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s
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p
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uth
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r
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P
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L
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k
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Dep
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m
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f
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g
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r
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,
Un
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lleg
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,
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m
a
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n
i
v
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s
it
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,
H
y
d
er
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I
n
d
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.
E
m
ail:
lo
k
en
d
er
.
p
@
u
ce
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u
.
ed
u
1.
I
NT
RO
D
UCT
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O
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P
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w
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s
y
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te
m
d
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g
n
s
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ld
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r
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g
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p
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ic
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m
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v
o
lta
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s
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ld
b
e
w
it
h
i
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th
e
s
p
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i
f
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ed
lim
i
ts
.
T
h
e
v
o
ltag
es
at
a
n
o
d
e
ar
e
v
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y
s
e
n
s
i
tiv
e
to
n
et
r
ea
ctiv
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p
o
w
er
o
f
th
e
n
o
d
e.
So
t
h
e
r
ea
cti
v
e
p
o
w
er
o
p
ti
m
iza
tio
n
i
s
t
h
e
w
a
y
to
i
m
p
r
o
v
e
t
h
e
v
o
ltag
e
p
r
o
f
i
le
.
T
h
e
o
p
tim
iza
tio
n
o
f
p
o
w
er
s
y
s
te
m
is
b
ec
o
m
in
g
co
m
p
le
x
b
ec
au
s
e
s
m
aller
s
a
f
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t
y
m
ar
g
i
n
s
in
g
e
n
er
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a
n
d
t
r
an
s
m
is
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d
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e
to
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t
m
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t
h
e
g
e
n
er
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an
d
tr
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s
m
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s
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io
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f
ac
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liti
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w
ith
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r
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w
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g
d
em
a
n
d
o
f
p
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s
u
p
p
l
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.
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ti
m
al
r
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p
o
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d
is
p
atch
(
OR
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is
a
m
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ti
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o
b
j
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tiv
en
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n
lin
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m
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m
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m
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,
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p
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r
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m
m
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tc
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ar
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p
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p
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in
th
e
liter
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r
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[
1
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]
.
Ho
w
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f
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a
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co
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p
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alg
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r
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m
s
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p
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p
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in
th
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li
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[
5
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]
s
u
c
h
as
b
ac
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f
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g
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r
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,
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Evaluation Warning : The document was created with Spire.PDF for Python.
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I
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2
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128
o
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t
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ti
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in
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d
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g
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d
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ae
e
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l
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a
l
.,
[
1
2
]
im
p
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te
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y
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r
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d
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a
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[
1
3
]
a
p
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d
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l
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w
ith
f
as
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e
r
c
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n
v
e
r
g
en
c
e
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
2
.
1
.
Rea
l
po
w
er
lo
s
s
o
bje
ct
iv
e
(
P
l
o
ss
)
T
h
e
lo
ad
f
lo
w
s
o
l
u
tio
n
g
iv
e
s
a
ll b
u
s
v
o
lta
g
e
m
a
g
n
itu
d
e
s
a
n
d
an
g
le
s
.
T
h
en
,
th
e
r
ea
l p
o
w
er
l
o
s
s
ca
n
b
e
ca
lcu
lated
as
f
o
llo
w
s
;
c
o
s
2
1
2
2
MW
V
V
V
V
g
P
l
i
n
e
N
k
j
i
j
i
j
i
k
l
o
s
s
(
1
)
w
h
er
e
P
loss
is
th
e
to
tal
r
ea
l
p
o
w
er
lo
s
s
,
N
line
is
to
tal
n
u
m
b
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o
f
tr
an
s
m
i
s
s
io
n
lin
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s
.
V
i
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d
V
j
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th
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v
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m
ag
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it
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d
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at
t
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t
w
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d
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K
th
lin
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ɵ
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d
ɵ
j
ar
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th
e
v
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ltag
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a
n
g
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K
th
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is
co
n
d
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cta
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K
th
li
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2
.
2
Vo
lt
a
g
e
s
t
a
bil
it
y
o
bje
c
t
iv
e
(
V
stab
ility
)
Vo
ltag
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s
tab
ili
t
y
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s
m
ea
s
u
r
ed
u
s
i
n
g
L
-
i
n
d
ex
;
=
∑
2
−
+
1
;
ℎ
=
|
1
−
∑
−
1
|
(
2
)
w
h
er
e
j
in
d
icate
s
all
lo
ad
b
u
s
es.
v
i
a
n
d
v
j
ar
e
v
o
lta
g
es
at
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th
an
d
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b
u
s
es.
