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(L
F
C)
b
y
o
p
ti
m
izin
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in
teg
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l
p
a
rt
(P
ID)
c
o
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tr
o
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u
sin
g
p
a
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c
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sw
a
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o
p
t
imiz
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ti
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(P
S
O).
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o
a
d
fre
q
u
e
n
c
y
c
o
n
tr
o
l
is
imp
o
rtan
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to
e
n
su
re
e
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e
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g
y
st
a
b
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b
y
m
a
in
tain
in
g
t
h
e
b
a
lan
c
e
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e
twe
e
n
p
ro
d
u
c
ti
o
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a
n
d
c
o
n
s
u
m
p
ti
o
n
.
Co
n
v
e
n
t
io
n
a
l
p
ro
p
o
rti
o
n
a
l
i
n
teg
ra
l
d
e
ri
v
a
ti
v
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c
o
n
tr
o
ll
e
rs
a
re
wid
e
ly
u
se
d
fo
r
th
i
s
p
u
rp
o
se
;
h
o
we
v
e
r,
th
e
ir
p
e
rfo
rm
a
n
c
e
c
a
n
b
e
fu
rth
e
r
imp
r
o
v
e
d
t
h
ro
u
g
h
o
p
t
imiz
a
ti
o
n
.
Th
is
wo
r
k
u
se
s
p
a
rti
c
le
sw
a
rm
o
p
ti
m
iza
ti
o
n
,
a
n
a
tu
re
-
in
s
p
ired
a
l
g
o
rit
h
m
,
to
se
t
th
e
p
a
ra
m
e
ters
o
f
th
e
p
r
o
p
o
rti
o
n
a
l
in
teg
ra
l
d
e
ri
v
a
ti
v
e
c
o
n
tr
o
ll
e
r
.
P
S
O
wa
s
c
h
o
se
n
b
e
c
a
u
se
it
c
a
n
se
a
rc
h
f
o
r
g
o
o
d
s
o
lu
t
io
n
sp
a
c
e
a
n
d
fin
d
a
g
o
o
d
a
g
re
e
m
e
n
t
b
e
twe
e
n
c
o
n
tro
l
p
a
ra
m
e
ters
,
th
u
s
imp
ro
v
i
n
g
th
e
d
y
n
a
m
ic
a
n
d
sta
b
le
re
sp
o
n
se
o
f
t
h
e
sy
ste
m
.
Th
is
a
rti
c
le
p
ro
v
id
e
s
a
c
o
m
p
re
h
e
n
siv
e
e
v
a
lu
a
ti
o
n
o
f
th
e
p
r
o
p
o
se
d
a
p
pr
o
a
c
h
,
i
n
c
lu
d
in
g
sim
u
latio
n
re
su
lt
s
a
n
d
c
o
m
p
a
riso
n
s
with
sta
n
d
a
rd
P
ID
c
o
n
tro
ll
e
rs.
T
h
e
e
ffe
c
ti
v
e
n
e
ss
o
f
th
e
o
p
ti
m
ize
d
P
ID
c
o
n
t
ro
ll
e
rs
in
re
d
u
c
i
n
g
th
e
fre
q
u
e
n
c
y
d
iffere
n
c
e
a
n
d
imp
r
o
v
i
n
g
th
e
o
v
e
ra
ll
e
fficie
n
c
y
o
f
t
h
e
p
o
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r
p
lan
t
u
n
d
e
r
d
iffere
n
t
c
o
n
d
it
i
o
n
s
is
d
e
m
o
n
stra
ted
.
T
h
is
stu
d
y
p
ro
v
id
e
s
in
sig
h
t
in
t
o
th
e
u
se
o
f
a
rti
ficia
l
i
n
telli
g
e
n
c
e
to
im
p
ro
v
e
c
o
n
tro
l
p
a
ra
m
e
ters
in
th
e
p
o
we
r
g
rid
,
p
ro
v
id
i
n
g
a
p
ro
m
isin
g
wa
y
to
imp
r
o
v
e
t
h
e
e
fficie
n
c
y
a
n
d
re
li
a
b
il
it
y
o
f
fre
q
u
e
n
c
y
c
o
n
tro
ll
e
rs.
K
ey
w
o
r
d
s
:
Go
v
er
n
o
r
co
n
t
r
o
l
L
o
ad
f
r
e
q
u
en
c
y
co
n
tr
o
l
Par
ticle
s
war
m
alg
o
r
ith
m
Prim
ar
y
co
n
tr
o
l
Seco
n
d
ar
y
c
o
n
tr
o
l
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Su
r
en
d
er
R
ed
d
y
Salk
u
ti
Dep
ar
tm
en
t o
f
R
ailr
o
ad
an
d
E
lectr
ical
E
n
g
in
ee
r
in
g
,
W
o
o
s
o
n
g
Un
iv
er
s
ity
J
ay
an
g
-
Do
n
g
,
Do
n
g
-
Gu
,
Dae
j
eo
n
3
4
6
0
6
,
R
ep
u
b
lic
o
f
Ko
r
ea
E
m
ail: su
r
en
d
er
@
wsu
.
ac
.
k
r
1.
I
NT
RO
D
UCT
I
O
N
Po
wer
s
y
s
tem
s
p
lay
a
cr
u
cial
r
o
le
in
our
ev
er
y
d
ay
liv
es
as
th
e
y
ar
e
r
esp
o
n
s
ib
le
f
o
r
s
u
p
p
ly
i
n
g
elec
tr
icity
to
th
e
en
tire
wo
r
ld
.
W
ith
o
u
t
a
s
tab
le
a
n
d
r
eliab
le
elec
tr
ic
n
etwo
r
k
p
o
wer
s
u
p
p
ly
,
o
u
r
s
o
cio
-
ec
o
n
o
m
ic
d
ev
elo
p
m
e
n
t
wo
u
ld
be
s
ev
e
r
ely
im
p
ac
ted
.
To
e
n
s
u
r
e
th
e
s
m
o
o
th
o
p
e
r
atio
n
of
p
o
wer
s
y
s
tem
s
,
it
is
n
ec
ess
ar
y
to
im
p
lem
en
t
v
a
r
io
u
s
p
r
o
tectio
n
an
d
c
o
n
tr
o
l
tech
n
iq
u
es
[
1
]
.
T
h
ese
tech
n
iq
u
es
aim
to
m
ai
n
tain
th
e
s
tab
ilit
y
of
p
o
wer
s
y
s
tem
s
by
ef
f
ec
tiv
ely
co
n
tr
o
llin
g
th
r
ee
im
p
o
r
tan
t
q
u
an
titi
es:
f
r
eq
u
en
cy
,
r
o
to
r
an
g
l
e,
an
d
v
o
ltag
e.
An
im
p
o
r
tan
t
asp
ec
t
of
e
n
er
g
y
m
an
ag
em
en
t
is
en
er
g
y
m
an
a
g
e
m
en
t
[
2
]
.
C
o
n
t
r
o
l
of
v
o
ltag
e
an
d
r
ea
ctiv
e
p
o
wer
en
s
u
r
es
th
at
th
e
y
r
e
m
ain
with
i
n
th
e
r
eq
u
i
r
ed
lim
its
.
Ad
d
itio
n
ally
,
p
o
wer
m
a
n
ag
em
e
n
t
co
n
tr
o
l
p
lay
s
a
cr
u
cial
r
o
le
in
im
p
r
o
v
in
g
t
h
e
p
er
f
o
r
m
an
ce
of
th
e
p
o
wer
tr
a
n
s
m
is
s
io
n
s
y
s
tem
by
in
cr
ea
s
in
g
en
er
g
y
ef
f
icie
n
cy
[
3
]
.
Am
o
n
g
th
e
d
if
f
e
r
en
t
co
n
tr
o
l
m
eth
o
d
s
,
f
r
eq
u
en
cy
co
n
tr
o
l
is
th
e
m
o
s
t
tim
e
-
co
n
s
u
m
in
g
m
eth
o
d
.
T
h
e
m
ain
r
ea
s
o
n
f
o
r
th
is
is
th
e
m
ec
h
an
ical
co
m
p
o
n
e
n
ts
in
clu
d
ed
in
th
e
co
n
tr
o
l
alg
o
r
ith
m
s
[
4
]
.
L
o
ad
f
r
eq
u
en
cy
co
n
tr
o
l
(
L
FC
)
s
y
s
tem
s
f
ac
e
p
r
o
b
lem
s
wh
en
d
ea
lin
g
with
co
m
p
lex
d
ata
an
aly
s
is
p
r
o
ce
s
s
es
due
to
th
e
s
a
f
ety
co
n
tr
o
l
s
y
s
tem
o
p
er
atin
g
f
o
r
m
o
r
e
th
a
n
a
s
ec
o
n
d
.
