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Un
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m
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(UC)
is
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ese
r
v
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co
n
s
tr
ai
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ts
[
1
]
,
[
2
]
.
T
h
e
g
o
al
b
eh
i
n
d
UC
p
r
o
b
l
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m
i
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p
ti
m
izi
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g
r
eso
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s
a
n
d
co
s
ts
[
3
]
.
I
n
f
ac
t,
th
e
elec
tr
icit
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m
a
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k
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ar
e
f
ac
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al
ch
a
lle
n
g
e
s
in
d
i
f
f
er
e
n
t
s
ta
g
es:
g
en
er
atio
n
,
tr
an
s
m
i
s
s
io
n
an
d
d
is
tr
ib
u
tio
n
.
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h
e
m
ai
n
p
r
o
b
lem
s
in
elec
tr
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p
o
w
er
s
y
s
te
m
s
ar
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UC
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d
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ts
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t
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s
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er
,
w
e
f
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s
o
n
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r
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n
ti
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g
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liter
atu
r
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r
ev
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w
o
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U
C
p
r
o
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class
if
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s
o
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p
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if
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m
it
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[
4
]
.
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s
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ated
in
to
d
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s
to
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UC
[
5
]
.
R
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[
6
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Oth
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I
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8
,
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3
,
J
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2
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1
8
:
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3
5
7
–
1372
1358
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u
lated
a
n
d
d
er
eg
u
lated
p
o
w
er
m
ar
k
et
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
.
W
ith
in
t
h
i
s
f
r
a
m
e
w
o
r
k
,
w
e
p
r
o
v
id
e
a
s
u
r
v
e
y
o
f
o
p
ti
m
izatio
n
tech
n
iq
u
es
u
s
ed
to
s
o
lv
e
t
h
e
UC
p
r
o
b
lem
.
T
h
e
p
ap
er
is
o
r
g
an
ized
as
f
o
l
lo
w
s
.
Sectio
n
2
p
r
esen
t
s
th
e
ev
o
lu
tio
n
o
f
U
C
p
r
o
b
lem
o
v
e
r
th
e
p
ast
y
ea
r
s
.
Sectio
n
3
p
r
o
v
id
es
th
e
class
ic
m
ix
ed
in
teg
er
lin
ea
r
f
o
r
m
u
latio
n
o
f
UC
p
r
o
b
lem
.
I
n
Sectio
n
4
w
e
w
il
l
f
o
cu
s
o
n
th
e
s
to
ch
a
s
tic
p
r
o
g
r
am
m
in
g
’
s
ap
p
licatio
n
in
U
C
p
r
o
b
lem
to
d
ea
l
w
it
h
u
n
c
er
tai
n
t
y
in
p
o
w
er
s
y
s
te
m
.
Sectio
n
5
p
r
o
v
id
es
a
r
e
v
ie
w
o
f
m
e
th
o
d
s
t
h
at
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
in
th
e
p
ast
f
e
w
d
ec
ad
es
f
o
r
U
C
p
r
o
b
lem
o
p
tim
izatio
n
.
W
e
en
d
th
e
p
ap
e
r
w
it
h
s
o
m
e
co
n
clu
d
i
n
g
r
e
m
ar
k
s
i
n
Sectio
n
6
.
2.
O
VE
RVI
E
W
O
F
T
H
E
UC
P
RO
B
L
E
M
Un
it
co
m
m
it
m
e
n
t
(
UC
)
i
s
a
p
r
o
b
lem
w
id
el
y
tr
ea
ted
b
y
th
e
r
esear
ch
er
s
s
i
n
ce
1
9
4
0
s
[
8
]
.
Giv
e
n
th
e
en
o
r
m
o
u
s
v
o
l
u
m
e
o
f
p
ap
er
s
in
t
h
is
f
ield
,
s
e
v
er
al
r
e
v
ie
w
ar
ticles
h
av
e
b
ee
n
p
r
esen
ted
.
Div
er
s
o
p
ti
m
izatio
n
m
et
h
o
d
s
f
o
r
s
o
lv
i
n
g
U
C
p
r
o
b
le
m
ar
e
o
u
tlin
ed
.
I
t
also
p
o
in
ts
o
u
t
U
C
’
s
d
if
f
er
en
t
co
n
s
id
er
atio
n
s
i
n
b
o
th
r
eg
u
lated
a
n
d
d
er
eg
u
lated
en
v
ir
o
n
m
e
n
t
s
.
L
atel
y
,
w
it
h
an
i
n
cr
ea
s
ed
i
n
co
r
p
o
r
atio
n
o
f
R
E
S
a
n
d
t
h
e
i
m
p
le
m
en
ta
tio
n
o
f
e
n
er
g
y
s
t
o
r
ag
e
d
ev
ices,
p
o
w
er
s
y
s
te
m
s
’
o
p
er
atio
n
s
tr
ate
g
ies
h
a
v
e
k
n
o
w
n
s
ig
n
i
f
ica
n
t
m
o
d
i
f
icat
io
n
s
[
5
]
.
So
m
e
ar
ticl
es
s
u
c
h
as
[
3
]
h
a
v
e
g
i
v
en
a
r
e
v
ie
w
o
f
r
ec
e
n
t
ap
p
r
o
ac
h
es
to
UC
p
r
o
b
le
m
i
n
th
e
p
r
esen
ce
o
f
in
ter
m
i
tten
t
R
E
S.
Fig
u
r
e
1
g
i
v
es a
n
o
v
er
v
ie
w
o
f
th
e
ev
o
l
u
tio
n
o
f
th
e
p
r
o
b
le
m
s
in
ce
its
ap
p
ea
r
an
ce
u
n
t
il
n
o
w
.
I
n
t
h
e
s
a
m
e
co
n
te
x
t,
T
a
b
le
1
(
ap
p
en
d
ix
)
p
r
o
v
id
es
a
d
etailed
r
ev
ie
w
o
f
t
h
e
h
is
t
o
r
y
o
f
U
C
p
r
o
b
lem
th
r
o
u
g
h
ti
m
e
b
y
r
ep
r
esen
tin
g
t
h
e
r
e
m
ar
k
ab
le
p
u
b
lica
tio
n
s
.
Fig
u
r
e
1
.
Su
m
m
ar
y
o
f
U
C
p
r
o
b
le
m
’
s
ev
o
l
u
tio
n
t
h
r
o
u
g
h
ti
m
e
I
n
g
e
n
er
al,
UC
is
NP
-
h
ar
d
o
p
tim
izatio
n
p
r
o
b
le
m
[
9
]
,
wh
er
e
th
e
S
y
s
te
m
o
p
er
ato
r
(
SO)
ai
m
s
at
m
i
n
i
m
izi
n
g
th
e
to
tal
p
r
o
d
u
ct
io
n
co
s
t
o
v
er
t
h
e
s
ch
ed
u
li
n
g
h
o
r
izo
n
.
