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[
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2]
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[
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[
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tech
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[
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.
On
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I
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8708
I
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y
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t
h
er
t
y
p
e
s
o
f
r
esear
c
h
l
ik
e
S
h
i
et
al.
[
11
]
,
Go
w
a
id
et
al.
[
12
]
,
C
h
en
g
et
al.
[
1
3
]
,
Sin
g
et
al.
[
1
4
]
,
Yaic
h
i
et
al.
[
1
5
]
,
etc.
h
a
v
e
ad
d
r
ess
ed
th
e
is
s
u
e
s
i
n
MP
PT
w
it
h
d
i
f
f
e
r
en
t
ap
p
r
o
ac
h
es.
T
h
e
b
eh
a
v
io
r
o
f
t
h
e
s
o
lar
W
SN
u
n
d
er
d
if
f
er
en
t
cli
m
atic
co
n
d
i
tio
n
is
d
is
cu
s
s
ed
i
n
Ha
m
il
i
et
al.
[
1
6
]
.
T
h
e
w
o
r
k
o
f
E
l
m
a
l
ah
et
al.
[
1
7
]
h
av
e
d
is
cu
s
s
ed
a
p
o
w
er
co
n
tr
o
l
m
ec
h
an
i
s
m
s
to
r
ed
u
ce
th
e
co
s
t
an
d
y
ield
in
g
h
ig
h
er
p
er
f
o
r
m
an
ce
.
I
n
a
w
o
r
k
o
f
Sa
m
o
s
ir
et
al.
[
1
8
]
th
e
f
u
zz
y
lo
g
ic
b
a
s
ed
s
i
m
u
latio
n
m
o
d
e
l
is
p
r
esen
ted
t
o
g
et
MP
P
T
f
o
r
P
V
ap
p
licatio
n
.
T
h
u
s
,
in
t
h
is
m
an
u
s
cr
ip
t,
a
m
o
d
i
f
ied
P
SO
alg
o
r
ith
m
f
o
r
MP
PT
in
th
e
P
V
ar
r
ay
is
p
r
esen
ted
to
o
v
er
co
m
e
th
e
r
ec
en
t
r
esear
c
h
is
s
u
e
a
n
d
b
r
in
g
m
o
r
e
e
f
f
ec
tiv
e
n
e
s
s
i
n
M
P
PT.
T
h
e
m
an
u
s
c
r
ip
t
i
s
ca
teg
o
r
ize
d
as,
s
ec
tio
n
1
d
is
cu
s
s
i
n
g
th
e
b
ac
k
g
r
o
u
n
d
o
f
P
V
cir
cu
it,
c
o
n
s
id
er
atio
n
o
f
P
SO
in
MP
PT
.
Sec
tio
n
2
g
i
v
es
r
esear
ch
p
r
o
b
lem
,
s
ec
tio
n
3
ex
p
lain
s
p
r
o
p
o
s
ed
m
o
d
i
f
ied
P
SO
alg
o
r
ith
m
alo
n
g
w
ith
al
g
o
r
ith
m
d
escr
ip
tio
n
an
d
i
m
p
le
m
en
ta
tio
n
,
s
ec
tio
n
4
ill
u
s
tr
ates t
h
e
r
es
u
l
t
s
an
al
y
s
is
a
n
d
s
ec
tio
n
5
g
iv
e
s
t
h
e
co
n
cl
u
s
io
n
o
f
th
e
p
r
o
p
o
s
ed
P
SO a
lg
o
r
ith
m
.
a.
T
h
e
b
ac
k
g
r
o
u
n
d
Fro
m
th
e
ex
i
s
ti
n
g
r
esear
ch
es
o
f
I
s
h
aq
u
e
et
al.
[
1
9
,
2
0
]
,
Yan
g
et
al.
[
2
1
]
,
C
h
u
n
h
u
a
et
al.
[
2
2
]
,
Do
n
g
r
as
et
al.
[
2
3
]
,
f
o
u
n
d
th
at
th
e
P
V
m
o
d
el
w
i
th
t
w
o
b
y
p
a
s
s
d
io
d
es
o
f
f
er
s
a
h
i
g
h
er
d
eg
r
ee
o
f
ac
cu
r
ac
y
.
T
h
e
s
a
m
e
co
n
ce
p
t is ad
ap
ted
in
d
esig
n
i
n
g
th
e
P
V
cir
cu
it a
n
d
h
as b
ee
n
p
r
esen
ted
in
Fi
g
u
r
e
1.
Fig
u
r
e
1
.
(
a)
P
V
cir
cu
it
,
(
b
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eq
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iv
a
len
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ir
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it
T
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m
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g
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2
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cr
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&
:
I
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tan
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:
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lu
te
te
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r
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ll.
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ig
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th
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f
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m
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f
P
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d
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n
ca
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e
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ted
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[
pp
ss
N
N
]
.
