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Dec
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
2252
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8792
IJ
A
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Vo
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6
,
No
.
3
,
Dec
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b
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2
0
1
7
: 1
2
3
–
132
124
T
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p
o
w
er
s
y
s
te
m
[
4
]
.
I
n
th
e
p
r
esen
t
i
n
v
e
s
ti
g
atio
n
I
n
ter
io
r
P
o
in
t
(
I
P
)
b
ased
OP
F
tech
n
iq
u
e
is
u
s
ed
to
o
b
tain
t
h
e
o
p
ti
m
al
r
esch
ed
u
li
n
g
o
f
g
en
er
ato
r
s
a
n
d
m
in
i
m
ize
t
h
e
p
er
d
ay
to
tal
g
en
er
atio
n
co
s
t
i
n
a
p
o
w
er
m
ar
k
et.
OP
F
m
ea
n
s
in
telli
g
e
n
tl
y
ad
j
u
s
ti
n
g
t
h
e
p
o
w
er
s
y
s
te
m
s
ett
in
g
s
in
s
u
ch
a
wa
y
t
h
at
it
m
a
n
a
g
es
lo
ad
f
lo
w
a
n
d
at
t
h
e
s
a
m
e
ti
m
e
o
p
tim
izin
g
th
e
o
p
er
atin
g
co
n
d
itio
n
s
w
h
ile
f
u
l
f
i
lli
n
g
p
ar
ticu
lar
co
n
s
tr
ain
ts
.
On
e
an
o
t
h
er
b
en
ef
it
o
f
u
s
i
n
g
th
e
o
p
tim
a
l
p
o
w
er
f
lo
w
t
ec
h
n
iq
u
e
is
r
ed
u
ce
s
t
h
e
lo
s
s
es
i
n
t
h
e
s
y
s
te
m
.
T
h
e
p
r
o
b
le
m
in
th
e
p
r
es
en
t
ti
m
e
s
ce
n
ar
io
is
as
th
e
p
o
w
er
s
y
s
te
m
h
as
e
m
er
g
ed
as
a
m
ar
k
et,
t
h
e
i
n
v
esto
r
s
w
a
n
t
m
o
r
e
p
r
o
f
it
b
y
i
n
j
ec
tin
g
an
d
d
r
a
w
i
n
g
m
o
r
e
an
d
m
o
r
e
p
o
w
er
t
h
r
o
u
g
h
th
e
tr
an
s
m
i
s
s
io
n
li
n
es
w
i
th
o
u
t
th
i
n
k
i
n
g
ab
o
u
t
t
h
e
ca
p
ab
ilit
y
o
f
th
e
tr
an
s
m
is
s
io
n
li
n
es
w
h
ic
h
r
es
u
lts
i
n
t
h
e
p
r
o
b
lem
o
f
co
n
g
e
s
tio
n
i
n
t
h
e
tr
an
s
m
i
s
s
io
n
s
y
s
te
m
a
n
d
u
l
ti
m
at
el
y
r
es
u
lti
n
g
in
t
h
e
in
s
tab
il
it
y
o
f
th
e
w
h
o
le
s
y
s
te
m
.
T
h
u
s
,
t
h
e
OP
F
b
ased
o
p
er
atio
n
h
a
s
a
b
etter
o
p
p
o
r
tu
n
i
t
y
f
o
r
ef
f
icie
n
t
a
n
d
s
ec
u
r
e
o
p
er
atio
n
f
o
r
th
e
p
o
w
er
s
y
s
te
m
[
5
-
8
].
T
h
e
p
r
esen
t
in
v
esti
g
atio
n
d
ea
ls
w
it
h
th
e
ec
o
n
o
m
ic
r
esc
h
ed
u
l
in
g
o
f
t
h
e
g
e
n
er
atio
n
o
f
elec
tr
i
cit
y
i
n
a
n
h
o
u
r
-
ah
ea
d
p
o
w
er
m
ar
k
e
t.
T
h
e
I
E
E
E
-
3
0
b
u
s
s
y
s
te
m
i
s
u
s
e
d
in
th
is
ca
s
e
f
o
r
th
e
s
t
u
d
y
o
f
th
e
r
esu
lts
.