L
o
ad
f
lo
w
s
o
l
u
tio
n
i
s
r
eq
u
ir
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to
co
m
p
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te
L
-
in
d
e
x
.
Fj
i
ca
n
b
e
o
b
tain
ed
f
r
o
m
t
h
e
Y
b
u
s
m
atr
i
x
as f
o
llo
w
s
;
L
G
LL
LG
GL
GG
L
G
V
V
Y
Y
Y
Y
I
I
(
3
)
w
h
er
e
I
G
,
I
L
,
an
d
V
G
,
V
L
r
ep
r
esen
t
c
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r
r
en
ts
a
n
d
v
o
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s
at
th
e
g
e
n
er
ato
r
b
u
s
es
an
d
lo
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b
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s
es.
R
ea
r
r
an
g
i
n
g
th
e
ab
o
v
e
eq
u
atio
n
w
e
g
et;
(
4
)
w
h
er
e
F
LG
=
-
[Y
LL
]
-
1
[Y
LG
]
ar
e
th
e
r
eq
u
ir
ed
v
alu
es.
T
h
e
L
-
i
n
d
ex
v
alu
e
s
ar
e
o
b
tain
ed
f
o
r
a
ll
lo
ad
b
u
s
s
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f
o
r
a
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iv
e
n
lo
ad
.
T
h
e
r
an
g
e
o
f
L
-
in
d
e
x
v
al
u
e
is
[
0
1
]
.
A
s
it
ap
p
r
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ac
h
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it
in
d
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tab
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As
it
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,
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d
icate
s
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v
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ltag
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llap
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S
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m
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y
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lo
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u
s
es.
2
.
3
.
Co
ntr
o
l v
a
ria
bles
T
h
e
c
o
n
t
r
o
l
v
a
r
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a
b
l
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s
c
o
n
s
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d
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r
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d
t
o
m
in
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m
iz
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t
h
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o
b
je
c
t
iv
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f
u
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c
t
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r
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g
s
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l
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g
(
O
L
T
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t
r
a
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s
f
o
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m
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r
s
,
g
en
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V
A
R
c
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m
p
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s
a
t
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g
s
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t
t
i
n
g
s
.
G
L
GG
GL
LG
LL
G
L
V
I
Y
K
F
Z
I
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
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p
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w
er
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g
I
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N:
2252
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8792
A
h
yb
r
id
b
a
cteria
l fo
r
a
g
in
g
-
p
a
r
ticle
s
w
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r
m
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p
t
imiz
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tio
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tech
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lvin
g
.
.
.
(
P
.
Lo
ke
n
d
er R
ed
d
y
)
129
2
.
4
.
Co
ns
t
ra
ints
T
h
ese
co
n
tr
o
l
v
ar
iab
les
h
av
e
th
eir
u
p
p
er
an
d
lo
w
er
li
m
its
.
T
h
ese
co
n
s
tr
ain
t
s
h
a
v
e
to
b
e
co
n
s
id
er
ed
w
h
i
le
p
er
f
o
r
m
in
g
t
h
e
o
p
ti
m
iza
tio
n
;
≤
≤
,
Є
≤
≤
,
Є
≤
≤
,
Є
(
5
)
w
h
er
e
t
ij
r
ep
r
esen
ts
th
e
tap
s
ettin
g
s
o
f
O
L
T
C
tr
an
s
f
o
r
m
er
co
n
n
ec
ted
b
et
w
ee
n
b
u
s
e
s
i
-
j
b
u
s
e
s
,
Ng
r
ep
r
esen
t
s
s
et
o
f
g
en
er
ato
r
b
u
s
es,
V
i
is
th
e
v
o
lta
g
e
o
f
i
th
g
en
er
ato
r
b
u
s
,
Q
ci
is
i
th
b
u
s
’
s
r
ea
ctiv
e
p
o
w
er
co
m
p
en
s
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io
n
ca
p
ac
it
y
an
d
N
qc
r
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r
esen
t
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t
o
f
lo
ad
b
u
s
e
s
,
w
h
ic
h
h
a
v
e
r
e
ac
tiv
e
p
o
w
er
s
u
p
p
o
r
t.
