I
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rna
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l J
o
urna
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Appl
ied P
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(
I
J
AP
E
)
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
,
p
p
.
744
~
7
5
9
I
SS
N:
2252
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8
7
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2
,
DOI
:
1
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.
1
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5
9
1
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.
v
1
5
.
i
2
.
pp
744
-
759
744
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In
re
c
e
n
t
y
e
a
rs,
a
n
e
lec
tro
c
h
e
m
i
c
a
l
p
ro
c
e
ss
c
a
ll
e
d
e
lec
tro
ly
sis
h
a
s
g
a
in
e
d
p
ro
m
in
e
n
c
e
.
Th
is
p
ro
c
e
ss
u
se
s
wa
ter
a
n
d
e
lec
tri
c
it
y
a
s
i
ts
m
a
in
so
u
rc
e
s,
sig
n
ifi
c
a
n
t
ly
re
d
u
c
i
n
g
th
e
c
a
r
b
o
n
fo
o
t
p
rin
t
o
f
h
y
d
r
o
g
e
n
p
ro
d
u
c
ti
o
n
.
Ad
d
it
i
o
n
a
ll
y
,
c
o
lo
rs
h
a
v
e
b
e
e
n
a
ss
ig
n
e
d
to
re
p
re
se
n
t
t
h
e
so
u
rc
e
o
f
h
y
d
ro
g
e
n
p
ro
d
u
c
ti
o
n
i
n
a
sim
p
le
wa
y
.
F
o
r
e
x
a
m
p
le,
g
re
e
n
re
fe
rs
to
h
y
d
r
o
g
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n
p
ro
d
u
c
e
d
b
y
e
lec
tro
l
y
sis
u
si
n
g
e
lec
tri
c
it
y
g
e
n
e
ra
ted
fro
m
n
o
n
-
c
o
n
v
e
n
ti
o
n
a
l
r
e
n
e
wa
b
le
e
n
e
rg
y
s
o
u
rc
e
s
(NCRES
).
F
o
r
p
l
a
n
ts
n
o
t
c
o
n
n
e
c
ted
to
th
e
n
a
ti
o
n
a
l
g
ri
d
,
th
e
c
o
n
n
e
c
ti
o
n
o
f
a
g
re
e
n
h
y
d
ro
g
e
n
p
lan
t
re
q
u
ires
th
a
t
NCRE
S
b
e
c
o
n
n
e
c
ted
t
o
a
n
iso
late
d
e
lec
tri
c
a
l
g
rid
.
I
n
th
e
se
c
a
se
s,
th
e
p
o
we
r
su
p
p
l
y
wi
ll
d
e
p
e
n
d
o
n
th
e
v
a
riab
il
it
y
o
f
t
h
e
so
u
rc
e
.
Th
is
p
a
p
e
r
p
re
se
n
ts
th
e
m
e
th
o
d
o
lo
g
y
t
o
p
la
n
a
n
d
siz
e
th
e
m
a
in
c
o
m
p
o
n
e
n
ts
o
f
t
h
e
win
d
p
o
we
r
p
lan
t
a
n
d
th
e
b
a
t
tery
e
n
e
r
g
y
sto
ra
g
e
sy
ste
m
(BES
S
)
to
e
n
su
re
th
a
t
th
e
e
lec
tro
ly
z
e
r
c
o
n
stra
in
ts
c
a
n
b
e
m
e
t
d
u
ri
n
g
th
e
stu
d
ied
p
e
rio
d
.
F
u
r
th
e
rm
o
re
,
i
t
in
tro
d
u
c
e
s
a
n
o
v
e
l
m
e
th
o
d
o
lo
g
y
th
a
t
u
se
s
th
e
a
u
to
re
g
re
ss
iv
e
m
o
v
in
g
a
v
e
ra
g
e
(ARMA)
m
o
d
e
l
to
g
e
n
e
ra
te
a
se
q
u
e
n
ti
a
l
M
o
n
te
Ca
rlo
sim
u
latio
n
a
lo
n
g
with
d
y
n
a
m
ic
o
p
t
imiz
a
ti
o
n
.
T
h
i
s
a
p
p
ro
a
c
h
a
ll
o
ws
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r
th
e
siz
in
g
o
f
t
h
e
win
d
p
o
we
r
p
lan
t
a
n
d
BES
S
,
c
o
n
si
d
e
rin
g
th
e
sto
c
h
a
stic b
e
h
a
v
io
r
o
f
t
h
e
win
d
.
K
ey
w
o
r
d
s
:
Au
to
r
eg
r
ess
iv
e
m
o
v
i
n
g
av
er
ag
e
Dy
n
am
ic
o
p
tim
izatio
n
Gr
ee
n
h
y
d
r
o
g
e
n
Seq
u
en
tial M
o
n
te
C
ar
lo
W
in
d
p
o
wer
v
ar
ia
b
ilit
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T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
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ing
A
uth
o
r
:
Ma
r
io
A.
R
io
s
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
in
ee
r
i
n
g
,
Sch
o
o
l o
f
E
n
g
in
ee
r
in
g
,
Un
iv
e
r
s
id
ad
d
e
lo
s
An
d
es
C
r
a
1
E
s
te
N° 1
9
A
–
4
0
,
E
d
if
i
cio
Ma
r
io
L
aser
n
a
ML
-
7
3
6
,
B
o
g
o
tá
,
C
o
lo
m
b
ia
E
m
ail
:
m
r
io
s
@
u
n
ian
d
es.e
d
u
.
c
o
1.
I
NT
RO
D
UCT
I
O
N
Du
e
to
th
e
r
ec
en
t
in
te
r
est
in
r
ed
u
cin
g
g
lo
b
al
war
m
in
g
,
o
n
e
o
f
th
e
m
ain
ca
u
s
es
of
CO
2
em
is
s
io
n
s
is
p
r
im
ar
ily
f
r
o
m
th
e
c
o
m
b
u
s
ti
o
n
o
f
c
o
al
an
d
h
y
d
r
o
ca
r
b
o
n
d
er
iv
ativ
es.
C
o
n
s
eq
u
en
tly
,
g
o
v
er
n
m
en
ts
an
d
th
e
in
d
u
s
tr
ial
s
ec
to
r
h
av
e
b
ee
n
d
ev
elo
p
in
g
m
ea
s
u
r
es
to
r
ed
u
ce
th
e
ca
r
b
o
n
f
o
o
t
p
r
in
t
o
f
th
ese
p
r
o
ce
s
s
es.
A
k
ey
elem
en
t in
th
is
ef
f
o
r
t is h
y
d
r
o
g
en
,
wh
ich
is
a
cr
u
cial
c
o
m
p
o
n
en
t in
v
ar
io
u
s
s
ec
to
r
s
s
u
ch
as
p
etr
o
ch
e
m
icals,
th
e
f
o
o
d
in
d
u
s
tr
y
,
c
o
al
m
in
in
g
,
a
n
d
ir
o
n
p
r
o
d
u
ctio
n
.
E
x
am
p
les
o
f
r
aw
m
ater
ials
th
at
in
v
o
lv
e
h
y
d
r
o
g
en
in
clu
d
e
am
m
o
n
ia,
eth
an
o
l,
an
d
u
r
ea
.
Ho
wev
er
,
h
y
d
r
o
g
en
p
r
o
d
u
ctio
n
h
as
tr
ad
itio
n
ally
r
elied
o
n
p
etr
o
ch
em
ical
p
r
o
ce
s
s
es
th
at
u
s
e
h
y
d
r
o
ca
r
b
o
n
s
o
r
c
o
a
l
as
s
o
u
r
ce
s
.
Fo
r
tu
n
ately
,
in
r
ec
en
t
y
ea
r
s
,
an
elec
tr
o
ch
em
i
ca
l
p
r
o
ce
s
s
ca
lled
e
l
e
c
t
r
o
l
y
s
is
h
a
s
g
a
i
n
e
d
p
r
o
m
i
n
en
c
e
.