I
n
t
h
i
s
w
o
r
k
,
t
h
e
lo
ad
b
u
s
es
h
a
v
e
ap
p
lied
an
h
o
u
r
l
y
b
ased
b
id
d
in
g
to
th
e
s
y
s
te
m
o
p
er
ato
r
an
d
o
n
th
e
b
asi
s
o
f
th
e
s
e
b
id
d
in
g
;
t
h
e
g
en
er
ato
r
s
h
a
v
e
s
ch
ed
u
led
t
h
eir
g
en
er
atio
n
s
.
T
h
e
o
p
ti
m
a
l
s
c
h
ed
u
le
s
o
f
g
e
n
er
atio
n
h
av
e
d
ec
id
ed
u
s
i
n
g
o
p
ti
m
izatio
n
tec
h
n
iq
u
e
.
T
h
e
o
p
tim
iza
tio
n
tech
n
iq
u
e
u
s
ed
in
th
i
s
ca
s
e
is
th
e
I
P
m
et
h
o
d
.
T
h
e
I
P
tech
n
iq
u
e
is
u
s
ed
f
o
r
th
e
ca
lc
u
latio
n
o
f
OP
F
o
f
lar
g
e
s
y
s
te
m
s
.
T
h
e
r
esu
lt
s
h
o
w
s
t
h
e
e
f
f
e
ct
o
f
th
e
p
r
o
p
o
s
ed
co
n
f
i
g
u
r
atio
n
o
v
er
t
h
e
co
s
t
o
f
t
h
e
g
e
n
er
ated
s
y
s
te
m
as
w
e
ll
as
t
h
e
ef
f
ec
t
s
w
h
ich
o
cc
u
r
o
n
t
h
e
co
n
g
e
s
tio
n
m
an
a
g
e
m
e
n
t
o
f
t
h
e
tr
a
n
s
m
is
s
i
o
n
li
n
es
a
n
d
t
h
e
lo
s
s
es
in
t
h
e
s
y
s
te
m
.
T
h
e
co
s
t
co
m
p
ar
i
s
o
n
i
s
d
o
n
e
b
et
w
ee
n
t
h
e
r
esu
lt
s
o
b
tain
ed
u
s
in
g
AC
lo
a
d
f
lo
w
s
t
u
d
y
a
n
d
OP
F b
ased
s
tu
d
y
.
T
h
e
p
u
r
p
o
s
e
o
f
th
e
p
r
ese
n
t
w
o
r
k
i
s
to
g
et
t
h
e
b
etter
s
o
lu
tio
n
f
o
r
t
h
e
s
y
s
te
m
w
h
ic
h
ca
n
p
r
o
v
id
e
a
les
s
co
s
t
l
y
o
p
er
atio
n
w
i
th
m
o
r
e
co
n
g
es
tio
n
f
r
ee
a
n
d
s
tab
le
s
y
s
te
m
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
E
x
p
lain
i
n
g
I
n
OP
F
b
ased
s
o
lu
tio
n
th
e
m
ai
n
o
b
j
ec
tiv
e
is
to
o
b
tain
th
e
m
i
n
i
m
u
m
g
en
er
atio
n
co
s
t.
OP
F
in
cl
u
d
es
th
e
co
s
t
o
f
g
e
n
er
ato
r
s
an
d
co
n
s
tr
ai
n
ts
as
v
ar
iab
le.
T
h
e
OP
F
b
ased
p
r
o
b
lem
f
o
r
m
u
l
atio
n
is
co
n
s
tit
u
ted
b
y
t
h
r
ee
ter
m
s
;
f
ir
s
t
r
elate
d
w
it
h
g
e
n
er
ati
n
g
co
s
t,
s
ec
o
n
d
ass
o
ciate
d
w
it
h
eq
u
alit
y
co
n
s
tr
ain
ts
an
d
th
e
t
h
ir
d
ter
m
is
as
s
o
ciate
d
w
ith
i
n
eq
u
a
lit
y
co
n
s
tr
ain
ts
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
d
ef
i
n
ed
a
s
;
∑
∑
(
1
)
2
.
1
.
