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,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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,
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PQ
(
1
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)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
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I
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&
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3
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–
1431
1426
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3.
CRO
W
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A
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AL
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M
C
r
o
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s
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C
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s
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r
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s
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a
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ar
k
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le
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lik
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le
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-
s
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n
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s
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s
,
co
m
m
u
n
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s
k
ill
s
an
d
ad
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tab
ilit
y
.
C
r
o
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s
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e
k
n
o
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n
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it
s
e
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m
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m
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y
,
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b
eh
a
v
io
r
o
f
cr
o
w
s
i
s
en
l
is
t
ed
[
2
3
]
,
a.
C
r
o
w
s
liv
e
i
n
g
r
o
u
p
s
b.
C
r
o
w
s
h
a
v
e
ex
ce
l
len
t
m
e
m
o
r
y
o
n
th
eir
p
o
s
itio
n
o
f
h
id
d
en
p
l
ac
es
c.
C
r
o
w
s
f
o
llo
w
s
ea
c
h
o
th
er
to
p
er
f
o
r
m
ac
ts
o
f
t
h
ie
v
is
h
n
es
s
d.
C
r
o
w
s
h
id
e
t
h
eir
co
llectiv
e
s
th
at
h
av
e
b
ee
n
t
h
e
f
t
C
r
o
w
Sear
c
h
A
l
g
o
r
ith
m
(
C
S
A
)
is
d
e
v
elo
p
ed
b
ased
o
n
th
e
ab
o
v
e
n
atu
r
e
a
n
d
b
eh
av
io
r
o
f
cr
o
w
s
.
T
h
e
alg
o
r
ith
m
h
a
s
d
-
d
i
m
e
n
s
io
n
al
e
n
v
ir
o
n
m
e
n
t
w
it
h
N
n
u
m
b
er
o
f
cr
o
w
s
an
d
th
e
p
o
s
itio
n
o
f
cr
o
w
s
(
k
i
X
)
w
h
ic
h
ca
n
b
e
s
p
ec
if
ied
b
y
a
v
ec
to
r
,
]
,....,
,
[
,
2
,
1
,
d
k
i
k
i
k
i
k
i
X
X
X
X
(
1
9
)
w
h
er
e
1
,
2
,
.
.
.
,
iN
;
m
a
x
1
,
2
,
.
.
.
,
k
i
t
e
r
;
m
a
x
i
t
e
r
is
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
I
n
ac
co
r
d
an
ce
w
it
h
its
m
e
m
o
r
y
ca
p
ac
it
y
,
th
e
al
g
o
r
ith
m
p
r
o
ce
ed
s
as,
at
k
th
iter
atio
n
,
th
e
p
o
s
itio
n
o
f
h
id
in
g
p
lace
o
f
i
th
cr
o
w
is
g
iv
en
b
y
,
M
i
k
.
Fo
r
b
etter
illu
s
tr
at
io
n
,
ass
u
m
e
t
h
at
j
th
cr
o
w
w
a
n
t
s
to
v
is
it
it
s
h
id
i
n
g
p
lace
at
k
th
iter
atio
n
,
at
t
h
i
s
in
s
tan
t
o
f
iter
atio
n
,
i
th
cr
o
w
f
o
ll
o
w
s
j
th
cr
o
w
to
k
n
o
w
its
h
id
d
en
p
lace
,
h
er
e
t
h
er
e
ar
e
t
w
o
p
o
s
s
ib
ilit
ie
s
,
P
o
s
s
ib
ilit
y
1
:
T
h
e
cr
o
w
j
b
ei
n
g
u
n
a
w
ar
e
o
f
cr
o
w
i
,
s
h
o
w
s
its
h
id
d
en
p
lace
,
h
en
ce
at
t
h
is
in
s
ta
n
t
th
e
n
e
w
p
o
s
itio
n
o
f
cr
o
w
i
b
ec
o
m
e,
)
(
1
i
t
e
r
i
i
t
e
r
i
i
t
e
r
i
i
i
t
e
r
i
i
t
e
r
i
X
M
fl
r
X
X
(
2
0
)
w
h
er
e
r
i
is
a
r
an
d
o
m
n
u
m
b
er
w
it
h
u
n
i
f
o
r
m
d
is
tr
ib
u
tio
n
b
e
t
w
ee
n
0
an
d
1
,
fl
i
iter
d
en
o
tes
t
h
e
f
l
ig
h
t
le
n
g
t
h
o
f
cr
o
w
i
at
iter
atio
n
i
ter
.
