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[
1
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I
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2733
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n
e
s
u
b
p
r
o
b
le
m
p
er
h
y
d
r
o
p
lan
t.
L
R
t
h
e
n
ev
al
u
ate
s
th
e
d
u
al
p
r
o
b
le
m
t
h
r
o
u
g
h
t
h
e
d
ec
o
m
p
o
s
ed
p
r
i
m
al
p
r
o
b
lem
,
in
co
r
p
o
r
atin
g
L
a
g
r
an
g
e
m
u
ltip
lier
s
o
f
g
lo
b
al
v
ar
iab
les,
b
y
s
o
l
v
i
n
g
t
h
e
s
u
b
p
r
o
b
lem
s
o
f
t
h
er
m
a
l
u
n
it
s
an
d
h
y
d
r
o
elec
tr
ic
o
n
es
[
3
]
.
Sin
ce
in
d
i
v
id
u
al
t
h
er
m
al
an
d
h
y
d
r
o
u
n
i
ts
ar
e
m
o
d
eled
as
s
ep
ar
ate
s
u
b
p
r
o
b
lem
s
in
L
R
,
d
ev
is
i
n
g
th
e
co
u
p
li
n
g
co
n
s
tr
ain
t
s
ca
n
b
e
f
o
r
m
id
ab
le.
As
co
m
p
ar
ed
w
ith
DP
,
L
R
d
o
es
n
o
t
s
u
f
f
er
f
r
o
m
th
e
c
u
r
s
e
o
f
d
i
m
e
n
s
io
n
alit
y
,
alb
eit
e
n
co
u
n
ter
in
g
i
n
s
tan
ce
s
o
f
u
n
n
ec
es
s
ar
y
co
m
m
i
t
m
en
t o
f
u
n
its
; r
en
d
er
in
g
h
i
g
h
er
p
r
o
d
u
ctio
n
co
s
ts
[
15
]
.
A
d
d
itio
n
all
y
,
h
e
u
r
is
tic
r
ea
s
o
n
i
n
g
i
s
r
eq
u
ir
ed
to
m
ee
t t
h
e
d
u
alit
y
g
a
p
[
6
]
.
Mix
ed
-
i
n
te
g
er
li
n
ea
r
p
r
o
g
r
am
m
i
n
g
(
MI
L
P
)
,
u
s
in
g
B
r
an
c
h
an
d
B
o
u
n
d
an
d
C
u
t
(
B
B
&
C
)
al
g
o
r
ith
m
,
i
s
a
p
o
w
er
f
u
l
to
o
l
to
s
o
lv
e
co
m
b
i
n
ato
r
ial
o
p
ti
m
izatio
n
p
r
o
b
le
m
s
[
16
]
.
Sin
ce
MI
L
P
o
b
v
iates
th
e
n
ee
d
f
o
r
h
eu
r
is
tic
r
ea
s
o
n
in
g
an
d
p
r
o
v
id
es
a
d
ir
ec
t
m
at
h
e
m
at
ical
m
o
d
eli
n
g
o
f
t
h
e
co
u
p
lin
g
co
n
s
tr
ain
t
s
,
it
s
u
r
p
ass
es
DP
an
d
L
R
ap
p
r
o
ac
h
es
[
15
]
.
M
I
L
P
co
n
v
er
ts
th
e
as
s
o
ciate
d
n
o
n
li
n
e
ar
ities
o
f
th
e
HT
S
m
o
d
el,
th
r
o
u
g
h
a
p
iece
w
i
s
e
lin
ea
r
izatio
n
,
i
n
to
a
s
et
o
f
lin
e
ar
in
eq
u
alitie
s
.
C
P
L
E
X,
an
o
f
f
-
th
e
-
s
h
el
f
s
o
f
t
w
ar
e
f
o
r
s
o
lv
i
n
g
lar
g
e
-
s
ca
le
MI
L
P
p
r
o
b
lem
s
u
s
i
n
g
B
B
&
C
al
g
o
r
ith
m
,
ca
n
th
e
n
b
e
ap
p
lied
[
8
,
1
0
, 1
1
,
13
,
15
]
.
I
n
m
an
y
o
f
th
e
HT
S in
v
e
s
ti
g
at
io
n
s
,
h
y
d
r
o
u
n
its
i
n
a
p
lan
t
w
e
r
e
co
m
m
o
n
l
y
a
g
g
r
eg
ated
as o
n
e
u
n
it [
7
]
.
W
h
ile
t
h
is
r
ed
u
ce
s
t
h
e
to
tal
n
u
m
b
er
o
f
d
ec
is
io
n
v
ar
iab
les
,
r
esu
lti
n
g
i
n
a
less
co
m
p
u
tat
io
n
all
y
d
e
m
a
n
d
in
g
p
r
o
b
lem
,
it
m
a
y
,
o
n
th
e
o
th
er
h
an
d
,
im
p
air
th
e
ac
cu
r
ac
y
o
f
t
h
e
s
o
lu
tio
n
.