I
n
g
en
er
al,
th
e
to
t
al
p
r
o
d
u
ctio
n
co
s
t
co
m
p
r
is
e
s
f
u
el
co
s
ts
,
w
h
ic
h
ar
e
r
elate
d
to
o
p
er
atio
n
o
f
th
er
m
al
u
n
it
s
,
s
tar
t
-
u
p
co
s
ts
,
an
d
s
h
u
td
o
w
n
co
s
ts
.
A
s
a
r
esu
lt,
th
e
U
C
p
r
o
b
lem
h
a
s
b
ee
n
tr
ad
itio
n
all
y
s
o
l
v
ed
in
p
o
w
er
s
y
s
te
m
s
to
d
eter
m
i
n
e
th
e
b
est
p
o
s
s
ib
le
co
m
m
i
t
m
e
n
t
s
tat
u
s
,
th
e
s
tar
t
-
u
p
/s
h
u
td
o
w
n
s
eq
u
e
n
ce
s
,
a
n
d
t
h
e
p
o
w
er
o
u
tp
u
ts
f
o
r
al
l
a
v
aila
b
le
u
n
its
,
s
u
b
j
ec
t
to
v
ar
io
u
s
co
n
s
tr
ai
n
ts
[
1
0
]
.
Usu
all
y
,
th
er
e
ar
e
th
r
ee
t
y
p
e
s
o
f
g
e
n
er
ati
n
g
u
n
i
ts
i
n
elec
tr
ical
p
o
w
e
r
s
y
s
te
m
s
:
th
er
m
a
l u
n
its
(
i
n
cl
u
d
e
n
u
clea
r
u
n
i
ts
)
,
h
y
d
r
o
u
n
it
s
,
an
d
R
E
S u
n
its
.
I
n
th
i
s
s
e
n
s
e,
t
h
e
UC
o
p
ti
m
iza
tio
n
p
r
o
b
lem
h
as t
h
e
f
o
llo
w
i
n
g
f
o
r
m
[
6
]
:
T
o
tal
p
r
o
d
u
ctio
n
co
s
ts
=
F
u
el
co
s
t +
Star
t
-
u
p
co
s
t +
Sh
u
td
o
w
n
co
s
t+
Ma
i
n
te
n
an
ce
co
s
t
T
o
b
e
m
i
n
i
m
ize
d.
O
th
er
co
s
t
s
s
u
ch
as
n
o
-
lo
ad
s
er
v
ed
co
s
t
a
n
d
i
n
v
e
s
t
m
en
t
co
s
t
ca
n
b
e
ad
d
in
g
to
U
C
p
r
o
b
lem
f
o
r
m
u
latio
n
.
T
h
i
s
m
in
i
m
izat
i
o
n
d
ep
en
d
s
o
n
m
an
y
co
n
s
tr
a
in
ts
r
ela
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to
o
p
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n
o
f
g
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atin
g
u
n
its
a
n
d
s
y
s
te
m
p
o
w
er
eq
u
ilib
r
iu
m
(
p
r
esen
ted
i
n
Sectio
n
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
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ab
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1
.
UC
Pr
o
b
lem
De
v
elo
p
m
en
t
,
f
r
o
m
1
9
4
0
to
2
0
1
7
Y
e
a
r
Ty
p
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o
f
p
r
o
b
l
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m
G
e
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p
r
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m
A
p
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s
y
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ms
.
[
8
]
1
9
5
9
S
o
l
u
t
i
o
n
t
o
U
C
p
r
o
b
l
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m
A
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a
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m
c
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d
P
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(
p
r
i
o
r
i
t
y
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st
)
sch
e
m
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w
a
s
p
r
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p
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d
,
i
n
w
h
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c
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s.
[
1
1
]
1
9
6
2
F
o
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mu
l
a
t
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f
U
C
p
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b
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p
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u
t
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a
s t
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3
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.
[
1
2
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1
9
6
6
S
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.
[
1
3
]
1
9
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e
m.
[
1
4
]
1
9
7
7
S
o
l
u
t
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o
U
C
p
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a
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s.
[
7
5
]
[
7
6
]
[
6
]
[
2
]
[
7
7
]
[
7
8
]
[
2
7
]
2
0
1
7
F
o
r
mu
l
a
t
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U
C
p
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I
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R
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b
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2
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U
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p
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b
l
e
m.
[
7
9
]
[
8
0
]
[
8
1
]
[
8
2
]
3.
UC
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
Ma
th
e
m
atica
ll
y
,
U
C
p
r
o
b
le
m
h
as b
ee
n
f
o
r
m
u
lated
a
s
a
n
o
n
-
co
n
v
e
x
,
lar
g
e
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s
ca
le,
n
o
n
-
li
n
ea
r
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an
d
MI
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co
m
b
i
n
ato
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ial
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p
ti
m
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n
p
r
o
b
lem
w
it
h
co
n
s
tr
ai
n
ts
[
1
0
]
,
[
5
1
]
,
[
6
6
]
.
T
h
e
n
o
n
-
co
n
v
ex
it
y
i
s
ca
u
s
ed
b
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in
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at
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UC
d
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(
ON/OF
F
)
.
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p
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s
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o
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m
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in
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eq
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ir
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b
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to
b
e
f
o
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m
u
lated
as
a
MI
P
p
r
o
b
lem
[
7
2
]
.
T
h
e
m
at
h
e
m
atica
l
f
o
r
m
u
la
tio
n
f
o
r
th
e
p
r
o
b
le
m
is
an
al
y
ticall
y
d
escr
ib
ed
in
t
h
e
f
o
llo
w
in
g
p
ar
ag
r
ap
hs
.
3
.
1
.
Det
er
m
i
nis
t
ic
f
o
r
m
ula
t
io
n o
f
u
nit
c
o
mm
it
m
ent
p
ro
b
le
m
T
h
e
d
eter
m
i
n
is
t
ic
f
o
r
m
u
lat
io
n
o
f
t
h
e
UC
p
r
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b
le
m
s
ca
n
b
e
co
n
s
id
er
ed
as
a
s
p
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ial
ca
s
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o
f
t
h
e
r
esp
ec
tiv
e
s
to
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h
asti
c
f
o
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m
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lat
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n
,
w
h
er
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o
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l
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s
in
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r
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p
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y
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p
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s
co
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s
id
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[
6
]
.
T
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MI
L
P
ap
p
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as
b
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p
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1
9
7
0
s
as
a
p
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ac
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d
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t
alter
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m
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f
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v
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ti
m
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p
r
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s
r
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to
s
h
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t
-
ter
m
o
p
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o
f
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tr
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s
y
s
t
e
m
s
,
in
p
ar
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lar
U
C
p
r
o
b
le
m
[
8
]
.
I
n
f
ac
t,
m
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s
t
r
esear
ch
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s
in
th
is
f
ield
h
a
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(
b
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v
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d
,
th
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r
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clas
s
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lin
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r
p
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r
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m
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[
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.
3
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1
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1
.
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k
s
[
6
8
]
,
[
7
1
]
.
