I
nte
rna
t
io
na
l J
o
urna
l o
f
Adv
a
nces in
Appl
ie
d Science
s
(
I
J
AAS)
Vo
l.
9
,
No
.
4
,
Dec
em
b
e
r
2
0
2
0
,
p
p
.
26
1
~
26
4
I
SS
N:
2
2
5
2
-
8
8
1
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijaas.v
9
.
i4
.
p
p
26
1
-
26
4
261
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
a
s
.
ia
esco
r
e.
co
m
Rea
l power lo
ss
r
eduction by
ar
ctic
char a
lg
o
rithm
L
enin
K
a
na
g
a
s
a
ba
i
De
p
a
rtme
n
t
o
f
EE
E
,
P
ra
sa
d
V.
P
o
tl
u
ri
S
id
d
h
a
rt
h
a
In
stit
u
te o
f
Tec
h
n
o
lo
g
y
,
In
d
ia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
a
n
3
,
2
0
20
R
ev
is
ed
Ma
r
4
,
2
0
20
Acc
ep
ted
J
u
n
8
,
2
0
2
0
Th
is
wo
rk
p
re
se
n
ts
Arc
ti
c
Ch
a
r
Alg
o
rit
h
m
(ACA
)
fo
r
so
lv
in
g
o
p
t
ima
l
re
a
c
ti
v
e
p
o
we
r
p
r
o
b
lem
.
In
N
o
rth
Am
e
rica
m
o
v
e
m
e
n
t
o
f
A
rc
ti
c
c
h
a
r
p
h
e
n
o
m
e
n
o
n
is
o
n
e
a
m
o
n
g
t
h
e
twe
lv
e
-
m
o
n
th
ly
i
n
n
a
te
a
c
ti
o
n
s.
De
e
d
s
o
f
Arc
ti
c
c
h
a
r
h
a
v
e
b
e
e
n
imitate
d
t
o
d
e
sig
n
t
h
e
a
lg
o
rit
h
m
.
In
st
o
c
h
a
stic
m
o
d
e
so
lu
ti
o
n
s
a
re
in
it
ialize
d
wi
th
o
n
e
se
g
m
e
n
t
o
n
e
v
e
ry
sid
e
o
f
to
th
e
ro
u
t
e
a
sc
e
n
d
a
n
c
y
;
p
a
rti
c
u
larly
in
b
e
twe
e
n
lo
we
r
b
o
u
n
d
a
n
d
u
p
p
e
r
b
o
u
n
d
s
.
P
re
v
i
o
u
s
to
th
e
m
o
v
e
m
e
n
t,
Arc
ti
c
c
h
a
r
c
o
m
e
to
a
d
e
c
isio
n
a
b
o
u
t
th
e
p
a
ss
a
g
e
wa
y
b
a
se
d
o
n
th
e
ir
p
e
rc
e
p
ti
o
n
.
T
h
is
imp
l
ies
sto
c
h
a
stic
m
i
x
u
p
o
f
c
o
n
tro
l
p
a
r
a
m
e
ters
to
p
u
sh
t
h
e
Arc
ti
c
c
h
a
r
g
ro
u
p
s
(p
re
li
m
in
a
ry
so
l
u
ti
o
n
)
i
n
m
u
tu
a
l
p
a
th
wa
y
(e
v
o
lu
ti
o
n
a
ry
o
p
e
ra
to
rs).
P
ro
jec
ted
Arc
ti
c
C
h
a
r
Al
g
o
ri
th
m
(ACA
)
h
a
s
b
e
e
n
tes
ted
in
sta
n
d
a
r
d
IE
EE
1
4
,
3
0
0
b
u
s
tes
t
s
y
ste
m
a
n
d
sim
u
lati
o
n
re
su
lt
s
sh
o
w
th
e
p
r
o
jec
ted
a
lg
o
rit
h
m
re
d
u
c
e
d
t
h
e
re
a
l
p
o
we
r
l
o
ss
e
x
ten
si
v
e
ly
.
K
ey
w
o
r
d
s
:
Ar
ctic
c
h
ar
Op
tim
al
r
ea
ctiv
e
p
o
wer
T
r
an
s
m
is
s
io
n
lo
s
s
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
L
en
in
Kan
ag
asab
ai
,
Dep
ar
tm
en
t o
f
E
E
E
,
Pra
s
ad
V.
Po
tlu
r
i Sid
d
h
ar
th
a
I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
,
Kan
u
r
u
,
Vijay
awa
d
a
,
An
d
h
r
a
Pra
d
esh
,
5
2
0
0
0
7
,
I
n
d
ia
.
E
m
ail:
g
k
len
in
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
R
ea
ctiv
e
p
o
wer
p
r
o
b
lem
p
la
y
s
a
k
ey
r
o
le
in
s
ec
u
r
e
an
d
ec
o
n
o
m
ic
o
p
e
r
atio
n
s
o
f
p
o
w
er
s
y
s
tem
.