Fu
r
th
er
,
to
en
h
a
n
ce
th
e
s
tr
u
ct
u
r
e
o
f
a
s
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p
ar
allel
cir
cu
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th
e
(
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ca
n
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m
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d
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f
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as,
r
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t
r
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1
(
3
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w
h
er
e,
pp
ss
N
N
b.
P
SO in
MP
PT
T
h
e
alg
o
r
ith
m
o
f
P
ar
ticle
S
war
m
Op
ti
m
izatio
n
(
P
SO)
is
p
r
esen
ted
b
y
Ken
n
ed
y
a
n
d
E
b
er
h
ar
t
[
2
0
]
.
T
h
is
is
a
s
ig
n
if
ican
t
m
et
h
o
d
w
h
ich
ca
n
b
e
u
s
ed
f
o
r
m
u
lti
m
o
d
al
f
u
n
ctio
n
o
p
ti
m
izatio
n
a
n
d
s
w
ar
m
o
p
ti
m
izatio
n
se
ar
ch
g
u
id
e
g
e
n
er
ated
f
r
o
m
co
m
p
etitio
n
an
d
co
o
p
er
atio
n
a
m
o
n
g
t
h
e
p
ar
ticle
s
i
n
s
w
ar
m
.
T
o
illu
s
tr
ate
th
e
P
SO a
lg
o
r
it
h
m
f
o
r
MP
PT
co
n
tr
o
ller
,
th
e
s
o
lu
t
io
n
v
ec
to
r
(
k
i
x
)
ca
n
b
e
d
ef
in
ed
.
]
,
.
.
.
,
,
,
[
3
2
1
j
j
k
i
d
d
d
d
d
x
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4
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w
h
er
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j
d
is
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ar
ticle
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u
t
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2
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3
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N
T
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e
o
b
j
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tiv
e
f
u
n
ctio
n
f
o
r
th
i
s
d
u
t
y
r
atio
ca
n
b
e
ca
lcu
lated
a
s
,
1
)
(
)
(
k
i
k
i
d
P
d
P
(
5)
T
h
e
p
r
o
p
e
r
ty
o
f
P
SO
i
s
t
h
at
it
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d
s
th
r
ee
d
u
t
y
c
y
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les
3
2
1
,
,
d
d
d
an
d
f
o
r
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ar
d
s
t
h
en
to
th
e
p
o
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er
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n
v
er
ter
s
to
in
itia
lize
th
e
o
p
ti
m
izat
io
n
p
r
o
ce
s
s
.
T
h
e
f
o
llo
w
i
n
g
Fig
u
r
e
2
g
iv
e
s
th
e
m
o
v
e
m
en
t
o
f
p
ar
ticles
in
s
ea
r
c
h
o
f
MP
P
at
d
if
f
er
e
n
t
i
ter
atio
n
s
.
T
h
e
tr
ian
g
le
s
r
ep
r
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t
t
h
e
d
u
t
y
c
y
cles.
I
n
t
h
e
f
ir
s
t
iter
atio
n
as
s
h
o
wn
in
F
ig
u
r
e
2
(
a)
o
f
t
h
e
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ar
ticle
m
o
v
e
m
e
n
t,
t
h
e
d
u
t
y
c
y
cle
s
ar
e
p
er
s
o
n
al
b
est
(
P
b
)
w
h
ile
d
2
is
g
lo
b
al
b
est
(
G
b
)
an
d
is
th
e
o
p
ti
m
al
v
a
lu
e
o
f
P
V
ar
r
ay
.
T
h
e
m
o
v
e
m
en
t
o
f
p
ar
ticles
i
n
th
e
s
ec
o
n
d
iter
atio
n
as
s
h
o
w
n
i
n
Fi
g
u
r
e
2
(
b
)
.
I
n
th
i
s
,
b
ec
au
s
e
o
f
G
b
,
w
h
ic
h
i
s
o
f
f
er
i
n
g
o
p
ti
m
al
v
al
u
e
o
f
p
o
w
er
(
5)
,
th
e
v
elo
cit
y
,
P
b
(
d
i)
is
ze
r
o
,
an
d
t
h
e
f
ac
t
o
r
G
b
(d
2
)
is
ze
r
o
.
Hen
ce
,
th
e
v
elo
cit
y
o
f
t
h
e
G
b
p
ar
ticle
(
d
2
)
is
ze
r
o
,
w
h
ic
h
lead
s
to
ze
r
o
s
p
ee
d
an
d
u
n
c
h
an
g
ed
d
u
t
y
r
atio
.
T
h
u
s
,
in
s
ea
r
ch
o
p
ti
m
izatio
n
,
th
e
p
ar
ticles
d
o
n
o
t
h
av
e
an
y
ef
f
ec
t.
I
n
o
r
d
er
to
u
t
iliz
e
th
is
s
it
u
atio
n
,
s
o
m
e
d
is
t
u
r
b
an
ce
w
i
ll
b
e
ad
d
ed
,
an
d
it
ass
u
r
es
t
h
e
ch
a
n
g
e
in
o
p
ti
m
al
v
al
u
e.