T
h
e
v
a
lu
e
o
f
fl
h
as
g
r
ea
t
i
m
p
ac
t
o
n
t
h
e
s
ea
r
c
h
s
p
ac
e
o
f
t
h
e
al
g
o
r
ith
m
,
i
f
fl
is
a
s
m
aller
v
alu
e
t
h
a
n
it r
es
u
lts
i
n
lo
ca
l se
ar
ch
an
d
if
fl
i
s
a
lar
g
er
v
al
u
e
i
t r
esu
lt
s
in
g
lo
b
al
s
ea
r
ch
.
P
o
s
s
ib
ilit
y
2
:
T
h
e
cr
o
w
j
a
w
ar
e
o
f
cr
o
w
i
th
at
it is
f
o
llo
w
i
n
g
it,
in
o
r
d
er
,
h
en
ce
to
p
r
o
t
ec
t it
s
co
llect
f
r
o
m
cr
o
w
i
,
cr
o
w
j
w
i
ll
m
o
v
e
to
an
o
t
h
er
p
o
s
itio
n
to
d
iv
er
t c
r
o
w
j
,
th
e
n
th
e
n
e
w
p
o
s
it
io
n
is
t
h
u
s
g
iv
e
n
b
y
,
o
t
h
e
r
w
i
s
e
p
o
s
i
t
i
o
n
r
a
n
d
o
m
a
AP
r
X
M
fl
r
X
X
ite
r
j
j
ite
r
i
ite
r
j
ite
r
i
i
ite
r
i
ite
r
i
)
(
1
(
2
1
)
w
h
er
e
AP
j
iter
d
en
o
te
s
th
e
a
w
a
r
en
ess
p
r
o
b
ab
ilit
y
o
f
cr
o
w
j
at
iter
atio
n
iter
.
T
h
is
f
ac
to
r
d
ec
id
es
w
h
eth
er
t
h
e
s
ea
r
ch
s
p
ac
e
is
i
n
te
n
s
i
f
ied
o
r
d
iv
er
s
i
f
ied
.
W
h
e
n
AP
i
s
i
n
c
r
ea
s
ed
,
th
e
s
ea
r
c
h
s
p
ac
e
g
et
s
in
cr
ea
s
ed
t
h
er
eb
y
,
r
esu
lt
s
in
g
lo
b
al
o
p
ti
m
al
an
d
v
ice
v
er
s
a.
4.
AP
P
L
I
CA
T
I
O
N
O
F
CRO
W
SE
ARCH
A
L
G
O
RI
T
H
M
F
O
R
O
RP
D
P
RO
B
L
E
M
T
h
e
s
eq
u
en
ce
o
f
s
tep
s
th
at
o
u
g
h
t
to
b
e
f
o
llo
w
ed
in
th
e
i
m
p
le
m
e
n
tatio
n
o
f
t
h
e
C
S
A
i
s
g
i
v
en
in
t
h
i
s
s
ec
tio
n
.
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:
2
0
8
8
-
8708
O
p
tima
l R
ea
ctive
P
o
w
er Disp
a
tch
u
s
in
g
C
r
o
w
S
ea
r
ch
A
lg
o
r
ith
m
(
La
ksh
mi
M
)
1427
Ste
p 1
:
I
nitia
liza
t
io
n o
f
a
lg
o
r
it
h
m
pa
ra
m
et
er
s
a
nd
co
ns
t
r
a
ints
T
h
e
alg
o
r
ith
m
p
ar
a
m
eter
s
co
m
p
r
i
s
es
o
f
p
o
p
u
latio
n
s
ize
(
N
)
,
m
ax
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
(
ite
r
max
)
,
f
li
g
h
t
le
n
g
t
h
(
fl
)
a
n
d
a
w
ar
e
n
es
s
p
r
o
b
ab
ilit
y
(
AP
)
an
d
t
h
e
co
n
s
tr
ain
t
s
i
n
cl
u
d
e
p
o
w
e
r
b
alan
ce
eq
u
alit
y
co
n
s
tr
ain
ts
,
li
n
e
f
lo
w
a
n
d
v
o
lt
ag
e
co
n
s
tr
ai
n
t
s
.
Ste
p 2
:
I
nitia
liza
t
io
n o
f
t
he
p
o
s
it
io
n a
nd
m
e
m
o
ry
o
f
cr
o
ws
T
h
e
N
p
o
p
u
latio
n
o
f
cr
o
w
s
is
r
an
d
o
m
l
y
p
o
s
itio
n
ed
in
a
d
-
d
i
m
e
n
s
io
n
al
s
ea
r
c
h
s
p
ac
e.