T
h
i
s
p
r
o
c
e
s
s
u
s
e
s
w
a
te
r
a
n
d
e
l
e
c
t
r
i
c
i
t
y
a
s
i
ts
m
ai
n
c
o
m
p
o
n
e
n
t
s
.
A
d
d
it
i
o
n
a
ll
y
,
co
lo
r
s
h
av
e
b
ee
n
ass
ig
n
ed
to
r
ep
r
esen
t
th
e
s
o
u
r
ce
o
f
h
y
d
r
o
g
en
p
r
o
d
u
ctio
n
:
g
r
ee
n
r
e
f
er
s
to
h
y
d
r
o
g
en
p
r
o
d
u
ce
d
by
elec
tr
o
ly
s
is
u
s
in
g
elec
tr
icit
y
g
en
er
ate
d
f
r
o
m
n
o
n
-
c
o
n
v
e
n
tio
n
al
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
(
NC
R
E
S)
[
1
]
.
T
h
e
p
r
im
a
r
y
s
tr
ateg
y
f
o
r
s
u
p
p
ly
in
g
elec
tr
ical
p
o
wer
to
a
g
r
e
en
h
y
d
r
o
g
en
p
lan
t
is
to
u
s
e
th
e
n
atio
n
a
l
g
r
id
.
No
r
m
ally
,
a
co
n
t
r
ac
t
with
a
g
en
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atio
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co
m
p
a
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r
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th
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en
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er
v
ice
f
r
o
m
NC
R
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S
d
u
r
in
g
th
e
s
p
ec
if
ied
p
er
io
d
.
C
o
n
s
eq
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en
tl
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,
th
e
elec
tr
o
ly
ze
r
ar
r
a
y
s
ar
e
s
u
b
jecte
d
to
th
e
s
am
e
elec
tr
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q
u
ality
p
ar
am
eter
s
(
co
n
tin
u
ity
,
r
eliab
ilit
y
)
as
a
ty
p
ical
in
d
u
s
tr
ial
p
lan
t
[
2
]
,
[
3
]
.
Ho
wev
er
,
in
r
em
o
te
ar
ea
s
s
u
ch
as
co
al
m
in
es
o
r
g
as
p
r
o
d
u
ctio
n
p
la
n
ts
,
wh
er
e
th
er
e
is
n
o
co
n
n
ec
tio
n
to
th
e
n
atio
n
al
g
r
id
,
th
e
g
r
ee
n
h
y
d
r
o
g
en
p
la
n
t
m
u
s
t
b
e
co
n
n
ec
ted
to
an
is
o
lated
g
r
i
d
p
o
wer
e
d
b
y
NC
R
E
S
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
to
ch
a
s
tic
p
la
n
n
in
g
f
o
r
feed
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g
a
g
r
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o
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p
la
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t in
to
a
n
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ted
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etw
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r
k
(
Mich
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lced
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745
Sev
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wo
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k
s
h
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r
r
ied
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to
allo
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s
ch
ed
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le
o
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s
ize
NC
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E
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b
a
tt
e
ry
e
n
e
rg
y
st
o
ra
g
e
sy
ste
m
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B
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an
d
h
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r
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en
p
r
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d
u
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p
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n
ts
;
f
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r
in
s
tan
ce
,
in
[
4
]
it
is
f
o
r
m
u
lated
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ix
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te
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er
q
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ad
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atica
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c
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ain
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p
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am
m
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(
MI
QC
P
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o
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tim
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p
r
o
b
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to
m
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h
y
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p
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ts
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e
lo
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p
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in
a
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ak
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r
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d
,
b
y
th
e
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th
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h
a
n
d
[
5
]
g
iv
es
an
s
tr
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to
lo
ca
te
th
e
B
E
SS
in
a
g
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id
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y
lo
s
s
es
in
th
e
g
r
id
.
On
t
h
e
o
th
e
r
h
a
n
d
,
in
[
6
]
,
it
p
r
esen
ts
a
m
u
ltip
er
i
o
d
p
o
w
er
f
lo
w
t
o
o
p
tim
ize
th
e
d
is
p
atch
o
f
th
e
s
o
u
r
ce
s
in
c
l
u
d
in
g
p
h
o
to
v
o
ltaic
(
PV
)
an
d
B
E
SS
in
d
is
tr
ib
u
tio
n
g
r
id
wh
e
r
e
also
it
is
u
s
ed
a
m
ix
ed
-
in
teg
e
r
n
o
n
lin
ea
r
p
r
o
g
r
am
m
in
g
(
MI
NL
P
)
o
p
tim
izatio
n
with
au
to
r
eg
r
ess
iv
e
p
ar
am
eter
s
(
AR
MA
)
in
o
r
d
er
to
p
r
ed
ict
th
e
lo
ad
,
Mo
r
a
is
et
a
l
.
[
7
]
p
r
esen
ts
a
lin
ea
r
ized
m
o
d
el
u
s
in
g
m
ix
e
d
-
in
teg
e
r
lin
ea
r
p
r
o
g
r
am
m
in
g
(
MI
L
P)
to
r
ed
u
ce
th
e
m
ar
g
in
al
co
s
t
in
n
o
n
-
is
o
lated
g
r
id
co
m
p
o
u
n
d
s
o
f
PV
s
y
s
tem
,
f
u
el
ce
ll
an
d
an
win
d
p
o
wer
p
lan
t,
an
d
Sh
er
at
u
r
e
et
a
l
.
[
8
]
p
r
o
p
o
s
e
an
s
tr
ateg
y
to
s
ch
ed
u
l
e
th
e
elec
tr
icity
ex
ce
s
s
in
an
is
o
lated
ar
ea
u
s
in
g
a
h
y
b
r
id
o
p
tim
izatio
n
m
o
d
el
.
Oth
er
r
esear
ch
es
h
a
v
e
f
o
cu
s
ed
o
n
p
r
o
v
id
in
g
m
et
h
o
d
s
o
f
r
atin
g
th
e
m
ai
n
co
m
p
o
n
en
ts
,
in
[
3
]
,
it
p
r
esen
ts
a
MI
L
P
m
o
d
el
in
o
r
d
er
to
s
ize
th
e
o
p
tim
al
s
ize
o
f
a
elec
tr
o
l
zy
er
a
r
r
ay
b
ased
o
n
a
d
u
e
win
d
p
lan
t
ch
ar
ac
ter
is
tics
,
b
y
th
e
o
th
er
h
an
d
[
9
]
,
[
1
0
]
p
r
o
p
o
s
es
a
s
im
ilar
MI
L
P
m
o
d
el
,
b
u
t
in
th
is
ca
s
e
to
s
ize
th
e
B
E
SS
an
d
win
d
p
la
n
t
co
n
s
id
er
in
g
an
ex
tr
a
d
iesel
g
e
n
er
ato
r
to
f
ee
d
a
n
r
esid
en
tial
l
o
ad
.
Pan
et
a
l
.
[
1
1
]
ap
p
r
o
ac
h
es
th
e
PV,
win
d
p
o
wer
p
lan
t,
a
n
d
s
to
r
a
g
e
ca
p
ac
ity
p
r
o
p
o
r
tio
n
to
p
r
o
d
u
ce
h
y
d
r
o
g
e
n
,
in
th
is
is
in
co
r
p
o
r
ated
th
e
tim
e
s
er
ies.
Fin
ally
,
Daw
o
u
d
et
a
l
.
