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t
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l J
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Art
if
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t
ellig
ence
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I
J
-
AI)
Vo
l.
9
,
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.
2
,
J
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n
e
2020
,
p
p
.
252
~
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0
I
SS
N:
2
2
5
2
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8938
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DOI
: 1
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1
1
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1
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252
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ttp
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a
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u
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pti
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i
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tion
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se study
of
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trica
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h
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d
y
o
f
th
e
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
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F
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f
o
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s
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se
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th
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d
b
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se
d
o
n
t
h
e
A
n
t
L
io
n
Op
ti
m
ize
r
(
AL
O)
a
l
g
o
rit
h
m
is
p
re
se
n
ted
a
n
d
h
a
s
b
e
e
n
c
o
n
f
irm
e
d
in
th
e
re
a
l
a
n
d
larg
e
r
sc
a
le
A
l
g
e
rian
1
1
4
-
b
u
s
s
y
ste
m
f
o
r
th
e
OP
F
p
ro
b
lem
w
it
h
a
n
d
w
it
h
o
u
t
sta
ti
c
V
A
R
c
o
m
p
e
n
sa
to
r
(S
V
C)
d
e
v
ice
s.
T
o
g
e
t
th
e
h
ig
h
e
st
i
m
p
a
c
t
o
f
S
V
C
d
e
v
ice
s
in
term
s
o
f
i
m
p
ro
v
in
g
th
e
v
o
lt
a
g
e
p
ro
f
il
e
,
m
in
i
m
iz
e
th
e
to
tal
g
e
n
e
ra
ti
o
n
c
o
st
a
n
d
re
d
u
c
ti
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c
ti
v
e
p
o
we
r
lo
ss
e
s,
th
e
AL
O
a
l
g
o
rit
h
m
wa
s
a
p
p
li
e
d
t
o
d
e
term
in
e
th
e
o
p
ti
m
a
l
a
ll
o
c
a
ti
o
n
o
f
S
V
C
d
e
v
ice
s.
T
h
e
re
su
lt
s
o
b
tai
n
e
d
b
y
th
e
AL
O
m
e
th
o
d
w
e
r
e
c
o
m
p
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re
d
w
it
h
o
th
e
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m
e
th
o
d
s
i
n
th
e
li
tera
tu
re
su
c
h
a
s
DE,
GA
-
ED
-
P
S
,
QP
,
a
n
d
M
OA
L
O,
to
se
e
th
e
e
fficie
n
c
y
o
f
th
e
p
r
o
p
o
se
d
m
e
th
o
d
.
T
h
e
p
r
o
p
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se
d
m
e
th
o
d
h
a
s
b
e
e
n
tes
ted
o
n
t
h
e
A
lg
e
rian
114
-
b
u
s
sy
ste
m
w
it
h
o
b
jec
ti
v
e
f
u
n
c
ti
o
n
s
is
th
e
m
in
im
iza
ti
o
n
o
f
to
tal
f
u
e
l
c
o
st
(TG
C)
w
it
h
tw
o
d
if
fe
re
n
t
v
e
c
to
rs o
f
v
a
riab
les
c
o
n
tro
l.
K
ey
w
o
r
d
s
:
An
t
lio
n
o
p
ti
m
ize
r
(
AL
O)
Op
ti
m
al
p
o
w
er
f
lo
w
(
OP
F)
Static
V
AR
c
o
m
p
en
s
ato
r
(
SVC
)
T
o
tal
g
en
er
atio
n
co
s
t (
T
GC
)
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
:
R
a
m
z
i K
o
u
ad
r
i
,
Dep
ar
t
m
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
Fer
h
at
A
b
b
as Seti
f
1
Un
i
v
er
s
it
y
,
Setif
,
A
l
g
er
ia
.
E
m
ail
:
r
a
m
zik
o
u
ad
r
i@
u
n
iv
-
s
e
tif
.
d
z
1.
I
NT
RO
D
UCT
I
O
N
T
o
d
ay
'
s
p
o
w
er
i
n
d
u
s
tr
y
n
ee
d
s
t
h
e
d
ev
elo
p
m
e
n
t
o
f
m
o
r
e
c
o
m
p
le
x
n
o
n
l
in
ea
r
p
o
w
er
s
y
s
t
e
m
m
o
d
els
an
d
o
p
ti
m
izatio
n
tec
h
n
iq
u
es
to
s
o
lv
e
t
h
e
m
,
t
h
ese
ar
e
c
alled
th
e
o
p
ti
m
al
p
o
w
er
f
lo
w
p
r
o
b
le
m
(
OP
F)
tech
n
iq
u
es
.
OP
F
i
s
o
n
e
o
f
t
h
e
m
o
s
t
i
m
p
o
r
tan
t
to
o
ls
f
o
r
i
n
ef
f
icie
n
t
p
lan
n
i
n
g
an
d
co
n
tr
o
llin
g
th
e
o
p
er
atio
n
o
f
p
o
w
er
s
y
s
te
m
s
.
I
t
w
as
f
ir
s
t
i
n
t
r
o
d
u
ce
d
b
y
[
1
]
.