E
ac
h
cr
o
w
d
en
o
tes
a
p
o
s
s
ib
ilit
y
o
f
f
ea
s
i
b
le
s
o
lu
tio
n
o
f
th
e
p
r
o
b
le
m
an
d
d
is
th
e
n
u
m
b
er
o
f
co
n
t
r
o
l
v
ar
iab
les
w
h
ic
h
in
cl
u
d
es
g
e
n
er
ato
r
v
o
ltag
es,
t
r
an
s
f
o
r
m
er
tap
s
ettin
g
s
a
n
d
r
ea
ctiv
e
p
o
w
er
o
u
tp
u
t
o
f
s
h
u
n
t
ca
p
ac
ito
r
.
T
h
e
m
e
m
o
r
y
o
f
ea
c
h
cr
o
w
i
s
i
n
it
iali
ze
d
.
A
t
t
h
e
b
eg
in
n
i
n
g
o
f
iter
atio
n
iter
,
i
t
is
a
s
s
u
m
ed
t
h
at
t
h
e
cr
o
w
s
h
a
v
e
h
id
d
en
th
e
ir
f
o
o
d
s
at
th
eir
i
n
iti
al
p
o
s
itio
n
s
.
Ste
p 3
:
E
v
a
lua
t
e
f
it
nes
s
(
o
bj
ec
t
iv
e)
f
un
ct
io
n
Fo
r
ea
ch
cr
o
w
,
th
e
p
o
s
itio
n
i
s
d
eter
m
in
ed
b
y
f
itti
n
g
th
e
c
o
n
tr
o
l
v
ar
iab
le
v
al
u
es
i
n
to
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
(
m
i
n
i
m
izatio
n
o
f
r
ea
l
p
o
w
er
lo
s
s
,
to
tal
v
o
lta
g
e
d
ev
i
atio
n
an
d
v
o
lta
g
e
s
tab
ili
t
y
i
n
d
i
ca
to
r
)
.
Ste
p 4
:
G
ener
a
t
e
new
po
s
it
io
n
C
r
o
w
s
f
i
n
d
s
a
n
e
w
p
o
s
i
tio
n
i
n
th
e
d
-
d
i
m
en
s
io
n
al
s
ea
r
ch
s
p
a
ce
b
y
as
f
o
llo
w
s
:
s
u
p
p
o
s
e
cr
o
w
i
w
a
n
ts
to
f
in
d
a
n
e
w
p
o
s
itio
n
.
Fo
r
th
i
s
,
th
e
cr
o
w
r
a
n
d
o
m
l
y
s
elec
t
s
o
n
e
o
f
th
e
cr
o
w
s
,
let
t
h
at
b
e
c
r
o
w
j
an
d
f
o
llo
w
s
it
to
d
is
co
v
er
t
h
e
P
o
s
itio
n
o
f
c
o
llectin
g
h
id
d
en
b
y
t
h
is
cr
o
w
(
m
j
)
.
T
h
e
n
e
w
p
o
s
itio
n
o
f
cr
o
w
i
i
s
g
iv
e
n
b
y
E
q
u
atio
n
s
(
20
)
an
d
(
21
)
.
Ste
p 5
:
Check
t
he
f
ea
s
i
bil
it
y
o
f
new
po
s
it
io
ns
T
h
e
v
iab
ilit
y
o
f
th
e
n
e
w
p
o
s
it
io
n
o
f
ea
ch
cr
o
w
th
u
s
o
b
tain
e
d
is
ch
ec
k
ed
an
d
t
h
e
p
o
s
itio
n
is
u
p
d
ated
b
ased
o
n
it.
I
f
th
e
n
e
w
p
o
s
itio
n
,
th
u
s
o
b
tain
ed
is
n
o
t
v
iab
le,
th
en
t
h
e
cr
o
w
d
s
ta
y
s
in
th
e
c
u
r
r
en
t
p
o
s
itio
n
an
d
d
o
es n
o
t
m
o
v
e
to
th
e
n
e
w
p
o
s
i
tio
n
f
o
u
n
d
.
Ste
p 6
:
E
v
a
lua
t
e
t
he
f
it
nes
s
f
un
ct
io
n o
f
new
po
s
it
io
ns
T
h
e
f
itn
e
s
s
f
u
n
ctio
n
i.e
.
o
b
j
ec
t
iv
e
f
u
n
ctio
n
v
al
u
e
f
o
r
th
e
n
e
w
p
o
s
itio
n
o
f
ea
ch
cr
o
w
is
e
v
alu
ated
.
