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8
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[1
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.
T
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[
2
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.
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[
3]
.
S
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of
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t
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s
[
4
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
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:
225
2
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88
14
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r
e
s
s
e
d [
5
]
.
T
he
s
u
ppl
i
e
r
pr
o
f
i
t
m
a
xi
m
i
z
a
t
i
on pr
o
bl
e
m
is
s
ol
ve
d a
s
m
ul
ti
ob
je
c
t
i
ve
o
pt
i
m
i
z
a
t
i
on pr
o
bl
e
m
by
c
o
ns
i
de
r
i
n
g t
he
r
i
v
a
l
b
i
ddi
n
g a
n
d
pr
o
f
i
t
f
u
nc
t
i
o
ns
a
l
s
o
b
y
u
s
i
n
g
G
e
n
e
t
i
c
A
l
g
o
r
i
t
hm
(
G
A)
[
6]
.
T
he
s
u
ppl
i
e
r
(
de
c
i
s
i
o
n m
a
ke
r
)
o
pt
i
m
i
z
a
t
i
on pr
obl
e
m
i
s
f
or
m
ul
a
te
d u
n
de
r
s
i
ngl
e
s
i
de
a
uc
t
i
on
e
ne
r
gy
m
a
r
ke
t
s
(
w
i
t
h
out
c
on
s
i
de
r
i
ng
t
h
e
s
pi
nni
n
g
r
e
s
e
r
ve
m
a
r
ke
t
s
)
a
nd
t
he
i
r
bi
d
q
u
a
nt
i
t
i
e
s
a
r
e
o
p
t
i
m
i
z
e
d
u
s
i
n
g
S
e
l
f
a
d
a
p
t
i
v
e
D
i
f
f
e
r
e
n
t
i
a
l
E
v
o
l
u
t
i
o
n
(
S
a
D
E
)
[7
]
.
I
n a
l
l
t
he
a
b
o
ve
l
i
t
e
r
a
t
ur
e
m
e
nt
i
one
d
,
c
o
ns
i
de
r
a
t
i
on
s
h
a
ve
be
e
n m
a
de
onl
y
t
o s
e
t
up t
he
e
ne
r
g
y
m
a
r
ke
t
s
a
n
d
no
t
on
r
e
s
e
r
ve
m
a
r
ke
t
s
.
I
n
t
hi
s
pa
pe
r
,
a
n
a
pp
r
oa
c
h
f
or
pr
o
vi
di
n
g
t
hi
s
a
nc
i
l
l
a
r
y
s
e
r
vi
c
e
i
s
t
o
s
e
t
u
p
r
es
er
v
e m
ar
k
et
s
w
h
i
ch
r
u
n
s
eq
u
en
t
i
al
l
y
f
ol
l
ow
i
ng t
he
e
ne
r
gy
a
n
d t
r
a
ns
m
i
s
s
i
on c
onge
s
t
i
on m
a
na
ge
m
e
nt
m
a
r
k
e
t
s
i
s
d
e
a
l
t
w
i
t
h
.
I
n
t
h
i
s
c
o
n
t
e
x
t
,
D
E
i
s
e
m
p
l
o
y
e
d
t
o
c
h
o
o
s
e
a
G
E
NC
O’s
op
tim
a
l
b
id
d
i
n
g
s
tr
a
te
g
y
a
m
ong
t
he
s
e
t
s
of
di
s
c
r
e
t
e
bi
ds
.