E
qu
a
lit
y
co
ns
t
ra
ints
∑
∑
(
2
)
∑
∑
(
3
)
2
.
2
.
I
nequ
a
lity
co
ns
t
ra
ints
T
h
e
ac
tiv
e
p
o
w
er
g
e
n
er
ated
b
y
ea
c
h
u
n
it
m
u
s
t
s
a
tis
f
y
t
h
e
m
ax
i
m
u
m
a
n
d
m
in
i
m
u
m
o
p
er
atin
g
li
m
it
s
d
u
r
in
g
co
n
ti
n
g
e
n
c
y
s
tate
s
(
4
)
(
5
)
T
h
e
v
o
ltag
e
s
ec
u
r
it
y
at
ea
c
h
b
u
s
al
s
o
co
n
s
id
er
f
o
r
b
o
th
ca
s
es
(
6
)
T
h
e
ac
tiv
e
p
o
w
er
f
lo
w
t
h
r
o
u
g
h
ea
c
h
b
r
an
c
h
o
f
th
e
n
et
w
o
r
k
m
u
s
t
s
a
tis
f
y
th
e
s
ec
u
r
it
y
li
m
it
s
d
u
r
i
n
g
b
o
th
p
r
e
an
d
p
o
s
t c
o
n
tin
g
e
n
cie
s
.
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
O
p
tima
l P
o
w
er F
lo
w
B
a
s
ed
E
co
n
o
mic
Gen
era
tio
n
S
ch
ed
u
lin
g
in
Da
y
-
a
h
e
a
d
…
(
K
s
h
itij
C
h
o
u
d
h
a
r
y
)
125
w
h
er
e
Op
er
atio
n
co
s
t;
Gen
er
ato
r
o
u
tp
u
t;
No
.
o
f
g
en
er
ato
r
s
;
A
cti
v
e
p
o
w
er
d
e
m
an
d
at
lo
ad
b
u
s
;
R
ea
cti
v
e
p
o
w
er
d
e
m
a
n
d
at
lo
ad
b
u
s
;
A
cti
v
e
p
o
w
er
lo
s
s
;
R
ea
cti
v
e
p
o
w
er
lo
s
s
;
No
.
o
f
lo
ad
b
u
s
es;
,
Min
i
m
u
m
ac
t
iv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
li
m
i
ts
o
f
g
en
er
ato
r
s
;
,
Ma
x
i
m
u
m
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
li
m
i
ts
o
f
g
en
er
ato
r
s
;
P
o
w
er
f
lo
w
in
li
n
es b
et
w
ee
n
b
u
s
i
a
n
d
j
;
Ma
x
i
m
u
m
li
m
i
t o
f
li
n
es b
et
w
e
en
b
u
s
i
a
n
d
j
;
p
r
e
co
n
tin
g
e
n
c
y
v
o
lta
g
e
at
b
u
s
.
3.
P
RO
P
O
SE
D
I
N
T
E
RIOR
P
O
I
NT
B
AS
E
D
O
P
F
SO
L
U
T
I
O
N
M
E
T
H
O
DO
L
O
G
Y
I
n
th
e
p
r
esen
t
w
o
r
k
,
t
h
e
in
ter
i
o
r
p
o
in
t
(
I
P
)
b
ased
o
p
tim
izati
o
n
h
as
b
ee
n
u
s
ed
as
s
o
lu
tio
n
tech
n
iq
u
e
an
d
ap
p
lied
to
o
b
tain
th
e
o
p
tim
al
g
e
n
er
atio
n
s
c
h
ed
u
les
to
th
e
m
i
n
i
m
u
m
g
en
er
at
io
n
co
s
t
[
6
]
.
I
n
g
en
er
al,
th
e
p
r
o
b
lem
d
ef
i
n
ed
as a
n
o
n
-
li
n
e
ar
o
p
tim
izatio
n
p
r
o
b
lem
.
Min
i
m
ize
Su
b
j
ec
t
to
(
8
)
an
d
(
9
)
W
h
er
e
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
f(
x
)
g
e
n
er
all
y
r
ep
r
esen
t
s
t
h
e
f
u
e
l
co
s
t
o
f
g
e
n
er
atio
n
,
tr
a
n
s
m
is
s
io
n
lo
s
s
,
o
r
th
e
co
r
r
ec
tiv
e
co
n
tr
o
ls
,
etc.