[
1
2
]
p
r
esen
ts
a
s
tate
o
f
ar
t
o
f
th
e
d
if
f
er
en
t
o
p
tim
izatio
n
m
eth
o
d
s
to
s
ize
th
e
is
o
lated
g
r
id
co
m
p
o
n
en
ts
,
b
u
t
b
ased
o
n
d
if
f
er
en
t
f
u
n
ctio
n
o
b
jectiv
es
,
s
u
ch
as
f
o
r
e
x
am
p
le
p
o
wer
s
u
p
p
ly
p
r
o
b
ab
ilit
y
,
in
v
estme
n
t
co
s
t
,
an
d
th
e
d
eter
m
in
is
tic
o
p
tim
izatio
n
m
eth
o
d
s
,
s
u
ch
as
h
y
b
r
id
SP
V,
PSO
,
an
d
L
OL
P.
T
h
u
s
,
th
is
p
ap
er
p
r
esen
ts
a
s
tr
ateg
y
to
s
ize
th
e
m
ajo
r
co
m
p
o
n
en
ts
in
in
s
o
lated
g
r
id
d
u
e
to
th
e
r
eq
u
ir
e
d
y
ea
r
ly
av
er
a
g
e
h
y
d
r
o
g
e
n
p
r
o
d
u
ctio
n
.
T
h
ese
m
ajo
r
co
m
p
o
n
e
n
ts
ar
e
th
e
win
d
p
o
wer
p
lan
t
a
n
d
B
E
SS
.
Giv
en
th
at
E
o
lic
en
er
g
y
d
ep
e
n
d
s
o
n
th
e
win
d
s
p
ee
d
,
an
d
it
is
k
n
o
wn
t
h
at
it
p
r
esen
ts
s
to
ch
asti
c
b
eh
a
v
io
r
,
b
ec
a
u
s
e
o
f
t
h
at,
it
is
n
ec
ess
ar
y
to
estab
lis
h
th
e
h
y
d
r
o
g
e
n
p
r
o
d
u
ctio
n
co
n
s
tr
ain
ts
in
ter
m
s
o
f
elec
tr
ical
p
o
wer
s
u
p
p
ly
.
T
h
e
n
,
th
r
o
u
g
h
s
to
ch
asti
c
o
p
tim
izatio
n
to
o
ls
it c
an
o
b
tain
th
e
r
ated
p
ar
am
eter
o
f
th
e
win
d
f
ar
m
an
d
b
atter
y
.
I
n
s
ec
tio
n
2
,
th
e
g
en
e
r
al
co
n
ce
p
ts
o
f
g
r
e
en
h
y
d
r
o
g
e
n
p
r
o
d
u
ctio
n
,
an
d
elec
tr
ical
r
eq
u
ir
em
en
ts
ar
e
p
r
esen
ted
,
th
e
B
E
SS
m
o
d
el
to
b
e
im
p
lem
en
ted
,
a
n
d
th
e
f
ir
s
t a
p
p
r
o
ac
h
to
th
e
s
to
ch
asti
c
o
p
tim
izatio
n
b
ases
is
p
r
e
s
en
ted
in
s
ec
tio
n
3
,
th
e
m
eth
o
d
o
lo
g
y
is
e
x
p
lain
ed
wh
er
e
th
e
two
ca
s
es
o
f
th
e
is
o
lated
g
r
id
to
f
ee
d
an
elec
tr
o
ly
ze
r
ar
r
a
y
ar
e
d
etailed
,
wh
er
e
th
e
f
ir
s
t
o
n
e
o
n
ly
co
n
s
i
d
er
s
a
win
d
p
o
wer
p
lan
t
a
n
d
a
B
E
SS
,
an
d
th
e
o
th
e
r
o
n
e
a
n
ad
d
itio
n
al
th
er
m
al
g
en
er
ato
r
,
d
e
f
in
in
g
th
e
c
o
n
s
tr
ain
t
s
an
d
o
b
jec
tiv
e
f
u
n
ctio
n
s
to
b
e
m
in
im
ized
.
Sectio
n
4
p
r
e
s
en
ts
a
ca
s
e
s
tu
d
y
.
Sectio
n
5
p
r
esen
ts
th
e
r
esu
lts
o
f
two
test
ca
s
es
,
an
d
f
in
ally
s
ec
tio
n
6
p
r
esen
ts
th
e
co
n
clu
s
io
n
s
o
f
th
is
p
ap
er
.
2.
T
H
E
O
R
E
T
I
CA
L
B
A
SE
S
2
.
1
.
G
re
en
hy
dro
g
en
def
ini
t
io
n
No
wad
ay
s
,
h
y
d
r
o
g
e
n
p
r
o
d
u
cti
o
n
p
r
o
ce
s
s
es
v
ar
y
d
ep
e
n
d
in
g
o
n
th
e
ap
p
licatio
n
an
d
a
r
e
u
s
ed
in
v
ar
io
u
s
ch
em
ical
p
r
o
ce
s
s
es,
p
r
im
a
r
ily
in
th
e
p
etr
o
leu
m
a
n
d
f
o
o
d
in
d
u
s
tr
ies.
Du
e
to
th
e
n
ec
ess
ity
o
f
a
n
en
er
g
y
tr
a
n
s
itio
n
,
th
er
e
is
a
g
lo
b
al
co
n
s
en
s
u
s
o
n
r
ed
u
cin
g
C
O
2
em
is
s
io
n
s
in
to
t
h
e
atm
o
s
p
h
er
e.
C
o
n
s
eq
u
en
tly
,
en
er
g
y
s
o
u
r
ce
s
f
o
r
p
r
o
d
u
cin
g
d
if
f
er
en
t
p
r
o
d
u
cts o
r
d
ev
elo
p
in
g
p
r
o
ce
s
s
es h
av
e
in
cr
ea
s
in
g
ly
f
o
c
u
s
ed
o
n
s
u
s
tain
a
b
ilit
y
,
lead
in
g
to
a
r
is
e
in
p
lan
ts
b
ased
o
n
NC
R
E
S.
Fu
r
th
er
m
o
r
e,
an
elec
tr
o
ch
e
m
ical
p
r
o
ce
s
s
ca
lled
el
e
ctr
o
ly
s
is
,
wh
ich
p
r
o
d
u
ce
s
h
y
d
r
o
g
en
b
y
ap
p
ly
in
g
d
ir
ec
t
c
u
r
r
en
t
to
wate
r
,
s
ep
ar
ates
th
e
wate
r
m
o
lecu
les
in
t
o
h
y
d
r
o
g
e
n
an
d
o
x
y
g
e
n
.
T
h
is
p
r
o
ce
s
s
h
as
en
ab
led
th
e
d
e
v
elo
p
m
en
t
o
f
v
ar
io
u
s
tech
n
o
lo
g
ies
o
v
er
th
e
last
twen
ty
y
ea
r
s
,
as
it
r
elies
o
n
elec
tr
icity
r
ath
er
th
a
n
d
ir
ec
tly
o
n
f
u
el
c
o
m
b
u
s
tib
les
[
1
]
,
[
1
3
]
,
[
1
4
]
.
T
h
u
s
,
a
c
o
lo
r
s
p
ec
tr
u
m
h
as
b
e
en
d
ef
i
n
ed
to
ea
s
ily
u
n
d
er
s
tan
d
h
y
d
r
o
g
en
p
r
o
d
u
ct
io
n
b
ased
o
n
th
e
s
o
u
r
ce
an
d
m
ater
ial
u
s
ed
,
u
ltima
tely
s
u
m
m
ar
izin
g
th
e
C
O
2
em
is
s
io
n
s
in
to
th
e
atm
o
s
p
h
er
e
,
as
s
h
o
wn
in
T
ab
le
1
.
T
ab
l
e
1
.
