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s
to
m
in
im
ize
th
e
lev
elis
ed
p
r
o
d
u
ctio
n
co
s
t
h
as
b
ee
n
p
r
o
p
o
s
e
d
in
[
1
0
]
.
A
d
ata
-
d
r
iv
en
l
o
ca
l
o
p
tim
iz
atio
n
o
f
g
lo
b
al
o
b
jectiv
es
tech
n
iq
u
e
to
co
n
tr
o
l
th
e
r
ea
ctiv
e
p
o
wer
d
is
p
atch
f
r
o
m
d
is
tr
ib
u
ted
en
er
g
y
s
o
u
r
ce
s
i
s
p
r
o
p
o
s
ed
in
[
1
1
]
.
R
ef
er
en
c
e
[
1
2
]
p
r
o
p
o
s
es
a
h
ier
ar
ch
ical
d
is
tr
ib
u
ted
ap
p
r
o
ac
h
b
ased
o
n
s
y
s
tem
o
f
s
y
s
tem
s
ap
p
r
o
ac
h
.
T
h
e
m
ath
em
ati
ca
l
f
o
r
m
u
latio
n
an
d
s
o
lu
tio
n
ap
p
r
o
ac
h
f
o
r
th
e
s
to
ch
asti
c
o
p
tim
al
r
ea
ctiv
e
p
o
w
er
s
ch
ed
u
lin
g
b
y
co
n
s
id
er
in
g
th
e
win
d
,
s
o
lar
PV
p
o
wer
s
an
d
lo
a
d
d
em
an
d
u
n
ce
r
tain
ties
h
as b
ee
n
p
r
o
p
o
s
ed
in
[
1
3
]
.
T
h
e
p
r
esen
t
p
ap
er
p
r
o
p
o
s
es
an
ap
p
r
o
ac
h
to
s
o
lv
e
th
e
co
m
p
lex
is
s
u
es
a
s
s
o
ciate
d
wi
th
th
e
r
estru
ctu
r
ed
p
o
wer
s
y
s
tem
,
i.e
.
,
s
o
lv
in
g
en
er
g
y
an
d
an
cillar
y
s
er
v
ices
m
a
r
k
ets
s
im
u
ltan
eo
u
s
ly
.
T
h
e
aim
is
to
ac
c
o
m
m
o
d
ate
n
ew
-
m
ar
k
et
r
elate
d
s
tr
u
ctu
r
e
t
o
th
e
m
ar
k
et
clea
r
in
g
p
r
o
ce
d
u
r
e.
Fo
r
s
im
p
licity
,
a
s
eq
u
en
tial
ap
p
r
o
ac
h
is
u
s
ed
f
o
r
ev
e
r
y
h
o
u
r
o
p
tim
izatio
n
,
with
g
en
er
ato
r
r
am
p
r
ate
co
n
s
tr
ain
ts
.
Ho
wev
er
,
it
ca
n
also
b
e
ex
ten
d
ed
to
f
u
ll
d
y
n
am
ic
d
is
p
atch
as
well,
if
r
eq
u
ir
ed
d
ep
en
d
in
g
o
n
th
e
m
ar
k
et
p
r
ac
tice.
I
n
th
is
wo
r
k
,
t
h
e
r
ea
ctiv
e
p
o
wer
s
u
p
p
lied
b
y
s
y
n
ch
r
o
n
o
u
s
g
en
e
r
ato
r
s
is
co
n
s
id
er
ed
as a
n
an
cil
lar
y
s
er
v
ice
wh
ich
s
h
o
u
ld
b
e
c
o
m
p
en
s
ated
b
y
th
e
SO
.
C
o
-
o
p
tim
izin
g
t
h
e
p
r
o
v
is
io
n
o
f
en
e
r
g
y
an
d
r
ea
ctiv
e
p
o
w
er
g
iv
es
th
e
m
o
s
t
ec
o
n
o
m
ical
d
is
p
atch
o
f
th
e
tw
o
co
m
m
o
d
ities
f
r
o
m
o
n
e
s
o
u
r
ce
i.e
.
,
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
.
2.
SE
Q
U
E
NT
I
A
L
AND
S
I
M
U
L
T
A
NE
O
US
M
ARK
E
T
C
L
E
ARI
NG
T
y
p
ically
,
th
e
SO so
lv
es th
e
m
ar
k
et
clea
r
in
g
p
r
o
b
lem
b
y
ta
k
in
g
b
id
s
f
r
o
m
g
e
n
er
ato
r
s
an
d
o
f
f
er
s
f
r
o
m
lo
ad
d
em
an
d
s
,
an
d
th
en
f
in
d
s
th
e
s
et
o
f
ac
ce
p
ted
b
id
s
an
d
o
f
f
er
s
o
f
g
en
er
ato
r
s
a
n
d
lo
ad
s
alo
n
g
with
th
e
m
ar
k
et
clea
r
in
g
p
r
ice
(
MCP
)
[
1
4
]
.
Fig
u
r
e
1
d
ep
icts
th
e
co
n
v
en
tio
n
al
s
eq
u
en
tial
an
d
p
r
o
p
o
s
ed
s
i
m
u
ltan
eo
u
s
m
ar
k
et
clea
r
in
g
o
f
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
s
.
T
wo
d
if
f
er
en
t
m
ar
k
e
t
m
o
d
els
ar
e
p
r
esen
ted
in
t
h
is
p
ap
er
,
an
d
th
ey
a
r
e
p
r
esen
ted
as sh
o
wn
:
-
M
a
rk
et
mo
del
1
:
C
o
n
v
e
n
tio
n
al/s
eq
u
en
tial m
ar
k
et
clea
r
in
g
.
-
M
a
rk
et
mo
del
2
:
P
r
o
p
o
s
ed
/s
im
u
ltan
eo
u
s
m
ar
k
et
clea
r
in
g
.
D
e
m
a
n
d
-
s
i
d
e
o
f
f
e
r
s
f
r
o
m
l
o
a
d
d
e
m
a
n
d
s
P
r
i
n
t
o
p
t
i
m
u
m
a
c
t
i
v
e
,
r
e
a
c
t
i
v
e
p
o
w
e
r
o
u
t
p
u
t
s
a
n
d
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
(
c
o
s
t
a
n
d
s
o
c
i
a
l
w
e
l
f
a
r
e
)
v
a
l
u
e
s
C
o
n
v
e
n
t
i
o
n
a
l
m
a
r
k
e
t
c
l
e
a
r
i
n
g
A
c
t
i
v
e
p
o
w
e
r
m
a
r
k
e
t
c
l
e
a
r
i
n
g
G
e
n
e
r
a
t
o
r
s
i
d
e
b
i
d
d
i
n
g
f
o
r
a
c
t
i
v
e
a
n
d
r
e
a
c
t
i
v
e
p
o
w
e
r
s
R
e
a
c
t
i
v
e
p
o
w
e
r
m
a
r
k
e
t
c
l
e
a
r
i
n
g
S
i
m
u
l
t
a
n
e
o
u
s
m
a
r
k
e
t
c
l
e
a
r
i
n
g
A
c
t
i
v
e
p
o
w
e
r
m
a
r
k
e
t
c
l
e
a
r
i
n
g
R
e
a
c
t
i
v
e
p
o
w
e
r
m
a
r
k
e
t
c
l
e
a
r
i
n
g
Fig
u
r
e
1
.