,
h
(
x
)
r
ep
r
esen
ts
t
h
e
p
o
w
er
f
lo
w
eq
u
atio
n
s
a
n
d
g
(
x)
i
n
clu
d
es
co
m
p
o
n
en
t
an
d
v
ar
iab
le
in
eq
u
ali
ties
.
I
n
t
h
i
s
m
et
h
o
d
th
e
in
eq
u
alit
y
co
n
s
tr
ain
ts
ar
e
tr
an
s
f
o
r
m
ed
i
n
to
eq
u
a
lit
y
co
n
s
tr
a
in
ts
b
y
th
e
ad
d
itio
n
o
f
n
o
n
n
e
g
ati
v
e
s
lac
k
v
ar
iab
les
.
T
h
is
m
o
d
i
f
icatio
n
ca
n
r
ef
o
r
m
u
late
E
q
u
atio
n
(
8
)
as:
Min
i
m
ize
Su
b
j
ec
t to
;
(
1
0
)
w
h
er
e
z
1
an
d
z
u
ar
e
s
lack
v
ar
ia
b
les.
T
h
e
L
ag
r
an
g
ia
n
f
u
n
ctio
n
f
o
r
th
e
s
y
s
te
m
o
f
(
1
0
)
m
a
y
b
e
w
r
itt
en
as
(
1
1
)
w
h
er
e
λ
,
π
1
an
d
π
u
ar
e
th
e
v
ec
to
r
s
o
f
L
ag
r
an
g
e
m
u
lt
ip
lier
s
.
T
h
e
KK
T
o
p
tim
al
co
n
d
itio
n
f
o
r
th
e
ab
o
v
e
ca
n
b
e
w
r
itte
n
as
(
1
2
)
(
1
3
)
(
1
4
)
(
1
5
)
(
1
6
)
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I
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I
J
A
P
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I
SS
N:
2252
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8792
O
p
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C
ase
1
:
L
o
ad
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s
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n
g
in
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ti
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C
ase
2
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co
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e
1
:
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I
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IJ
A
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Vo
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6
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3
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Dec
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b
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2
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1
7
: 1
2
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–
132
130
T
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a
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ased
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2
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ased
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ased
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ased
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t
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(
$
/
d
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)
1
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9
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5
.
1
T
h
ese
test
r
es
u
lts
r
e
v
ea
ls
t
h
at
ap
ar
t
f
r
o
m
ec
o
n
o
m
ic
g
e
n
er
at
io
n
s
c
h
ed
u
le
t
h
e
OP
F
b
ased
g
en
er
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n
r
esch
ed
u
li
n
g
p
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id
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v
ar
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o
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er
ad
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a
n
ta
g
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u
s
s
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lu
t
io
n
s
f
o
r
th
e
p
o
w
er
n
et
w
o
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k
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p
er
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s
s
u
ch
a
s
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n
g
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tio
n
m
an
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g
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m
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n
t
an
d
v
o
ltag
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co
n
tr
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l
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ch
b
u
s
es.
Deta
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al
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o
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ad
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eli
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in
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t s
u
b
s
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tio
n
.
5.
CO
NCLU
SI
O
N
I
n
th
is
w
o
r
k
,
lo
ad
f
lo
w
s
t
u
d
y
an
d
I
P
b
ased
OP
F
s
tu
d
ies
w
er
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p
er
f
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r
m
ed
o
n
th
e
I
E
E
E
-
3
0
b
u
s
s
y
s
te
m
an
d
th
e
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u
lts
f
o
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b
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th
th
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ca
s
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w
er
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o
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s
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p
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m
in
g
t
h
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L
F
s
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y
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d
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s
tu
d
y
.