Ste
p 7
:
Upda
t
e
m
e
m
o
ry
T
h
e
cr
o
w
s
u
p
d
ate
th
eir
m
e
m
o
r
y
as
f
o
llo
w
s
:
,
1
,
1
,
,1
,
(
)
(
)
i
i
t
e
r
i
i
t
e
r
i
i
t
e
r
i
i
t
e
r
i
i
t
e
r
x
f
x
is
b
e
tt
e
r
th
a
n
f
m
m
m
o
th
e
r
w
is
e
(
2
2
)
w
h
er
e
f
obj
d
en
o
tes th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
v
al
u
e.
I
t
is
s
ee
n
th
at
i
f
t
h
e
f
it
n
ess
f
u
n
ct
io
n
v
alu
e
o
f
th
e
n
e
w
p
o
s
itio
n
o
f
a
cr
o
w
is
b
etter
t
h
an
th
e
f
itn
e
s
s
f
u
n
ctio
n
v
al
u
e
o
f
t
h
e
m
e
m
o
r
iz
ed
p
o
s
itio
n
,
th
e
cr
o
w
u
p
d
ates i
ts
m
e
m
o
r
y
b
y
t
h
e
n
e
w
p
o
s
i
ti
o
n
.
Ste
p 8
:
Check
t
er
m
i
na
t
io
n c
rit
er
io
n
Step
s
4
to
7
ar
e
r
ep
ea
te
d
u
n
til
m
a
x
i
m
u
m
iter
atio
n
is
r
ea
ch
e
d
.
W
h
en
th
e
ter
m
in
a
tio
n
cr
iter
io
n
is
m
et,
th
e
b
es
t
p
o
s
itio
n
o
f
t
h
e
m
e
m
o
r
y
in
ter
m
s
o
f
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
v
al
u
e
i
s
r
ep
o
r
ted
as
th
e
s
o
lu
t
io
n
o
f
t
h
e
o
p
tim
iz
atio
n
p
r
o
b
le
m
.
5.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
N
T
h
e
p
r
esen
t
w
o
r
k
i
s
b
ein
g
tes
ted
o
n
s
tan
d
ar
d
I
E
E
E
-
3
0
,
5
7
an
d
1
1
8
b
u
s
s
y
s
te
m
s
an
d
t
h
e
r
esu
lt
s
ar
e
o
b
tain
ed
.
T
h
e
d
escr
ip
tio
n
o
f
th
ese
s
tu
d
ied
test
s
y
s
te
m
s
is
d
ep
icted
b
elo
w
.
T
h
e
s
o
f
t
w
ar
e
is
w
r
it
ten
i
n
MA
T
L
A
B
R
2
0
1
5
co
m
p
u
tin
g
en
v
ir
o
n
m
e
n
t.
T
h
e
v
ar
io
u
s
al
g
o
r
ith
m
p
ar
a
m
eter
s
ar
e
in
itializ
ed
an
d
ar
e
s
et
to
b
e
as:
T
h
e
v
al
u
e
o
f
f
lo
ck
s
ize
(
p
o
p
u
latio
n
)
is
s
et
to
7
5
,
th
e
a
war
en
ess
p
r
o
b
ab
ilit
y
in
d
e
x
d
ete
r
m
in
e
s
w
h
et
h
er
t
h
e
s
ea
r
ch
s
p
ac
e
is
in
te
n
s
if
ied
o
r
d
iv
er
s
if
ied
an
d
is
s
et
to
0
.
5
,
th
e
f
li
g
h
t
le
n
g
th
is
a
s
s
u
m
e
d
to
b
e
2
an
d
th
e
m
ax
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
p
er
f
o
r
m
ed
is
s
et
to
2
0
0
f
o
r
a
ll
th
e
test
ca
s
es
co
n
s
id
er
ed
.
T
h
e
r
esu
lts
o
f
in
ter
est
ar
e
b
o
ld
f
ac
ed
in
th
e
r
esp
ec
tiv
e
tab
les to
in
d
icate
th
e
o
p
ti
m
iza
tio
n
ca
p
ab
ilit
y
o
f
t
h
e
p
r
o
p
o
s
ed
a
lg
o
r
ith
m
.
5
.
1
.
Ca
s
e
-
1
:
M
ini
m
iza
t
io
n r
ea
l p
o
w
er
l
o
s
s
I
n
th
i
s
ca
s
e,
th
e
p
r
o
p
o
s
ed
al
g
o
r
ith
m
is
ex
ec
u
ted
co
n
s
id
er
in
g
t
h
e
m
i
n
i
m
izat
io
n
o
f
r
ea
l
p
o
w
er
lo
s
s
alo
n
e
as
t
h
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
.