Op
tim
al
r
ea
ctiv
e
p
o
wer
p
r
o
b
lem
h
as
b
ee
n
s
o
lv
ed
b
y
v
ar
iety
o
f
ty
p
es
o
f
m
eth
o
d
s
[
1
-
6
]
.
Nev
er
th
eless
,
n
u
m
er
o
u
s
s
cien
tific
d
if
f
icu
lties
ar
e
f
o
u
n
d
wh
ile
s
o
lv
in
g
p
r
o
b
lem
d
u
e
to
an
ass
o
r
tm
e
n
t
o
f
co
n
s
tr
ain
ts
.
E
v
o
lu
tio
n
a
r
y
tech
n
i
q
u
es
[
7
-
1
6
]
ar
e
ap
p
lied
to
s
o
lv
e
th
e
r
e
ac
tiv
e
p
o
wer
p
r
o
b
lem
,
b
u
t
th
e
m
ain
p
r
o
b
lem
is
m
an
y
al
g
o
r
ith
m
s
g
et
s
tu
ck
i
n
lo
ca
l
o
p
tim
al
s
o
lu
ti
o
n
&
f
ailed
to
b
alan
ce
t
h
e
E
x
p
lo
r
at
io
n
&
E
x
p
lo
itatio
n
d
u
r
in
g
th
e
s
ea
r
ch
o
f
g
lo
b
al
s
o
lu
tio
n
.
T
h
is
wo
r
k
p
r
esen
ts
Ar
ctic
C
h
ar
Alg
o
r
ith
m
(
AC
A)
f
o
r
s
o
lv
in
g
o
p
tim
al
r
ea
ctiv
e
p
o
we
r
p
r
o
b
lem
.
I
n
N
o
r
th
Am
er
ica
m
o
v
em
en
t
o
f
Ar
ctic
ch
ar
p
h
e
n
o
m
en
o
n
is
o
n
e
am
o
n
g
th
e
twelv
e
-
m
o
n
th
ly
in
n
ate
ac
tio
n
s
.
T
h
r
o
u
g
h
m
o
u
n
tain
s
tr
ea
m
s
m
illi
o
n
s
o
f
Ar
ctic
ch
ar
s
will
m
o
v
e
f
o
r
s
p
awn
in
g
.
Du
r
in
g
th
e
m
o
v
em
en
t
s
tar
v
in
g
b
ea
r
s
,
h
u
m
an
f
is
h
er
s
a
n
d
wate
r
f
alls
ar
e
g
en
er
ally
s
ig
n
if
ican
t
th
r
ea
t
s
th
ey
h
av
e
to
f
ac
e.
I
n
th
is
wo
r
k
d
ee
d
o
f
Ar
ctic
c
h
ar
h
as
b
ee
n
im
itated
to
d
esig
n
th
e
alg
o
r
ith
m
.
I
n
s
to
ch
asti
c
m
o
d
e
s
o
lu
tio
n
s
ar
e
in
itialized
with
o
n
e
s
eg
m
en
t
o
n
ev
e
r
y
s
id
e
o
f
to
t
h
e
r
o
u
te
ascen
d
an
cy
;
p
ar
ticu
la
r
ly
in
b
e
twee
n
lo
wer
b
o
u
n
d
an
d
u
p
p
er
b
o
u
n
d
s
.
Pro
jecte
d
Ar
ctic
C
h
ar
Alg
o
r
ith
m
(
AC
A)
h
as
b
ee
n
test
ed
in
s
tan
d
ar
d
I
E
E
E
1
4
,
3
0
0
b
u
s
test
s
y
s
tem
an
d
s
im
u
latio
n
r
esu
lts
s
h
o
w
th
e
p
r
o
jecte
d
alg
o
r
ith
m
r
ed
u
ce
d
th
e
r
ea
l p
o
we
r
lo
s
s
ex
ten
s
iv
ely
.
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
Ob
jectiv
e
o
f
th
e
p
r
o
b
lem
is
to
r
ed
u
ce
th
e
t
r
u
e
p
o
wer
lo
s
s
:
=
=
∑
∈
(
+
−
)
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
9
,
No
.
4
,
Dec
em
b
e
r
2
0
2
0
:
26
1
–
26
4
262
Vo
ltag
e
d
ev
iatio
n
g
iv
en
as f
o
l
lo
ws:
=
+
×
(
2
)
Vo
ltag
e
d
ev
iatio
n
g
iv
en
b
y
:
=
∑
|
−
|
=
(
3
)
C
o
n
s
tr
ain
t (
E
q
u
ality
)
=
+
(
4
)
C
o
n
s
tr
ain
ts
(
I
n
eq
u
ality
)
≤
≤
(
5
)
≤
≤
,
∈
(
6
)
≤
≤
,
∈
(
7
)
≤
≤
,
∈
(
8
)
Q
c
m
i
n
≤
Q
c
≤
Q
C
m
ax
,
i
∈
N
C
(
9
)
3.