I
t
is
cle
ar
th
at
t
h
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OP
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s
t
u
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y
p
r
o
v
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s
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ased
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F
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at
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h
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li
m
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te
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w
as
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lated
m
a
n
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ti
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e
s
an
d
th
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y
s
te
m
d
r
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f
ted
to
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ar
d
s
co
n
tin
g
e
n
c
y
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Als
o
,
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n
e
o
f
th
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m
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in
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ea
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o
n
s
f
o
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ich
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h
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y
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n
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ted
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to
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th
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ef
f
ec
t
o
f
OP
F
s
tu
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y
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n
t
h
e
p
r
ice
o
f
th
e
ac
ti
v
e
p
o
w
er
g
e
n
er
atio
n
.
Af
ter
t
h
e
co
m
p
ar
is
o
n
it
i
s
cle
ar
th
at
u
s
e
o
f
OP
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s
tu
d
y
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n
a
s
y
s
te
m
h
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s
g
i
v
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s
ig
n
if
ican
t
r
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u
ctio
n
in
th
e
g
en
er
atio
n
co
s
t
o
f
th
e
s
y
s
te
m
.
Hen
ce
,
th
e
p
r
esen
t
w
o
r
k
clea
r
l
y
s
h
o
w
s
th
at
th
e
g
en
er
atio
n
s
ch
ed
u
li
n
g
u
s
i
n
g
I
P
b
ased
OP
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p
r
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b
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es
u
lts
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d
m
a
k
es
th
e
s
y
s
te
m
m
o
r
e
ef
f
icie
n
t a
s
w
el
l a
s
less
co
s
t
l
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
6
,
No
.
3
,
Dec
em
b
er
2
0
1
7
: 1
2
3
–
132
132
RE
F
E
R
E
NC
E
S
[1
]
Jo
h
n
J.
G
ra
in
g
e
r
a
n
d
W
il
li
a
m
D.
S
tev
e
n
so
n
Jr
.
, "
P
o
w
e
r
S
y
ste
m
A
n
a
l
y
sis
,
"
M
c
G
ra
w
Hill
P
u
b
li
c
a
ti
o
n
,
1
9
9
4
.
[2
]
C.
L
.
W
a
d
h
wa
, "
El
e
c
tri
c
a
l
P
o
w
e
r
S
y
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e
m
,
"
Ne
w
Ag
e
In
tern
a
ti
o
n
a
l
P
u
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l
ish
e
rs,
2
0
1
0
.
[3
]
O.
A
lsa
c
a
n
d
B.
S
to
tt
,
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Op
ti
m
a
l
Lo
a
d
F
lo
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it
h
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tea
d
y
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tate
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e
c
u
rit
y
,
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in
IEE
E
T
ra
n
sa
c
ti
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s o
n
Po
we
r A
p
p
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ra
t
u
s
a
n
d
S
y
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ms
,
v
o
l.
P
A
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-
9
3
,
n
o
.
3
,
p
p
.
7
4
5
-
7
5
1
,
M
a
y
1
9
7
4
.
[4
]
F
.
S
a
li
h
e
t
a
l.
,"
A
S
e
c
u
rit
y
-
c
o
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stra
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Eco
n
o
m
ic
P
o
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r
Disp
a
tch
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e
c
h
n
iq
u
e
Us
in
g
M
o
d
if
ied
S
u
b
g
ra
d
ien
t
A
l
g
o
rit
h
m
Ba
se
d
o
n
F
e
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sib
le
Va
lu
e
s
a
n
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P
se
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d
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c
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to
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r
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In
c
lu
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it
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d
En
e
rg
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S
u
p
p
ly
T
h
e
r
m
a
l
Un
it
s
,
"
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
i
n
e
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rin
g
,
Esk
ise
h
ir
Os
m
a
n
g
a
z
i
Un
iv
e
rsit
y
,
Esk
ise
h
ir,
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u
rk
e
y
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2
0
1
1
.
[5
]
Ka
r
m
a
r
k
a
r,
N
,
"
A
n
e
w
p
o
ly
n
o
m
i
a
l
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ti
m
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a
lg
o
rit
h
m
f
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li
n
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m
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in
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m
b
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to
rica
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v
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l
4
,
n
o
.
4
,
p
p
.
3
7
3
-
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9
5
,
De
c
e
m
b
e
r
1984.
[6
]
Hu
a
W
e
i,
H.
S
a
sa
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i,
J.
