I
nte
rna
t
io
na
l J
o
urna
l o
f
I
nfo
rm
a
t
ics a
nd
Co
m
m
un
ica
t
io
n T
ec
hn
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lo
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y
(
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J
-
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)
Vo
l.
9
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No
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Ap
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2
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N:
2252
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:
h
ttp
:
//ij
ict.
ia
esco
r
e.
co
m
Enha
nced wormh
o
le optimizer
alg
o
rithm
for so
lv
ing
optima
l
reactiv
e power
pr
o
blem
K
a
na
g
a
s
a
ba
i Leni
n
De
p
a
rtme
n
t
o
f
EE
E
,
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ra
sa
d
V.
P
o
tl
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ri
S
id
d
h
a
rt
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a
In
stit
u
te o
f
Tec
h
n
o
lo
g
y
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In
d
ia
Art
icle
I
nfo
AB
S
T
RAC
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A
r
ticle
his
to
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y:
R
ec
eiv
ed
No
v
1
1
,
2
0
19
R
ev
is
ed
No
v
13
,
2
0
19
Acc
ep
ted
Dec
2
7
,
2
0
19
In
t
h
is
p
a
p
e
r
E
n
h
a
n
c
e
d
Wo
rm
h
o
le
Op
ti
m
ize
r
(E
WO)
a
lg
o
rit
h
m
is
u
se
d
to
so
lv
e
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
p
ro
b
lem
.
P
r
o
p
o
se
d
a
lg
o
r
it
h
m
b
a
s
e
d
o
n
t
h
e
Wo
rm
h
o
les
wh
ich
e
x
p
l
o
it
s
th
e
e
x
p
l
o
ra
ti
o
n
sp
a
c
e
.
Be
twe
e
n
d
iffere
n
t
u
n
i
v
e
rse
s
o
b
jec
ts
a
re
e
x
c
h
a
n
g
e
d
t
h
ro
u
g
h
wh
it
e
o
r
b
lac
k
h
o
l
e
tu
n
n
e
ls.
Re
g
a
rd
les
s
o
f
t
h
e
in
flati
o
n
ra
te,
t
h
ro
u
g
h
wo
rm
h
o
les
o
b
jec
ts
in
a
ll
u
n
i
v
e
rse
s
wh
ich
p
o
ss
e
ss
h
ig
h
p
ro
b
a
b
il
it
y
will
sh
ift
to
t
h
e
m
o
st
e
x
c
e
ll
e
n
t
u
n
iv
e
rse
.
In
th
e
p
ro
jec
ted
E
n
h
a
n
c
e
d
W
o
rm
h
o
le
Op
ti
m
ize
r
(EW
O)
a
l
g
o
rit
h
m
i
n
o
rd
e
r
t
o
a
v
o
id
th
e
so
lu
ti
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n
to
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o
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h
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ti
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e
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g
h
t
h
a
s
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e
e
n
a
p
p
li
e
d
.
P
ro
jec
ted
En
h
a
n
c
e
d
Wo
rm
h
o
le
Op
ti
m
ize
r
(EW
O)
a
lg
o
rit
h
m
h
a
s
b
e
e
n
tes
ted
in
st
a
n
d
a
rd
I
E
EE
1
4
,
3
0
,
5
7
,
1
1
8
,
3
0
0
b
u
s
tes
t
sy
ste
m
s a
n
d
sim
u
latio
n
re
su
lt
s s
h
o
w t
h
a
t
t
h
e
EW
O alg
o
rit
h
m
re
d
u
c
e
d
th
e
re
a
l
p
o
we
r
lo
ss
e
fficie
n
t
ly
.
K
ey
w
o
r
d
s
:
E
n
h
an
ce
d
wo
r
m
h
o
le
o
p
tim
izer
Op
tim
al
r
ea
ctiv
e
p
o
wer
T
r
an
s
m
is
s
io
n
lo
s
s
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
:
Kan
ag
asab
ai
L
en
in
,
Dep
ar
tm
en
t o
f
E
E
E
,
Pra
s
ad
V.
Po
tlu
r
i Sid
d
h
ar
th
a,
I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
,
Kan
u
r
u
,
Vijay
awa
d
a
,
An
d
h
r
a
Pra
d
esh
-
5
2
0
0
0
7
,
I
n
d
ia
.
E
m
ail:
g
k
len
in
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Fo
r
s
ec
u
r
e
an
d
ec
o
n
o
m
ic
o
p
e
r
atio
n
s
o
f
p
o
wer
s
y
s
tem
o
p
ti
m
al
r
ea
ctiv
e
p
o
wer
p
r
o
b
lem
p
lay
s
v
ital
r
o
le.
Sev
er
al
ty
p
es
o
f
tec
h
n
iq
u
e
s
[1
-
6
]
h
a
v
e
b
ee
n
u
tili
ze
d
t
o
s
o
lv
e
th
e
p
r
o
b
lem
p
r
ev
io
u
s
l
y
.
