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[
1
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2
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I
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:
2
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8
8
-
8708
I
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C
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Vo
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7
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No
.
5
,
Octo
b
er
2
0
1
7
:
23
49
–
23
5
6
2350
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esig
n
ed
t
o
s
o
lv
e
a
s
p
ec
i
f
ic
t
y
p
e
o
f
o
p
ti
m
i
za
tio
n
p
r
o
b
le
m
m
a
y
n
o
t
b
e
e
f
f
icien
t
in
s
o
l
v
in
g
o
t
h
er
t
y
p
e
o
f
p
r
o
b
lem
s
.
Fu
r
t
h
er
,
th
e
clas
s
ical
o
p
ti
m
izatio
n
tec
h
n
iq
u
e
s
ar
e
n
o
t
ef
f
icie
n
t
i
n
h
a
n
d
lin
g
t
h
e
p
r
o
b
le
m
s
w
it
h
d
is
cr
e
te
s
ea
r
ch
s
p
ac
e
[
4
-
5
]
.
Dif
f
ic
u
ltie
s
ar
is
e
in
t
h
e
class
ical
ap
p
r
o
ac
h
,
as
it
ass
u
m
e
s
all
v
ar
iab
les
to
b
e
co
n
ti
n
u
o
u
s
d
u
r
i
n
g
th
e
o
p
tim
izatio
n
a
n
d
th
er
e
a
f
ter
a
v
alu
e
c
lo
s
e
to
th
e
o
b
tai
n
ed
s
o
lu
tio
n
i
s
r
ec
o
m
m
en
d
ed
f
o
r
a
d
is
cr
ete
v
ar
iab
le.
C
o
m
p
le
x
r
ea
l
w
o
r
ld
o
p
tim
iza
tio
n
p
r
o
b
lem
s
ca
n
n
o
w
b
e
ea
s
il
y
s
o
l
v
ed
w
ith
t
h
e
p
ar
allel
co
m
p
u
ti
n
g
s
y
s
te
m
s
.
Mo
s
t
class
ical
al
g
o
r
it
h
m
s
u
s
e
p
o
in
t
-
by
-
p
o
in
t
ap
p
r
o
ac
h
es,
w
h
er
e
in
o
n
e
i
ter
atio
n
;
o
n
e
s
o
lu
tio
n
i
s
u
p
d
ated
u
s
i
n
g
th
e
p
r
ev
io
u
s
s
o
l
u
tio
n
.
T
h
er
ef
o
r
e,
th
e
ad
v
a
n
ta
g
e
o
f
p
ar
allel
co
m
p
u
ti
n
g
ca
n
n
o
t b
e
ex
p
lo
ited
f
u
ll
y
[
6
-
7
]
.
T
h
e
ab
o
v
e
d
is
cu
s
s
io
n
r
ev
ea
l
s
th
at
cla
s
s
ical
o
p
ti
m
izatio
n
a
lg
o
r
ith
m
s
m
a
y
f
ac
e
d
if
f
ic
u
ltie
s
in
s
o
l
v
i
n
g
th
e
p
r
ac
tical
r
ea
l
w
o
r
ld
o
p
ti
m
izatio
n
p
r
o
b
le
m
s
.
E
v
o
l
u
tio
n
ar
y
al
g
o
r
ith
m
s
f
i
n
d
ap
p
licatio
n
s
in
s
o
l
v
i
n
g
v
ar
io
u
s
o
p
tim
izatio
n
p
r
o
b
le
m
s
i
n
cl
u
d
in
g
s
cie
n
ce
,
co
m
m
er
ce
a
n
d
e
n
g
i
n
ee
r
i
n
g
[
8
]
.
Dif
f
er
en
t
c
las
s
es
o
f
ev
o
l
u
tio
n
ar
y
alg
o
r
ith
m
s
in
cl
u
d
e
E
v
o
l
u
tio
n
ar
y
P
r
o
g
r
a
m
m
i
n
g
(
E
P
)
,
E
v
o
l
u
tio
n
Stra
teg
ie
s
(
E
S),
Gen
eti
c
A
l
g
o
r
ith
m
(
G
A
)
,
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
(
P
SO)
,
an
d
Dif
f
er
en
tia
l
E
v
o
lu
tio
n
(
DE
)
,
etc.
A
ll
th
ese
m
et
h
o
d
s
ar
e
in
s
p
ir
ed
b
y
n
atu
r
e
’
s
ev
o
l
u
tio
n
.
A
ll
t
h
ese
o
p
tim
izatio
n
ap
p
r
o
ac
h
es
s
h
ar
e
a
co
m
m
o
n
co
n
ce
p
t
u
al
b
ase
o
f
s
i
m
u
la
tin
g
th
e
ev
o
lu
tio
n
o
f
i
n
d
iv
id
u
al
s
tr
u
ct
u
r
es.
I
n
th
e
liter
at
u
r
e,
a
n
u
m
b
er
o
f
class
ical
o
p
ti
m
izat
io
n
alg
o
r
it
h
m
s
h
a
v
e
b
ee
n
p
r
esen
ted
to
s
o
lv
e
th
e
r
ea
ctiv
e
p
o
w
er
s
c
h
ed
u
l
in
g
p
r
o
b
le
m
.
T
h
ese
tech
n
iq
u
e
s
in
c
lu
d
e
th
e
No
n
-
li
n
ea
r
p
r
o
g
r
a
m
m
in
g
,
Gr
ad
ien
t
m
et
h
o
d
,
L
i
n
ea
r
p
r
o
g
r
a
m
m
i
n
g
,
Q
u
ad
r
atic
p
r
o
g
r
a
m
m
in
g
an
d
I
n
ter
io
r
p
o
in
t
m
eth
o
d
[
9
]
.
A
lt
h
o
u
g
h
t
h
ese
m
et
h
o
d
s
h
a
v
e
b
ee
n
ap
p
lied
s
u
cc
ess
f
u
ll
y
f
o
r
th
e
s
o
l
u
tio
n
o
f
o
p
ti
m
al
r
ea
cti
v
e
p
o
w
er
s
ch
ed
u
li
n
g
p
r
o
b
le
m
,
s
till
t
h
er
e
ar
e
s
o
m
e
d
if
f
ic
u
lt
ies
a
s
s
o
ciate
d
w
i
th
th
e
m
.
O
n
e
i
s
t
h
e
m
u
lti
m
o
d
al
c
h
ar
ac
ter
is
tic
s
o
f
p
r
o
b
lem
s
to
b
e
h
an
d
led
.
A
l
s
o
,
b
ec
au
s
e
o
f
t
h
e
n
o
n
-
lin
ea
r
it
y
,
n
o
n
-
d
if
f
er
en
tial
an
d
n
o
n
-
co
n
v
e
x
n
atu
r
e
o
f
t
h
e
r
ea
cti
v
e
p
o
w
er
s
c
h
ed
u
lin
g
p
r
o
b
lem
,
m
aj
o
r
it
y
o
f
th
e
s
e
al
g
o
r
ith
m
s
co
n
v
er
g
e
to
a
lo
ca
l
o
p
tim
u
m
[
1
0
]
.