C
o
n
v
en
tio
n
al
s
eq
u
en
tial a
n
d
p
r
o
p
o
s
ed
s
im
u
ltan
eo
u
s
m
ar
k
et
clea
r
in
g
o
f
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
s
2
.
1
.
M
a
r
k
et
m
o
del 1
:
c
o
nv
e
ntio
na
l/s
eque
ntia
l m
a
rk
e
t
cl
ea
ring
I
n
th
is
m
a
r
k
et
m
o
d
el,
ac
tiv
e
p
o
wer
m
ar
k
et
is
clea
r
ed
f
ir
s
t
a
n
d
th
en
b
y
u
s
in
g
th
ese
r
esu
lts
th
e
r
ea
ctiv
e
p
o
wer
m
ar
k
et
is
clea
r
ed
n
ex
t.
Gen
er
ally
,
in
an
y
co
m
p
etitiv
e
elec
tr
icity
m
ar
k
et,
th
e
p
r
o
b
l
em
o
f
ac
tiv
e
p
o
we
r
d
is
p
atch
is
f
o
r
m
u
lated
b
y
u
s
in
g
th
e
co
s
t
m
in
im
izatio
n
o
r
s
o
cial
welf
ar
e
m
ax
im
izatio
n
[
1
5
]
.
I
n
th
is
m
ar
k
et
m
o
d
el,
two
o
b
jectiv
e
f
u
n
ctio
n
s
,
i.e
.
,
f
u
el
c
o
s
t
(
FC
)
m
in
im
iza
tio
n
an
d
s
o
cial
welf
ar
e
m
ax
i
m
izatio
n
(
SW
M)
ar
e
co
n
s
id
er
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
S
o
cia
l welfa
r
e
ma
ximiza
tio
n
b
a
s
ed
o
p
tima
l e
n
erg
y
a
n
d
r
ea
ct
ive
p
o
w
er…
(
S
u
r
en
d
er R
ed
d
y
S
a
lku
ti
)
1381
2
.
1
.
1
.
O
bje
ct
iv
e
1
:
f
uel c
o
s
t
(
F
C)
m
ini
m
iza
t
io
n
Her
e,
th
e
lo
ad
d
em
an
d
is
c
o
n
s
id
er
ed
as
in
elastic
to
p
r
ice.
Fir
s
t,
th
e
ac
tiv
e
p
o
wer
d
is
p
atch
p
r
o
b
lem
is
s
o
lv
ed
,
af
ter
th
at
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
p
r
o
b
lem
is
s
o
lv
e
d
[
1
6
]
.
I
n
th
is
ca
s
e,
th
e
o
b
jectiv
e
is
to
m
in
im
ize
th
e
to
tal
f
u
el
co
s
t o
f
th
e
r
m
al
g
e
n
e
r
ato
r
s
,
an
d
it is
f
o
r
m
u
lated
as,
=
∑
(
)
=
(
+
+
2
)
=
1
(
1
)
is
n
u
m
b
er
o
f
g
e
n
er
ato
r
s
,
(
)
is
t
h
e
f
u
el
co
s
t
f
u
n
ctio
n
f
o
r
ac
tiv
e
p
o
wer
g
en
er
atio
n
(
)
.
,
an
d
ar
e
g
en
er
ato
r
e
n
er
g
y
c
o
s
t
co
ef
f
icien
ts
f
o
r
th
e
ℎ
g
en
er
atin
g
u
n
it
.
I
n
th
is
co
n
v
en
tio
n
al
m
ar
k
et
c
lear
in
g
,
af
ter
o
p
tim
izin
g
th
e
r
ea
l
p
o
wer
co
s
t
m
in
im
izatio
n
,
r
ea
ctiv
e
p
o
w
er
s
ar
e
k
n
o
wn
af
ter
ac
tu
al
im
p
lem
en
tatio
n
[
1
7
]
.
Fro
m
th
e
o
b
tain
ed
r
ea
ctiv
e
p
o
wer
s
,
r
ea
ctiv
e
p
o
wer
c
o
s
t is ca
lcu
lated
u
s
in
g
,
(
)
=
(
+
+
2
)
(
2
)
wh
er
e
,
an
d
ar
e
th
e
c
o
n
s
ta
n
ts
d
ep
en
d
in
g
o
n
p
o
wer
f
ac
t
o
r
(
c
o
s
)
,
an
d
th
ey
ar
e
d
eter
m
in
ed
b
y
u
s
in
g
[
1
8
]
,
=
(
3
)
=
s
in
(
4
)
=
2
(
)
(
5
)
Her
e,
th
e
to
tal
g
e
n
er
atio
n
co
s
t
is
th
e
s
u
m
o
f
t
h
e
f
u
el
co
s
t
(
i.e
.
,
as
s
h
o
wn
in
(
1
)
)
an
d
th
e
r
ea
cti
v
e
p
o
wer
c
o
s
t
(
i.e
.
,
as sh
o
wn
in
(
2
)
)
[
1
9
]
.
2
.
1
.
2
.
O
bje
ct
iv
e
2
:
s
o
cia
l w
el
f
a
re
ma
x
im
iz
a
t
io
n
(
SWM
)
Gen
er
ally
,
g
e
n
er
ato
r
b
id
s
an
d
lo
ad
d
em
an
d
o
f
f
er
s
a
r
e
c
o
n
s
id
er
ed
f
o
r
th
e
m
ar
k
et
clea
r
in
g
p
r
o
ce
s
s
.
W
h
en
th
e
d
em
an
d
-
s
id
e
b
id
d
in
g
is
in
tr
o
d
u
ce
d
f
r
o
m
th
e
c
u
s
to
m
er
s
’
s
id
e,
th
en
th
e
f
u
el
co
s
t
m
in
im
izatio
n
o
b
jectiv
e
ch
a
n
g
es
to
SW
M
o
b
jectiv
e.
T
h
is
s
o
cial
welf
ar
e
(
SW
)
co
n
ce
p
t
is
ap
p
lied
f
o
r
t
h
e
ce
n
tr
alize
d
m
ar
k
et
co
n
s
id
er
in
g
t
h
e
d
em
a
n
d
elastic
ity
[
2
0
]
.
SW
r
ep
r
esen
ts
th
e
to
ta
l
s
u
r
p
lu
s
o
f
cu
s
to
m
er
s
an
d
g
e
n
er
ato
r
s
.
T
h
is
SW
M
o
b
jectiv
e
ca
n
b
e
ex
p
r
ess
ed
as,
=
[
∑
(
)
=
1
−
∑
(
)
=
1
]
(
6
)
wh
er
e,
(
)
=
−
−
2
(
7
)
is
th
e
n
u
m
b
er
o
f
lo
ad
s
p
ar
tic
ip
atin
g
in
th
e
m
ar
k
et
clea
r
in
g
p
r
o
ce
s
s
,
an
d
(
)
is
d
em
an
d
-
s
id
e
en
er
g
y
b
en
ef
it f
u
n
ctio
n
at
b
u
s
.