C
o
n
v
er
s
ely
m
an
y
d
if
f
icu
lties
ar
e
f
o
u
n
d
wh
ile
s
o
lv
in
g
p
r
o
b
lem
d
u
e
to
in
e
q
u
alit
y
co
n
s
tr
ain
t
s
.
E
v
o
lu
tio
n
a
r
y
te
ch
n
iq
u
es
[
7
-
15
]
ar
e
ap
p
lied
to
s
o
lv
e
th
e
r
ea
ctiv
e
p
o
wer
p
r
o
b
lem
.
T
h
is
p
ap
er
p
r
o
p
o
s
es
E
n
h
an
ce
d
W
o
r
m
h
o
le
Op
tim
izer
(
E
W
O)
a
lg
o
r
ith
m
f
o
r
s
o
lv
in
g
o
p
tim
a
l
r
ea
ctiv
e
p
o
wer
p
r
o
b
lem
.
W
o
r
m
h
o
le
Op
tim
izer
Alg
o
r
ith
m
is
b
ased
o
n
th
e
W
o
r
m
h
o
les wh
ich
ex
p
lo
it th
e
ex
p
lo
r
atio
n
s
p
ac
e
.
W
o
r
m
h
o
le
tu
n
n
el
ar
e
b
u
ilt
f
o
r
lo
ca
l c
h
an
g
e
in
ea
ch
u
n
i
v
er
s
e
m
th
r
o
u
g
h
m
o
s
t
ex
ce
l
len
t
u
n
iv
er
s
e
th
en
p
r
o
b
ab
ilit
y
o
f
r
ef
in
em
en
t
t
h
e
in
f
latio
n
r
ate
is
d
o
n
e
t
h
r
o
u
g
h
wo
r
m
h
o
les.
Ob
jects
ar
e
ex
ch
an
g
ed
th
r
o
u
g
h
tu
n
n
els
an
d
w
o
r
m
h
o
les
o
b
jects
wh
ich
p
o
s
s
ess
h
ig
h
p
r
o
b
a
b
ilit
y
will sh
if
t to
th
e
m
o
s
t e
x
ce
llen
t u
n
iv
er
s
e
.
I
n
th
e
p
r
o
jecte
d
E
n
h
an
ce
d
W
o
r
m
h
o
le
Op
tim
izer
(
E
W
O)
a
lg
o
r
ith
m
in
o
r
d
er
to
a
v
o
id
th
e
s
o
lu
tio
n
to
b
e
g
et
tr
ap
p
ed
i
n
to
th
e
lo
ca
l
o
p
tim
al
s
o
lu
tio
n
L
e
v
y
f
lig
h
t
h
as
b
ee
n
ap
p
lied
.
Pr
o
jecte
d
E
n
h
a
n
ce
d
W
o
r
m
h
o
le
Op
tim
izer
(
E
W
O)
a
lg
o
r
i
th
m
h
as
b
ee
n
test
ed
in
s
tan
d
ar
d
I
E
E
E
1
4
,
3
0
,
5
7
,
1
1
8
,
3
0
0
b
u
s
test
s
y
s
tem
s
a
n
d
s
im
u
latio
n
r
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lts
s
h
o
w
th
at
th
e
p
r
o
jecte
d
alg
o
r
ith
m
r
ed
u
ce
d
t
h
e
r
ea
l
p
o
wer
lo
s
s
ef
f
ec
tiv
ely
.
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
Ob
j
ec
t
iv
e
o
f
t
h
e
p
r
o
b
le
m
is
t
o
r
e
d
u
ce
t
h
e
t
r
u
e
p
o
w
e
r
l
o
s
s
:
F
=
P
L
=
∑
g
k
k
∈
Nbr
(
V
i
2
+
V
j
2
−
2
V
i
V
j
c
os
θ
ij
)
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
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8
7
7
6
I
n
t J I
n
f
&
C
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m
m
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n
T
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h
n
o
l
,
Vo
l.
9
,
No
.
1,
Ap
r
il
20
20
:
1
–
8
2
Vo
l
ta
g
e
d
e
v
ia
ti
o
n
g
i
v
e
n
as
f
o
ll
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ws:
F
=
P
L
+
ω
v
×
Vol
ta
ge
De
via
tio
n
(
2
)
Vol
ta
ge
De
via
tion
=
∑
|
V
i
−
1
|
N
p
q
i
=
1
(
3
)
C
o
n
s
tr
ain
t
(
E
q
u
ality
)
P
G
=
P
D
+
P
L
(
4
)
C
o
n
s
tr
ain
ts
(
I
n
eq
u
ality
)
P
g
s
l
ack
m
i
n
≤
P
g
s
l
ac
k
≤
P
g
s
l
ack
m
ax
(
5
)
Q
gi
m
i
n
≤
Q
gi
≤
Q
gi
m
ax
,
i
∈
N
g
(
6
)
V
i
m
i
n
≤
V
i
≤
V
i
m
ax
,
i
∈
N
(
7
)
T
i
m
i
n
≤
T
i
≤
T
i
m
ax
,
i
∈
N
T
(
8
)
Q
c
m
i
n
≤
Q
c
≤
Q
C
m
ax
,
i
∈
N
C
(
9
)
3.