T
h
e
MI
L
P
d
eter
m
i
n
is
tic
U
C
p
r
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b
lem
ca
n
b
e
f
o
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m
u
lated
as
[
1
9
]
,
[
2
7
]
:
M
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m
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o
pera
t
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na
l c
o
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t
(
O
C)
OC
=
∑
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tp
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t
[
3
6
]
,
[
7
1
]
:
(
)
=
,
an
d
ar
e
th
e
co
s
t c
o
ef
f
icie
n
t
s
.
P
r
ac
tically
th
is
co
s
t
i
s
m
o
d
ele
d
as
a
p
iece
w
i
s
e
-
lin
ea
r
f
u
n
c
tio
n
[
3
6
]
,
[
7
1
]
.
A
tig
h
t
f
o
r
m
u
la
ti
o
n
f
o
r
t
h
i
s
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w
i
s
e
-
l
in
ea
r
ap
p
r
o
x
i
m
at
io
n
is
g
iv
e
n
i
n
[
6
0
]
.
is
th
e
co
s
t
f
o
r
r
estar
tin
g
a
d
e
-
co
m
m
i
tted
th
er
m
al
u
n
it,
w
h
ic
h
is
d
ep
en
d
ed
to
th
e
te
m
p
er
at
u
r
e
o
f
th
e
b
o
iler
.
T
h
e
n
u
m
b
er
o
f
t
h
e
s
tar
t
-
u
p
an
d
s
h
u
td
o
w
n
a
n
d
th
eir
t
y
p
e
(
h
o
t
o
r
co
ld
)
ch
an
g
es
i
n
f
u
n
ct
io
n
o
f
th
e
ON
/
OF
F
s
tatu
s
o
f
t
h
e
u
n
it
s
[
3
]
.
I
t is ex
p
r
ess
ed
as f
o
llo
w
s
[
6
6
]
,
[
8
3
]
:
W
h
er
e
an
d
ar
e
r
esp
ec
tiv
ely
th
e
h
o
t
an
d
co
ld
s
tar
t
-
u
p
co
s
t
o
f
u
n
it
i
.
is
th
e
m
i
n
i
m
u
m
d
o
w
n
ti
m
e
o
f
u
n
it
i
.
is
th
e
co
n
tin
u
o
u
s
o
f
f
l
in
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p
er
io
d
o
f
u
n
it
i
at
h
o
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r
t.
is
th
e
co
ld
s
tar
t
h
o
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r
o
f
u
n
i
t
i
.
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e
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u
td
o
w
n
co
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s
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al
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ta
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eq
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al
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f
o
r
all
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n
its
[
3
]
,
[
7
2
]
.
3
.
1
.
2
.
Unit
c
o
mm
it
m
ent
c
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t
ra
int
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I
n
m
i
n
i
m
izi
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g
OC
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t
h
e
UC
p
r
o
b
lem
s
o
l
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tio
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m
u
s
t
r
esp
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t
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o
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en
er
ato
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p
h
y
s
ical
co
n
s
t
r
ain
ts
a
n
d
s
y
s
te
m
o
p
er
atio
n
al
co
n
s
t
r
ai
n
ts
[
2
7
]
,
[
6
6
]
.
T
h
ese
co
n
s
tr
ain
t
s
c
an
b
e
o
n
e
o
r
m
o
r
e
o
f
t
h
e
f
o
llo
w
i
n
g
t
y
p
es
:
a.
Gen
er
ati
n
g
li
m
i
ts
co
n
s
tr
ain
t
s
E
ac
h
g
e
n
er
atin
g
u
n
it
h
as
m
i
n
i
m
u
m
a
n
d
m
ax
i
m
u
m
li
m
it
s
.
T
h
e
p
o
w
er
o
u
tp
u
t
ca
n
n
o
t
ex
ce
ed
th
es
e
li
m
it
s
[
1
9
]
,
[
5
1
]
,
[
7
2
]
:
(
)
(
)
W
h
er
e
(
)
an
d
(
)
ar
e
r
esp
ec
tiv
el
y
t
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e
m
in
i
m
u
m
a
n
d
m
a
x
i
m
u
m
r
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l
p
o
w
er
o
u
tp
u
t
o
f
u
n
it
i
a
t
h
o
u
r
t
.
b.
P
o
w
er
b
alan
ce
co
n
s
tr
ai
n
t
T
h
e
eq
u
ilib
r
iu
m
b
et
w
ee
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lo
ad
d
em
a
n
d
an
d
p
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u
tp
u
t i
n
ea
ch
h
o
u
r
i
s
g
i
v
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n
b
y
[
3
]
,
[
6
6
]
,
[
7
2
]
:
∑
(
)
(
)
.
(
)
W
h
er
e
is
th
e
to
tal
d
e
m
a
n
d
at
h
o
u
r
t
.
c.
Min
i
m
u
m
u
p
/d
o
w
n
ti
m
e
co
n
s
tr
ain
ts
Min
i
m
u
m
u
p
-
ti
m
e
is
t
h
e
m
i
n
i
m
u
m
n
u
m
b
er
o
f
h
o
u
r
s
o
f
o
p
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n
at
o
r
ab
o
v
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th
e
m
i
n
i
m
u
m
g
en
er
at
io
n
ca
p
ac
it
y
.
I
t is e
x
p
r
ess
ed
as f
o
llo
w
s
[
3
]
,
[
6
6
]
:
≤
(
)
≤
(
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
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&
C
o
m
p
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n
g
,
Vo
l.
8
,
No
.
3
,
J
u
n
e
2
0
1
8
:
1
3
5
7
–
1372
1364
W
h
er
e
an
d
ar
e
th
e
to
tal
u
p
-
t
i
m
e
an
d
t
h
e
m
in
i
m
u
m
u
p
-
ti
m
e
o
f
u
n
it
i
.
Min
i
m
u
m
d
o
w
n
ti
m
e
is
th
e
m
i
n
i
m
u
m
n
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m
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n
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th
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er
ato
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g
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t o
n
li
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e
ag
a
in
to
g
e
n
er
ate
p
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w
er
[
3
]
,
[
66]
:
W
h
er
e
an
d
ar
e
th
e
to
tal
d
o
w
n
ti
m
e
an
d
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m
i
n
i
m
u
m
d
o
w
n
ti
m
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o
f
u
n
it
i
.
d.
R
a
m
p
r
ate
u
p
/d
o
w
n
co
n
s
tr
ai
n
t
s
T
h
e
g
en
er
ato
r
p
o
w
er
o
u
tp
u
t
i
s
n
o
t
c
h
a
n
g
in
g
i
n
s
tan
ta
n
eo
u
s
l
y
.
I
t
s
v
ar
ia
tio
n
d
ep
en
d
s
o
n
r
a
m
p
r
ate
li
m
it
s
.
T
h
ese
co
n
s
tr
ai
n
ts
ar
e
f
o
r
m
u
lated
b
ased
as o
n
t
h
e
f
o
ll
o
w
i
n
g
co
n
d
itio
n
s
[
3
]
,
[
5
1
]
,
[
7
2
]
:
≤
≤
W
h
er
e
an
d
ar
e
th
e
r
a
m
p
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g
u
p
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d
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am
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g
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o
w
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o
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u
n
it
i
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e.