T
h
e
m
o
v
e
m
en
t
o
f
p
ar
ticles
i
n
th
e
t
h
ir
d
i
ter
atio
n
i
s
p
r
esen
ted
in
Fi
g
u
r
e
2
(
c)
.
I
n
f
ir
s
t
t
w
o
i
ter
atio
n
s
y
ield
b
etter
f
i
tn
e
s
s
,
s
p
e
ed
,
an
d
th
e
p
ar
ticle
d
ir
ec
tio
n
is
u
n
c
h
a
n
g
ed
.
Hen
c
e,
th
e
y
s
ta
y
i
n
t
h
e
s
a
m
e
d
ir
ec
tio
n
alo
n
g
Gb
.
I
n
th
e
th
ir
d
iter
atio
n
,
all
th
e
d
u
t
y
c
y
cles
3
2
1
,
,
d
d
d
s
ta
y
at
lo
w
s
p
ee
d
f
o
r
MP
P
.
A
t
th
is
s
p
ee
d
,
th
e
d
u
t
y
r
atio
w
ill
b
e
co
n
s
ta
n
t,
a
n
d
th
e
s
y
s
te
m
w
il
l
o
cc
u
p
y
a
s
tab
le
o
p
er
atin
g
p
o
in
t,
w
h
ich
h
elp
s
in
m
i
n
i
m
i
zin
g
t
h
e
o
s
cillatio
n
s
o
f
MP
P
.
I
f
th
e
P
V
ar
r
ay
i
s
in
p
ar
tial
s
h
ad
e,
th
e
P
-
V
cu
r
v
e
f
a
ce
s
m
u
lti
-
p
ea
k
s
tate
P
1
,
P
2
,
a
n
d
P
4
lo
ca
l
p
o
les
w
h
ile
P
3
g
lo
b
al
p
o
les
(
o
b
tain
ed
f
r
o
m
4
th
iter
atio
n
a
s
s
h
o
w
n
in
Fig
u
r
e
2
(
d
)
.
T
h
e
o
u
tp
u
t
o
f
t
h
e
s
y
s
te
m
w
it
h
d
u
t
y
c
y
c
les
3
2
1
,
,
d
d
d
w
h
er
e
P
b
is
p
ar
ticles,
th
e
g
lo
b
al
p
ea
k
(
P
3
)
is
o
b
tain
ed
an
d
o
p
ti
m
izatio
n
is
in
itialized
at
i
n
itial d
u
t
y
r
atio
(
P
b
,
i)
.
c.
R
esear
ch
p
r
o
b
le
m
T
h
e
w
o
r
k
o
f
Yo
g
a
n
a
n
d
in
i
an
d
An
ita
[
2
4
]
h
av
e
p
r
o
v
id
ed
a
n
i
n
s
ig
h
t
in
to
MP
PT
tech
n
iq
u
es
in
P
V
m
o
d
u
les
b
y
d
ea
lin
g
w
it
h
ex
i
s
tin
g
r
esear
c
h
es,
r
esear
ch
g
a
p
,
an
d
o
f
f
er
ed
a
f
u
t
u
r
is
tic
id
ea
f
o
r
th
e
r
esear
ch
co
m
m
u
n
it
y
.
Fro
m
t
h
e
r
ec
e
n
t
r
esear
ch
s
u
r
v
e
y
,
it
i
s
o
b
s
er
v
e
d
th
at
at
t
h
e
s
lo
w
c
h
a
n
g
e
in
o
p
tim
a
l
r
ad
iatio
n
s
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
5
0
0
1
-
5008
5004
th
e
P
SO
n
ee
d
to
p
r
o
v
id
e
a
n
ap
p
r
o
p
r
iat
e
v
alu
e
o
f
d
u
t
y
c
y
cle.
Du
r
i
n
g
MP
P
tr
ac
k
i
n
g
,
c
h
an
g
es
i
n
air
r
atio
,
in
itial
izatio
n
,
an
d
v
ar
iat
io
n
in
d
u
t
y
r
atio
,
r
an
g
e
o
f
th
e
p
ar
ticles
in
P
V
-
cu
r
v
e
in
cr
ea
s
es.
Hen
ce
,
lar
g
e
f
l
u
ctu
a
tio
n
s
m
a
y
ap
p
ea
r
in
p
r
o
v
id
in
g
o
p
ti
m
al
s
ea
r
c
h
s
o
lu
tio
n
.
T
h
is
y
ield
s
h
i
g
h
co
m
p
u
ta
tio
n
al
co
s
t
an
d
en
er
g
y
w
a
s
tag
e.
An
o
t
h
er
p
r
o
b
lem
w
h
ich
n
ee
d
s
to
b
e
co
n
s
id
er
ed
is
t
h
at
tr
ac
k
in
g
o
f
MP
P
m
u
s
t
b
e
f
ast
en
o
u
g
h
to
tr
ac
k
s
p
ee
d
b
u
t,
t
h
e
d
u
t
y
r
atio
a
n
d
v
o
latilit
y
ar
e
n
o
t
f
ea
s
ib
le
i
n
t
h
e
P
SO
alg
o
r
it
h
m
,
a
n
d
it
d
o
e
s
n
o
t
y
ield
p
r
o
p
er
tr
ac
k
in
g
o
f
MP
P
.