E
nh
a
nce
d Wo
rm
ho
le
O
ptimizer
Alg
o
rit
hm
W
o
r
m
h
o
le
Op
tim
izer
Alg
o
r
it
h
m
is
b
ased
o
n
th
e
W
o
r
m
h
o
l
es
wh
ich
ex
p
l
o
it
th
e
e
x
p
lo
r
atio
n
s
p
ac
e.
T
h
r
o
u
g
h
wo
r
m
h
o
les
o
b
jects
wh
ich
h
as
h
ig
h
p
r
o
b
ab
ilit
y
will
s
h
if
t
to
th
e
m
o
s
t
ex
ce
llen
t
u
n
iv
er
s
e
an
d
it
m
o
d
eled
b
y
u
s
in
g
r
o
u
lette
wh
ee
l selec
tio
n
m
eth
o
d
o
l
o
g
y
as f
o
ll
o
ws,
=
[
11
⋯
1
⋮
⋱
⋮
1
⋯
]
(
1
0
)
Nu
m
b
er
o
f
th
e
v
ar
iab
les
is
in
d
icate
d
b
y
“d
”
a
n
d
n
u
m
b
e
r
o
f
u
n
iv
e
r
s
e
wh
ich
is
co
n
s
id
er
ed
as
ca
n
d
id
ate
s
o
lu
tio
n
is
in
d
icate
d
b
y
”n
”.
=
{
1
<
(
)
1
<
(
)
(
1
1
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T
h
r
o
u
g
h
r
o
u
lette
w
h
ee
l
s
elec
tio
n
′
“
j
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p
ar
am
eter
o
f
th
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“k
”
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s
e
will
b
e
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h
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s
en
,
in
th
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“i
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“j
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a
r
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r
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p
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ess
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y
,
ith
u
n
iv
er
s
e
in
f
latio
n
r
ate
in
d
icate
d
b
y
(
)
,
ith
u
n
iv
er
s
e
in
d
icate
d
b
y
,
1
∈
[
0
,
1
]
.
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n
b
etwe
en
two
u
n
iv
er
s
es
wo
r
m
h
o
le
tu
n
n
el
[
1
6
,
1
7
]
ar
e
b
u
il
t
th
en
th
e
lo
ca
l
ch
an
g
e
f
o
r
ea
c
h
u
n
iv
er
s
e
is
d
o
n
e
b
y
m
o
s
t
ex
ce
llen
t
u
n
iv
er
s
e
an
d
t
h
e
elev
ated
p
r
o
b
ab
ilit
y
o
f
r
ef
in
em
e
n
t
th
e
in
f
latio
n
r
ate
th
r
o
u
gh
wo
r
m
h
o
les is
d
o
n
e
b
y
,
=
{
{
+
.
×
(
(
−
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×
4
+
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3
<
0
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5
−
.
×
(
(
−
)
×
4
+
)
3
≥
0
.
5
2
≥
2
<
(
1
2
)
W
o
r
m
h
o
le
ex
is
ten
ce
p
r
o
b
a
b
ilit
y
in
d
icate
d
b
y
“w
e
p
”,
“tr
.
”
I
n
d
icate
s
th
e
tr
a
v
ellin
g
a
n
d
r
an
d
o
m
d
en
o
ted
b
y
“
r
an
d
”.
Du
r
in
g
th
e
o
p
tim
izatio
n
p
r
o
ce
d
u
r
e
ex
p
lo
itatio
n
h
as
b
ee
n
en
h
an
ce
d
as f
o
llo
ws,
Worm
h
ole
e
x
ist
e
nce
p
ro
ba
bilit
y
=
w
mi
ni
mu
m
+
cu
rre
nt
itera
t
io
n
(
w
m
a
xi
m
u
m
−
w
m
in
im
u
m
ma
x
i
mu
m
i
ter
a
ti
o
n
)
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
E
n
h
a
n
ce
d
w
o
r
mh
o
le
o
p
timiz
er a
lg
o
r
ith
m
fo
r
s
o
lvin
g
o
p
tima
l rea
ctive
…
(
K
a
n
a
g
a
s
a
b
a
i Len
in
)
3
I
n
o
r
d
er
to
im
p
r
o
v
e
th
e
lo
ca
l
s
ea
r
ch
p
r
ec
is
ely
tr
av
ellin
g
d
is
tan
ce
r
ate
will
b
e
in
cr
ea
s
ed
o
v
er
t
h
e
iter
atio
n
s
as f
o
ll
o
ws,
=
1
−
cu
r
r
e
nt
i
ter
a
ti
o
n
1
⁄
ma
x
i
mu
m
i
ter
a
ti
o
n
1
⁄
(
1
4
)
I
n
th
e
p
r
o
jecte
d
E
n
h
an
ce
d
W
o
r
m
h
o
le
O
p
tim
izer
(
E
W
O)
a
lg
o
r
ith
m
in
o
r
d
e
r
to
av
o
id
th
e
s
o
lu
tio
n
to
b
e
g
et
tr
ap
p
ed
in
to
th
e
lo
ca
l
o
p
tim
al
s
o
lu
ti
o
n
L
ev
y
f
lig
h
t
h
a
s
b
ee
n
a
p
p
lied
.