T
h
ese
s
y
s
tem
s
th
er
ef
o
r
e
b
e
co
m
e
more
s
u
s
ce
p
tib
le
to
c
o
m
p
r
o
m
is
es
an
d
cy
b
er
-
attac
k
s
[
5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
1
77
-
1
8
5
178
T
h
e
lo
ad
f
r
eq
u
e
n
cy
c
o
n
tr
o
l
s
y
s
tem
o
p
er
ates
u
s
in
g
co
n
tin
u
o
u
s
d
ig
ital
o
p
e
n
c
o
m
m
u
n
icatio
n
m
eth
o
d
s
,
m
in
im
izin
g
th
e
n
ee
d
f
o
r
h
u
m
an
in
ter
v
en
tio
n
[
6
]
.
W
h
ile
th
i
s
d
esig
n
p
r
o
v
id
es
co
n
v
e
n
ien
c
e,
it
also
m
ak
es
th
e
s
y
s
tem
v
u
ln
er
ab
le
to
n
etwo
r
k
th
r
ea
ts
.
Mo
r
eo
v
er
,
a
f
r
e
q
u
en
t
ch
an
g
e
due
to
a
c
h
an
g
e
in
a
r
eg
io
n
or
a
cy
b
er
-
attac
k
will
af
f
ec
t
all
p
ar
ts
of
th
e
p
o
wer
n
etwo
r
k
s
,
th
r
ea
ten
in
g
its
o
v
er
all
s
ec
u
r
ity
[
7
]
.
I
n
co
r
p
o
r
atin
g
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
(
R
E
S)
in
to
el
ec
tr
icity
g
en
er
atio
n
is
a
p
r
o
m
is
in
g
s
o
lu
tio
n
to
s
o
lv
e
en
v
ir
o
n
m
en
tal
p
r
o
b
lem
s
.
Ho
wev
er
,
th
e
in
ter
ac
tio
n
s
of
R
E
S
o
u
tp
u
t
p
o
wer
p
o
s
e
a
p
r
o
b
lem
in
ter
m
s
of
elec
tr
ical
p
o
wer
s
y
s
tem
s
tab
ilit
y
an
d
f
r
e
q
u
en
c
y
o
p
er
atio
n
.
Ho
w
ev
er
,
R
E
S
tech
n
o
lo
g
y
an
d
th
e
u
s
e
of
s
m
ar
t
in
v
er
ter
s
an
d
s
m
a
r
t
co
n
tr
o
ller
s
h
av
e
b
ee
n
ac
ce
p
ted
in
m
an
y
co
u
n
tr
ies
[
8
]
.
Sm
ar
t
in
v
er
ter
s
p
lay
an
im
p
o
r
tan
t
r
o
le
in
th
e
d
is
tr
ib
u
ted
elec
tr
ic
p
o
wer
(
DE
R
)
g
r
id
by
ac
tin
g
as
th
e
in
ter
f
ac
e
b
etwe
en
DE
R
s
an
d
th
e
g
r
id
,
c
o
n
tr
o
llin
g
p
o
wer
f
l
o
w,
an
d
d
etec
tin
g
f
au
lts
[
9
]
.
Ho
wev
er
,
th
ese
tech
n
o
lo
g
ies
also
ex
p
o
s
e
p
o
wer
s
y
s
tem
s
to
cy
b
er
-
attac
k
s
due
to
poor
co
m
m
u
n
icatio
n
an
d
v
u
ln
er
a
b
il
ities
[
1
0
]
.
It
is
im
p
o
r
tan
t
to
m
o
n
ito
r
an
d
c
o
n
tr
o
l
o
p
er
atin
g
f
r
e
q
u
en
cies
to
en
s
u
r
e
good
p
e
r
f
o
r
m
an
ce
,
s
af
ety
,
an
d
r
eliab
ilit
y
of
g
en
er
ato
r
s
.
C
h
an
g
in
g
th
e
n
o
m
in
al
f
r
eq
u
e
n
cy
v
a
lu
e
d
ir
ec
tly
af
f
ec
ts
th
e
p
er
f
o
r
m
an
ce
of
t
h
e
s
y
s
tem
.
L
FC
s
ch
em
es
ar
e
u
s
ed
to
co
n
tr
o
l
th
e
b
alan
ce
b
etwe
en
lo
a
d
an
d
f
r
eq
u
en
cy
in
th
e
p
o
wer
s
y
s
tem
an
d
m
in
im
iz
e
f
r
eq
u
e
n
cy
v
ar
iatio
n
s
[
1
1
]
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
L
F
C
s
y
s
t
em
c
o
nfig
ura
t
i
o
n
C
o
n
tr
o
l
lo
o
p
s
p
lay
an
im
p
o
r
ta
n
t
r
o
le
in
th
e
co
n
tr
o
l
of
elec
tr
o
n
ic
s
y
s
tem
s
,
in
clu
d
in
g
L
FC
d
e
v
ices.
L
FC
s
y
s
tem
s
p
r
o
v
id
e
co
n
tr
o
l
ce
n
t
er
s
,
f
ield
elec
tr
o
n
ics,
an
d
co
m
m
u
n
icatio
n
s
to
p
r
o
v
id
e
r
eli
ab
le
an
d
e
f
f
icien
t
tr
an
s
m
is
s
io
n
an
d
d
is
tr
ib
u
tio
n
[
1
2
]
.
Sen
s
o
r
s
co
llect
m
ea
s
u
r
em
en
ts
f
r
o
m
f
ield
eq
u
i
p
m
en
t,
s
u
ch
as
ter
m
in
al
v
o
ltag
e,
p
o
wer
f
l
o
w,
an
d
r
o
t
o
r
s
p
ee
d
,
en
ab
lin
g
co
n
tr
o
l
ce
n
ter
s
to
m
ak
e
in
f
o
r
m
ed
d
ec
is
io
n
s
f
o
r
ef
f
icien
t
p
o
we
r
m
an
ag
em
en
t
[
1
3
]
.
It
is
im
p
o
r
t
an
t
to
co
n
tr
o
l
t
h
e
s
tab
le
o
p
er
a
tio
n
of
th
e
g
en
er
ato
r
.
On
e
ap
p
r
o
ac
h
to
ac
h
iev
i
n
g
th
is
is
th
r
o
u
g
h
th
e
im
p
lem
e
n
tatio
n
of
a
s
in
g
le
-
ar
ea
L
FC
s
y
s
te
m
[
1
4
]
.
Un
lik
e
in
ter
c
o
n
n
ec
ted
s
y
s
tem
s
th
at
r
eq
u
ir
e
co
m
p
lex
ad
j
u
s
tm
en
ts
,
th
e
s
in
g
le
-
ar
ea
s
ch
em
e
f
o
c
u
s
es
s
o
lely
on
s
tab
ilizin
g
th
e
f
r
eq
u
e
n
cy
to
its
n
o
m
in
al
v
alu
e.
T
h
is
en
s
u
r
es
th
at
th
e
s
y
s
tem
o
p
er
ates
s
m
o
o
th
ly
a
n
d
e
f
f
icie
n
tly
[
1
5
]
.
Fig
u
r
e
1
r
e
p
r
esen
ts
a
Go
v
er
n
o
r
C
o
n
tr
o
l
L
o
o
p
with
in
a
p
o
wer
s
y
s
tem
,
wh
er
e
a
co
n
tr
o
l
ce
n
ter
m
o
n
ito
r
s
an
d
ad
ju
s
ts
th
e
s
y
s
tem
b
ased
on
d
ata
f
r
o
m
s
en
s
o
r
s
th
at
m
ea
s
u
r
e
p
ar
am
eter
s
lik
e
p
o
wer
f
lo
w
an
d
f
r
e
q
u
en
c
y
.
T
h
e
lo
ca
l
co
n
tr
o
ller
s
ets
v
alu
es
f
o
r
th
e
s
p
ee
d
ch
a
n
g
er
m
o
to
r
,
wh
ich
ad
ju
s
ts
th
e
g
o
v
er
n
o
r
.
T
h
e
g
o
v
er
n
o
r
th
en
r
e
g
u
lates
th
e
f
l
o
w
of
s
team
or
wate
r
to
t
h
e
tu
r
b
in
e
th
r
o
u
g
h
co
n
tr
o
l
v
alv
es,
in
f
lu
e
n
cin
g
th
e
g
en
er
at
o
r
'
s
p
o
wer
o
u
tp
u
t.