,
an
d
ar
e
d
em
an
d
-
s
id
e
b
id
d
in
g
c
o
ef
f
icien
ts
o
f
ℎ
lo
ad
/ d
em
an
d
.
2
.
2
.
M
a
r
k
et
m
o
del 2
:
pro
po
s
ed
s
im
ulta
neo
us
m
a
rk
et
cle
a
ring
I
n
th
is
m
ar
k
et
s
tr
u
ct
u
r
e,
b
o
th
t
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
m
ar
k
ets
ar
e
clea
r
ed
s
im
u
ltan
e
o
u
s
ly
.
Her
e,
th
e
p
r
o
cu
r
em
en
t
o
f
th
ese
s
er
v
ices
is
o
b
tain
ed
th
r
o
u
g
h
th
e
ce
n
tr
alize
d
d
is
p
atch
,
an
d
it
r
ec
o
g
n
izes
tr
ad
eo
f
f
b
etwe
en
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
.
T
h
is
m
a
r
k
et
s
tr
u
ctu
r
e
is
co
n
s
id
er
ed
as
ef
f
ec
tiv
e
b
ec
au
s
e
th
e
g
en
er
ato
r
p
ar
ticip
ates
in
b
o
th
th
e
m
ar
k
ets
s
i
m
u
ltan
eo
u
s
ly
wh
ich
all
o
ws
it
to
u
s
e
its
in
h
er
en
t
b
e
h
av
io
u
r
to
g
et
th
e
m
ax
im
u
m
b
en
ef
it.
2
.
2
.
1
.
O
bje
ct
iv
e
1
:
t
o
t
a
l c
o
s
t
(
T
C)
m
ini
m
iza
t
io
n
T
h
e
tr
ad
itio
n
al
co
s
t
m
in
im
izat
io
n
o
b
jectiv
e
c
o
n
s
is
ts
o
n
ly
th
e
ac
tiv
e
p
o
w
er
co
s
t
o
f
th
er
m
al
g
en
er
ato
r
s
.
Th
is
tr
ad
itio
n
al
co
s
t
m
in
im
iz
atio
n
o
b
jectiv
e
is
n
o
w
m
o
d
if
ied
to
in
clu
d
e
th
e
co
s
t
o
f
r
ea
ctiv
e
p
o
wer
in
th
e
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
is
g
iv
es
th
e
m
o
s
t
ec
o
n
o
m
ical
d
is
p
atc
h
f
r
o
m
a
s
in
g
le
s
o
u
r
ce
.
Hen
ce
,
th
e
m
o
d
if
ied
to
tal
co
s
t m
in
im
izatio
n
o
b
jectiv
e
f
u
n
ctio
n
is
,
Min
im
ize,
=
(
∑
(
)
=
1
+
∑
(
)
=
1
)
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1693
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
4
,
Au
g
u
s
t 2
0
2
1
: 1
3
7
9
-
1
3
8
7
1382
2
.
2
.
2
.
O
bje
ct
iv
e
2
:
m
o
dified
s
o
cia
l w
elf
a
re
m
a
x
im
iza
t
io
n
(
SWM
)
T
h
e
co
n
v
en
ti
o
n
al
SW
f
u
n
ctio
n
wh
ich
co
n
s
is
ts
o
f
co
s
t
f
u
n
ctio
n
o
f
ac
tiv
e
p
o
wer
g
en
er
atio
n
a
n
d
b
en
ef
it
f
u
n
ctio
n
o
f
cu
s
to
m
er
s
is
n
o
w
m
o
d
if
ied
to
in
clu
d
e
th
e
co
s
t
f
u
n
ctio
n
o
f
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
.
Hen
ce
,
th
e
m
o
d
if
ied
SW
M
o
b
jectiv
e
f
u
n
c
tio
n
is
f
o
r
m
u
lated
as [
2
1
]
,
m
a
x
im
ize,
=
[
∑
(
)
=
1
−
(
∑
(
)
=
1
+
∑
(
)
=
1
)
]
(
9
)
T
h
e
ab
o
v
e
o
b
jectiv
e
f
u
n
ctio
n
s
(
i.e
.
,
as
s
h
o
wn
in
(
1
)
,
(
2
)
,
(
8
)
an
d
(
9
)
)
ar
e
s
o
lv
ed
s
u
b
ject
ed
to
th
e
f
o
llo
win
g
eq
u
ality
an
d
in
eq
u
ality
c
o
n
s
tr
ain
ts
.
2
.
3
.
E
qu
a
lity
co
ns
t
ra
ints
T
h
ese
co
n
s
tr
ain
ts
in
clu
d
e
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
b
ala
n
ce
eq
u
atio
n
s
,
an
d
th
e
y
ar
e
e
x
p
r
ess
ed
as [
2
2
]
,
0
=
−
−
∑
|
|
c
os
(
+
−
)
,
(
+
)
=
1
(
1
0
)
0
=
−
−
∑
|
|
s
in
(
+
−
)
,
(
)
=
1
(
1
1
)
W
h
er
e
=
|
|
∠
,
=
∠
an
d
=
∠
.
an
d
ar
e
th
e
n
u
m
b
er
o
f
g
en
e
r
ato
r
a
n
d
lo
a
d
b
u
s
es,
r
esp
ec
tiv
ely
.
an
d
ar
e
ac
tiv
e
p
o
wer
s
at
g
en
er
ato
r
an
d
lo
ad
b
u
s
es.
an
d
ar
e
r
ea
ctiv
e
p
o
w
er
s
at
g
en
er
ato
r
an
d
l
o
ad
b
u
s
es.
2
.
4
.
I
nequ
a
lity
co
ns
t
ra
ints
2
.
4
.
1
.
G
ener
a
t
o
r
co
ns
t
ra
ints
Gen
er
ato
r
s
ac
tiv
e
p
o
wer
(
)
,
r
e
ac
tiv
e
p
o
wer
(
)
an
d
v
o
ltag
e
m
ag
n
itu
d
es
(
)
ar
e
lim
ited
b
y
th
ei
r
m
in
im
u
m
an
d
m
ax
im
u
m
lim
it
s
[
2
3
]
.
≤
≤
,
=
1
,
2
,
…
,
(
1
2
)
≤
≤
,
=
1
,
2
,
…
,
(
1
3
)
≤
≤
,
=
1
,
2
,
…
,
(
1
4
)
2
.
4
.
2
.
Dem
a
nd
lim
it
s
I
n
elastic lo
ad
d
em
a
n
d
,
th
e
lim
its
o
n
p
o
wer
d
em
an
d
ca
n
b
e
ex
p
r
ess
ed
as,
≤
≤
,
=
1
,
2
,
…
,
(
1
5
)
wh
er
e
an
d
ar
e
m
in
im
u
m
an
d
m
ax
im
u
m
p
o
wr
d
e
m
an
d
s
at
i
th
b
u
s
.
I
n
an
in
elastic
lo
ad
d
em
an
d
s
,
th
ese
two
lim
its
ar
e
eq
u
al,
i.e
.
,
=
=
.
2
.
4
.
3
.