L
ev
y
f
lig
h
t
is
a
r
a
n
k
o
f
n
o
n
-
Gau
s
s
ian
r
an
d
o
m
p
r
o
ce
d
u
r
e
wh
o
s
e
ca
p
r
icio
u
s
walk
s
ar
e
h
ag
g
ar
d
f
r
o
m
L
ev
y
s
tab
le
d
is
tr
ib
u
tio
n
.
Allo
ca
tio
n
b
y
L(s)
~
|s|
-
1
-
β
wh
er
e
0
<
ß
<
2
is
an
in
d
ex
.
Scien
tific
ally
d
e
f
in
ed
as,
(
,
,
)
=
{
√
2
0
≤
0
[
−
2
(
−
)
]
1
(
−
)
3
2
⁄
0
<
<
<
∞
(
1
5
)
I
n
ter
m
s
o
f
Fo
u
r
ier
tr
a
n
s
f
o
r
m
L
ev
y
d
is
tr
ib
u
tio
n
d
ef
i
n
ed
as
(
)
=
[
−
|
|
]
,
0
<
≤
2
,
(
1
6
)
Fre
s
h
s
tate
is
ca
lcu
lated
as,
+
1
=
+
⊕
(
)
(
1
7
)
+
1
=
+
(
(
)
)
⊕
(
)
(
1
8
)
I
n
th
e
p
r
o
jecte
d
E
n
h
a
n
ce
d
W
o
r
m
h
o
le
Op
tim
izer
(
E
W
O
)
alg
o
r
ith
m
w
h
ile
g
e
n
er
atio
n
o
f
n
ew
s
o
lu
tio
n
s
+
1
lev
y
f
lig
h
t (
y
)
will b
e
ap
p
lied
,
+
1
=
+
(
+
(
−
)
∗
(
)
)
×
(
1
9
)
L
ev
y
f
lig
h
t
will
b
e
a
p
p
lied
i
n
th
e
a
d
ap
tiv
e
m
o
d
e
t
o
b
ala
n
ce
th
e
e
x
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
b
y
ap
p
ly
in
g
lar
g
e
lev
y
weig
h
t in
it
ially
an
d
f
in
al
c
o
u
r
s
e
th
e
weig
h
t o
f
th
e
le
v
y
will b
e
d
ec
r
ea
s
ed
,
=
(
−
)
(
2
0
)
B
y
u
s
in
g
Ma
n
teg
n
a'
s
alg
o
r
ith
m
No
n
-
tr
iv
ial
s
ch
em
e
o
f
e
n
g
e
n
d
er
in
g
s
tep
s
ize
b
y
,
=
|
|
1
(
2
1
)
+
1
=
+
(
(
)
)
⊕
(
)
~
0
.
01
|
|
1
⁄
(
−
)
(
2
2
)
~
(
0
,
2
)
~
(
0
,
2
)
(
2
3
)
with
=
{
Г
(
1
+
)
(
/
2
)
Г
[
(
1
+
)
/
2
]
2
(
−
1
)
/
2
}
1
⁄
,
=
1
(
2
4
)
th
en
,
(
)
=
0
.
01
×
×
|
|
1
(
2
5
)
Star
t
I
n
p
u
t
;
“
d
”
&
“n
”
;
L
o
wer
b
o
u
n
d
=
[
L
b
1
,
L
b
2
,
.
.
.
,
L
bd
]
;
U
p
p
er
b
o
u
n
d
=
[
Ub
1
,
Ub
2
,
.
.
.
,
U
bd
]
;
Ma
x
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
Ou
tp
u
t: Op
tim
al
s
o
lu
tio
n
Step
a:
I
n
itializatio
n
o
f
p
a
r
am
eter
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
9
,
No
.
1,
Ap
r
il
20
20
:
1
–
8
4
E
n
g
en
d
e
r
ar
b
itra
r
y
u
n
iv
er
s
es “
U”
b
y
=
{
1
,
2
,
.
.
,
.
.