I
n
an
ac
tu
a
l
h
y
d
r
o
p
lan
t,
an
d
at
a
c
er
tain
in
s
ta
n
t
d
u
r
in
g
th
e
s
c
h
ed
u
li
n
g
p
er
io
d
,
s
o
m
e
u
n
its
m
a
y
b
e
co
m
m
itted
,
w
h
ile
o
t
h
er
s
ar
e
s
h
u
t
d
o
w
n
.
I
n
ad
d
itio
n
,
in
s
o
m
e
ca
s
es,
ca
s
ca
d
ed
r
eser
v
o
ir
s
o
v
er
th
e
s
a
m
e
r
iv
er
b
asi
n
w
er
e
ass
u
m
ed
to
b
e
in
d
ep
en
d
en
t,
s
u
c
h
th
a
t
th
e
co
m
p
le
x
it
y
o
f
t
h
e
m
o
d
e
l b
ec
o
m
es
m
o
r
e
m
a
n
ag
ea
b
le
[
3
,
17]
.
T
h
is
p
ap
er
av
er
ts
t
h
e
ab
o
v
e
is
s
u
es
an
d
p
r
o
p
o
s
es
a
co
m
p
r
eh
en
s
i
v
e,
f
i
n
e
-
g
r
ai
n
ed
s
y
s
t
e
m
m
o
d
el.
An
MI
L
P
-
b
ased
ap
p
r
o
ac
h
f
o
r
t
h
er
m
al
u
n
it
co
m
m
it
m
e
n
t
an
d
s
ch
ed
u
li
n
g
o
f
h
y
d
r
o
g
en
er
atio
n
u
n
i
ts
is
d
ev
elo
p
ed
,
u
s
i
n
g
t
h
e
B
B
&
C
al
g
o
r
ith
m
.
T
h
e
co
n
tr
ib
u
tio
n
o
f
th
i
s
p
ap
er
is
i
n
t
h
r
ee
m
aj
o
r
asp
ec
ts
.
First,
a
n
elab
o
r
ate
h
y
d
r
au
li
c
m
o
d
el
f
o
r
t
h
e
r
i
v
er
an
d
ca
s
c
ad
ed
r
eser
v
o
ir
s
s
y
s
te
m
w
i
th
co
m
p
lica
tin
g
co
n
s
tr
ai
n
ts
(
u
n
it
-
w
i
s
e,
h
ea
d
e
f
f
ec
t,
ca
s
ca
d
ed
r
eser
v
o
ir
s
,
r
ip
ar
ian
,
f
u
el)
is
d
e
v
el
o
p
ed
.
Seco
n
d
,
an
MI
L
P
f
o
r
m
u
latio
n
f
o
r
th
e
p
r
es
en
ted
h
y
d
r
o
-
t
h
er
m
a
l
s
ch
ed
u
lin
g
(
HT
S)
m
o
d
el
is
ca
r
r
ied
o
u
t.
No
n
-
co
n
v
ex
p
r
o
d
u
c
tio
n
co
s
t,
s
tar
t
-
u
p
/
s
h
u
t
-
d
o
w
n
co
s
t,
an
d
th
e
h
y
d
r
o
p
er
f
o
r
m
a
n
ce
cu
r
v
e,
ar
e
all
lin
ea
r
ized
ac
cu
r
ately
p
r
o
d
u
cin
g
a
f
in
er
cu
t
an
d
a
n
ar
r
o
w
e
r
s
ea
r
ch
s
p
ac
e.
L
ast,
to
m
ak
e
t
h
e
HT
S
s
o
l
u
tio
n
m
o
r
e
ef
f
icie
n
t
a
n
d
m
ak
e
th
e
m
ax
i
m
al
u
s
e
o
f
e
x
i
s
ti
n
g
r
eso
u
r
ce
s
,
m
u
ltit
h
r
ea
d
in
g
i
s
ex
p
lo
ited
to
en
h
a
n
ce
co
m
p
u
tat
io
n
al
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
s
o
lu
t
io
n
.
T
h
is
ca
n
o
n
l
y
b
e
ac
h
ie
v
ed
d
u
e
to
th
e
w
a
y
t
h
e
p
r
o
b
lem
is
s
tr
u
ct
u
r
ed
,
to
m
a
k
e
it
am
e
n
ab
le
f
o
r
p
ar
allel
p
r
o
ce
s
s
i
n
g
.
C
o
n
s
eq
u
e
n
tl
y
,
v
er
y
l
ar
g
e
s
y
s
te
m
s
,
w
i
th
th
o
r
o
u
g
h
h
y
d
r
au
lic
m
o
d
elin
g
,
ca
n
b
e
s
o
lv
ed
in
a
r
elati
v
el
y
s
h
o
r
t ti
m
e.