No
w
ad
a
y
s
,
m
an
y
e
v
o
lu
tio
n
ar
y
/
m
eta
-
h
e
u
r
is
tic
b
ased
o
p
ti
m
i
za
tio
n
alg
o
r
it
h
m
s
s
u
c
h
as
GA
[
1
1
]
,
E
P
[
1
2
]
an
d
B
i
o
g
eo
g
r
ap
h
y
B
ased
Op
ti
m
izatio
n
(
B
B
O)
[
1
3
]
h
av
e
b
ee
n
ap
p
lied
s
u
cc
ess
f
u
ll
y
to
s
o
lv
e
t
h
e
o
p
ti
m
al
s
c
h
ed
u
l
in
g
p
r
o
b
lem
.
R
ef
er
e
n
ce
[
1
4
]
p
r
esen
t
s
d
i
f
f
er
en
t c
o
n
v
e
n
tio
n
al
a
n
d
e
v
o
lu
t
io
n
ar
y
b
ased
co
m
p
u
tatio
n
a
l a
p
p
r
o
ac
h
es
f
o
r
s
o
lv
i
n
g
t
h
e
o
p
ti
m
al
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
p
r
o
b
lem
.
A
Qu
a
n
tu
m
Sti
r
r
ed
C
u
ck
o
o
Sea
r
ch
A
l
g
o
r
ith
m
(
QS
-
C
S
A
)
f
o
r
s
o
lv
i
n
g
th
e
o
p
ti
m
a
l
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
p
r
o
b
le
m
is
p
r
esen
ted
in
[
1
5
]
.
I
n
r
ec
en
t
y
ea
r
s
,
t
h
e
m
eta
-
h
eu
r
i
s
tic
tec
h
n
iq
u
es
h
av
e
b
e
en
clo
s
el
y
co
n
ce
r
n
ed
an
d
wid
el
y
u
s
ed
in
t
h
e
g
lo
b
al
o
p
ti
m
izatio
n
p
r
o
b
lem
.
T
h
er
ef
o
r
e,
T
a
b
u
Sear
ch
(
T
S)
,
Si
m
u
la
ted
A
n
n
ea
li
n
g
(
S
A
)
,
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
(
P
SO)
,
I
m
p
r
o
v
ed
P
SO,
Har
m
o
n
y
Sear
c
h
(
H
S),
Dif
f
er
en
t
ial
E
v
o
lu
tio
n
(
DE
)
a
n
d
A
r
ti
f
icial
I
m
m
u
n
e
A
l
g
o
r
ith
m
(
A
I
A
)
,
etc.
h
av
e
b
ee
n
u
s
ed
w
id
el
y
i
n
t
h
e
r
ea
ct
iv
e
p
o
w
er
o
p
ti
m
izatio
n
o
f
p
o
w
er
s
y
s
te
m
.
Ho
w
ev
er
,
t
h
e
m
a
in
s
h
o
r
tco
m
i
n
g
s
o
f
th
ese
al
g
o
r
ith
m
s
ar
e
t
h
e
p
r
e
m
atu
r
e
co
n
v
er
g
en
ce
a
n
d
th
e
co
n
v
er
g
en
ce
s
p
ee
d
.
R
ec
en
tl
y
,
a
n
e
w
m
e
ta
-
h
e
u
r
is
tic
tech
n
iq
u
e
p
r
o
p
o
s
ed
b
y
X.
S.
Yan
g
a
n
d
S.
Deb
i
n
2
0
0
9
[
16
]
i.e
.
,
C
u
c
k
o
o
Sear
ch
A
l
g
o
r
ith
m
(
C
S
A
)
h
a
s
b
ee
n
u
s
ed
to
o
v
er
co
m
e
th
e
ab
o
v
e
m
en
tio
n
ed
s
h
o
r
t
co
m
i
n
g
s
.
T
h
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
is
in
s
p
ir
ed
f
r
o
m
t
h
e
lif
e
o
f
th
e
f
a
m
il
y
o
f
c
u
c
k
o
o
.
R
ec
en
t
s
t
u
d
ies
s
h
o
w
th
at
th
e
C
S
A
is
m
o
r
e
ef
f
icie
n
t
t
h
a
n
t
h
e
G
A
a
n
d
P
SO
[
17
-
18
]
.
T
h
e
n
u
m
b
er
o
f
p
ar
a
m
eter
s
to
b
e
t
u
n
ed
i
n
t
h
e
C
S
A
is
less
t
h
an
t
h
e
G
A
a
n
d
P
SO,
a
n
d
h
e
n
ce
it
is
m
o
r
e
g
e
n
er
ic
to
ad
ap
t
to
a
w
id
er
class
o
f
o
p
ti
m
izatio
n
p
r
o
b
le
m
s
.
I
n
th
i
s
p
ap
er
,
C
SA
is
p
r
o
p
o
s
ed
f
o
r
s
o
lv
in
g
t
h
e
r
ea
cti
v
e
p
o
w
er
s
ch
ed
u
lin
g
o
p
ti
m
izat
io
n
.
T
h
e
p
r
o
p
o
s
ed
C
SA
ap
p
r
o
a
ch
is
ex
a
m
i
n
ed
o
n
t
h
e
W
ar
d
-
Hale
6
b
u
s
,
3
0
b
u
s
,
5
7
b
u
s
,
1
1
8
b
u
s
an
d
3
0
0
b
u
s
s
y
s
te
m
s
,
an
d
t
h
e
r
esu
lt
s
o
b
tain
ed
ar
e
co
m
p
ar
ed
w
i
th
m
an
y
o
th
er
o
p
ti
m
izatio
n
alg
o
r
ith
m
s
p
r
ese
n
ted
in
t
h
e
lit
er
atu
r
e.
T
h
e
r
est
o
f
th
e
p
ap
er
is
o
u
tlin
ed
as
f
o
llo
w
s
.
Sectio
n
2
p
r
esen
ts
t
h
e
d
etailed
f
o
r
m
u
l
at
io
n
o
f
r
ea
ctiv
e
p
o
w
er
s
ch
ed
u
li
n
g
p
r
o
b
lem
.
T
h
e
d
escr
ip
tio
n
o
f
C
u
c
k
o
o
Sear
ch
A
l
g
o
r
ith
m
(
C
S
A
)
is
d
escr
ib
ed
in
Sectio
n
3
.