Sp
in
n
in
g
r
eser
v
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s
co
n
s
tr
ain
t
Sp
in
n
in
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r
eser
v
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s
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n
i
n
d
icato
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o
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th
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a
m
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n
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p
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s
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ir
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to
f
u
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ce
n
tag
e
o
f
f
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p
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k
d
e
m
a
n
d
o
r
ca
p
ab
le
o
f
m
a
k
i
n
g
u
p
th
e
lo
s
s
o
f
th
e
m
o
s
t
i
m
p
o
r
tan
t
lo
ad
ed
u
n
it
in
ea
ch
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T
h
e
f
o
r
m
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latio
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f
o
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s
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r
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b
e
ex
p
r
ess
ed
as
[
3
]
,
[
5
1
]
,
[
6
6
]
:
∑
(
)
(
)
,
≤
≤
W
h
er
e
is
th
e
s
p
i
n
n
in
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r
eser
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at
h
o
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t
.
f.
Mu
s
t r
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n
a
n
d
m
u
s
t o
u
t u
n
it
s
T
h
e
m
u
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t
r
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u
n
it
s
ar
e
a
p
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e
s
ch
ed
u
led
u
n
i
t
w
h
ic
h
m
u
s
t
b
e
o
n
lin
e,
d
u
e
to
o
p
er
atin
g
r
eliab
ilit
y
o
r
ec
o
n
o
m
ic
p
u
r
p
o
s
es
.
T
h
e
R
E
S
u
n
its
ar
e
n
ec
es
s
ar
y
r
u
n
u
n
it
s
f
o
r
b
etter
ec
o
n
o
m
ic
s
y
s
te
m
o
p
er
atio
n
.
Mu
s
t
o
u
t
u
n
i
ts
ar
e
th
e
u
n
its
u
n
a
v
ailab
le
f
o
r
co
m
m
i
t
m
e
n
t b
ec
au
s
e
o
f
f
o
r
ce
d
o
u
tag
es o
r
m
ai
n
ten
a
n
ce
i
n
ter
v
e
n
tio
n
s
[
1
9
]
.
g.
T
r
an
s
m
is
s
io
n
co
n
s
tr
ain
ts
T
r
an
s
m
is
s
io
n
co
n
s
tr
ain
t
s
ar
e
to
s
atis
f
y
cu
s
to
m
er
lo
ad
d
em
a
n
d
s
an
d
m
ai
n
tai
n
tr
an
s
m
is
s
io
n
f
lo
w
s
an
d
b
u
s
v
o
lta
g
es
w
it
h
i
n
ad
m
is
s
ib
l
e
li
m
it
s
[
8
4
]
.
Gen
er
all
y
,
lin
ea
r
DC
(
d
ir
ec
t
cu
r
r
en
t
)
tr
an
s
m
i
s
s
io
n
co
n
s
tr
ai
n
t
s
ar
e
in
te
g
r
ated
in
UC
p
r
o
b
le
m
f
o
r
m
u
latio
n
f
o
r
s
y
s
te
m
s
ec
u
r
it
y
c
o
n
s
id
er
atio
n
s
[
4
]
.
h.
C
r
e
w
co
n
s
tr
ai
n
ts
I
n
a
p
lan
t
w
ith
m
a
n
y
u
n
i
ts
,
th
er
e
m
a
y
n
o
t
b
e
en
o
u
g
h
p
er
s
o
n
n
el
to
atte
n
d
b
o
th
th
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s
i
f
b
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g
u
p
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d
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s
h
u
tti
n
g
d
o
w
n
s
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m
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lta
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s
l
y
.
S
u
c
h
co
n
s
tr
ain
ts
w
o
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ld
b
e
s
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b
y
th
e
t
i
m
es
r
eq
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to
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u
p
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d
to
s
h
u
td
o
w
n
t
h
e
u
n
it [
1
9
]
.
3
.
2
.
Unit
c
o
mm
it
m
ent
i
n
d
er
eg
ul
a
t
ed
e
nv
iro
n
m
e
nt
Sin
ce
1
9
8
0
s
,
P
o
w
er
s
y
s
te
m
s
h
av
e
m
o
v
ed
f
r
o
m
a
v
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tical
l
y
i
n
teg
r
ated
s
tr
u
ct
u
r
e
to
a
d
er
e
g
u
lated
o
n
e.
I
n
an
i
n
teg
r
ated
e
n
v
ir
o
n
m
e
n
t,
cu
s
to
m
er
s
o
f
g
en
er
atio
n
co
m
p
an
ies
(
GE
N
C
Os)
ar
e
alr
ea
d
y
s
et
an
d
d
ef
in
ed
[
5
]
.
I
n
th
e
ca
s
e
o
f
d
er
eg
u
lated
m
ar
k
et
s
,
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m
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n
e
n
ts
o
f
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ctr
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ar
k
et
s
u
ch
a
s
g
e
n
er
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n
co
m
p
an
ie
s
(
GE
NC
Os),
tr
an
s
m
is
s
io
n
co
m
p
a
n
ie
s
(
T
R
A
NS
C
O
s
)
,
an
d
d
is
tr
ib
u
tio
n
co
m
p
a
n
ies
(
DI
S
C
Os),
co
n
s
tr
u
ct
t
h
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g
en
er
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n
o
f
f
er
s
b
ased
o
n
a
v
ailab
le
s
i
g
n
al
s
,
a
n
d
co
n
s
eq
u
e
n
tl
y
g
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n
g
UC
s
o
l
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tio
n
.
E
ac
h
o
f
f
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n
s
is
ts
o
f
a
co
s
t
f
u
n
c
tio
n
a
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d
a
s
et
o
f
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a
m
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s
t
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at
d
e
f
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e
th
e
o
p
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e
co
n
s
tr
ain
ts
o
f
g
e
n
er
ati
n
g
u
n
i
ts
,
w
h
ic
h
en
ab
le
s
to
d
eter
m
i
n
e
t
h
e
s
y
s
te
m
m
a
r
g
in
al
co
s
t
f
o
r
ea
c
h
p
er
io
d
[8
4
]
.
I
n
d
er
eg
u
lated
en
v
ir
o
n
m
en
t,
th
e
o
b
j
ec
tiv
e
ch
an
g
es
f
r
o
m
co
s
t
m
in
i
m
izat
io
n
to
p
r
o
f
it
m
a
x
i
m
izatio
n
[
1
9
]
.
T
h
e
s
tu
d
ies
i
n
[
8
5
],
[
8
6
]
p
r
esen
ted
a
n
e
w
f
o
r
m
u
latio
n
o
f
th
e
U
C
p
r
o
b
lem
i
n
a
d
er
eg
u
lated
m
ar
k
et.
3
.
3
.