T
h
e
g
en
e
r
ato
r
c
o
n
v
e
r
ts
m
ec
h
an
ical
p
o
wer
in
to
elec
tr
ical
en
er
g
y
,
a
n
d
s
en
s
o
r
s
p
r
o
v
id
e
r
ea
l
-
tim
e
f
ee
d
b
ac
k
to
th
e
co
n
tr
o
l
ce
n
ter
to
m
ai
n
tain
s
y
s
tem
s
tab
ilit
y
an
d
m
ee
t
lo
a
d
d
em
a
n
d
s
.
Fig
u
r
e
1
.
A
class
ic
L
FC
lo
o
p
2
.
2
.
D
y
n
a
m
ic
equ
a
t
i
o
ns
f
o
r
t
he
s
in
g
l
e
-
a
re
a
L
F
C
s
y
s
t
e
m
T
o
d
elv
e
d
ee
p
e
r
in
to
th
e
ev
o
lu
tio
n
o
f
lo
ca
l
L
FC
s
y
s
tem
s
,
l
et
u
s
co
n
s
id
er
d
if
f
er
en
tial
eq
u
atio
n
s
.
T
h
e
p
o
wer
-
lo
ad
d
y
n
a
m
ic
r
elatio
n
s
h
ip
b
etwe
en
th
e
m
is
m
atch
ed
p
o
wer
d
if
f
er
e
n
ce
(
∆P
m
(
t)
−∆
P
L
(
t)
)
an
d
th
e
f
r
e
q
u
en
c
y
d
ev
iatio
n
is
ex
p
r
ess
ed
m
ath
e
m
atica
lly
as
(
1
)
[
1
6
]
.
∆
(
)
=
1
∆
P
m
(
t
)
−
1
∆
P
l
(
t
)
−
1
D
∆
f
(
t
)
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Op
timiz
a
tio
n
o
f lo
a
d
fr
eq
u
e
n
c
y
co
n
tr
o
l sys
tems u
s
in
g
P
S
O
tech
n
iq
u
e
(
Deb
a
n
i
P
r
a
s
a
d
Mis
h
r
a
)
179
W
h
e
r
e
∆
P
m
(
t)
is
m
e
c
h
a
n
ic
al
p
o
we
r
ch
a
n
g
e
,
∆
P
L
(
t
)
is
l
o
a
d
c
h
a
n
g
e
,
a
n
d
M
is
e
q
u
i
v
al
e
n
t
in
e
r
tia
c
o
ef
f
i
cie
n
t
.
Ad
d
it
io
n
a
ll
y
,
t
u
r
b
in
e
d
y
n
a
m
ic
s
ca
n
be
e
x
p
lai
n
ed
as
(
2
)
.
∆
(
)
=
1
∆
(
)
−
1
∆
(
)
(
2
)
W
h
e
r
e
∆
P
m
(
t
)
is
m
e
ch
a
n
ic
al
p
o
we
r
ch
an
g
e
,
∆
P
g
(
t
)
is
g
o
v
e
r
n
o
r
o
u
t
p
u
t
c
h
an
g
e
,
an
d
T
t
is
t
u
r
b
i
n
e
t
im
e
c
o
n
s
ta
n
t
.
Simil
a
r
l
y
,
t
h
e
g
o
v
e
r
n
o
r
d
y
n
a
m
ics
ca
n
be
d
e
f
i
n
e
d
by
(
3
)
.
∆
P
g
(
t
)
=
1
∆
P
c
(
t
)
−
1
∆
f
(
t
)
−
1
∆
P
g
(
t
)
(
3
)
W
h
er
e
∆P
g
(
t)
is
th
e
g
o
v
er
n
o
r
o
u
tp
u
t
c
h
an
g
e
,
R
is
s
p
ee
d
d
r
o
p
ch
ar
ac
ter
is
tic
,
∆P
c
(
t)
is
c
o
n
tr
o
l
s
ig
n
al,
an
d
T
g
is
th
e
g
o
v
e
r
n
o
r
tim
e
co
n
s
tan
t
.
2
.
3
.
Appl
ica
t
io
n o
f
P
SO
,
s
ine c
o
s
ine,
a
nd
g
enet
ic
a
lg
o
rit
hm
f
o
r
o
pti
m
iza
t
io
n
o
f
P
I
D
co
ntr
o
ller
To
en
s
u
r
e
s
y
s
tem
s
tab
ilit
y
a
n
d
m
in
im
ize
v
ar
iab
ilit
y
,
th
e
co
m
m
o
n
ly
u
s
es
p
r
o
p
o
r
tio
n
a
l
-
in
teg
r
al
-
d
er
iv
ativ
e
(
PID
)
co
n
tr
o
ller
.
Ho
wev
er
,
due
to
th
e
weak
a
n
d
weak
ch
ar
ac
ter
is
tics
of
th
e
g
e
n
er
ato
r
,
it
m
ay
be
d
if
f
icu
lt
to
tu
n
e
th
e
PID
p
a
r
am
eter
s
f
o
r
g
o
o
d
p
er
f
o
r
m
a
n
ce
[
1
7
]
.
Par
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
an
d
g
en
etic
alg
o
r
ith
m
s
p
r
o
v
id
e
p
o
wer
f
u
l
m
eta
-
h
eu
r
is
tic
o
p
tim
izatio
n
al
g
o
r
ith
m
s
.
T
h
is
co
n
ten
t
p
r
o
v
id
es
an
in
-
d
ep
th
s
tu
d
y
of
th
e
ap
p
licatio
n
of
PSO
an
d
g
en
etic
alg
o
r
ith
m
s
to
d
ev
elo
p
PID
co
n
tr
o
ller
s
in
th
e
ca
s
e
of
a
lo
ca
l
L
FC
an
d
co
m
p
ar
e
th
e
m
f
o
r
th
e
f
r
eq
u
e
n
cy
r
esp
o
n
s
e
of
th
e
s
y
s
tem
[
1
8
]
.
T
h
e
m
ain
p
u
r
p
o
s
e
of
a
lo
ca
l
L
FC
s
y
s
tem
is
to
o
p
tim
ally
co
n
tr
o
l
t
h
e
p
o
wer
s
y
s
tem
f
r
eq
u
en
cy
by
ad
ju
s
tin
g
th
e
o
u
tp
u
t
p
o
wer
of
t
h
e
g
e
n
er
ato
r
.
PID
c
o
n
tr
o
ller
h
as
p
ar
allel,
f
u
n
d
am
en
tal,
an
d
tim
e
-
v
ar
y
in
g
elem
en
ts
an
d
p
l
ay
s
an
im
p
o
r
tan
t
r
o
le
in
r
esp
o
n
d
in
g
to
ch
a
n
g
es
an
d
r
esto
r
in
g
th
e
s
y
s
tem
to
its
n
o
m
in
al
f
r
eq
u
e
n
cy
[
1
9
]
.
2
.
4
.
P
SO
a
lg
o
rit
h
m
Go
in
g
to
th
e
in
-
d
ep
th
wo
r
k
in
g
of
th
e
PSO
alg
o
r
ith
m
,
th
e
b
est
s
o
lu
tio
n
f
o
r
th
e
p
r
o
b
lem
is
f
o
u
n
d
by
co
m
m
u
n
icatin
g
th
e
r
esu
lts
wit
h
ev
er
y
p
ar
ticle
of
th
e
s
war
m
an
d
lear
n
in
g
f
r
o
m
th
e
p
er
s
o
n
al
b
est
s
o
lu
tio
n
of
each
p
ar
ticle
an
d
g
o
in
g
to
war
d
s
th
e
d
ir
ec
tio
n
of
th
at
s
o
lu
tio
n
s
im
u
ltan
eo
u
s
ly
ch
ec
k
in
g
f
o
r
o
th
er
b
est
s
o
lu
tio
n
s
p
o
s
s
ib
le
on
th
e
way
.
E
ac
h
p
ar
t
icle
is
as
s
o
ciate
d
with
two
v
ec
to
r
s
,
a
p
r
o
ce
s
s
v
ec
to
r
,
an
d
a
p
o
s
itio
n
v
ec
to
r
as
we
can
s
ee
in
F
ig
u
r
e
2
[
2
0
]
.
B
o
th
ar
e
of
th
e
s
am
e
len
g
th
.
In
ad
d
i
tio
n
to
th
e
a
b
o
v
e
v
ec
t
o
r
s
,
each
p
ar
ticle
also
h
as
a
m
em
o
r
y
to
s
to
r
e
its
p
b
est
p
o
s
itio
n
.
T
h
e
g
r
o
u
p
also
h
as
th
e
wo
r
ld
’
s
b
est
m
em
o
r
y
an
d
th
e
b
e
s
t
wo
r
k
of
th
e
e
n
tire
g
r
o
u
p
.
