P
T
al
g
o
r
i
t
h
m
w
i
ll
b
e
u
s
e
d
to
c
o
n
t
r
o
l
t
h
e
c
o
n
v
e
r
t
e
r
a
n
d
t
o
m
o
n
i
t
o
r
t
h
e
d
u
t
y
c
y
c
l
e
D
,
o
p
t
i
m
i
z
i
n
g
i
t
s
v
al
u
e
w
i
t
h
e
a
c
h
c
h
a
n
g
e
i
n
e
n
v
i
r
o
n
m
e
n
t
a
l
c
o
n
d
i
t
i
o
n
s
.
2
.
2
.
M
P
P
T
-
ba
s
ed
f
uzzy
lo
g
i
c
co
ntr
o
l
T
h
e
FLC
d
o
es
n
o
t
r
e
q
u
ir
e
a
m
ath
em
atica
l
m
o
d
el.
I
t
is
b
ased
o
n
cu
r
r
en
t
–
v
o
ltag
e
in
p
u
t
v
ar
iab
les,
wh
ich
ar
e
r
ea
d
f
r
o
m
th
e
PV
p
an
el
to
d
eter
m
in
e
th
e
p
o
wer
o
u
tp
u
t.
T
h
e
s
y
s
tem
c
o
n
s
is
t
s
o
f
th
r
ee
m
ai
n
elem
en
ts
: f
u
zz
if
icatio
n
,
f
u
zz
y
in
f
er
en
ce
,
a
n
d
d
ef
u
zz
if
icatio
n
,
as sh
o
wn
in
Fig
u
r
e
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2792
-
2
8
0
3
2794
2
.
2
.
1
.
F
uzzif
ica
t
io
n
I
t
r
eq
u
ir
es
id
en
tify
in
g
th
e
in
p
u
t
an
d
th
e
o
u
tp
u
t
v
ar
iab
les
to
b
e
f
u
zz
if
ied
as
a
f
ir
s
t
s
tep
.
Fo
r
a
PV
s
y
s
tem
,
v
o
ltag
e
v
ar
iatio
n
(
∆V
)
,
cu
r
r
e
n
t
v
ar
iatio
n
s
(
∆I
)
,
p
o
w
er
v
ar
iatio
n
s
(
∆P)
,
e
r
r
o
r
v
ar
iat
io
n
s
,
an
d
er
r
o
r
s
.
.
.
ca
n
b
e
u
s
ed
as
in
p
u
t
v
ar
iab
les,
an
d
th
e
d
u
ty
cy
cle
as
an
o
u
t
p
u
t
v
ar
iab
le.
I
n
th
is
p
ap
er
,
th
e
e
r
r
o
r
v
a
r
iatio
n
(
∆E
)
an
d
th
e
er
r
o
r
(
E
)
ar
e
th
e
in
p
u
ts
,
wh
er
ea
s
th
e
d
u
ty
cy
cle
r
atio
v
a
r
iatio
n
(
D)
is
th
e
o
u
tp
u
t
o
f
th
e
f
u
zz
y
co
n
tr
o
ller
.
T
h
o
s
e
v
ar
iab
les
ar
e
ca
lcu
lated
b
y
(
1
)
an
d
(
2
)
[1
0
]
.
T
h
e
Ma
m
d
an
i
m
eth
o
d
en
ab
les
th
e
v
ar
iab
les'
f
u
zz
if
icatio
n
.
=
∆
/
∆
=
(
(
)
−
(
−
1
)
)
/
(
(
)
−
(
−
1
)
(
1
)
∆
=
(
)
−
(
−
1
)
(
2
)
W
ith
:
-
"P(
n
)
":
T
h
e
cu
r
r
en
t
p
o
wer
m
e
asu
r
ed
f
r
o
m
th
e
PV sy
s
tem
;
-
"P(
n
-
1
)
":
T
h
e
p
o
wer
m
ea
s
u
r
e
d
in
th
e
p
r
ev
io
u
s
tim
e
s
tep
;
-
"V(
n
)
":
T
h
e
c
u
r
r
en
t
v
o
ltag
e
f
r
o
m
th
e
PV sy
s
tem
;
-
"V(
n
-
1
)
":
T
h
e
v
o
ltag
e
in
th
e
p
r
ev
io
u
s
tim
e
s
tep
; a
n
d
-
"E
(
n
)
":
T
h
e
e
r
r
o
r
ca
lcu
lated
at
th
e
cu
r
r
e
n
t tim
e
s
tep
.