P
rice
-
b
a
s
ed
u
nit
c
o
mm
it
m
en
t
I
n
P
B
UC
,
s
ati
s
f
y
i
n
g
h
o
u
r
l
y
lo
ad
is
n
o
lo
n
g
er
a
r
estrictio
n
a
n
d
th
e
o
b
j
ec
tiv
e
is
to
m
a
x
i
m
ize
th
e
p
r
o
f
it
w
h
ile
s
ec
u
r
it
y
i
s
n
o
w
u
n
r
est
r
ain
ed
f
r
o
m
en
er
g
y
a
n
d
co
n
s
id
er
ed
as
an
cillar
y
s
er
v
ice.
T
h
u
s
,
i
n
t
h
e
P
B
UC
ap
p
r
o
ac
h
,
th
e
s
ig
n
al
th
a
t
w
o
u
ld
d
eter
m
i
n
e
a
u
n
it
’
s
co
m
m
it
m
en
t
s
tat
u
s
i
s
th
e
p
r
ice
o
f
d
if
f
er
en
t
s
er
v
ice
s
an
d
m
ater
ials
in
elec
tr
ical
o
p
er
ati
o
n
s
s
u
c
h
as
f
u
el
p
u
r
ch
ase
p
r
ice,
en
er
g
y
s
a
le
p
r
ice,
an
d
an
cillar
y
s
er
v
ice
s
ale
p
r
ice
[
5
4
]
,
[
8
4
]
.
T
h
e
en
er
g
y
s
u
p
p
lier
s
ar
e
r
esp
o
n
s
ib
le
f
o
r
t
h
e
w
a
y
t
h
e
y
s
ell
en
er
g
y
i
n
o
r
d
er
to
s
u
p
p
l
y
lo
ad
a
n
d
r
eser
v
e
m
ar
k
et
s
[
4
]
.
T
h
e
m
o
s
t
d
is
tin
c
t
ch
ar
ac
ter
i
s
tic
o
f
P
B
UC
is
th
a
t
all
m
ar
k
et
i
n
f
o
r
m
ati
o
n
ar
e
ex
p
r
ess
ed
i
n
m
ar
k
et
p
r
ice.
P
B
UC
p
r
o
b
lem
f
o
r
m
u
latio
n
s
ar
e
g
i
v
en
i
n
[
4
]
,
[
5
4
].
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
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N:
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8
8
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870
8
Un
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t P
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b
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in
E
lectrica
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ystem:
A
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)
1365
4.
ST
O
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AS
T
I
C
P
RO
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RAM
M
I
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’
S
AP
P
L
I
CAT
I
O
N
I
N
UNIT
CO
M
M
I
T
M
E
NT
No
w
ad
a
y
s
,
t
h
e
g
r
o
w
i
n
g
ca
p
ac
it
y
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o
r
r
en
e
w
ab
le
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lev
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t
h
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ea
l
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C
m
o
d
el
a
lar
g
e
-
s
ca
le,
n
o
n
-
co
n
v
ex
,
u
n
ce
r
tai
n
p
r
o
g
r
a
m
[8
7
]
.
T
h
e
in
te
g
r
atio
n
o
f
R
E
S
i
n
to
t
h
e
p
o
w
er
s
y
s
te
m
d
e
s
p
ite
it
s
i
n
ter
m
itte
n
t
n
atu
r
e
is
m
ain
l
y
j
u
s
ti
f
ied
b
y
its
ec
o
n
o
m
ic
an
d
en
v
ir
o
n
m
en
t
al
b
en
ef
its
f
o
r
th
e
s
y
s
te
m
.
So
u
r
ce
s
o
f
u
n
ce
r
tain
t
y
p
r
esen
t
in
r
ea
l
o
p
er
atio
n
al
en
v
i
r
o
n
m
e
n
t
s
ar
e
[
8
7
]
:
lo
a
d
d
e
m
an
d
,
r
en
e
w
ab
le
g
e
n
er
atio
n
,
u
n
it
av
ai
lab
ilit
y
,
in
f
lo
w
s
f
o
r
th
e
h
y
d
r
o
r
eser
v
o
ir
s
,
an
d
en
er
g
y
p
r
ices.
Gen
er
all
y
,
f
o
r
ec
ast
er
r
o
r
s
m
ai
n
l
y
r
esu
lt
f
r
o
m
lo
ad
v
ar
iatio
n
s
.
Ho
w
e
v
er
,
th
e
in
cr
e
ased
p
en
etr
atio
n
o
f
R
E
S
lead
to
s
u
p
p
le
m
en
tal
g
e
n
e
r
atio
n
f
o
r
ec
ast
er
r
o
r
s
d
u
e
to
its
i
n
ter
m
itte
n
ce
[
5
]
.
Sto
ch
a
s
ti
c
p
r
o
g
r
a
m
m
in
g
o
f
f
er
s
m
o
d
eli
n
g
an
d
s
o
lu
t
io
n
tec
h
n
iq
u
e
s
f
o
r
s
u
c
h
o
p
ti
m
izatio
n
p
r
o
b
lem
s
u
n
d
er
u
n
ce
r
tai
n
t
y
[
4
6
]
.
A
ctu
all
y
,
to
ac
h
ie
v
e
m
in
i
m
u
m
OC
s
u
b
j
ec
t
to
p
o
w
er
b
alan
ce
co
n
s
tr
ain
t
s
,
SOs
f
i
r
s
t
d
eter
m
i
n
e
g
en
er
ati
n
g
u
n
it
s
ON
/
O
FF
s
tat
u
s
es
a
n
d
p
r
o
d
u
ctio
n
ca
p
ac
ities
b
ased
o
n
f
o
r
ec
ast
v
al
u
es
a
n
d
tech
n
ical
co
n
s
tr
ai
n
ts
o
f
ea
ch
u
n
it.
A
f
ter
w
ar
d
s
,
a
r
e
-
d
is
p
atc
h
is
ca
r
r
ied
o
u
t
in
r
ea
l
-
ti
m
e
to
ad
j
u
s
t
th
e
d
if
f
er
en
ce
b
et
w
ee
n
th
e
r
ea
l
d
e
m
an
d
a
n
d
ex
p
ec
ted
o
u
tp
u
t.
T
h
e
r
ef
o
r
e,
UC
is
a
m
u
lti
-
s
ta
g
e
d
ec
is
io
n
p
r
o
ce
s
s
li
k
e
s
to
c
h
asti
c
p
r
o
g
r
am
m
i
n
g
(
SP
)
’
s
s
o
lv
i
n
g
p
r
o
ce
d
u
r
e,
w
h
ich
j
u
s
ti
f
ie
s
th
e
i
m
p
le
m
e
n
tatio
n
o
f
SP
f
o
r
s
o
lv
i
n
g
U
C
p
r
o
b
lem
w
it
h
u
n
ce
r
tai
n
tie
s
[
5
]
.
4
.
1
.
