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I
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pp
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3435
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),
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d
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m
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a
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d
v
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a
g
e
sta
b
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it
y
e
n
h
a
n
c
e
m
e
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t
in
d
e
x
(V
S
EI)
;
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n
d
t
h
e
se
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jec
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v
e
s ca
n
b
e
c
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m
b
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d
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s
p
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th
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it
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sim
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I
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8
,
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5
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Octo
b
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3
4
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7
–
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4
3
5
3428
(
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R
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e
n
ce
[
1
]
p
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p
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s
es
a
n
e
w
s
tr
u
ctu
r
e
f
o
r
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lt
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tain
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g
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ter
ac
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ti
v
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(
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o
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ith
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f
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p
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atilit
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p
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p
o
s
ed
in
[
2
]
.
R
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en
ce
[
3
]
p
r
o
p
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s
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d
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ased
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o
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ti
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p
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f
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co
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p
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p
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w
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a
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x
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n
d
t
h
e
lo
s
s
e
s
o
f
ac
ti
v
e
p
o
w
er
ar
e
m
i
n
i
m
ized
.
R
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en
ce
[
4
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d
ea
ls
w
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h
t
h
e
o
b
tai
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in
g
,
d
ec
o
m
p
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s
itio
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d
d
ed
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ctio
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o
f
b
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r
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f
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an
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o
n
e
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tab
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h
ed
co
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tr
ac
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s
h
ip
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u
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ar
k
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m
en
t
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ase
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k
et
s
tr
u
ctu
r
e
i
s
p
r
ese
n
ted
in
[
5
]
to
i
m
p
r
o
v
e
th
e
r
ea
ctiv
e
p
o
w
er
m
ar
k
et
an
d
cr
ea
te
f
air
co
m
p
et
itio
n
b
etw
ee
n
p
r
o
d
u
ce
r
s
.
An
e
f
f
icie
n
t
s
to
ch
asti
c
f
r
a
m
e
w
o
r
k
to
d
ev
elo
p
a
co
u
p
led
ac
ti
v
e
an
d
r
ea
ctiv
e
m
ar
k
et
i
n
s
m
ar
t
d
is
tr
ib
u
tio
n
s
y
s
te
m
s
is
p
r
o
p
o
s
ed
in
[
6
]
.
R
ef
er
en
ce
[
7
]
p
r
ese
n
ts
a
n
alg
o
r
it
h
m
f
o
r
p
r
o
cu
r
in
g
r
ea
ctiv
e
p
o
w
er
f
r
o
m
r
ea
ctiv
e
r
eso
u
r
ce
s
b
ased
o
n
a
r
ea
ctiv
e
p
o
w
er
p
r
icin
g
s
tr
u
ctu
r
e.
R
ef
er
e
n
ce
[
8
]
p
r
o
p
o
s
es
t
w
o
n
e
w
ac
ti
v
e/r
ea
ct
iv
e
d
is
p
atch
m
o
d
els
to
b
e
u
s
e
d
b
y
S
y
s
te
m
Op
er
ato
r
s
in
o
r
d
er
to
ass
ig
n
r
ea
ctiv
e
p
o
w
er
an
d
to
v
a
lid
ate
t
h
e
ec
o
n
o
m
ic
s
ch
ed
u
les
p
r
ep
ar
ed
b
y
Ma
r
k
et
Op
er
ato
r
s
to
g
et
h
er
w
it
h
t
h
e
i
n
j
ec
tio
n
s
r
elate
d
w
it
h
b
ilater
al
co
n
tr
ac
ts
.
A
d
eter
m
in
is
tic
m
o
d
el
o
f
co
m
p
lete
g
en
er
atio
n
-
g
r
id
s
y
s
te
m
to
o
b
tain
th
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
s
p
o
t
p
r
ices
an
d
th
eir
d
ec
o
m
p
o
s
itio
n
,
to
d
ed
u
ce
g
en
er
al
r
u
les
co
n
ce
r
n
i
n
g
t
h
eir
b
eh
a
v
io
u
r
,
an
d
to
an
al
y
ze
th
e
e
f
f
ec
t
o
f
th
e
ap
p
lied
co
n
s
tr
ain
t
s
is
p
r
o
p
o
s
ed
in
[
9
]
.
A
n
e
w
p
r
o
b
ab
il
is
tic
alg
o
r
it
h
m
f
o
r
o
p
tim
a
l r
ea
ctiv
e
p
o
w
er
p
r
o
v
is
i
o
n
in
h
y
b
r
id
elec
tr
icit
y
m
ar
k
e
t
s
is
p
r
o
p
o
s
ed
in
R
ef
er
en
ce
[
1
0
]
.
T
h
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
m
o
d
el
s
u
s
ed
b
y
t
h
e
I
SOs
to
as
s
i
g
n
t
h
e
r
ea
cti
v
e
p
o
w
er
a
n
d
to
v
alid
ate
t
h
e
ec
o
n
o
m
ic
s
c
h
ed
u
les
p
r
ep
ar
ed
b
y
t
h
e
m
ar
k
et
o
p
er
ato
r
s
w
it
h
b
ilater
al
co
n
tr
a
cts
i
s
d
escr
ib
ed
i
n
R
ef
er
e
n
ce
[
1
1
]
.
A
m
u
lti
-
o
b
j
e
ctiv
e
b
ased
d
a
y
-
a
h
ea
d
r
ea
cti
v
e
p
o
w
er
m
ar
k
e
t
clea
r
i
n
g
m
o
d
el
is
p
r
o
p
o
s
ed
in
R
ef
er
e
n
ce
[
1
2
]
.