T
h
e
OP
F
p
r
o
ce
d
u
r
e
co
n
s
i
s
ts
in
ch
o
o
s
i
n
g
t
h
e
o
p
ti
m
al
v
al
u
es
o
f
th
e
co
n
tr
o
l
v
ar
iab
les
o
f
a
n
ele
ctr
ical
s
y
s
te
m
to
o
p
ti
m
ize
a
n
o
b
j
ec
tiv
e
f
u
n
ctio
n
w
h
ile
s
at
is
f
y
in
g
th
e
co
n
s
tr
ai
n
ts
of
eq
u
alit
y
a
n
d
i
n
eq
u
alit
y
o
f
t
h
e
s
y
s
te
m
[
2
]
.
S
e
v
er
al
o
b
j
ec
ti
v
e
f
u
n
ctio
n
s
r
elate
d
to
t
h
e
elec
tr
ical
s
y
s
te
m
ca
n
b
e
o
p
tim
ized
,
s
u
c
h
a
s
:
m
i
n
i
m
ize
to
tal
g
e
n
er
atio
n
co
s
t
(
f
u
el
c
o
s
t
,
w
in
d
e
n
er
g
y
,
co
s
t
o
f
f
le
x
ib
le
tr
an
s
m
is
s
io
n
s
y
s
te
m
(
F
AC
T
S)
co
s
t,
etc.
)
,
tr
an
s
m
i
s
s
io
n
lo
s
s
e
s
,
v
o
ltag
e
d
ev
iatio
n
,
v
o
lta
g
e
s
tab
ilit
y
i
n
d
ex
,
to
x
ic
g
as
e
m
is
s
io
n
,
s
y
s
te
m
s
a
f
et
y
,
etc.
[3
-
5]
.
T
h
e
OP
F
p
r
o
b
lem
ca
n
b
e
co
n
s
id
er
ed
as
a
lar
g
e
p
r
o
b
lem
o
f
n
o
n
li
n
ea
r
o
p
tim
izatio
n
w
it
h
co
n
s
tr
ai
n
t
s
.
T
h
e
o
p
ti
m
izat
io
n
p
r
o
b
lem
s
o
lv
ed
b
y
s
e
v
er
al
d
e
v
el
o
p
ed
m
at
h
e
m
atica
l
tech
n
iq
u
es,
th
e
s
e
tec
h
n
iq
u
es
m
a
y
b
e
clas
s
i
f
ied
i
n
to
t
w
o
g
r
o
u
p
s
;
co
n
v
e
n
tio
n
al
m
et
h
o
d
s
an
d
r
ec
en
t
i
n
telli
g
e
n
ce
m
et
h
o
d
s
(
ev
o
l
u
tio
n
ar
y
o
r
m
eta
h
eu
r
i
s
tic
m
et
h
o
d
s
)
.
R
e
ce
n
tl
y
,
s
e
v
er
al
e
v
o
lu
tio
n
ar
y
o
r
m
eta
h
e
u
r
is
ti
c
o
p
tim
izatio
n
m
et
h
o
d
s
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
to
g
et
th
e
b
est
s
o
lu
tio
n
to
t
h
e
OP
F
p
r
o
b
lem
.
Me
tah
e
u
r
is
tic
al
g
o
r
ith
m
s
(
M
As)
m
ar
k
a
g
r
ea
t
r
e
v
o
lu
tio
n
i
n
th
e
f
ie
ld
o
f
o
p
ti
m
izat
io
n
,
al
lo
w
f
i
n
d
in
g
o
n
e
o
r
m
o
r
e
s
o
lu
tio
n
s
to
co
m
p
lex
o
p
ti
m
izatio
n
p
r
o
b
lem
s
[
6
]
.
A
cc
o
r
d
in
g
to
[
7
]
,
th
e
M
As
ca
n
b
e
r
eg
r
o
u
p
ed
in
to
f
o
u
r
m
ain
ca
teg
o
r
ies
:
e
v
o
lu
tio
n
-
b
ased
m
et
h
o
d
s
,
p
h
y
s
ics
-
b
ased
m
e
th
o
d
s
,
h
u
m
a
n
-
b
ased
m
et
h
o
d
s
,
an
d
s
w
ar
m
-
b
ased
m
eth
o
d
s
.
Sev
er
al
m
eta
h
e
u
r
is
tic
a
lg
o
r
it
h
m
s
a
r
e
i
m
p
le
m
en
ted
i
n
elec
tr
ical
p
o
w
er
s
y
s
te
m
f
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
r
ti
f
I
n
tell
I
SS
N:
2252
-
8938
OP
F
fo
r
la
r
g
e
s
ca
le
p
o
w
er sys
tem
u
s
in
g
a
n
t lio
n
o
p
timiz
a
tio
n
:
a
c
a
s
e
s
tu
d
y
o
f th
e
.
.
.