T
w
o
-
s
t
a
g
e
s
t
o
cha
s
t
ic
p
ro
g
ra
mm
i
ng
f
o
r
m
ula
t
io
n f
o
r
u
nit
c
o
mm
it
m
en
t
T
h
e
b
asic
UC
f
o
r
m
u
latio
n
(
with
o
u
t
co
n
s
id
er
in
g
s
ec
u
r
it
y
co
n
s
tr
ai
n
ts
)
s
er
v
es
as
t
h
e
s
u
p
p
o
r
t
f
o
r
SP
’
s
i
m
p
le
m
en
ta
tio
n
in
UC
p
r
o
b
lem
.
T
w
o
-
s
ta
g
e
SP
is
a
co
m
m
o
n
l
y
u
s
ed
ap
p
r
o
ac
h
to
ca
p
t
u
r
in
g
u
n
ce
r
tai
n
t
y
,
a
n
d
it
h
as t
h
e
f
o
llo
w
i
n
g
f
o
r
m
[
5
]
:
Min
+
E
[
(
)
]
,
s
.
t.
A
x
=
b
,
x
≥
0
W
h
er
e
(
)
=
m
i
n
{
q
y
(
)
,
W
y
(
)
= h
–
T x
,
y(
)
≥
0
}
Her
e,
x
an
d
y(
)
d
en
o
te
th
e
f
i
r
s
t
-
s
tag
e
a
n
d
s
ec
o
n
d
-
s
ta
g
e
d
ec
is
io
n
v
ar
iab
les
r
esp
ec
ti
v
el
y
.
Ma
in
l
y
,
v
ar
iab
les
x
r
ep
r
esen
t
th
e
d
ec
is
io
n
s
th
a
t
m
u
s
t
b
e
tak
e
n
b
e
f
o
r
e
th
e
u
n
ce
r
ta
in
t
y
i
s
s
o
l
v
e
d
,
an
d
th
e
f
u
n
ctio
n
(
)
r
ep
r
esen
t
th
e
d
ec
is
io
n
s
th
a
t
ca
n
b
e
tak
en
a
f
ter
th
e
u
n
ce
r
tai
n
t
y
is
s
o
l
v
ed
.
T
h
e
in
th
e
s
ec
o
n
d
-
s
ta
g
e
is
a
r
an
d
o
m
v
ec
to
r
an
d
E
[
(
)
]
is
u
s
e
d
to
r
etu
r
n
th
e
co
s
t
r
elate
d
to
th
is
r
an
d
o
m
v
ec
t
o
r
’
s
co
n
s
eq
u
en
ce
s
to
th
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
.
4
.
2
.
Securit
y
c
o
ns
t
ra
ined
u
nit
c
o
mm
i
t
m
e
nt
T
h
e
f
u
n
d
a
m
en
ta
l c
o
n
ce
p
t
in
t
h
e
r
eliab
le
an
d
ec
o
n
o
m
ic
o
p
er
atio
n
o
f
elec
tr
ic
p
o
w
er
s
y
s
te
m
s
is
SC
UC
.
SC
U
C
r
e
f
er
s
to
t
h
e
ec
o
n
o
m
ic
s
ch
ed
u
lin
g
o
f
g
en
er
ati
n
g
u
n
its
to
m
ee
t
t
h
e
h
o
u
r
l
y
lo
ad
d
e
m
a
n
d
w
h
ile
s
atis
f
y
i
n
g
te
m
p
o
r
al
an
d
o
p
er
atio
n
al
li
m
i
t
s
o
f
g
e
n
er
atio
n
a
n
d
tr
an
s
m
is
s
i
o
n
eq
u
ip
m
en
t
in
co
n
ti
n
g
en
c
y
p
o
w
er
s
y
s
te
m
s
[
2
7
]
.
I
n
a
v
er
t
icall
y
in
teg
r
ated
e
n
v
i
r
o
n
m
e
n
t,
SO
s
ap
p
l
y
SC
U
C
f
o
r
m
in
i
m
iz
in
g
t
h
e
O
C
w
h
ile
m
ee
ti
n
g
th
e
s
y
s
te
m
lo
ad
b
y
s
tar
ti
n
g
u
p
/s
h
u
tti
n
g
d
o
w
n
g
e
n
er
atin
g
u
n
it
s
.
I
n
r
estr
u
ctu
r
ed
p
o
w
er
m
ar
k
et
s
,
SC
U
C
is
u
tili
ze
d
b
y
I
SOs
to
lig
h
te
n
r
ea
l
ti
m
e
a
n
d
d
a
y
-
ah
ea
d
m
ar
k
et
s
,
w
it
h
th
e
o
b
j
e
ctiv
e
o
f
m
a
x
i
m
izi
n
g
t
h
e
s
o
cial
w
el
f
ar
e
b
ased
o
n
o
f
f
er
s
a
n
d
b
id
s
s
u
b
m
itted
b
y
m
ar
k
e
t
p
ar
ticip
an
ts
.
T
h
e
SC
UC
m
o
d
el
s
an
d
s
o
lu
tio
n
m
et
h
o
d
o
lo
g
ies
is
an
i
m
p
o
r
tan
t
k
e
y
d
ec
is
io
n
-
m
a
k
i
n
g
co
m
p
o
n
e
n
t
i
n
p
o
w
er
s
y
s
te
m
o
p
er
atio
n
s
,
p
ar
tic
u
lar
l
y
f
o
r
lar
g
e
s
y
s
te
m
s
.
Ma
th
e
m
atica
ll
y
,
th
e
S
C
UC
p
r
o
b
lem
is
a
lar
g
e
-
s
ca
le
MI
P
p
r
o
b
lem
w
it
h
m
a
n
y
b
i
n
ar
y
,
co
n
t
in
u
o
u
s
an
d
d
is
cr
ete
co
n
tr
o
l
v
ar
iab
les,
a
n
d
a
s
er
ies
o
f
co
n
s
tr
ain
t
s
[
4
]
.
SC
U
C
ap
p
r
o
ac
h
w
ith
AC
co
n
s
tr
ai
n
ts
is
p
r
o
p
o
s
ed
in
[
5
3
]
.
I
n
[4
5
]
,
a
SC
UC
m
o
d
el
f
o
r
o
p
en
m
ar
k
et,
w
h
ich
o
p
ti
m
izes
t
h
e
o
p
er
atio
n
s
ch
ed
u
li
n
g
a
n
d
p
r
ice
-
s
e
n
s
i
tiv
e
lo
ad
is
p
r
esen
ted
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
s
atis
f
y
g
en
er
a
t
io
n
,
r
eser
v
e
r
eq
u
ir
e
m
en
ts
,
tr
an
s
m
i
s
s
io
n
an
d
o
p
er
atin
g
co
n
s
tr
ain
ts
.
Deta
iled
f
o
r
m
u
lati
o
n
o
f
d
eter
m
i
n
is
t
ic
SC
U
C
p
r
o
b
le
m
is
p
r
o
p
o
s
ed
in
[2
7
]
.
4
.
3
.