A
jo
in
ed
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
m
ar
k
et
clea
r
in
g
i
n
th
e
r
estr
u
ct
u
r
ed
elec
tr
ica
l
s
y
s
te
m
s
is
p
r
esen
ted
in
R
e
f
er
en
ce
[
1
3
]
.
I
n
[
1
4
]
,
u
s
es
m
u
lt
i
-
o
b
j
ec
tiv
e
d
ir
ec
ted
b
e
e
co
lo
n
y
o
p
ti
m
i
za
tio
n
alg
o
r
it
h
m
to
o
p
tim
ize
t
h
e
co
m
b
i
n
ed
e
m
is
s
io
n
a
n
d
g
e
n
er
atio
n
co
s
t.
An
o
p
ti
m
al
r
ea
cti
v
e
p
o
w
er
s
c
h
ed
u
lin
g
p
r
o
b
le
m
i
n
r
estru
ct
u
r
ed
p
o
w
er
s
y
s
te
m
u
s
in
g
t
h
e
e
v
o
lu
tio
n
ar
y
b
ased
C
u
ck
o
o
Sear
c
h
A
l
g
o
r
ith
m
is
p
r
o
p
o
s
ed
in
[
1
5
]
.
A
m
eta
-
h
e
u
r
is
tic
b
ased
ap
p
r
o
ac
h
to
s
o
lv
e
th
e
Op
ti
m
al
R
ea
ct
iv
e
P
o
w
er
Di
s
p
atch
p
r
o
b
le
m
u
s
i
n
g
C
r
o
w
Sear
c
h
alg
o
r
ith
m
is
p
r
o
p
o
s
ed
in
[
1
6
]
.
Fro
m
t
h
e
liter
at
u
r
e
r
ev
ie
w
,
i
t
ca
n
b
e
o
b
s
er
v
ed
t
h
at
m
o
s
t
o
f
t
h
e
w
o
r
k
s
i
n
t
h
e
liter
at
u
r
e
d
o
esn
't
co
n
s
id
er
s
th
e
e
n
er
g
y
a
n
d
r
ea
ctiv
e
m
ar
k
ets,
s
i
m
u
lta
n
eo
u
s
l
y
.
T
h
er
ef
o
r
e,
th
e
m
o
ti
v
atio
n
o
f
th
is
p
ap
er
is
to
clea
r
th
e
m
ar
k
et
b
y
o
p
ti
m
izin
g
b
o
t
h
t
h
e
en
er
g
y
an
d
r
ea
cti
v
e
p
o
w
er
s
,
s
i
m
u
ltan
eo
u
s
l
y
,
a
n
d
co
n
s
id
er
in
g
t
h
e
v
o
lta
g
e
d
ep
en
d
en
t
lo
ad
m
o
d
eli
n
g
.
I
n
th
is
p
ap
er
,
it
is
co
n
s
id
er
ed
th
at
th
e
tr
ad
itio
n
al
s
i
n
g
le
o
b
j
ec
t
iv
es
s
u
c
h
as
So
cia
l
W
elf
ar
e
Ma
x
i
m
izatio
n
(
SW
M)
an
d
L
o
s
s
Mi
n
i
m
izatio
n
(
L
M)
o
b
j
ec
tiv
es
ar
e
n
o
t
f
ea
s
ib
le
w
i
th
v
o
ltag
e
d
ep
en
d
en
t
lo
ad
m
o
d
eli
n
g
d
u
e
to
th
e
r
ed
u
ctio
n
in
t
h
e
a
m
o
u
n
t
o
f
lo
ad
s
er
v
ed
(
L
S).
A
M
OO
is
r
eq
u
ir
ed
f
o
r
s
o
lv
i
n
g
t
h
e
p
r
o
b
le
m
s
o
f
t
h
i
s
k
i
n
d
.
2.
SE
P
ARA
T
E
ACT
I
V
E
AND
RE
AC
T
I
V
E
P
O
WE
R
M
AR
K
E
T
C
L
E
A
RIN
G
T
y
p
icall
y
,
t
h
e
m
ar
k
et
clea
r
i
n
g
p
r
o
b
lem
is
s
o
l
v
ed
b
y
t
h
e
s
y
s
t
e
m
o
p
er
ato
r
to
k
n
o
w
th
e
ac
ce
p
ted
o
f
f
er
s
an
d
b
id
s
an
d
th
e
r
es
u
lti
n
g
Ma
r
k
et
C
lear
i
n
g
P
r
ice
(
MCP
)
.
2
.
1
.
Cent
ra
lized
s
epa
ra
t
e
ener
g
y
m
a
r
k
et
T
h
e
co
n
ce
p
t
o
f
s
o
c
ial
w
el
f
ar
e
m
a
x
i
m
izatio
n
(
SW
M)
ca
n
b
e
ap
p
lied
f
o
r
th
e
ce
n
tr
alize
d
elec
tr
ici
t
y
m
ar
k
et
w
it
h
d
e
m
a
n
d
ela
s
ticit
y
.
T
h
e
s
o
cial
w
elf
ar
e
(
SW
)
is
t
h
e
to
tal
s
u
r
p
l
u
s
o
f
g
e
n
er
ato
r
s
an
d
cu
s
to
m
er
s
.
