I
nte
rna
t
io
na
l J
o
urna
l o
f
Adv
a
nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
2
0
,
p
p
.
186
~
191
I
SS
N:
2
2
5
2
-
8
8
1
4
,
DOI
: 1
0
.
1
1
5
9
1
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j
aa
s
.
v
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.
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p
p
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-
19
1
186
J
o
ur
na
l ho
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e
:
h
ttp
:
//ij
a
a
s
.
ia
esco
r
e.
co
m
Rea
l
po
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er los
s r
eduction by
hy
en
a
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zer
a
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enin K
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na
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De
p
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rtme
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id
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rt
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In
stit
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Art
icle
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nfo
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ticle
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p
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p
a
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ts
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Op
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ize
r
(H
O)
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m
a
n
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ro
m
th
e
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e
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a
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a
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ial
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th
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m
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a
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s
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re
a
n
a
lo
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o
u
s to
c
a
n
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s in
se
v
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r
a
l
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le
m
e
n
ts o
f
c
o
n
v
e
r
g
e
n
t
e
v
o
lu
ti
o
n
.
Hy
e
n
a
s
c
a
tch
th
e
p
re
y
w
it
h
th
e
ir
tee
th
ra
t
h
e
r
th
a
n
c
law
s
–
p
o
ss
e
ss
h
a
rd
e
n
e
d
sk
in
f
e
e
t
w
it
h
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e
,
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lu
n
t,
n
o
re
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le
c
la
w
s
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re
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ted
f
o
r
ru
n
n
in
g
a
n
d
m
a
k
e
sh
a
rp
tu
rn
s.
Ho
w
e
v
e
r,
th
e
h
y
e
n
a
s'
g
ro
o
m
in
g
,
sc
e
n
t
m
a
r
k
in
g
,
d
e
f
e
c
a
ti
n
g
h
a
b
it
s,
m
a
ti
n
g
a
n
d
p
a
re
n
tal
b
e
h
a
v
io
u
r
a
re
c
o
n
sta
n
t
w
it
h
th
e
d
e
e
d
s
o
f
o
th
e
r
f
e
li
f
o
r
m
s.
M
a
th
e
m
a
ti
c
a
l
m
o
d
e
ll
in
g
is
f
o
rm
u
late
d
f
o
r
th
e
b
a
sic
a
tt
rib
u
tes
o
f
H
y
e
n
a
.
S
tan
d
a
rd
IEE
E
1
4
,
3
0
0
b
u
s
tes
t
sy
ste
m
s
u
se
d
to
a
n
a
ly
z
e
th
e
p
e
rf
o
rm
a
n
c
e
o
f
H
y
e
n
a
Op
ti
m
ize
r
(HO
)
a
lg
o
rit
h
m
.
L
o
ss
h
a
s
b
e
e
n
re
d
u
c
e
d
w
it
h
c
o
n
tro
l
v
a
riab
les
a
re
w
it
h
in
t
h
e
li
m
it
s.
K
ey
w
o
r
d
s
:
H
y
e
n
a
Op
ti
m
izatio
n
R
ea
cti
v
e
p
o
w
er
R
ea
l
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
L
e
n
in
Ka
n
a
g
asab
ai
,
Dep
ar
t
m
en
t o
f
E
E
E
,
P
r
asad
V.
P
o
tlu
r
i Sid
d
h
ar
th
a
I
n
s
ti
tu
te
o
f
T
ec
h
n
o
lo
g
y
,
Kan
u
r
u
,
Vij
a
y
a
w
ad
a,
An
d
h
r
a
P
r
ad
esh
-
5
2
0
0
0
7
,
I
n
d
ia.
E
m
ail:
g
k
len
i
n
@
g
m
ai
l.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
R
ea
cti
v
e
p
o
w
er
p
r
o
b
lem
h
as
b
ee
n
th
e
k
e
y
i
n
p
o
w
er
s
y
s
te
m
o
p
er
atio
n
&
co
n
tr
o
l,
s
in
ce
i
t
p
la
y
s
m
aj
o
r
r
o
le
in
s
ec
u
r
e
&
ec
o
n
o
m
ic
o
p
er
atio
n
o
f
th
e
p
o
w
er
s
y
s
te
m
.