T
hi
s
pa
pe
r
i
s
o
r
ga
ni
z
e
d
a
s
f
ol
l
ow
s
:
S
e
c
t
i
on
2
pr
e
s
e
nt
s
t
he
m
a
r
k
e
t
c
l
e
a
r
i
n
g
m
e
c
h
a
n
i
s
m
i
n
c
o
m
p
e
t
i
t
i
v
e
e
ne
r
gy
a
nd r
e
s
e
r
ve
m
a
r
ke
t
s
,
s
e
c
t
i
on 3 pr
obl
e
m
s
t
a
t
e
m
e
nt
of
p
r
o
f
i
t
m
a
xim
i
z
a
ti
on of
de
c
i
s
i
on m
a
ke
r
s
s
ubm
i
t
t
i
ng bi
d
s
t
o m
a
r
ke
t
o
pe
r
a
t
or
s
,
s
e
c
t
i
on
4
de
a
l
s
w
i
t
h t
he
s
ol
ut
i
o
n
m
e
t
hod
ol
o
gy
t
o f
i
nd
t
he
o
p
t
im
u
m
s
ch
e
d
u
l
es
o
f
t
h
e
s
u
p
pl
i
e
r
,
s
e
c
t
i
on
5
p
r
e
s
e
nt
s
t
he
r
e
s
ul
t
s
a
n
d
di
s
c
us
s
i
o
ns
,
a
n
d
s
e
c
t
i
o
n
6
c
o
n
c
l
ude
s
.
2.
E
NE
RG
Y A
N
D
S
P
I
N
N
I
NG
RE
S
E
R
V
E
M
AR
K
E
T
S
In
t
h
e
re
s
t
r
u
c
t
u
re
d
p
o
w
e
r s
y
s
t
e
m
s
,
GE
N
C
Os
wi
l
l
s
u
b
m
i
t
b
i
d
c
u
rv
e
s
t
o
t
h
e
IS
O
,
a
n
d
t
h
e
n
IS
O c
l
e
a
r
s
m
a
r
ke
t
a
f
t
e
r
c
ol
l
e
c
t
i
ng bi
ds
.
I
n t
he
I
S
O
’
s
m
a
r
ke
t
c
l
e
a
r
i
n
g m
ode
l
,
I
S
O
di
s
pa
t
c
he
s
ge
n
e
r
a
t
i
ng
uni
t
s
i
n o
r
de
r
f
r
om
l
owe
s
t
t
o
hi
g
he
s
t
bi
d
a
s
ne
e
de
d
t
o
m
e
e
t
de
m
a
nd
w
hi
l
e
c
o
ns
i
de
r
i
n
g
ne
t
wo
r
k
c
o
ns
t
r
a
i
nt
s
.
O
nc
e
t
he
e
ne
r
gy
m
ar
k
et
i
s
cl
ear
ed
,
each
g
en
e
r
at
i
n
g
u
n
i
t
w
i
l
l
b
e p
ai
d
acco
r
d
i
n
g
t
o
p
r
i
ci
n
g
m
ech
an
i
s
m
o
f
m
a
rk
e
t
.
G
e
n
e
ra
l
l
y
t
h
er
e
a
r
e
t
w
o
p
r
i
ci
n
g
m
ech
an
i
s
m
s
:
p
ay
-
as
-
bi
d
a
nd
u
ni
f
or
m
pr
i
c
i
n
g
[
8]
.
U
n
d
er
t
h
e p
ay
-
as
-
bi
d
pr
i
c
i
ng
s
t
r
u
c
t
ur
e
,
e
ve
r
y
wi
nni
ng
ge
ne
r
a
t
i
ng
u
n
i
t
ge
t
s
i
t
s
bi
d pr
i
c
e
a
s
i
t
s
i
nc
om
e
.
Unde
r
t
h
e
uni
f
or
m
pr
i
c
i
ng s
t
r
uc
t
u
r
e
,
t
he
bi
d
pr
i
c
e
of
t
he
l
as
t
d
i
s
p
at
c
h
ed
u
n
i
t
s
et
s
t
h
e
m
ar
k
et
cl
ear
i
n
g
p
r
i
ce,
t
h
e
n
a
l
l
u
n
i
t
s
d
i
s
p
at
c
h
ed
r
ecei
v
e t
h
e s
am
e
M
CP
.
I
n
t
h
i
s
p
a
p
e
r
,
t
h
e
u
n
i
f
o
r
m
p
r
i
c
i
n
g
s
t
r
u
c
t
u
r
e
i
s
u
t
i
l
i
z
e
d
.
