In
t
er
na
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io
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l J
o
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f
E
lect
rica
l a
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Co
m
p
ute
r
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in
ee
ring
(
I
J
E
CE
)
Vo
l.
7
,
No
.
5
,
Octo
b
e
r
2
0
1
7
,
p
p
.
23
6
5
~
23
7
3
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
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e
.
v7
i
5
.
pp
23
6
5
-
23
7
3
2365
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in
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Pow
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G
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5
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Un
p
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p
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m
a
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p
p
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sy
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s
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su
f
f
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tl
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m
s
w
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l
su
ff
e
r
f
ro
m
i
n
sta
b
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ies
,
in
w
h
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o
lt
a
g
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s
d
ro
p
b
e
lo
w
a
c
c
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p
tab
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ls.
A
d
d
it
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a
l
p
o
w
e
r
so
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rc
e
s
a
re
n
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e
d
e
d
to
sa
ti
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th
e
d
e
m
a
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d
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m
a
ll
c
a
p
a
c
it
y
d
istri
b
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ted
g
e
n
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ra
to
rs
(DG
s)
se
r
v
e
f
o
r
th
is
p
u
r
p
o
se
w
e
ll
.
On
e
a
d
v
a
n
tag
e
o
f
D
G
s
is
th
a
t
th
e
y
c
a
n
b
e
in
sta
ll
e
d
c
lo
se
to
l
o
a
d
s,
so
a
s
t
o
m
in
i
m
ise
lo
se
s.
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ti
m
u
m
p
lac
e
m
e
n
ts
a
n
d
siz
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g
o
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DG
s
a
r
e
c
rit
ica
l
to
i
n
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re
a
se
s
y
ste
m
v
o
lt
a
g
e
s
a
n
d
t
o
re
d
u
c
e
lo
se
s.
T
h
is
w
il
l
f
in
a
ll
y
in
c
re
a
se
th
e
o
v
e
ra
ll
s
y
ste
m
e
ff
icie
n
c
y
.
T
h
is
w
o
rk
e
x
p
lo
it
s
Qu
a
n
tu
m
Ev
o
lu
ti
o
n
a
ry
A
lg
o
rit
h
m
(QE
A
)
f
o
r
th
e
p
lac
e
m
e
n
ts
a
n
d
siz
in
g
.
T
h
is
o
p
ti
m
isa
ti
o
n
targ
e
ts
th
e
c
h
e
a
p
e
st
g
e
n
e
ra
ti
o
n
c
o
st.
Qu
a
n
t
u
m
Ev
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lu
ti
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ry
A
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Ev
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ry
Alg
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h
m
ru
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n
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q
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a
n
t
u
m
c
o
m
p
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ti
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g
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w
h
ich
w
o
rk
s
b
a
se
d
o
n
q
u
b
it
s
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n
d
sta
tes
su
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rp
o
sit
io
n
o
f
q
u
a
n
t
u
m
m
e
c
h
a
n
ics
.
Ev
o
lu
ti
o
n
a
ry
a
lg
o
rit
h
m
w
it
h
q
u
b
i
t
re
p
re
se
n
tatio
n
h
a
s a b
e
tt
e
r
c
h
a
ra
c
teristic o
f
d
iv
e
rsity
th
a
n
c
las
sic
a
l
a
p
p
ro
a
c
h
e
s,
sin
c
e
it
c
a
n
re
p
re
se
n
t
su
p
e
rp
o
siti
o
n
o
f
sta
tes
.
K
ey
w
o
r
d
s
:
Dis
tr
ib
u
ted
g
e
n
er
atio
n
E
co
n
o
m
ic
d
is
p
atch
Qu
a
n
tu
m
g
en
et
ic
alg
o
r
it
h
m
Co
p
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rig
h
t
©
2
0
1
7
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ni
Ketu
t
A
r
y
an
i,
P
o
w
er
S
y
s
te
m
S
i
m
u
latio
n
L
ab
,
Dep
ar
tm
e
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t o
f
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lectr
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n
g
in
ee
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g
,
I
n
s
tit
u
t T
ek
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o
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g
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u
l
u
h
No
p
em
b
er
(
I
T
S),
Su
r
ab
ay
a,
I
n
d
o
n
esia.
E
m
ail:
k
et
u
t.a
r
y
a
n
i
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Dis
tr
ib
u
ted
g
e
n
er
atio
n
h
a
s
an
i
m
p
o
r
tan
t
r
o
le
in
a
m
o
d
er
n
an
d
co
m
p
le
x
elec
tr
ic
al
p
o
w
e
r
s
y
s
te
m
.
DG
s
ar
e
o
f
s
m
all
s
izes,
h
i
g
h
ef
f
icie
n
cie
s
,
lo
w
in
v
e
s
t
m
e
n
t
co
s
ts
an
d
th
e
m
o
s
t
i
m
p
o
r
tan
t
ly
i
s
th
eir
ab
ilit
y
to
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u
n
o
n
r
en
e
w
ab
le
e
n
er
g
y
s
o
u
r
ce
s
.
DG
s
ca
n
also
p
r
o
v
id
e
s
ta
n
d
-
alo
n
e
r
e
m
o
te
ap
p
licatio
n
s
w
it
h
t
h
eir
r
eq
u
ir
ed
p
o
w
er
.
Ho
w
ev
er
,
i
m
p
r
o
p
er
p
lace
m
en
t
o
f
Di
s
tr
ib
u
ted
Ge
n
er
at
io
n
w
ill
r
es
u
lt
in
i
n
cr
ea
s
ed
s
y
s
te
m
lo
s
s
e
s
,
r
esu
lti
n
g
in
h
i
g
h
er
co
s
t
s
.