"E
(
n
-
1
)
":
"T
h
e
er
r
o
r
f
r
o
m
th
e
p
r
ev
io
u
s
tim
e
s
tep
.
2
.
2
.
2
.
I
nfe
re
nce
s
y
s
t
em
T
o
estab
lis
h
a
lin
k
b
etwe
en
t
h
e
o
u
tp
u
t
an
d
in
p
u
t
v
ar
ia
b
les,
a
s
et
o
f
r
u
les
m
u
s
t
b
e
d
ef
in
e
d
b
ased
o
n
ex
p
er
im
en
tatio
n
an
d
o
b
s
er
v
at
io
n
.
I
n
t
h
is
p
ap
er
,
th
ese
r
u
les
ar
e
u
s
ed
to
in
cr
ea
s
e
o
r
d
ec
r
ea
s
e
th
e
d
u
ty
c
y
cle
[1
0
]
.
T
h
e
co
m
p
lete
s
et
o
f
r
u
les is
p
r
esen
ted
in
T
ab
le
2
[
2
4
]
.
2
.
2
.
3
.
Def
uzzif
ica
t
io
n
I
t
r
ep
r
esen
ts
th
e
r
ev
er
s
e
p
r
o
ce
s
s
o
f
f
u
zz
if
icatio
n
.
T
h
e
o
p
er
atio
n
is
ca
r
r
ied
o
u
t
u
s
in
g
th
e
f
u
zz
y
ce
n
tr
o
id
m
eth
o
d
,
wh
ich
ca
l
cu
lates
th
e
ce
n
tr
o
id
af
ter
r
u
le
ag
g
r
eg
atio
n
.
T
h
e
f
u
zz
y
MPPT
co
n
tr
o
l
is
im
p
lem
en
ted
u
s
in
g
th
e
MPPT
alg
o
r
ith
m
s
h
o
wn
in
Fig
u
r
e
4
.
Fig
u
r
e
1
.
V
-
I
ch
ar
ac
ter
is
tics
Fig
u
r
e
2
.
PV sy
s
tem
b
lo
ck
d
ia
g
r
am
Fig
u
r
e
3
.
Stru
ctu
r
e
o
f
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
P
V
M
od
u
l
e
DC
-
D
C
C
on
v
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er
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S
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c
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L
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A
D
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P
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D
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F
u
z
z
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In
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en
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e
S
y
s
t
em
F
u
z
z
y
R
u
l
e
B
a
s
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
S
u
p
p
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ce
n
tr
ic
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S
O
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b
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z
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tu
n
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(
A
m
el
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ma
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2795
T
ab
le
1
.
Par
am
eter
s
o
f
th
e
SE
PIC c
o
n
v
er
ter
P
a
r
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me
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3
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5
L2
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0
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-
3
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e
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R
10
T
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le
2
.
I
n
f
er
e
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ce
r
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les
∆E/
E
NS
NL
ZE
PL
PS
NS
PS
PS
PL
PS
PS
NL
PS
PL
PL
PL
PS
ZE
NL
NL
ZE
PL
PL
PL
NS
NL
NL
NL
NS
PS
NS
NS
NL
NS
NS
2
.
3
.
F
uzzy
lo
g
ic
co
ntr
o
ller
o
ptim
ized
by
t
he
P
SO
a
lg
o
rit
hm
A
s
al
r
e
a
d
y
m
e
n
t
i
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d
w
i
t
h
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n
th
e
f
i
r
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t
s
e
ct
i
o
n
,
t
h
e
P
SO
a
l
g
o
r
i
t
h
m
is
a
n
a
l
g
o
r
it
h
m
t
h
a
t
r
e
p
r
o
d
u
c
e
s
t
h
e
b
e
h
a
v
i
o
r
o
b
s
e
r
v
e
d
i
n
a
n
i
m
a
l
g
r
o
u
p
s
s
u
c
h
a
s
b
i
r
d
s
a
n
d
f
i
s
h
[
2
5
]
.