A
ls
o
,
ch
a
n
g
e
in
th
e
i
n
ten
s
it
y
o
f
s
o
lar
r
ad
iatio
n
,
an
d
it
lead
s
to
v
ar
iatio
n
in
o
p
er
atin
g
p
o
in
t.
I
n
th
is
s
ce
n
ar
io
,
s
m
all
c
h
a
n
g
e
s
in
d
u
t
y
c
y
c
le
m
a
y
lead
to
s
l
o
w
er
s
ea
r
c
h
in
MP
P
.
T
h
is
is
m
o
r
e
cr
it
ical
d
u
r
i
n
g
s
h
ad
o
w
co
n
d
itio
n
.
Hen
ce
,
t
h
e
e
m
p
t
y
r
atio
is
n
o
t
u
s
e
d
to
s
ea
r
ch
th
e
P
V
cu
r
v
e
i
n
a
lar
g
e
ar
ea
w
h
er
e
th
e
tr
ac
ed
MP
P
m
a
y
b
e
lo
ca
l
p
ea
k
t
h
an
th
e
g
lo
b
al
p
ea
k
.
T
h
u
s
,
t
h
er
e
i
s
a
n
ee
d
f
o
r
th
e
m
o
d
i
f
ied
al
g
o
r
ith
m
to
o
v
er
co
m
e
th
e
ab
o
v
e
-
s
tated
p
r
o
b
lem
.
He
n
ce
,
th
e
p
r
o
b
lem
s
tate
m
en
t
is
“to
in
tr
o
d
u
ce
a
m
o
d
ified
P
S
O
a
lg
o
r
it
h
m
to
en
h
a
n
ce
th
e
p
erfo
r
ma
n
ce
o
f MP
P
T fr
o
m
P
V
a
r
r
a
y.
"
1
st
iter
atio
n
2
nd
iter
atio
n
3
rd
iter
atio
n
4
th
iter
atio
n
Fig
u
r
e
2
.
Mo
v
e
m
e
n
t o
f
p
ar
ticl
es in
d
if
f
er
e
n
t iter
atio
n
s
2.
M
O
DIFIE
D
P
SO
A
L
G
O
RI
T
H
M
F
O
R
M
P
P
T
T
h
e
p
r
ev
io
u
s
w
o
r
k
o
f
Yo
g
a
n
a
n
d
in
i
a
n
d
An
ita
[
2
5
]
h
av
e
p
r
e
s
en
ted
a
co
s
t
-
e
f
f
ec
tiv
e
MP
PT
tech
n
iq
u
e
f
o
r
MP
PT
,
w
h
er
e
co
m
p
u
tatio
n
al
ti
m
e
is
r
ed
u
ce
d
an
d
ac
h
i
ev
ed
co
s
t
o
p
ti
m
izatio
n
.
T
h
is
m
an
u
s
cr
ip
t
ai
m
s
to
en
h
a
n
ce
t
h
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
MP
P
b
y
in
tr
o
d
u
ci
n
g
t
h
e
m
o
d
i
f
ied
P
SO
f
o
r
th
e
P
V
ar
r
a
y
.
I
n
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
t
h
e
d
u
t
y
c
y
cle
i
s
p
ar
titi
o
n
ed
in
to
t
w
o
p
ar
ts
.
T
h
e
p
r
ev
io
u
s
d
u
t
y
r
atio
e
x
h
ib
its
t
h
e
f
ac
to
r
o
f
lin
ea
r
izatio
n
(
K
1
)
i
n
cr
ea
s
es
o
r
d
ec
r
ea
s
es
t
h
e
r
atio
b
ased
o
n
P
V
ar
r
ay
o
u
tp
u
t.
S
i
m
ilar
l
y
,
in
p
r
o
v
id
in
g
n
e
w
P
V
cu
r
v
e
f
o
r
MP
P
b
y
u
s
in
g
s
ea
r
c
h
o
p
ti
m
izat
io
n
,
t
w
o
d
u
t
y
c
y
cle
s
d
1
an
d
d
3
in
th
e
p
o
s
iti
v
e
a
n
d
n
eg
ati
v
e
d
ir
ec
tio
n
to
K
2
co
n
s
tan
t
v
al
u
e
p
er
tu
r
b
at
io
n
.
T
h
e
f
o
llo
w
i
n
g
Fi
g
u
r
e
3
p
r
o
v
id
es
an
esti
m
at
io
n
m
o
d
el
f
o
r
K
1
w
h
er
e
it
ca
n
b
e
o
b
s
er
v
e
d
th
at
th
e
m
ax
i
m
u
m
p
o
w
er
o
f
ar
r
a
y
a
n
d
r
esp
ec
tiv
e
p
o
w
er
(
p
MP
P
)
,
d
u
ty
r
ati
o
,
th
e
r
elatio
n
s
h
ip
a
m
o
n
g
P
b
,
G
b
to
DC
/
DC
co
n
v
er
ter
h
av
in
g
p
M
P
P
d
w
it
h
r
esp
ec
t
to
d
u
t
y
r
atio
.