T
h
e
s
y
s
te
m
o
p
er
ato
r
s
o
lv
es t
h
e
S
W
M
[
1
7
]
o
b
j
ec
tiv
e
f
u
n
ctio
n
,
a
n
d
it is
f
o
r
m
u
lated
as,
[
∑
(
)
∑
(
)
]
(
1
)
W
h
er
e
(
)
(
2
)
(
)
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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p
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I
SS
N:
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0
8
8
-
8708
M
u
lti
-
Ob
jective
b
a
s
ed
Op
ti
ma
l E
n
erg
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a
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d
R
ea
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P
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w
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p
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tch
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(
S
u
r
en
d
er R
ed
d
y
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a
lku
ti
)
3429
2
.
2
.
Rea
ct
iv
e
po
w
er
m
a
r
k
et
clea
ring
T
h
e
s
y
n
c
h
r
o
n
o
u
s
g
en
er
ato
r
'
s
ca
p
ab
ilit
y
cu
r
v
e
[
1
8
]
co
n
s
is
t
s
o
f
3
o
p
er
atin
g
r
eg
io
n
s
.
T
h
es
e
r
eg
io
n
s
r
ef
lect
th
e
ar
m
at
u
r
e,
f
ield
cu
r
r
en
t h
ea
t
in
g
s
a
n
d
th
e
u
n
d
er
-
ex
c
itatio
n
li
m
it
s
.
2
.
2
.
1
.
Rea
ct
iv
e
po
w
er
bid
s
t
ruct
ur
e
Si
m
i
lar
to
th
e
r
ea
l
p
o
w
er
,
s
y
n
c
h
r
o
n
o
u
s
g
en
er
ato
r
s
b
id
s
f
o
r
th
e
r
ea
ctiv
e
p
o
w
er
[
1
8
]
.
T
h
ese
b
id
s
co
n
s
is
t
o
f
a
ca
p
ac
it
y
co
m
p
o
n
e
n
t
w
h
ic
h
i
s
p
aid
i
n
ad
v
an
ce
f
o
r
th
eir
r
ea
d
in
e
s
s
to
ab
s
o
r
b
/
p
r
o
d
u
ce
th
e
r
ea
cti
v
e
p
o
w
er
.
E
x
p
ec
ted
P
ay
m
e
n
t
Fu
n
ctio
n
(
E
P
F)
:
T
h
e
r
ea
ctiv
e
p
o
w
er
p
a
y
m
en
t
o
f
g
e
n
er
ato
r
s
co
n
s
i
s
ts
o
f
d
if
f
er
en
t
co
s
t
co
m
p
o
n
en
t
s
d
ep
en
d
in
g
u
p
o
n
th
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p
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atin
g
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e
g
io
n
s
.
E
P
F
is
a
m
at
h
e
m
a
tical
f
o
r
m
u
latio
n
o
f
g
en
er
ato
r
r
ea
ctiv
e
p
o
w
er
co
s
t
co
m
p
o
n
en
ts
o
f
g
e
n
er
ato
r
’
s
e
x
p
ec
tati
o
n
o
f
p
a
y
m
en
t
to
w
ar
d
s
u
tili
za
tio
n
,
ca
p
ac
it
y
an
d
co
m
p
e
n
s
at
io
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m
p
o
n
e
n
t
s
.
Fi
g
u
r
e
1
d
e
p
icts
th
e
E
P
F
o
f
a
g
e
n
er
atin
g
u
n
i
t,
as
a
f
u
n
ctio
n
o
f
a
m
o
u
n
t
o
f
r
ea
cti
v
e
p
o
w
er
o
u
tp
u
t.
T
h
e
ter
m
s
o
f
E
P
F i.
e.
,
o
p
p
o
r
tu
n
it
y
co
s
t,
co
s
t
o
f
lo
s
s
ar
e
p
r
esen
ted
in
R
ef
er
e
n
ce
[
1
8
]
.
E
P
F
Q
m
i
n
Q
B
a
s
e
0
Q
B
Q
A
a
0
m
2
m
3
Q
m
1
O
p
p
o
r
t
u
n
i
t
y
C
o
s
t
C
o
s
t
o
f
L
o
s
s
A
v
a
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l
a
b
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l
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t
y
C
o
s
t
R
e
g
i
o
n
-
I
R
e
g
i
o
n
-
I
I
R
e
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i
o
n
-
I
I
I
Fig
u
r
e
1
.
Stru
ct
u
r
e
o
f
r
ea
ctiv
e
p
o
w
er
o
f
f
er
s
f
r
o
m
t
h
e
g
e
n
er
ati
n
g
u
n
its
Fig
u
r
e
1
d
ep
icts
th
e
o
p
er
atin
g
r
eg
io
n
s
o
f
g
en
er
ato
r
o
n
th
e
r
ea
ctiv
e
p
o
w
er
co
o
r
d
in
ates
an
d
th
ese
r
eg
io
n
s
ar
e
clea
r
l
y
p
r
esen
ted
in
R
e
f
er
e
n
ce
[
1
9
]
.
T
h
e
ex
p
ec
ted
p
ay
m
e
n
t
f
u
n
ctio
n
(
E
P
F)
o
f
a
g
e
n
er
ato
r
is
ex
p
r
ess
ed
as,
∫
∫
∫
(
4
)
W
h
er
e
a
0
,
m
1
,
m
2
a
n
d
m
3
in
t
h
e
ab
o
v
e
eq
u
atio
n
r
ep
r
ese
n
t
d
if
f
er
e
n
t
co
m
p
o
n
e
n
t
s
o
f
r
ea
ct
iv
e
p
o
w
er
c
o
s
t
o
f
f
er
ed
b
y
t
h
e
g
en
er
ato
r
.
m
1
i
s
co
s
t
o
f
lo
s
s
p
r
ice
o
f
f
er
f
o
r
o
p
er
atio
n
in
th
e
u
n
d
er
-
ex
c
ited
m
o
d
e
(Q
m
in
≤
Q
≤
0
)
(
$
/Mv
ar
-
h
)
,
m
2
is
co
s
t
o
f
lo
s
s
p
r
ice
o
f
f
er
f
o
r
th
e
o
p
er
atin
g
in
r
eg
io
n
(
Q
base
≤
Q
≤
Q
A
)
in
(
$
/Mv
ar
-
h
)
,
an
d
m
3
is
o
p
p
o
r
t
u
n
i
t
y
p
r
ice
o
f
f
er
,
f
o
r
o
p
er
atin
g
i
n
r
e
g
io
n
(
Q
A
≤
Q
≤
Q
B
)
(
(
$
MV
ar
-
h
)
/MVa
r
-
h
)
.