C
o
lo
r
class
if
icatio
n
o
f
h
y
d
r
o
g
e
n
p
r
o
d
u
ctio
n
[
1
3
]
C
o
l
o
r
P
r
o
c
e
ss
S
o
u
r
c
e
CO
2
e
mi
ss
i
o
n
s
B
l
a
c
k
G
a
si
f
i
c
a
t
i
o
n
C
o
a
l
H
i
g
h
t
G
r
a
y
S
t
e
a
m
r
e
f
o
r
m
i
n
g
N
a
t
u
r
a
l
g
a
s
H
i
g
h
B
l
u
e
S
t
e
a
m
r
e
f
o
r
m
i
n
g
w
i
t
h
c
a
r
b
o
n
c
a
p
t
u
r
e
N
a
t
u
r
a
l
g
a
s
Lo
w
C
i
a
n
P
y
r
o
l
y
s
i
s
N
a
t
u
r
a
l
g
a
s
N
o
n
d
i
r
e
c
t
C
O
2
e
mi
ss
i
o
n
s
G
r
e
e
n
El
e
c
t
r
o
l
y
si
s
W
a
t
e
r
/
e
l
e
c
t
r
i
c
i
t
y
f
r
o
m re
n
e
w
a
b
l
e
e
n
e
r
g
y
p
l
a
n
t
s
N
o
n
d
i
r
e
c
t
C
O
2
e
mi
ss
i
o
n
s
R
o
s
e
El
e
c
t
r
o
l
y
si
s
W
a
t
e
r
/
e
l
e
c
t
r
i
c
i
t
y
f
r
o
m
n
u
c
l
e
a
r
e
n
e
r
g
y
p
l
a
n
t
s
N
o
n
d
i
r
e
c
t
C
O
2
e
mi
ss
i
o
n
s
Y
e
l
l
o
w
El
e
c
t
r
o
l
y
si
s
W
a
t
e
r
/
e
l
e
c
t
r
i
c
i
t
y
f
r
o
m s
o
l
a
r
e
n
e
r
g
y
p
l
a
n
t
s
N
o
n
d
i
r
e
c
t
C
O
2
e
mi
ss
i
o
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
744
-
759
746
2
.
2
.
E
lect
ro
ly
s
is
pro
ce
s
s
T
o
d
a
y
,
v
a
r
i
o
u
s
t
e
c
h
n
o
l
o
g
i
e
s
e
x
i
s
t
t
h
a
t
u
ti
l
i
ze
e
l
e
c
t
r
o
c
h
e
m
ic
a
l
p
r
o
c
e
s
s
es
t
o
s
e
p
a
r
a
te
w
a
t
e
r
m
o
le
c
u
l
e
s
i
n
t
o
h
y
d
r
o
g
en
(
H2
)
a
n
d
o
x
y
g
en
(
O
)
.
T
h
ese
tech
n
o
lo
g
ies ar
e
[
1
]
,
[
1
4
]
: a
lk
alin
e
(
AL
K)
,
p
r
o
to
n
e
x
ch
an
g
e
m
em
b
r
an
e
(
PEM
)
,
s
o
lid
o
x
id
e
elec
tr
o
ly
z
er
(
SOE)
,
an
d
an
io
n
ex
ch
a
n
g
e
m
em
b
r
an
e
(
AE
M)
.
AL
K
a
n
d
PEM
tech
n
o
lo
g
ies
ar
e
th
e
m
o
s
t
d
ev
elo
p
ed
in
d
u
s
tr
ially
,
m
ak
in
g
th
em
th
e
m
o
s
t
wi
d
ely
u
s
ed
.
T
h
is
p
ap
er
f
o
c
u
s
es
o
n
PEM
tech
n
o
lo
g
y
d
u
e
to
its
ad
v
a
n
tag
es,
s
u
ch
as
th
e
n
o
n
-
r
ep
lace
m
e
n
t o
f
p
ar
ts
d
u
r
in
g
its
life
tim
e
an
d
its
q
u
ick
ac
tiv
atio
n
tim
e.
2
.
3
.
P
E
M
elec
t
ro
ly
ze
r
T
h
is
ty
p
e
o
f
elec
tr
o
ly
ze
r
u
s
es
a
p
r
o
t
o
n
e
x
ch
an
g
e
m
e
m
b
r
a
n
e
as
th
e
s
ep
ar
ato
r
b
etwe
en
th
e
a
n
o
d
e
a
n
d
ca
th
o
d
e.
W
h
en
a
d
ir
ec
t
cu
r
r
e
n
t
is
ap
p
lied
,
wate
r
is
s
ep
ar
at
ed
in
to
H
2
an
d
O,
with
h
y
d
r
o
g
en
p
r
o
to
n
s
p
ass
in
g
th
r
o
u
g
h
th
e
m
em
b
r
a
n
e
to
f
o
r
m
h
y
d
r
o
g
e
n
g
as
o
n
th
e
ca
th
o
d
e
s
id
e
[
1
]
,
[
1
5
]
.
Fig
u
r
e
1
s
h
o
w
s
a
s
ch
em
atic
o
f
th
e
PEM
p
r
o
ce
s
s
.
T
h
e
ad
v
an
tag
es
o
f
th
is
tech
n
o
lo
g
y
in
clu
d
e
its
ef
f
icien
cy
at
lo
w
tem
p
er
atu
r
es
an
d
its
co
m
p
ac
t
s
ize
co
m
p
ar
ed
to
o
th
e
r
ty
p
es
o
f
elec
tr
o
ly
ze
r
s
.
Ho
wev
er
,
s
o
m
e
o
f
its
co
m
p
o
n
en
ts
,
s
u
ch
as
p
l
atin
u
m
,
a
r
e
p
r
ec
io
u
s
m
etals,
wh
ich
in
cr
ea
s
es th
e
co
s
t
[
1
6
]
.
Fig
u
r
e
1
.
PEM
p
r
o
ce
s
s
s
ch
em
atic
[
1
]
2
.
4
.
E
lect
rica
l po
wer
s
up
ply
re
qu
irem
ent
s
T
h
e
o
b
jectiv
e
o
f
th
e
p
o
wer
s
u
p
p
ly
is
to
m
ax
im
ize
ef
f
icien
cy
d
u
r
in
g
th
e
elec
tr
o
ly
s
is
p
r
o
ce
s
s
,
im
p
r
o
v
e
th
e
p
u
r
ity
o
f
h
y
d
r
o
g
en
,
an
d
e
x
ten
d
th
e
life
tim
e
o
f
th
e
elec
tr
o
ly
ze
r
wh
ile
ac
h
iev
in
g
th
e
p
o
la
r
izatio
n
cu
r
v
e
[
4
]
,
[
1
3
]
,
[
1
7
]
,
[
1
8
]
.
Fig
u
r
e
2
s
h
o
ws
th
e
s
ch
em
atic
d
iag
r
am
o
f
t
h
e
elec
tr
o
ly
s
is
s
u
p
p
l
y
o
f
p
o
w
er
[
1
9
]
.
I
n
ad
d
itio
n
,
t
h
e
f
o
llo
win
g
co
n
s
tr
ain
ts
m
u
s
t
b
e
m
et
at
th
e
elec
tr
o
ly
ze
r
p
o
in
t
o
f
p
o
wer
s
u
p
p
ly
[
4
]
,
[
1
7
]
,
[
20
]
.
T
h
e
cu
r
r
e
n
t
d
en
s
ity
is
r
elate
d
to
v
o
ltag
e
i
n
p
u
t
an
d
tem
p
er
atu
r
e
.
Fo
r
a
d
eter
m
in
ed
tem
p
e
r
atu
r
e
it
is
a
cu
r
r
en
t
d
en
s
ity
p
o
in
t
th
at
p
r
o
d
u
ce
s
b
etter
ef
f
icie
n
cy
,
an
d
h
y
d
r
o
g
en
p
r
o
d
u
ctio
n
r
el
ates p
o
s
itiv
ity
with
cu
r
r
en
t d
e
n
s
ity
.
2
.
5
.