,
}
I
n
itialize
W
o
r
m
h
o
le
ex
is
ten
ce
p
r
o
b
a
b
ilit
y
,
tr
av
ellin
g
d
is
tan
c
e
r
ate
,
o
b
jectiv
e
f
u
n
ctio
n
t =
0
Step
b
:
ca
teg
o
r
izatio
n
an
d
r
eo
r
g
an
ize;
ar
r
a
n
g
e
th
e
u
n
iv
e
r
s
es;
u
n
iv
er
s
e
in
f
latio
n
r
ate
(
UI
)
will
b
e
r
eo
r
g
a
n
ized
Step
c:
I
ter
atio
n
; w
h
ile
t <
Ma
x
im
u
m
iter
atio
n
C
o
m
p
u
te
u
n
iv
e
r
s
e
in
f
latio
n
r
at
e;
UI
(
)
;
i =
1
,
2
,
.
.
.
,
n
Fo
r
ev
er
y
u
n
iv
e
r
s
e
“U
i
”;
m
o
d
er
n
ize
W
o
r
m
h
o
le
e
x
is
ten
ce
p
r
o
b
ab
ilit
y
,
tr
av
ellin
g
d
is
tan
ce
r
ate
by
W
or
m
hol
e
e
xiste
n
c
e
pr
ob
a
b
il
ity
=
w
m
i
n
i
m
u
m
+
c
urr
e
n
t
ite
r
a
ti
on
(
w
m
axim
u
m
−
w
m
ini
mum
m
ax
i
m
um
i
t
er
at
i
o
n
)
=
1
−
cu
r
r
e
n
t
i
t
er
at
i
o
n
1
⁄
m
ax
i
m
um
i
t
er
at
i
o
n
1
⁄
; Bl
ac
k
h
o
le
in
d
ex
v
alu
e
=
i
Mo
d
er
n
ize
th
e
v
alu
e
“U”
b
y
+
1
=
+
(
+
(
−
)
∗
(
)
)
×
Fo
r
ev
er
y
o
b
ject
;
1
=
r
an
d
o
m
(
0
,
1
)
;
If
1
<
UI
(
U
i
)
; w
h
ite
h
o
le
in
d
ex
=
r
o
u
lette
wh
ee
l selec
tio
n
(
-
UI
)
;
U
(
b
lack
h
o
le
in
d
ex
,
j)
=
SU(
wh
ite
h
o
le
in
d
e
x
,
j)
;
E
n
d
if
2
=
r
an
d
o
m
(
0
,
1
)
;
If
2
<
W
o
r
m
h
o
le
ex
is
ten
ce
p
r
o
b
ab
ilit
y
3
=
r
an
d
o
m
(
0
,
1
)
;
4
=
r
an
d
o
m
(
0
,
1
)
;
If
3
<
0
.
5
=
(
)
+
∗
(
(
(
)
−
(
)
)
∗
4
+
(
)
)
Or
else
=
(
)
−
∗
(
(
(
)
−
(
)
)
∗
4
+
(
)
)
E
n
d
if
E
n
d
f
o
r
t =
t+1
E
n
d
wh
ile
Step
d
: E
n
d
; o
u
tp
u
t th
e
o
p
tim
a
l so
lu
tio
n
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
At
f
ir
s
t
in
s
tan
d
ar
d
I
E
E
E
1
4
b
u
s
s
y
s
tem
[
1
8
]
th
e
v
alid
ity
o
f
th
e
p
r
o
p
o
s
ed
E
n
h
an
ce
d
W
o
r
m
h
o
le
Op
tim
izer
(
E
W
O)
a
lg
o
r
ith
m
h
as
b
ee
n
test
ed
,
T
a
b
le
1
s
h
o
ws
th
e
co
n
s
tr
ain
ts
o
f
co
n
tr
o
l
v
ar
iab
les
T
ab
le
2
s
h
o
ws th
e
lim
its
o
f
r
ea
ctiv
e
p
o
wer
g
en
er
ato
r
s
an
d
c
o
m
p
ar
is
o
n
r
esu
lts
ar
e
p
r
esen
ted
i
n
T
ab
l
e
3
.
T
ab
le
1
.
C
o
n
s
tr
ain
ts
o
f
c
o
n
tr
o
l
v
ar
iab
les
S
y
st
e
m
V
a
r
i
a
b
l
e
s
M
i
n
i
m
u
m
(PU)
M
a
x
i
m
u
m
(PU)
I
EEE
1
4
B
u
s
G
e
n
e
r
a
t
o
r
V
o
l
t
a
g
e
0
.
9
5
1
.
1
Tr
a
n
sf
o
r
mer
Ta
p
o
.
9
1
.
1
V
A
R
S
o
u
r
c
e
0
0
.
2
0
T
ab
le
2
.