T
h
e
co
n
v
er
g
en
ce
c
h
ar
ac
ter
is
tic
o
f
th
e
al
g
o
r
ith
m
co
n
s
id
e
r
in
g
t
h
e
r
ea
l
p
o
w
er
lo
s
s
is
s
h
o
w
n
in
Fig
u
r
e
1
,
w
h
ich
in
d
icate
s
f
a
s
t
an
d
s
m
o
o
th
co
n
v
er
g
e
n
ce
o
f
C
S
A
.
T
h
e
s
u
p
er
io
r
it
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h
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o
r
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C
S
A
b
ased
ap
p
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ch
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r
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o
lv
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n
g
OR
P
D
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r
o
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le
m
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e
w
it
n
ess
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r
o
m
th
e
co
m
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ar
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ad
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b
et
w
ee
n
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th
er
o
p
ti
m
izatio
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t
ec
h
n
iq
u
es
f
r
o
m
T
ab
le
1
,
T
ab
le
2
an
d
T
ab
le
3.
T
h
e
b
est
p
o
w
er
lo
s
s
o
b
tai
n
ed
u
s
i
n
g
C
S
A
f
o
r
I
E
E
E
3
0
,
5
7
an
d
1
1
8
b
u
s
s
y
s
te
m
s
ar
e
2
.
8
5
0
7
MW
,
1
5
.
1
9
3
4
MW
an
d
7
6
.
7
7
8
3
MW
r
esp
ec
tiv
el
y
,
w
h
ic
h
is
le
s
s
er
t
h
an
r
esu
l
t r
ep
o
r
ted
in
[
1
2
]
,
[
14
]
,
[
19
]
,
[
2
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
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&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
3
,
J
u
n
e
2
0
1
8
:
1
4
2
3
–
1431
1428
T
ab
le
1
.
C
o
m
p
ar
is
o
n
o
f
r
esu
l
t
s
f
o
r
m
i
n
i
m
izatio
n
o
f
ac
ti
v
e
p
o
w
er
lo
s
s
f
o
r
I
E
E
E
-
3
0
b
u
s
s
y
s
te
m
M
e
t
h
o
d
o
l
o
g
y
C
S
A
C
L
P
S
O
[
1
4
]
G
S
A
[
2
1
]
P
o
w
e
r
l
o
ss (M
W
)
2
.
8
5
0
7
4
.
5
6
1
5
4
.
5
1
4
3
T
ab
le
2
.
C
o
m
p
ar
is
o
n
o
f
r
esu
l
t
s
f
o
r
I
E
E
E
5
7
-
b
u
s
s
y
s
te
m
M
e
t
h
o
d
o
l
o
g
y
C
S
A
C
L
P
S
O
[
1
4
]
S
O
A
[
1
9
]
G
S
A
[
2
1
]
P
o
w
e
r
l
o
ss (M
W
)
1
5
.
1
9
3
4
2
4
.
5
1
5
2
2
4
.
2
6
5
4
2
3
.
4
6
11
T
ab
le
3
.
C
o
m
p
ar
is
o
n
o
f
r
esu
l
t
s
f
o
r
I
E
E
E
1
1
8
-
b
u
s
s
y
s
te
m
M
e
t
h
o
d
o
l
o
g
y
C
S
A
P
S
O
[
1
2
]
S
O
A
[
1
9
]
G
S
A
[
2
1
]
P
o
w
e
r
l
o
ss (M
W
)
7
6
.
7
7
8
3
1
3
1
.
9
9
1
1
4
.
9
5
0
1
1
2
7
.
7
6
0
3
Fig
u
r
e
1
.
C
o
n
v
er
g
en
ce
c
h
ar
ac
t
er
is
tics
co
n
s
id
er
in
g
th
e
r
ea
l p
o
w
er
lo
s
s
a
s
o
b
j
ec
tiv
e
5
.
2
.
Ca
s
e
-
2:
M
in
i
m
iza
t
io
n o
f
t
o
t
a
l v
o
lt
a
g
e
dev
ia
t
io
n
T
h
e
p
r
o
p
o
s
ed
C
S
A
ap
p
r
o
ac
h
is
also
ap
p
lied
f
o
r
m
i
n
i
m
izati
o
n
o
f
to
tal
v
o
lta
g
e
d
ev
iatio
n
o
f
IEEE
-
3
0
b
u
s
test
n
e
t
w
o
r
k
an
d
th
e
r
es
u
lt
y
ield
ed
f
r
o
m
th
i
s
ap
p
r
o
ac
h
is
illu
s
tr
ated
in
T
ab
le
4
an
d
ar
e
co
m
p
ar
ed
w
it
h
th
o
s
e
r
ep
o
r
ted
in
th
e
li
ter
atu
r
e.
