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p
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tr
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o
f
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[
4
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F
A
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o
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k
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y
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[
4
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-
[
8
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.
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n
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Os
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Sectio
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
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Vo
l.
5
,
No
.
1
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A
p
r
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2
0
1
6
:
40
–
50
42
2.
M
O
DE
L
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UT
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I
N
E
Fig
u
r
e
1
d
ep
icts
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e
f
lo
w
ch
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o
f
t
h
e
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ed
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C
m
o
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el.
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h
is
m
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d
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m
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ass
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s
N
C
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F o
v
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th
e
2
4
-
h
h
o
r
izo
n
.
NC
OP
F
u
t
il
izes
t
h
e
UC
s
o
l
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tio
n
,
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e
o
p
tim
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i
s
p
atch
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ased
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en
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er
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o
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s
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tili
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to
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o
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p
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e
N
C
UC
p
r
o
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le
m
i
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m
al
ler
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d
ea
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ier
to
s
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lv
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s
u
b
p
r
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b
lem
s
[
9
]
-
[
1
2
]
.
T
h
e
m
a
s
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er
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s
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t
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ar
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th
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le
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n
its
(
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e
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n
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et
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k
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n
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tr
ain
ts
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s
te
ad
y
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ta
t
e
[
1
3
]
-
[
2
4
]
.
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h
e
SS
FD
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e
in
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r
p
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b
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t
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k
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ase
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ased
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f
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co
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ased
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r
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g
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a
g
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n
r
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tio
n
(
AL
R
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ap
p
lied
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t
Fig
u
r
e
1
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Flo
w
c
h
ar
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f
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C
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w
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SF
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m
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a
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m
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n
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3.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
3
.
1
.
UC
F
o
r
m
ula
t
io
n
T
h
e
o
b
j
ec
tiv
e
o
f
th
e
UC
p
r
o
b
le
m
is
to
d
eter
m
in
e
th
e
s
et
o
f
g
e
n
er
ati
n
g
u
n
its
w
h
i
le
m
in
i
m
ize
s
th
e
to
tal
p
r
o
d
u
ctio
n
co
s
t
o
v
er
th
e
s
ch
ed
u
lin
g
p
er
io
d
.
T
h
er
ef
o
r
e,
th
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
is
ex
p
r
e
s
s
ed
as
t
h
e
s
u
m
o
f
f
u
e
l,
s
tar
t
-
u
p
a
n
d
s
h
u
t d
o
w
n
c
o
s
ts
o
f
t
h
e
g
e
n
er
atin
g
u
n
it
s
.
T
h
e
U
C
p
r
o
b
le
m
ca
n
b
e
m
ath
e
m
atica
ll
y
f
o
r
m
u
la
ted
as [
1
8
]
:
Min
T
GC
∑
∑
{
[
(
)
(
(
)
)
]
(
)
(
)
}
(
1
)
Du
e
to
th
e
o
p
er
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n
al
r
eq
u
ir
e
m
en
ts
,
th
e
m
i
n
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m
izatio
n
o
f
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
i
s
s
u
b
j
ec
ted
to
th
e
f
o
llo
w
in
g
co
n
s
tr
ain
ts
:
(
a)
P
o
w
er
b
alan
ce
co
n
s
tr
ai
n
ts
∑
(
2
)
∑
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
Shunt
-
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F
A
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Dev
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(
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43
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b
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Sp
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∑
[
]
(
3
)
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[
]
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c)
Min
i
m
u
m
u
p
/d
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w
n
ti
m
e
co
n
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t
r
ain
ts
[
(
)
]
[
(
)
]
(
4
)
[
(
)
]
[
(
)
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(
d
)
P
o
w
er
g
e
n
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n
l
i
m
it c
o
n
s
tr
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ts
(
5
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e)
R
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(
(
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(
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(
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(
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(
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)
(
6
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I
n
o
r
d
er
to
s
o
lv
e
UC
,
th
e
AL
R
m
et
h
o
d
is
e
m
p
lo
y
ed
f
o
r
r
elax
in
g
p
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s
y
s
te
m
co
n
s
tr
ai
n
ts
(
2
)
,
(
3
)
.
T
h
e
r
elax
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p
r
o
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lem
is
d
ec
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m
p
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s
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in
to
N
s
u
b
p
r
o
b
lem
s
f
o
r
ea
ch
u
n
it.
D
y
n
a
m
ic
p
r
o
g
r
a
m
m
in
g
(
DP
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in
cl
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d
in
g
m
i
n
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m
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m
u
p
/d
o
w
n
ti
m
e
l
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m
it
(
5
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,
an
d
r
a
m
p
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m
its
(
6
)
is
u
s
ed
to
s
ea
r
ch
f
o
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th
e
o
p
ti
m
a
l
co
m
m
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t
m
e
n
t
o
f
a
s
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o
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tire
s
t
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y
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er
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d
.