T
he
f
or
m
a
t
i
on a
n
d o
pe
r
a
t
i
o
n o
f
e
ne
r
gy
m
a
r
ke
t
s
w
e
r
e
di
s
c
us
s
e
d
i
n [
7]
.
S
p
i
n
n
i
n
g
r
es
e
r
v
e
,
a
g
en
er
at
i
o
n
b
as
e
d
a
n
ci
l
l
ar
y
s
er
v
i
ce can
b
e
m
ad
e c
o
m
p
et
i
t
i
v
e an
d
di
f
f
e
r
e
nt
f
r
om
e
ne
r
gy
m
a
r
ke
t
.
T
he
s
pi
n
ni
ng
r
e
s
e
r
ve
s
e
r
vi
c
e
c
a
n
be
pr
oc
u
r
e
d
by
I
S
O
t
h
r
ou
gh
da
i
l
y
c
om
pe
t
i
t
i
ve
a
uc
t
i
on
s
.
T
he
i
-
t
h
s
u
ppl
i
e
r
s
pi
nni
ng
r
e
s
e
r
ve
bi
d
di
n
g
f
u
nc
t
i
o
n
c
a
n
be
r
e
p
r
e
s
e
nt
e
d
a
s
[
9]
(
)
(
)
=
φ
(
)
+ϕ
(
)
(
)
t
=
1
,
2
,
…
T
(
1)
∑
(
)
j
=
1
=
SR
;
t
=
1
,
2
,
.
.
.
(
2)
mi
n
≤
it
≤
ma
x
(
3)
w
h
e
re
SR
t
is
the
r
e
s
e
r
v
e
a
t
hou
r
t
,
(
)
,
ϕ
(
)
a
r
e
t
he
i
nt
e
r
c
e
pt
a
n
d
s
l
op
e
o
f
t
he
s
pi
n
ni
ng
r
e
s
e
r
ve
bi
d
di
n
g
c
ur
ve
o
f
t
h
e
s
u
p
p
l
i
e
r
s
r
e
s
p
e
c
t
i
v
e
l
y
,
it
i
s
t
h
e
r
e
s
e
r
v
e
g
e
n
e
r
a
t
i
o
n
o
u
t
p
u
t
w
i
t
h
i
n
t
h
e
s
e
t
o
f
r
e
s
e
r
v
e
l
i
m
i
t
s
mi
n
an
d
ma
x
.
T
h
e
M
CP
f
o
r
s
p
i
n
n
i
n
g
r
e
s
e
r
v
e
(
M
CP
R)
i
s
c
a
l
c
u
l
a
t
e
d
a
s
t
=
1
,
2
,
…
T
(
4)
T
h
e
s
p
i
n
n
i
n
g
r
es
er
v
e
d
i
s
p
at
ch
b
y
eac
h
s
u
p
p
l
i
er
ca
n
b
e
cal
cu
l
at
ed
as
it
=
MC
P
R
−
(
)
(
)
i
=
1
,
2
…
N
(
5)
3.
S
UP
P
L
I
E
R
P
R
O
F
I
T
M
A
X
I
MI
Z
AT
I
O
N
P
R
O
B
L
E
M
F
O
R
MUL
A
T
I
O
N
T
he
pr
of
i
t
m
a
xi
m
i
z
a
t
i
on o
bj
e
c
t
i
ve
of
s
u
p
p
l
i
e
r
s
pa
r
t
i
c
i
pa
t
i
ng i
n e
ne
r
gy
a
nd
r
e
s
e
r
ve
m
a
r
ke
t
s
a
n
d
c
om
pe
t
i
ng
wi
t
h
t
he
ot
he
r
s
u
p
pl
i
e
r
s
c
a
n
be
s
t
a
t
e
d
a
s
M
a
x
i
m
i
z
e
:
PF=
RV
-
TC
.