P
lace
m
en
t
s
a
n
d
s
izin
g
s
of
DG
ar
e
cr
itical
to
th
e
o
v
er
all
s
y
s
te
m
e
f
f
icien
c
y
.
T
h
e
u
s
e
o
f
d
is
tr
ib
u
ted
g
e
n
er
at
o
r
in
th
e
s
y
s
te
m
h
a
s
s
o
m
e
ad
v
an
tag
e
s
i
n
ter
m
s
o
f
ec
o
n
o
m
i
c,
tech
n
ical
an
d
en
v
ir
o
n
m
en
tal.
E
n
v
ir
o
n
m
en
tal
ad
v
a
n
ta
g
es
e
n
tail
r
ed
u
ct
io
n
s
o
f
s
o
u
n
d
p
o
llu
tio
n
an
d
e
m
is
s
io
n
o
f
g
ases
.
Th
e
ec
o
n
o
m
ical
ad
v
a
n
ta
g
es
ar
e
r
ed
u
ctio
n
s
in
tr
an
s
m
i
s
s
io
n
an
d
d
is
tr
ib
u
tio
n
co
s
t
s
,
elec
tr
icit
y
p
r
ice
s
an
d
s
av
i
n
g
s
on
f
u
e
l.
T
ec
h
n
ical
ad
v
an
ta
g
es
co
v
er
w
id
e
v
ar
iet
i
es
o
f
b
en
ef
it
s,
f
o
r
ex
a
m
p
le
s
,
lin
e
lo
s
s
r
ed
u
ctio
n
,
in
cr
ea
s
ed
s
y
s
te
m
v
o
ltag
e
p
r
o
f
i
les a
n
d
i
n
cr
ea
s
ed
p
o
w
er
s
tab
il
it
y
a
n
d
r
eliab
ilit
y
.
I
t
ca
n
also
p
r
o
v
id
e
s
tan
d
-
alo
n
e
r
e
m
o
te
ap
p
licatio
n
s
w
it
h
t
h
eir
p
o
w
er
n
ee
d
.
P
lan
n
i
n
g
o
f
an
e
lectr
ic
al
p
o
wer
s
y
s
te
m
s
in
v
o
lv
in
g
D
Gs
r
e
q
u
ir
es
t
h
e
d
e
f
in
itio
n
o
f
s
ev
er
al
f
ac
to
r
s
,
s
u
c
h
as:
t
h
e
b
est
tech
n
o
lo
g
y
a
n
d
m
et
h
o
d
to
u
s
e
,
t
h
e
n
u
m
b
er
an
d
th
e
ca
p
ac
it
y
o
f
t
h
e
u
n
its
,
th
e
b
est
lo
ca
tio
n
,
th
e
n
et
w
o
r
k
co
n
n
ec
tio
n
w
a
y
,
a
n
d
alik
e
.
R
esear
ch
er
s
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a
v
e
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s
ed
ev
o
lu
tio
n
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y
co
m
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e
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atc
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J
o
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P
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g
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er
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cu
lati
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g
H
y
b
r
id
Op
ti
m
izatio
n
o
f
E
m
is
s
io
n
an
d
E
co
n
o
m
ic
Dis
p
atc
h
[
1
]
,
Hy
b
r
id
Op
tim
izatio
n
o
f
E
m
i
s
s
io
n
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ic
Di
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p
atch
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Sig
m
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Dec
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er
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W
eig
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tech
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izatio
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
5
,
Octo
b
er
2
0
1
7
:
23
6
5
–
23
7
3
2366
I
n
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W
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w
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3
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P
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4
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o
p
er
atio
n
s
o
f
elec
tr
ic
p
o
w
er
g
e
n
er
atio
n
s
y
s
te
m
s
.
T
h
e
m
a
in
u
t
ilit
y
tar
g
et
is
to
ac
h
ie
v
e
th
e
m
in
i
m
u
m
o
p
er
atin
g
co
s
t
a
n
d
s
y
s
te
m
s
tab
ili
t
y
.
As
w
e
ll
as
to
f
i
n
d
t
h
e
m
in
i
m
u
m
o
p
er
atin
g
co
s
t
u
s
i
n
g
ec
o
n
o
m
ic
d
is
p
atc
h
m
et
h
o
d
.
T
h
er
e
ar
e
s
ev
er
al
k
i
n
d
s
o
f
m
e
th
o
d
s
to
ca
lcu
late
th
e
o
p
er
atin
g
co
s
ts
.
L
ag
r
an
g
e
is
th
e
m
o
s
t
co
m
m
o
n
l
y
u
s
ed
to
ca
lcu
late
th
e
m
i
n
i
m
u
m
co
s
t
o
f
elec
tr
ica
l
en
er
g
y
g
e
n
er
atio
n
[
5
]
.
I
n
ad
d
itio
n
to
th
is
m
eth
o
d
th
er
e
ar
e
s
ev
er
al
o
th
er
s
t
h
at
h
av
e
b
ee
n
d
e
v
elo
p
ed
by
r
esear
ch
er
s
.
Qu
a
n
tu
m
t
h
eo
r
y
h
as
b
ee
n
u
s
ed
w
id
el
y
in
t
h
e
f
ield
o
f
elec
tr
ical
en
er
g
y
s
y
s
te
m
s
.
I
n
s
ev
er
a
l
p
u
b
licatio
n
s
,
q
u
a
n
t
u
m
EA
s
ar
e
u
tili
ze
d
to
ca
lcu
late
ec
o
n
o
m
ic
d
is
p
atch
.
Fo
r
ex
a
m
p
le
in
th
e
r
ef
er
en
ce
s
[
6
]
,
[
7
]
an
d
[
8
]
.