I
t
o
p
e
r
a
t
e
s
wi
t
h
3
k
e
y
c
o
m
p
o
n
e
n
t
s
,
w
h
i
c
h
a
r
e:
-
T
h
e
p
ar
ticle:
an
in
d
iv
id
u
al
e
n
t
ity
s
u
ch
as a
s
in
g
le
b
ir
d
.
-
T
h
e
s
war
m
:
r
ef
er
s
to
th
e
p
o
p
u
latio
n
o
f
p
ar
ticles
m
o
v
in
g
to
g
eth
er
,
ak
in
to
th
e
co
llectiv
e
m
o
v
em
en
t
o
f
a
f
lo
ck
[
2
6
]
.
-
T
h
e
s
o
lu
tio
n
:
T
h
is
r
ep
r
esen
ts
th
e
tar
g
eted
o
u
tco
m
e
o
f
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
,
in
th
e
s
am
e
way
as
th
e
s
ea
r
ch
f
o
r
a
s
o
u
r
ce
o
f
f
o
o
d
f
o
r
b
ir
d
s
[
2
6
]
.
E
ac
h
p
ar
ticle
h
as
its
p
o
s
itio
n
an
d
v
elo
city
,
wh
ich
g
u
id
e
its
m
o
v
em
en
t
to
war
d
t
h
e
o
p
tim
al
s
o
lu
tio
n
[
2
5
]
,
[
2
6
]
.
Par
ticles
co
o
p
er
at
e
b
y
ex
ch
an
g
in
g
th
e
k
n
o
wled
g
e
th
ey
h
av
e
g
at
h
er
ed
d
u
r
i
n
g
th
e
ex
p
lo
r
atio
n
p
r
o
ce
s
s
.
T
h
ey
m
ain
tain
two
i
m
p
o
r
tan
t
p
o
s
itio
n
s
[
2
6
]
:
-
Per
s
o
n
al
B
est
(
p
b
est)
p
o
s
itio
n
:
T
h
is
r
ep
r
esen
ts
th
e
b
est
p
o
s
itio
n
a
p
a
r
ticle
h
as
ac
h
iev
ed
b
ased
o
n
its
p
er
s
o
n
al
p
ast ex
p
e
r
ien
ce
s
.
-
Glo
b
al
B
est
(
g
b
est)
p
o
s
itio
n
:
T
h
is
s
ig
n
if
ies
th
e
b
est
p
o
s
it
io
n
d
is
co
v
er
e
d
b
y
a
n
y
p
a
r
ticle
in
th
e
en
tire
s
war
m
,
p
r
o
v
i
d
in
g
a
s
h
a
r
ed
tar
g
et
f
o
r
all
th
e
p
ar
ticles.
B
y
ex
ch
an
g
in
g
in
f
o
r
m
atio
n
,
th
e
p
ar
ticles
u
p
d
ate
th
eir
p
o
s
itio
n
s
an
d
v
elo
cities
iter
ativ
ely
an
d
co
n
v
er
g
e
co
llectiv
ely
to
war
d
th
e
o
p
tim
al
s
o
lu
tio
n
[
2
5
]
.
T
h
e
f
lo
wch
ar
t
s
h
o
wn
in
Fig
u
r
e
5
will
p
r
o
v
id
e
a
m
o
r
e
d
etailed
o
v
er
v
iew
o
f
th
e
PS
O
alg
o
r
ith
m
.