ARCT
I
C
CH
AR
A
L
G
O
RIT
H
M
I
n
No
r
t
h
Am
er
ica
m
o
v
em
e
n
t
o
f
Ar
ctic
ch
a
r
p
h
en
o
m
en
o
n
is
o
n
e
a
m
o
n
g
th
e
twelv
e
-
m
o
n
th
ly
in
n
at
e
ac
tio
n
s
.
T
h
r
o
u
g
h
m
o
u
n
tain
s
tr
ea
m
s
m
illi
o
n
s
o
f
Ar
ctic
ch
ar
s
will
m
o
v
e
f
o
r
s
p
awn
in
g
.
Du
r
in
g
th
e
m
o
v
em
e
n
t
s
tar
v
in
g
b
ea
r
s
,
h
u
m
a
n
f
is
h
er
s
an
d
wate
r
f
alls
ar
e
g
en
er
ally
s
ig
n
if
ican
t
th
r
ea
ts
th
ey
h
a
v
e
to
f
ac
e.
I
n
th
is
wo
r
k
d
ee
d
o
f
Ar
ctic
ch
ar
h
as b
ee
n
i
m
itated
to
d
esig
n
th
e
alg
o
r
ith
m
.
I
n
s
to
ch
asti
c
m
o
d
e
s
o
l
u
tio
n
s
ar
e
in
itialized
with
o
n
e
s
eg
m
en
t
o
n
ev
er
y
s
id
e
o
f
to
th
e
r
o
u
t
e
ascen
d
an
cy
;
p
ar
tic
u
lar
ly
in
b
e
twee
n
lo
wer
b
o
u
n
d
a
n
d
u
p
p
er
b
o
u
n
d
s
.
So
lu
tio
n
s
ar
e
in
itiali
ze
d
ar
b
itra
r
y
m
o
d
e
with
r
ev
er
en
ce
t
o
th
e
s
o
lu
tio
n
s
p
ac
e.
=
+
∗
(
−
)
(
1
0
)
Pre
v
io
u
s
to
th
e
m
o
v
em
en
t,
Ar
ctic
ch
ar
co
m
e
to
a
d
ec
is
io
n
ab
o
u
t
th
e
p
ass
ag
ewa
y
b
as
ed
o
n
th
eir
p
er
ce
p
tio
n
.
T
h
is
im
p
lies
s
to
ch
asti
c
m
ix
u
p
o
f
co
n
tr
o
l
p
ar
am
ete
r
s
to
p
u
s
h
th
e
Ar
ctic
ch
ar
g
r
o
u
p
s
(
p
r
elim
in
a
r
y
s
o
lu
tio
n
)
in
m
u
tu
al
p
ath
wa
y
(
e
v
o
lu
tio
n
ar
y
o
p
er
ato
r
s
)
.
∶
{
1
=
[
∗
]
2
=
−
1
(
1
1
)
W
h
er
e
1
is
th
e
to
tal
n
u
m
b
er
o
f
Ar
ctic
ch
a
r
g
r
o
u
p
s
wh
ich
p
a
s
s
th
r
o
u
g
h
o
ce
a
n
a
n
d
p
o
n
d
s
,
2
is
th
e
to
tal
n
u
m
b
er
o
f
Ar
ctic
ch
a
r
g
r
o
u
p
tr
an
s
it
th
r
o
u
g
h
f
o
r
est ar
ea
an
d
m
o
u
n
tain
v
alley
,
is
t
h
e
to
tal
n
u
m
b
er
o
f
Ar
ctic
ch
ar
g
r
o
u
p
s
wh
ich
p
ar
tak
e
in
th
e
r
elo
ca
tio
n
an
d
is
Di
s
tr
ib
u
tio
n
f
ac
to
r
is
s
y
m
b
o
lizes
th
e
Ar
cti
c
c
h
ar
in
tu
itio
n
.
C
r
o
s
s
in
g
o
f
o
ce
an
,
lak
es
an
d
p
o
n
d
s
h
as b
ee
n
s
cien
tific
ally
m
o
d
eled
as,
{
=
+
(
,
(
−
)
)
=
+
(
,
(
−
)
)
(
1
2
)
W
h
er
e
t
s
y
m
b
o
lizes
th
e
p
r
esen
t
iter
atio
n
n
u
m
b
e
r
,
s
y
m
b
o
lize
a
n
ew
-
f
a
n
g
led
p
er
ce
iv
e
r
eg
io
n
(
f
r
es
h
s
o
lu
tio
n
)
an
d
s
h
o
ws th
e
p
r
ev
io
u
s
ar
ea
o
f
th
e
ex
p
lo
r
e
co
n
v
ey
(
p
r
ec
ed
in
g
s
o
lu
tio
n
)
.