Co
ns
t
ra
ints o
n
t
ra
ns
f
o
rm
er
T
h
ese
co
n
s
tr
ain
ts
ar
e
ex
p
r
ess
ed
as,
≤
≤
,
=
1
,
2
,
…
,
(
1
6
)
2
.
4
.
4
.
Rea
ct
iv
e
po
wer
c
a
pa
bil
it
y
co
ns
t
ra
ints o
f
s
y
nchro
no
us
g
ener
a
t
o
r
T
h
e
ac
tiv
e
p
o
wer
o
u
tp
u
t o
b
tai
n
ed
f
r
o
m
a
s
y
n
c
h
r
o
n
o
u
s
g
en
er
ato
r
is
lim
ited
b
y
th
e
p
r
im
e
m
o
v
er
o
f
th
e
g
en
er
ato
r
,
wh
er
ea
s
th
e
ca
p
ab
i
lity
o
f
r
ea
ctiv
e
p
o
wer
is
lim
ited
b
y
ar
m
atu
r
e
an
d
f
ield
c
u
r
r
en
ts
,
an
d
th
ey
ar
e
ep
r
ess
ed
b
y
u
s
in
g
as sh
o
wn
(
1
7
)
an
d
(
1
8
)
,
r
esp
ec
tiv
ely
[
2
4
]
.
2
+
2
≤
(
1
7
)
2
+
(
+
2
)
2
≤
(
)
2
(
1
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
S
o
cia
l welfa
r
e
ma
ximiza
tio
n
b
a
s
ed
o
p
tima
l e
n
erg
y
a
n
d
r
ea
ct
ive
p
o
w
er…
(
S
u
r
en
d
er R
ed
d
y
S
a
lku
ti
)
1383
2
.
4
.
5
.
Co
ns
t
ra
ints o
n
s
wit
cha
ble
VAR
s
o
urce
s
T
h
ese
co
n
s
tr
ain
ts
ar
e
ex
p
r
ess
ed
as,
≤
≤
,
=
1
,
2
,
…
,
(
1
9
)
2
.
4
.
6
.
Securit
y
co
ns
t
ra
ints
T
h
ese
in
clu
d
e
th
e
lo
ad
b
u
s
v
o
ltag
e
m
ag
n
itu
d
es
(
)
an
d
lin
e
f
lo
w
(
)
co
n
s
tr
ain
ts
,
an
d
th
ey
ar
e
ex
p
r
ess
ed
as,
≤
≤
,
=
1
,
2
,
…
,
(
2
0
)
≤
,
=
1
,
2
,
…
,
(
2
1
)
3.
ANT L
I
O
N
O
P
T
I
M
I
Z
A
T
I
O
N
(
AL
O
)
AL
G
O
RI
T
H
M
AL
O
is
an
ev
o
lu
tio
n
ar
y
b
ased
alg
o
r
ith
m
wh
ich
m
o
d
els
th
e
i
n
ter
ac
tio
n
b
etwe
en
th
e
a
n
ts
an
d
an
t
lio
n
s
in
o
u
r
n
at
u
r
e.
AL
O
m
im
ics h
u
n
tin
g
b
eh
a
v
io
r
o
f
an
t lio
n
s
.
T
wo
im
p
o
r
tan
t stag
es in
v
o
lv
e
d
in
th
is
alg
o
r
ith
m
ar
e
lar
v
ae
s
tag
e
(
i.e
.
,
h
u
n
tin
g
p
r
e
y
)
an
d
ad
u
lt
s
tag
e
(
i.e
.
,
r
ep
r
o
d
u
ct
io
n
)
[
2
5
]
,
[
2
6
]
.
Var
io
u
s
s
tep
s
/o
p
er
atio
n
s
in
v
o
lv
ed
in
im
p
lem
en
tin
g
th
is
alg
o
r
ith
m
in
clu
d
e
r
an
d
o
m
walk
o
f
an
t
s
,
b
u
ild
in
g
o
f
tr
ap
s
,
an
d
e
n
tr
a
p
m
en
t
o
f
th
e
a
n
ts
in
an
t
lio
n
p
its
,
ad
ap
tiv
e
s
h
r
in
k
i
n
g
o
f
tr
ap
s
,
ca
tch
in
g
p
r
e
y
s
an
d
r
eb
u
ild
i
n
g
tr
ap
s
[
2
7
]
.
Fig
u
r
e
2
p
r
esen
ts
th
e
f
lo
w
ch
ar
t
o
f
AL
O
tech
n
iq
u
e
f
o
r
s
o
lv
in
g
t
h
e
p
r
o
p
o
s
ed
o
p
tim
al
e
n
er
g
y
an
d
r
ea
ctiv
e
p
o
wer
d
is
p
atch
p
r
o
b
lem
.
Fo
r
m
o
r
e
d
etails o
n
AL
O
alg
o
r
ith
m
,
th
e
r
ea
d
e
r
m
ay
r
ef
er
r
ef
er
e
n
ce
s
[
2
8
]
,
[
2
9
]
.
S
t
a
r
t
R
e
a
d
t
e
s
t
s
y
s
t
e
m
d
a
t
a
,
c
o
s
t
d
a
t
a
,
c
o
n
t
r
o
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v
a
r
i
a
b
l
e
s
d
a
t
a
a
n
d
t
h
e
d
a
t
a
r
e
l
a
t
e
d
t
o
a
n
t
l
i
o
n
a
l
g
o
r
i
t
h
m
N
o
G
e
n
e
r
a
t
e
i
n
i
t
i
a
l
p
o
p
u
l
a
t
i
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o
f
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n
t
s
C
h
e
c
k
w
h
e
t
h
e
r
a
l
l
t
h
e
r
a
n
d
o
m
s
o
l
u
t
i
o
n
s
o
f
t
h
e
p
r
o
b
l
e
m
a
r
e
a
s
s
i
g
n
e
d
c
o
r
r
e
c
t
l
y
t
o
t
h
e
a
n
t
p
o
s
i
t
i
o
n
.
S
e
t
i
t
e
r
a
t
i
o
n
c
o
u
n
t
=
0
.
D
e
t
e
r
m
i
n
e
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a
n
t
f
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t
n
e
s
s
f
u
n
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t
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s
f
o
r
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m
a
r
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e
t
m
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n
s
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d
e
r
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n
g
t
h
e
c
o
s
t
m
i
n
i
m
i
z
a
t
i
o
n
(
e
q
u
a
t
i
o
n
s
(
1
)
,
(
2
)
,
(
8
)
)
a
n
d
s
o
c
i
a
l
w
e
l
f
a
r
e
m
a
x
i
m
i
z
a
t
i
o
n
(
e
q
u
a
t
i
o
n
s
(
6
)
,
(
9
)
)
,
s
u
b
j
e
c
t
e
d
t
o
v
a
r
i
o
u
s
e
q
u
a
l
i
t
y
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4
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1
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1
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1
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2
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M
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m
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2
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re
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a
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m
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SWM
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T
h
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s
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s
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lated
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p
tim
izatio
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.
T
h
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co
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lcu
lated
u
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in
g
as
s
h
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in
(2
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.