S
T
A
R
T
R
E
A
D
V
(
n
)
,
I
(
n
)
f
rom P
V
P
a
n
e
l
E
(
n
)
=
Δ
P
(
n
)
Δ
V
(
n
)
=
P
(
n
)
-
P
(
n
-
1
)
V
(
n
)
-
V
(
n
-
1
)
Δ
P(
n)=
P(n)
-
P(n
-
1)
Δ
V(n)
=V(
n)
-
V(n
-
1)
P
(
n)
=
V(
n)
.I(
n)
∆
E
=
E
(
n
)
-
E
(
n
-
1
)
Δ
P(n
)
Δ
V
(
n)
=
=
0
Δ
P
(n)
Δ
V(n
)
>0
D
(
n
)
=D
(
n
-
1
)
+
∆
D
D
(
n
)
=D
(
n
-
1
)
-
∆D
Y
E
S
NO
R
E
T
U
R
N
NO
Y
E
S
V(
n
-
1)
I(n
-
1)
P
(
n
-
1)
UP
D
A
T
E
S
St
a
r
t
It
i
a
l
i
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e
th
e
s
w
a
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m
(
a
p
o
p
u
l
a
ti
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n
o
f
p
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n
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m
p
o
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n
s
a
n
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E
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th
e
f
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e
s
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o
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c
h
p
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e
b
a
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e
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o
b
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n
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Fi
n
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a
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te
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a
n
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b
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p
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a
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th
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p
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v
el
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i
ti
es
U
p
d
a
te
th
e
p
a
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c
l
e
s
p
o
s
i
ti
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n
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i
s
t
h
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mi
n
a
t
i
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ri
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a
s
a
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i
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ed
G
b
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t
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th
e
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ti
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u
m
s
o
l
u
ti
o
n
E
n
d
NO
Y
E
S
Fig
u
r
e
4
.
MPPT
alg
o
r
ith
m
Fig
u
r
e
5
.
Par
ticle
s
war
m
o
p
tim
izatio
n
alg
o
r
ith
m
2
.
3
.
1
.
O
ptim
iza
t
io
n o
f
m
em
b
er
s
hip
f
u
nct
io
ns
u
s
ing
P
SO
T
o
im
p
r
o
v
e
th
e
FLC
an
d
o
v
e
r
co
m
e
th
e
d
r
awb
ac
k
s
e
x
p
er
ie
n
ce
d
d
u
r
in
g
t
h
e
in
itial
im
p
le
m
en
tatio
n
,
th
e
s
u
p
p
o
r
t
o
f
th
e
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
f
o
r
b
o
th
in
p
u
ts
a
n
d
o
u
tp
u
ts
will
b
e
o
p
tim
ized
.
E
ac
h
v
a
r
iab
le
is
d
escr
ib
ed
b
y
5
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
.
B
y
m
ain
tain
in
g
th
e
p
ea
k
s
f
ix
ed
an
d
f
o
c
u
s
in
g
o
n
o
p
tim
izin
g
th
e
s
u
p
p
o
r
ts
o
f
ea
c
h
m
em
b
er
s
h
ip
f
u
n
ctio
n
,
3
0
s
u
p
p
o
r
ts
S1
to
S3
0
h
av
e
b
ee
n
o
p
tim
ized
as illu
s
tr
ated
in
Fig
u
r
e
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2792
-
2
8
0
3
2796
a)
C
r
ea
tio
n
o
f
th
e
in
itial p
o
p
u
lati
o
n
As
p
r
esen
ted
in
th
e
f
lo
wch
ar
t
d
ep
icted
in
Fig
u
r
e
5
,
th
e
f
ir
s
t
s
tep
co
n
s
is
t
s
o
f
cr
ea
tin
g
a
p
o
p
u
latio
n
.
T
h
e
m
ax
im
u
m
an
d
m
in
im
u
m
v
alu
es
f
o
r
ea
ch
p
ar
am
eter
ar
e
d
ef
in
ed
,
f
o
llo
we
d
b
y
th
e
g
en
er
atio
n
o
f
a
s
war
m
(
p
o
p
u
latio
n
)
o
f
3
0
0
p
a
r
ticles
r
an
d
o
m
ly
.