C
o
n
s
tr
ain
s
o
f
r
ea
ctiv
e
p
o
wer
g
e
n
er
ato
rs
S
y
st
e
m
V
a
r
i
a
b
l
e
s
Q
M
i
n
i
mu
m
(PU)
Q
M
a
x
i
mu
m
(PU)
I
EEE
1
4
B
u
s
1
0
10
2
-
40
50
3
0
40
6
-
6
24
8
-
6
24
T
ab
le
3
.
Simu
latio
n
r
esu
lts
o
f
I
E
E
E
−1
4
s
y
s
tem
C
o
n
t
r
o
l
v
a
r
i
a
b
l
e
s
B
a
se
c
a
se
M
P
S
O
[
1
9
]
P
S
O
[
1
9
]
EP [
1
9
]
S
A
R
G
A
[
1
9
]
EWO
−1
1
.
0
6
0
1
.
1
0
0
1
.
1
0
0
N
R
*
N
R
*
1
.
0
1
3
−
2
1
.
0
4
5
1
.
0
8
5
1
.
0
8
6
1
.
0
2
9
1
.
0
6
0
1
.
0
1
4
−
3
1
.
0
1
0
1
.
0
5
5
1
.
0
5
6
1
.
0
1
6
1
.
0
3
6
1
.
0
0
2
−
6
1
.
0
7
0
1
.
0
6
9
1
.
0
6
7
1
.
0
9
7
1
.
0
9
9
1
.
0
1
7
−
8
1
.
0
9
0
1
.
0
7
4
1
.
0
6
0
1
.
0
5
3
1
.
0
7
8
1
.
0
2
1
8
0
.
9
7
8
1
.
0
1
8
1
.
0
1
9
1
.
0
4
0
.
9
5
0
.
9
1
0
9
0
.
9
6
9
0
.
9
7
5
0
.
9
8
8
0
.
9
4
0
.
9
5
0
.
9
1
3
10
0
.
9
3
2
1
.
0
2
4
1
.
0
0
8
1
.
0
3
0
.
9
6
0
.
9
2
7
−
9
0
.
1
9
1
4
.
6
4
0
.
1
8
5
0
.
1
8
0
.
0
6
0
.
1
2
0
2
7
2
.
3
9
2
7
1
.
3
2
2
7
1
.
3
2
N
R
*
N
R
*
2
7
1
.
7
8
(
M
v
a
r
)
8
2
.
4
4
7
5
.
7
9
7
6
.
7
9
N
R
*
N
R
*
7
5
.
7
9
R
e
d
u
c
t
i
o
n
i
n
P
L
o
ss (%)
0
9
.
2
9
.
1
1
.
5
2
.
5
2
5
.
8
5
To
t
a
l
P
Lo
s
s (M
w
)
1
3
.
5
5
0
1
2
.
2
9
3
1
2
.
3
1
5
1
3
.
3
4
6
1
3
.
2
1
6
1
0
.
0
4
7
N
R
*
-
N
o
t
r
e
p
o
r
t
e
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
E
n
h
a
n
ce
d
w
o
r
mh
o
le
o
p
timiz
er a
lg
o
r
ith
m
fo
r
s
o
lvin
g
o
p
tima
l rea
ctive
…
(
K
a
n
a
g
a
s
a
b
a
i Len
in
)
5
T
h
en
E
n
h
a
n
ce
d
W
o
r
m
h
o
le
Op
tim
izer
(
E
W
O)
a
lg
o
r
ith
m
h
a
s
b
ee
n
test
ed
,
in
I
E
E
E
3
0
B
u
s
s
y
s
tem
.
T
ab
le
4
s
h
o
ws
th
e
co
n
s
tr
ain
ts
o
f
co
n
tr
o
l
v
ar
iab
les,
T
ab
le
5
s
h
o
ws
th
e
lim
its
o
f
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5.
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o
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ap
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it
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test
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latio
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esu
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alg
o
r
ith
m
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ed
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ce
d
t
h
e
r
ea
l
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s
s
ef
f
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tly
.
Per
ce
n
tag
e
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f
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l
p
o
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s
s
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ed
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ctio
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h
as
b
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h
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d
wh
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to
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th
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s
tan
d
ar
d
alg
o
r
ith
m
s
.
RE
F
E
R
E
NC
E
S
[1
]
K.
Y.
Lee
,
“
F
u
e
l
-
c
o
st
m
in
imis
a
ti
o
n
fo
r
b
o
t
h
re
a
l
a
n
d
re
a
c
ti
v
e
-
p
o
we
r
d
isp
a
tch
e
s,”
Pro
c
e
e
d
in
g
s
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
a
n
d
Distrib
u
ti
o
n
C
o
n
fer
e
n
c
e
,
v
o
l
.
1
3
1
,
n
o
.
3
,
p
p
.
8
5
-
93
,
1
9
8
4
.
[2
]
N.
I.