W
h
er
e
V
⃗
⃗
(
t
)
is
a
clip
p
in
g
v
ec
to
r
,
P
⃗
⃗
(
t
)
is
o
n
e’
s
in
d
iv
id
u
al
b
est
p
o
s
itio
n
,
X
⃗
⃗
(
t
)
is
p
o
s
itio
n
v
ec
to
r
an
d
∆
G
(
t
)
is
th
e
g
lo
b
al
b
est
p
o
s
itio
n
of
t
h
e
g
r
o
u
p
.
Fig
u
r
e
2
.
Vec
to
r
d
iag
r
a
m
o
f
th
e
p
o
s
itio
n
o
f
a
PS
O
p
ar
ticle
2
.
4
.
1.
P
s
eudo
c
o
de
f
o
r
P
SO
a
lg
o
rit
hm
T
h
e
p
s
eu
d
o
co
d
e
is
in
Alg
o
r
ith
m
1
,
an
d
it
in
itializes
a
P
SO
b
y
s
ettin
g
d
im
en
s
io
n
s
,
b
o
u
n
d
s
,
co
s
t
f
u
n
ctio
n
,
s
war
m
s
ize,
iter
atio
n
s
,
an
d
co
ef
f
icien
ts
.
Par
ticles
'
p
o
s
itio
n
s
(
Xij)
an
d
v
elo
cities
(
Vij)
ar
e
r
an
d
o
m
ly
s
et.
E
ac
h
p
ar
ticle'
s
co
s
t
is
ev
alu
ated
,
an
d
th
e
b
est
p
o
s
itio
n
s
(
lo
ca
l
an
d
g
lo
b
al)
a
r
e
u
p
d
ated
to
o
p
tim
ize
th
e
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
e
p
s
eu
d
o
co
d
e
in
Alg
o
r
ith
m
2
d
escr
ib
es
th
e
PS
O
p
r
o
ce
s
s
ac
r
o
s
s
iter
atio
n
s
.
Fo
r
ea
c
h
p
ar
ticle
in
th
e
s
war
m
,
v
elo
citi
es
V
(ij)
an
d
p
o
s
itio
n
s
X
(ij)
ar
e
u
p
d
ated
.
T
h
e
c
o
s
t
F(X
ij
)
is
ca
lc
u
lated
,
an
d
th
e
b
est
p
er
s
o
n
al
an
d
g
lo
b
al
p
o
s
itio
n
s
ar
e
u
p
d
ated
.
Af
ter
r
ea
c
h
in
g
th
e
m
ax
im
u
m
iter
atio
n
,
th
e
g
lo
b
al
b
est
s
o
lu
tio
n
is
f
in
alize
d
[
2
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
1
77
-
1
8
5
180
Alg
o
r
ith
m
1.
I
n
itializatio
n
of
PSO
Set v
ar
iab
le
d
im
en
s
io
n
; Set
u
p
p
er
b
o
u
n
d
o
f
d
im
en
s
io
n
s
; Set
lo
wer
b
o
u
n
d
o
f
d
im
e
n
s
io
n
s
; Set
co
s
t f
u
n
ctio
n
;
Set swar
m
s
ize;
Set m
ax
iter
at
io
n
s
; Set
in
er
tia
co
ef
f
icien
t; Set
ac
ce
ler
atio
n
co
ef
f
icien
ts
.
Select
r
an
d
o
m
ly
X
ij
a
n
d
V
ij
f
o
r
ea
ch
p
a
r
ticle;
E
v
alu
ate
F(X
ij
)
f
o
r
ea
ch
p
ar
ticle;
Set F
min
as th
e
m
in
v
alu
e
o
f
F(
X
ij
)
am
o
n
g
all
t
h
e
p
ar
ticles;
u
p
d
ate
X
ij(particle
best)
an
d
X
ij(global
best)
b
est
Alg
o
r
ith
m
2.
Ma
in
lo
o
p
of
PSO
alg
o
r
ith
m
Fo
r
i=1
to
i=
I
ter
atio
n
(max)
do;
-
Fo
r
j=1
to
j=
Par
ticle
n
u
m
b
er
d
o
;
Up
d
ate
V
(ij)
;
Up
d
ate
X
(ij)
;
C
alcu
late
F(X
ij
);
Up
d
ate
F
(min)
;
Up
d
ate
X
ij(particle
bes)
;
-
E
n
d
;
E
n
d
;
Up
d
ate
X
ij(global
best)
;
C
h
ec
k
if
iter
atio
n
=
I
ter
atio
n
(max)
;
Fin
al
v
alu
e
X
ij(global
best)
2
.
5
.
G
enet
ic
a
lg
o
rit
h
m
Gen
etic
alg
o
r
ith
m
s
(
GA)
wo
r
k
on
p
o
p
u
latio
n
s
with
m
u
ltip
le
s
o
lu
tio
n
s
wh
er
e
th
e
p
o
p
u
latio
n
s
ize
is
th
e
s
o
lu
tio
n
.
E
v
er
y
s
o
lu
tio
n
is
ca
lled
p
er
s
o
n
al.
E
v
er
y
s
u
b
s
tan
ce
h
as
a
ch
r
o
m
o
s
o
m
e.
C
h
r
o
m
o
s
o
m
es
ar
e
r
ep
r
esen
ted
as
ch
ar
ac
ter
is
tics
th
at
d
ef
in
e
a
p
er
s
o
n
[
2
2
]
.
E
ac
h
ch
r
o
m
o
s
o
m
e
co
n
tain
s
a
pool
of
g
e
n
es.
E
v
er
y
o
n
e
h
as
a
f
itn
ess
lev
el.
Use
in
ter
m
ed
iar
ies
to
ch
o
o
s
e
th
e
b
est
ca
n
d
id
ates.
T
h
e
s
o
lu
tio
n
to
th
e
p
h
y
s
ical
p
r
o
b
le
m
is
th
e
f
itn
ess
v
alu
e
th
at
r
ep
r
esen
ts
th
e
o
p
tim
al
s
o
l
u
tio
n
[
2
3
]
.
T
h
e
g
r
ea
ter
t
h
e
n
u
m
b
er
,
th
e
b
etter
th
e
r
eso
lu
tio
n
.
Selectin
g
th
e
b
est
in
d
iv
id
u
als
b
ased
on
p
er
f
o
r
m
an
ce
is
u
s
ed
to
cr
ea
te
a
m
atin
g
pool
f
r
o
m
wh
ich
in
d
iv
id
u
al
s
with
b
etter
r
esu
lts
will
be
s
elec
ted
in
th
e
m
atin
g
p
o
o
l;
I
n
d
iv
i
d
u
als
with
b
etter
r
esu
lts
f
r
o
m
th
is
pool
ar
e
s
elec
ted
in
to
th
e
m
atin
g
p
o
o
l.
T
h
e
p
e
o
p
le
liv
in
g
in
th
is
lak
e
ar
e
ca
lled
p
ar
en
ts
[
2
4
]
.
E
ac
h
p
air
ch
o
s
en
f
r
o
m
th
e
p
o
o
l
will
p
r
o
d
u
ce
two
o
f
f
s
p
r
in
g
(
ch
ild
r
en
)
.
E
ac
h
g
r
o
u
p
f
o
r
m
ed
is
ca
lled
a
g
en
er
ati
o
n
.
2
.
5
.
1
.
P
s
eudo
co
de
f
o
r
g
enet
i
c
a
lg
o
rit
hm
T
h
e
p
s
eu
d
o
c
o
d
e
in
Alg
o
r
ith
m
3
in
itializes
th
e
p
o
p
u
latio
n
g
en
etic
alg
o
r
ith
m
.
At
each
iter
atio
n
,
it
ev
alu
ates
th
e
p
o
p
u
latio
n
,
s
elec
ts
p
ar
en
ts
,
cr
ea
tes
o
f
f
s
p
r
in
g
th
r
o
u
g
h
c
o
m
p
etitio
n
,
a
n
d
r
etu
r
n
s
th
e
b
est
in
d
iv
id
u
al
wh
en
a
d
ec
is
io
n
is
m
ad
e
.
T
h
e
p
s
eu
d
o
co
d
e
in
Alg
o
r
ith
m
4
s
wap
s
th
e
ch
ild
r
en
,
e
v
alu
ate
s
th
em
,
r
ep
lace
s
th
e
cu
r
r
en
t
in
d
iv
i
d
u
al
with
th
e
n
ew
ch
ild
,
an
d
r
etu
r
n
s
th
e
b
es
t
in
d
iv
id
u
al.
Of
f
s
p
r
in
g
ar
e
p
r
o
d
u
ce
d
by
cr
o
s
s
in
g
s
elec
ted
p
ar
en
ts
.