(
R
a
mzi
K
o
u
a
d
r
i
)
253
s
o
lv
i
n
g
t
h
e
o
p
ti
m
al
p
o
w
er
f
l
o
w
p
r
o
b
le
m
w
it
h
d
i
f
f
er
e
n
t
o
b
j
ec
tiv
e
f
u
n
ct
io
n
s
s
u
c
h
as
m
o
th
f
la
m
e
o
p
ti
m
izer
(
MFO)
[
4
]
,
en
r
ich
ed
b
r
ain
s
to
r
m
o
p
ti
m
izat
io
n
(
E
B
SO)
[
8
]
,
m
o
th
s
w
ar
m
alg
o
r
it
h
m
(
MS
A
)
[
9
]
,
p
a
r
ticle
s
w
ar
m
o
p
tim
izatio
n
(
P
SO)
[
1
0
]
,
ca
t
s
w
ar
m
o
p
ti
m
izatio
n
(
C
SO)
[
1
1
]
,
ch
ao
tic
w
h
ale
o
p
ti
m
iz
at
io
n
al
g
o
r
ith
m
(
I
A
B
C
)
[
1
2
]
,
im
p
r
o
v
ed
s
tr
e
n
g
th
P
ar
eto
ev
o
lu
tio
n
ar
y
alg
o
r
it
h
m
(
I
E
A
)
[
1
3
]
,
s
y
m
b
io
tic
o
r
g
an
is
m
s
s
ea
r
ch
al
g
o
r
ith
m
(
SOS
A
)
[
1
4
]
,
s
tu
d
k
r
ill
h
er
d
alg
o
r
ith
m
(
SKH)
[
1
5
]
,
m
o
d
if
ied
Gr
ey
w
o
l
f
o
p
ti
m
izer
(
MG
W
O)
[
1
6
]
,
d
if
f
er
en
tial
s
ea
r
ch
alg
o
r
it
h
m
(
DS
A
)
[
1
7
]
a
n
d
in
te
g
r
ated
alg
o
r
ith
m
(
I
A
)
[
1
8
]
.
T
h
is
p
ap
er
p
r
esen
ts
o
n
e
o
f
t
h
e
n
e
w
e
s
t
f
le
x
ib
ilit
y
a
n
d
e
f
f
ici
en
t
o
p
ti
m
izatio
n
m
eta
h
eu
r
i
s
ti
c
m
et
h
o
d
,
ca
lled
an
t
lio
n
o
p
ti
m
izatio
n
(
AL
O)
.
R
ec
en
tl
y
,
m
a
n
y
r
esear
ch
er
s
ar
e
i
n
ter
es
ted
in
t
h
is
m
e
th
o
d
f
o
r
s
o
l
v
i
n
g
t
h
e
o
p
tim
izatio
n
p
r
o
b
le
m
,
a
s
i
n
[
1
9
-
20]
.
I
n
th
i
s
s
t
u
d
y
,
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
h
a
s
b
ee
n
ap
p
lied
f
o
r
s
o
lv
in
g
t
h
e
OP
F
p
r
o
b
lem
f
o
r
lar
g
e
s
ca
le
p
o
w
er
s
y
s
te
m
s
w
h
ich
is
t
h
e
A
l
g
er
ia
n
1
1
4
-
b
u
s
p
o
w
er
s
y
s
te
m
.
T
w
o
d
if
f
er
e
n
t
ca
s
e
s
ar
e
co
n
s
id
er
ed
,
w
it
h
an
d
w
ith
o
u
t
th
e
p
r
esen
ce
o
f
SVC
d
ev
ice
s
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
u
s
e
d
in
th
is
p
ap
er
is
m
i
n
i
m
izi
n
g
t
h
e
to
tal
f
u
el
co
s
t
(
T
FC
)
.
2.
M
O
DE
L
I
N
G
O
F
SVC
D
E
V
I
CE
T
h
e
s
tatic
V
A
R
co
m
p
e
n
s
ato
r
SVC
is
m
o
d
eled
b
y
s
h
u
n
t
v
ar
iab
le
ad
m
itta
n
ce
.
S
in
ce
t
h
e
p
o
w
er
lo
s
s
o
f
th
e
SV
C
d
ev
ice
is
a
s
s
u
m
ed
n
e
g
li
g
ib
le,
s
o
th
e
ad
m
ittan
ce
i
s
a
s
s
u
m
ed
p
u
r
el
y
i
m
ag
i
n
ar
y
a
s
f
o
llo
w
:
S
V
C
S
V
C
y
j
b
(
1
)
T
h
e
s
u
s
ce
p
ta
n
ce
ca
n
b
e
ca
p
a
citiv
e
o
r
in
d
u
cti
v
e
to
r
esp
ec
ti
v
el
y
p
r
o
v
id
e
o
r
ab
s
o
r
b
th
e
r
ea
ctiv
e
p
o
w
er
.
T
h
e
p
lace
m
e
n
t
o
f
SV
C
d
ev
ice
s
in
th
i
s
s
tu
d
y
i
s
in
s
t
alled
in
th
e
p
o
w
er
s
y
s
te
m
a
s
a
P
V
b
u
s
w
it
h
th
e
r
ea
l
p
o
w
er
g
en
er
atio
n
eq
u
al
to
0
MW
.
T
h
e
r
ea
cti
v
e
p
o
w
er
ab
s
o
r
b
ed
b
y
t
h
e
SVC
d
ev
ice
an
d
a
ls
o
in
j
ec
ted
in
to
n
o
d
e
i is g
i
v
en
b
y
(
2
)
:
2
.
S
V
C
i
S
V
C
Q
V
b
(
2
)
3.
O
P
T
I
M
AL
P
O
WE
R
F
L
O
W
(OPF)
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
3
.
1
.
F
o
r
m
ula
t
io
n
p
ro
ble
m
T
h
e
s
o
lu
tio
n
o
f
t
h
e
OP
F
p
r
o
b
l
e
m
ai
m
s
to
m
i
n
i
m
ize
o
r
m
ax
i
m
ize
an
o
b
j
ec
tiv
e
f
u
n
ct
io
n
f
o
r
g
etti
n
g
a
n
o
p
tim
a
l
ad
j
u
s
t
m
e
n
t
o
f
co
n
tr
o
l
v
ar
iab
les
in
th
e
p
o
w
er
s
y
s
t
e
m
b
y
s
a
tis
f
y
in
g
b
o
th
co
n
s
tr
ain
ts
,
eq
u
a
lit
y
a
n
d
in
eq
u
ali
t
y
co
n
s
tr
ai
n
ts
.