T
h
e
o
r
g
an
izatio
n
o
f
th
e
p
ap
er
is
as
f
o
llo
w
s
:
Sectio
n
2
p
r
esen
ts
th
e
f
o
r
m
u
latio
n
o
f
th
e
HT
S
p
r
o
b
l
em
.
Sectio
n
3
b
r
ief
l
y
d
e
s
cr
ib
es th
e
lin
ea
r
izatio
n
o
f
th
e
p
r
o
d
u
ctio
n
co
s
t,
s
tair
-
w
i
s
e
s
tar
t
-
u
p
co
s
t
an
d
s
h
u
t
-
d
o
w
n
co
s
t
m
o
d
el
s
o
f
t
h
e
MI
L
P
-
HT
S
p
r
o
b
lem
.
C
ase
s
tu
d
ies
an
d
n
u
m
er
ical
r
es
u
lts
ar
e
d
e
m
o
n
s
tr
ated
in
Sectio
n
4
.
Sectio
n
5
p
r
o
v
id
es c
o
n
clu
s
io
n
s
.
2.
H
YDRO
T
H
E
RM
AL
SCH
E
DULI
NG
P
RO
B
L
E
M
T
h
e
H
T
S p
r
o
b
lem
ca
n
b
e
m
at
h
e
m
a
ticall
y
f
o
r
m
u
la
ted
as
:
2
.
1
.
O
bje
c
t
iv
e
f
un
ct
io
n
T
h
e
o
b
j
ec
tiv
e
o
f
t
h
e
HT
S
s
c
h
ed
u
lin
g
i
s
to
m
in
i
m
ize
t
h
e
p
r
o
d
u
ctio
n
co
s
t,
s
tar
t
-
u
p
co
s
t,
an
d
s
h
u
t
-
d
o
wn
co
s
ts
o
f
all
g
en
er
ati
n
g
u
n
i
ts
,
o
v
er
th
e
s
ch
ed
u
li
n
g
h
o
r
izo
n
T
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
is
co
n
s
tr
ain
ed
b
y
d
e
m
a
n
d
an
d
r
eser
v
e
r
eq
u
ir
e
m
e
n
t
s
[
2
].
J
j
T
t
t
c
t
s
t
c
sd
j
T
t
J
j
su
j
p
j
,
),
(
)
(
)
(
M
i
n
.
(
1
)
Su
b
j
ec
t to
I
i
J
j
T
t
t
D
t
p
t
p
I
i
i
J
j
j
,
,
)
(
)
(
)
(
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
2
0
8
8
-
8708
I
n
t J
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lec
&
C
o
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p
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g
,
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
27
3
2
-
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2734
)
(
)
(
)
(
)
(
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(
m
a
x
m
a
x
t
SR
D
(
t
)
t
p
t
t
p
t
y
I
i
i
J
j
j
(
3
)
J
j
T
t
t
t
p
j
j
,
),
(
)
(
(
4
)
I
i
T
t
t
t
p
i
i
,
),
(
)
(
(
5
)
I
n
th
e
ab
o
v
e
f
o
r
m
u
latio
n
,
p
r
o
d
u
ctio
n
co
s
t
in
c
lu
d
es
m
ai
n
ten
an
ce
co
s
ts
as
a
f
i
x
ed
co
m
p
o
n
en
t
p
er
u
n
it
e
n
er
g
y
.
T
h
e
o
p
e
r
atio
n
co
s
t o
f
h
y
d
r
o
u
n
its
i
s
n
o
t a
cc
o
u
n
ted
f
o
r
in
t
h
e
ab
o
v
e
f
o
r
m
u
la
tio
n
,
s
i
n
ce
it i
s
n
eg
l
ig
ib
le
.
T
h
e
co
s
t
f
u
n
ctio
n
is
s
u
b
j
ec
t
t
o
th
e
p
o
w
er
b
alan
ce
eq
u
atio
n
s
,
(
2
)
an
d
(
3
)
,
s
u
ch
th
at,
to
tal
g
en
er
atio
n
f
r
o
m
h
y
d
r
o
an
d
th
er
m
al
u
n
its
m
u
s
t
m
a
tch
d
e
m
a
n
d
an
d
s
p
in
n
in
g
r
eser
v
e
(
1
0
% o
f
th
e
lo
ad
a
t th
is
p
ap
er
)
at
ea
ch
in
ter
v
a
l.
T
h
e
m
o
d
el
also
e
n
co
m
p
a
s
s
e
s
in
s
ta
n
t
r
eser
v
e
s
th
a
t
ca
n
b
e
av
ailab
le
in
f
i
v
e
m
in
u
te
s
o
n
l
y
.
T
h
e
latter
ca
n
b
e
ex
p
r
ess
ed
in
th
e
s
a
m
e
w
a
y
as
s
p
in
n
in
g
r
eser
v
e
s
(
3
)
.