Alg
o
r
ith
m
3
.
Gen
etic
alg
o
r
ith
m
m
ain
lo
o
p
%
I
n
itializatio
n
Po
p
u
latio
n
=
I
n
itializePo
p
u
latio
n
(
)
%
Ma
in
L
o
o
p
:
W
h
ile
ter
m
in
atio
n
cr
iter
ia
n
o
t
m
et:
C
alcu
latePo
p
u
latio
n
(
p
o
p
u
latio
n
)
Selecte
d
_
p
ar
en
ts
=
SelectPar
en
ts
(
p
o
p
u
latio
n
)
O
f
f
s
p
r
in
g
=
C
r
o
s
s
o
v
er
(
s
elec
ted
_
p
ar
e
n
ts
)
r
etu
r
n
B
estIn
d
iv
id
u
al(
p
o
p
u
lati
o
n
)
Alg
o
r
ith
m
4
.
Gen
etic
alg
o
r
ith
m
m
u
tatio
n
% M
u
tatio
n
Mu
tate(
o
f
f
s
p
r
in
g
)
% E
v
alu
atio
n
E
v
alu
atePo
p
u
latio
n
(
o
f
f
s
p
r
in
g
)
p
o
p
u
latio
n
=
R
ep
lace
(
p
o
p
u
lati
o
n
,
o
f
f
s
p
r
in
g
)
%
R
etu
r
n
b
est in
d
iv
id
u
al
f
o
u
n
d
r
etu
r
n
B
estIn
d
iv
id
u
al(
p
o
p
u
lati
o
n
)
o
f
f
s
p
r
in
g
=
C
r
o
s
s
o
v
er
(
s
elec
ted
_
p
ar
e
n
ts
)
2
.
6
.
Sine
co
s
ine
a
lg
o
rit
hm
Sin
e
co
s
in
e
alg
o
r
ith
m
(
SC
A
)
is
an
o
p
tim
izatio
n
b
ased
on
th
e
o
s
cillato
r
y
b
eh
av
io
r
of
s
in
e
an
d
co
s
in
e
f
u
n
ctio
n
s
.
It
f
o
ll
o
ws
th
e
m
o
v
em
en
ts
of
ce
lest
ial
o
b
jects
in
th
e
s
k
y
,
wh
er
e
th
e
s
in
e
an
d
c
o
s
in
e
f
u
n
ctio
n
s
ar
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Op
timiz
a
tio
n
o
f lo
a
d
fr
eq
u
e
n
c
y
co
n
tr
o
l sys
tems u
s
in
g
P
S
O
tech
n
iq
u
e
(
Deb
a
n
i
P
r
a
s
a
d
Mis
h
r
a
)
181
im
p
o
r
tan
t.
T
h
e
SC
A
can
be
u
s
ed
f
o
r
th
e
o
p
tim
izatio
n
of
PID
co
n
tr
o
ller
s
[
2
5
]
.
T
h
e
r
an
d
o
m
i
n
itial
p
o
p
u
latio
n
of
p
o
ten
tial
s
o
lu
tio
n
s
.
T
h
ese
s
o
lu
tio
n
s
r
ep
r
esen
t
d
if
f
er
e
n
t
s
ets
of
PID
p
ar
am
eter
s
(
co
m
m
o
n
g
a
in
,
tim
e
in
teg
r
atio
n
,
tim
e
d
if
f
er
e
n
ce
)
.
Def
in
e
an
o
b
jectiv
e
f
u
n
ctio
n
th
at
ev
a
lu
ates
th
e
p
er
f
o
r
m
a
n
ce
of
t
h
e
PID
co
n
tr
o
ller
.
T
h
is
in
clu
d
es
how
well
th
e
co
n
tr
o
l
s
y
s
tem
tr
ac
k
s
s
ig
n
al
u
s
ag
e
r
ed
u
ce
s
n
o
is
e,
ad
ju
s
ts
s
p
ee
d
,
an
d
m
ea
s
u
r
es
[
2
6
]
,
[
2
7
]
.
T
h
is
wo
r
k
ev
alu
ates
th
e
s
ec
u
r
ity
of
each
s
o
lu
tio
n
.
E
n
ter
each
s
o
lu
tio
n
as
a
v
ec
t
o
r
r
ep
r
esen
tin
g
PID
p
ar
am
eter
s
.
Fo
r
ex
am
p
le,
th
e
s
o
lu
tio
n
can
be
ex
p
r
ess
ed
as
[
Kp
,
T
i,
T
d
]
;
wh
er
e
Kp
is
th
e
eq
u
atio
n
,
Ti
is
th
e
in
teg
r
atio
n
tim
e
,
a
n
d
Td
is
t
h
e
d
iv
er
g
en
ce
tim
e.
I
ter
ate
s
o
lu
tio
n
s
ac
r
o
s
s
g
en
er
atio
n
s
an
d
m
o
d
if
y
th
em
as
n
ec
ess
ar
y
.
E
v
alu
ate
th
e
s
ec
u
r
it
y
of
each
s
o
lu
tio
n
u
s
in
g
th
e
tar
g
et
f
u
n
ctio
n
.
Up
d
ated
t
h
e
p
o
s
it
io
n
of
ea
c
h
s
o
lu
tio
n
u
s
in
g
th
e
eq
u
iv
alen
t
s
in
e
-
co
s
in
e
alg
o
r
ith
m
,
wh
ich
in
clu
d
es
o
s
cillato
r
y
m
o
tio
n
b
ased
on
s
in
e
an
d
co
s
in
e
p
o
wer
s
.
T
h
e
aim
of
th
is
is
to
f
in
d
b
ette
r
s
o
lu
tio
n
s
in
th
e
s
ea
r
ch
s
p
ac
e
.
Use
th
e
s
ea
r
ch
p
r
o
ce
s
s
an
d
a
p
p
r
o
p
r
iate
u
s
ag
e
to
ac
h
iev
e
a
b
alan
ce
b
etwe
en
e
x
p
lo
r
in
g
n
ew
ar
ea
s
of
th
e
s
ea
r
ch
s
p
ac
e
an
d
u
s
in
g
ef
f
ec
tiv
e
s
o
lu
t
io
n
s
[
2
8
]
,
[
2
9
]
.
Re
-
p
er
f
o
r
m
th
e
ab
o
v
e
s
tep
s
u
n
t
il
th
e
s
to
p
is
co
m
p
lete
(
i.e
.
,
m
ax
im
u
m
n
u
m
b
er
of
r
e
p
etitio
n
s
,
s
atis
f
ac
to
r
y
p
er
f
o
r
m
an
ce
is
ac
h
iev
e
d
)
.
Af
ter
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
co
n
v
er
g
es
or
r
ea
ch
es
a
s
to
p
p
i
n
g
cr
iter
io
n
,
ex
tr
ac
t
t
h
e
b
est
s
o
lu
tio
n
(
s
)
f
o
u
n
d
.
T
h
ese
s
o
lu
tio
n
s
r
e
p
r
e
s
en
t
th
e
o
p
tim
al
PID
p
ar
am
eter
s
th
at
b
est
s
u
it
th
e
co
n
tr
o
l
p
r
o
b
lem
u
n
d
e
r
co
n
s
id
er
atio
n
.
I
m
p
lem
en
t
th
e
o
p
tim
ized
PID
co
n
tr
o
ller
with
th
e
ex
tr
ac
ted
p
ar
am
eter
s
in
th
e
r
ea
l
s
y
s
tem
or
s
im
u
latio
n
en
v
ir
o
n
m
en
t
[
3
0
]
,
[
3
1
]
.
T
h
e
s
in
e
-
c
o
s
in
e
alg
o
r
ith
m
h
elp
s
in
ef
f
icien
tly
ex
p
lo
r
in
g
th
e
s
o
lu
tio
n
s
p
ac
e
an
d
f
in
d
in
g
o
p
tim
al
or
n
ea
r
-
o
p
tim
al
PID
p
ar
am
eter
s
.
L
e
v
er
ag
in
g
o
s
cillato
r
y
m
o
v
e
m
en
ts
in
s
p
ir
ed
by
s
in
e
an
d
co
s
in
e
f
u
n
ctio
n
s
,
p
r
o
v
id
es
a
b
alan
ce
b
etwe
en
e
x
p
lo
r
atio
n
a
n
d
ex
p
lo
itatio
n
,
lea
d
in
g
to
ef
f
ec
tiv
e
o
p
tim
izatio
n
r
esu
lts
[
3
2
]
.