Qu
a
n
tu
m
-
I
n
s
p
ir
ed
E
v
o
lu
tio
n
ar
y
A
l
g
o
r
ith
m
f
o
r
R
ea
l
an
d
R
ea
cti
v
e
P
o
w
er
Dis
p
atch
,
i
n
t
h
i
s
p
ap
e
r
,
QE
A
d
eter
m
in
e
s
th
e
s
etti
n
g
s
o
f
co
n
tr
o
l
v
ar
iab
les,
s
u
c
h
as
g
en
er
ato
r
o
u
tp
u
ts
,
g
en
er
ato
r
v
o
ltag
es,
tr
a
n
s
f
o
r
m
er
tap
s
an
d
s
h
u
n
t V
AR
co
m
p
en
s
atio
n
d
ev
ices
f
o
r
o
p
ti
m
al
P
-
Q
d
is
p
atch
co
n
s
id
er
i
n
g
t
h
e
b
id
-
o
f
f
er
ed
co
s
t [
6
]
.
C
h
ao
tic
Qu
a
n
t
u
m
E
v
o
lu
tio
n
a
r
y
A
l
g
o
r
ith
m
is
u
s
ed
to
s
o
l
v
e
E
n
v
ir
o
n
m
en
ta
l
E
co
n
o
m
ic
Dis
p
atch
o
f
S
m
ar
t
Mic
r
o
g
r
id
C
o
n
tain
i
n
g
Dis
tr
ib
u
ted
Ge
n
er
atio
n
S
y
s
te
m
P
r
o
b
lem
s
.
Q
u
an
tu
m
e
v
o
lu
t
io
n
ar
y
alg
o
r
it
h
m
is
u
s
ed
to
co
n
f
ir
m
th
e
ac
cu
r
ac
y
an
d
v
alid
it
y
o
f
th
e
m
at
h
e
m
ati
ca
l
m
o
d
el
u
s
ed
f
o
r
d
eter
m
i
n
i
n
g
e
n
v
ir
o
n
m
en
t
a
n
d
ec
o
n
o
m
ic
d
is
p
atc
h
o
f
S
m
ar
t
M
icr
o
G
r
id
,
w
h
ic
h
is
co
n
s
id
er
ed
as g
en
er
atio
n
co
s
t a
n
d
e
m
is
s
io
n
co
s
t [
9
].
I
n
th
i
s
w
o
r
k
,
q
u
a
n
t
u
m
ev
o
l
u
ti
o
n
ar
y
al
g
o
r
ith
m
is
u
s
ed
f
o
r
th
e
p
lace
m
en
t
o
f
DG
s
in
th
e
n
e
t
w
o
r
k
a
n
d
f
o
r
d
eter
m
i
n
i
n
g
t
h
e
ca
p
ac
it
y
r
eq
u
ir
ed
to
r
aise
th
e
v
o
lt
a
g
e
on
t
h
e
b
u
s
e
s
,
s
o
th
at
t
h
e
v
o
lta
g
e
at
each
bus
i
s
i
n
s
af
e
co
n
d
it
io
n
an
d
i
n
cr
ea
s
e
s
t
h
e
s
y
s
te
m
lo
ad
ab
ilit
y
.
F
in
al
l
y
,
we
p
er
f
o
r
m
t
h
e
ca
lcu
latio
n
f
o
r
th
e
ec
o
n
o
m
ic
d
is
p
atch
to
g
et
t
h
e
ch
ea
p
es
t
co
s
t o
f
g
e
n
er
atio
n
.
Q
u
a
n
tu
m
e
v
o
lu
tio
n
ar
y
al
g
o
r
ith
m
is
al
s
o
u
s
e
d
in
s
i
m
ilar
w
a
y
i
n
r
ef
er
en
ce
[
1
0
]
,
[
1
1
]
.
2
.
RE
SE
ARCH
M
E
T
H
O
D
2
.
1
.
E
co
no
m
ic
Dis
pa
t
ch
T
he
o
ry
T
h
e
m
at
h
e
m
atica
l
f
o
r
m
u
latio
n
o
f
th
e
to
tal
co
s
t
f
u
n
ctio
n
is
f
o
r
m
u
la
ted
as f
o
llo
w
s
:
min
=
∑
(
)
=
1
+
∑
(
)
ℎ
=
1
(
1
)
w
h
er
e
is
th
e
to
tal
f
u
el
co
s
t f
o
r
th
e
i
th
g
en
er
ato
r
(
in
$
/h
)
.
Gen
er
all
y
,
t
h
e
f
u
el
co
s
t o
f
th
er
m
al
g
e
n
er
ati
n
g
u
n
it is
r
ep
r
ese
n
ted
in
p
o
l
y
n
o
m
ia
l f
u
n
ctio
n
,
(
)
=
+
+
2
(
2
)
w
h
er
e
,
an
d
ar
e
co
s
t c
o
ef
f
ici
en
ts
o
f
g
e
n
er
ato
r
.
T
h
e
DG
g
en
er
atio
n
co
s
t.
(
)
=
(
3
)
w
h
er
e
is
co
s
t c
o
ef
f
icie
n
ts
o
f
DG
C
o
n
v
en
t
io
n
all
y
,
th
er
e
is
n
o
o
r
n
eg
li
g
ib
le
DG
ca
p
ac
it
y
ex
is
tin
g
in
th
e
p
o
w
er
s
y
s
te
m
.
I
n
ec
o
n
o
m
i
c
d
is
p
atch
,
th
e
s
y
s
te
m
d
e
m
a
n
d
an
d
d
eliv
er
y
lo
s
s
ar
e
s
er
v
ed
b
y
u
til
it
y
g
e
n
er
ato
r
s
o
n
l
y
.