T
h
e
d
em
a
n
d
D
(
t
)
in
clu
d
es
tr
a
n
s
m
i
s
s
io
n
lo
s
s
es
as
w
ell.
I
n
itiall
y
,
lo
s
s
e
s
ar
e
ac
co
u
n
ted
f
o
r
as
f
i
x
ed
,
b
u
t
g
et
u
p
d
ated
in
s
u
b
s
eq
u
e
n
t
iter
atio
n
s
.
T
h
e
f
ea
s
ib
le
r
eg
io
n
t
h
a
t
ea
ch
th
er
m
al
a
n
d
h
y
d
r
o
u
n
it
is
p
er
m
i
tted
to
o
p
er
ate
w
ith
in
ar
e
r
ep
r
esen
ted
b
y
(
4
)
an
d
(
5
)
.
Un
it
-
w
i
s
e
l
i
m
itat
io
n
s
s
u
c
h
as r
a
m
p
u
p
/d
o
w
n
,
m
i
n
i
m
u
m
u
p
/d
o
w
n
,
an
d
u
n
i
t’
s
g
e
n
er
atio
n
ca
p
ac
it
y
f
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u
n
d
er
th
e
s
e
eq
u
atio
n
s
.
2
.
2
.
T
her
m
a
l c
o
ns
t
ra
ints
J
j
T
t
t
y
P
t
p
t
y
P
j
j
j
j
j
,
),
(
)
(
)
(
m
a
x
m
i
n
(
6
)
J
j
T
t
RU
t
p
t
p
j
j
j
,
,
)
1
(
)
(
(
7
)
J
j
T
t
RD
t
p
t
p
j
j
j
,
,
)
(
)
1
(
(
8
)
J
j
T
t
V
t
V
T
t
J
j
t
o
t
a
l
g
j
,
,
)
(
(
9
)
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(
)
(
)
(
2
t
p
c
t
p
b
t
y
a
V
j
j
j
j
j
j
g
j
(
1
0
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E
q
u
atio
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(
6
)
ex
p
r
ess
es
th
e
u
p
p
er
/lo
w
er
b
o
u
n
d
s
f
o
r
th
er
m
al
g
e
n
er
atio
n
u
n
it
o
u
tp
u
t,
w
h
er
ea
s
th
e
ca
p
ab
ilit
y
o
f
ea
ch
u
n
it
to
r
a
m
p
u
p
/d
o
w
n
ca
n
b
e
m
o
d
eled
as
(
7
)
-
(
8
)
.
A
th
er
m
al
u
n
it
j
ca
n
r
a
m
p
u
p
/d
o
w
n
f
r
o
m
th
e
cu
r
r
en
t
/p
r
ec
ed
in
g
i
n
ter
v
al
to
th
e
co
n
s
ec
u
tiv
e
/cu
r
r
en
t
ti
m
e
-
i
n
ter
v
al
le
s
s
th
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n
a
p
r
e
-
s
p
ec
i
f
ied
r
ate
o
f
r
am
p
i
n
g
RU
j
/
RD
j
.
Min
i
m
u
m
u
p
/d
o
w
n
t
i
m
e
co
n
s
tr
ain
t
s
an
d
s
p
i
n
n
in
g
r
eser
v
e
allo
ca
tio
n
ar
e
d
etaile
d
in
[
8
].
On
e
o
f
th
e
co
u
p
li
n
g
co
n
s
tr
ai
n
ts
,
t
h
at
co
u
p
le
all
th
er
m
a
l
g
en
er
ato
r
s
in
th
e
m
i
x
,
is
th
e
li
m
ited
f
u
el
av
ailab
ilit
y
o
v
er
t
h
e
s
c
h
ed
u
li
n
g
h
o
r
izo
n
.
T
h
e
to
tal
u
s
e
o
f
g
as
o
v
er
a
ti
m
e
s
p
an
,
T
,
is
less
th
an
th
e
a
v
ailab
le
g
a
s
v
o
lu
m
e
(
9
)
.
T
h
e
f
u
el
co
n
s
u
m
p
tio
n
is
r
ep
r
esen
ted
b
y
a
q
u
ad
r
a
tic
f
u
n
ct
io
n
(
1
0
)
.
2
.
3
.
H
y
dra
uli
c
co
ns
t
ra
ints
T
h
e
tw
o
k
i
n
d
s
o
f
h
y
d
r
au
lic
co
n
s
tr
ain
ts
,
f
i
x
ed
-
h
ea
d
h
y
d
r
o
u
n
i
t
an
d
v
ar
iab
le
h
ea
d
h
y
d
r
o
u
n
it,
ar
e
co
n
s
id
er
ed
to
d
em
o
n
s
tr
ate
th
e
h
y
d
r
au
lic
h
ea
d
v
ar
iatio
n
ef
f
ec
t.