L
ag
r
a
n
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ia
n
m
u
ltip
lier
s
ar
e
u
p
d
ated
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ased
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v
io
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n
s
o
f
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m
co
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tr
ai
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.
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h
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co
n
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n
ce
cr
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is
s
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f
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i
f
t
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d
u
a
lit
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n
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m
al
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t
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i
s
w
it
h
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n
a
g
i
v
e
n
li
m
it.
[
1
8
]
.
2
.
2
.
NCUC
w
it
h L
C
B
ased
o
n
UC
r
esu
lt
s
,
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
(
9
)
is
to
m
i
n
i
m
i
ze
OP
F
an
d
L
C
co
s
t
s
at
s
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s
tate
a
n
d
w
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co
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en
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h
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s
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n
its
th
a
t
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l
b
e
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s
ed
if
OP
F
is
in
f
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asib
le.
C
o
n
s
tr
ai
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ts
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1
0
)
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d
(
1
1
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r
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p
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t
th
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alan
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atin
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ased
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th
e
ab
o
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e
ass
u
m
p
ti
o
n
f
o
r
L
C
[
1
8
]
.
Min
T
GC
∑
∑
*
(
)
+
∑
∑
(
)
(
)
(
a)
P
o
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(
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b
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n
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n
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ain
t
s
∑
[
]
(
∑
)
∑
[
]
(
∑
)
(
)
(
c)
Gen
er
atio
n
li
m
i
t c
o
n
s
tr
ai
n
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
l.
5
,
No
.
1
,
A
p
r
il
2
0
1
6
:
40
–
50
44
(
1
0
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(
d
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R
a
m
p
i
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Up
/Do
w
n
li
m
it
s
(
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[
(
(
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)
]
(
(
)
)
(
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[
(
)
(
)
]
(
)
(
)
(
1
1
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e)
T
h
e
p
o
w
er
f
lo
w
eq
u
a
tio
n
s
(
)
(
1
2
)
(
f
)
T
h
e
tr
an
s
m
i
s
s
io
n
li
n
e
f
lo
w
s
co
n
s
tr
ai
n
t
(
1
3
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(
g
)
T
h
e
v
o
ltag
e
o
f
t
h
e
b
u
s
e
s
(
1
4
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(
h
)
T
h
e
SS
FD c
o
n
s
tr
ai
n
t
(
1
5
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T
h
e
s
tate
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ec
to
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m
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o
f
t
h
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b
u
s
v
o
ltag
e
p
h
a
s
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an
g
les
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d
m
a
g
n
it
u
d
es.
T
h
e
co
n
tr
o
l
v
ec
to
r
U
co
m
p
r
is
e
s
o
f
all
t
h
e
co
n
tr
o
llab
le
s
y
s
te
m
v
ar
iab
le
s
li
k
e
r
ea
l
p
o
w
er
g
e
n
er
atio
n
s
an
d
r
ea
cti
v
e
p
o
w
er
g
e
n
er
ated
b
y
SS
FD.
T
h
e
p
ar
a
m
eter
v
ec
t
o
r
C
in
clu
d
es
all
t
h
e
u
n
co
n
tr
o
llab
le
s
y
s
te
m
p
ar
a
m
e
ter
s
s
u
ch
as
lin
e
p
ar
a
m
eter
s
,
lo
ad
s
,
etc
[
1
8
]
.
3.
CASE
S
T
UD
I
E
S
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
is
ap
p
lied
to
a
th
ir
t
y
-
b
u
s
test
s
y
s
te
m
t
o
illu
s
tr
ate
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
NC
UC
.
3
.
1
.
T
hirt
y
-
B
us
t
est
Sy
s
t
e
m
T
h
e
th
ir
t
y
-
b
u
s
s
y
s
te
m
d
ep
ic
ted
in
Fig
u
r
e
2
h
as
f
iv
e
u
n
its
,
f
o
r
t
y
-
o
n
e
tr
an
s
m
is
s
io
n
lin
es.
T
h
e
ch
ar
ac
ter
is
tic
s
o
f
u
n
it
s
,
tr
an
s
m
is
s
io
n
li
n
es,
a
n
d
t
h
e
h
o
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l
y
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ad
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2
4
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h
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e
g
i
v
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i
n
T
ab
les I
–
I
I
I
,
r
esp
ec
tiv
el
y
[
]
.