T
h
e
s
i
m
u
latio
n
r
es
u
lt
s
o
n
d
i
f
f
er
en
t
test
s
y
s
te
m
s
a
n
d
th
e
co
m
p
ar
is
o
n
o
f
r
es
u
lt
s
w
it
h
p
r
ev
io
u
s
al
g
o
r
ith
m
s
p
r
esen
ted
in
th
e
liter
at
u
r
e
ar
e
p
r
o
v
id
ed
in
Sectio
n
4
.
Fin
all
y
,
th
e
co
n
tr
ib
u
tio
n
s
w
it
h
th
e
co
n
clu
d
i
n
g
r
e
m
ar
k
s
ar
e
p
r
esen
ted
in
Sectio
n
5
.
2.
RE
AC
T
I
V
E
P
O
WE
R
SCH
E
DULI
NG
:
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
Fo
r
th
e
r
ea
ctiv
e
p
o
w
er
s
c
h
e
d
u
lin
g
p
r
o
b
le
m
,
th
e
m
in
i
m
iz
atio
n
o
f
s
y
s
te
m
tr
a
n
s
m
is
s
io
n
lo
s
s
es
is
s
elec
te
d
as
th
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
.
T
r
an
s
m
i
s
s
io
n
lo
s
s
i
n
ea
c
h
lin
e
is
ca
lcu
lated
f
r
o
m
t
h
e
p
o
w
er
f
lo
w
s
o
lu
t
io
n
.
T
h
e
co
n
v
er
g
ed
p
o
w
er
f
lo
w
s
o
lu
tio
n
g
i
v
es
t
h
e
b
u
s
v
o
ltag
e
m
a
g
n
i
tu
d
es
a
n
d
p
h
ase
an
g
le
s
.
Usi
n
g
th
e
s
e,
th
e
ac
tiv
e
p
o
w
er
f
lo
w
t
h
r
o
u
g
h
th
e
tr
an
s
m
i
s
s
io
n
li
n
es
c
an
b
e
ev
a
lu
ated
.
T
h
e
to
tal
p
o
w
er
lo
s
s
is
th
e
s
u
m
o
f
p
o
w
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Op
tima
l R
ea
ctive
P
o
w
er S
ch
e
d
u
lin
g
Usi
n
g
C
u
ck
o
o
S
ea
r
ch
A
lg
o
r
ith
m
(
S
.
S
u
r
en
d
er R
ed
d
y
)
2351
lo
s
s
es
i
n
ea
c
h
tr
an
s
m
i
s
s
io
n
li
n
e.
I
n
t
h
is
p
ap
er
,
th
e
g
en
er
at
o
r
b
u
s
v
o
ltag
e
m
a
g
n
it
u
d
es,
tr
an
s
f
o
r
m
er
tap
li
m
it
s
an
d
th
e
li
m
its
o
n
s
w
itc
h
ab
le
s
h
u
n
t
V
A
R
s
o
u
r
ce
s
ar
e
co
n
s
i
d
er
ed
as
th
e
co
n
tr
o
l
v
ar
iab
les.
T
h
e
o
b
j
ec
tiv
e
o
f
r
ea
ctiv
e
p
o
w
er
s
ch
ed
u
li
n
g
p
r
o
b
le
m
is
to
d
eter
m
i
n
e
t
h
e
o
p
ti
m
al
s
etti
n
g
s
o
f
v
ar
io
u
s
co
n
tr
o
ls
w
h
ich
m
in
i
m
ize
s
th
e
p
o
w
er
lo
s
s
e
s
d
u
r
in
g
t
h
e
co
n
tr
o
l
an
d
o
p
er
atio
n
o
f
a
n
et
w
o
r
k
.
T
h
e
p
o
w
er
lo
s
s
i
s
a
n
o
n
l
in
ea
r
f
u
n
ctio
n
o
f
b
u
s
v
o
ltag
e
s
an
d
p
h
ase
a
n
g
les
w
h
i
ch
ar
e
i
m
p
l
icitl
y
t
h
e
f
u
n
ctio
n
s
o
f
co
n
tr
o
l v
ar
iab
les.
T
h
e
r
ea
l
p
o
w
er
lo
s
s
(
P
loss
)
is
r
ep
r
esen
ted
as [
1
9
]
.
=
∑
∑
[
2
+
2
−
2
(
−
)
]
=
1
≠
=
1
(
1
)
w
h
er
e
G
ij
is
co
n
d
u
c
tan
ce
o
f
a
tr
an
s
m
is
s
io
n
li
n
e
co
n
n
ec
ted
b
et
w
ee
n
th
e
b
u
s
es
i
an
d
j
.
N
is
th
e
to
tal
n
u
m
b
er
o
f
b
u
s
es i
n
t
h
e
s
y
s
te
m
.
an
d
ar
e
th
e
v
o
lta
g
e
m
ag
n
it
u
d
e
an
d
p
h
a
s
e
an
g
le
at
b
u
s
i,
r
esp
ec
ti
v
el
y
.
2
.
1
.
P
r
o
ble
m
co
n
s
t
ra
ints
2
.
1
.
1
.
E
qu
a
lity
co
ns
t
ra
ints:
T
h
ese
co
n
s
tr
ain
t
s
i
n
clu
d
e
t
h
e
t
y
p
ica
l p
o
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er
f
lo
w
eq
u
a
tio
n
s
,
an
d
th
e
y
ar
e
r
ep
r
esen
ted
as,
=
−
−
∑
[
+
]
=
0
=
1
(
2
)
=
−
−
∑
[
−
]
=
0
=
1
(
3
)
I
n
th
e
ab
o
v
e
eq
u
atio
n
s
,
i
=1
,
2
,
3
,
.
.
.
.
.
,
N.
P
Gi
an
d
Q
Gi
ar
e
th
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
g
e
n
e
r
atio
n
s
at
b
u
s
-
i,
P
Di
an
d
Q
Di
ar
e
th
e
co
r
r
esp
o
n
d
in
g
ac
tiv
e
an
d
r
ea
cti
v
e
lo
ad
d
em
a
n
d
s
.
2
.
1
.
2
.
I
nequ
a
lity
Co
ns
t
ra
ints
T
h
ese
co
n
s
tr
ain
t
s
r
ep
r
esen
t o
p
er
atin
g
l
i
m
its
o
f
t
h
e
p
o
w
er
s
y
s
te
m
.
Genera
to
r
C
o
n
s
tr
a
i
nts
:
Ge
n
er
ato
r
Vo
ltag
e
m
ag
n
it
u
d
es
(
V
Gi
)
,
Gen
er
ato
r
ac
tiv
e
p
o
w
e
r
o
u
tp
u
ts
(
P
Gi
)
an
d
r
ea
ctiv
e
p
o
w
er
g
e
n
er
atio
n
(
Q
Gi
)
ar
e
lim
i
ted
b
y
t
h
eir
lo
w
er
an
d
u
p
p
er
lim
i
ts
.