P
r
o
f
i
t
(
PF
)
i
s
de
f
i
ne
d a
s
t
he
r
e
ve
nue
(
RV
)
f
r
om
t
he
s
a
l
e
s
of
e
ne
r
gy
a
n
d r
e
s
e
r
ve
m
i
nus
t
h
e
t
o
t
a
l
(
pr
odu
c
tio
n)
c
o
s
t
(
TC
).
PF
=
∑
∑
MC
P
.
i
t
+
MC
P
R
.
it
−
(
i
t
+R
i
t
)
t=
1
i=
1
i
t
(
6)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-
88
14
IJ
A
A
S
V
o
l
.
7
,
N
o
.
1
,
Ma
r
c
h
2
018
:
4
6
–
53
48
W
he
r
e
Xi
t
t
he
ON
/
O
F
F
s
t
a
t
us
of
t
he
s
u
ppl
i
e
r
s
de
c
i
de
d
by
I
S
O
a
nd
Ci
(
P
i
t
)
i
s
t
h
e
f
u
e
l
c
o
s
t
f
u
n
c
t
i
o
n
o
f
t
h
e
s
u
p
p
l
i
e
r
s
.
T
h
e co
n
s
t
r
ai
n
t
s
i
n
cl
u
d
e
d
a
r
e a)
P
o
w
e
r
b
al
an
ce an
d
b
)
M
i
n
i
m
u
m
an
d
m
ax
i
m
u
m
cap
aci
t
y
l
i
m
i
t
s
o
f
s
u
p
p
l
i
e
r
s
.
a)
P
o
w
er
b
al
an
ce
co
n
s
t
r
ai
n
t
s
T
he
t
ot
a
l
ge
ne
r
a
t
i
on
(
i
nc
l
udi
n
g
s
pi
n
ni
n
g
r
e
s
e
r
ve
)
of
G
E
N
C
O
s
pa
r
t
i
c
i
pa
t
i
ng
i
n
t
he
e
l
e
c
t
r
i
c
i
t
y
m
a
r
ke
t
s
m
ay
b
e
g
r
eat
er
t
h
an
o
r
e
q
u
a
l
t
o
t
h
e
d
e
m
a
n
d
p
r
o
f
i
l
e
o
f
t
h
e
c
u
s
t
o
m
e
r
s
.
∑
(
it
+R
it
)
j
=
1
it
≥
∑
t=
1
t
=
1
,
2
,
.
.
.
(7
)
b
)
M
i
n
i
m
u
m
a
n
d
m
a
x
i
m
u
m
c
a
p
a
c
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m
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t
c
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r
a
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a
t
i
o
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n
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t
s
h
a
v
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l
o
w
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n
d
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p
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p
r
o
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t
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o
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l
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m
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t
s
t
h
a
t
a
r
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d
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IJ
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14
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EF
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C
ES
[1]
G
i
be
s
c
u.
M
a
nd
L
i
u C.
C
,
“
O
pt
i
m
i
z
a
t
i
on of
a
nc
i
l
l
a
r
y
s
e
rv
i
c
e
s
for s
y
s
t
e
m
s
e
c
uri
t
y
”
,
P
r
oc
e
e
d
i
ngs
of
B
ul
k
powe
r
s
y
s
t
e
m
dy
nam
i
c
s
and c
on
t
r
ol
I
V
-
R
es
t
r
u
ct
u
r
i
n
g
,
s
y
mp
o
si
u
ms
,
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-
358,
1998
.
[2]
S
i
ngh.
H
a
nd
A
.
P
a
pa
l
e
xopou
l
os
,
“
Com
pe
t
i
t
i
ve
proc
ur
e
m
e
nt
of a
n
c
i
l
l
a
r
y
s
e
rvi
c
e
s
b
y
a
n
i
n
de
pe
nde
n
t
s
y
s
t
e
m
ope
ra
t
or
”,
IE
E
E
T
r
ans
P
owe
r
Sy
s
t
e
m
s
,
V
ol
.