De
e
b
,
“
An
e
fficie
n
t
tec
h
n
i
q
u
e
f
o
r
re
a
c
ti
v
e
p
o
we
r
d
is
p
a
tch
u
sin
g
a
re
v
is
e
d
l
in
e
a
r
p
ro
g
ra
m
m
in
g
a
p
p
r
o
a
c
h
,
”
El
e
c
tric P
o
we
r S
y
ste
m R
e
se
a
rc
h
,
v
o
l.
1
5
,
n
o
.
2
,
p
p
.
1
2
1
–
1
3
4
,
1
9
9
8
.
[3
]
M
.
R.
Bjelo
g
rli
c
,
M
.
S
.
Ca
lo
v
ic,
B.
S
.
Ba
b
ic
,
“
Ap
p
li
c
a
ti
o
n
o
f
N
e
wto
n
’s
o
p
ti
m
a
l
p
o
we
r
flo
w
in
v
o
lt
a
g
e
/rea
c
ti
v
e
p
o
we
r
c
o
n
tro
l
,”
IEE
E
T
ra
n
s
Po
w
e
r S
y
ste
m
,
v
o
l.
5
,
no
.
4
,
p
p
.
1
4
4
7
-
1
4
5
4
,
1
9
9
0
.
[4
]
S
.
G
ra
n
v
il
le
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
d
i
sp
a
tch
t
h
ro
u
g
h
i
n
terio
r
p
o
i
n
t
m
e
t
h
o
d
s
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
m
,
v
o
l.
9
,
n
o
.
1
,
p
p
.
1
3
6
–
1
4
6
,
1
9
9
4
.
[5
]
N.
G
ru
d
in
i
n
,
“
Re
a
c
ti
v
e
p
o
we
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
t
h
o
d
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r S
y
ste
m
,
v
o
l.
13
,
n
o
.
4
,
p
p
.
1
2
1
9
–
1
2
2
5
,
1
9
9
8
.
[6
]
Ng
S
h
in
M
e
i,
R.
,
S
u
laim
a
n
,
M
.
H.,
M
u
sta
ffa
,
Z.
,
Da
n
i
y
a
l,
H.
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
so
l
u
ti
o
n
b
y
l
o
ss
m
in
imiz
a
ti
o
n
u
sin
g
m
o
th
-
flam
e
o
p
ti
m
iza
ti
o
n
tec
h
n
i
q
u
e
,”
A
p
p
l.
S
o
ft
Co
mp
u
t
.
,
v
o
l.
5
9
,
p
p
.
2
1
0
–
2
2
2
,
2
0
1
7
.
[7
]
Ch
e
n
,
G
.
,
L
iu
,
L.
,
Z
h
a
n
g
,
Z
.
,
H
u
a
n
g
,
S
.
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
b
y
imp
ro
v
e
d
G
S
A
-
b
a
se
d
a
lg
o
rit
h
m
wit
h
th
e
n
o
v
e
l
s
trate
g
ies
t
o
h
a
n
d
le c
o
n
stra
in
ts
,
”
Ap
p
l.
S
o
ft
C
o
m
p
u
t.
,
v
o
l
.
5
0
,
p
p
.
5
8
–
7
0
,
2
0
1
7
.
[8
]
Ro
y
,
P
r
o
v
a
s
Ku
m
a
r
a
n
d
S
u
sa
n
ta
Du
tt
,
“
Eco
n
o
m
ic
l
o
a
d
d
isp
a
tch
:
Op
ti
m
a
l
p
o
we
r
flo
w
a
n
d
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
c
o
n
c
e
p
t,
”
O
p
ti
ma
l
Po
we
r F
lo
w
Us
in
g
Ev
o
lu
t
io
n
a
ry
Al
g
o
ri
th
ms
,
IG
I
G
lo
b
a
l,
p
p
.
46
-
64
,
2
0
1
9
.
[9
]
Ch
risti
a
n
Bi
n
g
a
n
e
,
M
ig
u
e
l
F
.
A
n
jo
s,
S
é
b
a
stien
Le
Dig
a
b
e
l,
“
Ti
g
h
t
-
a
n
d
-
c
h
e
a
p
c
o
n
ic
re
lax
a
ti
o
n
f
o
r
t
h
e
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
is
p
a
tch
p
ro
b
lem
,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
ste
ms
,
v
o
l.
3
4
,
n
o
.
6
,
2
0
1
9
.
[1
0
]
Dh
a
rm
b
ir
P
ra
sa
d
&
Viv
e
k
a
n
a
n
d
a
M
u
k
h
e
rjee
,
“
S
o
l
u
ti
o
n
o
f
O
p
ti
m
a
l
Re
a
c
ti
v
e
P
o
we
r
Disp
a
tch
b
y
S
y
m
b
io
ti
c
Org
a
n
ism
S
e
a
rc
h
Al
g
o
rit
h
m
In
c
o
rp
o
ra
ti
n
g
F
ACT
S
De
v
ice
s,
”
IET
E
J
o
u
rn
a
l
o
f
Res
e
a
rc
h
,
v
o
l.