W
i
th
t
h
e
o
u
t
s
p
r
ea
d
o
f
DG's
i
n
d
is
tr
ib
u
t
io
n
n
et
w
o
r
k
s
,
th
e
n
o
n
D
G
s
y
s
te
m
e
v
o
lv
e
s
in
to
a
h
y
b
r
id
g
e
n
er
atio
n
e
n
v
ir
o
n
m
e
n
t.
T
h
e
D
G
g
en
er
atio
n
ca
p
ac
it
y
h
as
to
b
e
tak
en
in
to
ac
co
u
n
t
i
n
t
h
e
n
e
w
en
v
ir
o
n
m
e
n
t.
T
o
ac
h
iev
e
t
h
is
,
a
m
o
d
i
f
icatio
n
o
f
th
e
co
n
v
e
n
tio
n
al
ec
o
n
o
m
ic
d
is
p
atch
.
I
n
ad
d
itio
n
,
N
g
e
n
e
r
ato
r
s
ar
e
co
n
n
ec
ted
to
th
e
s
y
s
te
m
.
T
h
e
p
o
w
er
b
alan
ce
co
n
s
tr
ai
n
t b
ec
o
m
es:
∑
+
∑
ℎ
=
+
(
4
)
w
h
er
e
∑
is
th
e
to
tal
p
o
w
er
g
e
n
er
ated
b
y
u
tili
t
y
g
en
er
ato
r
s
a
n
d
∑
is
th
e
to
tal
p
o
w
er
f
r
o
m
DG
in
s
ta
lled
in
b
u
s
e
s
,
w
h
ile
is
to
tal
lo
ad
an
d
is
to
tal
lo
s
s
es o
f
t
h
e
s
y
s
te
m
.
C
o
n
s
eq
u
en
tl
y
,
t
h
e
g
e
n
er
atio
n
co
s
t
co
n
s
is
t
s
o
f
t
w
o
p
ar
ts
:
th
e
p
o
w
er
g
e
n
er
ated
f
r
o
m
e
x
is
t
in
g
an
d
p
o
w
er
f
r
o
m
DG
in
lo
ad
b
u
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
E
co
n
o
mic
Dis
p
a
tch
u
s
in
g
Qu
a
n
tu
m
E
vo
lu
tio
n
a
r
y
A
lg
o
r
ith
m
in
E
lectrica
l P
o
w
e
r
…
(
N
i Ke
t
u
t A
r
ya
n
i
)
2367
=
∑
+
∑
ℎ
(
5
)
is
o
b
tain
ed
b
y
ec
o
n
o
m
icall
y
d
is
p
atch
i
n
g
lo
ad
a
n
d
d
eliv
er
y
l
o
s
s
a
m
o
n
g
t
h
ese
o
n
lin
e
g
e
n
er
ato
r
s
an
d
DGs.
So
m
e
co
n
s
tr
ai
n
ts
f
o
r
ea
ch
g
e
n
er
ato
r
m
u
s
t
b
e
al
s
o
s
at
is
f
ied
.
Gen
er
atio
n
p
o
w
er
o
f
ea
ch
g
en
er
ato
r
s
h
o
u
ld
b
e
laid
b
et
w
ee
n
m
a
x
i
m
u
m
a
n
d
m
in
i
m
u
m
li
m
i
ts
.
T
h
e
co
n
s
tr
ai
n
t
f
o
r
ea
ch
g
e
n
er
ato
r
is
≤
≤
(
6
)
w
h
er
e
an
d
ar
e
th
e
o
u
tp
u
t
o
f
th
e
m
in
i
m
u
m
a
n
d
m
ax
i
m
u
m
o
p
er
atio
n
o
f
th
e
g
en
er
ati
n
g
u
n
it
i
(
in
MW
)
,
r
esp
ec
tiv
el
y
.
Vo
ltag
e
at
lo
ad
b
u
s
es
<
<
(
7
)
w
h
er
e
an
d
ar
e
v
o
ltag
e
m
i
n
i
m
u
m
a
n
d
m
a
x
i
m
u
m
ea
c
h
b
u
s
es.
L
ine
P
o
w
er
F
lo
w
N
e
w
th
o
n
R
ap
s
o
n
(
N
R
)
is
a
v
er
y
co
m
m
o
n
m
e
th
o
d
u
s
ed
to
ca
lcu
late
t
h
e
p
o
w
er
f
lo
w
o
n
th
e
s
y
s
te
m
.
T
h
e
NR
p
o
w
er
f
lo
w
i
s
u
s
ed
t
o
ca
lcu
late
t
h
e
lo
s
s
es
in
t
h
e
s
y
s
te
m
an
d
th
e
v
o
l
ta
g
e
o
n
ea
c
h
b
u
s
.
T
h
e
t
h
eo
r
y
o
f
p
o
w
er
f
lo
w
u
s
ed
in
t
h
is
p
ap
er
r
ef
er
s
to
th
e
r
ef
er
e
n
ce
[
5
]
.
I
nje
ct
ed
P
o
w
er
T
h
e
co
m
p
lex
p
o
w
er
at
b
u
s
'
i
'
i
s
:
∗
=
∗
∑
=
1
(
8
)
T
h
e
v
ar
iab
les u
p
d
ated
af
ter
k
th
iter
atio
n
ar
e
g
i
v
e
n
as
:
∆
(
+
1
)
=
∆
(
)
+
∆
(9
)
|
|
(
+
1
)
=
|
|
(
)
+
∆
|
|
(
10
)
P
o
w
er
f
lo
w
f
r
o
m
i
th
b
u
s
to
j
t
h
b
u
s
t
h
r
o
u
g
h
t
h
e
li
n
e
co
n
n
ec
t
ed
b
etw
ee
n
t
h
ese
b
u
s
es i
s
g
i
v
e
n
b
y
:
=
∗
=
(
−
+
0
)
(
11
)
T
h
e
p
o
w
er
f
lo
w
f
r
o
m
t
h
e
j
th
b
u
s
to
i
th
b
u
s
is
:
=
∗
=
(
−
+
0
)
(
12
)
L
ine
L
o
s
s
es
=
∑
∑
(
+
)
=
=
(
13
)
=
∑
∑
{
(
+
)
+
(
+
)
}
=
=
(
14
)
2
.