On
e
m
o
r
e
th
i
n
g
n
ee
d
to
b
e
co
n
s
id
er
ed
w
h
ile
m
in
i
m
izin
g
th
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
s
is
t
h
e
d
ep
en
d
en
t
v
ar
iab
le
s
,
r
ea
ctiv
e
p
o
w
er
o
u
tp
u
t
o
f
th
e
g
en
er
ato
r
s
an
d
v
o
ltag
e
o
f
all
lo
ad
b
u
s
es.
T
h
e
y
s
h
o
u
ld
also
n
o
t e
x
ce
ed
th
e
ir
li
m
i
ts
.
≤
≤
,
Є
≤
≤
,
Є
(
6
)
is
t
h
e
r
ea
cti
v
e
p
o
w
er
g
e
n
er
at
ed
b
y
th
e
i
th
g
en
er
ato
r
.
V
i
r
ep
r
esen
ts
th
e
v
o
lta
g
e
m
a
g
n
itu
d
e
at
i
th
lo
ad
b
u
s
an
d
N
L
i
s
n
u
m
b
er
o
f
lo
ad
b
u
s
e
s
.
T
h
e
v
al
u
es
o
f
t
h
e
co
n
tr
o
l
v
ar
iab
les
s
et
to
t
h
eir
b
o
u
n
d
s
i
f
t
h
e
y
e
x
ce
ed
.
T
h
e
d
ep
en
d
en
t
v
ar
iab
le
co
n
s
tr
ain
ts
ar
e
d
ea
lt
b
y
u
s
i
n
g
p
en
alt
y
f
ac
to
r
s
.
B
y
co
n
s
id
er
in
g
th
e
co
n
s
tr
ai
n
ts
w
it
h
p
en
alties,
t
h
e
o
b
j
ec
ti
v
e
f
u
n
ctio
n
s
b
ec
o
m
e
s
as f
o
llo
w
s
;
(7
)
2
1
m
i
n
m
a
x
lim
2
2
1
1
m
i
n
m
a
x
lim
1
2
L
L
N
i
gi
gi
gi
gi
n
g
j
N
i
i
i
i
i
j
L
Q
Q
Q
Q
V
V
V
V
L
V
(8
)
β1
an
d
β2
ar
e
p
en
alt
y
f
ac
to
r
s
.
Vili
m
,
Q
g
ili
m
ca
n
b
e
ex
p
r
ess
e
d
as
;
,
,
,
m
i
n
m
i
n
m
a
x
m
a
x
lim
m
i
n
m
i
n
m
a
x
m
a
x
lim
o
t
h
e
r
s
Q
Q
,
Q
Q
Q
,
Q
Q
Q
o
t
h
e
r
s
V
V
,
V
V
V
,
V
V
V
gi
gi
gi
gi
gi
gi
gi
gi
i
i
i
i
i
i
i
i
(9
)
3.
H
YB
RID B
ACTE
RIA F
O
R
AG
I
N
-
P
ART
I
CL
E
S
WAR
M
O
P
T
I
M
I
Z
A
T
I
O
N
A
L
G
O
RIT
H
M
3
.
1
.
B
a
s
ic
P
SO
a
lg
o
rit
hm
I
n
P
SO
alg
o
r
it
h
m
,
s
ea
r
ch
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e
g
in
s
w
it
h
a
p
o
p
u
latio
n
o
f
r
a
n
d
o
m
l
y
g
e
n
er
ated
p
ar
ticles,
w
h
er
e
ea
ch
p
ar
ticle
is
a
p
o
ten
tial
s
o
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s
w
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it
f
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s
a
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o
th
er
d
ir
ec
tio
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t
h
r
o
u
g
h
t
u
m
b
le
.
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s
u
c
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t
u
m
b
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f
ai
lu
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esu
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s
in
s
lo
w
i
n
g
d
o
w
n
t
h
e
alg
o
r
it
h
m
.
3
.
3
.
P
ro
po
s
ed
hy
brid B
F
-
P
SO
a
lg
o
rit
h
m
BF
-
P
SO a
l
g
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r
ith
m
co
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b
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es
t
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P
SO a
b
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y
o
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m
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d
B
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a
b
ilit
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to
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d
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l
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tio
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b
y
e
li
m
in
at
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an
d
d
is
p
er
s
io
n
.