T
h
e
f
i
x
ed
-
h
ea
d
h
y
d
r
o
u
n
i
t c
an
b
e
ex
p
r
ess
ed
as [
17
]
:
I
i
T
t
t
q
f
t
p
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,
,
)
(
)
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(
1
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1
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h
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v
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h
ea
d
h
y
d
r
o
u
n
i
t c
an
b
e
r
ep
r
esen
ted
as [
18
]:
I
i
T
t
t
h
t
q
f
t
p
i
i
i
,
,
)
(
),
(
)
(
(
1
3
)
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r
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1
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T
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ip
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ex
p
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m
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1
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1
3
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.
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1
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5
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ized
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1
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(
1
6
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T
h
e
w
ater
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in
u
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h
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eser
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s
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m
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s
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lin
ea
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n
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ip
as
ill
u
s
tr
ate
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in
(
1
6
)
.
T
h
e
w
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ter
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o
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ir
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ciate
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ep
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ater
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is
ch
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f
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m
th
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m
e
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o
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illed
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ater
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u
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ts
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ciate
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w
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th
t
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e
r
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s
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B
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ith
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m
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3.
M
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-
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RM
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ch
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ter
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t
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as
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as
t
h
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co
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s
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ts
.
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li
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atic
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h
y
d
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m
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ce
cu
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v
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co
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s
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n
b
e
lin
ea
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ized
to
f
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m
an
eq
u
i
v
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n
t M
I
L
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f
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m
u
la
tio
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,
s
o
th
a
t it
ca
n
b
e
s
o
l
v
ed
ef
f
icie
n
tl
y
.
T
o
ca
ter
f
o
r
th
e
n
o
n
li
n
ea
r
it
y
r
etai
n
ed
b
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t
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e
m
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x
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n
teg
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n
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n
lin
ea
r
m
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d
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s
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m
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t
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s
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tr
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ts
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n
s
eq
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en
t
l
y
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lar
g
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-
s
c
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p
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b
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ca
n
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e
m
o
d
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ated
an
d
m
a
n
a
g
ed
ef
f
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n
tl
y
.
3
.
1
.
L
inea
rize
d
pro
du
ct
io
n c
o
s
t
E
q
u
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n
(
2
0
)
o
f
t
h
e
q
u
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r
ati
c
p
r
o
d
u
ctio
n
co
s
t
(
$
-
MW
)
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n
b
e
p
iece
w
is
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li
n
ea
r
l
y
ap
p
r
o
x
i
m
ated
,
(
2
1
)
-
(
2
6
)
,
b
y
co
n
te
m
p
lati
n
g
s
u
f
f
icien
t
n
u
m
b
er
o
f
b
r
ea
k
p
o
in
t
s
[
8
]
.
A
s
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n
g
le
t
y
p
e
o
f
b
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n
ar
y
v
ar
iab
le
y
j
(
t
)
to
m
o
d
el
th
e
en
tire
MI
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P
f
o
r
m
u
latio
n
is
d
ee
m
ed
s
u
f
f
ic
ien
t
[
8
]
.
C
h
o
o
s
in
g
an
ad
eq
u
ate
n
u
m
b
er
o
f
b
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ea
k
p
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in
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in
th
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izo
n
tal
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s
m
a
k
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p
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tat
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m
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t
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tical
to
th
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al
n
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n
li
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ea
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cu
r
v
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as
d
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tr
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F
ig
u
r
e
1
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On
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p
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w
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s
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li
n
ea
r
izatio
n
ca
n
d
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m
p
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o
v
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t
h
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ap
p
r
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x
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m
at
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n
ac
cu
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ac
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.
On
th
e
o
t
h
er
h
a
n
d
,
w
i
th
i
n
cr
ea
s
ed
n
u
m
b
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f
b
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ea
k
p
o
in
ts
,
th
e
p
r
o
b
lem
s
ize
m
a
y
b
e
s
wo
llen
an
d
th
e
co
m
p
u
tatio
n
al
p
r
o
ce
s
s
co
u
ld
b
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c
o
m
p
r
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m
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s
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.
Fo
u
r
p
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w
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s
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s
eg
m
e
n
ts
p
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v
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d
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ad
eq
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m
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d
eli
n
g
o
f
th
e
q
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atic
co
s
t
f
u
n
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,
r
en
d
er
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g
a
s
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t
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w
it
h
ac
ce
p
tab
le
ac
cu
r
ac
y
an
d
in
a
m
o
d
er
ate
ti
m
e
[
8]
,
[
1
5
]
.
I
n
th
e
ab
o
v
e
f
o
r
m
u
latio
n
,
v
ar
iab
le
o
p
er
atin
g
co
s
t;
n
a
m
el
y
t
h
e
m
ai
n
ten
a
n
ce
co
s
t o
f
th
e
u
n
it th
at
in
cr
ea
s
es
w
h
e
n
th
e
a
m
o
u
n
t o
f
g
en
er
atio
n
r
a
m
p
s
u
p
,
is
in
c
o
r
p
o
r
ate
d
in
to
(
2
1
)
.