T
h
e
T
o
tal
P
ay
m
e
n
t
F
u
n
ct
io
n
(
T
P
F)
is
ex
p
r
ess
ed
as
[
2
0
]
,
T
h
e
last
ter
m
in
eq
u
atio
n
5
r
ep
r
esen
ts
t
h
e
L
O
C
p
ay
m
e
n
t.
∑
[
(
)
(
)
(
(
)
)
]
(
5
)
3.
DE
S
I
G
N
O
F
CO
UP
L
E
D
A
CT
I
V
E
AND
R
E
AC
T
I
VE
P
O
WE
R
M
ARK
E
T
CL
E
AR
I
NG
I
n
th
i
s
s
ec
tio
n
,
d
if
f
er
en
t o
b
j
ec
tiv
e
f
u
n
ctio
n
s
f
o
r
th
e
co
u
p
led
AR
P
MC a
r
e
p
r
o
p
o
s
ed
.
3
.
1
.
L
o
s
s
o
pp
o
rt
un
it
y
co
s
t
(
L
O
C)
f
o
rm
ula
t
io
n
T
h
e
L
OC
o
f
a
g
e
n
er
ato
r
p
la
y
s
a
v
ital
r
o
le
in
t
h
e
r
ea
cti
v
e
p
o
w
er
s
ch
ed
u
lin
g
a
n
d
p
r
icin
g
[
1
9
]
.
T
o
u
s
e
th
e
L
O
C
in
E
q
u
atio
n
(
7
)
,
th
e
r
esu
lt
s
o
f
s
ep
ar
ate
en
er
g
y
d
is
p
atch
ar
e
r
eq
u
ir
ed
.
T
h
er
ef
o
r
e,
t
h
e
s
ep
ar
ate
en
er
g
y
d
is
p
atch
m
u
s
t
b
e
p
er
f
o
r
m
ed
b
ef
o
r
e
th
e
co
u
p
led
A
R
P
MC
p
r
o
b
lem
.
Her
e,
th
e
L
O
C
o
f
a
g
en
er
ato
r
,
w
h
ic
h
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
4
2
7
–
3
4
3
5
3430
f
o
r
ce
d
to
p
r
o
d
u
ce
th
e
r
ea
ctiv
e
p
o
w
er
,
ca
n
b
e
ex
p
r
ess
ed
as [
2
0
]
:
{
(
6
)
[
(
)
]
(
7
)
T
h
e
T
P
F
f
o
r
r
ea
ctiv
e
p
o
w
e
r
co
m
p
e
n
s
atio
n
i
n
co
u
p
led
AR
P
MC
co
n
s
is
t
s
o
n
l
y
o
p
er
atio
n
an
d
av
ailab
ilit
y
p
a
y
m
e
n
ts
[
1
8
]
,
an
d
th
is
ca
n
b
e
ex
p
r
es
s
ed
as,
∑
[
(
)
]
(
8
)
3
.
2
.
L
o
a
d
m
o
delin
g
Gen
er
all
y
,
t
h
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
lo
ad
s
ar
e
m
o
d
eled
as
th
e
co
n
s
ta
n
t
p
o
w
er
lo
ad
s
.
B
u
t,
th
e
y
ar
e
v
o
ltag
e
d
ep
en
d
en
t
[
2
1
]
i
n
th
e
p
r
ac
tical
r
ea
l
ti
m
e
o
p
er
atio
n
.
I
n
th
is
p
ap
er
,
f
o
r
th
e
s
ak
e
o
f
s
i
m
p
licit
y
,
ex
p
o
n
en
t
ial
lo
ad
d
em
a
n
d
m
o
d
el
is
u
s
ed
,
an
d
it c
an
b
e
ex
p
r
es
s
ed
as,
(
)
(
9
)
(
)
(
1
0
)
w
h
er
e
np
an
d
nq
ar
e
d
ep
en
d
o
n
co
m
p
o
s
it
io
n
an
d
t
y
p
e
o
f
t
h
e
lo
ad
d
em
an
d
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
s
co
n
s
id
er
ed
in
th
e
ce
n
tr
alize
d
DA
co
u
p
l
ed
AR
P
MC p
r
o
b
lem
ar
e
as f
o
llo
w
s
.
3
.
3
.
So
cia
l
w
elf
a
re
m
a
x
i
m
i
za
t
io
n (
SWM
)
in
c
o
up
led A
RP
M
C
I
n
t
h
is
p
ap
er
,
an
OP
F
b
ased
a
p
p
r
o
ac
h
is
u
s
ed
to
f
i
n
d
t
h
e
m
a
r
k
et
clea
r
i
n
g
p
r
ice
(
M
C
P
)
,
an
d
to
g
et
t
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
s
c
h
ed
u
le
s
th
at
s
ati
s
f
y
t
h
e
s
y
s
te
m
o
p
er
atio
n
r
eq
u
ir
e
m
e
n
t
s
.