Ma
n
y
co
n
v
en
tio
n
al
tec
h
n
iq
u
es
[
1
-
6
]
u
s
ed
f
o
r
s
o
lv
i
n
g
t
h
e
p
r
o
b
le
m
.
B
u
t
m
an
y
d
r
a
w
b
ac
k
s
h
a
v
e
b
ee
n
f
o
u
n
d
in
t
h
e
co
n
v
e
n
tio
n
al
m
eth
o
d
s
an
d
m
a
in
l
y
d
if
f
ic
u
lt
y
i
n
h
an
d
li
n
g
th
e
i
n
eq
u
alit
y
co
n
s
tr
ai
n
ts
.
L
a
s
t
t
wo
d
ec
ad
es
m
an
y
e
v
o
lu
tio
n
ar
y
al
g
o
r
ith
m
s
[
7
-
1
8
]
co
n
tin
u
o
u
s
l
y
ap
p
lied
to
s
o
l
v
e
th
e
p
r
o
b
lem
.
T
h
is
p
ap
er
p
r
o
j
ec
ts
H
y
en
a
Op
ti
m
izer
(
HO
)
,
in
w
h
ic
h
H
y
e
n
a
b
eh
av
io
u
r
i
m
i
tated
to
s
o
lv
e
t
h
e
p
r
o
b
lem
.
C
o
llab
o
r
ativ
e
b
e
h
av
io
u
r
&
So
cial
r
elatio
n
s
h
ip
b
et
w
ee
n
H
y
en
a
s
is
th
e
k
e
y
co
n
ce
p
tio
n
in
t
h
is
al
g
o
r
ith
m
[
19
]
.
H
y
e
n
as
a
f
o
r
m
o
f
ca
r
n
iv
o
r
an
m
a
m
m
al
&
d
ee
d
s
ar
e
an
alo
g
o
u
s
to
ca
n
in
e
s
i
n
s
e
v
er
al
ele
m
en
ts
o
f
co
n
v
er
g
en
t
e
v
o
lu
tio
n
.
H
y
en
a
s
ca
tc
h
t
h
e
p
r
e
y
w
it
h
t
h
eir
teet
h
r
at
h
er
t
h
an
cla
ws
–
p
o
s
s
ess
h
ar
d
en
ed
s
k
in
f
ee
t
w
it
h
lar
g
e,
b
l
u
n
t,
n
o
r
etr
ac
tab
le
cla
w
s
ar
e
ad
ap
ted
f
o
r
r
u
n
n
i
n
g
an
d
m
a
k
e
s
h
ar
p
tu
r
n
s
.
Ho
w
e
v
er
,
th
e
h
y
en
a
s
'
g
r
o
o
m
i
n
g
,
s
ce
n
t
m
ar
k
in
g
,
d
ef
e
ca
tin
g
h
ab
it
s
,
m
at
in
g
an
d
p
ar
en
tal
b
eh
a
v
io
u
r
ar
e
co
n
s
ta
n
t
w
it
h
th
e
d
ee
d
s
o
f
o
th
er
f
eli
f
o
r
m
s
.
H
y
e
n
as
clea
n
th
e
m
s
el
v
es
h
ab
itu
all
y
b
y
le
g
s
ar
e
s
p
r
ea
d
w
it
h
o
n
e
leg
p
o
in
ti
n
g
v
er
t
icall
y
u
p
w
ar
d
b
y
s
itti
n
g
o
n
t
h
e
lo
w
er
b
ac
k
.
C
o
n
v
er
s
e
l
y
,
u
n
lik
e
o
t
h
er
f
e
lif
o
r
m
s
,
th
e
y
d
o
n
o
t
clea
n
t
h
eir
f
ac
es.
T
er
r
ito
r
ies
ar
e
b
u
ilt
b
y
u
s
i
n
g
th
e
ir
an
al
g
l
an
d
s
.