H
o
wev
er
,
as
with
an
y
o
p
tim
izatio
n
al
g
o
r
ith
m
,
t
h
e
p
er
f
o
r
m
a
n
ce
of
th
e
s
in
e
-
c
o
s
in
e
alg
o
r
ith
m
ca
n
v
ar
y
d
ep
e
n
d
in
g
on
th
e
p
r
o
b
le
m
ch
ar
ac
ter
is
tics
an
d
p
ar
am
eter
s
ettin
g
s
.
T
h
er
ef
o
r
e,
it'
s
es
s
e
n
tial
to
v
alid
ate
th
e
o
b
tain
ed
r
esu
lts
an
d
f
i
n
e
-
tu
n
e
th
e
alg
o
r
ith
m
p
ar
am
eter
s
if
n
ec
ess
ar
y
[
3
3
]
.
T
h
e
p
s
eu
d
o
co
d
e
in
A
lg
o
r
ith
m
5
in
itializes
th
e
r
an
d
o
m
s
o
lu
tio
n
X
i
,
ev
alu
ates
th
e
tar
g
et
v
alu
e,
u
p
d
ates
th
e
tar
g
et
P,
ad
ju
s
ts
th
e
in
eq
u
ality
,
u
p
d
ates
th
e
s
o
lu
tio
n
u
s
in
g
th
e
eq
u
atio
n
,
an
d
r
e
p
ea
ts
th
is
p
r
o
ce
s
s
u
n
til
th
e
m
ax
im
u
m
iter
atio
n
is
co
m
p
leted
.
A
lg
o
r
ith
m
5.
Sin
e
co
s
in
e
alg
o
r
ith
m
I
n
itialize
th
e
r
an
d
o
m
s
et
o
f
s
o
l
u
tio
n
s
X
i
(
i= 1
,
2
,
……
.
.
,
n
)
W
h
ile
t
less
th
an
T
max
do
E
v
alu
ate
th
e
o
b
jectiv
e
v
alu
e
f
o
r
ea
ch
X
i
R
ev
is
e
th
e
d
esti
n
atio
n
(
P=
X)
R
ev
is
e
th
e
r
an
d
o
m
p
ar
am
eter
s
R
ev
is
e
th
e
s
o
lu
tio
n
u
s
in
g
th
e
e
q
u
atio
n
(
6
)
E
n
d
wh
ile
R
etu
r
n
th
e
d
esti
n
atio
n
P
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
In
F
ig
u
r
e
3
,
th
e
p
er
f
o
r
m
an
ce
of
th
e
tu
n
ed
PID
co
n
tr
o
ller
is
m
ea
s
u
r
ed
by
s
im
u
latin
g
its
r
esp
o
n
s
e
to
v
ar
io
u
s
lo
ad
d
is
tu
r
b
an
ce
s
an
d
in
co
r
p
o
r
atin
g
t
h
e
u
n
ce
r
tain
ty
of
th
e
s
y
s
tem
.
T
h
e
f
r
eq
u
e
n
cy
r
esp
o
n
s
e
of
th
e
s
y
s
tem
af
ter
o
p
tim
izatio
n
with
o
u
t
u
s
in
g
a
PID
c
o
n
tr
o
ller
.
Fig
u
r
e
4
s
h
o
ws
th
e
in
teg
r
ated
r
esp
o
n
s
e
of
a
l
o
ca
l
L
FC
s
y
s
tem
w
ith
an
d
with
o
u
t
th
e
o
p
tim
izatio
n
tech
n
iq
u
e.
W
h
ile
o
b
s
er
v
in
g
t
h
e
g
r
a
p
h
it
is
r
ea
lized
th
at
with
th
e
u
s
e
of
o
p
tim
izatio
n
tech
n
iq
u
e
s
,
th
e
s
y
s
tem
can
be
s
tab
ilize
d
with
in
th
e
n
eg
lig
ib
le
tim
e
p
er
io
d
.
Alth
o
u
g
h
f
o
r
co
m
p
lex
s
y
s
tem
s
th
is
tim
e
m
ay
en
lar
g
e.
To
o
v
e
r
co
m
e
th
is
,
u
s
e
d
if
f
er
en
t
o
p
tim
izatio
n
tech
n
iq
u
es
f
o
r
i
m
p
r
o
v
e
d
r
esu
lts
.
B
elo
w,
th
r
ee
alg
o
r
ith
m
s
wer
e
ex
ec
u
ted
:
PSO
alg
o
r
ith
m
,
g
en
etic
alg
o
r
ith
m
,
an
d
s
in
e
co
s
in
e
alg
o
r
ith
m
.
Fig
u
r
e
4
is
th
e
o
p
tim
izatio
n
r
esu
lts
of
th
e
PSO
alg
o
r
ith
m
wh
er
e
it
h
as
s
tab
ilized
th
e
cu
r
v
e
well
b
ef
o
r
e
th
e
n
at
u
r
al
s
tab
ilizatio
n
of
th
e
s
ig
n
al.
B
u
t
in
Fig
u
r
e
5,
th
e
o
p
tim
izati
o
n
r
esu
lts
of
t
he
g
en
etic
alg
o
r
ith
m
o
u
tp
er
f
o
r
m
th
e
PSO
alg
o
r
ith
m
with
a
m
ar
g
in
of
0
.
0
1
8
8
7
3
9
s
ec
.
T
h
is
can
be
b
ec
au
s
e
GAs
ar
e
p
ar
ticu
lar
ly
e
f
f
ec
tiv
e
in
p
r
o
b
lem
s
with
m
an
y
lo
ca
l
o
p
tim
a.
T
h
e
cr
o
s
s
o
v
er
an
d
m
u
tatio
n
o
p
er
a
tio
n
s
in
GAs
can
h
elp
ex
p
lo
r
e
th
e
s
ea
r
ch
s
p
ac
e
more
th
o
r
o
u
g
h
ly
an
d
a
v
o
id
p
r
em
atu
r
e
c
o
n
v
e
r
g
en
ce
to
lo
c
al
o
p
tim
a,
wh
ich
ca
n
be
a
ch
al
len
g
e
f
o
r
PS
O.
Fig
u
r
e
6
is
th
e
o
p
tim
izatio
n
r
esu
lts
of
th
e
s
in
e
co
s
in
e
alg
o
r
ith
m
.
Fro
m
th
e
f
ig
u
r
e,
o
n
e
ca
n
co
n
cl
u
d
e
th
at
alth
o
u
g
h
th
e
SC
A
p
er
f
o
r
m
ed
b
etter
th
a
n
th
e
PSO
alg
o
r
ith
m
but
it
f
ailed
to
g
iv
e
b
etter
r
esu
lts
th
an
th
e
GA.
T
h
e
GA
o
u
tp
er
f
o
r
m
s
th
e
SC
A
with
a
tim
e
m
ar
g
in
of
0
.
0
0
6
4
0
2
7
s
ec
.
GAs,
with
th
eir
cr
o
s
s
o
v
er
an
d
m
u
tatio
n
o
p
er
atio
n
s
,
is
well
-
s
u
ited
f
o
r
n
av
ig
atin
g
co
m
p
lex
,
m
u
ltimo
d
a
l
lan
d
s
ca
p
es.
T
h
ey
can
escap
e
lo
ca
l
o
p
tim
a
m
o
r
e
ef
f
ec
tiv
ely
th
a
n
SC
As,
wh
ich
r
ely
on
d
eter
m
in
is
tic
s
in
e
an
d
co
s
in
e
f
u
n
ctio
n
s
f
o
r
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
.
In
T
ab
le
1
,
th
e
s
tab
ilizatio
n
t
im
e
th
at
each
alg
o
r
ith
m
to
o
k
to
s
tab
ilize
th
e
s
ig
n
al.
T
h
e
ta
b
le
also
s
h
o
ws
th
e
s
tab
ilized
f
in
al
f
r
eq
u
e
n
cy
a
f
ter
th
e
alg
o
r
ith
m
is
ex
ec
u
te
d
.
Fo
r
th
e
a
b
o
v
e
ca
s
e
of
o
p
tim
izatio
n
of
PID
c
o
n
tr
o
ller
in
a
s
in
g
le
ar
ea
lo
ad
f
r
eq
u
en
c
y
co
n
tr
o
l,
th
e
g
e
n
etic
alg
o
r
ith
m
o
u
tp
er
f
o
r
m
s
PSO
an
d
SC
A
with
a
s
tab
iliza
tio
n
tim
e
d
if
f
er
en
ce
of
0
.
0
1
8
8
7
3
9
s
ec
an
d
0
.
0
0
6
7
6
2
7
s
ec
,
r
esp
ec
tiv
ely
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
1
77
-
1
8
5
182
Fig
u
r
e
3
.