2
.
Q
ua
ntu
m
E
v
o
lutio
na
ry
Alg
o
rit
h
m
(
Q
E
A)
T
h
e
b
ase
th
eo
r
ies
o
f
Q
u
an
t
u
m
E
v
o
l
u
tio
n
ar
y
A
l
g
o
r
ith
m
m
eth
o
d
ar
e
th
e
co
n
ce
p
ts
o
f
q
u
b
its
an
d
t
h
e
s
u
p
er
p
o
s
itio
n
o
f
s
tate
s
o
f
q
u
a
n
tu
m
m
ec
h
a
n
ics.
Q
u
b
it
is
th
e
s
m
al
lest
u
n
it
o
f
in
f
o
r
m
atio
n
s
t
o
r
ed
in
a
t
w
o
-
s
ta
te
q
u
an
t
u
m
co
m
p
u
ter
.
A
q
u
b
it
m
a
y
b
e
in
t
h
e
s
tate
‘
1
’
o
r
in
t
h
e
s
tate
‘
0
’
o
r
in
an
y
s
u
p
er
p
o
s
itio
n
o
f
t
h
e
t
w
o
.
T
h
e
s
tate
o
f
a
q
u
b
i
t c
an
b
e
r
ep
r
esen
ted
as
,
|
〉
=
|
|
2
+
|
|
2
(
15
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
5
,
Octo
b
er
2
0
1
7
:
23
6
5
–
23
7
3
2368
As
also
ilu
s
tr
ated
in
f
i
g
u
r
e
1
,
α
an
d
β
ar
e
co
m
p
lex
n
u
m
b
er
s
s
p
ec
if
y
i
n
g
th
e
p
r
o
b
ab
ilit
y
a
m
p
l
itu
d
es
o
f
t
h
e
s
tate
‘
0
’
an
d
‘
1
’
r
esp
ec
ti
v
el
y
.
|
|
2
g
iv
e
s
th
e
p
r
o
b
ab
ilit
y
th
a
t
th
e
q
u
b
it
w
il
l
b
e
f
o
u
n
d
in
‘
0
’
s
tate
an
d
|
|
2
g
iv
es
th
e
p
r
o
b
a
b
ilit
y
th
a
t th
e
q
u
b
it
w
i
ll
b
e
f
o
u
n
d
i
n
th
e
‘
1
’
s
tate.
No
r
m
aliza
tio
n
o
f
t
h
e
s
tate
to
u
n
it
y
g
u
ar
a
n
tees
,
|
|
2
+
|
|
2
=
1
(
16
)
2
s
tates
ca
n
b
e
r
ep
r
esen
ted
at
th
e
s
a
m
e
ti
m
e
b
y
a
s
y
s
te
m
o
f
m
q
u
b
its
.
QG
A
is
b
ased
o
n
th
e
co
n
ce
p
t
o
f
q
u
b
its
.
On
e
q
u
b
it i
s
d
ef
i
n
ed
with
a
p
air
o
f
co
m
p
lex
n
u
m
b
er
s
(
α
,
β
)
as
,
[
]
(
17
)
w
h
ic
h
is
c
h
ar
ac
ter
ized
b
y
(
8
)
an
d
(
9
)
.
A
n
d
an
m
-
q
u
b
its
r
ep
r
esen
tat
io
n
is
d
e
f
in
ed
as
[
1
1
|
2
2
|
…
…
|
]
(
18
)
w
h
er
e
|
|
2
+
|
|
2
=
1
,
i =
1
,
2
,
3
.
.
.
m
T
h
e
ad
v
an
tag
e
o
f
t
h
is
r
ep
r
esen
tatio
n
is
t
h
at
i
t
can
r
ep
r
ese
n
t
an
y
s
u
p
er
p
o
s
itio
n
o
f
s
tate
s
.
F
o
r
in
s
ta
n
ce
,
i
n
a
th
r
ee
q
u
b
its
s
y
s
te
m
w
ith
t
h
r
ee
p
air
s
o
f
a
m
p
lit
u
d
es s
u
ch
a
s
,
[
1
√
2
1
√
2
|
√
3
2
1
2
|
1
.
0
0
]
(
19
)
T
h
e
s
tate
o
f
th
e
s
y
s
te
m
ca
n
b
e
r
ep
r
esen
ted
as
,
√
3
2
√
2
|
000
〉
+
0
|
001
〉
+
1
2
√
2
|
010
〉
+
0
|
011
〉
+
√
3
2
√
2
|
100
〉
+
0
|
101
〉
+
1
2
√
2
|
110
〉
+
0
|
111
〉
T
h
e
ab
o
v
e
r
esu
lt
m
ea
n
s
th
at
t
h
e
p
r
o
b
ab
ilit
ies
t
o
r
ep
r
esen
t
th
e
s
tate
|
000
〉
,
|
010
〉
,
|
100
〉
an
d
|
110
〉
ar
e
3
8
,
1
8
,
3
8
an
d
1
8
r
esp
ec
ti
v
el
y
.