Ge
n
er
al
l
y
,
th
e
o
p
ti
m
izatio
n
p
r
o
b
le
m
c
an
b
e
r
ep
r
esen
ted
m
at
h
e
m
at
ic
all
y
as
f
o
llo
w
s
:
Min
F
x
,
u
(
3
)
Su
b
j
ec
ted
to
g
x
,
u
0
(
4
)
,
0
h
x
u
(
5
)
w
h
er
e:
F
r
ep
r
esen
ts
th
e
o
b
j
ec
t
iv
e
f
u
n
c
tio
n
,
r
ep
r
esen
ts
th
e
v
ec
to
r
o
f
th
e
s
tate
v
ar
iab
les
an
d
r
ep
r
esen
ts
th
e
v
ec
to
r
o
f
th
e
co
n
tr
o
l
v
ar
iab
les.
3
.
2
.
O
bje
c
t
iv
e
f
un
ct
io
n
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
i
n
th
is
s
tu
d
y
i
s
t
h
e
q
u
ad
r
atic
eq
u
atio
n
o
f
g
e
n
er
atio
n
f
u
el
co
s
t
o
f
ea
c
h
av
ailab
le
co
n
v
en
t
io
n
al
g
en
er
at
o
r
s
u
b
j
ec
t to
o
p
er
atin
g
co
n
s
tr
a
in
ts
a
n
d
f
o
r
m
u
lated
as
f
o
llo
w
s
:
2
1
NG
t
G
i
i
i
G
i
i
G
i
i
C
P
a
b
P
c
P
(
6
)
w
h
er
e
(
)
is
th
e
f
u
el
co
s
t
o
f
t
h
e
th
g
e
n
er
ato
r
,
is
th
e
ac
ti
v
e
p
o
w
er
g
e
n
er
ated
b
y
t
h
e
th
er
m
a
l
g
en
er
ato
r
s
,
,
an
d
ar
e
th
e
co
s
t
co
ef
f
icie
n
t
s
o
f
th
g
e
n
er
ato
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
I
n
t J
A
r
ti
f
I
n
tell
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
20
2
0
:
252
–
2
6
0
254
E
q
u
alit
y
co
n
s
tr
ai
n
ts
:
T
h
e
eq
u
alit
y
co
n
s
tr
ain
t
s
r
ep
r
esen
t t
h
e
f
lo
w
eq
u
atio
n
s
o
f
t
h
e
b
alan
ce
d
p
o
w
er
s
as
f
o
llo
w
s
:
1
c
os
si
n
ii
N
G
d
i
j
ij
ij
ij
ij
j
P
P
V
V
g
z
(
7
)
1
sin
c
os
ii
N
G
d
i
j
ij
ij
ij
ij
j
Q
Q
V
V
g
z
(
8
)
I
n
eq
u
alit
y
co
n
s
tr
ain
t
s:
T
h
e
eq
u
alit
y
co
n
s
tr
ai
n
ts
r
ep
r
e
s
en
t
th
e
l
i
m
its
o
f
v
ar
iab
le
co
n
t
r
o
l
an
d
s
tate
co
n
tr
o
l
o
f
th
e
p
o
w
er
s
y
s
te
m
an
d
ca
n
b
e
g
iv
e
n
as f
o
llo
w
s
:
m
in
m
ax
G
i
G
i
G
i
m
in
m
ax
G
i
G
i
G
i
m
in
m
ax
G
i
G
i
G
i
m
in
m
ax
N
Ti
N
Ti
N
Ti
m
in
m
ax
SV
C
i
SV
C
i
SV
C
i
m
ax
Li
Li
P
P
P
Q
Q
Q
V
V
V
T
T
T
QQQ
SS
(
9
)
T
h
e
v
ec
to
r
s
o
f
co
n
tr
o
l
v
ar
iab
l
es
1
an
d
2
ar
e
r
esp
ec
tiv
el
y
th
e
c
ases
w
it
h
o
u
t
a
n
d
w
it
h
th
e
p
r
e
s
en
ce
o
f
SVC
d
e
v
ices o
n
t
h
e
p
o
w
er
s
y
s
te
m
,
a
n
d
ca
n
b
e
d
e
s
cr
ib
ed
as f
o
llo
w
s
:
12
G
G
N
G
u
PP
(
10
)
2
2
1
1
,
,
G
G
N
G
G
G
N
G
S
V
C
N
S
V
C
P
P
V
V
Q
u
Q
(
11
)
W
h
er
e:
ar
e
th
e
ac
t
iv
e
p
o
w
e
r
s
g
e
n
er
ated
,
is
t
h
e
g
en
er
at
o
r
v
o
ltag
e
a
n
d
is
th
e
r
ea
cti
v
e
p
o
w
e
r
in
j
ec
ted
b
y
t
h
e
SV
C
d
ev
ice.
4.