T
h
e
m
i
n
i
m
u
m
to
tal
v
o
lta
g
e
d
ev
iatio
n
o
b
tain
ed
b
y
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
is
0
.
0
9
0
7
,
w
h
ic
h
is
less
er
th
a
n
r
e
s
u
lt
s
r
ep
o
r
ted
in
[
1
2
]
,
[
1
4
]
.
T
h
e
co
n
v
er
g
en
ce
ch
ar
ac
ter
i
s
tic
o
f
v
o
ltag
e
d
ev
iat
io
n
v
er
s
u
s
n
u
m
b
er
o
f
iter
atio
n
s
is
d
ep
icted
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
C
o
n
v
er
g
en
ce
c
h
ar
ac
t
er
is
tics
co
n
s
id
er
in
g
v
o
lta
g
e
d
ev
iatio
n
a
s
o
b
j
ec
tiv
e
T
ab
le
4
.
C
o
m
p
ar
is
o
n
s
o
f
r
es
u
l
ts
f
o
r
v
o
lta
g
e
p
r
o
f
ile
i
m
p
r
o
v
e
m
en
t I
E
E
E
-
3
0
b
u
s
s
y
s
te
m
M
e
t
h
o
d
o
l
o
g
y
C
S
A
P
S
O
[
1
2
]
C
L
P
S
O
[
1
4
]
Σ
V
o
l
t
a
g
e
d
e
v
i
a
t
i
o
n
(
p
.
u
)
0
.
0
9
0
7
0
.
2
4
5
0
0
.
2
5
7
7
0
20
40
60
80
100
120
140
160
180
200
2
.
5
3
3
.
5
4
4
.
5
5
5
.
5
6
6
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7
.
5
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t
e
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t
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o
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Po
w
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r
L
o
s
s
(M
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0
20
40
60
80
100
120
140
160
180
200
0
.
0
5
0
.
1
0
.
1
5
0
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2
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3
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4
I
t
e
ra
t
i
o
n
Vo
l
t
a
g
e
D
e
v
i
a
t
i
o
n
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:
2
0
8
8
-
8708
O
p
tima
l R
ea
ctive
P
o
w
er Disp
a
tch
u
s
in
g
C
r
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w
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ea
r
ch
A
lg
o
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ith
m
(
La
ksh
mi
M
)
1429
5
.
3
.
Ca
s
e
-
3
:
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nh
a
nce
m
ent
o
f
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o
lt
a
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s
t
a
bil
it
y
I
n
th
i
s
ca
s
e
t
h
e
en
h
a
n
ce
m
en
t
o
f
v
o
lta
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e
Stab
ilit
y
i
s
tak
en
as
o
b
j
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tiv
e
f
u
n
c
tio
n
.
T
h
e
s
o
lu
ti
o
n
o
b
tain
ed
b
y
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
an
d
r
ep
o
r
ted
in
li
ter
atu
r
e
b
y
o
th
er
m
et
h
o
d
s
i
s
il
lu
s
tr
at
ed
in
T
ab
le
5
.
T
h
e
v
o
ltag
e
s
tab
ilit
y
i
n
d
icato
r
o
b
tain
ed
b
y
t
h
e
C
S
A
i
s
0
.
1
1
8
0
,
w
h
ic
h
is
less
er
th
a
n
r
es
u
lt
s
r
ep
o
r
ted
in
[
2
0
]
,
[
2
1
]
an
d
w
h
ic
h
i
s
p
r
o
v
in
g
t
h
e
ex
ce
llen
ce
o
f
t
h
e
a
f
o
r
esaid
C
S
A
al
g
o
r
ith
m
o
v
er
o
th
er
o
p
ti
m
izati
o
n
tech
n
iq
u
e
s
.
T
h
e
co
n
v
e
r
g
e
n
ce
ch
ar
ac
ter
i
s
tic
o
f
L
-
in
d
e
x
v
er
s
u
s
n
u
m
b
er
o
f
iter
atio
n
s
ar
e
d
ep
icted
in
Fig
u
r
e
3
,
w
h
ic
h
s
h
o
w
s
f
a
s
t
an
d
s
m
o
o
t
h
co
n
v
er
g
en
ce
c
h
ar
ac
ter
is
tics
o
f
C
S
A
.
T
ab
le
5
.
C
o
m
p
ar
is
o
n
o
f
r
esu
l
t
s
f
o
r
en
h
an
ce
m
e
n
t o
f
v
o
ltag
e
s
tab
ilit
y
I
E
E
E
-
3
0
b
u
s
s
y
s
te
m
M
e
t
h
o
d
o
l
o
g
y
C
S
A
D
E
[
2
0
]
G
S
A
[
2
1
]
L
-
i
n
d
e
x
(
p
.
u
)
0
.