(
,
)
is
co
m
p
u
ted
b
y
,
(
,
)
=
∗
∗
(
1
−
)
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2
2
5
2
-
8
8
1
4
R
ea
l p
o
w
er lo
s
s
r
ed
u
ctio
n
b
y
a
r
ctic
ch
a
r
a
lg
o
r
ith
m
(
Len
in
K
a
n
a
g
a
s
a
b
a
i
)
263
W
h
er
e
T
in
d
icate
s
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
,
b
is
an
ar
b
itra
r
y
n
u
m
b
er
n
o
r
m
ally
lar
g
er
th
an
v
alu
e
1
C
h
ief
h
u
n
te
r
s
d
is
co
v
er
th
e
r
e
g
io
n
s
with
a
s
atis
f
ac
to
r
y
A
r
ctic
ch
ar
co
n
ce
n
tr
atio
n
(
s
o
lu
tio
n
f
itn
ess
)
.
Su
b
s
eq
u
en
t
to
th
at,
th
ey
n
o
t
if
y
th
e
en
g
ag
e
d
ag
en
t
to
m
a
k
e
u
s
e
o
f
clo
s
e
b
y
ar
ea
to
d
is
co
v
er
ad
d
itio
n
al
co
n
ce
n
tr
a
ted
r
eg
io
n
s
(
s
o
lu
tio
n
with
elev
ated
f
itn
ess
)
.
T
h
is
o
p
er
atio
n
h
as
b
ee
n
p
r
ec
is
ely
d
e
f
in
ed
b
y
,
=
∗
(
1
−
2
)
+
1
(
1
4
)
W
h
er
e
β
is
a
ar
b
itra
r
y
n
u
m
b
e
r
wh
ich
s
p
an
f
r
o
m
0
a
n
d
1
w
ith
co
n
s
is
ten
t
d
is
tr
ib
u
tio
n
,
Y
R
s
tan
d
f
o
r
th
e
f
r
esh
ly
s
p
o
tted
s
o
lu
tio
n
b
y
t
h
e
en
g
ag
e
d
ag
e
n
t,
Y
M1
is
th
e
s
o
lu
tio
n
ac
q
u
ir
e
d
b
y
th
e
p
r
im
ar
y
k
ey
h
u
n
te
r
an
d
Y
M2
is
th
e
s
o
lu
tio
n
ac
q
u
ir
e
d
b
y
th
e
s
u
b
s
eq
u
e
n
t o
n
e.
Seco
n
d
o
p
er
ato
r
s
im
u
lates
th
e
b
ea
r
s
h
u
n
t
lin
e
o
f
ass
au
lt.
Natu
r
ally
th
e
y
n
o
tify
ea
ch
o
th
er
wh
en
th
e
y
f
in
d
an
ap
p
r
o
p
r
iate
r
eg
io
n
.
W
h
en
th
ey
d
is
co
v
er
a
r
eg
i
o
n
wi
th
s
u
p
er
io
r
Ar
ctic
ch
ar
c
o
n
ce
n
tr
atio
n
,
th
e
y
n
o
tify
to
o
th
er
b
ea
r
s
.
I
t e
x
p
r
ess
ed
as,
=
(
)
∗
(
−
)
+
(
1
5
)
W
h
er
e
Y
B
s
y
m
b
o
lizes
th
e
n
e
w
-
f
an
g
led
s
p
o
tted
a
r
ea
,
B
T
R
i
s
th
e
m
o
s
t
ex
ce
llen
t
ac
co
u
n
te
d
ar
ea
b
y
th
e
h
u
n
tin
g
s
q
u
ad
,
C
L
R
is
t
h
e
p
r
esen
t
a
r
ea
f
o
r
wh
ic
h
t
h
e
b
ea
r
s
h
av
e
d
eter
m
in
ed
to
ex
ec
u
te
t
h
e
lo
ca
l
ex
p
lo
itatio
n
a
n
d
φ
is
a
ca
p
r
ici
o
u
s
an
g
le
with
a
s
eg
m
en
t
o
n
ev
er
y
s
id
e
o
f
0
to
3
6
0
d
eg
r
ee
s
.
co
s
(
φ)
ar
ticu
late
th
e
b
ea
r
s
to
th
eir
o
b
jectiv
e.
E
n
d
o
f
th
e
r
e
p
o
s
itio
n
in
g
,
s
ta
y
aliv
e
Ar
ctic
ch
ar
will
g
et
to
g
eth
er
in
th
eir
m
ar
k
f
o
r
s
p
awn
in
g
.
I
n
Ar
ctic
ch
ar
th
is
n
o
r
m
al
ev
e
n
t
is
r
ep
licated
th
r
o
u
g
h
a
co
m
p
ilatio
n
s
tem
.
Af
ter
Ar
ctic
ch
ar
s
u
r
p
ass
th
r
o
u
g
h
th
eir
p
ass
ag
ewa
y
(
o
p
er
ato
r
’
s
p
er
f
o
r
m
an
ce
)
,
th
e
Ar
ctic
ch
ar
s
u
b
g
r
o
u
p
s
(
s
o
lu
tio
n
s
)
ar
e
co
m
p
o
s
ed
in
a
ex
clu
s
iv
e
s
tem
.
So
lu
tio
n
s
a
r
e
ex
to
r
ted
f
r
o
m
m
u
tu
al
o
p
er
ato
r
s
an
d
m
ak
e
an
ex
clu
s
iv
e
p
o
p
u
latio
n
.