T
H
E
AN
T
L
I
O
N
O
P
T
I
M
I
Z
AT
I
O
N
(
A
L
O
)
AL
G
O
RI
T
H
M
T
h
e
an
t
lio
n
o
p
ti
m
i
ze
r
(
AL
O
)
is
co
n
s
id
er
ed
as
t
h
e
m
o
s
t
r
ec
en
t
n
a
tu
r
e
-
i
n
s
p
i
r
ed
p
r
o
p
o
s
e
d
b
y
[
2
1
]
.
T
h
e
m
o
d
elin
g
o
f
t
h
e
AL
O
alg
o
r
ith
m
b
ased
o
n
th
e
h
u
n
ti
n
g
m
ec
h
a
n
i
s
m
o
f
an
tlio
n
s
i
n
n
atu
r
e
.
T
h
e
m
a
in
o
b
j
ec
tiv
e
o
f
th
e
AL
O
alg
o
r
it
h
m
is
to
s
o
lv
e
an
y
o
p
ti
m
izat
io
n
p
r
o
b
lem
s
o
f
co
n
s
tr
ai
n
ed
en
g
in
ee
r
i
n
g
,
it
ca
n
g
et
an
o
p
ti
m
al
s
o
l
u
tio
n
f
o
r
m
in
i
m
izi
n
g
th
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
b
y
s
at
is
f
y
in
g
v
ar
io
u
s
co
n
s
t
r
ain
ts
.
I
n
t
h
e
AL
O
m
ec
h
a
n
i
s
m
,
it
ca
n
be
h
u
n
ti
n
g
th
e
p
r
e
y
(
an
t)
th
r
o
u
g
h
f
i
v
e
m
a
in
s
tep
s
as
f
o
llo
w
;
r
an
d
o
m
w
a
lk
o
f
an
t
s
,
b
u
ild
in
g
tr
ap
s
,
tr
ap
p
in
g
i
n
an
t
lio
n
s
tr
ap
s
,
s
lid
i
n
g
p
r
e
y
to
w
ar
d
a
n
tlio
n
an
d
f
i
n
al
s
tep
ar
e
c
atch
i
n
g
p
r
e
y
s
a
n
d
r
eb
u
ild
in
g
tr
ap
s
f
o
r
a
n
e
w
s
tep
o
f
h
u
n
ti
n
g
.
T
h
e
AL
O
m
et
h
o
d
m
i
m
ics
t
h
e
h
u
n
ti
n
g
b
eh
a
v
io
r
o
f
an
t
lio
n
s
,
th
e
e
x
p
r
ess
io
n
m
a
th
e
m
atic
all
y
o
f
th
e
r
an
d
o
m
w
alk
s
o
f
a
n
t
s
to
d
etec
t
th
e
lo
ca
tio
n
o
f
f
o
o
d
is
d
escr
ib
es a
s
f
o
llo
w
:
12
0
,
2
1
,
2
1
,
,
2
1
n
X
t
c
u
m
s
u
r
t
c
u
m
s
u
r
t
c
u
m
s
u
r
t
(
12
)
w
h
er
e
d
en
o
tes
th
e
r
an
d
o
m
walk
s
o
f
an
t
s
,
is
th
e
cu
m
u
lati
v
e
s
u
m
,
is
th
e
s
tep
o
f
r
a
n
d
o
m
w
al
k
,
is
th
e
m
a
x
i
m
u
m
iter
atio
n
s
an
d
(
)
s
h
o
w
th
e
s
to
ch
as
tic
f
u
n
ctio
n
a
n
d
g
iv
e
n
as
f
o
llo
w
s
:
1
0.
5
0
0.
5
if
ra
nd
rt
if
ra
nd
(
13
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
r
ti
f
I
n
tell
I
SS
N:
2252
-
8938
OP
F
fo
r
la
r
g
e
s
ca
le
p
o
w
er sys
tem
u
s
in
g
a
n
t lio
n
o
p
timiz
a
tio
n
:
a
c
a
s
e
s
tu
d
y
o
f th
e
.
.
.
(
R
a
mzi
K
o
u
a
d
r
i
)
255
w
h
er
e
r
ep
r
esen
ts
a
r
an
d
o
m
l
y
n
u
m
b
er
u
n
i
f
o
r
m
l
y
d
is
tr
ib
u
ted
in
th
e
r
a
n
g
e
o
f
[
0
,
1
]
.
T
h
e
Deta
ils
o
f
d
if
f
er
en
t
s
tep
s
d
escr
ib
e
th
e
r
elatio
n
s
h
ip
b
et
w
ee
n
p
r
ed
ato
r
s
an
d
p
r
ey
s
i
n
th
e
AL
O
m
et
h
o
d
ar
e
ex
p
lain
ed
as f
o
llo
w
:
4
.
1
.
R
a
nd
o
m
w
a
lk
o
f
a
nts
I
n
ev
er
y
s
tep
o
f
o
p
ti
m
izatio
n
in
t
h
e
AL
O
al
g
o
r
ith
m
,
a
n
ts
m
o
v
e
r
a
n
d
o
m
l
y
i
n
s
id
e
th
e
b
o
u
n
d
ar
ies
o
f
th
e
s
ea
r
ch
s
p
ac
e
b
ased
o
n
th
e
(
1
4
)
,
th
e
r
an
d
o
m
w
al
k
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o
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ts
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e
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y
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s
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g
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llo
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:
*
t
t
t
i
i
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i
tt
ii
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a
b
c
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ba
(
14
)
w
h
er
e
th
e
;
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en
o
tes
th
e
m
in
i
m
u
m
a
n
d
m
ax
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m
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r
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m
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ax
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ℎ
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ℎ
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n
.