E
ac
h
p
ar
ticle
with
in
th
e
s
war
m
will
b
e
r
ep
r
esen
te
d
b
y
a
v
ec
to
r
o
f
3
0
elem
en
ts
,
co
r
r
esp
o
n
d
in
g
to
th
e
s
u
p
p
o
r
ts
b
ein
g
o
p
tim
ized
.
b)
Fit
n
ess
ev
alu
atio
n
T
h
is
is
a
cr
u
cial
s
tep
in
th
e
P
SO
alg
o
r
ith
m
,
wh
ich
will
e
v
a
lu
ate
th
e
e
f
f
icien
cy
o
f
ev
er
y
g
en
er
ated
p
ar
ticle
in
ac
h
iev
in
g
th
e
o
p
ti
m
al
s
o
lu
tio
n
.
T
h
is
ev
al
u
atio
n
will
b
e
p
er
f
o
r
m
ed
b
y
u
s
in
g
th
e
o
b
jectiv
e
f
u
n
ctio
n
,
wh
ich
is
th
e
m
ea
n
s
q
u
a
r
ed
er
r
o
r
o
f
t
h
e
p
o
we
r
as in
(
3
)
.
=
1
∑
(
−
)
2
=
1
(
3
)
W
h
er
e
"P
max
"
,
"
P
cc
"
,
"
n
"
r
ep
r
esen
t m
ax
im
u
m
p
o
wer
,
ca
lcu
lated
p
o
wer
an
d
th
e
am
o
u
n
t o
f
d
ata
.
c)
Up
d
ate
th
e
p
b
est an
d
g
b
est
T
h
e
f
itn
ess
p
ar
ticle
v
alu
es
will
b
e
r
an
k
e
d
f
r
o
m
th
e
b
est
to
th
e
w
o
r
s
t
to
d
eter
m
in
e
th
e
“p
b
est”
p
o
s
itio
n
an
d
th
e
“g
b
est”
p
o
s
it
io
n
.
I
f
t
h
e
n
ewe
s
t
f
itn
ess
v
alu
e
is
h
ig
h
er
th
an
t
h
e
p
r
e
v
io
u
s
v
alu
e,
th
e
p
a
r
ticle
u
p
d
ates
its
p
er
s
o
n
al
b
est
“p
b
e
s
t”.
T
h
e
p
ar
ticle
with
th
e
h
ig
h
est
p
er
f
o
r
m
an
ce
in
th
e
g
r
o
u
p
“b
est
f
itn
ess
v
alu
e”
tak
es o
n
th
e
s
tatu
s
o
f
th
e
g
lo
b
al
b
est “g
b
est”.
d)
Up
d
ate
th
e
v
elo
city
an
d
p
o
s
itio
n
o
f
p
ar
ticles
T
h
e
v
elo
city
a
n
d
th
e
p
o
s
itio
n
will b
e
u
p
d
ated
b
y
u
s
in
g
(
4
)
a
n
d
(
5
)
,
r
esp
ec
tiv
ely
.
(
+
1
)
=
1
(
)
+
2
(
−
(
)
)
1
+
3
(
−
(
)
)
2
(
4
)
(
+
1
)
=
(
)
+
(
+
1
)
(
5
)
W
h
er
e:
i)
"v
(
t+1
)
"
an
d
"v
(
t
)
"
ar
e
t
h
e
ac
tu
al
a
n
d
t
h
e
p
r
e
v
io
u
s
v
elo
cities;
ii)
"x
(
t+1
)
"
an
d
"x
(
t
)
"
ar
e
th
e
ac
tu
al
an
d
th
e
p
r
ev
io
u
s
p
o
s
itio
n
s
;
an
d
iii)
"c
1
"
is
th
e
in
er
tia
weig
h
t,
"
c
2
"
is
th
e
co
g
n
itiv
e
co
ef
f
icien
t
a
n
d
"c
3
"
is
th
e
s
o
cial
co
ef
f
icien
t.
"r
an
d
1
"
an
d
"
r
an
d
2
"
ar
e
two
d
iag
o
n
al
m
atr
ices
o
f
r
a
n
d
o
m
elem
en
ts
th
at
b
elo
n
g
to
th
e
[
0
,
1
]
in
ter
v
al.