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h
e
tu
m
b
le
d
ir
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tio
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in
ch
e
m
o
tactic
m
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v
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m
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t
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f
B
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A
i
s
ca
lcu
lated
b
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s
in
g
g
lo
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al
b
est
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h
b
ac
ter
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p
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s
o
n
al
b
est
a
s
d
o
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e
i
n
P
SO.
I
t
av
o
id
s
co
m
p
le
x
ca
lcu
latio
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s
an
d
also
r
an
d
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m
n
es
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w
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d
ela
y
t
h
e
co
n
v
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g
en
ce
.
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n
r
ep
r
o
d
u
ctio
n
s
tep
,
all
b
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ter
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w
h
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ar
e
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e
t
h
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ch
e
m
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tactic
s
te
p
,
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e
s
o
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ted
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est
h
al
f
o
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b
ac
ter
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ar
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r
etain
ed
a
n
d
w
o
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s
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h
al
f
o
f
b
ac
ter
ia
d
ie.
T
o
r
ed
u
ce
th
e
c
h
an
ce
to
tr
ap
in
lo
ca
l
m
i
n
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m
u
m
,
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h
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h
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s
e
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n
P
SO
al
g
o
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it
h
m
,
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r
tai
n
n
u
m
b
er
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f
r
ep
licated
b
ac
ter
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is
r
an
d
o
m
l
y
d
is
p
er
s
ed
in
to
th
e
s
ea
r
ch
s
p
ac
e
at
a
ce
r
tain
r
ate.
T
h
is
m
ea
s
u
r
e
ca
n
in
cr
ea
s
e
th
e
r
ate
o
f
ac
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v
i
n
g
o
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ti
m
al
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tio
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n
d
av
o
id
p
r
em
a
tu
r
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c
o
n
v
er
g
e
n
ce
.
3
.
4
.
T
he
p
s
eudo
co
de
o
f
t
he
H
B
F
P
SO
a
lg
o
rit
h
m
Read line data, bus data,
write NR load flow subro
utine to calculate objective function P
loss
and L
j index.
Initialize PSO and BFA parameters C1, C2, inertia, population size, maximum number of
iteration of PSO(max iter),
reproduction steps and number of elimination and dispersion
steps and probability of elimination and dispersion(P
ed
)
generate initial population randomly .
for l=1: no of elimination and dispersion steps.
for k=1: no of reproduction steps
for j=1: max iter
Check for control variable constraints
Get the fitness value of objective function (7
-
8) from NR load flow subroutine.
Compute pbest and gbest.
Update velocity and position of each bacteria(10
).
end for j
sort bacteria according to the fitness
remove the worst half and replace with best half
end for k
replace certain bacteria with new ones with the probability of P
ed
end for l
printing of the results.
4.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
Si
m
u
latio
n
s
ar
e
co
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,
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ith
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ter
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p
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[
1
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4
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v
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ith
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4
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
A
p
p
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I
SS
N:
2252
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8792
A
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n
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c
o
m
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r
ith
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h
e
Me
a
n
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3
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s
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s
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m
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m
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ar
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to
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FA
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B
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Me
an
v
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u
es
o
f
th
e
p
r
o
p
o
s
ed
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an
d
th
e
lo
w
v
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o
f
s
tan
d
ar
d
d
ev
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n
i
n
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icat
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te
n
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y
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f
p
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p
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s
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o
r
ith
m
f
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r
m
u
l
tip
le
r
u
n
s
.
Fig
u
r
e
3
.
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er
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ce
c
h
ar
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tics
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f
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F
A
,
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SO a
n
d
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o
r
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loss
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d
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o
b
j
e
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5.
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NCLU
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O
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h
h
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ed
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e
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m
izat
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o
f
t
w
o
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b
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tiv
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s
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d
v
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t
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d
ex
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h
e
p
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o
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ith
m
is
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o
n
s
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ar
d
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3
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s
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m
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d
a
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2
4
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ith
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iv
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d
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r
ith
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m
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n
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r
ith
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e
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134
RE
F
E
R
E
NC
E
S
[1
]
J.
Qiu
a
n
d
S
.