B
E
SS
m
o
del
Fig
u
r
e
3
p
r
esen
ts
a
s
tr
aig
h
tf
o
r
war
d
m
o
d
el
th
at
illu
s
tr
ates
th
e
m
ain
p
ar
am
eter
s
,
th
er
eb
y
ex
p
lain
in
g
th
e
b
eh
av
io
r
o
f
t
h
e
B
E
SS
as f
o
llo
ws
[
9
]
,
[
2
1
]
,
[
2
2
]
:
i)
On
ly
two
s
tag
es a
r
e
co
n
s
id
er
e
d
: c
h
ar
g
e
a
n
d
d
is
ch
ar
g
e.
T
h
e
s
tan
d
b
y
m
o
d
e
is
n
e
g
lecte
d
f
o
r
t
h
is
an
aly
s
is
.
ii)
r
ep
r
esen
ts
th
e
s
tate
o
f
ch
ar
g
e,
o
p
er
atin
g
with
in
th
e
r
a
n
g
e
o
f
m
in
im
u
m
an
d
m
ax
im
u
m
v
alu
es
,
m
u
ltip
lied
b
y
t
h
e
B
E
SS
r
atin
g
.
iii)
d
en
o
tes
th
e
en
er
g
y
a
b
s
o
r
b
ed
b
y
th
e
g
r
id
d
u
r
in
g
d
is
ch
ar
g
e,
ac
co
u
n
tin
g
f
o
r
s
elf
-
lo
ad
d
is
ch
ar
g
e
(
SLD)
an
d
ch
ar
g
e
p
r
o
ce
s
s
lo
s
s
es,
wh
i
ch
d
ep
e
n
d
o
n
th
e
lo
a
d
ch
ar
g
e
ef
f
icien
cy
.
iv
)
s
ig
n
if
ies
th
e
en
er
g
y
d
eliv
er
ed
to
th
e
g
r
id
d
u
r
in
g
ch
ar
g
e,
co
n
s
id
er
in
g
SLD
an
d
d
is
ch
ar
g
e
p
r
o
ce
s
s
lo
s
s
es
,
wh
ich
d
ep
e
n
d
o
n
th
e
lo
a
d
d
is
c
h
ar
g
e
ef
f
icien
cy
.
v)
Ad
d
itio
n
ally
,
th
e
cu
r
v
e
s
lo
p
e
m
u
s
t
r
em
ain
with
in
th
e
lim
its
s
p
ec
if
ied
b
y
th
e
m
an
u
f
ac
t
u
r
er
,
d
en
o
te
d
b
y
τ
B
.
Alth
o
u
g
h
th
is
f
ac
to
r
v
ar
ies
b
et
wee
n
th
e
ch
ar
g
e
an
d
d
is
ch
ar
g
e
p
r
o
ce
s
s
es,
th
is
p
ap
er
ass
u
m
e
s
s
y
m
m
etr
y
f
o
r
th
e
an
aly
s
is
.
Fig
u
r
e
2
.
Simp
le
s
ch
em
atic
o
f
elec
tr
o
ly
s
is
p
o
wer
s
u
p
p
ly
[
19
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
to
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s
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p
la
n
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o
r
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g
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g
r
ee
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o
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e
n
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to
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etw
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r
k
(
Mich
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el
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lced
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747
Fig
u
r
e
3.
B
E
SS
b
eh
av
io
r
2
.
6
.
St
o
cha
s
t
ic
o
ptim
iza
t
i
o
n
T
h
e
p
r
o
b
lem
to
s
o
lv
e
in
t
h
is
p
ap
er
is
to
s
ize
th
e
B
E
SS
an
d
win
d
p
o
we
r
p
lan
t,
b
u
t
t
h
e
m
ain
en
er
g
y
r
eso
u
r
ce
is
th
e
win
d
.
Fu
r
th
er
m
o
r
e,
as p
r
ev
io
u
s
ly
m
en
tio
n
ed
,
ch
ar
g
e
an
d
d
is
ch
ar
g
e
cy
cles lim
its
d
ep
en
d
o
n
th
e
r
ated
v
alu
es
o
f
t
h
e
B
E
SS
,
wh
ich
is
wh
y
it
is
also
n
ec
ess
ar
y
to
tak
e
in
to
co
n
s
id
er
atio
n
th
e
tim
e.
I
n
co
n
s
eq
u
en
ce
,
a
g
en
er
al
o
p
tim
izatio
n
p
r
o
b
le
m
th
at
co
n
s
id
er
s
s
to
ch
asti
c
asp
ec
ts
is
th
e
m
in
im
izatio
n
o
f
th
e
o
b
jectiv
e
f
u
n
ctio
n
(
)
,
as
(
1
)
[
2
3
]
.
min
{
(
)
:
(
)
≤
0
;
∀
=
1
,
…
,
}
(
1
)
W
h
er
e:
(
)
is
th
e
s
et
o
f
r
estrictio
n
s
at
t,
is
th
e
v
ec
to
r
o
f
th
e
v
a
r
iab
les
to
o
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tim
ize,
an
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is
th
e
r
estrictio
n
.
Du
e
to
th
ese
r
estrictio
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s
,
d
o
n
o
t c
o
n
s
id
er
s
to
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city
,
an
o
th
er
v
ec
to
r
is
in
clu
d
ed
,
wh
ich
is
th
e
v
ec
to
r
o
f
th
e
r
an
d
o
m
p
ar
am
eter
th
at
f
o
llo
ws a
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
.
T
h
u
s
,
th
e
o
p
tim
izatio
n
p
r
o
b
le
m
b
ec
o
m
es
(
2
)
.
min
{
(
)
:
(
,
)
≤
0
;
∀
=
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…
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}
(
2
)
T
h
e
s
o
lu
tio
n
to
th
is
p
r
o
b
lem
a
ls
o
y
ield
s
a
s
to
ch
asti
c
r
esu
lt.
T
h
er
e
ar
e
two
way
s
to
ad
d
r
es
s
th
is
:
f
ir
s
t,
th
r
o
u
g
h
m
u
ltis
tag
e
s
to
ch
asti
c
o
p
tim
iz
atio
n
,
an
d
s
ec
o
n
d
,
th
r
o
u
g
h
d
y
n
am
ic
o
p
tim
izatio
n
.
Sin
ce
o
u
r
p
r
o
ce
s
s
in
v
o
lv
es
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
b
atte
r
ies,
d
y
n
am
ic
o
p
tim
izatio
n
p
r
o
v
id
es
an
ac
cu
r
ate
s
o
lu
tio
n
.
Fig
u
r
e
4
illu
s
tr
ates
th
e
d
y
n
am
ic
p
r
o
ce
s
s
.
Fig
u
r
e
4
.
Dy
n
am
ic
o
p
tim
izatio
n
p
r
o
ce
s
s
[
2
3
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
744
-
759
748
Per
ea
ch
tim
e
is
d
ef
in
ed
as
a
s
tate
o
f
th
e
s
y
s
tem
,
an
d
th
e
s
tate
f
o
r
ea
ch
will
d
ep
e
n
d
o
n
t
h
e
p
ast
b
eh
av
io
r
an
d
r
esu
lts
[
2
3
]
.
+
1
=
(
0
,
1
,
1
,
…
)
(
3
)
T
h
u
s
,
th
is
p
r
o
b
lem
ca
n
b
e
s
o
lv
ed
in
s
tate
-
s
p
ac
e
with
th
e
(
4
)
[
2
3
]
.
min
{
(
)
≔
ℛ
[
(
1
(
1
)
,
2
(
2
)
,
…
,
(
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)
]
|
0
=
0
,
+
1
=
+
1
(
,
,
+
1
)
,
=
0
,
…
,
−
1
}
(
4
)
T
h
at
m
ea
n
s
(
)
is
th
e
o
b
jectiv
e
f
u
n
ctio
n
,
is
th
e
s
et
o
f
r
estrictio
n
s
f
o
r
ea
c
h
tim
e
s
tate,
c
o
n
s
id
er
i
n
g
th
at
ea
ch
s
tate
d
ep
en
d
s
o
n
th
e
p
r
ev
io
u
s
s
tate,
an
d
th
u
s
,
th
e
o
p
tim
izatio
n
p
r
o
b
lem
co
m
p
lex
ity
in
c
r
ea
s
es
ac
co
r
d
in
g
to
th
e
tim
e
T
to
b
e
s
tu
d
ied
.