4
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2
.
T
ra
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ing
in a
ntlio
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ra
ps
T
h
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d
o
m
w
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k
s
o
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an
t
s
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e
in
f
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ce
d
by
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tlio
n
s
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ap
s
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d
ar
e
m
o
d
eled
as f
o
llo
w
s
:
t
t
t
ij
c
A
n
tli
o
n
c
(
15
)
t
t
t
ij
d
A
n
tli
o
n
d
(
16
)
4
.
3
.
B
uil
din
g
t
ra
ps
I
n
th
i
s
w
o
r
k
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t
h
e
AL
O
al
g
o
r
it
h
m
is
r
eq
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ir
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e
a
r
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l
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elec
tio
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ato
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o
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th
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ased
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ig
h
er
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i
tn
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s
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o
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h
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g
h
c
h
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ce
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o
r
ca
tch
i
n
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an
t
s
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4
.
4
.
Sli
din
g
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nts t
o
w
a
rd
a
ntl
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n
W
h
en
t
h
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e
to
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r
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ce
n
ter
o
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h
e
p
it.
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wev
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n
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t
lio
n
s
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lize
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h
at
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a
n
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ap
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o
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t
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ter
o
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it.
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o
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ec
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at
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t
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s
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ec
r
ea
s
ed
co
r
r
esp
o
n
d
in
g
l
y
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s
in
g
(
1
7
)
an
d
(
1
8
)
:
t
t
c
c
I
(
17
)
t
t
d
d
I
(
18
)
4
.
5
.
Ca
t
ching
prey
s
a
nd
re
bu
ild
i
ng
t
he
t
ra
ps
T
h
e
f
in
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l
s
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o
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h
u
n
ti
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g
is
wh
en
th
e
p
r
e
y
r
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ch
e
s
i
n
to
t
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e
b
o
tt
o
m
o
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tlio
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s
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h
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t
lio
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w
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ter
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ag
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n
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lls
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tlio
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ate
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t
t
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j
An
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t
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(
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litis
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n
t
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escr
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at
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n
:
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tt
t
AE
i
RR
A
n
t
(
20
)
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–
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256
w
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5.
RE
SU
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Fi
g
u
r
e
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.
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u
r
e
1
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e
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t
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.
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.
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f
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r
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3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
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ti
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I
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tell
I
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N:
2252
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8938
OP
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fo
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.
(
R
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257
T
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1
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th
e
ca
s
e
w
it
h
o
u
t
a
n
d
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it
h
S
V
C
d
ev
ice
s
,
s
ep
ar
a
t
e
l
y
o
r
m
u
lti
p
le
in
b
u
s
es
N°
6
8
an
d
N°
89.
Fro
m
t
h
ese
r
es
u
lt
s
o
b
tain
ed
,
it
ca
n
b
e
o
b
s
er
v
ed
th
at
t
h
e
p
r
esen
ce
o
f
SVC
d
e
v
i
c
es
in
all
ca
s
es
i
m
p
r
o
v
ed
co
n
s
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ab
ly
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e
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s
s
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h
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o
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ce
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ed
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g
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ith
m
is
s
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o
w
n
i
n
F
ig
u
r
e
4
.
Fro
m
th
is
f
i
g
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r
e,
w
e
n
o
tice
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h
at
t
h
e
al
g
o
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ith
m
AL
O
co
n
v
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d
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o
p
ti
m
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m
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t
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e
iter
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1
0
0
f
o
r
all
ca
s
es st
u
d
y
w
h
e
n
th
e
S
VC
d
e
v
ices i
n
s
ta
lled
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Fig
u
r
e
4
.
C
o
n
v
er
g
en
ce
p
lo
t
of
AL
O
m
et
h
o
d
s
in
t
h
e
A
l
g
er
ian
1
1
4
b
u
s
p
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y
s
te
m
On
t
h
e
o
th
er
h
a
n
d
,
SV
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d
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ic
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h
a
v
e
m
a
n
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g
ed
to
i
m
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e
t
h
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v
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lta
g
e
p
r
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f
ile
as
s
h
o
w
n
i
n
F
ig
u
r
e
5
,
f
r
o
m
t
h
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ig
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r
e
,
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ca
n
b
e
n
o
ted
th
at
th
e
ca
s
e
w
it
h
o
u
t
th
e
p
r
esen
c
e
o
f
SV
C
,
th
e
t
w
o
cir
cles
in
t
h
is
f
i
g
u
r
e
d
eter
m
in
e
t
h
e
t
w
o
ar
ea
s
th
at
h
av
e
cr
itical
lo
ad
b
u
s
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o
ltag
e
in
A
lg
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1
1
4
-
b
u
s
s
y
s
te
m
.
So
,
w
h
en
t
h
e
SV
C
20
40
60
80
100
120
140
160
180
200
1
.
9
1
.
9
5
2
2
.
0
5
2
.
1
2
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1
5
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0
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N
b
r
o
f
I
t
e
ra
t
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o
n
F
u
e
l
c
o
s
t
($
/
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r)
W
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t
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o
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t
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V
C
S
V
C
a
t
6
8
S
V
C
a
t
8
9
S
V
C
a
t
6
8
&
8
9
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
r
ti
f
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n
tell
I
SS
N:
2252
-
8938
OP
F
fo
r
la
r
g
e
s
ca
le
p
o
w
er sys
tem
u
s
in
g
a
n
t lio
n
o
p
timiz
a
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n
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a
c
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s
e
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tu
d
y
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f th
e
.