Fro
m
an
y
f
o
r
m
o
f
a
ttac
k
t
h
e
y
d
ef
e
n
d
its
e
lf
f
er
o
cio
u
s
l
y
a
n
d
ca
p
ab
le
o
f
p
r
o
d
u
c
in
g
a
n
u
m
b
er
o
f
d
if
f
er
e
n
t
s
o
u
n
d
s
co
n
s
is
t
in
g
o
f
w
h
o
o
p
s
,
g
r
u
n
t
s
,
g
r
o
an
s
,
lo
w
s
,
g
ig
g
le
s
,
y
ell
s
,
g
r
o
w
ls
,
la
u
g
h
s
a
n
d
w
h
i
n
es.
Ma
t
h
e
m
a
tic
al
m
o
d
ellin
g
is
f
o
r
m
u
lated
f
o
r
th
e
b
asic
attr
ib
u
tes
o
f
H
y
en
a.
Sta
n
d
ar
d
I
E
E
E
1
4
,
3
0
0
b
u
s
tes
t
s
y
s
te
m
s
u
s
ed
to
a
n
al
y
ze
t
h
e
p
er
f
o
r
m
an
ce
o
f
H
y
e
n
a
Op
ti
m
izer
(
HO)
alg
o
r
ith
m
.
L
o
s
s
h
as b
ee
n
r
ed
u
ce
d
w
it
h
co
n
tr
o
l v
ar
iab
les ar
e
w
it
h
i
n
t
h
e
li
m
its
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
R
ea
l
p
o
w
er lo
s
s
r
ed
u
ctio
n
b
y
h
ye
n
a
o
p
timiz
er a
lg
o
r
ith
m
… (
Len
in
K
a
n
a
g
a
s
a
b
a
i
)
187
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
Ma
in
ai
m
is
to
m
in
i
m
ize
t
h
e
s
y
s
te
m
r
ea
l p
o
w
er
lo
s
s
&
g
iv
e
n
as,
P
l
o
s
s
=
∑
g
k
(
V
i
2
+
V
j
2
−
2
V
i
V
j
c
o
s
θ
ij
)
n
k
=
1
k
=
(
i
,
j
)
(
1
)
V
o
ltag
e
d
ev
iatio
n
m
a
g
n
it
u
d
es
(
VD)
is
,
Min
(
VD
)
=
∑
|
V
k
−
1
.
00
|
nl
k
=
1
(
2
)
L
o
ad
f
lo
w
eq
u
alit
y
co
n
s
tr
ain
ts
:
P
Gi
–
P
Di
−
V
i
∑
V
j
nb
j
=
1
[
G
ij
c
os
θ
ij
+
B
ij
s
in
θ
ij
]
=
0
,
i
=
1
,
2
…
.
,
nb
(
3
)
Q
Gi
−
Q
Di
−
V
i
∑
V
j
nb
j
=
1
[
G
ij
s
in
θ
ij
+
B
ij
c
os
θ
ij
]
=
0
,
i
=
1
,
2
…
.
,
nb
(
4
)
I
n
eq
u
alit
y
co
n
s
tr
ain
t
s
ar
e:
V
Gi
m
i
n
≤
V
Gi
≤
V
Gi
m
ax
,
i
∈
ng
(
5
)
V
Li
m
i
n
≤
V
Li
≤
V
Li
m
ax
,
i
∈
nl
(
6
)
Q
Ci
m
i
n
≤
Q
Ci
≤
Q
Ci
m
ax
,
i
∈
nc
(
7
)
Q
Gi
m
i
n
≤
Q
Gi
≤
Q
Gi
m
ax
,
i
∈
ng
(
8
)
T
i
m
i
n
≤
T
i
≤
T
i
m
ax
,
i
∈
nt
(
9
)
S
Li
m
i
n
≤
S
Li
m
ax
,
i
∈
nl
(
10
)
3.