2
.
7
.
ARMA
m
o
del
B
ased
o
n
th
e
p
r
e
v
io
u
s
ly
d
e
f
in
ed
o
p
tim
izatio
n
f
r
am
ew
o
r
k
,
it
is
n
ec
ess
ar
y
to
in
co
r
p
o
r
at
e
a
m
o
d
el
ca
p
ab
le
o
f
g
en
er
atin
g
a
win
d
s
p
ee
d
tim
e
s
er
ies.
T
h
is
is
p
ar
ticu
lar
ly
im
p
o
r
tan
t
b
ec
a
u
s
e
av
ailab
le
win
d
d
ata
is
ty
p
ically
lim
ited
to
s
h
o
r
t
m
ea
s
u
r
em
en
t
p
er
i
o
d
s
.
Mo
r
e
o
v
er
,
t
h
e
in
clu
s
io
n
o
f
a
B
E
SS
,
wh
o
s
e
b
eh
av
i
o
r
d
e
p
en
d
s
o
n
its
p
r
ev
io
u
s
s
tate,
r
eq
u
ir
es
a
tim
e
-
d
ep
en
d
e
n
t
m
o
d
elin
g
ap
p
r
o
ac
h
.
T
o
ad
d
r
ess
th
ese
ch
allen
g
es,
th
e
AR
MA
m
o
d
el
is
em
p
lo
y
ed
to
g
en
er
at
e
th
e
r
e
q
u
ir
ed
win
d
s
p
ee
d
tim
e
s
er
ies.
T
h
e
g
en
er
al
f
o
r
m
o
f
t
h
e
AR
MA
m
o
d
el
is
ex
p
r
ess
ed
as
(
5
)
[
2
4
]
.
=
1
−
1
+
⋯
−
+
+
1
+
⋯
+
(
5
)
W
h
er
e
,
is
th
e
tim
e
,
is
n
o
r
m
al
wh
ite;
n
o
is
e
with
n
o
r
m
al
d
is
tr
ib
u
tio
n
,
m
ea
n
0
,
an
d
v
ar
ia
n
ce
.
is
th
e
v
alu
e
o
f
th
e
s
er
ies
at
tim
e
t
,
is
t
h
e
au
to
r
eg
r
ess
iv
e
p
ar
am
eter
,
is
th
e
av
e
r
ag
e
s
lid
in
g
p
ar
a
m
eter
,
is
th
e
au
to
r
eg
r
ess
iv
e
o
r
d
er
,
an
d
is
th
e
av
er
ag
e
s
lid
in
g
o
r
d
er
.
T
h
u
s
,
f
o
r
th
e
p
r
o
b
lem
s
tu
d
ied
in
th
is
p
ap
er
,
th
e
ex
p
ec
ted
win
d
s
p
ee
d
is
g
iv
en
b
y
(
6
)
[
2
]
.
=
+
(
6
)
W
h
er
e:
is
ex
p
ec
ted
win
d
s
p
ee
d
f
o
r
tim
e
t,
is
av
er
ag
e
win
d
s
p
ee
d
o
f
m
ea
s
u
r
e
m
en
t
d
ata,
an
d
is
s
tan
d
ar
d
d
ev
iatio
n
o
f
m
ea
s
u
r
em
en
t i
n
p
u
t d
ata.
T
h
e
alg
o
r
ith
m
s
a
n
d
a
n
aly
tical
m
eth
o
d
s
u
s
ed
to
d
er
iv
e
th
e
AR
MA
m
o
d
el
p
ar
am
eter
s
ar
e
b
e
y
o
n
d
th
e
s
c
o
p
e
o
f
th
is
p
ap
er
a
n
d
ar
e
th
o
r
o
u
g
h
ly
d
is
cu
s
s
ed
in
[
2
4
]
.
Fo
r
th
e
p
u
r
p
o
s
es
o
f
th
is
s
tu
d
y
,
th
e
ec
o
n
o
m
etr
ics
m
o
d
u
le
av
ailab
le
in
th
e
co
m
m
e
r
cial
s
o
f
twar
e
MA
T
L
AB
is
em
p
lo
y
ed
to
p
er
f
o
r
m
t
h
e
n
ec
ess
ar
y
tim
e
s
er
ies an
aly
s
is
.
3.
M
E
T
H
O
DO
L
O
G
Y
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
y
is
b
ased
in
two
s
ce
n
ar
io
s
(
Fig
u
r
e
s
5
(
a)
an
d
5
(
b
)
)
.
I
n
th
e
f
ir
s
t
s
ce
n
ar
io
,
th
e
s
y
s
tem
is
d
esig
n
ed
to
s
u
p
p
l
y
a
g
r
ee
n
h
y
d
r
o
g
en
p
lan
t
with
p
r
ed
ef
in
ed
h
y
d
r
o
g
en
p
r
o
d
u
ctio
n
r
eq
u
i
r
em
en
ts
.
As
a
r
esu
lt,
th
e
n
o
m
in
al
p
o
wer
r
atin
g
o
f
th
e
elec
tr
o
ly
ze
r
is
tr
ea
ted
as
a
f
ix
ed
in
p
u
t,
al
o
n
g
s
id
e
th
e
p
lan
t’
s
o
p
er
atio
n
al
lo
ad
s
,
wh
ich
in
clu
d
e
p
u
m
p
s
,
c
o
m
p
r
ess
o
r
s
,
lig
h
tin
g
,
an
d
o
th
e
r
au
x
iliar
y
s
y
s
tem
s
s
h
o
wn
in
F
ig
u
r
e
5
(
a)
.
(
a)
(
b
)
Fig
u
r
e
5
.
Stu
d
y
ca
s
es f
o
r
g
r
ee
n
h
y
d
r
o
g
e
n
p
lan
ts
co
n
n
ec
ted
t
o
is
o
lated
g
r
id
: (
a
)
f
ix
e
d
-
d
em
a
n
d
s
y
s
tem
co
n
f
ig
u
r
atio
n
a
n
d
(
b
)
c
o
n
s
tr
ain
ed
r
en
ewa
b
le
s
y
s
tem
co
n
f
ig
u
r
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
to
ch
a
s
tic
p
la
n
n
in
g
f
o
r
feed
in
g
a
g
r
ee
n
h
yd
r
o
g
e
n
p
la
n
t in
to
a
n
is
o
la
ted
n
etw
o
r
k
(
Mich
a
el
S
a
lced
o
)
749
A
win
d
p
o
wer
p
lan
t
an
d
a
B
E
SS
p
r
o
v
id
e
th
e
e
n
er
g
y
,
b
o
th
o
f
wh
ich
ar
e
ex
p
ec
ted
to
en
s
u
r
e
co
n
tin
u
o
u
s
p
o
wer
d
eliv
er
y
.
I
n
th
is
co
n
f
ig
u
r
atio
n
,
th
e
win
d
p
o
we
r
p
lan
t
in
jects e
n
er
g
y
in
to
th
e
g
r
i
d
,
w
h
ile
th
e
B
E
SS
eith
er
s
u
p
p
lies
o
r
ab
s
o
r
b
s
p
o
wer
d
e
p
en
d
in
g
o
n
its
o
p
e
r
atio
n
al
m
o
d
e.