Securit
y
co
ns
t
ra
ined un
it
co
mm
i
t
m
e
nt
w
it
h uncer
t
a
inties
T
h
er
e
ar
e
at
least
th
r
ee
s
o
lu
ti
o
n
tech
n
iq
u
es
t
h
at
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
m
an
a
g
i
n
g
u
n
ce
r
tain
tie
s
in
SC
U
C
,
in
cl
u
d
in
g
s
to
ch
a
s
tic
p
r
o
g
r
am
m
i
n
g
(
SP
)
,
r
o
b
u
s
t
o
p
tim
izatio
n
(
R
O)
,
an
d
ch
an
ce
-
co
n
s
tr
ai
n
ed
o
p
tim
izatio
n
(
C
C
O)
.
E
ac
h
tec
h
n
iq
u
e
h
as
d
i
f
f
er
en
t
p
r
ac
tical
an
d
co
m
p
u
ta
tio
n
al
r
eq
u
ir
e
m
e
n
ts
f
o
r
r
ep
r
esen
ti
n
g
an
d
li
m
iti
n
g
t
h
e
u
n
ce
r
tai
n
tie
s
in
p
o
w
er
s
y
s
te
m
[
8
7
]
.
SC
U
C
p
r
o
b
lem
w
it
h
u
n
ce
r
tain
ties
is
a
lar
g
e
-
s
ca
le,
n
o
n
-
co
n
v
e
x
,
NP
-
h
ar
d
p
r
o
b
lem
w
it
h
d
if
f
icu
lt
s
o
lu
tio
n
[
2
7
]
.
T
h
er
ef
o
r
e,
in
th
e
th
r
ee
m
o
d
els,
th
e
o
r
ig
in
al
lar
g
e
-
s
ca
le
MI
P
p
r
o
b
lem
i
s
u
s
u
all
y
d
ec
o
m
p
o
s
ed
to
a
m
a
s
ter
p
r
o
b
le
m
a
n
d
m
an
y
s
u
b
p
r
o
b
lem
s
b
y
B
en
d
er
s
d
ec
o
m
p
o
s
i
tio
n
tech
n
iq
u
e
[
6
1
]
.
T
h
e
n
ex
t p
ar
ag
r
ap
h
s
b
r
ief
l
y
d
i
s
cu
s
s
t
h
e
th
r
ee
m
et
h
o
d
o
lo
g
ies p
r
o
p
o
s
ed
in
liter
atu
r
e.
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
.
3
,
J
u
n
e
2
0
1
8
:
1
3
5
7
–
1372
1366
4
.
3
.
1
.
Sto
cha
s
t
ic
p
ro
g
ra
m
m
i
ng
SP
is
a
r
e
n
o
w
n
ed
o
p
ti
m
izati
o
n
tech
n
iq
u
e
to
s
o
l
v
e
SC
U
C
p
r
o
b
lem
w
i
th
u
n
ce
r
tai
n
tie
s
.
I
n
t
h
e
SP
ap
p
r
o
ac
h
,
p
o
w
er
s
y
s
te
m
u
n
ce
r
tain
ties
ar
e
r
ep
r
esen
ted
b
y
a
s
et
o
f
s
ce
n
ar
io
s
f
o
r
th
e
p
o
s
s
ib
le
r
ea
lizatio
n
o
f
d
if
f
er
e
n
t
u
n
ce
r
tain
t
ies
[
6
]
.
SP
tech
n
iq
u
e
is
b
ased
o
n
s
ce
n
a
r
io
tr
ee
in
w
h
ic
h
u
n
ce
r
tai
n
t
y
is
s
u
p
p
o
s
ed
to
b
e
k
n
o
w
n
i
n
its
ea
c
h
n
o
d
e
s
in
ce
f
u
r
t
h
er
m
o
r
e
u
n
ce
r
tai
n
t
y
is
n
o
w
d
is
cr
etize
d
o
n
t
h
e
tr
ee
,
es
s
e
n
tiall
y
t
h
e
q
u
a
n
tit
y
f
o
r
s
o
lv
i
n
g
a
d
eter
m
in
i
s
tic
l
ar
g
e
-
s
ca
le
UC
p
r
o
b
le
m
[
8
7
]
.
Usu
al
l
y
,
t
h
e
s
ce
n
ar
io
-
b
ased
ap
p
r
o
ac
h
g
en
er
ates
s
ce
n
ar
io
s
v
ia
a
s
s
u
m
ed
p
r
o
b
a
b
ilit
y
d
is
tr
ib
u
tio
n
f
u
n
ctio
n
s
f
o
r
s
i
m
u
lati
n
g
u
n
ce
r
tai
n
ties
a
n
d
ea
ch
s
ce
n
ar
io
i
s
attr
ib
u
ted
a
ce
r
tain
p
r
o
b
ab
ilit
y
f
o
r
its
r
ea
lizatio
n
.
I
n
SP
,
m
an
y
s
ce
n
ar
io
s
ar
e
n
ee
d
ed
f
o
r
r
ea
ch
in
g
a
n
ac
ce
p
tab
le
s
o
lu
tio
n
,
w
h
ic
h
r
is
e
s
t
h
e
s
ize
o
f
th
e
m
o
d
el,
ex
te
n
d
s
t
h
e
c
o
m
p
u
tatio
n
b
u
r
d
en
,
a
n
d
li
m
i
t
s
th
e
ap
p
licat
io
n
to
lar
g
e
s
ize
p
o
w
er
s
y
s
te
m
s
.
T
h
u
s
,
t
h
e
s
ce
n
ar
io
r
ed
u
ctio
n
tec
h
n
iq
u
es
ar
e
u
s
u
al
l
y
ad
o
p
ted
t
o
r
ed
u
ce
th
e
s
ca
le
o
f
th
e
s
to
c
h
asti
c
m
o
d
el
an
d
th
e
r
eq
u
ir
ed
co
m
p
u
tatio
n
e
f
f
o
r
t,
w
h
ich
e
n
ab
les to
k
ee
p
clo
s
e
s
ce
n
ar
io
s
b
y
m
ea
s
u
r
in
g
th
e
p
r
o
b
ab
ilis
tic
d
is
tan
ce
b
et
w
ee
n
s
ce
n
ar
io
s
an
d
eli
m
i
n
ates s
ce
n
ar
io
s
w
it
h
v
er
y
lo
w
p
r
o
b
ab
ilit
ies
[
2
7
]
.
4
.
3
.
2
.
Ro
bu
s
t
o
pti
m
iza
t
io
n
R
O
is
an
alter
n
ati
v
e
tech
n
iq
u
e
f
o
r
d
ea
lin
g
w
it
h
u
n
ce
r
tai
n
ti
es
in
t
h
e
SC
U
C
p
r
o
b
lem
.
R
O
u
s
es
t
h
e
n
o
tio
n
o
f
u
n
ce
r
tai
n
t
y
s
et
b
e
le
s
s
d
e
m
an
d
i
n
g
o
n
t
h
e
r
ep
r
esen
t
atio
n
o
f
u
n
ce
r
tain
t
y
,
w
h
ic
h
a
s
s
e
m
b
les t
h
e
ad
v
er
s
e
ev
en
t
s
ag
a
in
s
t
w
h
ich
w
e
w
i
s
h
to
p
r
o
tect
o
u
r
s
elv
e
s
.