M
.
S
h
a
h
i
d
e
h
p
o
u
r
,
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e
w
a
p
p
ro
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ro
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IEE
E
T
ra
n
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ti
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o
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Po
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r S
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ms
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2
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p
p
.
2
8
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9
5
,
1
9
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7
.
[2
]
D.
T
h
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k
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ra
m
,
K.
P
a
rth
a
sa
ra
th
y
,
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P
.
K
h
in
c
h
a
,
N
.
Ud
u
p
a
,
a
n
d
A
.
Ba
n
silal,
“
V
o
lt
a
g
e
sta
b
il
it
y
i
m
p
ro
v
e
m
e
n
t:
C
a
se
stu
d
ies
o
f
In
d
ian
p
o
w
e
r
n
e
tw
o
rk
s,
”
El
e
c
tric P
o
we
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
4
4
,
n
o
.
1
,
p
p
.
3
5
-
4
4
,
1
9
9
8
[3
]
A
.
L
o
m
i,
D
.
T
h
u
k
a
ra
m
,
“
Op
ti
m
u
m
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
f
o
r
a
ll
e
v
iatio
n
o
f
v
o
lt
a
g
e
d
e
v
iatio
n
s
,
”
T
e
lec
o
mm
u
n
ica
ti
o
n
,
Co
mp
u
t
in
g
,
El
e
c
tro
n
ics
a
n
d
Co
n
t
ro
l
,
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l
.
1
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o
.
2
,
p
p
.
2
5
7
-
2
6
4
,
2
0
1
2
.
[4
]
T
.
Dh
a
d
b
a
n
jan
a
n
d
G
.
Ye
su
ra
tn
a
m
,
“
Co
m
p
a
riso
n
o
f
o
p
ti
m
u
m
r
e
a
c
ti
v
e
p
o
we
r
sc
h
e
d
u
le
w
it
h
d
if
f
e
re
n
t
o
b
jec
ti
v
e
s
u
sin
g
L
P
t
e
c
h
n
i
q
u
e
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Eme
rg
i
n
g
El
e
c
tric P
o
we
r S
y
ste
ms
,
v
o
l.
7
,
n
o
.
3
,
p
p
.
1
-
2
9
,
2
0
0
6
.
[5
]
X
.
W
u
,
Z
.
P
iao
,
Y
.
L
iu
,
a
n
d
H
.
L
u
o
,
“
Re
a
c
ti
v
e
p
o
w
e
r
a
n
d
v
o
lt
a
g
e
c
o
n
tro
l
b
a
se
d
o
n
im
p
ro
v
e
d
p
a
rti
c
le
sw
a
r
m
o
p
t
i
m
i
z
a
t
i
o
n
i
n
p
o
w
e
r
s
y
s
t
e
m
,
”
8
t
h
W
o
r
l
d
C
o
n
g
r
e
s
s
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I
n
t
e
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g
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A
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n
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n
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p
p
.
5
2
9
1
-
5
2
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5
,
2
0
1
0
.
[6
]
M
.
T
r
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p
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t
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y
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n
d
S
.
M
i
s
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r
a
,
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p
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i
m
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n
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v
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g
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t
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,
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2
0
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6
I
n
t
e
r
n
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t
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o
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l
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l
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w
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l
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i
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p
p
.
1
-
6
,
2
0
0
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.
[7
]
M
.
K
.
M
.
Zam
a
n
i,
I
.
M
u
siri
n
,
M
.
S
.
Om
a
r,
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.
I
.
S
u
l
im
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n
,
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A
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G
h
a
n
i
,
a
n
d
N
.
A
.
M
.
Ka
m
a
r
i
,
“
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ra
v
it
a
ti
o
n
a
l
se
a
rc
h
a
lg
o
rit
h
m
b
a
se
d
tec
h
n
i
q
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e
f
o
r
v
o
lt
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g
e
sta
b
il
it
y
im
p
ro
v
e
m
e
n
t
,
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d
o
n
e
sia
n
J
o
u
rn
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o
f
E
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trica
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E
n
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m
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ter
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e
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ol
.
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o
.
1
,
p
p
.
1
2
3
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3
0
,
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8
.
[8
]
T
.
O.
T
in
g
,
K.
P
.
W
o
n
g
,
a
n
d
C.