14,
N
o.
2,
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[3]
S
ul
l
i
va
n M
.
J
a
nd M
a
l
l
e
y
M
.
J
,
“
A
ne
w
m
e
t
hodol
og
y
f
or t
h
e
p
rovi
s
i
on of re
s
e
r
ve
i
n a
n i
s
ol
a
t
e
d pow
e
r s
y
s
t
e
m
”
,
IE
E
E
T
r
ans
ac
t
i
o
ns
on P
owe
r
Sy
s
t
e
m
s
,
V
ol
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14,
pp
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174
-
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,
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[4]
A
n
g
at
h
a,
V
.V
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., C
h
an
d
r
am
,
K
. an
d
L
ax
m
i
,
A
.J
,
“
Bi
ddi
ng
S
t
ra
t
e
g
y
i
n
D
e
re
gul
a
t
e
d
P
ow
e
r M
a
rke
t
U
s
i
n
g
D
i
ffe
re
nt
i
a
l
E
vo
l
ut
i
on A
l
gor
i
t
hm
”
,
Jo
ur
nal
o
f
P
o
we
r
and E
n
e
r
gy
E
ngi
ne
e
r
i
ng
,
3
, 3
7
-
46,
2015
.
[5]
S
a
y
y
ad
N
o
j
av
an
, K
az
em
Z
ar
e,
M
o
h
am
m
ed
R
eza, “
O
p
t
i
m
al
b
i
d
d
i
n
g
s
t
r
at
eg
y
o
f
g
en
er
a
t
i
o
n
s
t
at
i
o
n
i
n
p
o
w
er
m
ar
k
e
t
us
i
ng Inform
a
t
i
o
n ga
p d
e
c
i
s
i
on t
h
e
or
y
”
,
El
e
ct
r
i
c
P
o
w
e
r S
y
st
e
ms
R
e
s
ea
r
ch
,
96
,
26
-
6
3,
2013
.
[6]
A
z
e
de
h.
A
,
G
ha
de
ri
.
S
.
F
,
P
ourva
l
i
kha
n
.
B,
S
he
i
kha
l
i
s
ha
hi
.
M
,
“
A
ne
w
ge
ne
t
i
c
a
l
gori
t
hm
a
pproa
c
h for opt
i
m
i
z
i
n
g
bi
ddi
ng s
t
ra
t
e
g
y
vi
e
w
poi
nt
of profi
t
m
a
xi
m
i
z
a
t
i
o
n of a
ge
ne
ra
t
i
on
c
om
pa
n
y
”
,
E
x
p
e
r
t
s
y
s
t
e
m
s
wi
t
h appl
i
c
at
i
ons
,
39,
1565
-
1574,
201
2.
[7]
B.
Ra
m
pri
y
a
,
“
P
rofi
t
m
a
xi
m
i
z
a
t
i
on a
nd opt
i
m
a
l
bi
ddi
ng s
t
ra
t
e
gi
e
s
of G
E
N
CO
s
i
n e
l
e
c
t
i
c
i
t
y
m
a
rke
t
s
us
i
ng s
e
l
f
a
da
pt
i
ve
di
ff
e
re
nt
i
a
l
e
vol
u
t
i
on”
,
Int
e
r
nat
i
ona
l
J
our
nal
of
E
l
e
c
t
r
i
c
al
E
ngi
ne
e
r
i
n
g and Inf
or
m
at
i
c
s
, V
o
l
. 8
, N
o
.
4
,
2016.
[8]
S
ol
e
y
m
a
ni
.
S
,
“
Bi
ddi
ng s
t
ra
t
e
g
y of ge
n
e
ra
t
i
on c
om
pa
ni
e
s
us
i
ng
P
S
O
c
om
bi
ne
d w
i
t
h S
A
m
e
t
hod i
n t
h
e
pa
y
a
s
bi
d
m
ar
k
et
s
”,
E
l
ect
r
i
ca
l
P
o
w
er
a
n
d
E
n
er
g
y S
ys
t
em
s
,
V
ol
.