T
h
e
y
ar
e
r
ep
r
esen
ted
as,
≤
≤
=
1
,
2
,
3
,
…
.
.
,
(
4
)
≤
≤
=
1
,
2
,
3
,
…
.
.
,
(
5
)
≤
≤
=
1
,
2
,
3
,
…
.
.
,
(
6
)
T
r
a
ns
f
o
r
m
er C
o
ns
tr
a
i
nts
:
T
r
a
n
s
f
o
r
m
er
tap
s
h
a
v
e
lo
w
er
an
d
u
p
p
er
s
ettin
g
s
.
T
h
e
y
ar
e
ex
p
r
e
s
s
ed
as,
≤
≤
=
1
,
2
,
3
,
…
.
.
,
(
7
)
Sw
itc
ha
b
le
V
A
R
s
o
ur
ce
s
:
T
h
e
s
o
u
r
ce
s
h
a
v
e
li
m
itat
io
n
s
a
s
,
≤
≤
=
1
,
2
,
3
,
…
.
.
,
(
8
)
Sec
ur
ity
co
n
s
tr
a
in
ts
:
T
h
ese
co
n
s
tr
ain
ts
i
n
cl
u
d
e
th
e
li
m
its
o
n
lo
ad
b
u
s
v
o
lta
g
e
m
a
g
n
itu
d
e
s
an
d
tr
an
s
m
i
s
s
io
n
lin
e
f
lo
w
s
.
≤
≤
=
1
,
2
,
3
,
…
.
.
,
(
9
)
≤
=
1
,
2
,
3
,
…
.
.
,
(
1
0
)
3.
CUCK
O
O
SE
ARCH
A
L
G
O
RIT
H
M
(
CSA)
T
h
e
C
SA
i
s
a
n
o
v
e
l
ev
o
lu
tio
n
ar
y
tec
h
n
iq
u
e
w
h
ich
i
s
n
at
u
r
e
-
in
s
p
ir
ed
b
y
C
u
c
k
o
o
s
'
s
ea
r
c
h
f
o
r
th
eir
n
est
s
w
h
er
e
t
h
e
y
co
u
ld
la
y
th
eir
eg
g
s
.
C
u
c
k
o
o
Sear
ch
A
l
g
o
r
ith
m
(
C
S
A
)
[
20
-
22
]
is
o
n
e
o
f
th
e
r
ec
en
t
o
p
tim
izatio
n
ap
p
r
o
ac
h
es
a
n
d
it
d
ev
elo
p
ed
f
r
o
m
t
h
e
i
n
s
p
ir
at
io
n
f
r
o
m
o
b
lig
ate
b
r
o
o
d
p
ar
a
s
itis
m
o
f
s
o
m
e
t
h
e
cu
ck
o
o
s
p
ec
ies
la
y
t
h
eir
eg
g
s
in
n
est
s
o
f
o
th
er
h
o
s
t
b
ir
d
s
w
h
ic
h
ar
e
o
f
o
th
er
s
p
ec
ies.
T
h
is
tec
h
n
iq
u
e
w
as
p
r
o
p
o
s
ed
b
y
X.
S.
Yan
g
an
d
S.
Deb
[
1
6
]
,
th
ey
o
p
ti
m
ized
1
0
s
tan
d
ar
d
test
f
u
n
ctio
n
s
an
d
t
h
e
n
g
a
v
e
th
e
w
o
r
k
i
n
g
p
r
in
cip
le
o
f
C
S
A
.
R
e
f
er
en
ce
[
1
7
]
p
r
esen
ts
t
h
e
ex
te
n
s
io
n
o
f
R
ef
er
e
n
ce
[
1
6
]
,
it
u
s
es
t
h
e
s
ta
n
d
ar
d
test
f
u
n
ct
io
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
5
,
Octo
b
er
2
0
1
7
:
23
49
–
23
5
6
2352
as
w
ell
as
t
h
e
s
to
ch
a
s
tic
f
u
n
c
ti
o
n
s
f
o
r
test
i
n
g
t
h
e
ef
f
icien
c
y
o
f
th
e
alg
o
r
it
h
m
.
T
h
is
C
S
A
is
d
ev
elo
p
ed
b
ased
o
n
th
e
f
o
llo
w
i
n
g
p
r
in
cip
les [
2
0
-
2
1
]
:
1.
E
ac
h
C
u
ck
o
o
la
y
s
o
n
e
eg
g
at
a
ti
m
e,
an
d
d
u
m
p
s
it
s
eg
g
in
a
r
an
d
o
m
l
y
c
h
o
s
e
n
n
e
s
t.
2.
B
est n
est
s
w
it
h
h
i
g
h
q
u
alit
y
o
f
eg
g
s
w
ill
ca
r
r
y
o
v
er
to
th
e
n
e
x
t iter
atio
n
s
/ g
e
n
er
atio
n
s
.
3.
T
h
e
n
u
m
b
er
o
f
a
v
ailab
le
h
o
s
t
n
est
s
is
f
ix
ed
a
n
d
th
e
eg
g
lai
d
b
y
a
C
u
ck
o
o
is
id
e
n
ti
f
ied
b
y
th
e
h
o
s
t
b
ir
d
w
i
th
a
p
r
o
b
ab
ilit
y
i
n
th
e
r
an
g
e
b
et
w
ee
n
0
an
d
1
.
I
n
th
i
s
s
itu
a
tio
n
,
t
h
e
h
o
s
t b
ir
d
ca
n
t
h
r
o
w
t
h
e
eg
g
a
w
a
y
o
r
ab
an
d
o
n
th
e
en
tire
n
e
s
t,
an
d
b
u
ild
a
co
m
p
letel
y
n
e
w
n
est.
B
ased
o
n
th
ese
p
r
in
cip
les,
t
h
e
f
lo
w
ch
ar
t o
f
C
S
A
i
s
d
ep
icted
in
Fi
g
u
r
e
1
.
I
s
p
o
p
u
l
a
t
i
o
n
l
e
s
s
t
h
a
n
m
a
x
i
m
u
m
v
a
l
u
e
?
C
h
e
c
k
s
u
r
v
i
v
a
l
o
f
e
g
g
s
i
n
n
e
s
t
s
I
s
s
t
o
p
p
i
n
g
c
r
i
t
e
r
i
a
s
a
t
i
s
f
i
e
d
?