T
h
e
PS
O
p
ar
am
ete
r
s
u
s
ed
in
th
is
p
ap
er
ar
e
p
r
esen
ted
in
T
ab
le
3
.
Fig
u
r
e
6
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
s
s
u
p
p
o
r
t
T
ab
le
3
.
C
o
n
tr
o
l p
ar
am
ete
r
s
v
ec
to
r
f
o
r
PS
O
A
l
g
o
r
i
t
h
m
C
o
n
t
r
o
l
p
a
r
a
me
t
e
r
s
v
e
c
t
o
r
V
a
l
u
e
PSO
P
o
p
u
l
a
t
i
o
n
s
i
z
e
3
0
0
I
n
e
r
t
i
a
w
e
i
g
h
t
(
C
1
)
1
.
5
A
c
c
e
l
e
r
a
t
i
o
n
c
o
n
st
a
n
t
(
c
o
g
n
i
t
i
v
e
p
a
r
a
met
e
r
)
(
C
2
)
2
.
5
A
c
c
e
l
e
r
a
t
i
o
n
c
o
n
st
a
n
t
(
so
c
i
a
l
p
a
r
a
me
t
e
r
)
(
C
3
)
1
.
4
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
S
u
p
p
o
r
t
-
ce
n
tr
ic
P
S
O
-
b
a
s
ed
f
u
z
z
y
MPP
T
tu
n
in
g
fo
r
…
(
A
m
el
S
ma
ili
)
2797
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
NS
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
o
b
tain
ed
r
esu
lts
s
im
u
latio
n
u
s
in
g
MA
T
L
AB
/
Simu
lin
k
.
T
h
e
s
im
u
latio
n
s
wer
e
ex
ec
u
te
d
to
ass
ess
th
e
o
v
er
all
e
f
f
icien
cy
o
f
th
e
f
u
zz
y
MPPT
alg
o
r
ith
m
a
n
d
to
an
aly
ze
th
e
im
p
ac
t
o
f
o
p
tim
izatio
n
u
s
in
g
t
h
e
PS
O
alg
o
r
ith
m
.
A
n
o
v
e
r
v
iew
o
f
t
h
e
o
v
er
all
Simu
lin
k
m
o
d
el
o
f
th
e
PV
s
y
s
tem
,
wh
ich
co
n
tain
s
a
PV
ar
r
ay
,
t
h
e
SEPI
C
co
n
v
er
ter
,
an
d
th
e
FLC
b
lo
ck
,
ca
n
b
e
v
iewe
d
in
Fig
u
r
e
7
.
Fig
u
r
e
8
d
ep
icts
a
d
etailed
v
iew
o
f
th
e
elem
en
ts
co
m
p
o
s
in
g
th
e
FLC
b
lo
ck
.
T
o
ca
r
r
y
o
u
t
th
e
s
im
u
latio
n
.
A
“1
So
ltech
1
STH
-
215
-
P”
PV
m
o
d
u
le
was
u
s
ed
u
n
d
er
id
ea
l
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
o
f
2
5
°C
an
d
1
0
0
0
W
/m
².
T
wo
d
if
f
e
r
en
t
m
em
b
er
s
h
ip
f
u
n
ctio
n
co
n
f
ig
u
r
atio
n
s
ar
e
s
im
u
lated
to
e
v
alu
ate
th
e
alg
o
r
ith
m
'
s
ef
f
ec
tiv
en
ess
o
f
th
eir
o
p
tim
izatio
n
an
d
en
h
a
n
cin
g
t
h
e
s
y
s
tem
’
s
ef
f
icien
cy
.
T
h
e
d
if
f
er
en
ce
b
etwe
en
th
e
th
r
ee
c
o
n
f
ig
u
r
atio
n
s
lies
in
th
e
s
u
p
p
o
r
ts
an
d
th
e
c
o
r
es c
h
o
s
en
f
o
r
ea
ch
m
em
b
e
r
s
h
ip
f
u
n
c
tio
n
.
Fig
u
r
e
7
.