T
h
e
m
ag
n
it
u
d
e
o
f
v
o
lta
g
e
at
ea
c
h
b
u
s
m
u
s
t b
e
b
et
w
ee
n
0
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9
5
an
d
1
.
0
5
.
I
n
o
r
d
er
to
an
al
y
ze
th
e
e
f
f
icie
n
c
y
o
f
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
,
th
e
f
o
llo
w
i
n
g
f
iv
e
ca
s
e
s
t
u
d
ies
w
ith
co
r
r
esp
o
n
d
in
g
co
n
s
tr
ai
n
ts
is
co
n
s
id
er
ed
:
C
ase
1
)
UC
(
w
it
h
o
u
t
n
et
w
o
r
k
co
n
s
tr
ain
ts
)
;
C
ase
2
)
NC
U
C
;
C
ase
2
_
1
)
NC
UC
w
it
h
o
u
t
SS
F
D.
C
ase
2
_
2
)
NC
UC
w
it
h
S
C
FD
in
li
n
es 2
9
an
d
3
0
.
C
ase
2
_
3
)
NC
UC
w
it
h
S
FD a
t
b
u
s
es 8
,
1
7
,
1
9
,
2
0
,
2
1
an
d
3
0
.
C
ase
2
_
4
)
NC
UC
w
it
h
S
C
FD
in
li
n
es 2
9
an
d
3
0
an
d
SF
D
at
b
u
s
es 8
,
1
7
,
1
9
,
2
0
,
2
1
an
d
3
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
Shunt
-
S
eries
F
A
C
TS
Dev
ices
o
n
N
etw
o
r
k
C
o
n
s
tr
a
in
ed
Un
it C
o
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t
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(
G.
A
.
M.Ho
s
a
i
n
i H
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jiva
r
)
45
I
n
s
o
m
e
ca
s
es,
ac
co
r
d
in
g
T
a
b
le
I
V,
SS
FD
ar
e
co
n
s
id
er
ed
.
T
h
ese
d
ev
ices
ar
e
m
o
d
eled
u
s
i
n
g
th
e
p
r
o
p
o
s
ed
R
P
I
M
[
1
8
]
.
C
ase
1
)
in
t
h
is
ca
s
e,
UC
w
i
l
l
d
eter
m
in
e
t
h
e
b
ase
ca
s
e
s
c
h
ed
u
le
o
f
u
n
its
,
w
h
e
n
d
is
r
eg
ar
d
in
g
t
h
e
n
et
w
o
r
k
co
n
s
tr
ain
ts
.
T
h
e
co
m
m
it
m
e
n
t
s
ch
ed
u
le
is
s
h
o
w
n
i
n
T
ab
le
I
V
in
w
h
ic
h
1
an
d
0
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ep
r
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n
t
h
o
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l
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o
n
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f
f
s
tates
o
f
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n
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ts
,
an
d
h
o
u
r
0
r
ep
r
esen
ts
th
e
in
it
ial
co
n
d
itio
n
.
T
h
e
o
p
ti
m
al
g
e
n
er
atio
n
d
is
p
atch
o
f
u
n
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ts
is
s
h
o
w
n
in
T
ab
le
V.
I
n
ad
d
itio
n
,
t
h
e
d
ail
y
b
id
-
b
ased
g
en
er
atio
n
d
is
p
atc
h
co
s
t
g
iv
e
n
i
n
T
ab
le
I
V
is
$
1
4
2
2
0
3
.
6
1
4
5
.
T
h
e
o
p
ti
m
al
g
e
n
er
ati
o
n
d
is
p
atch
g
iv
e
n
in
T
a
b
le
V.
I
n
th
is
ca
s
e,
th
e
ec
o
n
o
m
ica
l
u
n
i
ts
1
,
2
an
d
4
s
u
p
p
ly
t
h
e
b
ase
lo
ad
,
w
h
ic
h
ar
e
co
m
m
i
tted
at
th
e
en
tire
s
ch
ed
u
li
n
g
h
o
r
izo
n
.
T
h
e
u
n
it
3
is
co
m
m
i
tted
at
ce
r
tai
n
h
o
u
r
s
(
1
1
-
2
1
)
to
s
u
p
p
l
y
p
ea
k
lo
ad
an
d
to
m
i
n
i
m
ize
T
GC
.
Mo
r
e
ex
p
en
s
iv
e
u
n
i
ts
5
an
d
6
ar
e
n
o
t c
o
m
m
i
tte
d
at
all
h
o
u
r
s
.