1
1
8
0
0
.
1
2
4
6
0
.
1
3
6
8
Fig
u
r
e
3
.
C
o
n
v
er
g
en
ce
c
h
ar
ac
t
er
is
tics
co
n
s
id
er
in
g
v
o
lta
g
e
s
t
ab
ilit
y
i
n
d
icato
r
as o
b
j
ec
tiv
e
T
h
e
o
p
tim
al
s
ett
in
g
o
f
t
h
e
co
n
tr
o
l
v
ar
iab
les
f
o
r
th
e
I
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E
E
-
3
0
b
u
s
s
y
s
te
m
is
ill
u
s
tr
ated
i
n
T
ab
le
6
.
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RE
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NC
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[1
]
K.
Y.
L
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,
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t
a
l
,
“
F
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c
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Ge
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T
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d
Distrib
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C
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1
3
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3
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[2
]
N.
I.
De
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,
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li
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ra
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p
p
ro
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c
h
,
”
El
e
c
tric P
o
we
r S
y
ste
m R
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se
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rc
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,
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l
/i
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:
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.
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–
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4
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8
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.
[3
]
S
.
G
ra
n
v
il
le,
“
Op
ti
m
a
l
re
a
c
ti
v
e
d
isp
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tch
t
h
ro
u
g
h
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n
terio
r
p
o
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n
t
m
e
th
o
d
s
,
”
IEE
E
T
ra
n
sa
c
ti
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n
s
o
n
Po
we
r
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y
ste
m
,
v
ol
/i
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1
)
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6
–
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6
,
1
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9
4
.
[4
]
N.
G
ru
d
in
in
,
“
Re
a
c
ti
v
e
p
o
w
e
r
o
p
ti
m
iza
ti
o
n
u
sin
g
su
c
c
e
ss
iv
e
q
u
a
d
ra
ti
c
p
ro
g
ra
m
m
in
g
m
e
th
o
d
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
P
o
we
r S
y
ste
m
, v
ol
/i
ss
u
e
:
13
(
4
)
,
p
p
.
1
2
1
9
–
1
2
2
5
,
1
9
9
8
.
[5
]
W
u
,
e
t
a
l
.
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
u
sin
g
a
n
a
d
a
p
ti
v
e
g
e
n
e
ti
c
a
l
g
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
a
n
d
E
n
e
rg
y
S
y
ste
ms
, v
ol
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ss
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:
20
(
8
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p
p
.
5
6
3
–
5
6
9
,
1
9
9
8
.
[6
]
S
.
Du
ra
iraj,
e
t
a
l
,
“
G
e
n
e
ti
c
a
lg
o
rit
h
m
b
a
se
d
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tc
h
f
o
r
v
o
lt
a
g
e
sta
b
il
it
y
i
m
p
ro
v
e
m
e
n
t
,
”
El
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trica
l
Po
we
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n
d
E
n
e
rg
y
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ste
ms
,
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p
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1
1
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6
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2
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1
0
.
[7
]
M
.
I
.
A
z
im
,
e
t
a
l
.
,
“
G
e
n
e
ti
c
a
l
g
o
rit
h
m
b
a
se
d
re
a
c
ti
v
e
p
o
we
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m
a
n
a
g
e
m
e
n
t
b
y
S
V
C
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l
/i
ss
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:
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2
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,
p
p
.
2
0
0
–
2
0
6
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2
0
1
4
.
[8
]
D.
De
v
a
r
a
j,
“
I
m
p
ro
v
e
d
g
e
n
e
ti
c
a
lg
o
rit
h
m
f
o
r
m
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lt
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jec
ti
v
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c
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p
o
w
e
r
d
isp
a
tch
p
ro
b
l
e
m
,
”
Eu
ro
p
e
a
n
T
ra
n
sa
c
ti
o
n
s
o
n
El
e
c
trica
l
Po
we
r
,
v
o
l
/i
ss
u
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:
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(
6
)
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p
p
.
5
6
9
–
5
8
1
,
2
0
0
7
.
[9
]
D.
De
v
a
ra
j,
e
t
a
l
.
,
“
Re
a
l
p
a
ra
m
e
te
r
g
e
n
e
ti
c
a
lg
o
rit
h
m
to
m
u
lt
io
b
j
e
c
ti
v
e
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r a
n
d
E
n
e
rg
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s
tem
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v
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l
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ss
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e
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1
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p
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1
7
1
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3
,
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0
0
8
.