W
ith
th
e
s
a
m
e
ar
g
u
m
e
n
t
ar
ti
cu
lated
f
o
r
(
2
0
)
-
(
2
6
)
,
th
e
q
u
ad
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atic
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n
-
co
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ca
v
e
p
o
w
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s
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ch
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(p
-
q
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f
th
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h
y
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p
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f
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m
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s
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[
27
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28
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25
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w
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d
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[
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0
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0
1
7
.
RE
F
E
R
E
NC
E
S
[1
]
I.
A
.
Et
h
m
a
n
e
,
M
.
M
a
a
ro
u
f
i,
A
.
K.
M
a
h
m
o
u
d
,
a
n
d
A
.
Ya
h
f
d
h
o
u
,
“
Op
ti
m
iza
ti
o
n
f
o
r
El
e
c
tri
c
P
o
w
e
r
L
o
a
d
F
o
re
c
a
st,”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
tric
a
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
E
CE
)
,
v
o
l/
issu
e
:
8
(5
)
,
p
p
.
3
4
5
3
-
3
4
6
2
,
Oc
t.
2
0
1
8
.
[2
]
A
.
J.
W
o
o
d
,
B.
F
.
W
o
ll
e
n
b
e
rg
,
a
n
d
G
.
B.
S
h
e
b
le,
P
o
w
e
r
Ge
n
e
ra
ti
o
n
,
Op
e
ra
ti
o
n
,
a
n
d
Co
n
tr
o
l,
3
r
d
e
d
.
:
W
il
e
y
,
p
p
.
1
4
7
-
1
8
6
,
2
0
1
3
.
[3
]
M
.
S
.
S
a
lam
,
K.
M
.
No
r,
a
n
d
A
.
R.
Ha
m
d
a
m
,
“
H
y
d
ro
th
e
r
m
a
l
S
c
h
e
d
u
li
n
g
Ba
se
d
L
a
g
ra
n
g
ian
Re
la
x
a
ti
o
n
A
p
p
r
o
a
c
h
t
o
H
y
d
ro
th
e
rm
a
l
Co
o
rd
i
n
a
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
P
o
we
r S
y
ste
ms
,
v
o
l/
issu
e
:
1
3
(
1
),
p
p
.
2
2
6
-
2
3
5
,
F
e
b
.
1
9
9
8
.
[4
]
S
.
S
.
S
a
k
th
i,
R.
K
.
S
a
n
th
i,
N.
M
.
Krish
n
a
n
,
S
.
G
a
n
e
sa
n
,
a
n
d
S
.
S
u
b
ra
m
a
n
ian
,
“
W
in
d
I
n
teg
ra
ted
T
h
e
rm
a
l
Un
it
Co
m
m
it
m
e
n
t
S
o
lu
ti
o
n
u
si
n
g
G
re
y
W
o
lf
Op
ti
m
iz
e
r,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l/
issu
e
:
7
(5
)
,
p
p
.
2
3
0
9
-
2
3
2
0
,
Oc
t.
2
0
1
7
.
[5
]
R.
W
.
F
e
rre
ro
,
J.
F
.
Riv
e
ra
,
a
n
d
S
.
M
.
S
h
a
h
i
d
e
h
p
o
u
r
,
“
Dy
n
a
m
ic P
ro
g
ra
m
m
in
g
Tw
o
-
S
ta
g
e
A
l
g
o
rit
h
m
f
o
r
L
o
n
g
-
T
e
r
m
H
y
d
ro
th
e
rm
a
l
S
c
h
e
d
u
li
n
g
o
f
M
u
l
ti
re
se
rv
o
ir
S
y
st
e
m
s,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
P
o
we
r
S
y
ste
ms
,
v
o
l/
is
su
e
:
1
3
(
4
),
p
p
.
1
5
3
4
-
1
5
4
0
,
N
o
v
.
1
9
9
8
.
[6
]
H.
Zey
n
a
l,
L
.
X
.
Hu
i,
Y.
Jia
z
h
e
n
,
M
.
Ei
d
ian
i,
a
n
d
B.
A
z
z
o
p
a
rd
i,
“
Im
p
ro
v
in
g
L
a
g
ra
n
g
i
a
n
Re
lax
a
ti
o
n
Un
it
Co
m
m
it
m
e
n
t
w
it
h
Cu
c
k
o
o
S
e
a
rc
h
A
lg
o
rit
h
m
,
”
in
Pro
c
.
IEE
E
In
t
.
Co
n
f.
Po
we
r
a
n
d
E
n
e
rg
y
(
PE
Co
n
)
,
Ku
c
h
i
n
g
,
S
a
ra
wa
k
,
M
a
la
y
sia
,
p
p
.
7
7
-
8
2
,
2
0
1
4
.
[7
]
G
.
W
.