T
h
e
th
r
ee
q
u
b
it
s
s
y
s
te
m
o
f
(
1
1
)
h
as
f
o
u
r
s
tate
s
i
n
f
o
r
m
atio
n
a
t
th
e
s
a
m
e
ti
m
e.
E
v
o
lu
tio
n
ar
y
al
g
o
r
it
h
m
w
it
h
q
u
b
it
r
ep
r
esen
tatio
n
h
as
a
b
etter
ch
ar
ac
ter
is
tic
o
f
d
iv
er
s
it
y
th
a
n
cla
s
s
ica
l
ap
p
r
o
ac
h
es,
s
in
ce
it
ca
n
r
ep
r
es
en
t
s
u
p
er
p
o
s
itio
n
o
f
s
ta
tes.
O
n
e
q
u
b
it
s
tr
in
g
s
u
ch
a
s
(
1
1
)
is
en
o
u
g
h
to
r
ep
r
esen
t
f
o
u
r
s
tate
s
.
C
o
n
v
er
g
e
n
ce
ca
n
b
e
also
o
b
tain
ed
w
it
h
th
e
q
u
b
i
t
r
ep
r
esen
tatio
n
.
A
s
|
|
2
o
r
|
|
2
ap
p
r
o
ac
h
es
to
1
o
r
0
,
th
e
q
u
b
it
s
tr
i
n
g
co
n
v
er
g
es
to
a
s
i
n
g
le
s
tate
a
n
d
t
h
e
p
r
o
p
er
ty
o
f
d
i
v
er
s
it
y
d
i
s
ap
p
ea
r
s
g
r
ad
u
all
y
.
T
h
at
is
,
s
i
m
u
lta
n
eo
u
s
l
y
,
th
e
q
u
b
it
r
ep
r
esen
tatio
n
h
a
s
b
o
th
th
e
c
h
ar
ac
ter
is
tic
o
f
e
x
p
lo
r
atio
n
an
d
t
h
e
ch
ar
ac
ter
is
tic
o
f
ex
p
lo
itati
o
n
.
Ro
t
a
t
io
n G
a
t
e
[
1
0
]
Q
-
g
ate
(
r
o
tatio
n
g
a
te)
is
d
ef
i
n
ed
as
a
v
ar
iatio
n
o
p
er
ato
r
o
f
Q
E
A
,
b
y
w
h
ich
o
p
er
atio
n
a
n
y
u
p
d
ated
q
u
b
it
s
h
o
u
ld
at
all
ti
m
e
s
ati
s
f
y
th
e
n
o
r
m
al
izatio
n
co
n
d
it
io
n
,
|
′
|
2
+
|
′
|
2
=
1
,
w
h
er
e
′
an
d
′
ar
e
th
e
v
alu
e
s
o
f
t
h
e
u
p
d
ated
q
u
b
it.
T
h
e
f
o
llo
w
i
n
g
r
o
tatio
n
g
ate
i
s
u
s
ed
as a
q
u
b
it:
[
(
+
1
)
(
+
1
)
]
=
(
)
×
[
(
)
(
)
]
(
=
1
,
2
,
…
,
)
(
20
)
(
)
=
[
c
os
∆
−
s
in
∆
s
in
∆
c
os
∆
]
(
=
1
,
2
,
…
,
)
(
21
)
∆
is
a
r
o
tatio
n
an
g
le
(
F
ig
.
1
)
o
f
ea
ch
m
e
m
b
er
o
f
t
h
e
p
o
p
u
lat
io
n
.
T
h
e
r
o
tatio
n
a
n
g
le
∆
is
r
elate
d
to
t
h
e
n
o
r
m
al
ized
d
i
f
f
er
e
n
ce
∆
b
et
w
ee
n
ac
h
ie
v
e
m
e
n
t
o
f
ea
c
h
o
f
m
e
m
b
er
o
f
p
o
p
u
latio
n
an
d
th
e
g
lo
b
al
b
est
o
p
tim
u
m
.
∆
=
∆
×
(
−
)
×
[
×
s
in
∆
−
×
(
1
−
c
os
〖
∆
)
〗
]
(
22
)
w
h
er
e
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
E
co
n
o
mic
Dis
p
a
tch
u
s
in
g
Qu
a
n
tu
m
E
vo
lu
tio
n
a
r
y
A
lg
o
r
ith
m
in
E
lectrica
l P
o
w
e
r
…
(
N
i Ke
t
u
t A
r
ya
n
i
)
2369
∆
=
×
(
1
−
(
)
(
(
)
)
(
=
1
,
2
,
…
,
)
(
23
)
(
−
)
=
{
+
1
≥
−
1
<
(
24
)
[
×
s
in
∆
−
×
(
1
−
∆
)
]
=
{
+
1
×
s
in
∆
≥
×
(
1
−
∆
)
−
1
×
s
in
∆
<
×
(
1
−
∆
)
(
25
)
Fig
u
r
e
1
.
B
asic Q
u
an
tu
m
-
b
it (
q
u
b
it)
2
.
3
.
P
r
o
ble
m
F
o
r
m
ula
t
io
n
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
o
f
th
i
s
p
r
o
p
o
s
ed
m
et
h
o
d
is
:
min
=
∑
(
)
=
1
+
∑
(
)
ℎ
=
1
(
26
)
w
h
er
e
is
th
e
to
tal
f
u
el
co
s
t
f
o
r
th
e
i
th
th
er
m
al
g
en
er
ato
r
(
$
/h
)
,
is
th
e
to
tal
co
s
t
f
o
r
g
en
er
ated
p
o
w
er
o
f
DG
(
$
/h
)
.