6
4
,
n
o
.
1
,
p
p
.
1
4
9
-
1
6
0
,
2
0
1
8
.
[1
1
]
TM
Aljo
h
a
n
i
,
e
t
a
l,
“
S
in
g
le
a
n
d
m
u
lt
io
b
jec
ti
v
e
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
b
a
se
d
o
n
h
y
b
ri
d
a
rti
ficia
l
p
h
y
si
cs
–
p
a
rti
c
le sw
a
rm
o
p
ti
m
iza
ti
o
n
,
”
En
e
rg
ies
,
v
o
l
.
12
,
n
o
.
1
2
,
p
.
2
3
3
3
,
2
0
1
9
[1
2
]
Ra
m
Ki
sh
a
n
M
a
h
a
te,
&
Him
m
a
t
S
in
g
h
,
“
M
u
lt
i
-
Ob
jec
ti
v
e
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
we
r
Disp
a
tch
Us
i
n
g
Diffe
re
n
ti
a
l
Ev
o
l
u
ti
o
n
,”
I
n
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
n
g
i
n
e
e
rin
g
T
e
c
h
n
o
lo
g
ies
a
n
d
M
a
n
a
g
e
me
n
t
Re
se
a
rc
h
,
v
o
l.
6
,
n
o
.
2
,
p
p
.
2
7
–
3
8
,
2
0
1
9
.
[1
3
]
Ya
lçın
,
E,
Tap
lam
a
c
ıo
ğ
l
u
,
M
.
,
Ç
a
m
,
E
.
,
“
Th
e
Ad
a
p
ti
v
e
Ch
a
o
t
ic
S
y
m
b
io
t
ic
Org
a
n
ism
s
S
e
a
rc
h
Alg
o
rit
h
m
P
ro
p
o
sa
l
fo
r
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
we
r
Dis
p
a
tch
P
ro
b
lem
in
P
o
we
r
S
y
ste
m
s,”
El
e
c
trica
,
v
o
l.
19
,
n
o
.
1
,
p
p
.
3
7
-
4
7
,
2
0
1
9
.
[1
4
]
M
o
u
a
ss
a
,
S
.
a
n
d
B
o
u
k
ti
r
,
T
.
,
“
M
u
lt
i
-
o
b
jec
ti
v
e
a
n
t
li
o
n
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
t
o
so
lv
e
larg
e
-
sc
a
le
m
u
lt
i
-
o
b
jec
ti
v
e
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
p
ro
b
lem
,
”
COM
PE
L
-
T
h
e
i
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ter
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ti
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ti
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p
p
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[1
5
]
Taw
fiq
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.
Alj
o
h
a
n
i,
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h
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d
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.
Eb
ra
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a
m
a
M
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,
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lt
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tch
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rid
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2
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o
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1
2
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p
p
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0
1
9
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[1
6
]
Ab
d
e
c
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iri
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y
b
o
d
i
M
R
a
n
d
Ba
h
ra
m
i
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,
“
Ga
se
s
Bro
wn
ian
m
o
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p
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iz
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:
An
a
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fo
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iza
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(G
BM
O),”
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p
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o
ft
Co
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g
,
v
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l.
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o
.
5
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p
p
.
2
9
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2
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2
9
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6
,
2
0
1
3
.
[1
7
]
M
irj
a
li
li
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d
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tam
lo
u
A.
,
“
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u
lt
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m
ize
r
:
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n
a
t
u
re
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in
sp
ired
a
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o
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iza
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ra
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m
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s
,
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l.
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o
.
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p
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.
4
9
5
–
5
1
3
,
2
0
1
6
.
[1
8
]
IEE
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“
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I
EE
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sy
ste
m
s,”
1
9
9
3
.
h
tt
p
:/
/www
.
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wa
sh
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g
to
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.
e
d
u
/t
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rc
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/p
stc
a
/
.
[1
9
]
Ali
Na
ss
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r
Hu
ss
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in
,
Ali
Ab
d
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la
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b
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s
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d
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r
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a
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o
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iza
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ti
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re
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ti
v
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p
o
we
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isp
a
tc
h
,”
Res
e
a
rc
h
J
o
u
rn
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l
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f
A
p
p
li
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s,
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g
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T
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v
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l.
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p
p
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.
[2
0
]
S
.
S
u
re
n
d
e
r
Re
d
d
y
,
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ti
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re
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h
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d
u
li
n
g
u
sin
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c
u
c
k
o
o
se
a
rc
h
a
lg
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rit
h
m
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
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rin
g
(IJ
ECE
)
,
v
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l.
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.
5
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p
.
2
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6
.
2
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1
7
.
[2
1
]
S
.
S
.
Re
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y
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t
a
l.
,
“
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ry
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lg
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m
b
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se
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p
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p
o
we
r
flo
w
u
sin
g
i
n
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
.
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