T
h
is
u
n
ce
r
tain
t
y
s
e
t
co
n
s
id
er
s
a
li
m
ited
le
v
el
o
f
in
f
o
r
m
atio
n
o
n
u
n
ce
r
tai
n
q
u
a
n
titi
e
s
,
n
a
m
el
y
t
h
e
m
ea
n
v
al
u
e
an
d
s
o
m
e
est
i
m
a
te
o
f
th
e
v
a
r
ian
ce
o
r
a
r
an
g
e
o
f
p
o
s
s
ib
le
v
ar
iatio
n
s
ar
o
u
n
d
th
e
m
ea
n
[
2
7
]
.
C
o
n
s
eq
u
e
n
tl
y
,
th
e
R
O
m
o
d
el
s
ee
k
s
an
o
p
ti
m
a
l
co
m
m
it
m
en
t
a
n
d
d
is
p
atch
s
o
l
u
tio
n
o
f
t
h
e
g
e
n
er
atin
g
u
n
it
s
f
o
r
p
r
ev
en
ti
n
g
th
e
s
o
lu
tio
n
a
g
ai
n
s
t t
h
e
w
o
r
s
t e
co
n
o
m
ic
co
n
d
itio
n
(
t
h
e
h
ig
h
e
s
t
m
i
n
i
m
u
m
d
is
p
atc
h
co
s
t)
,
w
h
ic
h
w
o
u
l
d
p
r
o
tect
th
e
p
o
w
er
s
y
s
te
m
a
g
ai
n
s
t
ea
ch
e
v
en
t
in
t
h
e
s
p
ec
if
ied
u
n
ce
r
tai
n
t
y
s
et
r
e
g
ar
d
less
o
f
it
s
p
r
o
b
ab
ilit
y
[
8
7
]
.
4
.
3
.
3
.
Cha
nce
-
c
o
ns
t
ra
ined
o
pti
m
iz
a
t
io
n
C
C
O
is
a
n
o
th
er
ap
p
licab
le
a
p
p
r
o
ac
h
f
o
r
h
an
d
li
n
g
u
n
ce
r
ta
in
tie
s
i
n
t
h
e
h
o
u
r
l
y
SC
UC
p
r
o
b
lem
,
i
n
w
h
ic
h
te
m
p
o
r
al
co
n
s
tr
ain
ts
c
an
b
e
v
io
lated
w
it
h
a
p
r
ed
ef
i
n
ed
lev
el
o
f
p
r
o
b
ab
ilit
y
.
C
C
O
ap
p
ea
r
s
as
a
g
o
o
d
alter
n
ati
v
e
to
s
elec
t
t
h
e
tr
ad
eo
f
f
b
et
w
ee
n
co
s
t
a
n
d
r
o
b
u
s
tn
es
s
b
ased
o
n
t
h
e
p
r
o
b
ab
ilit
y
t
h
at
t
h
e
s
elec
ted
s
o
lu
tio
n
is
t
h
e
f
ea
s
ib
le
o
n
e
wh
ich
is
ea
s
y
f
o
r
SO
to
u
n
d
er
s
t
an
d
an
d
m
a
n
a
g
e
[
8
7
]
.
C
C
O
m
atch
es
t
h
e
n
at
u
r
e
o
f
th
e
S
C
UC
o
p
er
atio
n
th
at
o
n
e
m
a
y
n
o
t
ac
tu
all
y
b
e
ab
le
to
g
u
ar
an
tee
th
at
tr
a
n
s
m
i
s
s
io
n
s
ec
u
r
it
y
co
n
s
tr
ai
n
t
s
(
s
u
c
h
as
s
y
s
te
m
lo
ad
b
alan
ce
o
r
tr
an
s
m
i
s
s
io
n
ca
p
ac
it
y
)
w
i
ll
n
e
v
er
b
e
v
io
lated
.
R
ath
er
,
o
n
e
s
h
o
u
ld
p
r
o
v
id
e
SC
U
C
s
o
lu
t
io
n
s
t
h
at
ar
e
r
ea
s
o
n
ab
l
y
f
ea
s
ib
le
b
y
o
f
f
er
i
n
g
li
m
ited
lo
ad
s
h
ed
d
in
g
,
u
n
d
er
all
ex
ce
p
t
th
e
m
o
s
t
u
n
l
ik
el
y
s
ce
n
ar
io
s
[
2
7
]
.
4
.
3
.
4
.
Co
m
pa
riso
n o
f
s
o
lutio
n
a
pp
ro
a
ches
T
h
e
th
r
ee
S
C
U
C
f
o
r
m
u
latio
n
s
w
it
h
u
n
ce
r
tain
t
ies
m
a
y
r
ep
r
esen
t
d
if
f
er
en
t
p
er
f
o
r
m
a
n
ce
s
,
in
cl
u
d
in
g
s
o
lu
tio
n
r
o
b
u
s
t
n
es
s
i
n
t
h
e
f
ac
e
o
f
u
n
ce
r
tai
n
tie
s
,
t
h
e
co
s
t
o
f
g
en
er
atio
n
s
ch
ed
u
les,
a
n
d
t
h
e
c
o
m
p
u
tatio
n
al
co
s
t.
T
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
s
m
a
y
b
e
ef
f
ec
tiv
el
y
co
m
b
in
ed
f
o
r
en
h
a
n
ci
n
g
t
h
e
q
u
alit
y
o
f
th
e
SC
U
C
s
o
lu
tio
n
an
d
au
g
m
e
n
ti
n
g
t
h
e
co
m
p
u
t
atio
n
al
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
p
r
o
p
o
s
ed
h
e
u
r
is
tic
s
[
2
7
]
.
I
n
th
i
s
c
o
n
tex
t,
w
o
rk
in
[
6
9
]
p
r
esen
ted
UC
p
r
o
b
le
m
w
i
th
u
n
ce
r
tai
n
w
i
n
d
g
en
er
atio
n
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
i
n
clu
d
e
s
b
o
th
th
e
t
w
o
-
s
tag
e
s
to
ch
ast
ic
p
r
o
g
r
a
m
a
n
d
t
h
e
c
h
an
ce
-
co
n
s
tr
ai
n
ed
s
to
ch
a
s
tic
p
r
o
g
r
am
tech
n
iq
u
es,
w
h
ic
h
h
as
allo
w
ed
g
et
tin
g
a
g
o
o
d
q
u
alit
y
s
o
lu
tio
n
.
T
ab
le
2
p
r
o
v
id
es
a
co
m
p
ar
is
o
n
b
et
w
e
en
th
e
t
h
r
ee
s
o
lu
tio
n
tech
n
iq
u
es
p
r
esen
ted
in
th
i
s
s
ec
tio
n
.
T
ab
le
2
.
C
o
m
p
ar
is
o
n
b
et
w
ee
n
S
o
lu
tio
n
A
ap
p
r
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