T
h
e
m
o
d
if
ie
d
SW
is
ca
lcu
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af
ter
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o
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r
atin
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th
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m
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ig
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Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
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cia
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ma
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S
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1385
4
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2
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Resul
t
s
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del 2
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pro
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neo
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m
a
r
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clea
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4
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2
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1
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M
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rk
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o
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ca
s
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1
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t
o
t
a
l c
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m
ini
m
iz
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Her
e,
th
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d
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ltan
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ly
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i.e
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b
y
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s
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8
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m
ar
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3
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Sch
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ase
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M
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a
re
m
a
x
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m
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(
SWM
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n
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th
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m
o
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SW
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i.e
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s
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(
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th
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it
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tiv
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d
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.
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t
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at
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t
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lcu
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s
is
ten
t w
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p
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t m
ar
k
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p
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ab
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5
.
Sch
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p
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s
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d
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b
jectiv
e
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alu
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r
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el
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2.
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5
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M
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1693
-
6
9
3
0
T
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L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
4
,
Au
g
u
s
t 2
0
2
1
: 1
3
7
9
-
1
3
8
7
1386
5.
CO
NCLU
SI
O
NS
I
n
th
is
p
ap
er
,
s
im
u
ltan
eo
u
s
/jo
in
t
en
er
g
y
an
d
r
ea
ctiv
e
p
o
wer
m
ar
k
et
clea
r
in
g
is
p
r
o
p
o
s
ed
b
ased
o
n
th
e
m
in
im
izatio
n
o
f
to
tal
g
en
er
atio
n
co
s
t
o
r
th
e
m
a
x
im
izatio
n
o
f
s
o
cial
welf
ar
e.
T
h
e
co
n
v
en
ti
o
n
al
co
s
t
an
d
s
o
cial
welf
ar
e
o
b
jectiv
es
ar
e
m
o
d
if
i
ed
to
in
clu
d
e
th
e
co
s
t
o
f
r
ea
ct
iv
e
p
o
wer
.
T
h
e
m
o
s
t
im
p
o
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ta
n
t
d
if
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er
e
n
ce
is
th
at
in
s
tead
o
f
d
o
i
n
g
co
s
t
ca
lcu
lati
o
n
in
p
o
s
t
-
f
ac
to
m
an
n
e
r
as
in
co
n
v
en
tio
n
al
p
r
ac
tice,
s
im
u
lt
an
eo
u
s
a
p
p
r
o
a
ch
is
p
r
o
p
o
s
ed
in
th
is
wo
r
k
.
T
h
e
c
ase
s
tu
d
ies
o
n
I
E
E
E
3
0
b
u
s
s
y
s
tem
p
r
esen
t
t
h
e
b
e
n
ef
it
o
f
c
lear
in
g
th
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
m
ar
k
et
s
s
im
u
ltan
eo
u
s
ly
o
v
er
th
e
co
n
v
en
ti
o
n
al
m
ar
k
et
clea
r
in
g
p
r
o
ce
s
s
.
Simu
latio
n
r
esu
lts
s
h
o
ws
co
n
s
id
er
ab
le
r
ed
u
ctio
n
in
to
tal
co
s
t,
an
d
a
n
im
p
r
o
v
ed
s
o
cial
welf
ar
e
u
s
in
g
p
r
o
p
o
s
ed
s
im
u
ltan
eo
u
s
ap
p
r
o
ac
h
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
is
r
esear
ch
wo
r
k
was
f
u
n
d
e
d
by
“
W
o
o
s
o
n
g
Un
iv
e
r
s
ity
's
Aca
d
em
ic
R
esear
ch
Fu
n
d
in
g
-
2
02
1
”
.
RE
F
E
R
E
NC
E
S
[1
]
O.
D.
M
o
n
t
o
y
a
a
n
d
W.
G
.
G
o
n
z
á
lez
,
“
Dy
n
a
m
ic
a
c
ti
v
e
a
n
d
re
a
c
ti
v
e
p
o
we
r
c
o
m
p
e
n
sa
ti
o
n
i
n
d
istri
b
u
ti
o
n
n
e
two
rk
s
with
b
a
tt
e
ries
:
A
d
a
y
-
a
h
e
a
d
e
c
o
n
o
m
ic
d
is
p
a
tch
a
p
p
r
o
a
c
h
,
”
C
o
mp
u
t
e
rs
&
El
e
c
trica
l
E
n
g
in
e
e
rin
g
,
v
o
l
.
8
5
,
Ju
l
y
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
c
o
m
p
e
lec
e
n
g
.
2
0
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0
.
1
0
6
7
1
0
.
[2
]
N.
H.
Kh
a
n
,
Y.
Wan
g
,
D.
T
ian
,
M
.
A.
Z.
Ra
ja,
R.
Ja
m
a
l,
a
n
d
Y.
M
u
h
a
m
m
a
d
,
“
De
sig
n
o
f
F
ra
c
ti
o
n
a
l
P
a
rti
c
le
S
wa
rm
Op
ti
m
iza
ti
o
n
G
ra
v
it
a
ti
o
n
a
l
S
e
a
rc
h
Alg
o
rit
h
m
fo
r
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
we
r
Disp
a
tch
P
ro
b
lem
s,”
IEE
E
Acc
e
ss
,
v
o
l.
8
,
p
p
.
1
4
6
7
8
5
-
1
4
6
8
0
6
,
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g
.
2
0
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0
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o
i:
1
0
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1
1
0
9
/ACCE
S
S
.
2
0
2
0
.
3
0
1
4
2
1
1
.
[3
]
T.
Di
n
g
,
S
.
Li
u
,
W.
Yu
a
n
,
Z
.
B
i
e
,
a
n
d
B.
Zen
g
,
“
A
Two
-
S
tag
e
R
o
b
u
st
Re
a
c
ti
v
e
P
o
we
r
O
p
ti
m
iza
ti
o
n
Co
n
sid
e
rin
g
Un
c
e
rtain
Wi
n
d
P
o
we
r
In
teg
ra
ti
o
n
in
Ac
ti
v
e
Distri
b
u
t
io
n
Ne
two
rk
s
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
u
sta
i
n
a
b
le
En
e
rg
y
,
v
o
l.
7
,
n
o
.
1
,
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p
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-
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1
1
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n
.
2
0
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6
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0
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1
1
0
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S
TE
.
2
0
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5
.
2
4
9
4
5
8
7
.
[4
]
J.
Li
u
,
Y.
C
h
e
n
,
C.
D
u
a
n
,
J.
Li
n
,
a
n
d
J
.
Ly
u
,
“
Distrib
u
ti
o
n
a
ll
y
Ro
b
u
st
O
p
ti
m
a
l
Re
a
c
ti
v
e
P
o
we
r
Disp
a
tch
with
Was
se
rste
in
Dista
n
c
e
in
Ac
ti
v
e
D
istri
b
u
t
io
n
Ne
two
r
k
,
”
J
o
u
rn
a
l
o
f
M
o
d
e
rn
P
o
we
r
S
y
ste
ms
a
n
d
Cle
a
n
E
n
e
rg
y
,
v
o
l.
8
,
n
o
.
3
,
p
p
.