At
th
is
co
n
d
itio
n
,
th
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
h
as r
ea
ch
e
d
th
e
e
n
d
in
g
s
tag
e
o
f
th
e
p
r
im
ar
y
i
ter
atio
n
.
Step
1
.
Dete
r
m
in
e
th
e
p
o
p
u
latio
n
s
ize,
s
o
lu
tio
n
s
p
ac
e,
t
o
tal
n
u
m
b
er
o
f
v
a
r
iab
les,
iter
atio
n
s
Step
2
.
R
eg
u
late
th
e
Ar
ctic
ch
a
r
s
u
b
g
r
o
u
p
s
ch
a
o
tically
Step
3
.
Dep
en
d
in
g
o
n
m
ig
r
atio
n
p
ass
ag
ewa
y
is
ch
o
s
en
Step
4
.
C
o
m
p
u
te
th
e
f
itn
ess
o
f
h
u
n
ted
Ar
ctic
c
h
ar
Step
5
.
Ar
ctic
ch
ar
u
s
ed
f
o
r
s
p
awn
h
as b
ee
n
r
u
m
p
le
t
o
g
eth
er
Step
6
.
I
f
y
es
o
b
tain
th
e
g
lo
b
al
s
o
lu
tio
n
o
r
else g
o
to
s
tep
n
u
m
b
er
3
.
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
At
f
ir
s
t
in
s
tan
d
ar
d
I
E
E
E
1
4
b
u
s
s
y
s
tem
th
e
v
alid
ity
o
f
th
e
p
r
o
p
o
s
ed
Ar
ctic
C
h
ar
Alg
o
r
ith
m
(
AC
A)
h
as b
ee
n
test
ed
&
co
m
p
ar
is
o
n
r
esu
lts
ar
e
p
r
esen
ted
in
T
a
b
le
1
.
T
ab
le
1
.
T
h
e
v
alid
ity
o
f
th
e
p
r
o
p
o
s
ed
Ar
ctic
C
h
ar
Alg
o
r
ith
m
(
AC
A)
C
o
n
t
r
o
l
v
a
r
i
a
b
l
e
s
A
B
C
O
[
17
]
I
A
B
C
O
[
17
]
A
C
A
V1
1
.
0
6
1
.
0
5
1
.
0
0
V2
1
.
0
3
1
.
0
5
1
.
0
5
V3
0
.
9
8
1
.
0
3
1
.
0
3
V6
1
.
0
5
1
.
0
5
1
.
0
1
V8
1
.
0
0
1
.
0
4
0
.
9
0
Q9
0
.
1
3
9
0
.
1
3
2
0
.
1
0
0
T5
6
0
.
9
7
9
0
.
9
6
0
0
.
9
0
0
T4
7
0
.
9
5
0
0
.
9
5
0
0
.
9
0
0
T4
9
1
.
0
1
4
1
.
0
0
7
1
.
0
0
0
P
l
o
ss
(
M
W
)
5
.
9
2
8
9
2
5
.
5
0
0
3
1
4
.
1
6
5
2
T
h
en
I
E
E
E
3
0
0
b
u
s
s
y
s
tem
[
1
8
]
is
u
s
ed
as tes
t sy
s
tem
to
v
alid
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
A
r
ctic
C
h
ar
Alg
o
r
ith
m
(
AC
A)
.
T
ab
le
2
s
h
o
ws th
e
co
m
p
ar
is
o
n
o
f
r
ea
l p
o
wer
lo
s
s
o
b
tain
ed
af
ter
o
p
tim
i
za
tio
n
.
T
ab
le
2
.
C
o
m
p
a
r
is
o
n
o
f
r
ea
l p
o
wer
lo
s
s
P
a
r
a
me
t
e
r
M
e
t
h
o
d
EG
A
[
19
]
M
e
t
h
o
d
EEA
[
19
]
M
e
t
h
o
d
C
S
A
[
2
0
]
A
C
A
P
LO
S
S
(
M
W
)
6
4
6
.
2
9
9
8
6
5
0
.
6
0
2
7
6
3
5
.
8
9
4
2
6
1
6
.
2
5
9
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
9
,
No
.
4
,
Dec
em
b
e
r
2
0
2
0
:
26
1
–
26
4
264
5.
CO
NCLU
SI
O
N
I
n
th
is
wo
r
k
Ar
ctic
C
h
ar
Alg
o
r
ith
m
(
AC
A)
s
u
cc
ess
f
u
lly
s
o
l
v
ed
th
e
o
p
tim
al
r
ea
ctiv
e
p
o
we
r
p
r
o
b
lem
.
Dee
d
s
o
f
Ar
ctic
ch
ar
h
av
e
b
e
en
im
itated
to
d
esig
n
th
e
alg
o
r
ith
m
.
E
n
d
o
f
th
e
r
ep
o
s
itio
n
in
g
,
s
tay
aliv
e
Ar
ctic
ch
ar
will
g
et
to
g
eth
e
r
in
th
ei
r
m
ar
k
f
o
r
s
p
awn
i
n
g
.