Ch
a
n
g
,
M
.
A
g
a
n
a
g
ic,
J.
G
.
W
a
ig
h
t,
J.
M
e
d
in
a
,
T
.
Bu
rto
n
,
S
.
Re
e
v
e
s
,
a
n
d
M
.
Ch
risto
f
o
ri
d
is,
“
Ex
p
e
rien
c
e
s
w
it
h
M
ix
e
d
In
teg
e
r
L
in
e
a
r
P
r
o
g
ra
m
m
i
n
g
Ba
se
d
A
p
p
ro
a
c
h
e
s
o
n
S
h
o
rt
-
T
e
r
m
H
y
d
ro
S
c
h
e
d
u
l
in
g
,
”
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
ste
ms
,
v
o
l/
issu
e
:
1
6
(
4
),
p
p
.
7
4
3
-
7
4
9
,
No
v
.
2
0
0
1
.
[8
]
M
.
Ca
rrió
n
a
n
d
J.
M
.
A
rro
y
o
,
“
A
Co
m
p
u
tatio
n
a
ll
y
Eff
icie
n
t
M
ix
e
d
-
In
teg
e
r
L
in
e
a
r
F
o
r
m
u
latio
n
f
o
r
th
e
T
h
e
r
m
a
l
Un
it
Co
m
m
it
m
e
n
t
P
ro
b
lem
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l/
issu
e
:
2
1
(3
),
p
p
.
1
3
7
1
-
1
3
7
8
,
A
u
g
.
2
0
0
6
.
[9
]
J.
Os
tro
w
sk
i,
M
.
F
.
A
n
jo
s,
a
n
d
A
.
V
a
n
n
e
ll
i,
“
T
ig
h
t
M
ix
e
d
In
teg
e
r
L
in
e
a
r
P
ro
g
ra
m
m
in
g
F
o
r
m
u
latio
n
s
f
o
r
th
e
Un
it
Co
m
m
it
m
e
n
t
P
ro
b
lem
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l/
issu
e
:
2
7
(1
),
p
p
.
3
9
-
4
6
,
F
e
b
.
2
0
1
2
.
[1
0
]
H.
Zey
n
a
l
a
n
d
M
.
E
id
ian
i,
“
Hy
d
ro
th
e
rm
a
l
S
c
h
e
d
u
li
n
g
F
lex
ib
i
li
ty
En
h
a
n
c
e
m
e
n
t
w
it
h
P
u
m
p
e
d
-
S
to
ra
g
e
Un
it
s,”
in
Pro
c
.
2
2
n
d
Ir
a
n
i
a
n
C
o
n
f.
El
e
c
trica
l
En
g
in
e
e
rin
g
(
ICEE
),
T
e
h
ra
n
,
Ira
n
,
p
p
.
8
2
0
-
8
2
5
,
2
0
1
4
.
[1
1
]
W.
-
S
.
T
a
n
,
M
.
P
.
A
b
d
u
ll
a
h
,
a
n
d
M
.
S
h
a
a
b
a
n
,
“
Ch
a
n
c
e
-
Co
n
stra
i
n
e
d
S
c
h
e
d
u
li
n
g
o
f
V
a
riab
le
G
e
n
e
ra
ti
o
n
a
n
d
En
e
rg
y
S
to
ra
g
e
in
a
M
u
lt
i
-
T
im
e
s
c
a
le
F
ra
m
e
w
o
rk
,
”
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
&
T
e
c
h
n
o
l
o
g
y
,
v
o
l/
issu
e
:
1
2
(5
)
,
p
p
.
1
7
0
9
-
1
7
1
8
,
S
e
p
.
2
0
1
7
.
[1
2
]
A
.
M
o
re
ira,
G
.
S
trb
a
c
,
R.
M
o
r
e
n
o
,
A
.
S
tree
t,
a
n
d
I.
Ko
n
sta
n
t
e
lo
s,
“
A
F
iv
e
-
L
e
v
e
l
M
IL
P
M
o
d
e
l
f
o
r
F
lex
ib
le
T
ra
n
s
m
issio
n
Ne
tw
o
rk
P
lan
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3
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v
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0
0
5
.
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6
]
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E.
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h
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ll
,
“
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a
n
d
-
Cu
t
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p
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7
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2
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.
[1
7
]
S
.
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lam
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M
.
No
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n
d
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.
R.
Ha
m
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a
n
,
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n
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ra
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8
]
A
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M
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,
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Co
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.
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lf
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4
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1
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7
2
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v
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2
0
0
2
.
[1
9
]
R.
Ch
risti
e
.
P
o
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S
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m
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.
R
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Ca
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H.
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4
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Tec
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Ex
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5
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n
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Un
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c
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t
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M
IL
P
Re
f
o
rm
u
latio
n
,
”
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E
T
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n
sa
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ti
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v
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.
[2
6
]
H.