I
n
co
u
p
led
A
R
P
MC
m
o
d
el,
th
e
o
b
j
ec
tiv
e
is
to
m
a
x
i
m
ize
s
o
cial
w
el
f
ar
e
(
SW
)
.
S
W
M
o
b
j
ec
tiv
e
f
u
n
ct
io
n
ca
n
b
e
f
o
r
m
u
lated
as
[
1
7
]
,
SW
M
is
an
i
m
p
o
r
tan
t o
b
j
ec
tiv
e
u
n
d
er
all
s
y
s
te
m
o
p
er
atin
g
co
n
d
itio
n
s
.
m
ax
i
m
ize,
∑
(
)
∑
(
)
∑
(
)
(
1
1
)
3
.
4
.
L
o
s
s
m
i
ni
m
i
za
t
io
n (
L
M
)
T
h
e
g
o
al
o
f
th
is
o
b
j
ec
tiv
e
is
to
f
in
d
th
e
o
p
ti
m
al
s
e
tti
n
g
s
o
f
co
n
tr
o
l
v
ar
iab
les
w
h
ic
h
r
esu
lt
in
o
p
tim
u
m
tr
an
s
m
is
s
io
n
lo
s
s
es.
T
h
e
L
M
o
b
j
ec
tiv
e
is
s
u
itab
le
o
n
l
y
f
o
r
th
e
co
n
s
ta
n
t
lo
ad
m
o
d
eli
n
g
at
lig
h
t
lo
ad
i
n
g
co
n
d
itio
n
.
I
f
lo
ad
d
e
m
a
n
d
s
ar
e
m
o
d
eled
as
v
o
lta
g
e
d
ep
en
d
e
n
t,
t
h
e
SW
M
an
d
L
M
o
b
j
ec
tiv
es
lead
to
t
h
e
lo
ad
s
er
v
ed
(
L
S)
r
ed
u
ctio
n
th
r
o
u
g
h
th
e
v
o
lta
g
e
r
ed
u
ctio
n
.
T
h
is
L
M
o
b
j
ec
tiv
e
is
ex
p
r
es
s
ed
as [
2
2
]
,
∑
*
(
(
)
)
+
(
1
2
)
3
.
5
.
A
m
o
un
t
o
f
lo
a
d serv
ed
m
a
x
i
m
i
za
t
io
n
(
L
SM
)
T
h
e
p
r
ac
tice,
th
e
lo
ad
d
e
m
an
d
s
ar
e
th
e
f
u
n
c
tio
n
o
f
v
o
ltag
e
s
,
th
er
e
f
o
r
e
th
e
v
o
lta
g
e
d
ep
en
d
en
t
lo
ad
m
o
d
eli
n
g
is
u
t
ilized
.
T
h
e
im
p
r
o
v
e
m
e
n
t
o
f
s
y
s
te
m
v
o
lta
g
es
i
n
cr
ea
s
es
t
h
e
a
m
o
u
n
t
o
f
lo
ad
s
er
v
ed
(
L
S).
Un
d
er
th
e
v
o
lta
g
e
d
ep
en
d
en
t
lo
ad
m
o
d
elin
g
,
th
e
L
SM
o
b
j
ec
tiv
e
is
ap
p
r
o
p
r
iate
at
lig
h
t
lo
ad
in
g
c
o
n
d
itio
n
s
,
an
d
it
is
f
o
r
m
u
lated
as
Eq
u
at
io
n
(
13
)
.
T
h
is
L
SM
o
b
j
ec
tiv
e
w
ill
n
ev
er
b
e
u
s
ed
as a
n
i
n
d
ep
en
d
en
t o
b
jectiv
e.
∑
(
)
(
1
3
)
3
.
6
.
Vo
lt
a
g
e
s
t
a
bil
it
y
enha
nce
m
e
nt
ind
ex
(
V
SE
I
)
T
o
m
o
n
ito
r
th
e
v
o
ltag
e
s
tab
ilit
y
in
t
h
e
s
y
s
te
m
,
L
-
i
n
d
ex
[
2
3
]
o
f
th
e
lo
ad
/d
e
m
a
n
d
b
u
s
e
s
is
c
o
n
s
id
er
ed
.
L
-
in
d
e
x
/V
SEI
u
s
e
s
th
e
i
n
f
o
r
m
atio
n
f
r
o
m
t
h
e
p
o
w
er
f
lo
w
an
d
is
i
n
th
e
r
a
n
g
e
o
f
0
(
n
o
lo
ad
)
to
1
(
v
o
ltag
e
co
llap
s
e)
.
L
-
i
n
d
ex
p
r
ese
n
ts
t
h
e
s
tab
ilit
y
o
f
co
m
p
lete
s
y
s
te
m
,
an
d
it is
ex
p
r
es
s
ed
as,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
M
u
lti
-
Ob
jective
b
a
s
ed
Op
ti
ma
l E
n
erg
y
a
n
d
R
ea
ctive
P
o
w
er
Dis
p
a
tch
…
(
S
u
r
en
d
er R
ed
d
y
S
a
lku
ti
)
3431
|
∑
|
(
1
4
)
∑
(
1
5
)
w
h
er
e
j
=
n
g
+
1
,
.
.
.
,
n
.
T
h
e
v
alu
e
s
o
f
F
ji
ar
e
ca
lcu
la
ted
f
r
o
m
t
h
e
Y
-
B
u
s
m
atr
i
x
[
1
8
]
.