K
i
l
l
C
u
c
k
o
o
s
a
r
e
w
o
r
s
t
a
r
e
a
N
o
Y
e
s
I
n
i
t
i
a
l
i
z
e
C
u
c
k
o
o
s
w
i
t
h
e
g
g
s
S
t
a
r
t
L
a
y
e
g
g
s
i
n
d
i
f
f
e
r
e
n
t
n
e
s
t
s
S
o
m
e
o
f
e
g
g
s
a
r
e
d
e
t
e
c
t
e
d
a
n
d
k
i
l
l
e
d
F
i
n
d
e
g
g
l
a
y
i
n
g
r
a
d
i
u
s
f
o
r
e
a
c
h
C
u
c
k
o
o
M
o
v
e
a
l
l
C
u
c
k
o
o
s
t
o
w
a
r
d
b
e
s
t
e
n
v
i
r
o
n
m
e
n
t
F
i
n
d
C
u
c
k
o
o
s
o
c
i
e
t
i
e
s
F
i
n
d
n
e
s
t
w
i
t
h
b
e
s
t
s
u
r
v
i
v
a
l
r
a
t
e
S
t
o
p
L
e
t
e
g
g
s
g
r
o
w
N
o
Y
e
s
Fig
u
r
e
1
.
Flo
w
C
h
ar
t o
f
C
u
c
k
o
o
Sear
ch
A
l
g
o
r
ith
m
(
C
S
A
)
.
T
h
e
s
tep
s
to
i
m
p
le
m
e
n
t t
h
e
C
S
A
ca
n
b
e
d
escr
ib
ed
as f
o
llo
w
s
[
2
0
-
2
3
]
:
Step
1
:
I
n
itialize
t
h
e
p
o
p
u
lati
o
n
s
ize
(
n
h
o
s
t
n
est
s
i.e
.
,
x
i
(
i
=1
,
2
,
3
,
.
.
.
,
n
)
)
an
d
m
a
x
i
m
u
m
n
u
m
b
er
o
f
i
ter
atio
n
s
/
g
en
er
atio
n
s
.
Step
2
:
Dete
r
m
i
n
e
t
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,
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(
x
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n
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3:
Fin
d
th
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c
u
r
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b
est
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i.e
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r
en
t b
est.
Step
5
:
Up
d
ate
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g
en
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co
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t.
Ge
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Ge
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1
.
Step
6
:
I
f
th
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n
u
m
b
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o
f
g
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s
is
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est o
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est n
e
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d
it is
th
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m
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4.
RE
SU
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
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C
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Vo
l.
7
,
No
.
5
,
Octo
b
er
2
0
1
7
:
23
49
–
23
5
6
2354
T
ab
le
2
p
r
esen
ts
th
e
o
p
ti
m
u
m
co
n
tr
o
l
v
ar
iab
le
s
an
d
o
p
ti
m
u
m
lo
s
s
v
al
u
es
u
s
i
n
g
th
e
d
if
f
er
e
n
t
o
p
tim
izatio
n
al
g
o
r
it
h
m
s
p
r
ese
n
ted
in
th
e
l
iter
atu
r
e.
Fro
m
t
h
is
T
ab
le,
it
ca
n
b
e
o
b
s
er
v
ed
th
at
t
h
e
o
p
ti
m
u
m
tr
an
s
m
is
s
io
n
lo
s
s
es
o
b
tai
n
ed
u
s
in
g
t
h
e
C
S
A
(
i.e
.
,
4
.
1
0
6
6
M
W
)
is
b
etter
th
an
all
o
t
h
er
o
p
tim
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n
alg
o
r
it
h
m
s
p
r
esen
t
ed
in
t
h
e
liter
at
u
r
e
i.e
.
,
G
A
[
2
]
,
P
SO
[
2
]
,
I
m
p
r
o
v
ed
P
SO
[
2
]
,
DE
[
2
7
]
,
Op
p
o
s
itio
n
-
b
ased
Gr
av
itatio
n
al
Sear
ch
A
l
g
o
r
ith
m
(
OGS
A
)
[
2
8
]
,
Fire
ly
A
l
g
o
r
ith
m
(
F
A
)
[
2
9
]
an
d
Gr
av
itatio
n
al
Sear
ch
A
l
g
o
r
ith
m
[
3
0
]
.
4
.
3
.
Si
m
ula
t
io
n Re
s
ults o
n I
E
E
E
5
7
bu
s
t
est
s
y
s
t
e
m
IEE
E
5
7
b
u
s
s
y
s
te
m
[
2
5
]
co
n
s
is
t
s
o
f
7
g
en
er
atin
g
u
n
it
s
,
8
0
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an
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is
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io
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li
n
es
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1
5
b
r
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ith
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an
s
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o
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m
er
tap
s
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s
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T
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es
1
8
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2
5
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5
3
[
3
1
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.
T
h
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tal
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tiv
e
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n
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ea
cti
v
e
p
o
w
er
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y
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te
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a
r
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1
2
5
0
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8
MW
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3
3
6
.
4
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R
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r
esp
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E
E
E
5
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u
s
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is
g
i
v
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n
in
T
ab
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3
.
T
h
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p
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m
lo
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tain
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u
s
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n
g
d
if
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t
o
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ti
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izatio
n
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o
r
ith
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s
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.
,
C
o
m
p
r
e
h
en
s
i
v
e
L
ea
r
n
i
n
g
P
SO
(
C
L
P
SO)
[
3
2
]
,
DE
[
3
1
]
,
Gr
av
itatio
n
al
Sear
c
h
A
l
g
o
r
ith
m
(
G
S
A
)
[
3
1
]
,
Op
p
o
s
itio
n
-
b
ased
G
S
A
(
OGS
A
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[
3
3
]
,
Seek
er
Op
ti
m
izatio
n
Alg
o
r
it
h
m
(
SO
A
)
[
3
2
]
,
Qu
asi
-
Op
p
o
s
iti
o
n
al
DE
[
3
1
]
an
d
C
S
A
tech
n
i
q
u
es
is
p
r
ese
n
ted
in
T
ab
le
4
.
Fro
m
th
i
s
T
ab
le,
it
c
an
b
e
o
b
s
er
v
ed
th
at
th
e
o
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ti
m
u
m
lo
s
s
o
b
tain
ed
u
s
i
n
g
t
h
e
C
S
A
is
b
etter
th
a
n
t
h
e
alg
o
r
ith
m
s
r
ep
o
r
ted
in
th
e
li
ter
atu
r
e.
T
ab
le
3
.
Gen
er
atio
n
d
ata
o
f
I
E
E
E
5
7
b
u
s
test
s
y
s
te
m
.
Gener
a
t
o
r
N
u
m
b
e
r
(
M
W
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(
M
W
)
(MVAR)
(MVAR)
1
20
50
0
0
2
15
90
50
-
17
3
10
5
0
0
60
-
10
4
10
50
25
-
8
5
12
50
2
0
0
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1
4
0
6
10
3
6
0
9
-
3
7
50
5
5
0
1
5
5
-
50
T
ab
le
4
.
C
o
m
p
ar
is
o
n
o
f
o
p
ti
m
u
m
lo
s
s
o
b
tain
ed
f
o
r
I
E
E
E
5
7
b
u
s
s
y
s
te
m
u
s
i
n
g
d
if
f
er
en
t o
p
t
i
m
izatio
n
alg
o
r
ith
m
s
.