C
ase
2
)
i
n
ca
s
e
2
_
1
,
th
e
i
m
p
ac
t
o
f
ac
n
et
w
o
r
k
co
n
s
tr
ain
ed
at
s
tead
y
s
ta
te
o
n
u
n
it
co
m
m
it
m
e
n
t
(
N
C
UC
)
i
s
s
tu
d
ied
.
I
f
w
e
u
s
e
t
h
e
U
C
r
es
u
lts
in
C
a
s
e
1
f
o
r
N
C
OP
F
ca
l
cu
latio
n
s
,
m
ag
n
it
u
d
e
v
o
ltag
e
v
io
latio
n
s
w
il
l
o
cc
u
r
at
b
u
s
es
1
2
-
2
0
.
I
n
o
r
d
er
to
co
n
s
id
er
in
g
t
h
e
n
et
w
o
r
k
co
n
s
tr
ai
n
ts
,
w
e
f
in
d
t
h
at
th
e
o
th
er
UC
in
C
ase
2
_
1
.
So
,
th
e
co
m
m
it
m
en
t
s
ch
ed
u
le
is
s
h
o
w
n
in
T
ab
le
VI
a
n
d
t
h
e
o
p
ti
m
al
g
en
er
at
io
n
d
is
p
atc
h
o
f
NC
OP
F
i
s
ch
a
n
g
ed
as
s
h
o
w
n
in
T
ab
le
VI
I
.
T
h
e
h
ig
h
l
ig
h
ted
ite
m
s
i
n
m
en
t
io
n
ed
T
ab
le
s
h
o
w
d
if
f
er
e
n
ce
s
b
et
w
ee
n
C
ase
1
a
n
d
C
a
s
e
2
_
1
.
I
n
o
r
d
er
to
m
ai
n
tai
n
in
g
th
e
m
a
g
n
it
u
d
e
v
o
lta
g
e
b
u
s
e
s
to
th
eir
li
m
its
(
0
9
5
≤
V
≤
1
0
5
)
an
d
lin
e
ca
p
ac
it
y
li
m
its
i
n
ac
c
o
r
d
an
ce
T
ab
le
I
I
,
th
e
g
en
er
ati
o
n
d
is
p
atch
o
f
th
e
ec
o
n
o
m
ical
u
n
it
s
1
,
2
,
3
an
d
4
is
ch
an
g
ed
.
T
h
e
r
elativ
el
y
ex
p
e
n
s
i
v
e
u
n
it
s
5
an
d
6
ar
e
d
is
p
atch
ed
to
s
u
p
p
l
y
th
e
s
y
s
te
m
lo
ad
.
A
cc
o
r
d
in
g
l
y
,
th
e
d
aily
co
s
t
o
f
b
id
-
b
ased
g
e
n
er
atio
n
d
is
p
atc
h
in
cr
ea
s
es to
$
1
6
9
5
0
5
.
1
9
.
I
n
C
ase
s
2
_
2
-
2
_
4
,
th
e
SC
FD,
SC
F
a
n
d
SS
F
D
in
j
ec
t
th
e
co
n
tr
o
llab
le
r
ea
ctiv
e
p
o
w
er
to
t
h
e
n
et
w
o
r
k
an
d
a
ls
o
m
a
n
ag
e
r
ea
cti
v
e
p
o
w
er
f
lo
w
s
an
d
ac
co
r
d
in
g
l
y
ad
j
u
s
t
b
u
s
v
o
lta
g
e
lev
e
ls
.
T
h
e
SS
FD
is
t
h
e
b
est
o
p
tio
n
to
d
ec
r
ea
s
e
th
e
r
ea
ctiv
e
p
o
w
er
f
lo
w
o
n
t
h
e
n
et
w
o
r
k
lin
e
s
an
d
t
h
er
ef
o
r
e
i
n
cr
ea
s
e
th
e
tr
an
s
f
er
ca
p
ab
ilit
y
o
f
t
h
e
l
in
e
s
.
I
n
ca
s
e
2
_
2
-
2
_
4
th
e
v
o
lta
g
e
at
all
b
u
s
e
s
a
n
d
t
h
e
r
ea
cti
v
e
p
o
w
er
f
lo
w
at
n
et
w
o
r
k
li
n
es
is
c
h
an
g
ed
.
T
h
e
r
ea
ctiv
e
p
o
w
er
g
e
n
er
atio
n
b
y
SF
D
is
s
h
o
w
n
i
n
Fi
g
u
r
e
3
.
T
h
e
co
m
m
i
t
m
e
n
t
s
ch
ed
u
le
i
s
s
h
o
w
n
i
n
T
ab
le
VI
an
d
th
e
o
p
t
i
m
al
g
e
n
er
atio
n
d
is
p
atc
h
o
f
NC
OP
F
is
ch
an
g
ed
as
s
h
o
w
n
i
n
T
ab
le
V
I
I
.