I
n
th
e
ca
s
e
o
f
v
o
ltag
e
d
ep
en
d
en
t
lo
ad
m
o
d
elin
g
,
t
h
e
L
-
in
d
e
x
/VSEI
m
i
n
i
m
i
za
tio
n
o
b
j
ec
tiv
e
i
m
p
r
o
v
es
t
h
e
v
o
ltag
e
p
r
o
f
ile
o
f
th
e
s
y
s
te
m
a
n
d
h
en
ce
t
h
e
a
m
o
u
n
t o
f
lo
ad
s
er
v
ed
(
L
S).
3
.
7
.
E
qu
a
lity
a
nd
ine
qu
a
lity
co
ns
t
ra
ints f
o
r
t
he
co
up
le
d AR
P
M
C
p
ro
ble
m
3
.
7
.
1.
E
qu
a
lity
co
ns
t
ra
ints
T
h
e
n
o
d
al
p
o
w
er
b
alan
ce
co
n
s
tr
ain
t
s
in
cl
u
d
e
th
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
b
alan
ce
eq
u
at
io
n
s
.
T
h
e
y
ar
e
ex
p
r
ess
ed
as,
∑
[
(
)
]
(
1
6
)
∑
[
(
)
]
(
17)
3
.
7
.
2
.
G
ener
a
t
o
r
co
ns
t
ra
ints
T
h
e
g
en
er
ato
r
o
u
tp
u
ts
ar
e
li
m
i
ted
b
y
t
h
eir
m
i
n
i
m
u
m
a
n
d
m
a
x
i
m
u
m
ac
ti
v
e
p
o
w
er
o
u
tp
u
ts
a
s
,
[
]
[
]
(
1
8
)
Usi
n
g
t
h
e
r
ea
ctiv
e
p
o
w
er
o
f
f
er
s
f
r
o
m
t
h
e
g
e
n
er
ato
r
s
in
d
i
f
f
er
en
t
o
p
er
atin
g
r
eg
io
n
s
,
t
h
e
co
n
s
tr
ain
ts
ar
e
f
o
r
m
u
la
ted
as,
(
1
9
)
(
2
0
)
(
2
1
)
(
2
2
)
3
.
7
.
3
.
De
m
a
nd
li
m
it
s
(
2
3
)
(
2
4
)
3
.
7
.
4
.
Co
ns
t
ra
ints o
n M
CP
s
(
2
5
)
(
2
6
)
(
2
7
)
3
.
7
.
5
.
G
ener
a
t
o
r
re
a
ct
iv
e
po
w
er
co
ns
t
ra
ints
√
(
)
(
)
(
2
8
)
√
(
)
(
2
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
4
2
7
–
3
4
3
5
3432
T
h
e
m
i
n
i
m
u
m
li
m
it o
f
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ea
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p
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(
)
is
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b
y
,
(
3
0
)
3
.
7
.
6
.
Securit
y
c
o
ns
t
ra
ints
(
3
1
)
|
|
(
3
2
)
(
3
3
)
w
h
er
e
is
p
o
w
er
fl
o
w
i
n
a
li
n
e/M
V
A
fl
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i
s
m
a
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i
m
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m
p
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s
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e
co
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ted
b
et
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n
th
e
b
u
s
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p
an
d
q
.
I
n
th
i
s
p
ap
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,
th
e
s
in
g
le
o
b
j
ec
tiv
e
o
p
ti
m
izat
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n
p
r
o
b
lem
i
s
s
o
l
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u
s
in
g
th
e
Gen
etic
Alg
o
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it
h
m
(
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,
an
d
th
e
Stre
n
g
t
h
P
ar
eto
E
v
o
lu
tio
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y
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o
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it
h
m
2
+
(
SP
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m
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ed
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led
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m
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ax
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p
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[
2
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u
s
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to
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eter
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in
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est
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co
m
p
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[
2
4
]
.
4.
SI
M
UL
AT
I
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UL
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A
ND
DIS
CUSS
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N
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e,
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m
[
2
5
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is
co
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to
test
th
e
ef
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e
ctiv
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n
ess
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d
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alize
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d
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ah
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A
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2
1
p
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ar
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e
x
p
o
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i.e
.
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v
o
ltag
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ep
en
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en
t)
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o
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g
w
i
th
n
p
=
1
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d
n
q
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2
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e
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tili
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d
[
1
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.
I
n
th
is
p
ap
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e
y
ass
u
m
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Base
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ax
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at
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m
it
;
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B
=
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5
∗
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A
.
4
.
1
.
Ca
s
e
s
t
ud
y
1
:
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o
lv
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t
he
co
up
led
ARP
M
C
pro
ble
m
u
s
i
ng
t
he
co
ns
t
a
nt
lo
a
d
m
o
deli
ng
w
it
h
lig
h
t
lo
a
din
g
co
nd
it
io
n
T
ab
le
1
p
r
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t
h
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co
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tr
o
l v
ar
i
ab
les an
d
o
b
j
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tiv
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f
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n
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lu
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s
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th
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ase
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y
1
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s
i
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g
le
a
n
d
m
u
ltip
le
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b
j
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ctiv
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w
it
h
co
n
s
tan
t
lo
ad
m
o
d
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g
.
W
h
e
n
th
e
SW
M
o
b
j
e
ctiv
e
is
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p
ti
m
ized
in
d
ep
en
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en
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th
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8
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s
s
es
ar
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d
ev
iated
f
r
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m
t
h
e
o
p
ti
m
u
m
.