C
L
PSO
[
3
2
]
D
E
[
3
1
]
GS
A
[
3
1
]
OG
S
A
[
3
3
]
S
OA
[
3
2
]
QO
D
E
[
3
1
]
C
S
A
P
Lo
s
s
(
M
W
)
2
4
.
5
1
5
2
1
6
.
7
8
5
7
2
3
.
4
6
1
1
2
3
.
4
3
2
4
.
2
6
5
4
1
5
.
8
4
7
3
1
5
.
5
1
4
9
4
.
4
.
Si
m
ula
t
io
n Re
s
ults o
n I
E
E
E
1
1
8
bu
s
t
est
s
y
s
t
e
m
T
h
is
test
s
y
s
te
m
co
n
s
is
t
s
o
f
5
4
g
en
er
ati
n
g
u
n
i
ts
,
6
4
lo
ad
d
e
m
an
d
s
,
9
tap
s
ettin
g
tr
an
s
f
o
r
m
er
s
an
d
1
4
s
w
itc
h
ab
le
s
h
u
n
t
V
A
R
co
m
p
en
s
ato
r
s
.
T
h
is
test
s
y
s
te
m
d
ata
in
clu
d
i
n
g
lo
w
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d
u
p
p
er
li
m
its
o
f
r
ea
cti
v
e
p
o
w
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o
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r
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s
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d
tr
an
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er
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ar
e
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t
ed
in
[
3
1
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.
T
h
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tal
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tiv
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r
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ctiv
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p
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4
2
4
2
MW
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3
8
MV
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R
,
r
esp
ec
ti
v
el
y
[
3
4
]
.
A
s
m
e
n
tio
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ed
ea
r
lier
,
th
e
g
en
er
ato
r
v
o
ltag
e
m
ag
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it
u
d
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tr
an
s
f
o
r
m
er
tap
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an
d
s
w
itc
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ab
le
V
A
R
s
o
u
r
ce
s
ar
e
co
n
s
id
er
ed
as
th
e
co
n
tr
o
l
v
ar
iab
les.
Hen
ce
,
th
e
to
tals
o
f
7
7
co
n
tr
o
l
v
ar
iab
les
ar
e
r
eq
u
ir
ed
to
b
e
o
p
tim
ized
.
T
ab
le
5
p
r
esen
ts
th
e
o
p
ti
m
u
m
p
o
w
er
lo
s
s
o
b
tain
ed
u
s
i
n
g
t
h
e
C
S
A
a
n
d
v
ar
io
u
s
o
p
ti
m
izatio
n
al
g
o
r
ith
m
s
r
ep
o
r
ted
in
th
e
liter
at
u
r
e
i.e
.
,
P
SO
[
3
1
]
,
C
o
m
p
r
e
h
en
s
iv
e
L
ea
r
n
i
n
g
P
SO
(
C
L
P
SO)
[
3
4
]
,
Gr
av
itatio
n
al
Sear
c
h
A
l
g
o
r
ith
m
(
GS
A
)
[
3
4
]
,
Op
p
o
s
itio
n
-
b
ased
GS
A
[
3
1
]
,
DE
[
3
1
]
,
G
r
ay
W
o
lf
Op
ti
m
izer
(
GW
O)
[
3
4
]
,
Qu
asi
-
o
p
p
o
s
itio
n
al
DE
(
QODE
)
[
3
1
]
an
d
C
S
A
tec
h
n
iq
u
es.
Fro
m
th
is
T
ab
le,
it
ca
n
b
e
o
b
s
er
v
ed
th
at
t
h
e
to
tal
tr
an
s
m
i
s
s
io
n
lo
s
s
o
b
tain
ed
b
y
u
s
in
g
t
h
e
C
S
A
i
s
s
u
p
er
io
r
to
th
e
o
th
er
alg
o
r
ith
m
s
r
ep
o
r
ted
in
th
e
liter
atu
r
e.
T
ab
le
5
.
C
o
m
p
ar
is
o
n
o
f
o
p
ti
m
u
m
lo
s
s
o
b
tain
ed
f
o
r
I
E
E
E
1
1
8
b
u
s
s
y
s
te
m
u
s
in
g
d
if
f
er
e
n
t o
p
ti
m
izatio
n
alg
o
r
ith
m
s
.
PSO
[
3
1
]
C
L
PSO
[
3
4
]
GS
A
[
3
4
]
OG
S
A
[
3
1
]
D
E
[
3
1
]
GW
O
[
3
4
]
QO
D
E
[
3
1
]
C
S
A
P
Lo
s
s
(
M
W
)
1
3
1
.
9
9
1
3
0
.
9
6
1
2
7
.
7
6
1
2
6
.
9
9
8
2
.
2
4
7
3
1
2
0
.
6
5
8
0
.
9
2
5
7
8
0
.
5
8
6
4
4
.
5
.
Si
m
ula
t
io
n Re
s
ults o
n I
E
E
E
3
0
0
bu
s
t
est
s
y
s
t
e
m
T
h
is
test
s
y
s
te
m
[
2
5
]
co
n
s
is
t
s
o
f
6
9
g
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[1
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K.H.A
.
Ra
h
m
a
n
,
e
t
a
l.
,
“
Re
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ti
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sin
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p
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S
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Ku
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t
a
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“
Im
p
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d
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In
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Qu
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.
[4
]
K.
De
b
,
M
u
lt
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o
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ti
v
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Op
ti
miza
ti
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n
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si
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g
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lu
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ry
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lg
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s
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n
d
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s,
2
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[5
]
S
.
S
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re
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r
Re
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d
y
,
e
t
a
l.
,
“
F
a
ste
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lu
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n
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b
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l
p
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w
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f
lo
w
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sin
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in
c
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m
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tal
v
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riab
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n
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l
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ms
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p
p
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1
9
8
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0
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n
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2
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.
[6
]
R.
Ba
ld
ick
,
e
t
a
l.
,
“
A
F
a
st
Distri
b
u
ted
im
p
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n
tatio
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f
Op
ti
m
a
l
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w
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n
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ms
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1
4
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.
[7
]
W
.
P
.
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a
l.
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“
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sig
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in
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a
p
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l
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.
[8
]
A
.
A
b
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m
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t
a
l.
,
Evo
lu
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a
ry
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]
D.
T
h
u
k
a
ra
m
,
e
t
a
l.
,
“
Co
m
p
a
riso
n
o
f
Op
ti
m
u
m
R
e
a
c
ti
v
e
P
o
w
e
r
S
c
h
e
d
u
le
w
it
h
Diff
e
re
n
t
Ob
jec
t
iv
e
s
Us
in
g
L
P
T
e
c
h
n
iq
u
e
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Eme
rg
in
g
El
e
c
tric P
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r
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ms
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l.
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o
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3
,
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p
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6
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1
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2
9
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n
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2
0
0
6
.