I
n
Ar
c
tic
ch
ar
th
is
n
o
r
m
al
ev
e
n
t
is
r
ep
licated
t
h
r
o
u
g
h
a
co
m
p
ilatio
n
s
tem
.
Af
ter
Ar
c
tic
ch
ar
s
u
r
p
ass
th
r
o
u
g
h
th
eir
p
ass
ag
ewa
y
(
o
p
er
at
o
r
’
s
p
e
r
f
o
r
m
an
ce
)
,
th
e
Ar
ctic
ch
ar
s
u
b
g
r
o
u
p
s
(
s
o
lu
tio
n
s
)
ar
e
co
m
p
o
s
ed
in
a
e
x
clu
s
iv
e
s
tem
.
So
lu
tio
n
s
ar
e
ex
to
r
ted
f
r
o
m
m
u
tu
al
o
p
e
r
ato
r
s
an
d
m
a
k
e
a
n
e
x
clu
s
iv
e
p
o
p
u
la
tio
n
.
Pro
jecte
d
Ar
ctic
C
h
ar
Al
g
o
r
ith
m
(
AC
A)
h
as
b
ee
n
test
ed
in
s
tan
d
ar
d
I
E
E
E
1
4
,
3
0
0
b
u
s
test
s
y
s
tem
an
d
s
im
u
latio
n
r
esu
lts
s
h
o
w
th
e
p
r
o
jecte
d
al
g
o
r
ith
m
r
ed
u
c
ed
th
e
r
ea
l
p
o
we
r
lo
s
s
ex
ten
s
iv
ely
.
RE
F
E
R
E
NC
E
S
[1
]
K.
Y.
Lee
.
,
“
F
u
e
l
-
c
o
st
m
in
imis
a
ti
o
n
f
o
r
b
o
t
h
re
a
l
a
n
d
re
a
c
ti
v
e
-
p
o
we
r
d
isp
a
tc
h
e
s,”
Pro
c
e
e
d
in
g
s
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
a
n
d
Distrib
u
ti
o
n
C
o
n
fer
e
n
c
e
,
v
o
l.
1
3
1
,
n
o
.
3
,
p
p
.
8
5
-
93
,
1
9
8
4
.
[2
]
N.
I.
De
e
b
.
,
“
An
e
fficie
n
t
tec
h
n
i
q
u
e
f
o
r
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
u
sin
g
a
re
v
ise
d
li
n
e
a
r
p
ro
g
ra
m
m
in
g
a
p
p
ro
a
c
h
,
”
El
e
c
tric P
o
we
r S
y
ste
m R
e
se
a
rc
h
,
v
o
l.
1
5
,
n
o
.
2
,
p
p
.
1
2
1
–
1
3
4
,
1
9
9
8
.
[3
]
M
.
R
.
Bjel
o
g
rl
ic,
M
.
S
.
Ca
lo
v
ic,
B.
S
.
Ba
b
ic.
,
”
Ap
p
li
c
a
ti
o
n
o
f
N
e
wto
n
’s
o
p
t
ima
l
p
o
we
r
fl
o
w
in
v
o
lt
a
g
e
/rea
c
ti
v
e
p
o
we
r
c
o
n
tro
l
,
”
IEE
E
T
ra
n
s
Po
w
e
r S
y
ste
m
,
v
o
l.
5
,
n
o
.
4
,
p
p
.
1
4
4
7
-
1
4
5
4
,
1
9
9
0
.
[4
]
S
.
G
ra
n
v
il
le.
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
d
isp
a
tch
th
r
o
u
g
h
in
terio
r
p
o
in
t
m
e
th
o
d
s,”
I
EE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
m
,
vo
l.
9
,
n
o
.
1
,
p
p
.
1
3
6
–
1
4
6
,
1
9
9
4
.
[5
]
N.
G
ru
d
in
in
.
,
“
Re
a
c
ti
v
e
p
o
we
r
o
p
ti
m
iza
ti
o
n
u
sin
g
su
c
c
e
ss
iv
e
q
u
a
d
ra
ti
c
p
ro
g
ra
m
m
in
g
m
e
th
o
d
,
”
IE
EE
T
ra
n
s
a
c
ti
o
n
s
o
n
P
o
we
r S
y
ste
m
,
v
o
l.
1
3
,
n
o
.
4
,
p
p
.
1
2
1
9
–
1
2
2
5
,
1
9
9
8
.
[6
]
Wei
Ya
n
,
J.
Yu
,
D.
C.
Yu
,
K.
Bh
a
tt
a
ra
i.
,
”
A
n
e
w
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
flo
w
m
o
d
e
l
in
re
c
tan
g
u
l
a
r
fo
rm
a
n
d
it
s
so
lu
ti
o
n
b
y
p
re
d
icto
r
c
o
rre
c
to
r
p
rima
l
d
u
a
l
in
teri
o
r
p
o
in
t
m
e
th
o
d
,”
IEE
E
T
ra
n
s.