W
h
en
L
M
o
b
j
ec
tiv
e
is
o
p
ti
m
i
ze
d
in
d
ep
en
d
en
tl
y
,
t
h
e
n
th
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o
b
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o
p
ti
m
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m
lo
s
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2
.
8
9
7
7
MW,
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u
t
th
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o
b
tai
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ed
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d
VSEI
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n
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o
p
ti
m
u
m
.
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n
th
e
s
a
m
e
w
a
y
,
wh
en
o
n
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
is
o
p
ti
m
ized
in
d
ep
en
d
en
tl
y
,
t
h
e
n
t
h
e
o
t
h
er
o
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jectiv
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ar
e
d
ev
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f
r
o
m
t
h
e
o
p
ti
m
u
m
v
al
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e.
T
h
er
ef
o
r
e,
th
er
e
ex
is
t
s
a
co
n
flict
b
et
w
ee
n
t
h
e
o
p
ti
m
u
m
o
b
j
ec
tiv
e
v
alu
e
s
w
h
e
n
o
n
e
o
b
j
ec
tiv
e
is
o
p
ti
m
ized
in
d
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en
d
en
tl
y
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ab
le
1
.
Op
tim
u
m
Ob
j
ec
tiv
e
Fu
n
ctio
n
Val
u
e
s
an
d
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o
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tr
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l V
ar
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les f
o
r
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ase
S
t
u
d
y
1
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b
j
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
M
u
lti
-
Ob
jective
b
a
s
ed
Op
ti
ma
l E
n
erg
y
a
n
d
R
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P
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w
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Dis
p
a
tch
…
(
S
u
r
en
d
er R
ed
d
y
S
a
lku
ti
)
3433
I
n
th
is
ca
s
e
s
t
u
d
y
,
SW
M
an
d
L
M
o
b
j
ec
tiv
es
ar
e
s
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ted
a
s
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p
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iate
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o
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th
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D
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m
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R
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MC
p
r
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lem
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s
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t
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n
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h
e
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w
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o
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o
n
ee
d
to
o
p
t
i
m
ize
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e
VE
SI
o
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j
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e.
F
i
g
u
r
e
2
d
ep
icts
t
h
e
P
ar
eto
o
p
tim
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s
et
o
f
SW
M
a
n
d
L
M
o
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j
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ased
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led
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R
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e
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y
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.
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n
th
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s
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E
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o
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ith
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i
s
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s
ed
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th
e
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est
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m
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e
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et
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e
o
f
4
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0
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1
$
/h
r
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d
t
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s
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o
f
3
.
7
4
5
1
MW
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d
t
h
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is
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e
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etter
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m
p
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m
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e
s
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l
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tio
n
as
co
m
p
ar
ed
to
th
e
s
i
n
g
le
o
b
j
ec
ti
v
e
co
u
p
led
AR
P
MC
p
r
o
b
le
m
.
Fig
u
r
e
2
.
P
ar
eto
o
p
tim
al
f
r
o
n
t
o
f
SW
M
an
d
L
M
o
b
j
ec
tiv
es
f
o
r
ca
s
e
s
tu
d
y
1
4
.
2
.
Ca
s
e
Study
2
:
Co
up
led A
RP
M
C
w
it
h v
o
lt
a
g
e
depend
ent
lo
a
d
m
o
deli
ng
a
t
lig
ht
lo
a
din
g
co
nd
it
io
n
T
ab
le
2
d
ep
icts
th
e
co
n
tr
o
l
v
ar
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les
an
d
o
b
j
ec
tiv
e
f
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e
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ed
w
h
e
n
t
h
e
s
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le
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d
m
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le
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j
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ti
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ized
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o
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en
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ax
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h
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g
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n
t
h
is
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s
e,
t
h
e
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M
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ctio
n
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n
v
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e
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d
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er
e
f
o
r
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e
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n
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e
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m
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n
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u
e
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s
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M
s
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o
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ld
n
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t
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e
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ized
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.
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h
en
th
e
L
SM
o
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j
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is
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ti
m
i
ze
d
in
d
iv
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al
l
y
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t
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en
t
h
e
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m
o
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n
t
o
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er
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s
3
1
4
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0
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b
u
t
t
h
e
s
o
cial
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elf
ar
e
h
a
s
d
ec
r
ea
s
ed
to
5
3
7
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7
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r
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As
e
x
p
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e
d
ea
r
lier
,
th
e
L
SM
o
b
j
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tiv
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ca
n
n
o
t b
e
u
s
ed
as a
n
in
d
ep
en
d
en
t o
b
j
ec
tiv
e.
T
ab
le
2
.
Op
tim
u
m
Ob
j
ec
tiv
e
Fu
n
ctio
n
Val
u
e
s
an
d
C
o
n
tr
o
l V
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les
f
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r
C
ase
S
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d
y
2
O
b
j
e
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t
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v
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C
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V
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S
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O
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j
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R
P
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M
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440
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480
500
520
540
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n
X
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7
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5
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:
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9
0
.
7
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
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n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
4
2
7
–
3
4
3
5
3434
co
n
d
itio
n
.
T
h
er
ef
o
r
e,
th
e
SW
M
an
d
L
SM
o
b
j
ec
tiv
es
ar
e
co
n
s
id
er
ed
to
b
e
th
e
ap
p
r
o
p
r
iate
m
u
ltip
le
o
b
j
ec
tiv
es
to
b
e
o
p
tim
ized
s
i
m
u
lta
n
eo
u
s
l
y
.
T
h
e
co
m
p
r
o
m
is
e
s
o
l
u
tio
n
h
as
s
o
cial
w
el
f
ar
e
o
f
5
6
2
.
7
0
$
/
h
r
an
d
2
8
9
.