Simu
lin
k
m
o
d
el
o
f
P
V
s
y
s
tem
Fig
u
r
e
8
.
Fu
zz
y
MPPT
alg
o
r
it
h
m
b
lo
c
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2792
-
2
8
0
3
2798
Fro
m
th
e
s
im
u
latio
n
d
ata
s
h
o
wn
in
T
ab
le
4
,
Fig
u
r
e
9
,
an
d
T
ab
le
5
,
Fig
u
r
e
1
0
f
o
r
co
n
f
ig
u
r
atio
n
s
1
an
d
2
,
r
esp
ec
tiv
ely
,
it'
s
clea
r
th
at:
-
Fo
r
th
e
1
s
t
co
n
f
ig
u
r
atio
n
,
t
h
e
s
y
s
tem
b
ef
o
r
e
o
p
tim
izatio
n
ac
h
iev
ed
a
c
o
m
m
en
d
ab
l
e
ef
f
icien
cy
o
f
ap
p
r
o
x
im
ately
9
9
.
5
6
%.
Ho
we
v
er
,
th
e
ap
p
licatio
n
o
f
t
h
e
PS
O
alg
o
r
ith
m
f
u
r
th
er
im
p
r
o
v
ed
th
is
ef
f
icien
c
y
,
r
ea
ch
in
g
9
9
.
6
3
%.
T
h
e
Po
wer
R
esp
o
n
s
e
h
ig
h
lig
h
ts
th
at
af
t
er
o
p
tim
izatio
n
,
th
e
f
lu
ctu
ati
o
n
s
ar
o
u
n
d
th
e
MPP a
r
e
s
lig
h
tly
r
ed
u
ce
d
.
-
Fo
r
th
e
2
n
d
co
n
f
ig
u
r
atio
n
,
we
ca
n
clea
r
ly
s
ee
t
h
at
th
e
ef
f
ici
en
cy
b
ef
o
r
e
o
p
tim
izatio
n
is
a
r
o
u
n
d
9
8
.
9
3
%,
wh
ich
is
s
atis
f
ac
to
r
y
b
u
t
n
o
t
o
p
tim
al.
Af
ter
o
p
tim
izin
g
th
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
,
th
e
e
f
f
icien
cy
v
alu
e
was im
p
r
o
v
ed
to
ar
o
u
n
d
9
9
.
6
7
%,
a
h
ig
h
ly
f
av
o
u
r
ab
le
o
u
tco
m
e.
-
T
h
e
f
lu
ctu
atio
n
s
in
th
e
p
o
wer
r
esp
o
n
s
e
wer
e
s
ig
n
if
ican
tly
r
e
d
u
ce
d
af
te
r
o
p
tim
izatio
n
.
-
Fo
r
b
o
th
co
n
f
ig
u
r
atio
n
s
,
th
e
PS
O
alg
o
r
ith
m
s
u
cc
ess
f
u
lly
o
p
tim
ized
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
,
en
ab
lin
g
th
e
s
y
s
tem
to
o
p
er
ate
at
a
h
ig
h
er
ef
f
icien
cy
v
alu
e
c
o
m
p
ar
e
d
t
o
th
e
r
esu
lts
o
b
tain
ed
b
ef
o
r
e
o
p
tim
izatio
n
.
I
n
c
o
n
f
ig
u
r
a
ti
o
n
3
,
t
h
e
f
u
z
zy
m
e
m
b
er
s
h
i
p
f
u
n
ct
io
n
was
p
u
r
p
o
s
el
y
s
et
to
b
e
p
o
o
r
ly
c
o
n
f
i
g
u
r
e
d
to
s
e
e
i
f
th
e
o
p
ti
m
iz
ati
o
n
p
r
o
ce
s
s
c
o
u
l
d
im
p
r
o
v
e
it.