Pwr.
S
y
st
.
,
v
o
l
.
2
1
,
n
o
.
1
,
p
p
.
6
1
-
6
7
,
2
0
0
6
.
[7
]
Ap
a
ra
ji
ta
M
u
k
h
e
rjee
,
Vi
v
e
k
a
n
a
n
d
a
M
u
k
h
e
rjee
,
“
S
o
l
u
ti
o
n
o
f
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
b
y
c
h
a
o
ti
c
k
ril
l
h
e
rd
a
lg
o
ri
t
h
m
,
”
IET
Ge
n
e
r.
T
ra
n
sm
.
Distrib
, v
o
l.
9
,
v
o
l.
1
5
,
p
p
.
2
3
5
1
–
2
3
6
2
,
2
0
1
5
.
[8
]
Hu
,
Z.
,
Wan
g
,
X.
&
Tay
l
o
r.
,
“
S
to
c
h
a
stic
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
:
F
o
rm
u
lati
o
n
a
n
d
s
o
lu
ti
o
n
m
e
th
o
d
,”
El
e
c
tr.
Po
we
r E
n
e
rg
y
S
y
st.,
v
o
l
.
3
2
,
p
p
.
6
1
5
-
6
2
1
,
2
0
1
0
.
[9
]
M
a
h
a
letc
h
u
m
i
A/P
M
o
rg
a
n
,
No
r
Ru
l
Ha
sm
a
Ab
d
u
ll
a
h
,
M
o
h
d
He
rwa
n
S
u
laim
a
n
,
M
a
h
f
u
z
a
h
M
u
sta
fa
a
n
d
Ro
sd
i
y
a
n
a
S
a
m
a
d
,
“
M
u
lt
i
-
o
b
jec
ti
v
e
e
v
o
lu
ti
o
n
a
ry
p
ro
g
ra
m
m
in
g
(
M
OEP
)
u
sin
g
m
u
tati
o
n
b
a
se
d
o
n
a
d
a
p
ti
v
e
m
u
tatio
n
o
p
e
ra
to
r
(AMO)
a
p
p
li
e
d
f
o
r
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tc
h
,”
AR
PN
J
o
u
rn
a
l
o
f
En
g
in
e
e
rin
g
a
n
d
A
p
p
li
e
d
S
c
ien
c
e
s
,
vol
.
1
1
,
no
.
1
4
,
2
0
1
6
.
[1
0
]
P
a
n
d
iara
jan
,
K.
&
Ba
b
u
lal,
C.
K.
,
“
F
u
z
z
y
h
a
rm
o
n
y
se
a
rc
h
a
l
g
o
rit
h
m
b
a
se
d
o
p
t
ima
l
p
o
we
r
f
lo
w
f
o
r
p
o
we
r
s
y
ste
m
se
c
u
rit
y
e
n
h
a
n
c
e
m
e
n
t
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
El
e
c
tric P
o
we
r E
n
e
rg
y
S
y
st
.
,
v
o
l.
7
8
,
p
p
.
7
2
-
79
,
2
0
1
6
.
[1
1
]
M
a
h
a
letc
h
u
m
i
M
o
rg
a
n
,
No
r
Ru
l
Ha
sm
a
Ab
d
u
ll
a
h
,
M
o
h
d
He
rwa
n
S
u
laim
a
n
,
M
a
h
fu
z
a
h
M
u
sta
fa
,
R
o
sd
iy
a
n
a
S
a
m
a
d
,
“
Be
n
c
h
m
a
rk
stu
d
ies
o
n
o
p
ti
m
a
l
r
e
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
(ORPD)
b
a
se
d
m
u
lt
i
-
o
b
jec
ti
v
e
e
v
o
l
u
ti
o
n
a
r
y
p
r
o
g
ra
m
m
in
g
(M
OEP
)
u
sin
g
m
u
ta
ti
o
n
b
a
se
d
o
n
a
d
a
p
ti
v
e
m
u
tatio
n
a
d
a
p
ter
(AMO)
a
n
d
p
o
ly
n
o
m
ial
m
u
tatio
n
o
p
e
ra
to
r
(P
M
O),
”
J
o
u
rn
a
l
o
f
El
e
c
trica
l
S
y
ste
ms
,
v
o
l
.
1
2
,
n
o
.
1
,
p
p
.
1
2
1
-
1
3
2
,
2
0
1
6
.
[1
2
]
Re
b
e
c
c
a
Ng
S
h
in
M
e
i,
M
o
h
d
He
r
wa
n
S
u
laim
a
n
,
Zu
ria
n
i
M
u
sta
ffa
,
“
An
t
li
o
n
o
p
ti
m
ize
r
fo
r
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
s
o
lu
t
io
n
,”
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
S
y
ste
ms
,
S
p
e
c
ial
Iss
u
e
AM
P
E2
0
1
5
,
p
p
.
6
8
-
74
,
2
0
1
6
.
[1
3
]
G
a
g
li
a
n
o
A.,
No
c
e
ra
F
.