6
3
M
W
o
f
lo
ad
s
er
v
ed
.
Fig
u
r
e
3
d
ep
icts
th
e
P
ar
eto
o
p
tim
al
f
r
o
n
t
o
f
SW
M
an
d
L
SM
o
b
j
ec
tiv
es
f
o
r
th
e
co
u
p
l
ed
AR
P
MC f
o
r
C
a
s
e
St
u
d
y
2
.
Fig
u
r
e
3
.
P
ar
eto
o
p
tim
al
s
e
t o
f
SW
M
an
d
L
SM
o
b
j
ec
tiv
es
f
o
r
ca
s
e
s
tu
d
y
2
I
n
th
is
p
ap
er
,
it
h
as
b
ee
n
s
h
o
w
n
th
at
t
h
e
L
M
a
n
d
SW
M
o
b
j
ec
tiv
es
d
o
n
o
t
m
a
k
e
v
alid
s
in
g
le
o
r
j
o
in
t
o
b
j
ec
tiv
es
w
it
h
th
i
s
v
o
ltag
e
d
ep
en
d
en
t
lo
ad
m
o
d
el,
d
u
e
to
r
ed
u
ctio
n
o
f
lo
ad
s
er
v
ed
.
SW
M
an
d
L
SM
ar
e
b
est
s
u
ited
o
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j
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tiv
es to
b
e
o
p
tim
iz
ed
s
i
m
u
lta
n
eo
u
s
l
y
f
o
r
lig
h
t to
m
o
d
er
ate
lo
ad
in
g
co
n
d
itio
n
.
5.
CO
NCLU
SI
O
NS
T
h
is
p
ap
er
h
as
p
r
o
p
o
s
ed
a
d
a
y
-
a
h
ea
d
(
D
A
)
m
u
l
ti
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o
b
j
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tiv
e
b
ased
ce
n
tr
a
lized
co
u
p
led
ac
tiv
e
a
n
d
r
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c
tiv
e
p
o
w
er
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ch
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li
n
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a
n
d
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g
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h
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n
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s
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r
ac
tical
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e
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en
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t
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g
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Dif
f
er
en
t
o
b
j
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e
f
u
n
ctio
n
s
s
u
ch
as
SW
M,
L
SM,
L
M
a
n
d
VSEI
ar
e
p
r
o
p
o
s
ed
.
T
h
e
SW
M
o
b
j
ec
tiv
e
in
cl
u
d
es
th
e
o
f
f
er
co
s
t
f
o
r
g
e
n
er
ato
r
s
ac
tiv
e
p
o
w
er
p
r
o
d
u
ctio
n
,
r
ea
ctiv
e
co
m
p
e
n
s
atio
n
s
a
n
d
th
e
L
O
C
p
a
y
m
e
n
ts
f
o
r
g
en
er
ato
r
s
a
n
d
b
en
e
fi
t
f
u
n
ct
io
n
o
f
c
u
s
to
m
er
s
.
I
n
t
h
i
s
p
ap
er
,
it
is
s
h
o
w
n
th
at
SW
M
an
d
L
M
o
b
j
ec
tiv
es
d
o
n
o
t
m
ak
e
v
alid
s
i
n
g
le
o
r
m
u
ltip
le
o
b
j
ec
tiv
es
w
i
th
t
h
e
v
o
lta
g
e
d
ep
en
d
en
t
lo
ad
m
o
d
el,
d
u
e
to
th
e
r
ed
u
ctio
n
in
t
h
e
a
m
o
u
n
t
o
f
lo
ad
s
er
v
ed
(
L
S).
S
i
m
u
latio
n
s
t
u
d
ies
o
n
I
E
E
E
3
0
b
u
s
tes
t
s
y
s
te
m
s
h
o
w
s
t
h
e
s
u
it
ab
le
an
d
o
p
ti
m
u
m
ch
o
ice
o
f
m
u
l
tip
le
o
b
j
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tiv
es
to
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e
s
elec
ted
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o
r
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g
iv
e
n
o
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er
atin
g
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n
d
itio
n
.
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M
a
n
d
L
SM
o
b
j
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tiv
es
ar
e
ap
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r
o
p
r
iate
f
o
r
u
n
s
tr
ess
ed
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ad
in
g
co
n
d
itio
n
to
m
o
d
er
ate
lo
ad
in
g
co
n
d
it
io
n
,
w
it
h
v
o
lta
g
e
d
ep
en
d
en
t
lo
ad
m
o
d
eli
n
g
.
T
h
e
P
ar
et
o
o
p
tim
a
l
f
r
o
n
t
allo
w
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th
e
s
y
s
te
m
o
p
er
ato
r
to
m
ak
e
a
b
etter
d
ec
is
io
n
,
b
y
co
n
s
id
er
in
g
th
e
b
etter
co
m
p
r
o
m
i
s
ed
s
o
lu
tio
n
.
ACK
NO
WL
E
D
G
M
E
NT
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T
h
is
r
esear
ch
w
o
r
k
is
b
ased
o
n
th
e
s
u
p
p
o
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t
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f
“
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o
s
o
n
g
Un
iv
er
s
it
y
A
ca
d
e
m
ic
R
esear
ch
Fu
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d
in
g
-
2018
”
.
RE
F
E
R
E
NC
E
S
[1
]
H.
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h
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d
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F
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[5
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4
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5
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6
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7
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8
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9
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[
On
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]
.
A
v
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a
b
le
:
h
tt
p
:/
/w
ww
.
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.
wa
sh
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to
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.
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/res
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rc
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/p
stc
a
.
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