T
h
e
r
esp
o
n
s
e
o
p
tim
ized
1
ca
n
b
e
m
in
i
m
ized
to
0
.
1
,
s
tep
0
.
1
.
Ho
w
e
v
er
,
t
h
er
e
ex
i
s
t
t
wo
ex
p
r
ess
io
n
s
ar
e
co
n
s
id
er
ed
,
w
h
ic
h
b
r
in
g
s
t
h
e
r
el
a
ti
o
n
s
h
i
p
b
e
tw
ee
n
d
b
e
s
t
a
n
d
p
M
PP
.
A
l
s
o
,
th
e
r
e
e
x
i
s
t
s
a
l
i
n
e
a
r
r
e
l
at
i
o
n
s
h
i
p
b
e
t
w
e
en
a
r
r
ay
p
o
w
e
r
an
d
d
u
ty
.
M
P
P
M
P
P
o
l
d
o
l
d
n
e
w
P
P
K
d
d
,
1
1
o
l
d
d
is
a
p
r
ev
io
u
s
d
u
t
y
r
atio
f
o
r
G
b
.
T
h
e
s
lo
p
e
(
1
K
)
d
p
MMP
f
o
r
lin
ea
r
r
elatio
n
ch
an
g
es a
s
p
er
ch
an
g
e
in
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
-
8708
A
mo
d
ified
p
a
r
ticle
s
w
a
r
m
o
p
timiz
a
tio
n
(
P
S
O)
a
lg
o
r
ith
m
to
…
(
Yo
g
a
n
a
n
d
in
i
A
.
P
.
)
5005
o
p
er
atin
g
p
o
w
er
a
n
d
its
v
alu
e
is
al
m
o
s
t
eq
u
al
to
t
h
e
n
e
w
o
p
t
i
m
al
d
u
t
y
c
y
cle.
He
n
ce
,
t
h
e
in
itializatio
n
o
f
d
u
t
y
r
atio
m
u
s
t p
er
f
o
r
m
t
h
e
s
ea
r
ch
i
n
g
o
f
th
e
P
-
V
c
u
r
v
e
a
n
d
w
ill q
u
ick
l
y
d
o
th
e
tr
ac
k
in
g
o
f
n
e
w
MP
P
.
Fig
u
r
e
3
.
R
elatio
n
a
m
o
n
g
Gb
,
d
u
t
y
c
y
cle
an
d
p
MP
P
Fro
m
t
h
e
ab
o
v
e
a
n
al
y
s
is
,
it
h
as
b
ee
n
f
o
u
n
d
th
a
t,
th
e
r
ed
u
ctio
n
i
n
s
o
lar
r
ad
iatio
n
(
f
r
o
m
w
a
v
ele
n
g
th
1
1
.
0
)
al
w
a
y
s
lead
s
to
lo
ad
lin
e
in
P
V
ar
r
ay
I
-
V
g
iv
e
s
m
ax
i
m
u
m
MP
P
v
o
ltag
e
(
VM
P
P
)
to
th
e
r
ig
h
t
o
f
p
lo
t
cu
r
v
e.
T
h
e
in
cr
e
m
e
n
t
in
s
u
n
s
h
in
e
b
r
in
g
s
lo
ad
li
n
e
t
o
th
e
r
ig
h
t.
T
h
e
d
if
f
er
en
ce
b
e
t
w
ee
n
VM
P
P
an
d
o
u
tp
u
t
v
o
ltag
e
w
ill
b
ec
o
m
e
s
m
all,
a
n
d
it
lead
s
to
a
s
m
all
v
ar
iatio
n
i
n
p
o
w
er
.
He
n
ce
,
th
e
s
a
m
e
v
alu
e
o
f
d
old
&
K
1
is
n
o
t
to
b
e
d
elete
d
.
T
h
u
s
,
th
e
P
SO
alg
o
r
ith
m
n
ee
d
s
to
h
a
v
e
m
o
r
e
iter
ati
o
n
to
tr
ac
k
MPP.
T
o
n
eu
tr
alize
s
u
c
h
t
y
p
e
o
f
p
r
o
b
le
m
s
,
a
s
i
m
p
le
ass
u
m
p
tio
n
i
s
m
ad
e
w
ith
t
w
o
d
i
f
f
er
e
n
t
v
alu
e
s
o
f
K
1
.
i.e
.
,
0
2
0
1
1
1
P
if
K
P
if
K
K
I
n
th
i
s
eq
u
atio
n
,
old
P
P
P
T
h
e
v
alu
e
o
f
P
>0
&
P
<0
in
d
icate
s
th
e
d
ec
r
e
m
e
n
t
an
d
in
cr
e
m
en
t
in
s
u
n
s
h
i
n
e
r
ad
iatio
n
.