.
.
(
R
a
mzi
K
o
u
a
d
r
i
)
259
d
ev
ices
w
er
e
in
s
talled
at
b
u
s
s
es
6
8
an
d
8
9
s
ep
ar
a
t
e
l
y
o
r
m
u
ltip
le,
t
h
e
v
o
ltag
e
v
al
u
es
o
f
th
i
s
o
p
ti
m
al
e
m
p
lace
m
e
n
t
w
er
e
in
cr
e
ased
t
o
1
p
.
u
as
s
h
o
w
n
i
n
Fi
g
u
r
e
5
,
r
esp
ec
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el
y
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F
u
r
th
er
m
o
r
e,
t
h
is
in
cr
e
m
e
n
t
i
n
t
h
e
v
o
ltag
e
v
al
u
es
in
t
h
e
o
p
ti
m
al
p
lace
m
en
t
o
f
S
VC
al
lo
w
s
f
o
r
i
m
p
r
o
v
i
n
g
th
e
v
o
lta
g
e
at
t
h
e
cr
i
tical
lo
ad
b
u
s
es
co
m
p
ar
ed
to
th
e
p
r
ev
io
u
s
ca
s
e
(
w
it
h
o
u
t
t
h
e
p
r
esen
ce
o
f
SVC
d
ev
ice
)
.
Fig
u
r
e
5
.
T
h
e
ef
f
ec
t o
f
SV
C
d
ev
ice
o
n
t
h
e
v
o
lta
g
e
p
r
o
f
ile
in
th
e
A
l
g
er
ian
114
-
b
u
s
p
o
w
er
s
y
s
te
m
6.
CO
NCLU
SI
O
N
I
n
th
i
s
p
ap
er
,
w
e
h
av
e
v
alid
ate
d
th
e
n
e
w
m
etah
e
u
r
is
t
ic
tech
n
i
q
u
e
,
ca
lled
,
A
n
t
L
io
n
Op
ti
m
iz
er
(
A
L
O)
f
o
r
r
ea
l
an
d
lar
g
e
s
ca
le
A
l
g
er
ian
114
-
b
u
s
p
o
w
er
s
y
s
te
m
to
s
o
lv
e
o
p
ti
m
al
p
o
w
er
f
lo
w
(
OR
F
)
p
r
o
b
le
m
.
T
h
e
AL
O
alg
o
r
it
h
m
w
a
s
s
u
cc
es
s
f
u
ll
y
ap
p
lied
to
s
o
l
v
e
t
h
e
OP
F
p
r
o
b
lem
w
it
h
an
d
w
it
h
o
u
t
SV
C
d
ev
ice
s
.
Fro
m
t
h
e
r
esu
lt
s
o
b
tain
ed
in
t
h
e
ca
s
e
w
it
h
o
u
t
t
h
e
S
VC
d
ev
ice,
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
h
a
s
b
ee
n
th
e
b
est
r
es
u
lt
co
m
p
ar
ed
w
it
h
t
h
e
m
e
th
o
d
d
ev
elo
p
ed
b
y
u
s
,
ca
lled
,
g
r
e
y
w
o
lf
o
p
ti
m
izatio
n
an
d
o
t
h
er
m
eth
o
d
s
i
n
t
h
e
liter
atu
r
e
d
e
f
in
ed
in
th
is
p
ap
er
,
lik
e
DE
,
G
A
-
ED
-
PS
,
an
d
O
P
.
I
n
th
e
ca
s
e
w
i
th
t
h
e
p
r
ese
n
ce
o
f
S
VC
d
ev
ice
s
,
th
e
AL
O
al
g
o
r
ith
m
w
as
u
s
ed
to
id
en
t
if
y
th
e
o
p
ti
m
al
s
izi
n
g
a
n
d
p
lace
m
e
n
t
o
f
SV
C
d
e
v
ice
s
i
n
t
h
e
A
l
g
er
ian
114
-
b
u
s
s
y
s
te
m
b
a
s
ed
on
t
h
e
l
o
ca
tio
n
o
f
t
h
e
lo
w
e
s
t
v
o
ltag
e
l
o
ad
b
u
s
es
i
n
t
h
e
p
o
w
er
s
y
s
te
m
.
T
h
e
o
p
tim
iza
tio
n
r
esu
lt
s
ac
h
ie
v
ed
b
y
u
s
i
n
g
th
e
AL
O
al
g
o
r
ith
m
w
i
th
p
r
ese
n
ce
th
e
o
f
SVC
d
e
v
ices
g
i
v
en
th
e
b
est
r
es
u
lt
s
to
m
i
n
i
m
ize
th
e
to
tal
f
u
el
co
s
t
,
r
ed
u
ce
th
e
ac
tiv
e
p
o
w
er
lo
s
s
es
an
d
i
m
p
r
o
v
in
g
th
e
v
o
ltag
e
p
r
o
f
ile
b
ased
on
th
e
o
p
tim
a
l
p
lace
m
e
n
t
an
d
s
izin
g
o
f
SVC
d
e
v
ice
s
.