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0
]
K.
V
a
isa
k
h
,
e
t
a
l.
,
“
Diffe
re
n
ti
a
l
e
v
o
lu
ti
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n
p
a
rti
c
le
sw
a
r
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p
ti
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iz
a
ti
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n
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lg
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m
f
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re
d
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c
ti
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n
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f
n
e
tw
o
rk
lo
ss
a
n
d
v
o
lt
a
g
e
in
sta
b
il
it
y
”
,
IEE
E
W
o
rld
Co
n
g
re
ss
o
n
Na
tu
re
a
n
d
B
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n
sp
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,
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3
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1
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K
P
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c
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,
KK
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h
a
p
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'
T
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KOM
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[1
2
]
I.
M
u
siri
n
,
e
t
a
l.
,
“
Ev
o
l
u
ti
o
n
a
ry
p
ro
g
ra
m
m
in
g
o
p
ti
m
iza
ti
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n
tec
h
n
iq
u
e
f
o
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so
lv
in
g
re
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c
ti
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e
p
o
we
r
p
lan
n
i
n
g
in
p
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w
e
r
s
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ste
m
”
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f
6
th
W
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2
3
9
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2
4
4
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2
0
0
5
.
[1
3
]
A
.
Bh
a
tt
a
c
h
a
r
y
a
,
e
t
a
l.
,
“
S
o
lu
ti
o
n
o
f
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
w
e
r
F
lo
w
u
sin
g
Bio
g
e
o
g
ra
p
h
y
-
Ba
s
e
d
Op
ti
m
iza
ti
o
n
”
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l,
C
o
mp
u
ter
,
En
e
rg
e
ti
c
,
El
e
c
tro
n
ic
a
n
d
C
o
mm
u
n
ica
ti
o
n
En
g
in
e
e
rin
g
,
v
o
l.
4
,
n
o
.
3
,
2
0
1
0
.
[1
4
]
T
.
S
h
a
r
m
a
,
e
t
a
l.
,
“
Co
m
p
a
r
a
ti
v
e
S
tu
d
y
o
f
M
e
th
o
d
s
f
o
r
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
w
e
r
Disp
a
tch
”
,
El
e
c
trica
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
:
A
n
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
,
v
o
l.
3
,
n
o
.
3
,
p
p
.
5
3
-
6
1
,
A
u
g
.
2
0
1
4
.
[1
5
]
K.
L
e
n
in
,
e
t
a
l.
,
“
Qu
a
n
t
u
m
stirred
c
u
c
k
o
o
se
a
rc
h
a
lg
o
rit
h
m
f
o
r
so
lv
in
g
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
p
r
o
b
lem
”
,
Ame
ric
a
n
J
o
u
r
n
a
l
o
f
S
c
ien
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
1
,
n
o
.
4
,
p
p
.
1
9
9
-
2
0
5
,
2
0
1
4
.
[1
6
]
X
.
S
.
Ya
n
g
,
e
t
a
l.
,
“
C
u
c
k
o
o
se
a
rc
h
v
ia
lev
y
f
li
g
h
ts
”
,
Pro
c
.
o
f
I
E
EE
W
o
rld
C
o
n
g
re
ss
o
n
N
a
t
u
re
&
Bi
o
lo
g
ica
l
ly
In
sp
ire
d
C
o
mp
u
ti
n
g
,
I
n
d
ia,
De
c
.
2
0
0
9
,
p
p.
2
1
0
-
21
4.
[1
7
]
X
.
S
.
Ya
n
g
,
e
t
a
l
.
,
“
En
g
i
n
e
e
rin
g
o
p
ti
m
isa
ti
o
n
b
y
Cu
c
k
o
o
S
e
a
rc
h
”
,
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
M
a
t
h
e
ma
ti
c
a
l
M
o
d
e
ll
in
g
a
n
d
Nu
me
ric
a
l
O
p
ti
misa
t
io
n
,
v
o
l
.
2
,
n
o
.
4
,
p
p
.
3
3
0
-
3
4
3
,
2
0
1
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
5
,
Octo
b
er
2
0
1
7
:
23
49
–
23
5
6
2356
[1
8
]
A
.
B.
M
o
h
a
m
a
d
,
e
t
a
l
.
,
“
Cu
c
k
o
o
S
e
a
rc
h
A
lg
o
rit
h
m
f
o
r
Op
ti
m
iza
ti
o
n
P
ro
b
lem
s
-
A
L
it
e
ra
tu
re
Re
v
ie
w
a
n
d
it
s
A
p
p
li
c
a
ti
o
n
s”
,
A
p
p
li
e
d
Arti
fi
c
i
a
l
I
n
telli
g
e
n
c
e
,
v
o
l.
2
8
,
n
o
.
5
,
p
p
.
4
1
9
-
4
4
8
,
2
0
1
4
.
[1
9
]
S
.
S
.
S
h
a
rif
,
e
t
a
l.
,
“
On
-
li
n
e
Op
ti
m
a
l
P
o
w
e
r
F
lo
w
b
y
En
e
rg
y
L
o
ss
M
in
im
iza
ti
o
n
”
,
Pro
c
.
o
f
3
5
th
IE
EE
Co
n
fer
e
n
c
e
o
n
De
c
isio
n
a
n
d
Co
n
tro
l
,
Ko
b
e
,
J
a
p
a
n
,
De
c
.
1
9
9
6
,
p
p
.
1
-
6.
[2
0
]
P
.
Jia
n
g
,
e
t
a
l.
,
“
Cu
c
k
o
o
se
a
rc
h
-
d
e
sig
n
a
ted
f
ra
c
tal
in
terp
o
latio
n
f
u
n
c
ti
o
n
s
w
it
h
w
in
n
e
r
c
o
m
b
in
a
ti
o
n
f
o
r
e
sti
m
a
ti
n
g
m
is
sin
g
v
a
lu
e
s in
ti
m
e
se
ries
”
,
Ap
p
li
e
d
M
a
t
h
e
ma
ti
c
a
l
M
o
d
e
ll
in
g
,
M
a
y
2
0
1
6
.
[2
1
]
A
.
H.
G
a
n
d
o
m
i
,
e
t
a
l.
,
“
Cu
c
k
o
o
se
a
rc
h
a
lg
o
rit
h
m
:
a
m
e
tah
e
u
risti
c
a
p
p
ro
a
c
h
t
o
so
lv
e
stru
c
t
u
ra
l
o
p
t
im
iza
ti
o
n
p
ro
b
lem
s
”
,
En
g
in
e
e
rin
g
wit
h
Co
mp
u
ter
s
,
v
o
l.
2
9
,
n
o
.
1
,
p
p
.
1
7
-
3
5
,
Ja
n
.
2
0
1
3
.
[2
2
]
R.