Fre
q
u
en
cy
r
esp
o
n
s
e
o
f
s
in
g
le
ar
ea
L
FC
s
y
s
tem
Fig
u
r
e
4
.
Fre
q
u
en
cy
r
esp
o
n
s
e
u
s
in
g
PS
O
alg
o
r
ith
m
Fig
u
r
e
5
.
Fre
q
u
en
cy
r
esp
o
n
s
e
u
s
in
g
g
en
etic
alg
o
r
ith
m
Fig
u
r
e
6
.
Fre
q
u
en
cy
r
esp
o
n
s
e
u
s
in
g
s
in
e
co
s
in
e
alg
o
r
ith
m
T
ab
le
1
.
Op
tim
izatio
n
r
esu
lts
A
l
g
o
r
i
t
h
m
S
t
a
b
i
l
i
z
a
t
i
o
n
t
i
m
e
(
s
e
c
)
S
t
a
b
i
l
i
z
e
d
f
r
e
q
u
e
n
c
y
(
H
z
)
PSO
a
l
g
o
r
i
t
h
m
0
.
0
6
1
9
5
7
0
60
G
e
n
e
t
i
c
a
l
g
o
r
i
t
h
m
0
.
0
4
3
0
8
3
1
60
S
i
n
e
c
o
si
n
e
a
l
g
o
r
i
t
h
m
0
.
0
4
9
8
4
5
8
60
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Op
timiz
a
tio
n
o
f lo
a
d
fr
eq
u
e
n
c
y
co
n
tr
o
l sys
tems u
s
in
g
P
S
O
tech
n
iq
u
e
(
Deb
a
n
i
P
r
a
s
a
d
Mis
h
r
a
)
183
4.
CO
NCLU
SI
O
N
In
th
e
co
n
tex
t
of
o
p
tim
izin
g
l
o
ca
l
L
FC
an
d
o
p
tim
izin
g
PID
co
n
tr
o
ller
p
ar
am
eter
s
,
th
e
p
er
f
o
r
m
an
ce
of
th
e
g
en
etic
alg
o
r
ith
m
(
GA)
m
ay
d
if
f
er
d
ep
en
d
in
g
on
th
e
s
it
u
atio
n
c
o
m
p
ar
e
d
to
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
.
Her
e
ar
e
s
o
m
e
r
ea
s
o
n
s
wh
y
GA
is
p
r
ef
er
r
ed
o
v
e
r
PSO
in
th
is
p
ar
ticu
lar
ca
s
e
GA
ty
p
ically
ex
ce
ls
in
th
e
ex
p
lo
r
atio
n
of
th
e
s
o
lu
tio
n
s
p
a
ce
due
to
its
ab
ilit
y
to
m
ai
n
tain
a
d
iv
er
s
e
p
o
p
u
latio
n
an
d
p
e
r
f
o
r
m
g
lo
b
al
s
ea
r
ch
th
r
o
u
g
h
o
p
er
atio
n
s
lik
e
c
r
o
s
s
o
v
er
a
n
d
m
u
tatio
n
.
In
s
in
g
le
-
ar
ea
L
FC
,
wh
er
e
th
e
s
y
s
te
m
d
y
n
a
m
ics
can
be
co
m
p
lex
an
d
non
-
lin
ea
r
,
ef
f
ec
t
iv
e
ex
p
lo
r
atio
n
of
th
e
s
o
lu
tio
n
s
p
ac
e
is
cr
u
cial
to
f
in
d
in
g
o
p
tim
al
or
n
ea
r
-
o
p
tim
al
PID
co
n
tr
o
ller
p
ar
am
eter
s
.
P
SO,
wh
ile
ef
f
ec
tiv
e
in
ex
p
lo
itatio
n
due
to
its
ab
ilit
y
to
q
u
ick
ly
co
n
v
er
g
e
to
p
r
o
m
is
in
g
r
eg
io
n
s
,
m
ig
h
t
s
tr
u
g
g
le
in
ex
p
l
o
r
in
g
d
iv
e
r
s
e
r
eg
i
o
n
s
of
th
e
s
o
lu
tio
n
s
p
ac
e,
p
o
t
en
tially
lead
in
g
to
s
u
b
o
p
tim
al
s
o
lu
tio
n
s
.
W
h
ile
GA
m
ay
h
av
e
ad
v
a
n
tag
es
o
v
e
r
PSO
in
ce
r
tain
asp
ec
ts
,
it'
s
ess
en
tial
to
n
o
te
t
h
at
th
e
p
er
f
o
r
m
an
ce
of
o
p
tim
izati
o
n
alg
o
r
ith
m
s
can
v
ar
y
d
ep
e
n
d
in
g
on
th
e
s
p
ec
if
ic
ch
ar
ac
ter
i
s
tics
of
th
e
p
r
o
b
lem
,
th
e
im
p
lem
en
tatio
n
d
etails,
an
d
th
e
tu
n
in
g
of
alg
o
r
ith
m
p
ar
am
eter
s
.
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h
er
ef
o
r
e,
it'
s
o
f
ten
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en
ef
icial
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p
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im
en
t
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ltip
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izatio
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o
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ith
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to
f
in
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th
e
m
o
s
t
s
u
itab
le
one
f
o
r
a
p
ar
ticu
lar
ap
p
licatio
n
,
s
u
ch
as
o
p
tim
izin
g
PID
co
n
t
r
o
ller
s
in
s
in
g
le
-
ar
ea
L
FC
.
T
h
e
ch
o
ice
of
SC
A
an
d
GA
to
o
p
tim
ize
th
e
PID
co
n
tr
o
ller
d
o
es
not
d
ep
e
n
d
on
f
ac
to
r
s
s
u
ch
as
th
e
co
m
p
lex
ity
of
th
e
co
n
tr
o
l
p
r
o
b
lem
,
av
aila
b
le
co
m
p
u
tatio
n
al
ab
ilit
y
,
an
d
th
e
s
p
ec
if
ic
r
eq
u
ir
em
en
ts
of
th
e
ap
p
licatio
n
.
It
is
o
f
ten
a
good
id
ea
to
ex
p
er
i
m
en
t
with
m
u
ltip
le
alg
o
r
ith
m
s
an
d
co
m
p
ar
e
th
eir
p
er
f
o
r
m
a
n
ce
on
y
o
u
r
s
p
ec
if
ic
o
p
tim
izatio
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p
r
o
b
lem
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eter
m
i
n
e
wh
ich
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o
r
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wo
r
k
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est
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p
r
ac
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th
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r
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th
at
th
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g
en
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etter
th
an
th
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d
th
e
s
in
e
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d
co
s
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ith
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s
f
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th
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izatio
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PID
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n
tr
o
l
ler
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th
e
lo
ca
l
lo
ad
f
r
eq
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e
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cy
co
n
tr
o
l
s
y
s
tem
.
F
UNDING
I
NF
O
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M
A
T
I
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esear
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k
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RE
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NC
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S
[
1
]
M.
A.
Eb
r
a
h
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m,
R.
M.
A.
F
a
t
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h
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2
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I.
M.
H.
N
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,
E.
R
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sh
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n
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,
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M
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El
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[
4
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K.
J
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t
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n
,
B.
A
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,
S.
S
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ma
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d
V.
E.
B
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l
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5
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R.
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[
6
]
N.
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b
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P,
J.
M.
G
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o
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[
7
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G.
D
e
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al
.,
“
I
mp
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EEE
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.
[
8
]
A
.
D
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z
,
S
.
A
.
M
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k
,
A
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[
9
]
T.
K
.
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h
a
u
,
S
.
S
.
Y
u
,
T
.
F
e
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M
.
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ma
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,
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I
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[
1
0
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A
.
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me
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,
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1
1
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V
.
V
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r
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sam
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1
2
]
X
.
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S
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T
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[
1
3
]
C.
-
H
.
Y
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n
,
B
.
Li
u
,
P
.
X
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EEE
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6
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.
[
1
4
]
H
.
A
b
u
b
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k
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t
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l
.
,
“
A
d
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p
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mi
c
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s,
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c
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5
.
[
1
5
]
Y
.
M
a
,
Z
.
H
u
,
a
n
d
Y
.
S
o
n
g
,
“
A
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l
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t
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so
u
r
c
e
s,
”
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E
EE
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r
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sa
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t
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o
n
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Po
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s
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0
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3
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6
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5
4
3
.
[
1
6
]
N
.
M
.
A
l
-
Y
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z
i
d
i
,
Y
.
A
.
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n
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S
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M
a
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mo
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d
,
“
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sy
s
t
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ms,
”
I
EEE
Ac
c
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,
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p
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[
1
7
]
J.
S
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n
,
L.
W
u
,
a
n
d
X
.