33
,
pp
.
127
2
-
1278,
2011
.
[9]
F
us
hua
n W
e
n a
nd A
.
K
.
D
a
vi
d,
“
S
t
ra
t
e
gi
c
bi
ddi
ng i
n
re
s
e
rv
e
m
a
rke
t
”
,
P
r
o
c
e
e
d
i
ngs
of
t
he
5t
h In
t
e
r
nat
i
on
al
Conf
e
r
e
nc
e
on
A
dv
anc
e
s
i
n
P
o
we
r
Sy
s
t
e
m
Con
t
r
ol
,
O
pe
r
at
i
on
and Manage
m
e
n
t
,
A
P
SCO
M 200
0
,
H
ong K
ong,
pp.
80
-
85,
2000
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[10]
F
us
hua
n W
e
n,
A
.
K
um
a
r D
a
vi
d,
“
O
pt
i
m
a
l
bi
ddi
ng s
t
ra
t
e
g
i
e
s
a
nd m
ode
l
i
ng of i
m
pe
rfe
c
t
i
nfo
rm
a
t
i
on a
m
ong
co
m
p
et
i
t
i
v
e g
en
er
at
o
r
s
”
,
I
E
E
E
T
r
ans
ac
t
i
ons
on p
ow
e
r sy
st
e
ms
,
V
ol
.
16
,
N
o
.
1,
pp.
15
-
21,
2001
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[11]
F
us
hua
n W
e
n a
nd A
.
K
.
D
a
vi
d
,
“
Coordi
na
t
i
on
of bi
ddi
ng s
t
r
a
t
e
gi
e
s
i
n
da
y
-
a
h
e
a
d e
n
e
rg
y
a
nd
s
pi
nni
ng re
s
e
rv
e
m
ar
k
et
s
”,
Int
e
r
n
at
i
onal
J
our
nal
of
E
l
e
c
t
r
i
c
al
P
o
w
er
and
E
n
er
g
y S
ys
t
em
s
,
V
ol
.
24
,
pp
.
251
-
261
,
2
002.
[12]
A
bou A
.
A
,
A
bi
do.
M
.
A
,
S
pe
a
S
.
R,
“
D
i
ffe
re
n
t
i
a
l
E
vo
l
ut
i
on
a
l
g
ori
t
hm
for e
m
i
s
s
i
on c
ons
t
ra
i
n
e
d
e
c
onom
i
c
pow
e
r
di
s
pa
t
c
h
probl
e
m
”
,
E
l
ec
t
r
i
c
P
o
w
er
S
ys
t
em
s
R
es
ea
r
ch
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V
ol
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80,
p
p.
1286
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1292,
20
10.
[13]
A
bou E
l
E
l
a
A
.
A
.
,
M
.
A
.
A
bi
do
,
S
.
R.
S
pe
a
,
“
O
p
t
i
m
a
l
pow
e
r fl
o
w
us
i
ng di
ffe
re
n
t
i
a
l
e
vol
u
t
i
on
a
l
gori
t
hm
”
,
E
le
c
tr
ic
P
o
w
er
S
ys
t
em
s
R
es
ea
r
ch
,
V
ol
.
8
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878
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2010.
[14]
Ba
bu B.
V
,
P
.
G
.
Cha
kol
e
,
J
.
H
.
S
.
M
ube
e
n,
“
D
i
ffe
r
e
nt
i
a
l
E
vo
l
ut
i
on
S
t
ra
t
e
g
y
for
O
pt
i
m
a
l
D
e
s
i
gn of G
a
s
T
ra
ns
m
i
s
s
i
on
N
e
t
w
ork”
,
a
va
i
l
a
bl
e
onl
i
n
e
a
t
:
w
w
w
.
vs
ppub.
c
om
,
2010.
Evaluation Warning : The document was created with Spire.PDF for Python.