I
n
o
r
d
er
to
g
et
th
e
d
u
t
y
r
at
io
o
f
n
e
w
p
er
tu
r
b
atio
n
f
o
r
d
1
an
d
d
3
r
esp
ec
tiv
e
l
y
.
T
h
e
f
o
llo
w
i
n
g
f
o
r
m
u
la
o
f
d
ata
r
atio
u
p
d
at
es
p
o
s
itio
n
,
an
d
n
e
g
ati
v
e
d
ir
ec
tio
n
.
)
(
,
),
(
)
(
3
3
2
2
1
K
d
d
K
d
d
n
e
w
i
W
h
er
e
05
.
0
2
K
T
h
e
s
elec
tio
n
m
ec
h
a
n
i
s
m
o
f
t
h
is
0
.
0
5
h
elp
s
to
m
an
a
g
e
lo
w
p
o
w
er
f
l
u
ct
u
atio
n
b
u
t,
d
u
r
i
n
g
th
e
p
ar
tial
s
h
ad
e,
th
e
w
o
r
k
i
n
g
v
o
lta
g
e
m
a
y
in
cr
ea
s
es
u
p
to
8
5
%,
th
i
s
h
e
l
p
s
P
S
O
alg
o
r
ith
m
to
tr
ac
k
g
lo
b
al
p
ea
k
m
o
r
e.
T
h
e
f
o
llo
w
i
n
g
s
ec
tio
n
g
i
v
es t
h
e
alg
o
r
ith
m
i
m
p
le
m
e
n
tatio
n
.
Algorithm of modified PSO
Input: I
p
, V
p
Output: G
b
and P
b
Start
Step
-
1:
initialize & detect I
p
and V
p
Step
-
2:
Compute
p
p
i
I
V
P
)
(
Step
-
3:
Check if
0
;
0
P
P
Compute (d) at V
i
=(1,2,3)=0, N
p
=3, K=0
Else increment i=i+1;
Check i>N
p
Increment k=k+1;
If K=1;
Pbest=d
i
Else check i=1;
Step
-
4:
Compute P
b
&G
b
Step
-
5:
Update
disturbances
End
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
5
0
0
1
-
5008
5006
T
h
e
alg
o
r
ith
m
is
i
n
itialized
b
y
d
et
ec
ti
n
g
th
e
P
V
cu
r
r
e
n
t
(
I
p
)
an
d
P
V
v
o
ltag
e
(
Vp
)
(
Step
-
1
)
.
Fu
r
t
h
er
,
th
e
in
i
tial
p
o
w
er
o
f
t
h
e
P
V
ce
ll
is
co
m
p
u
ted
b
y
u
s
in
g
t
h
e
g
e
n
er
al
f
o
r
m
u
la
o
f
p
o
w
er
p
p
i
I
V
P
)
(
(
Step
-
2
)
.
L
ater
,
th
e
co
n
d
itio
n
o
f
P
>0
o
r
P
<0
is
v
er
if
ied
(
Ste
p
-
3
)
.
I
f
th
e
co
n
d
itio
n
is
s
ati
s
f
i
ed
,
th
e
d
u
t
y
r
atio
(
d
)
is
ca
lc
u
lated
at
d
u
t
y
c
y
cles
(
1
,
2
,
3
)
o
f
v
o
ltag
e
Vi(
1
,
2
,
2
)
=0
n
u
m
b
er
o
f
p
ar
ticles
(
Np
)
=3
,
co
n
s
ta
n
t
k
=0
.
I
f
i
t
is
n
o
t
s
at
is
f
ied
,
t
h
en
th
e
n
u
m
b
er
o
f
iter
atio
n
s
w
ill
b
e
in
cr
e
m
en
ted
b
y
1
.
F
u
r
th
er
,
it
is
ch
ec
k
e
d
f
o
r
"
i>Np
"
an
d
if
it
is
s
atis
f
ied
,
th
e
n
‘
k
'
v
alu
e
i
s
in
cr
e
m
e
n
ted
b
y
1
.
I
f
k
=1
,
t
h
e
"
Pb
"
v
alu
e
w
ill
b
e
d
u
t
y
c
y
cle
(
d
i)
i.e
.
,
P
b
=
d
i.
Si
m
i
lar
l
y
,
i
f
‘
k
=1
'
i
s
n
o
t
s
ati
s
f
ied
,
it
w
il
l
b
e
ch
ec
k
ed
f
o
r
i=
1
.
T
h
en
,
t
h
e
v
al
u
e
o
f
P
b
ca
n
b
e
co
m
p
u
ted
af
ter
v
ar
y
i
n
g
th
e
co
n
d
itio
n
P
(
i)
>P(
i
-
1
)
.
I
n
ca
s
e,
th
e
co
n
d
itio
n
is
s
atis
f
ied
,
th
e
n
“
P
b
=d
i”
else
“
P
b
=d
(
i
-
1
)
.
”.