Y
a
n
g
,
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t
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m,
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In
2
0
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0
I
EE
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t
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4
7
3
.
[
1
8
]
M
.
I
.
M
o
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a
m
e
d
,
G
.
E
l
-
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a
a
d
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,
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n
d
A
.
M
.
Y
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u
sef
,
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P
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Evaluation Warning : The document was created with Spire.PDF for Python.
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I
SS
N:
2252
-
8
7
9
2
Op
timiz
a
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fr
eq
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tems u
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tech
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iq
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(
Deb
a
n
i
P
r
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d
Mis
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)
185
[
3
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X.
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i
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Wu
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u
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b
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sa
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a
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rtme
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ter
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ti
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stit
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o
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n
fo
rm
a
ti
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n
Tec
h
n
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o
g
y
B
h
u
b
a
n
e
sw
a
r,
Od
i
sh
a
.
He
c
o
m
p
lete
d
h
is
b
a
c
h
e
l
o
r'
s
d
e
g
re
e
in
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lec
tri
c
a
l
e
n
g
in
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rin
g
fr
o
m
Bij
u
P
a
t
n
a
ik
Un
iv
e
rsity
o
f
Tec
h
n
o
l
o
g
y
,
Od
ish
a
,
in
2
0
0
6
,
fo
ll
o
we
d
b
y
a
m
a
ste
r'
s
d
e
g
re
e
in
p
o
we
r
sy
ste
m
s
fro
m
IIT
De
lh
i,
In
d
ia
,
in
2
0
1
0
.
In
2
0
1
9
,
h
e
su
c
c
e
ss
fu
ll
y
o
b
tai
n
e
d
h
is
P
h
.
D
.
i
n
p
o
we
r
sy
s
tem
s
fro
m
Ve
e
r
S
u
re
n
d
ra
S
a
i
U
n
iv
e
rsit
y
o
f
Tec
h
n
o
lo
g
y
,
Od
ish
a
,
In
d
ia.
Wi
th
a
p
r
o
fo
u
n
d
a
c
a
d
e
m
ic
b
a
c
k
g
ro
u
n
d
a
n
d
e
x
ten
siv
e
k
n
o
wle
d
g
e
o
f
p
o
we
r
sy
ste
m
s,
h
e
a
c
ti
v
e
ly
e
n
g
a
g
e
s
in
te
a
c
h
in
g
a
n
d
re
se
a
rc
h
a
c
ti
v
it
ies
.
He
is
d
e
e
p
ly
p
a
ss
io
n
a
te
a
b
o
u
t
sh
a
rin
g
h
is
e
x
p
e
rti
se
a
n
d
g
u
id
i
n
g
a
sp
ir
in
g
stu
d
e
n
ts
i
n
t
h
e
c
a
p
t
iv
a
ti
n
g
fiel
d
o
f
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
d
e
b
a
n
i@ii
i
t
-
b
h
.
a
c
.
in
.
Rud
r
a
n
a
r
a
y
a
n
S
e
n
a
p
a
ti
re
c
e
iv
e
d
th
e
B.
Tec
h
.
i
n
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
fro
m
t
h
e
Utk
a
l
Un
i
v
e
rsity
,
Od
is
h
a
,
I
n
d
i
a
,
in
2
0
0
1
a
n
d
t
h
e
M
.
Tec
h
.
i
n
c
o
m
m
u
n
ica
ti
o
n
sy
ste
m
e
n
g
in
e
e
rin
g
i
n
2
0
0
8
fr
o
m
KIIT
Un
iv
e
rsity
,
Od
is
h
a
.
He
h
a
s
b
e
e
n
a
wa
rd
e
d
a
P
h
.
D.
d
e
g
re
e
i
n
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
fro
m
KIIT
d
e
e
m
e
d
to
b
e
Un
iv
e
rsit
y
,
P
a
ti
a
B
h
u
b
a
n
e
sw
a
r,
Od
ish
a
,
In
d
ia,
in
2
0
1
8
.
He
is
c
u
rre
n
t
ly
se
rv
in
g
a
s
a
ss
istan
t
p
r
o
fe
ss
o
r
in
th
e
S
c
h
o
o
l
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
KIIT,
d
e
e
m
e
d
to
b
e
Un
iv
e
rsit
y
,
P
a
ti
a
,
Bh
u
b
a
n
e
sw
a
r,
Od
ish
a
.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
so
lar
fo
re
c
a
stin
g
,
b
l
o
c
k
c
h
a
i
n
tec
h
n
o
l
o
g
y
,
re
n
e
wa
b
le
i
n
teg
ra
ti
o
n
t
o
p
o
we
r
s
y
ste
m
s
,
a
n
d
p
o
we
r
q
u
a
li
t
y
.
He
c
a
n
b
e
c
o
n
tac
te
d
a
t
e
m
a
il
:
rse
n
a
p
a
ti
fe
l@k
ii
t.
a
c
.
i
n
.
Lin
g
a
m
Ya
sw
a
n
th
is
c
u
rre
n
tl
y
p
u
rs
u
in
g
a
B.
Tec
h
.
d
e
g
re
e
in
e
lec
tri
c
a
l
a
n
d
e
lec
tro
n
ics
e
n
g
i
n
e
e
rin
g
a
t
I
n
tern
a
ti
o
n
a
l
In
st
it
u
te
o
f
In
f
o
rm
a
ti
o
n
Tec
h
n
o
l
o
g
y
,
Bh
u
b
a
n
e
sw
a
r,
Od
ish
a
,
In
d
ia
(Ba
tch
2
0
2
1
-
2
0
2
5
).
His
in
tere
sts
a
re
in
d
o
m
a
in
s
o
f
c
y
b
e
r
se
c
u
rit
y
,
a
p
p
li
e
d
m
a
th
e
m
a
ti
c
s
,
a
n
d
d
i
g
it
a
l
e
l
e
c
tro
n
i
c
s.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
b
3
2
1
0
2
1
@
ii
it
-
b
h
.
a
c
.
i
n
.
Pee
so
d
i
Uda
y
is
c
u
rre
n
tl
y
p
u
rs
u
in
g
a
B.
Tec
h
.
d
e
g
re
e
i
n
e
lec
tri
c
a
l
a
n
d
e
lec
tro
n
ics
e
n
g
in
e
e
rin
g
a
t
I
n
tern
a
ti
o
n
a
l
In
sti
t
u
te
o
f
I
n
fo
rm
a
ti
o
n
Tec
h
n
o
l
o
g
y
,
B
h
u
b
a
n
e
sw
a
r,
Od
is
h
a
,
I
n
d
ia
(Ba
tch
2
0
2
1
-
2
0
2
5
).
His
i
n
tere
sts
a
re
in
th
e
field
s
o
f
UI/UX
d
e
sig
n
a
n
d
a
rti
ficia
l
in
tell
ig
e
n
c
e
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
b
3
2
1
0
2
5
@iii
t
-
b
h
.
a
c
.
in
.
S
u
r
e
n
d
e
r
Re
d
d
y
S
a
l
k
u
ti
re
c
e
i
v
e
d
th
e
P
h
.
D.
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
fro
m
th
e
I
n
d
ian
I
n
stit
u
te
o
f
Tec
h
n
o
l
o
g
y
,
Ne
w
De
l
h
i,
In
d
ia,
i
n
2
0
1
3
.
He
wa
s
a
p
o
std
o
c
to
ra
l
re
se
a
rc
h
e
r
with
Ho
wa
rd
U
n
iv
e
r
sity
,
Was
h
in
g
to
n
,
DC,
USA,
fr
o
m
2
0
1
3
t
o
2
0
1
4
.
He
is
c
u
rre
n
tl
y
a
n
a
ss
o
c
iate
p
ro
fe
ss
o
r
with
th
e
De
p
a
rtme
n
t
o
f
Ra
il
ro
a
d
a
n
d
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Wo
o
s
o
n
g
Un
i
v
e
rsity
,
Da
e
jeo
n
,
S
o
u
t
h
Ko
re
a
.
His
c
u
rre
n
t
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
m
a
rk
e
t
c
lea
rin
g
,
in
c
l
u
d
i
n
g
re
n
e
wa
b
le
e
n
e
rg
y
so
u
rc
e
s,
d
e
m
a
n
d
re
sp
o
n
se
,
a
n
d
sm
a
rt
g
rid
d
e
v
e
l
o
p
m
e
n
t
with
in
teg
ra
ti
o
n
o
f
win
d
a
n
d
so
lar
p
h
o
to
v
o
l
taic
e
n
e
rg
y
s
o
u
rc
e
s.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
su
re
n
d
e
r@ws
u
.
a
c
.
k
r
.
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