H
YE
NA
O
P
T
I
M
I
Z
E
R
A
L
G
O
RIT
H
M
H
y
e
n
a
o
p
ti
m
izer
(
HO)
al
g
o
r
ith
m
s
i
m
i
tated
f
o
r
m
H
y
e
n
a
w
h
i
ch
i
s
co
m
p
lica
ted
,
in
te
llig
e
n
t
[
19
]
.
W
h
en
a
n
e
w
f
o
o
d
s
o
u
r
ce
i
s
f
o
u
n
d
H
y
e
n
a
p
r
o
d
u
ce
a
t
y
p
ical
s
o
u
n
d
ali
k
e
to
lau
g
h
i
n
g
s
o
u
n
d
o
f
h
u
m
a
n
b
ein
g
s
to
co
m
m
u
n
icate
ab
o
u
t
th
e
f
in
d
i
n
g
s
.
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I
SS
N
: 2
2
5
2
-
8814
I
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A
d
v
A
p
p
l Sci
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Vo
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
R
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8814
I
n
t J
A
d
v
A
p
p
l Sci
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
2
0
:
1
86
–
1
9
1
190
5.
CO
NCLU
SI
O
N
I
n
t
h
is
w
o
r
k
H
y
e
n
a
Op
ti
m
i
ze
r
(
HO)
ef
f
icie
n
tl
y
s
o
lv
ed
th
e
r
ea
cti
v
e
p
o
w
er
p
r
o
b
le
m
.
Dee
d
s
o
f
th
e
H
y
en
a
h
as
b
ee
n
m
at
h
e
m
atica
ll
y
m
o
d
elled
s
u
cc
e
s
s
f
u
ll
y
&
e
m
p
lo
y
ed
to
s
o
l
v
e
th
e
p
r
o
b
lem
.
A
ttac
k
in
g
th
e
p
r
e
y
h
as
b
ee
n
m
at
h
e
m
at
icall
y
m
o
d
elled
a
n
d
t
h
r
o
u
g
h
th
at
v
ec
to
r
h
w
ill
b
e
s
p
ec
i
f
ied
.
E
x
p
lo
r
atio
n
&
ex
p
lo
itatio
n
ca
p
ab
ilit
ie
s
i
n
t
h
e
s
ea
r
ch
i
m
p
r
o
v
ed
.
Stan
d
ar
d
I
E
E
E
1
4
,
3
0
0
b
u
s
test
s
y
s
te
m
s
u
s
ed
to
a
n
al
y
ze
th
e
p
er
f
o
r
m
a
n
ce
o
f
H
y
e
n
a
O
p
ti
m
izer
(
HO)
alg
o
r
it
h
m
.
L
o
s
s
h
a
s
b
ee
n
r
ed
u
ce
d
w
it
h
co
n
tr
o
l
v
ar
iab
les
ar
e
w
it
h
i
n
t
h
e
li
m
its
.
RE
F
E
R
E
NC
E
S
1.
K.
Y.
L
ee
,
“
Fu
e
l
-
co
s
t
m
i
n
i
m
is
a
tio
n
f
o
r
b
o
th
r
ea
l
an
d
r
ea
ctiv
e
-
p
o
w
er
d
is
p
atc
h
es,”
P
r
o
ce
ed
in
g
s
Gen
era
tio
n
,
Tr
a
n
s
mis
s
io
n
a
n
d
Dis
tr
ib
u
tio
n
C
o
n
feren
ce
,
v
o
l
,
131
,
n
o
.
3
,
p
p
.
8
5
-
9
3
,
1
9
8
4
.
2.
N.
I
.
Dee
b
,
“
An
ef
f
icie
n
t
tech
n
iq
u
e
f
o
r
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
u
s
in
g
a
r
ev
is
ed
lin
ea
r
p
r
o
g
r
am
m
in
g
ap
p
r
o
ac
h
,
”
E
lectric P
o
w
er S
ystem
R
esea
r
ch
,
v
o
l
,
15
,
n
o
.
2
,
p
p
.
1
2
1
–
1
3
4
,
1
9
8
8
.
3.
M.
R
.
B
j
elo
g
r
lic,
M.
S.
C
alo
v
ic,
B
.