Si
m
i
lar
l
y
,
to
ca
lcu
la
te
g
lo
b
al
b
est
(
Gb
)
s
am
e
p
r
o
ce
d
u
r
e
o
f
i
n
cr
e
m
e
n
ti
n
g
(
i=i+1
)
an
d
ch
ec
k
in
g
"
i>Np
.
"
B
ased
o
n
th
i
s
co
n
d
itio
n
,
Gb
is
co
m
p
u
ted
as,
)
m
a
x
(
b
b
P
G
Fin
all
y
,
th
e
d
is
t
u
r
b
an
ce
a
m
o
n
g
P
b
,
o
u
tp
u
t
v
o
lta
g
e,
an
d
Gb
is
u
p
d
ated
.
T
h
e
d
u
t
y
c
y
cle
o
f
d
is
tu
r
b
an
c
e
is
co
m
p
u
ted
b
y
u
s
i
n
g
p
r
ev
io
u
s
d
u
t
y
r
atio
d
i(
k
)
a
n
d
lo
ca
l
P
b
.
T
h
e
d
if
f
er
en
ce
b
et
w
ee
n
‘
i
’
an
d
p
r
ev
io
u
s
d
i(
k
)
an
d
Gb
.
Hen
ce
,
th
e
p
o
w
er
co
n
v
er
ter
an
d
tr
ac
k
i
n
g
b
est P
b
,
Gb
an
d
I
ar
e
p
o
s
s
ib
le
in
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
T
h
e
s
ig
n
if
ica
n
ce
o
f
p
r
o
p
o
s
ed
P
SO
is
th
at
i
t
y
ield
s
f
a
s
ter
s
ea
r
ch
an
d
tr
ac
k
s
th
e
MP
P
o
p
tim
al
s
o
lu
tio
n
.
Af
ter
ac
q
u
ir
in
g
th
e
MP
P
b
y
p
ar
ticles,
th
e
v
elo
cit
y
al
m
o
s
t
b
ec
o
m
es
ze
r
o
.
Hen
ce
,
n
o
o
s
cillatio
n
s
w
ill
b
e
o
b
s
er
v
e
d
in
s
tead
y
s
tate.
T
h
e
s
tead
y
s
tate
o
s
cil
latio
n
is
n
ec
ess
ar
y
as
it
i
s
h
elp
f
u
l
i
n
g
ett
i
n
g
t
h
e
ef
f
icie
n
c
y
o
f
MP
PT
.
A
n
o
th
er
s
i
g
n
i
f
ica
n
t
f
e
atu
r
e
o
f
m
o
d
i
f
ied
P
SO
i
s
t
h
at
it
e
x
h
ib
its
3
-
d
u
t
y
c
y
cle
s
,
an
d
h
e
n
ce
,
it
d
o
es
n
o
t
lo
s
e
d
ir
ec
tio
n
in
s
h
o
r
t te
r
m
f
lu
ctu
atio
n
s
.
T
h
e
p
r
o
p
o
s
ed
P
SO
ef
f
ec
tiv
e
l
y
ab
le
to
tr
ac
k
t
h
e
g
l
o
b
al
p
ea
k
.
3.
RE
SU
L
T
ANAL
YSI
S
T
h
e
p
r
o
p
o
s
ed
s
y
s
te
m
m
o
d
el
i
s
s
i
m
u
lated
u
s
in
g
M
A
T
L
A
B
.
I
n
th
e
o
p
ti
m
izatio
n
p
r
o
ce
s
s
,
th
e
f
itn
e
s
s
v
alu
e
is
u
p
d
ated
b
y
P
V
ar
r
a
y
o
u
tp
u
t
p
o
w
er
.
T
h
e
p
er
f
o
r
m
a
n
ce
a
n
al
y
s
is
o
f
th
e
m
o
d
i
f
ie
d
P
SO
is
d
o
n
e
w
it
h
tr
ad
itio
n
al
P
SO
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
ai
m
in
g
wit
h
ac
cu
r
ate
MP
P
tr
ac
k
in
g
.
F
ig
u
r
e
4
r
ep
r
esen
ts
th
e
tr
ac
k
i
n
g
r
es
u
lt
o
f
tr
ad
iti
o
n
al
P
SO,
w
h
er
e
it
is
o
b
s
er
v
ed
th
at
a
lar
g
e
r
an
g
e
o
f
f
l
u
ctu
a
tio
n
s
ex
i
s
ts
i
n
o
p
tim
izatio
n
.
T
h
is
m
is
j
u
d
g
e
s
t
h
e
MP
P
an
d
tak
es ~0
.
0
4
5
s
ec
f
o
r
tr
ac
k
in
g
t
h
e
MP
P
.
Fig
u
r
e
4
.