4
2
6
-
4
3
6
,
M
a
y
2
0
2
0
,
d
o
i:
1
0
.
3
5
8
3
3
/
M
P
CE.
2
0
1
9
.
0
0
0
5
7
.
[5
]
H.
G
a
o
,
J.
Li
u
,
a
n
d
L.
Wan
g
,
“
Ro
b
u
st
C
o
o
r
d
in
a
ted
Op
t
imiz
a
ti
o
n
o
f
Ac
ti
v
e
a
n
d
Re
a
c
ti
v
e
P
o
we
r
in
Ac
ti
v
e
Distrib
u
ti
o
n
S
y
ste
m
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
m
a
rt
Gr
id
,
v
o
l.
9
,
n
o
.
5
,
p
p
.
4
4
3
6
-
4
4
4
7
,
S
e
p
t.
2
0
1
8
,
d
o
i:
1
0
.
1
1
0
9
/T
S
G
.
2
0
1
7
.
2
6
5
7
7
8
2
.
[6
]
Z.
Li
,
J.
Wan
g
,
H.
S
u
n
,
F
.
Qiu
,
a
n
d
Q.
G
u
o
,
“
R
o
b
u
st
E
stim
a
ti
o
n
o
f
Re
a
c
ti
v
e
P
o
we
r
fo
r
a
n
Ac
ti
v
e
Distrib
u
ti
o
n
S
y
ste
m
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
P
o
we
r
S
y
ste
ms
,
v
o
l.
3
4
,
n
o
.
5
,
p
p
.
3
3
9
5
-
3
4
0
7
,
S
e
p
t.
2
0
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9
,
d
o
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1
0
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0
9
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P
WRS
.
2
0
1
9
.
2
9
0
2
1
3
6
.
[7
]
S
.
M
u
g
e
m
a
n
y
i,
Z
.
Q
u
,
F
.
X.
Ru
g
e
m
a
,
Y.
Do
n
g
,
C.
Ba
n
a
n
e
z
a
,
a
n
d
L.
Wan
g
,
“
Op
t
ima
l
Re
a
c
ti
v
e
P
o
we
r
Disp
a
tch
Us
in
g
Ch
a
o
ti
c
Ba
t
Al
g
o
rit
h
m
,
”
IEE
E
Acc
e
ss
,
v
o
l.
8
,
p
p
.
6
5
8
3
0
-
6
5
8
6
7
,
2
0
2
0
.
[8
]
M
.
Alra
m
law
i,
E.
M
o
h
a
g
h
e
g
h
i,
P
.
Li
,
“
P
re
d
ictiv
e
a
c
t
iv
e
-
re
a
c
ti
v
e
o
p
t
ima
l
p
o
we
r
d
isp
a
tch
i
n
P
V
-
b
a
tt
e
ry
-
d
ies
e
l
m
icro
g
rid
c
o
n
si
d
e
rin
g
re
a
c
ti
v
e
p
o
we
r
a
n
d
b
a
tt
e
ry
li
fe
ti
m
e
c
o
sts,”
S
o
l
a
r
E
n
e
rg
y
,
v
o
l.
1
9
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,
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p
.
5
2
9
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.
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0
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o
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/j
.
s
o
len
e
r.
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0
1
9
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0
9
.
0
3
4
.
[9
]
R.
H.
Li
a
n
g
,
J.
C.
Wan
g
,
Y.
T
.
C
h
e
n
,
a
n
d
W.
T.
Tse
n
g
,
“
An
e
n
h
a
n
c
e
d
firefl
y
a
l
g
o
r
it
h
m
to
m
u
lt
i
-
o
b
jec
ti
v
e
o
p
t
ima
l
a
c
ti
v
e
/rea
c
ti
v
e
p
o
we
r
d
is
p
a
tch
wi
t
h
u
n
c
e
rtain
ti
e
s
c
o
n
si
d
e
ra
ti
o
n
,
”
I
n
t
e
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
P
o
we
r
&
E
n
e
rg
y
S
y
ste
ms
,
v
o
l.
6
4
,
p
p
.
1
0
8
8
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1
0
9
7
,
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n
.
2
0
1
5
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d
o
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1
0
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0
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ij
e
p
e
s.2
0
1
4
.
0
9
.
0
0
8
.
[1
0
]
N.
Wan
g
,
J.
Li
,
X.
Y
u
,
D.
Zh
o
u
,
W.
Hu
,
Q.
Hu
a
n
g
,
Z.
C
h
e
n
,
a
n
d
F
.
Blaa
b
jerg
,
“
Op
ti
m
a
l
a
c
ti
v
e
a
n
d
re
a
c
ti
v
e
p
o
we
r
c
o
o
p
e
ra
ti
v
e
d
isp
a
tch
stra
teg
y
o
f
win
d
fa
rm
c
o
n
si
d
e
rin
g
lev
e
li
se
d
p
ro
d
u
c
ti
o
n
c
o
s
t
m
in
imiz
a
ti
o
n
,
”
Re
n
e
wa
b
le
E
n
e
rg
y
,
v
o
l.
1
4
8
,
p
p
.
1
1
3
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2
3
,
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r.
2
0
2
0
,
d
o
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:
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0
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0
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6
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.
re
n
e
n
e
.
2
0
1
9
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1
2
.
0
2
2
.
[1
1
]
O.
Ga
n
d
h
i,
W
.
Zh
a
n
g
,
C.
D.
R.
Ga
ll
e
g
o
s,
H.
Ve
rb
o
is,
H.
S
u
n
,
T.
Re
in
d
l,
a
n
d
D.
S
ri
n
iv
a
sa
n
,
“
Lo
c
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tc
h
o
p
ti
m
isa
ti
o
n
m
in
imis
in
g
g
lo
b
a
l
o
b
jec
ti
v
e
s,
”
Ap
p
li
e
d
E
n
e
rg
y
,
v
o
l.
2
6
2
,
M
a
r.
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
a
p
e
n
e
rg
y
.
2
0
2
0
.
1
1
4
5
2
9
.
[1
2
]
M
.
Ha
sh
e
m
i
a
n
d
M
.
H.
Zarif
,
“
A
n
o
v
e
l
h
iera
rc
h
ica
l
d
istri
b
u
ted
fra
m
e
wo
rk
fo
r
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tc
h
b
a
se
d
o
n
a
sy
ste
m
o
f
sy
ste
m
s
stru
c
tu
re
,
”
Co
mp
u
ter
s
&
El
e
c
trica
l
En
g
i
n
e
e
rin
g
,
v
o
l
.
7
8
,
p
p
.
1
6
2
-
1
8
3
,
S
e
p
t.
2
0
1
9
,
d
o
i:
1
0
.
1
0
1
6
/j
.
c
o
m
p
e
lec
e
n
g
.
2
0
1
9
.
0
7
.
0
0
2
.
[1
3
]
P.
P
.
B
iswa
s,
P
.
N.
S
u
g
a
n
t
h
a
n
,
R.
M
a
ll
i
p
e
d
d
i,
a
n
d
G.
A.
J.