S.
B
ab
ic,
et.
al.
,
”A
p
p
licatio
n
o
f
Ne
w
to
n
’
s
o
p
ti
m
al
p
o
w
er
f
lo
w
in
v
o
ltag
e/r
ea
cti
v
e
p
o
w
er
co
n
tr
o
l,”
I
E
E
E
Tr
a
n
s
P
o
w
er S
yste
m
,
v
o
l.
5
,
n
o
.
4
,
p
p
.
1
4
4
7
-
1
4
5
4
,
1
9
9
0
.
4.
S.
Gr
an
v
i
lle,
“
Op
ti
m
al
r
ea
cti
v
e
d
is
p
atch
th
r
o
u
g
h
in
ter
io
r
p
o
in
t
m
eth
o
d
s
,
”
IEEE
Tr
a
n
s
a
cti
o
n
s
o
n
P
o
w
er
S
ystem
,
v
o
l,
9
,
n
o
.
1
,
p
p
.
1
3
6
–
1
4
6
,
1
9
9
4
.
5.
N.
Gr
u
d
in
i
n
,
“
R
ea
cti
v
e
p
o
w
e
r
o
p
tim
izat
io
n
u
s
i
n
g
s
u
cc
e
s
s
i
v
e
q
u
ad
r
atic
p
r
o
g
r
a
m
m
i
n
g
m
eth
o
d
,
”
I
E
E
E
Tr
a
n
s
a
ctio
n
s
o
n
P
o
w
er S
ystem
,
v
o
l.
13
,
n
o
.
4
,
p
p
.
1
2
1
9
–
1
2
2
5
,
1
9
9
8
.
6.
W
ei
Yan
,
J
.
Yu
,
D.
C
.
Yu
an
d
K.
B
h
attar
ai,
”A
n
e
w
o
p
ti
m
al
r
ea
ctiv
e
p
o
w
er
f
lo
w
m
o
d
el
in
r
ec
tan
g
u
lar
f
o
r
m
an
d
its
s
o
l
u
tio
n
b
y
p
r
ed
icto
r
co
r
r
ec
to
r
p
r
i
m
al
d
u
al
in
te
r
io
r
p
o
in
t
m
eth
o
d
,
”
I
E
E
E
Tr
a
n
s
.
P
w
r
.
S
yst
.,
v
o
l.2
1
,
n
o
.
1
,
pp
.
61
-
6
7
,
2
0
0
6
.
7.
A
p
ar
aj
ita
Mu
k
h
er
j
ee
,
Viv
e
k
an
an
d
a
Mu
k
h
er
j
ee
,
“
So
l
u
tio
n
o
f
o
p
tim
a
l
r
ea
ctiv
e
p
o
w
er
d
is
p
at
ch
b
y
c
h
ao
tic
k
r
ill h
er
d
alg
o
r
it
h
m
,
”
IE
T Ge
n
er.
Tr
a
n
s
m.
Dis
t
r
ib
,
v
o
l.
9
,
n
o
.
1
5
,
p
p
.
2
3
5
1
–
2
3
6
2
,
2
0
1
5
.
8.
Hu
,
Z
.
,
W
an
g
,
X.
&
T
ay
lo
r
,
G.
Sto
ch
as
tic
o
p
ti
m
a
l
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
:
Fo
r
m
u
latio
n
a
n
d
s
o
lu
t
io
n
m
et
h
o
d
.
E
lectr.
P
o
w
er E
n
erg
y
S
yst
.
,
v
o
l.
3
2
,
p
p
.
6
1
5
-
6
2
1
,
2
0
1
0
.
9.