T
r
ac
k
in
g
o
f
MP
P
w
i
th
tr
ad
itio
n
al
P
SO
T
h
e
p
r
o
p
o
s
ed
,
m
o
d
if
ied
P
SO
co
n
s
id
er
ed
s
ea
r
ch
-
b
ased
o
p
tim
izatio
n
u
s
e
s
3
-
d
u
t
y
c
y
cle
s
an
d
d
o
es
n
o
t
lo
s
e
its
d
ir
ec
tio
n
i
n
s
h
o
r
t
ter
m
f
l
u
ctu
a
tio
n
.
Fi
g
u
r
e
5
s
h
o
w
s
t
h
e
p
o
w
er
V
s
.
ti
m
e
c
u
r
v
e
o
b
tain
ed
f
r
o
m
p
r
o
p
o
s
ed
P
SO
is
s
m
o
o
th
er
th
a
n
tr
ad
iti
o
n
al
P
SO,
an
d
it
tak
es
o
n
l
y
~0
.
0
3
8
s
ec
f
o
r
MPP
tr
ac
k
in
g
,
w
h
ich
i
s
i
m
p
r
o
v
ed
ab
o
u
t
0
.
0
8
s
ec
s
.
Hen
ce
,
th
e
m
o
d
if
ied
P
SO
m
a
k
es
t
h
e
p
r
o
ce
s
s
m
o
r
e
s
tab
le
an
d
i
m
p
r
o
v
es
t
h
e
MP
P
p
er
f
o
r
m
a
n
ce
.
T
h
e
p
r
o
p
o
s
ed
P
S
O
i
m
p
r
o
v
ed
th
e
d
y
n
a
m
ic
r
esp
o
n
s
e
s
p
ee
d
tr
ac
k
i
n
g
ac
c
u
r
ac
y
i
n
a
s
tead
y
s
tate.
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
-
8708
A
mo
d
ified
p
a
r
ticle
s
w
a
r
m
o
p
timiz
a
tio
n
(
P
S
O)
a
lg
o
r
ith
m
to
…
(
Yo
g
a
n
a
n
d
in
i
A
.
P
.
)
5007
.
Fig
u
r
e
5
.
T
r
ac
k
in
g
o
f
MP
P
w
i
th
p
r
o
p
o
s
ed
P
SO
4.
CO
NCLU
SI
O
N
I
n
t
h
is
r
esear
ch
,
th
e
p
r
o
p
o
s
ed
MP
P
tr
ac
k
in
g
s
y
s
te
m
i
s
ai
m
ed
to
en
h
an
ce
t
h
e
tr
ac
k
in
g
ac
cu
r
ac
y
a
n
d
s
p
ee
d
.
T
h
e
p
r
o
p
o
s
ed
s
y
s
te
m
i
n
tr
o
d
u
ce
d
an
MP
PT
tech
n
iq
u
e
b
ased
o
n
th
e
m
o
d
i
f
ied
P
SO
alg
o
r
ith
m
s
w
h
ic
h
b
r
in
g
h
i
g
h
ef
f
icie
n
c
y
.
T
h
e
s
ea
r
ch
b
ased
m
et
h
o
d
is
co
n
s
i
d
er
ed
w
it
h
3
-
d
u
t
y
c
y
c
les
an
d
d
o
es
n
o
t
lo
s
e
its
d
ir
ec
tio
n
in
s
h
o
r
t
ter
m
f
lu
ct
u
atio
n
in
s
tead
y
s
ta
te.
An
o
t
h
e
r
s
ig
n
i
f
ican
ce
i
s
th
a
t
th
e
p
r
o
p
o
s
ed
P
SO
h
as
tak
e
n
less
ti
m
e
(
0
.
0
3
8
s
ec
s
)
to
tr
ac
k
th
e
MP
P
th
an
tr
ad
itio
n
al
M
P
P
(
0
.
0
4
5
s
ec
)
f
o
u
n
d
i
m
p
r
o
v
e
m
en
t
o
f
0
.
0
0
8
s
ec
s
.
T
h
is
g
i
v
e
s
t
h
at
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
MP
P
T
is
en
h
a
n
ce
d
w
i
th
an
e
f
f
icien
c
y
o
f
9
9
%.
T
h
e
s
co
p
e
o
f
th
e
p
r
o
p
o
s
ed
s
tu
d
y
i
s
th
at
it
ca
n
b
e
co
n
s
id
er
ed
w
i
th
o
t
h
er
m
ac
h
i
n
e
lear
n
i
n
g
ap
p
r
o
ac
h
es
u
n
d
er
d
if
f
er
en
t
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
.
F
u
r
t
h
er
,
th
e
r
esear
ch
ca
n
b
e
ca
r
r
ied
o
u
t
w
it
h
d
if
f
er
e
n
t t
y
p
es o
f
P
V
ar
r
ay
s
.
RE
F
E
R
E
NC
E
S
[1
]
El
la
b
b
a
n
,
Om
a
r,
Ha
it
h
a
m
A
b
u
-
Ru
b
,
a
n
d
F
re
d
e
Bl
a
a
b
jerg
,
"
Re
n
e
w
a
b
le
e
n
e
rg
y
re
so
u
r
c
e
s
:
C
u
r
re
n
t
sta
t
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