Y.
Ch
u
n
g
,
"
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y
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rid
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o
n
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ti
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a
lg
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rit
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/p
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c
le
s
w
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p
ti
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isa
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lo
a
d
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lo
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a
lg
o
rit
h
m
,
"
IET
Ge
n
e
ra
ti
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ra
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issio
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&
Distrib
u
ti
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l
.
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o
.
6
,
p
p
.
8
0
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2
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.
[9
]
M
.
M
.
A
.
A
l
q
a
d
a
s
i
,
S
.
M
.
O
t
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n
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R
a
h
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t
,
a
n
d
F
.
A
b
d
u
l
l
a
h
,
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O
p
t
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m
i
z
a
t
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n
o
f
P
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D
f
o
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u
l
i
c
a
c
tu
a
to
r
u
sin
g
P
S
OG
S
A
,
”
T
EL
K
OM
NIKA
T
e
lec
o
mm
u
n
ica
ti
o
n
,
Co
mp
u
ti
n
g
,
El
e
c
tro
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ics
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n
d
Co
n
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v
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l.
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o
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p
p
.
2
6
2
5
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6
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5
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2
0
1
9
.
[1
0
]
F
.
L
a
o
u
a
f
i,
A
.
Bo
u
k
a
d
o
u
m
,
a
n
d
S
.
L
e
u
lm
i
,
“
A
h
y
b
rid
f
o
r
m
u
latio
n
b
e
tw
e
e
n
d
iff
e
r
e
n
ti
a
l
e
v
o
lu
ti
o
n
a
n
d
sim
u
late
d
a
n
n
e
a
li
n
g
a
lg
o
rit
h
m
s
f
o
r
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
,”
T
e
lec
o
mm
u
n
ica
ti
o
n
,
Co
m
p
u
ti
n
g
,
E
lec
tro
n
ics
a
n
d
Co
n
tro
l
,
v
ol
.
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6
,
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o
.
2
,
p
p
.
5
1
3
-
5
2
4
,
2
0
1
8
.
[1
1
]
G
.
X
iao
,
H.
L
iu
,
Y.
Zh
o
u
,
a
n
d
Y.
G
u
o
,
“
Re
se
a
rc
h
o
n
c
h
a
o
ti
c
f
iref
l
y
a
lg
o
rit
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m
a
n
d
th
e
a
p
p
li
c
a
ti
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in
o
p
t
im
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
,
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T
e
lec
o
m
mu
n
ica
t
io
n
,
Co
m
p
u
t
in
g
,
El
e
c
tro
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d
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,
v
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l.
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o
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1
,
p
p
.
9
3
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0
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2
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.
[1
2
]
A
.
S
.
El
-
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a
k
e
e
l,
A
.
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-
E
.
K
.
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.
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li
ss
y
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n
d
A
.
M
.
A
b
d
e
lh
a
m
e
d
,
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h
y
b
rid
b
a
c
teria
l
f
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ra
g
in
g
-
p
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rti
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le
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tec
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ra
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ti
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p
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t
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sh
les
s
DC
m
o
to
r
,
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lec
tric P
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ts a
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p
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[1
3
]
F
.
Zh
a
o
,
X
.
Jia
n
g
,
C
.
Z
h
a
n
g
,
a
n
d
J
.
W
a
n
g
,
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A
ch
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m
o
ta
x
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n
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n
c
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teria
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ti
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sh
o
p
sc
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d
u
li
n
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p
ro
b
lem
,
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In
ter
n
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ti
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o
u
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Co
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p
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ter
In
teg
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ted
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[1
4
]
S
.
M
o
u
a
ss
a
,
T
.
Bo
u
k
ti
r
,
a
n
d
A
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a
lh
i,
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A
n
t
li
o
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m
ize
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p
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s
y
ste
m
s,”
En
g
in
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c
ie
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d
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e
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h
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o
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n
In
ter
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o
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l.
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3
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p
.
8
8
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5
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[1
5
]
K.Y.
L
e
e
,
Y.M
.
P
a
rk
,
a
n
d
J.L
.
Ori
tz,
“
Op
ti
m
a
l
re
a
l
a
n
d
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
,”
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e
c
tric
Po
we
r
Res
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rc
h
,
v
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l.
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,
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o
.
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p
.
2
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