B
u
s
v
o
lta
g
e
co
n
s
tr
ain
:
|
|
≤
|
|
≤
|
|
(
27
)
C
ap
ac
it
y
DG
co
n
s
tr
ai
n
:
≤
≤
(
28
)
2
.
4
.
T
he
P
ro
po
s
ed
M
et
ho
d
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
ca
n
b
e
d
escr
ib
ed
in
th
e
f
o
ll
o
w
i
n
g
s
te
p
s
an
d
th
e
f
lo
w
ch
ar
t
o
f
t
h
e
al
g
o
r
ith
m
is
in
f
ig
u
r
e
2
.
1.
Star
t
w
ith
t =
0
2.
I
n
itialize
a
p
o
p
u
latio
n
o
f
n
m
e
m
b
er
s
(
q
u
b
it st
r
i
n
g
)
:
(
0
)
=
{
1
(
0
)
,
2
(
0
)
,
…
,
(
0
)
}
3.
E
ac
h
q
u
b
it st
r
i
n
g
i
s
r
ep
r
esen
t
ed
:
1
(
0
)
=
[
|
1
(
0
)
1
(
0
)
|
|
2
(
0
)
2
(
0
)
|
.
.
.
|
(
0
)
(
0
)
|
]
4.
Fo
r
all
q
u
b
it
s
tr
in
g
s
i
n
itialize
th
e
a
m
p
li
tu
d
e
a
m
p
l
if
ica
tio
n
at
:
1
(
0
)
=
|
1
√
2
1
√
2
…
1
√
2
1
√
2
…
|
5.
R
an
d
o
m
l
y
,
m
ak
e
a
s
e
t b
in
ar
y
s
o
lu
tio
n
P
(
0
)
b
y
o
b
s
er
v
i
n
g
Q(
0
)
s
tate
:
(
0
)
=
{
1
(
0
)
,
2
(
0
)
,
…
,
(
0
)
}
6.
E
ac
h
DG
is
r
ep
r
esen
ted
b
y
8
b
it
b
in
ar
y
n
u
m
b
er
.
T
h
e
MSB
(
Mo
s
t
S
ig
n
ifica
n
t
B
it
)
s
ig
n
i
f
ie
s
w
h
et
h
er
th
e
DG
is
p
r
esen
t.
I
f
th
i
s
b
it
is
1
,
DG
is
p
r
esen
t
at
th
e
b
u
s
an
d
th
is
DG’
s
o
u
tp
u
t
p
o
w
er
is
d
eter
m
i
n
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
5
,
Octo
b
er
2
0
1
7
:
23
6
5
–
23
7
3
2370
b
y
t
h
e
r
est
7
b
its
a
n
d
also
b
as
ed
o
n
th
e
an
d
s
p
ec
if
ied
in
t
h
e
in
p
u
t
p
ar
a
m
eter
m
atr
i
x
.
I
f
th
e
MSB
is
0
,
DG
is
n
o
t p
r
esen
t a
n
d
t
h
e
b
u
s
i
s
co
n
s
id
er
ed
as
lo
ad
b
u
s
.
7.
E
v
alu
a
te
ea
ch
(
0
)
(
=
1
,
2
,
…
,
)
,
p
r
ep
a
r
e
b
u
s
d
a
ta
m
atr
i
x
8.
Usi
n
g
t
h
e
b
u
s
d
ata,
r
u
n
lo
ad
f
l
o
w
an
d
o
b
tain
p
o
w
er
g
en
er
ate
d
by
ea
ch
g
en
er
ato
r
.
9.
C
alcu
late
th
e
o
b
j
ec
tiv
e
f
u
n
cti
o
n
an
d
s
to
r
e
th
e
f
itn
e
s
s
v
alu
e.
Fo
r
th
is
ec
o
n
o
m
ic
d
is
p
atch
,
w
e
u
s
e
(
26
)
as th
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
.
10.
P
er
f
o
r
m
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(
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(
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f
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c
h
p
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m
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m
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.
11.
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d
p
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p
u
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n
m
e
m
b
e
r
w
it
h
th
e
h
i
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t
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th
is
a
s
th
e
b
est
s
tr
i
n
g
o
f
th
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iter
atio
n
.
12.
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t iter
atio
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(
t =
t +
1
)
13.
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ate
t
h
e
n
e
x
t p
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p
u
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f
r
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m
th
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er
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s
clo
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er
to
t
h
e
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es
t
s
tr
i
n
g
.
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f
ig
1
.
R
o
tatio
n
i
s
d
o
n
e
b
y
r
o
tato
r
m
atr
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t
h
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d
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er
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u
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s
(
20
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(
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.
14.
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I
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2373
RE
F
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R
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NC
E
S
[1
]
Jo
k
o
P
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to
n
o
,
A
d
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p
ri
jan
to
,
a
n
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Hi
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Co
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Ch
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mic
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tch
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Ga
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rg
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s 3
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(2
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2
9
7
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3
0
7
,
E
L
S
IV
IER.
[3
]
Ho
ss
e
in
S
h
a
h
in
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a
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h
1
,
S
a
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d
M
o
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se
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Na
sr
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A
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d
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Na
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re
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Ja
n
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sa
ri3
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“
Ap
p
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Pa
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to
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Eco
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Disp
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Un
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Po
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Po
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,
In
ter
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ti
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Jo
u
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f
El
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c
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Co
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in
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rin
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(IJECE)
[4
]
G
.
S
re
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n
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a
sa
n
,
Dr.
C.
H.
S
a
ib
a
b
u
,
Dr.S
.