W
ith
o
u
t
th
e
SC
FD,
S
C
F
an
d
SS
FD,
th
e
v
o
lta
g
e
d
r
o
p
o
cc
u
r
at
all
b
u
s
es
m
o
s
tl
y
at
p
ea
k
h
o
u
r
s
.
H
o
w
e
v
er
,
th
e
r
ea
ctiv
e
p
o
w
er
in
j
ec
tio
n
to
th
e
n
et
w
o
r
k
i
n
cr
ea
s
es
th
e
b
u
s
v
o
ltag
e
s
a
n
d
p
r
ev
e
n
ts
v
o
lta
g
e
an
d
li
n
e
ca
p
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[
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I
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IJ
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2252
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8792
Shunt
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
2
2
5
2
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8792
IJ
A
P
E
Vo
l.
5
,
No
.
1
,
A
p
r
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2
0
1
6
:
40
–
50
48
T
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0
6
8
0
0
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0
.
5
3
1
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24
7
4
.
7
5
8
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.
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4.
CO
NCLU
SI
O
NS
T
h
e
NC
UC
r
esu
lt
s
o
f
n
u
m
er
ical
test
s
s
h
o
w
t
h
e
ef
f
ec
ti
v
en
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
in
m
in
i
m
izi
n
g
b
id
b
ased
g
en
er
atio
n
co
s
t
a
n
d
m
a
in
ta
in
n
et
w
o
r
k
s
ec
u
r
it
y
in
s
tead
y
s
tate
a
n
d
co
n
ti
n
g
e
n
c
y
.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
co
u
ld
s
o
lv
e
b
o
th
NC
UC
m
o
d
u
les
b
ased
o
n
ac
co
n
s
tr
ain
t
s
an
d
ad
v
ice
a
g
o
o
d
s
e
t
o
f
co
r
r
ec
tiv
e
an
d
p
r
ev
en
ti
v
e
co
n
tr
o
l p
r
o
to
co
l f
o
r
th
e
s
ec
u
r
e
a
n
d
ec
o
n
o
m
ical
o
p
er
atio
n
o
f
p
o
w
er
s
y
s
te
m
s
.
I
m
p
ac
t
o
f
SC
FD,
S
C
F
an
d
S
SF
D
ad
j
u
s
t
m
e
n
t
w
a
s
i
n
v
esti
g
ated
in
to
t
h
e
N
C
U
C
w
it
h
A
C
n
et
w
o
r
k
co
n
s
tr
ain
ts
at
s
tead
y
s
tate
a
n
d
co
n
tin
g
e
n
c
y
.
T
o
en
h
an
ce
t
h
e
p
r
o
p
o
s
ed
A
C
s
o
l
u
tio
n
o
f
NC
U
C
,
SC
FD,
SC
F
an
d
SS
FD
w
er
e
co
n
s
id
er
ed
.
A
R
P
I
M
w
as
u
s
ed
to
m
o
d
el
th
e
e
f
f
ec
t
o
f
SC
FD,
S
C
F
a
n
d
SS
F
D
in
t
h
e
AC
p
o
w
er
f
lo
w
,
u
s
in
g
r
ea
cti
v
e
p
o
w
er
i
n
j
ec
tio
n
s
to
s
y
s
te
m
lo
ad
b
u
s
e
s
.
W
e
co
n
clu
d
ed
th
at
th
e
i
n
co
r
p
o
r
atio
n
o
f
SC
FD,
SC
F
an
d
SS
F
D
w
o
u
ld
en
h
a
n
ce
th
e
h
o
u
r
l
y
NC
U
C
s
o
lu
tio
n
w
h
e
n
co
n
s
id
er
in
g
b
u
s
v
o
lta
g
e
an
d
li
n
e
ca
p
ac
it
y
co
n
s
tr
ain
ts
.
I
f
th
e
S
C
FD,
SC
F
an
d
S
S
F
D
w
i
th
t
h
e
s
u
f
f
icie
n
t
ca
p
ac
it
y
at
f
u
ll
lo
ad
ce
n
ter
s
to
b
e
in
s
tal
led
an
d
u
tili
ze
d
,
m
o
r
e
e
f
f
ec
t
iv
e
i
n
t
h
e
s
h
o
r
t
-
ter
m
p
o
w
er
s
y
s
te
m
p
lan
n
in
g
w
i
ll
y
ie
ld
.
Dis
tr
ib
u
ted
f
as
t c
o
n
tr
o
llab
le
s
h
u
n
t
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