Zey
n
a
l,
Im
p
le
m
e
n
tatio
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o
f
M
i
x
e
d
In
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L
in
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m
m
in
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f
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T
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l
G
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T
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.
Warla
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d
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.
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.
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p
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Hy
d
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P
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w
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tatu
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9
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,
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No
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In
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J
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rn
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o
f
Po
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r E
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d
Dr
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S
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(
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)
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e
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.
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0
]
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.
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Da
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a
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d
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in
d
P
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w
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r
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o
n
g
st
Co
n
v
e
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ti
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n
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l
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e
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e
ra
ti
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M
ix
a
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d
En
e
rg
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to
ra
g
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,
”
IET
Ren
e
wa
b
le
Po
we
r
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n
e
r
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ti
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,
v
o
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issu
e
:
1
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),
p
p
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,
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c
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2
0
1
7
.
NO
M
E
NCLAT
UR
E
V
a
r
ia
b
les
)
(
t
c
p
j
:
P
r
o
d
u
ctio
n
co
s
t o
f
t
h
er
m
al
u
n
i
t
j
in
p
er
io
d
t
.
)
(
t
c
su
j
:
Star
t
-
u
p
co
s
t o
f
th
er
m
al
u
n
it
j
in
p
er
io
d
t
.
)
(
t
c
sd
j
:
Sh
u
t
-
d
o
w
n
co
s
t o
f
t
h
er
m
a
l u
n
i
t
j
in
p
er
io
d
t
.
)
(
t
p
j
:
MW
o
u
tp
u
t o
f
t
h
er
m
al
u
n
it
j
a
t p
er
io
d
t
.
)
(
t
p
i
:
MW
o
u
tp
u
t o
f
h
y
d
r
o
u
n
i
t
i
at
p
er
io
d
t
.
)
(
t
y
j
:
B
in
ar
y
s
tat
u
s
(
1
/0
)
o
f
th
er
m
al
u
n
i
t
j
at
p
er
io
d
t
.
)
,
(
t
j
l
:
P
o
w
er
g
e
n
er
atio
n
at
b
lo
ck
l
o
f
p
iece
w
is
e
l
in
ea
r
f
u
n
ctio
n
f
o
r
u
n
i
t
j
at
p
er
io
d
t
.
)
(
t
V
g
j
:
Gas v
o
l
u
m
e
co
n
s
u
m
p
tio
n
b
y
u
n
it
j
at
p
er
io
d
t
.
)
(
t
q
i
:
W
ater
d
is
ch
ar
g
e
o
f
h
y
d
r
o
u
n
it
i
at
p
er
io
d
t
.
)
(
t
i
:
B
in
ar
y
s
tat
u
s
(
1
/0
)
f
o
r
h
y
d
r
o
u
n
it
i
at
p
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d
t
.
)
(
t
X
i
:
R
eser
v
o
ir
as
s
o
ciate
d
to
h
y
d
r
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n
i
t
i
at
p
er
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d
t
.
)
(
t
h
i
:
R
eser
v
o
ir
h
ea
d
f
o
r
h
y
d
r
o
u
n
it
i
at
p
er
io
d
t
.
mi
m
t
q
:
Dis
ch
ar
g
e
o
f
h
y
d
r
o
u
n
it
i
at
p
er
io
d
t
f
r
o
m
u
p
s
tr
ea
m
h
y
d
r
o
u
n
its
m
af
ter
tr
a
v
er
s
al
ti
m
e
.
)
(
t
s
i
:
W
ater
s
p
illag
e
o
f
t
h
e
r
eser
v
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ir
ass
o
ciate
d
w
i
th
h
y
d
r
o
u
n
it
i
at
p
er
io
d
t
.
C
o
n
s
ta
nt
s
)
(
t
D
:
De
m
a
n
d
at
p
er
io
d
t
.
)
(
t
SR
:
Sp
in
n
in
g
r
eser
v
e
a
m
o
u
n
t a
t p
e
r
io
d
t
.
)
(
t
j
:
Feasib
le
r
eg
io
n
f
o
r
th
er
m
al
u
n
it
j
at
p
er
io
d
t
.
)
(
t
i
:
Feasib
le
r
eg
io
n
f
o
r
h
y
d
r
o
u
n
it
i
at
p
er
io
d
t
.
a
,
b
,
c
:
C
o
ef
f
icie
n
ts
o
f
q
u
ad
r
atic
f
u
n
c
t
io
n
.
A
:
C
o
ef
f
icie
n
t o
f
p
iece
w
i
s
e
lin
ea
r
f
u
n
ctio
n
.
m
i
n
j
P
,
m
a
x
j
P
:
Min
/Ma
x
g
e
n
er
atio
n
o
f
u
n
it
j
.
lj
F
:
Slo
p
e
o
f
s
eg
m
e
n
t
l
in
p
iece
w
i
s
e
f
u
n
ctio
n
f
o
r
u
n
it
j
.
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