T
h
e
s
y
s
tem
is
ass
u
m
ed
to
in
clu
d
e
co
n
tr
o
l
m
ec
h
an
is
m
s
ca
p
ab
le
o
f
m
an
ag
in
g
p
o
wer
d
e
f
icits
o
r
s
u
r
p
lu
s
es
r
elativ
e
to
th
e
c
o
m
b
in
e
d
d
e
m
a
n
d
o
f
th
e
p
lan
t
an
d
th
e
elec
tr
o
ly
ze
r
.
I
n
th
e
s
ec
o
n
d
s
ce
n
ar
io
,
th
e
a
v
ailab
ilit
y
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
co
n
s
tr
ain
s
th
e
g
r
ee
n
h
y
d
r
o
g
en
p
r
o
d
u
ctio
n
.
T
o
ad
d
r
ess
th
is
,
a
th
er
m
al
g
en
e
r
ato
r
o
p
er
atin
g
in
is
o
lated
m
o
d
e
is
in
tr
o
d
u
ce
d
to
s
u
p
p
lem
en
t
th
e
en
er
g
y
s
u
p
p
ly
d
u
r
in
g
p
er
i
o
d
s
o
f
in
s
u
f
f
icien
t w
in
d
g
e
n
er
atio
n
.
Fig
u
r
e
5
(
b
)
i
llu
s
tr
ates th
e
s
ec
o
n
d
s
ce
n
ar
i
o
.
3
.
1
.
Ca
s
e
1
I
n
ca
s
e
1
,
as
m
e
n
tio
n
ed
,
h
y
d
r
o
g
en
p
r
o
d
u
ctio
n
is
p
r
e
v
io
u
s
ly
d
o
n
e
b
y
a
n
elec
tr
o
l
y
ze
r
a
r
r
ay
,
wh
ich
is
ass
u
m
ed
as
an
in
p
u
t
g
iv
en
b
y
th
e
n
ec
ess
ities
o
f
th
e
p
r
o
ce
s
s
.
I
n
th
is
ca
s
e
,
th
e
f
u
n
ctio
n
to
b
e
m
in
im
ized
will
b
e
th
e
lev
elize
d
co
s
t o
f
h
y
d
r
o
g
e
n
(
L
C
OH)
,
wh
ich
is
d
ef
in
ed
as
(
7
)
[
3
]
.
=
∑
2
,
=
1
(
7
)
W
h
er
e
2
,
is
th
e
p
r
o
d
u
ce
d
h
y
d
r
o
g
en
,
an
d
is
th
e
p
r
esen
t
co
s
t
o
f
th
e
in
v
estme
n
t
(
win
d
p
o
wer
p
lan
t,
B
E
SS
,
an
d
elec
tr
o
ly
ze
r
ar
r
a
y
)
.
T
h
u
s
,
C
PF
is
ca
lcu
lated
as
(
8
)
[
3
]
.
=
+
(
8
)
Ass
u
m
in
g
th
at
th
e
OPEX
is
p
r
o
p
o
r
tio
n
al
to
t
h
e
C
APEX
,
th
e
v
alu
e
o
f
th
e
C
PF
ca
n
th
en
b
e
d
eter
m
in
ed
,
ass
u
m
in
g
in
s
tallatio
n
v
alu
es
d
ep
en
d
in
g
o
n
th
e
s
y
s
tem
u
n
itar
y
co
s
t
,
th
er
ef
o
r
e,
it
ca
n
b
e
p
o
s
s
ib
le
to
ca
lcu
late
th
e
C
PF
with
(
9
)
[
3
]
.
=
,
+
,
+
(
9
)
W
h
er
e,
is
th
e
u
n
it
p
r
esen
t
co
s
t
o
f
th
e
win
d
p
o
wer
p
lan
t,
is
th
e
u
n
it
p
r
esen
t
co
s
t
o
f
t
h
e
B
E
SS
,
is
th
e
u
n
it
p
r
esen
t
co
s
t
o
f
th
e
B
E
SS
,
,
is
th
e
r
ated
p
o
wer
o
f
th
e
win
d
p
o
wer
p
lan
t,
,
is
th
e
r
ated
p
o
wer
o
f
th
e
B
E
SS
,
an
d
is
th
e
r
ated
p
o
wer
o
f
th
e
elec
tr
o
l
y
ze
r
ar
r
ay
.
3
.
1
.
1
.
O
bje
ct
iv
e
f
un
ct
io
n c
a
s
e
1
Sin
ce
th
e
r
ated
p
o
wer
o
f
th
e
elec
tr
o
ly
ze
r
is
tr
ea
ted
as
a
f
ix
ed
in
p
u
t,
h
y
d
r
o
g
en
p
r
o
d
u
ctio
n
r
em
ain
s
n
ea
r
ly
co
n
s
tan
t
th
r
o
u
g
h
o
u
t
th
e
an
aly
s
is
p
er
io
d
.
As
a
r
esu
lt,
th
e
o
p
tim
izatio
n
p
r
o
b
lem
is
s
im
p
lifie
d
to
m
in
im
ize
th
e
p
r
esen
t
in
v
estme
n
t
co
s
t
a
s
s
o
ciate
d
with
t
h
e
w
in
d
p
o
we
r
p
lan
t
a
n
d
th
e
B
E
SS
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
is
th
er
ef
o
r
e
as
(
1
0
)
[
3
]
.
min
(
)
=
,
+
,
(
10
)
3
.
1
.
2
.
Co
ns
t
ra
ints c
a
s
e
1
T
h
is
o
p
tim
izatio
n
p
r
o
b
lem
is
s
u
b
ject
to
s
ev
er
al
co
n
s
tr
ain
ts
,
in
clu
d
in
g
p
o
wer
b
alan
ce
,
o
p
er
atio
n
al
lim
itatio
n
s
o
f
th
e
B
E
SS
,
an
d
p
er
f
o
r
m
a
n
ce
r
e
q
u
ir
em
e
n
ts
o
f
t
h
e
elec
tr
o
ly
ze
r
.
T
h
ese
c
o
n
s
tr
ain
ts
m
u
s
t
b
e
s
atis
f
ied
at
ea
ch
tim
e
s
tep
th
r
o
u
g
h
o
u
t
th
e
s
im
u
latio
n
h
o
r
iz
o
n
.
T
h
u
s
,
t
h
e
in
jecte
d
an
d
c
o
n
s
u
m
ed
p
o
wer
m
u
s
t
b
e
eq
u
al;
th
er
ef
o
r
e
,
t
h
e
(
1
1
)
a
p
p
lie
s
[
3
]
.
,
+
,
=
,
+
,
+
,
+
,
(
11
)
W
h
er
e,
,
is
th
e
in
jecte
d
win
d
p
o
wer
,
,
is
th
e
B
E
SS
d
is
ch
ar
g
ed
en
er
g
y
,
,
is
th
e
B
E
S
S
ch
ar
g
ed
en
er
g
y
,
,
is
th
e
elec
tr
o
ly
ze
r
’
s
co
n
s
u
m
e
d
p
o
wer
,
,
is
th
e
lo
ad
p
o
wer
,
is
th
e
d
u
m
p
p
o
wer
,
an
d
is
th
e
tim
e.
B
u
t,
co
n
s
id
er
in
g
th
at
win
d
p
o
wer
f
o
llo
ws
a
s
im
ilar
d
is
tr
ib
u
tio
n
o
f
o
n
ly
o
n
e
tu
r
b
in
e,
th
e
f
o
llo
win
g
r
elatio
n
is
d
ef
in
ed
as (
1
2
)
.
,
=
,
(
12
)
W
h
er
e
,
,
is
th
e
r
ated
p
o
wer
o
f
t
h
e
win
d
p
o
we
r
p
la
n
t
,
a
n
d
is
th
e
u
n
it
f
ac
to
r
o
f
th
e
w
in
d
p
o
we
r
g
en
e
r
atio
n
.