Ma
h
aletc
h
u
m
i
A
/P
Mo
r
g
an
,
No
r
R
u
l
Has
m
a
A
b
d
u
l
lah
,
M
o
h
d
Her
w
an
S
u
lai
m
a
n
,
Ma
h
f
u
za
h
M
u
s
ta
f
a
an
d
R
o
s
d
i
y
a
n
a
Sa
m
ad
,
“Co
m
p
u
tat
io
n
al
i
n
telli
g
e
n
ce
tech
n
iq
u
e
f
o
r
s
tatic
V
A
R
co
m
p
en
s
ato
r
(
SVC
)
in
s
ta
llatio
n
co
n
s
id
e
r
i
n
g
m
u
l
ti
-
co
n
t
in
g
e
n
cies
(
N
-
m
)
,
”
A
R
P
N
Jo
u
r
n
a
l
o
f
E
n
g
in
ee
r
in
g
a
n
d
A
p
p
lied
S
cien
ce
s
,
v
o
l
.
1
0
,
no
.
2
2
,
2
0
1
5
.
10.
Mo
h
d
Her
w
a
n
S
u
lai
m
a
n
,
Z
u
r
ian
i
M
u
s
ta
f
f
a,
Ha
m
d
a
n
Da
n
i
y
al,
Mo
h
d
R
u
s
lli
m
Mo
h
a
m
ed
an
d
O
m
ar
A
li
m
a
n
,
“
So
l
v
i
n
g
o
p
ti
m
al
r
ea
ctiv
e
p
o
w
er
p
la
n
n
in
g
p
r
o
b
le
m
u
tili
zi
n
g
n
at
u
r
e
i
n
s
p
ir
ed
co
m
p
u
tin
g
tech
n
iq
u
es
”,
A
R
P
N
Jo
u
r
n
a
l o
f E
n
g
in
ee
r
in
g
a
n
d
A
p
p
lied
S
cie
n
ce
s
,
v
o
l
.
1
0
,
no
.
2
1
,
p
p
.
9
7
7
9
-
9
7
8
5
.
2
0
1
5
11.
Mo
h
d
Her
w
a
n
Su
lai
m
an
,
W
o
n
g
L
o
I
n
g
,
Z
u
r
ian
i
M
u
s
taf
f
a
an
d
Mo
h
d
R
u
s
lli
m
Mo
h
a
m
ed
,
“
Gr
e
y
w
o
l
f
o
p
tim
izer
f
o
r
s
o
lv
i
n
g
ec
o
n
o
m
ic
d
is
p
atch
p
r
o
b
le
m
w
it
h
v
alv
e
-
lo
ad
i
n
g
e
f
f
ec
ts
,”
A
R
P
N
Jo
u
r
n
a
l
o
f
E
n
g
in
ee
r
in
g
a
n
d
A
p
p
lied
S
cien
ce
s
,
v
o
l
.
1
0
,
no
.
2
1
,
p
p
.
9
7
9
6
-
9
8
0
1
,
2
0
1
5
.
12.
P
an
d
iar
aj
an
,
K.
&
B
ab
u
lal,
C
.
K.
,
“
Fu
zz
y
h
ar
m
o
n
y
s
ea
r
ch
alg
o
r
it
h
m
b
ased
o
p
ti
m
al
p
o
w
er
f
lo
w
f
o
r
p
o
w
er
s
y
s
te
m
s
ec
u
r
it
y
en
h
a
n
ce
m
e
n
t,”
I
n
tern
a
tio
n
a
l
Jo
u
r
n
a
l
E
lectric
P
o
w
e
r
E
n
erg
y
S
yst.,
v
o
l.
7
8
,
p
p
.
7
2
-
79,
2
0
1
6
.
13.
Mu
s
ta
f
f
a,
Z
.
,
Su
la
i
m
a
n
,
M.
H.
,
Yu
s
o
f
,
Y.
,
Ka
m
ar
u
lza
m
a
n
,
S.
F.,
“A
n
o
v
e
l h
y
b
r
id
m
eta
h
e
u
r
i
s
tic
al
g
o
r
ith
m
f
o
r
s
h
o
r
t
ter
m
lo
ad
f
o
r
ec
asti
n
g
,
”
I
n
tern
a
tio
n
a
l
Jo
u
r
n
a
l
o
f
S
i
mu
la
tio
n
:
S
ystem
s
,
S
cien
ce
a
n
d
Tech
n
o
lo
g
y
,
v
o
l.