Ra
jab
io
u
n
,
“
Cu
c
k
o
o
o
p
t
im
iza
ti
o
n
a
lg
o
rit
h
m
”
,
Ap
p
li
e
d
S
o
ft
C
o
mp
u
t
in
g
,
v
o
l
.
1
1
,
n
o
.
8
,
p
p
.
5
5
0
8
-
5
5
1
8
,
De
c
.
2
0
1
1
.
[2
3
]
R.
R.
Bu
lato
v
ić
,
e
t
a
l
.
,
“
Cu
c
k
o
o
S
e
a
rc
h
a
lg
o
rit
h
m
:
A
m
e
tah
e
u
risti
c
a
p
p
ro
a
c
h
to
s
o
lv
in
g
th
e
p
r
o
b
le
m
o
f
o
p
ti
m
u
m
s
y
n
th
e
sis o
f
a
six
-
b
a
r
d
o
u
b
le d
w
e
ll
li
n
k
a
g
e
”
,
M
e
c
h
a
n
ism a
n
d
M
a
c
h
i
n
e
T
h
e
o
ry
,
v
o
l.
6
1
,
p
p
.
1
-
1
3
,
M
a
r.
2
0
1
3
.
[2
4
]
K.H.
A
b
d
u
l
-
Ra
h
m
a
n
,
e
t
a
l.
,
“
A
F
u
z
z
y
Ba
se
d
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
w
e
r
Co
n
tro
l”,
IEE
E
T
ra
n
s.
Po
we
r
S
y
st.
,
v
o
l.
7
8
,
n
o
.
2
,
p
p
.
6
6
2
-
6
7
0
,
M
a
y
1
9
9
2
.
[2
5
]
Av
a
il
a
b
le.
[
On
l
in
e
]
.
h
tt
p
:/
/w
ww
2
.
e
e
.
w
a
sh
in
g
to
n
.
e
d
u
/res
e
a
rc
h
/p
stc
a
/
[2
6
]
A
.
Ra
jan
,
e
t
a
l.
,
“
Ex
c
h
a
n
g
e
M
a
rk
e
t
A
l
g
o
rit
h
m
b
a
se
d
Op
ti
m
u
m
Re
a
c
ti
v
e
P
o
w
e
r
Disp
a
tch
”
,
Ap
p
li
e
d
S
o
ft
Co
m
p
u
ti
n
g
,
v
o
l.
4
3
,
p
p
.
3
2
0
-
3
3
6
,
2
0
1
6
.
[2
7
]
A
.
A
.
A
.
E.
El
a
,
e
t
a
l.
,
“
Dif
fe
re
n
ti
a
l
e
v
o
lu
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
w
e
r
d
isp
a
tch
”
,
El
e
c
trica
l
Po
we
r
S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
8
1
,
p
p
.
4
5
8
-
4
6
4
,
2
0
1
1
.
[2
8
]
B.
S
h
a
w
,
e
t
a
l.
,
“
S
o
lu
t
io
n
o
f
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tc
h
o
f
p
o
w
e
r
s
y
st
e
m
s
b
y
a
n
o
p
p
o
siti
o
n
-
b
a
se
d
g
ra
v
it
a
ti
o
n
a
l
se
a
rc
h
a
lg
o
rit
h
m
”
,
El
e
c
trica
l
Po
we
r a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
5
5
,
p
p
.
2
9
-
4
0
,
2
0
1
4
.
[2
9
]
A
.
Ra
j
a
n
,
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
h
y
b
rid
Ne
ld
e
r
–
M
e
a
d
sim
p
lex
b
a
se
d
f
ire
f
l
y
a
lg
o
rit
h
m
”
,
El
e
c
tric
a
l
Po
we
r a
n
d
En
e
rg
y
S
y
st
e
ms
,
v
o
l.
6
6
,
p
p
.
9
-
2
4
,
2
0
1
5
.
[3
0
]
S
.
Du
m
a
n
,
e
t
a
l.
,
“
Op
ti
m
a
l
r
e
a
c
t
iv
e
p
o
w
e
r
d
isp
a
tch
u
sin
g
a
g
ra
v
i
tatio
n
a
l
se
a
rc
h
a
lg
o
rit
h
m
”
,
IET
Ge
n
e
r.
T
ra
n
sm
.
a
n
d
Distrib
.
,
v
o
l.
6
,
n
o
.
6
,
p
p
.
5
6
3
-
5
7
6
,
2
0
1
2
.
[3
1
]
M
.
Ba
su
,
“
Qu
a
si
-
o
p
p
o
siti
o
n
a
l
d
i
ff
e
r
e
n
ti
a
l
e
v
o
lu
ti
o
n
f
o
r
o
p
ti
m
a
l
r
e
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
”
,
El
e
c
tri
c
a
l
Po
we
r
a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
7
8
,
p
p
.
2
9
-
4
0
,
2
0
1
6
.
[3
2
]
C.
Da
i
,
e
t
a
l.
,
“
S
e
e
k
e
r
o
p
ti
m
iza
ti
o
n
a
lg
o
ri
th
m
f
o
r
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
”
,
IEE
E
T
ra
n
s.
P
o
we
r
S
y
ste
ms
,
v
o
l.
2
4
,
n
o
.
3
,
p
p
.
1
2
1
8
-
1
2
3
1
,
2
0
0
9
.
[3
3
]
B.
S
h
a
w
,
e
t
a
l.
,
“
S
o
l
u
ti
o
n
o
f
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
o
f
p
o
w
e
r
s
y
st
e
m
s
b
y
a
n
o
p
p
o
siti
o
n
-
b
a
se
d
g
ra
v
i
tatio
n
a
l
se
a
rc
h
a
lg
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 E
n
e
rg
y
S
y
ste
ms
,
v
o
l.
5
5
,
p
p
.
2
9
-
4
0
,
2
0
1
4
.
[3
4
]
M
.
H.
S
u
laim
a
n
,
e
t
a
l.
,
“
Us
in
g
t
h
e
g
ra
y
w
o
l
f
o
p
ti
m
iz
e
r
f
o
r
so
lv
in
g
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
p
ro
b
lem
”
,
Ap
p
li
e
d
S
o
ft
Co
mp
u
ti
n
g
,
v
o
l.
3
2
,
p
p
.
2
8
6
-
2
9
2
,
2
0
1
5
.
[3
5
]
S
.
S
.
Re
d
d
y
,
e
t
a
l.
,
“
F
a
ste
r
e
v
o
lu
ti
o
n
a
ry
a
l
g
o
rit
h
m
b
a
se
d
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
u
sin
g
in
c
re
m
e
n
tal
v
a
riab
les
”
,
El
e
c
trica
l
Po
we
r a
n
d
En
e
rg
y
S
y
st
e
ms
,
v
o
l.
5
4
,
p
p
.
1
9
8
-
2
1
0
,
2
0
1
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.