,
“
An
a
ly
sis
o
f
th
e
p
e
rf
o
rm
a
n
c
e
s
o
f
e
lec
tri
c
e
n
e
rg
y
sto
ra
g
e
in
re
sid
e
n
ti
a
l
a
p
p
li
c
a
ti
o
n
s,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
He
a
t
a
n
d
T
e
c
h
n
o
lo
g
y
,
v
o
l.
3
5
,
S
p
e
c
ial
Iss
u
e
1
,
p
p
.
S
4
1
-
S
4
8
,
2
0
1
7
.
[1
4
]
Ca
ld
e
ra
M
.
,
Un
g
a
ro
P
.
,
Ca
m
m
a
ra
ta G
.
,
P
u
g
li
si G
.
,
“
S
u
r
v
e
y
-
b
a
se
d
a
n
a
ly
sis o
f
th
e
e
lec
tri
c
a
l
e
n
e
rg
y
d
e
m
a
n
d
in
Italia
n
h
o
u
se
h
o
l
d
s,
”
M
a
th
e
ma
ti
c
a
l
M
o
d
e
ll
in
g
o
f
En
g
in
e
e
rin
g
Pr
o
b
lem
s
,
v
o
l.
5
,
n
o
.
3
,
p
p
.
2
1
7
-
2
2
4
,
2
0
1
8
.
[1
5
]
P
u
ris.
A,
Be
ll
o
,
R.
,
M
o
li
n
a
,
D.
&
He
rre
ra
,
F
.
“
V
a
riab
le
m
e
sh
o
p
ti
m
iza
ti
o
n
fo
r
c
o
n
ti
n
u
o
u
s
o
p
t
imiz
a
ti
o
n
p
ro
b
lem
s,”
S
o
ft
Co
mp
u
ti
n
g
,
v
o
l.
1
6
,
n
o
.
3
,
p
p
.
5
1
1
-
5
2
3
,
2
0
1
2
.
[1
6
]
P
rice
.
K,
R.
M
.
S
to
r
n
,
a
n
d
J.
A.
Lam
p
in
e
n
,
Dif
fer
e
n
ti
a
l
e
v
o
l
u
ti
o
n
:
A
p
ra
c
ti
c
a
l
a
p
p
ro
a
c
h
t
o
g
lo
b
a
l
o
p
t
imiza
ti
o
n
,
S
p
rin
g
e
r,
2
0
0
6
.
[1
7
]
Ch
a
n
d
ra
g
u
p
ta
M
a
u
r
y
a
n
Ku
p
p
a
m
u
th
u
S
i
v
a
li
n
g
a
m
,
S
u
b
ra
m
a
n
ian
R
a
m
a
c
h
a
n
d
ra
n
,
P
u
rrn
ima
a
S
h
iv
a
S
a
k
th
i
Ra
jam
a
n
i
,
“
Re
a
c
ti
v
e
p
o
we
r
o
p
ti
m
iza
ti
o
n
i
n
a
p
o
we
r
sy
ste
m
n
e
tw
o
rk
th
r
o
u
g
h
m
e
tah
e
u
risti
c
a
l
g
o
ri
th
m
s,”
T
u
r
k
ish
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
Co
m
p
u
ter
S
c
ien
c
e
s
,
v
o
l.
2
5
,
n
o
.
6
,
p
p
.
4
6
1
5
-
4
6
2
3
,
2
0
1
7
.
[1
8
]
I
E
E
E
,
“T
h
e
I
E
E
E
-
test
s
y
s
tem
s
”
R
etr
eiv
ed
f
r
o
m
:
h
ttp
://www.
ee
.
wash
in
g
to
n
.
ed
u
/trsear
ch
/p
s
tca/,
1
9
9
3
.
[1
9
]
S
.
S
.
Re
d
d
y
,
e
t
a
l.
,
“
F
a
ste
r
e
v
o
lu
ti
o
n
a
ry
a
lg
o
rit
h
m
b
a
se
d
o
p
ti
m
a
l
p
o
we
r
fl
o
w
u
sin
g
i
n
c
re
m
e
n
tal
v
a
riab
les
,
”
El
e
c
trica
l
Po
we
r a
n
d
En
e
rg
y
S
y
st
e
ms
,
v
o
l.
5
4
,
p
p
.
1
9
8
-
2
1
0
,
2
0
1
4
.
[2
0
]
S.
Su
r
en
d
e
r
R
ed
d
y
,
“O
p
tim
al
r
ea
ctiv
e
p
o
wer
s
ch
e
d
u
lin
g
u
s
i
n
g
c
u
ck
o
o
s
ea
r
ch
alg
o
r
ith
m
,
”
I
n
tern
a
tio
n
a
l
Jo
u
r
n
a
l o
f E
lectrica
l a
n
d
C
o
m
p
u
ter E
n
g
in
ee
r
in
g
,
v
o
l.
7
,
n
o
.
5
,
p
p
.
2
3
4
9
-
2
3
5
6
,
2
0
1
7
.
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