1
7
,
n
o
.
4
1
,
p
p
.
6
.
1
-
6
.
6
,
2
0
1
7
.
14.
Su
lai
m
a
n
,
M.
H.
,
Mu
s
ta
f
f
a,
Z
.
,
Mo
h
a
m
ed
,
M.
R
.
,
A
li
m
a
n
,
O
.
,
“An
ap
p
licatio
n
o
f
m
u
lti
-
v
e
r
s
e
o
p
ti
m
izer
f
o
r
o
p
ti
m
al
r
ea
ctiv
e
p
o
w
er
d
i
s
p
atch
p
r
o
b
le
m
s
,
”
I
n
tern
a
tio
n
a
l
Jo
u
r
n
a
l
o
f
S
imu
la
tio
n
:
S
ys
tems,
S
c
ien
ce
a
n
d
Tech
n
o
lo
g
y
,
v
o
l.
1
7
,
n
o
.
4
1
,
pp,
5
.
1
-
5
.
5
,
2
0
1
7
.
15.
Ma
h
aletc
h
u
m
i
A
/P
Mo
r
g
a
n
,
N
o
r
R
u
l
Has
m
a
A
b
d
u
lla
h
,
Mo
h
d
Her
w
a
n
Su
la
i
m
a
n
,
Ma
h
f
u
za
h
M
u
s
ta
f
a
an
d
R
o
s
d
i
y
a
n
a
Sa
m
ad
,
“
M
u
lt
i
-
o
b
j
ec
tiv
e
ev
o
lu
t
io
n
ar
y
p
r
o
g
r
am
m
in
g
(
MO
E
P
)
u
s
i
n
g
m
u
ta
tio
n
b
ased
o
n
ad
ap
tiv
e
m
u
tatio
n
o
p
er
ato
r
(
A
MO
)
ap
p
lied
f
o
r
o
p
tim
a
l
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
,”
A
R
P
N
Jo
u
r
n
a
l
o
f
E
n
g
in
ee
r
in
g
a
n
d
A
p
p
lied
S
cien
ce
s
,
v
o
l
.
1
1
,
no
.
1
4
,
2
0
1
6
.
16.
R
eb
ec
ca
N
g
S
h
i
n
Me
i,
Mo
h
d
Her
w
a
n
Su
lai
m
an
,
Z
u
r
ia
n
i
Mu
s
ta
f
f
a,
“
an
t
lio
n
o
p
ti
m
iz
er
f
o
r
o
p
ti
m
a
l
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
s
o
l
u
tio
n
,
”
Jo
u
r
n
a
l
o
f
E
lectrica
l
S
ystems
,
"
Sp
ec
ial
I
s
s
u
e
A
MP
E
2
0
1
5
"
,
pp
.
6
8
-
7
4
,
2
0
1
6
.
17.
Ma
h
aletc
h
u
m
i
Mo
r
g
a
n
,
No
r
R
u
l
Has
m
a
A
b
d
u
lla
h
,
Mo
h
d
Her
w
a
n
Su
la
i
m
a
n
,
Ma
h
f
u
za
h
M
u
s
ta
f
a,
R
o
s
d
i
y
a
n
a
Sa
m
ad
,
“
B
en
ch
m
ar
k
s
t
u
d
ies
o
n
o
p
ti
m
al
r
ea
ct
iv
e
p
o
w
er
d
is
p
atc
h
(
OR
P
D)
b
ased
m
u
l
ti
-
o
b
j
ec
tiv
e
ev
o
l
u
tio
n
ar
y
p
r
o
g
r
a
m
m
in
g
(
M
OE
P
)
u
s
i
n
g
m
u
t
atio
n
b
ased
o
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ad
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tiv
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m
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tatio
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ter
(
A
MO
)
an
d
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y
n
o
m
ia
l
m
u
tat
io
n
o
p
er
at
o
r
(
P
MO
)
,
”
J
o
u
r
n
a
l
o
f E
lectrica
l S
ystems
,
p
p
.