S
iv
a
n
a
g
a
ra
ju
,
“
S
o
lu
t
io
n
o
f
Dy
n
a
mic
Ec
o
n
o
mic
L
o
a
d
Disp
a
tch
(
DEL
D)
Pro
b
lem
wit
h
V
a
lve
P
o
in
t
L
o
a
d
in
g
Ef
fec
ts
a
n
d
R
a
mp
Ra
te
L
imit
s
Us
in
g
PS
O
”
,
I
n
tern
a
ti
o
n
a
l
Jo
u
r
n
a
l
o
f
El
e
c
tri
c
a
l
a
n
d
Co
m
p
u
ter E
n
g
in
e
e
rin
g
(IJECE)
V
o
l
.
1
,
No
.
1
,
S
e
p
tem
b
e
r
2
0
1
1
,
p
p
.
x
x
~
x
x
IS
S
N:
2
0
8
8
-
8
7
0
8
[5
]
Ha
d
i
S
a
a
d
a
t,
“
Po
we
r
S
y
ste
m A
n
a
l
y
sis
”
,
M
c
G
ra
w
-
Hill
,
In
tern
a
ti
o
n
a
l
Ed
it
i
o
n
s
1
9
9
9
.
[6
]
Jo
h
n
G
.
V
lac
h
o
g
ian
n
is
a
n
d
Kw
a
n
g
Y.
L
e
e
,
:
Qu
a
n
tu
m
-
In
sp
ire
d
E
v
o
lu
ti
o
n
a
ry
Al
g
o
ri
th
m
f
o
r
Rea
l
a
n
d
Rea
c
ti
v
e
Po
we
r Disp
a
tc
h
”
,
I
EE
E
T
RA
NS
A
C
T
ION
S
ON
P
OW
ER
S
YST
EM
S
,
V
OL
.
2
3
,
NO
.
4
,
NO
V
EM
B
ER
2
0
0
8
.
[7
]
Jo
h
n
G
.
V
lac
h
o
g
ian
n
is
a
n
d
Kw
a
n
g
Y.
L
e
e
,
“
Us
in
g
Ch
a
o
ti
c
Q
u
a
n
tu
m
Ge
n
e
ti
c
Al
g
o
rit
h
m
S
o
lvin
g
E
n
v
iro
n
me
n
t
a
l
Eco
n
o
mic
Disp
a
tc
h
o
f
S
ma
rt
M
icr
o
g
rid
Co
n
ta
i
n
in
g
Distri
b
u
te
d
Ge
n
e
ra
ti
o
n
S
y
ste
m
Pro
b
lem
s
”
,
2
0
1
0
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
P
o
w
e
r
S
y
st
e
m
Tec
h
n
o
lo
g
y
.
[8
]
Jú
li
o
X
a
v
ier
V
ian
n
a
Ne
to
a
,
Di
e
g
o
L
u
is
d
e
A
n
d
ra
d
e
Be
rn
e
rt
b
,
L
e
a
n
d
ro
d
o
s
S
a
n
to
s
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e
lh
o
b
,
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ro
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e
d
q
u
a
n
t
u
m
-
in
sp
ire
d
e
v
o
lu
ti
o
n
a
ry
a
l
g
o
rit
h
m
wit
h
d
ive
rs
it
y
in
fo
rm
a
ti
o
n
a
p
p
li
e
d
t
o
e
c
o
n
o
mic
d
is
p
a
tch
p
ro
b
lem
wit
h
p
ro
h
i
b
it
e
d
o
p
e
ra
ti
n
g
z
o
n
e
s E
n
e
rg
y
Co
n
v
e
rs
io
n
a
n
d
M
a
n
a
g
e
me
n
t
5
2
(2
0
1
1
)
8
–
1
4
,
EL
S
IV
IER.
[9
]
Gw
o
-
Ch
in
g
L
iao
,
”
Us
in
g
Ch
a
o
ti
c
Qu
a
n
tu
m
Ge
n
e
ti
c
Al
g
o
rith
m
S
o
lvin
g
En
v
iro
n
me
n
ta
l
Ec
o
n
o
mic
Disp
a
tch
o
f
S
ma
rt
M
icr
o
g
rid
C
o
n
t
a
i
n
in
g
D
i
strib
u
ted
Ge
n
e
ra
t
io
n
S
y
ste
m
Pro
b
lem
s
”
,
2
0
1
0
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
P
o
w
e
r
S
y
ste
m
T
e
c
h
n
o
lo
g
y
.
[1
0
]
Jo
h
n
G
.
V
lac
h
o
g
ian
n
is
a
,
*
,
J
a
c
o
b
Øs
terg
a
a
rd
,
”
Rea
c
ti
v
e
p
o
we
r
a
n
d
v
o
lt
a
g
e
c
o
n
tro
l
b
a
se
d
o
n
g
e
n
e
ra
l
q
u
a
n
t
u
m
g
e
n
e
ti
c
a
l
g
o
rit
h
ms
”,
EL
S
EV
I
ER
,
Ex
p
e
rt
S
y
ste
m
s
w
it
h
A
p
p
li
c
a
ti
o
n
s 3
6
(2
0
0
9
)
6
1
1
8
–
6
1
2
6
.
[1
1
]
Ha
n
,
K.
-
H.,
&
Ki
m
,
J.
-
H.
(2
0
0
0
)
,
“
Ge
n
e
ti
c
q
u
a
n
t
u
m
a
l
g
o
rit
h
m
a
n
d
it
s
a
p
p
l
ica
ti
o
n
t
o
c
o
mb
i
n
a
t
o
ria
l
o
p
ti
miz
a
ti
o
n
p
ro
b
lem
”
.
P
r
o
c
e
e
d
in
g
s o
f
Co
n
g
re
ss
o
n
Ev
o
l
u
ti
o
n
a
ry
Co
m
p
u
tatio
n
,
1
3
5
4
–
1
3
6
0
.
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