B
ased
o
n
th
e
r
esu
lts
o
f
b
o
th
ca
s
e
s
t
u
d
ies
i
n
th
is
p
ap
er
,
it
ca
n
b
e
co
n
clu
d
ed
th
a
t
t
h
e
AL
O
a
l
g
o
r
ith
m
i
s
ca
p
ab
le
o
f
s
o
lv
i
n
g
th
e
OP
F
p
r
o
b
le
m
fo
r
a
lar
g
e
s
ca
le
p
o
w
er
s
y
s
te
m
w
it
h
a
n
d
w
ith
o
u
t
th
e
p
r
ese
n
ce
o
f
SVC
d
e
v
ices.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
e
au
th
o
r
s
w
o
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ld
li
k
e
to
a
ck
n
o
w
led
g
e
t
h
e
R
esear
c
h
M
an
ag
e
m
e
n
t
(
R
MC)
UiT
M
Sh
ah
A
la
m
,
Selan
g
o
r
,
Ma
la
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a
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in
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E
d
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ca
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n
,
Ma
la
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(
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f
o
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f
in
a
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ci
al
s
u
p
p
o
r
t
o
f
th
is
r
esear
ch
.
T
h
is
r
esear
ch
is
s
u
p
p
o
r
ted
b
y
MO
E
u
n
d
er
F
u
n
d
a
m
en
tal
R
e
s
ea
r
ch
Gr
an
t Sc
h
e
m
e
(
FR
G
S)
w
it
h
p
r
o
j
ec
t c
o
d
e:
600
-
I
R
MI
/FR
G
S 5
/3
(
0
8
2
/
2
0
1
9
)
.
RE
F
E
R
E
NC
E
S
[1
]
J.
Ca
rp
e
n
ti
e
r.
C
o
n
tr
ib
u
ti
o
n
t
o
t
h
e
e
c
o
n
o
m
ic d
isp
a
tch
p
r
o
b
lem
.
Bu
ll
S
o
c
Fmn
c
Ef
e
c
i
,
v
o
l.
3
,
p
p
.
4
3
1
–
4
4
7
,
1
9
6
2
.
[2
]
M
.
Eb
e
e
d
,
S
.
Ka
m
e
l,
a
n
d
F
.
Ju
ra
d
o
,
Op
t
ima
l
p
o
we
r fl
o
w
u
sin
g
re
c
e
n
t
o
p
ti
miz
a
ti
o
n
tec
h
n
iq
u
e
s
.
El
se
v
ier In
c
.
,
2
0
1
8
.
[3
]
K.
Tee
p
a
rth
i
a
n
d
D.
M
.
V
in
o
d
Ku
m
a
r.
M
u
lt
i
-
o
b
jec
ti
v
e
h
y
b
rid
P
S
O
-
A
P
O
a
lg
o
rit
h
m
b
a
s
e
d
se
c
u
rit
y
c
o
n
stra
in
e
d
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
w
it
h
w
in
d
a
n
d
th
e
rm
a
l
g
e
n
e
ra
to
rs
.
En
g
.
S
c
i.
T
e
c
h
n
o
l
.
a
n
I
n
t.
J
.
,
v
o
l
.
2
0
,
n
o
.
2
,
p
p
.
4
1
1
–
4
2
6
,
2
0
1
7
.
[4
]
I.
N.
T
ri
v
e
d
i,
P
.
Ja
n
g
ir,
S
.
A
.
P
a
rm
a
r,
a
n
d
N
.
Ja
n
g
ir
.
Op
ti
m
a
l
p
o
we
r
f
lo
w
w
it
h
v
o
lt
a
g
e
sta
b
il
it
y
i
m
p
ro
v
e
m
e
n
t
a
n
d
lo
ss
re
d
u
c
ti
o
n
i
n
p
o
w
e
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s
y
s
te
m
u
s
in
g
M
o
t
h
-
F
lam
e
Op
ti
m
iz
e
r.
Ne
u
ra
l
Co
m
p
u
t
.
Ap
p
l.
,
v
o
l.
3
0
,
n
o
.
6
,
p
p
.
1
8
8
9
–
1
9
0
4
,
2
0
1
8
.
[5
]
A
.
M
u
k
h
e
rjee
a
n
d
V
.
M
u
k
h
e
rjee
.
S
o
l
u
ti
o
n
o
f
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
w
it
h
F
A
C
T
S
d
e
v
ice
s
u
sin
g
a
n
o
v
e
l
o
p
p
o
siti
o
n
a
l
0,
85
0,
9
0,
95
1
1,
05
1,
1
1,
15
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
64
67
70
73
76
79
82
85
88
91
94
97
100
103
106
109
112
Vo
l
t
ag
e
p
r
o
f
i
l
e
(
pu
)
B
us
N
°
W
i
t
ho
ut
S
VC
S
V
C
N
°
68
S
V
C
N
°
89
S
V
C
N
°
68
& 89
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
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8938
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A
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l.
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No
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2
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u
n
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–
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260
k
ril
l
h
e
rd
a
lg
o
rit
h
m
.
In
t.
J
.
El
e
c
tr.
Po
we
r E
n
e
rg
y
S
y
st.
,
v
o
l
.
7
8
,
p
p
.
7
0
0
–
7
1
4
,
2
0
1
6
.
[6
]
J.
Ra
d
o
sa
v
lj
e
v
ic.
M
e
tah
e
u
risti
c
Op
t
im
iza
ti
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