12
-
1
,
2
0
1
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
R
ea
l
p
o
w
er lo
s
s
r
ed
u
ctio
n
b
y
h
ye
n
a
o
p
timiz
er a
lg
o
r
ith
m
… (
Len
in
K
a
n
a
g
a
s
a
b
a
i
)
191
18.
R
eb
ec
ca
Ng
S
h
i
n
Me
i,
Mo
h
d
Her
w
a
n
S
u
lai
m
an
,
Z
u
r
ian
i
M
u
s
ta
f
f
a,
Ha
m
d
a
n
Dan
i
y
al,
“
O
p
ti
m
al
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
s
o
lu
tio
n
b
y
lo
s
s
m
i
n
i
m
izatio
n
u
s
i
n
g
m
o
t
h
-
f
la
m
e
o
p
ti
m
izatio
n
tec
h
n
iq
u
e
,”
A
p
p
lied
S
o
f
t
C
o
mp
u
tin
g
,
v
o
l.
5
9
,
p
p
.
2
1
0
-
2
2
2
,
2
0
1
7
.
19.
Gau
r
av
D
h
i
m
an
,
Vij
a
y
K
u
m
ar
,
“
Sp
o
tted
h
y
e
n
a
o
p
ti
m
izer
:
A
n
o
v
el
b
io
-
i
n
s
p
ir
ed
b
ased
m
etah
e
u
r
is
t
ic
tech
n
iq
u
e
f
o
r
en
g
i
n
ee
r
i
n
g
ap
p
l
icatio
n
s
,
”
A
d
va
n
ce
s
in
E
n
g
in
e
erin
g
S
o
ftw
a
r
e
,
v
o
l.
1
1
4
,
p
p
.
4
8
-
7
0
,
2
0
1
7
.
20.
C
h
a
n
d
r
ag
u
p
ta
Ma
u
r
y
a
n
K
u
p
p
am
u
t
h
u
Si
v
ali
n
g
a
m
1
,
Su
b
r
a
m
an
ian
R
a
m
ac
h
a
n
d
r
an
,
P
u
r
r
n
i
m
aa
Sh
i
v
a
Sak
t
h
i
R
aj
am
a
n
i,
“Reacti
v
e
p
o
w
er
o
p
ti
m
i
za
tio
n
in
a
p
o
w
er
s
y
s
te
m
n
et
w
o
r
k
t
h
r
o
u
g
h
m
eta
h
eu
r
i
s
tic
alg
o
r
ith
m
s
,
”
Tu
r
ki
s
h
Jo
u
r
n
a
l
o
f
E
lectrica
l
E
n
g
in
e
erin
g
&
C
o
mp
u
ter
S
cien
ce
,
v
o
l.
2
5
,
p
p
.
4
6
1
5
–
4
6
2
3
,
2
0
1
7
.
21.
S.S.
R
ed
d
y
,
et
al.
,
“
Fas
ter
ev
o
lu
tio
n
ar
y
al
g
o
r
ith
m
b
ase
d
o
p
tim
al
p
o
w
er
f
lo
w
u
s
i
n
g
in
cr
e
m
en
tal
v
ar
iab
les,”
I
n
tern
a
tio
n
a
l J
o
u
r
n
a
l o
f E
lectrica
l P
o
w
er
&
E
n
erg
y
S
ystems
,
v
o
l.
5
4
,
p
p
.
1
9
8
-
2
1
0
,
2
0
1
4
.
22.
S.
S
u
r
en
d
er
R
ed
d
y
,
“
Op
ti
m
al
r
ea
ctiv
e
p
o
w
er
s
c
h
ed
u
li
n
g
u
s
i
n
g
cu
c
k
o
o
s
ea
r
c
h
al
g
o
r
ith
m
,
”
I
n
tern
a
tio
n
a
l
Jo
u
r
n
a
l o
f E
lectrica
l a
n
d
C
o
m
p
u
ter E
n
g
in
ee
r
in
g
,
v
o
l.
7
,
n
o
.
5
,
p
p
.
2
3
4
9
-
2
3
5
6
,
2
0
1
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.