Ku
b
o
k
a
wa
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k
o
y
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m
a
,
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n
in
terio
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li
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n
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ta
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c
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re
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c
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d
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s
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2
0
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In
ter
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mp
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ter
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p
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c
a
ti
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l
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m
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u
s,
OH
,
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,
1
9
9
7
,
p
p
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1
3
4
-
1
4
1
.
[7
]
A
.
Ra
jab
i
-
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h
a
h
n
a
v
ieh
,
M
.
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o
t
u
h
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iru
z
a
b
a
d
,
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.
S
h
a
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e
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p
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d
R.
F
e
u
il
let,
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ti
m
a
l
A
ll
o
c
a
ti
o
n
o
f
A
v
a
il
a
b
le
T
ra
n
s
f
e
r
Ca
p
a
b
il
it
y
in
Op
e
ra
ti
n
g
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rizo
n
,
"
in
I
EE
E
T
ra
n
s
a
c
ti
o
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s
o
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Po
we
r
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ms
,
v
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l.
2
4
,
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2
,
p
p
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9
6
7
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9
7
5
,
M
a
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2
0
0
9
.
[8
]
Zh
a
n
g
Ch
a
n
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-
h
u
a
,
Ch
e
n
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Yu
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e
n
Yo
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a
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a
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o
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n
g
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h
u
a
,
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v
a
il
a
b
le
tra
n
sf
e
r
c
a
p
a
b
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it
y
a
ss
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m
e
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t
c
o
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sid
e
rin
g
e
c
o
n
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m
ic
c
o
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stra
in
t,
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2
0
0
8
T
h
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I
n
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
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e
o
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El
e
c
tric
Util
it
y
De
re
g
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la
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d
Res
tru
c
t
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a
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in
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,
2
0
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,
p
p
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7
7
-
3
8
0
.
B
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AUTH
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Ks
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it
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),
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9
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,
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rs
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n
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ro
m
M
a
n
g
a
la
y
a
tan
Un
iv
e
rsit
y
,
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li
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rh
(
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).
(
k
sh
i
ti
j.
jai
n
1
5
2
1
@g
m
a
il
.
c
o
m
)
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h
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m
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lo
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to
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rh
(UP
)
,
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is
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0
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0
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1
9
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2
,
p
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rs
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in
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h
in
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n
g
in
e
e
rin
g
f
ro
m
M
a
n
g
a
la
y
a
tan
Un
iv
e
rsit
y
,
A
li
g
a
rh
(
UP
).
(rk
b
a
ly
a
n
1
0
8
@g
m
a
il
.
c
o
m
)
Dh
e
e
re
sh
Up
a
d
h
y
a
y
b
e
lo
n
g
to
Alig
a
rh
(U
P
),
DO
B
is
2
0
.
0
7
.
1
9
8
8
,
Re
c
e
iv
e
d
h
is
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E.
in
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e
c
tro
n
ics
a
n
d
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str
u
m
e
n
tatio
n
E
n
g
in
e
e
rin
g
in
2
0
0
9
a
n
d
M
.
T
e
c
h
(Co
n
tro
l
sy
s
tem
)
in
2
0
1
3
f
ro
m
d
e
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
IIT
(
BHU
)
V
a
ra
n
a
si
-
In
d
ia.
P
re
se
n
tl
y
h
e
is
fa
c
u
lt
y
o
f
d
e
p
a
rt
m
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
I
n
stit
u
te
o
f
En
g
in
e
e
rin
g
a
n
d
T
e
c
h
n
o
lo
g
y
,
M
a
n
g
a
la
y
a
tan
Un
iv
e
rsity
,
A
li
g
a
rh
.
His
f
ield
o
f
in
tere
st
in
c
lu
d
e
s
a
p
p
li
c
a
ti
o
n
o
f
a
rti
f
it
ial
in
telli
g
e
n
c
e
a
n
d
o
p
ti
m
iz
a
ti
o
n
tec
h
n
iq
u
e
s
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
.
(d
h
e
e
re
sh
u
p
a
d
h
y
a
y
1
2
3
@g
m
a
il
.
c
o
m
)
Brij
e
sh
S
i
n
g
h
b
e
lo
n
g
t
o
Ja
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