Am
a
ra
tu
n
g
a
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
wit
h
u
n
c
e
rtain
ti
e
s
in
l
o
a
d
d
e
m
a
n
d
a
n
d
re
n
e
wa
b
le
e
n
e
rg
y
s
o
u
rc
e
s
a
d
o
p
ti
n
g
sc
e
n
a
rio
-
b
a
se
d
a
p
p
ro
a
c
h
,
”
Ap
p
li
e
d
S
o
ft
Co
mp
u
t
in
g
,
v
o
l
.
7
5
,
p
p
.
6
1
6
-
6
3
2
,
F
e
b
.
2
0
1
9
,
d
o
i:
1
0
.
1
0
1
6
/
j.
a
so
c
.
2
0
1
8
.
1
1
.
0
4
2
.
[1
4
]
S.
S
.
Re
d
d
y
,
A.
R.
Ab
h
y
a
n
k
a
r,
a
n
d
P.
R.
Bij
we
,
“
Re
a
c
ti
v
e
P
o
we
r
P
rice
Clea
rin
g
u
sin
g
M
u
lt
i
-
Ob
jec
ti
v
e
Op
ti
m
iza
ti
o
n
,”
En
e
rg
y
,
v
o
l.
3
6
,
n
o
.
5
,
p
p
.
3
5
7
9
-
3
5
8
9
,
M
a
y
2
0
1
1
,
d
o
i
:
1
0
.
1
0
1
6
/j
.
e
n
e
rg
y
.
2
0
1
1
.
0
3
.
0
7
0
.
[1
5
]
S.
R.
S
a
l
k
u
ti
,
“
M
u
lt
i
-
O
b
jec
ti
v
e
b
a
se
d
Op
ti
m
a
l
En
e
rg
y
a
n
d
Re
a
c
ti
v
e
P
o
we
r
Disp
a
tch
i
n
De
re
g
u
l
a
ted
El
e
c
tri
c
it
y
M
a
rk
e
ts
,”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
En
g
i
n
e
e
rin
g
,
v
o
l.
8
,
n
o
.
5
,
p
p
.
3
4
2
7
-
3
4
3
5
.
Oc
t.
2
0
1
8
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
e
c
e
.
v
8
i
5
.
p
p
3
4
2
7
-
3
4
3
5
.
[1
6
]
M
.
Lak
sh
m
i,
a
n
d
A.
R.
Ku
m
a
r,
“
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
we
r
Disp
a
t
c
h
u
sin
g
Cro
w
S
e
a
rc
h
Alg
o
rit
h
m
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l.
8
,
n
o
.
3
,
p
p
.
1
4
2
3
-
1
4
3
1
.
J
u
n
.
2
0
1
8
,
d
o
i:
1
0
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1
1
5
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1
/
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c
e
.
v
8
i
3
.
p
p
1
4
2
3
-
1
4
3
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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1387
[1
7
]
P.
L.
Re
d
d
y
a
n
d
G
.
Ye
su
ra
tn
a
m
,
“
A
m
o
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ifi
e
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c
teria
l
fo
ra
g
in
g
a
l
g
o
rit
h
m
b
a
se
d
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
,
”
In
d
o
n
e
sia
n
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
,
v
o
l.
1
3
,
n
o
.
1
,
p
p
.
3
6
1
-
3
6
7
,
Ja
n
.
2
0
1
9
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
e
e
c
s.v
1
3
.
i1
.
p
p
3
6
1
-
3
6
7
.
[1
8
]
S.
R.
S
a
lk
u
ti
,
“
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
we
r
S
c
h
e
d
u
l
in
g
Us
in
g
C
u
c
k
o
o
S
e
a
rc
h
Al
g
o
ri
th
m
,”
I
n
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l.
7
,
n
o
.
5
,
p
p
.
2
3
4
9
-
2
3
5
6
.
Oc
t.
2
0
1
7
,
d
o
i
:
1
0
.
1
1
5
9
1
/
ij
e
c
e
.
v
7
i5
.
p
p
2
3
4
9
-
2
3
5
6
.
[1
9
]
S.
R.
S
a
lk
u
ti
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
siz
in
g
i
n
a
d
istri
b
u
ted
n
e
t
wo
rk
,”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
En
g
i
n
e
e
rin
g
&
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
7
,
n
o
.
4
,
p
p
.
3
3
1
2
-
3
3
1
6
,
Ja
n
.
2
0
1
8
,
d
o
i:
1
0
.
1
4
4
1
9
/
ij
e
t.
v
7
i4
.
1
9
5
3
0
.
[2
0
]
H.
V.
Tran
,
e
t
a
l
.,
“
F
in
d
in
g
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tc
h
so
l
u
t
io
n
s
b
y
u
si
n
g
a
n
o
v
e
l
im
p
ro
v
e
d
sto
c
h
a
stic
fra
c
tal
se
a
rc
h
o
p
ti
m
iza
ti
o
n
a
l
g
o
r
it
h
m
,
”
T
EL
KOM
NIKA
T
e
lec
o
mm
u
n
ica
ti
o
n
Co
mp
u
ti
n
g
El
e
c
tro
n
ics
a
n
d
C
o
n
tro
l
,
v
o
l.
1
7
,
n
o
.
5
,
p
p
.
2
5
1
7
-
2
5
2
6
,
Oc
t.
2
0
1
9
,
d
o
i:
1
0
.
1
2
9
2
8
/
telk
o
m
n
ik
a
.
v
1
7
i5
.
1
0
7
6
7
.
[2
1
]
F
.
Lao
u
a
fi,
A.
Bo
u
k
a
d
o
u
m
,
a
n
d
S
.
Leu
lmi
,
“
A
Hy
b
rid
F
o
rm
u
lati
o
n
b
e
twe
e
n
Diffe
re
n
ti
a
l
Ev
o
lu
ti
o
n
a
n
d
S
im
u
late
d
An
n
e
a
li
n
g
Alg
o
rit
h
m
s
fo
r
O
p
ti
m
a
l
Re
a
c
ti
v
e
P
o
we
r
Disp
a
tch
,
”
T
EL
KOM
NIKA
T
e
lec
o
mm
u
n
ica
ti
o
n
C
o
mp
u
ti
n
g
El
e
c
tro
n
ics
a
n
d
C
o
n
tro
l
,
v
o
l.
1
6
,
n
o
.
2
,
p
p
.
5
1
3
-
5
2
4
,
A
p
r.
2
0
1
8
,
d
o
i:
1
0
.
1
2
9
2
8
/
telk
o
m
n
ik
a
.
v
1
6
i3
.
8
4
3
4
.
[2
2
]
S.
S
.
Re
d
d
y
,
A.
R
.
A
b
h
y
a
n
k
a
r,
a
n
d
P.
R.
Bij
we
,
“
Op
ti
m
a
l
d
a
y
-
a
h
e
a
d
jo
i
n
t
En
e
r
g
y
a
n
d
Re
a
c
ti
v
e
P
o
we
r
S
c
h
e
d
u
li
n
g
with
v
o
l
tag
e
d
e
p
e
n
d
e
n
t
l
o
a
d
m
o
d
e
ls,
”
IEE
E
T
ra
n
sp
o
rta
ti
o
n
El
e
c
t
rifi
c
a
ti
o
n
C
o
n
fer
e
n
c
e
a
n
d
Exp
o
,
Asia
-
Pa
c
if
ic
(IT
EC
Asia
-
Pa
c
if
ic)
,
2
0
1
6
,
p
p
.