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0
]
W
u
,
e
t
a
l
.
,
“
P
o
w
e
r
s
y
st
e
m
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
u
sin
g
e
v
o
lu
ti
o
n
a
ry
p
ro
g
ra
m
m
in
g
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
ste
m
,
v
o
l
/
issu
e
:
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3
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p
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9
5
.
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1
]
W
.
Ya
n
,
e
t
a
l
.
,
“
A
n
o
v
e
l
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
m
e
th
o
d
b
a
se
d
o
n
a
n
im
p
ro
v
e
d
h
y
b
rid
e
v
o
lu
ti
o
n
a
ry
p
ro
g
ra
m
m
in
g
tec
h
n
iq
u
e
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
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[1
2
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H.
Yo
sh
i
d
a
,
e
t
a
l
.
,
“
A
p
a
rti
c
le
sw
a
r
m
o
p
ti
m
iza
ti
o
n
f
o
r
re
a
c
ti
v
e
p
o
w
e
r
a
n
d
v
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lt
a
g
e
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o
n
tro
l
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sid
e
rin
g
v
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lt
a
g
e
se
c
u
rit
y
a
ss
e
s
s
m
e
n
t
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
P
o
we
r S
y
ste
m
,
v
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l
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[1
3
]
A.
A.
A
.
Esm
in
,
e
t
a
l
.
,
“
A
h
y
b
rid
p
a
rti
c
le
sw
a
r
m
o
p
ti
m
iza
ti
o
n
a
p
p
li
e
d
t
o
l
o
ss
p
o
w
e
r
m
in
imiz
a
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
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m
,
v
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2
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p
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5
.
[1
4
]
K.
M
a
h
a
d
e
v
a
n
,
e
t
a
l
.,
“
Co
m
p
re
h
e
n
siv
e
lea
rn
in
g
p
a
rti
c
le
s
w
a
r
m
o
p
ti
m
iza
ti
o
n
f
o
r
re
a
c
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v
e
p
o
w
e
r
d
isp
a
tch
,
”
Ap
p
li
e
d
S
o
ft
Co
mp
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g
,
v
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p
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[1
5
]
M
.
M
e
h
d
i
n
e
jad
,
e
t
a
l
.
,
“
S
o
l
u
ti
o
n
o
f
o
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ti
m
a
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re
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c
ti
v
e
p
o
we
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d
isp
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f
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o
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st
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m
s
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sin
g
h
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rid
p
a
rti
c
le
sw
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r
m
o
p
ti
m
iza
ti
o
n
a
n
d
im
p
e
rialist
c
o
m
p
e
ti
ti
v
e
a
lg
o
rit
h
m
s
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
P
o
we
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n
d
En
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ste
ms
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l.
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3
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p
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1
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[1
6
]
A
.
E
.
El
a
,
e
t
a
l
.,
“
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ti
m
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l
re
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c
ti
v
e
p
o
we
r
d
isp
a
tch
u
sin
g
a
n
t
c
o
lo
n
y
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
,
”
El
e
c
trica
l
En
g
i
n
e
e
rin
g
,
v
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l
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p
p
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1
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1
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6
,
2
0
1
1
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[1
7
]
K.
L
e
n
in
,
e
t
a
l
.
,
“
Op
ti
m
a
l
p
o
w
e
r
f
lo
w
u
sin
g
a
n
t
c
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y
se
a
r
c
h
a
lg
o
rit
h
m
to
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v
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lu
a
te
lo
a
d
c
u
rtail
m
e
n
t
in
c
o
rp
o
ra
ti
n
g
v
o
lt
a
g
e
sta
b
il
it
y
m
a
rg
in
c
rit
e
rio
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
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n
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rin
g
,
v
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l
/i
ss
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5
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,
p
p
.
6
0
3
–
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1
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2
0
1
3
.
[1
8
]
M
.
T
rip
a
th
y
,
e
t
a
l
.
,
“
Ba
c
teria
f
o
ra
g
in
g
-
b
a
se
d
so
lu
ti
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n
to
o
p
ti
m
ize
b
o
t
h
re
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l
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o
w
e
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lo
ss
a
n
d
v
o
lt
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g
e
sta
b
il
it
y
li
m
it
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
st
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m
,
v
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l
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ss
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e
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1
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,
p
p
.
2
4
0
–
2
4
8
,
2
0
0
7
.
[1
9
]
C.
Da
i,
e
t
a
l
.
,
“
O
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
f
o
r
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
Po
we
r
S
y
ste
m
,
v
o
l
/i
ss
u
e
:
24
(
3
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,
p
p
.
1
2
1
8
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