I
n
c
o
n
s
i
d
e
r
a
ti
o
n
o
f
t
h
e
r
es
u
l
ts
p
r
ese
n
t
ed
i
n
T
ab
l
e
6
an
d
Fi
g
u
r
e
1
1
,
th
e
i
n
i
tial
s
y
s
te
m
p
er
f
o
r
m
ed
p
o
o
r
l
y
,
wit
h
a
n
ac
c
u
r
a
cy
o
f
a
r
o
u
n
d
1
.
8
1
0
9
%
,
co
n
f
i
r
m
in
g
t
h
at
it
was
n
'
t
ef
f
e
cti
v
e.
Af
t
er
a
p
p
l
y
i
n
g
t
h
e
o
p
ti
m
iz
ati
o
n
,
t
h
e
p
e
r
f
o
r
m
an
ce
i
m
p
r
o
v
e
d
s
ig
n
i
f
i
ca
n
tl
y
t
o
9
9
.
7
6
9
8
%
,
d
em
o
n
s
t
r
at
in
g
t
h
e
r
o
b
u
s
t
n
ess
a
n
d
th
e
co
r
r
e
cti
v
e
ca
p
ac
it
y
o
f
t
h
e
p
r
o
p
o
s
e
d
m
et
h
o
d
.
T
a
b
l
e
7
p
r
es
e
n
ts
a
co
m
p
ar
is
o
n
b
etwe
e
n
t
h
e
p
r
o
p
o
s
e
d
m
et
h
o
d
a
p
p
li
ed
t
o
t
h
e
d
if
f
e
r
e
n
t
c
o
n
f
ig
u
r
at
io
n
s
a
n
d
th
e
e
x
is
t
in
g
wo
r
k
s
i
n
t
h
e
li
te
r
a
tu
r
e
.
As
illu
s
tr
ated
in
T
ab
le
7
,
th
e
FLC
-
PS
O
m
eth
o
d
d
ev
elo
p
e
d
in
th
is
s
tu
d
y
o
u
tp
er
f
o
r
m
s
th
e
co
n
f
i
g
u
r
atio
n
s
p
r
esen
ted
in
t
h
e
liter
atu
r
e,
ac
h
iev
in
g
h
ig
h
er
ef
f
icien
cy
v
alu
es a
cr
o
s
s
all
test
ed
ca
s
es.
T
ab
le
4
.
I
n
p
u
ts
an
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I
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ts
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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w
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2088
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ate
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a
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eg
ar
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less
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ig
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f
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tem
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:
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ar
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o
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ten
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s
y
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tem
b
eh
av
io
r
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h
e
r
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lt
o
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th
is
co
n
f
ig
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r
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n
d
em
o
n
s
tr
ate
s
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o
w
th
e
p
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s
ed
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tim
izatio
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m
eth
o
d
ca
n
e
f
f
ec
tiv
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f
i
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e
th
e
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em
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ip
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ar
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eter
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im
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e
f
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f
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1
.
8
1
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9
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to
9
9
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7
6
9
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er
e
b
y
im
p
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p
er
f
o
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m
a
n
ce
with
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u
t
th
e
n
ee
d
f
o
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ex
p
e
r
t
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ter
v
e
n
tio
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o
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m
an
u
al
tu
n
in
g
.
C
o
m
p
ar
ed
to
r
ec
en
t
MPPT
tech
n
i
q
u
es
f
o
u
n
d
i
n
th
e
liter
atu
r
e,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
h
as
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h
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ed
s
u
p
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ce
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ter
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s
o
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tr
ac
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g
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icien
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,
m
ak
in
g
it
ef
f
ec
tiv
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an
d
r
o
b
u
s
t u
n
d
e
r
th
e
test
ed
co
n
d
itio
n
s
.
F
UNDING
I
NF
O
R
M
A
T
I
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T
h
e
au
th
o
r
s
d
ec
lar
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th
at
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f
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n
d
in
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was r
ec
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e
d
to
s
u
p
p
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t
th
is
r
esear
ch
.
AUTHO
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h
is
jo
u
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s
es
th
e
C
o
n
tr
ib
u
to
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o
les
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ax
o
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o
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y
(
C
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ed
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to
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ize
in
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iv
id
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al
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th
o
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co
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tr
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tio
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,
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ed
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ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.