1
9
8
-
2
0
2
,
d
o
i:
1
0
.
1
1
0
9
/IT
EC
-
AP
.
2
0
1
6
.
7
5
1
2
9
4
7
.
[2
3
]
M.
N.
G
il
v
a
e
i,
H.
Ja
fa
ri,
M
.
J.
G
h
a
d
i,
a
n
d
L.
Li
,
“
A
n
o
v
e
l
h
y
b
ri
d
o
p
ti
m
iza
ti
o
n
a
p
p
ro
a
c
h
fo
r
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
p
ro
b
lem
c
o
n
si
d
e
rin
g
v
o
l
tag
e
sta
b
i
li
ty
in
d
e
x
,
”
En
g
in
e
e
rin
g
A
p
p
l
ica
ti
o
n
s
o
f
Arti
fi
c
i
a
l
I
n
telli
g
e
n
c
e
,
v
o
l.
9
6
,
No
v
.
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
e
n
g
a
p
p
a
i.
2
0
2
0
.
1
0
3
9
6
3
.
[2
4
]
S.
S
.
Re
d
d
y
,
A.
R
.
Ab
h
y
a
n
k
a
r,
a
n
d
P.
R.
Bi
jwe
,
“
M
a
rk
e
t
Clea
rin
g
o
f
Jo
i
n
t
E
n
e
rg
y
a
n
d
Re
a
c
ti
v
e
P
o
we
r
u
sin
g
M
u
l
ti
Ob
jec
ti
v
e
Op
ti
m
iza
ti
o
n
c
o
n
sid
e
ri
n
g
Vo
lt
a
g
e
De
p
e
n
d
e
n
t
Lo
a
d
M
o
d
e
ls
,
”
IEE
E
P
o
we
r
a
n
d
E
n
e
rg
y
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
,
p
p
.
1
-
8
,
Ju
l.
2
0
1
1
,
d
o
i
:
1
0
.
1
1
0
9
/P
E
S
.
2
0
1
1
.
6
0
3
9
6
5
2
.
[2
5
]
M
.
Wan
g
,
A.
A.
He
id
a
ri,
M
.
Ch
e
n
,
H.
Ch
e
n
,
X.
Z
h
a
o
,
a
n
d
X.
Ca
i,
“
E
x
p
l
o
ra
to
r
y
d
iffere
n
ti
a
l
a
n
t
li
o
n
-
b
a
se
d
o
p
ti
m
iza
ti
o
n
,”
Exp
e
rt
S
y
ste
ms
wit
h
Ap
p
li
c
a
ti
o
n
s
,
v
o
l.
1
5
9
,
No
v
.
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/
j.
e
sw
a
.
2
0
2
0
.
1
1
3
5
4
8
.
[2
6
]
M
.
Wan
g
,
X.
Zh
a
o
,
A.
A.
He
id
a
ri,
a
n
d
H.
Ch
e
n
,
“
Ev
a
l
u
a
ti
o
n
o
f
c
o
n
stra
in
t
i
n
p
h
o
to
v
o
l
taic
m
o
d
e
ls
b
y
e
x
p
lo
it
in
g
a
n
e
n
h
a
n
c
e
d
a
n
t
li
o
n
o
p
t
imiz
e
r
,
”
S
o
l
a
r E
n
e
rg
y
,
v
o
l.
2
1
1
,
p
p
.
5
0
3
-
5
2
1
,
No
v
.
2
0
2
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
so
len
e
r
.
2
0
2
0
.
0
9
.
0
8
0
.
[2
7
]
J.
Wan
g
a
,
P
.
D
u
a
,
H.
L
u
b
,
W.
Ya
n
g
a
,
a
n
d
T.
Niu
,
“
An
imp
r
o
v
e
d
g
re
y
m
o
d
e
l
o
p
ti
m
ize
d
b
y
m
u
lt
i
-
o
b
j
e
c
ti
v
e
a
n
t
li
o
n
o
p
ti
m
iza
ti
o
n
a
l
g
o
ri
th
m
f
o
r
a
n
n
u
a
l
e
lec
tri
c
it
y
c
o
n
s
u
m
p
ti
o
n
fo
r
e
c
a
stin
g
,”
Ap
p
li
e
d
S
o
ft
Co
m
p
u
ti
n
g
,
v
o
l
.
7
2
,
p
p
.
3
2
1
-
3
3
7
,
No
v
.
2
0
1
8
,
d
o
i:
1
0
.
1
0
1
6
/j
.
a
so
c
.
2
0
1
8
.
0
7
.
0
2
2
.
[2
8
]
M.
J.
H.
M
o
g
h
a
d
d
a
m
,
S
.
A.
N
o
wd
e
h
,
M
.
Big
d
e
li
,
D.
Az
izia
n
,
“
A
m
u
lt
i
-
o
b
jec
ti
v
e
o
p
ti
m
a
l
siz
i
n
g
a
n
d
siti
n
g
o
f
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
u
si
n
g
a
n
t
li
o
n
o
p
ti
m
iza
ti
o
n
tec
h
n
iq
u
e
,”
Ai
n
S
h
a
ms
E
n
g
i
n
e
e
rin
g
J
o
u
rn
a
l
,
v
o
l.
9
,
n
o
.
4
,
p
p
.
2
1
0
1
-
2
1
0
9
,
De
c
.
2
0
1
8
,
d
o
i
:
1
0
.
1
0
1
6
/j
.
a
se
j.
2
0
1
7
.
0
3
.
0
0
1
.
[2
9
]
H.
M
.
Du
b
e
y
,
M
.
P
a
n
d
it
,
a
n
d
B.
K.
P
a
n
i
g
ra
h
i
,
“
Hy
d
ro
-
t
h
e
r
m
a
l
-
win
d
sc
h
e
d
u
li
n
g
e
m
p
lo
y
in
g
n
o
v
e
l
a
n
t
l
io
n
o
p
ti
m
iza
ti
o
n
tec
h
n
i
q
u
e
wit
h
c
o
m
p
o
site
ra
n
k
i
n
g
in
d
e
x
,”
Ren
e
wa
b
le
En
e
rg
y
,
v
o
l.
9
9
,
De
c
.
2
0
1
6
,
d
o
i:
1
0
.
1
0
1
6
/j
.
re
n
e
n
e
.
2
0
1
6
.
0
6
.
0
3
9
.
[3
0
]
M
.
Ba
su
,
“
M
u
lt
i
-
o
b
jec
ti
v
e
o
p
t
ima
l
re
a
c
ti
v
e
p
o
we
r
d
is
p
a
tch
u
sin
g
m
u
lt
i
-
o
b
jec
ti
v
e
d
iffere
n
ti
a
l
e
v
o
lu
ti
o
n
,”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
8
2
,
p
p
.
2
1
3
-
2
2
4
,
No
v
.
2
0
1
6
,
d
o
i:
1
0
.
1
0
1
6
/j
.
ij
e
p
e
s.2
0
1
6
.
0
3
.
0
2
4
.
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