T
h
u
s
,
r
ep
lacin
g
in
p
r
ev
io
u
s
eq
u
atio
n
,
th
e
p
o
wer
b
alan
ce
eq
u
ality
is
as (
1
3
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
744
-
759
750
,
+
,
=
,
+
,
+
,
+
;
[
0
,
1
]
(
13)
Th
e
B
E
SS
co
n
s
tr
ain
ts
p
er
tain
to
th
e
s
tate
o
f
ch
ar
g
e,
wh
ich
d
ep
en
d
s
o
n
th
e
p
r
e
v
io
u
s
s
tag
e
as
well
a
s
th
e
d
is
ch
ar
g
e
o
r
ch
a
r
g
e,
as
(
1
4
)
[
3
]
.
,
=
(
1
−
)
,
−
1
+
,
−
,
(
14
)
W
h
er
e
,
is
th
e
B
E
S
S
s
tag
e
o
f
ch
ar
g
e,
is
th
e
B
E
S
S
s
elf
-
d
i
s
ch
ar
g
e
r
atio
,
is
th
e
B
E
S
S
c
h
ar
g
in
g
ef
f
icien
cy
,
a
n
d
is
th
e
B
E
SS
d
i
s
ch
ar
g
in
g
ef
f
icien
cy
.
B
E
SS
is
o
n
ly
ch
a
r
g
ed
o
r
u
n
ch
ar
g
ed
at
an
y
tim
e:
,
=
,
,
=
(
1
−
)
,
}
;
[
0
,
1
]
(
15
)
T
h
u
s
,
ca
n
b
e
0
o
r
1
,
wh
ich
c
o
n
d
itio
n
ates
th
at
i
f
,
is
p
o
s
itiv
e,
,
will
b
e
0
,
b
u
t
i
n
th
e
o
p
p
o
s
ite
ca
s
e,
,
is
p
o
s
itiv
e,
,
will
b
e
0
[
3
]
,
[
2
5
]
.
As
p
r
ev
io
u
s
ly
m
en
tio
n
e
d
,
th
e
r
ate
at
wh
ich
th
e
B
E
SS
is
ch
ar
g
ed
o
r
d
is
ch
ar
g
ed
will
b
e
lim
i
ted
b
y
th
e
f
o
llo
win
g
f
ac
t
o
r
s
[
3
]
.
1
,
≤
,
−
,
−
1
≤
1
,
(
16
)
W
h
er
e
is
th
e
B
E
SS
ch
ar
g
e/d
is
ch
ar
g
e
r
atio
,
a
n
d
B
E
SS
s
tate
o
f
ch
ar
g
e
s
h
o
u
l
d
b
e
u
n
d
er
th
e
o
p
er
atio
n
lim
its
:
,
≤
,
≤
,
(
17
)
w
h
er
e,
:
is
th
e
B
E
S
S m
in
im
u
m
lim
it o
f
ch
ar
g
e
; a
n
d
:
is
th
e
B
E
SS
m
ax
im
u
m
lim
it o
f
ch
a
r
g
e
.
I
n
th
e
ca
s
e
o
f
th
e
in
itial
s
tate
o
f
ch
ar
g
e,
th
is
v
alu
e
is
n
o
t
ar
b
it
r
ar
ily
ass
ig
n
ed
b
u
t
is
in
s
tead
tr
ea
ted
as
a
d
ec
is
io
n
v
ar
ia
b
le
with
in
t
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
.
T
h
e
lo
wer
b
o
u
n
d
is
n
o
t
en
f
o
r
ce
d
,
allo
win
g
th
e
B
E
SS
to
b
eg
in
o
p
er
atio
n
i
n
a
f
u
lly
d
is
ch
ar
g
e
d
s
t
ate
[
3
]
.
,
0
≤
,
(
18
)
T
h
e
f
in
al
co
n
s
tr
ain
t
in
th
e
o
p
tim
izatio
n
p
r
o
b
lem
p
er
tain
s
t
o
th
e
p
o
wer
r
eq
u
i
r
em
en
ts
o
f
th
e
elec
tr
o
ly
ze
r
.
T
o
en
s
u
r
e
p
r
o
p
e
r
o
p
er
atio
n
,
th
e
s
u
p
p
lied
p
o
wer
m
u
s
t
r
em
ain
with
in
th
e
s
p
ec
if
ied
o
p
er
atio
n
al
lim
its
a
t
ea
ch
tim
e
s
tep
.
,
≤
,
≤
,
(
19
)
3
.
2
.
Ca
s
e
2
I
n
c
ase
2
,
an
ad
d
itio
n
al
th
er
m
al
g
en
er
ato
r
is
in
co
r
p
o
r
ated
in
to
th
e
s
y
s
tem
.
As
a
r
esu
lt,
th
e
p
o
wer
b
alan
ce
eq
u
atio
n
is
m
o
d
if
ied
t
o
in
clu
d
e
th
e
e
n
er
g
y
in
jecte
d
b
y
th
e
th
er
m
al
p
lan
t,
w
h
ich
s
u
p
p
lem
en
ts
th
e
win
d
an
d
B
E
SS
co
n
tr
ib
u
tio
n
s
d
u
r
in
g
p
er
io
d
s
o
f
in
s
u
f
f
icien
t r
en
ew
ab
le
g
en
er
atio
n
.
,
+
,
+
ℎ
,
=
,
+
,
+
,
+
(
20
)
W
h
er
e
ℎ
,
is
th
e
th
er
m
al
p
lan
t'
s
in
jecte
d
p
o
wer
,
an
d
ℎ
,
o
p
er
ate
s
u
n
d
er
(
2
1
)
.
ℎ
≤
ℎ
,
≤
ℎ
(
21
)
Acc
o
r
d
in
g
ly
,
th
e
o
b
jectiv
e
f
u
n
ctio
n
is
ex
p
an
d
e
d
to
in
clu
d
e
th
e
co
s
t
o
f
th
er
m
al
en
er
g
y
g
en
er
atio
n
o
v
er
th
e
an
aly
s
is
p
er
io
d
.
min
(
)
=
,
+
,
+
∑
ℎ
,
=
1
(
22
)
W
h
er
e
is
th
e
u
n
it p
r
ice
o
f
co
n
s
u
m
ed
en
er
g
y
o
f
th
e
th
e
r
m
al
g
en
er
ato
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
to
ch
a
s
tic
p
la
n
n
in
g
f
o
r
feed
in
g
a
g
r
ee
n
h
yd
r
o
g
e
n
p
la
n
t in
to
a
n
is
o
la
ted
n
etw
o
r
k
(
Mich
a
el
S
a
lced
o
)
751
3
.
3
.
O
pti
m
iza
t
io
n pro
ce
s
s
C
o
n
s
id
er
in
g
th
e
co
n
s
tr
ain
ts
p
r
ev
io
u
s
ly
d
ef
i
n
ed
,
th
e
o
v
er
all
o
p
tim
izatio
n
f
r
a
m
ewo
r
k
is
ill
u
s
tr
ated
in
Fig
u
r
e
6
[
6
]
.
T
h
is
s
ch
em
atic
o
u
tlin
es
th
e
p
r
o
ce
s
s
u
s
ed
to
s
o
l
v
e
th
e
o
p
tim
izatio
n
p
r
o
b
lem
u
n
d
er
th
e
co
n
d
itio
n
s
s
p
ec
if
ied
f
o
r
b
o
t
h
ca
s
e
s
tu
d
ies
.
Fo
r
ea
ch
p
er
io
d
,
th
e
f
o
llo
win
g
g
en
er
al
o
p
tim
izatio
n
p
r
o
ce
s
s
s
h
all
b
e
p
er
f
o
r
m
ed
.
min
{
(
)
=
|
|
≤
=
∈
[
,
]
⋀
∈
ℛ
∈
[
0
,
1
]
⋀
ℤ
∀
=
1
,
2
,
⋯
,
}
(
23
)
(
a)
(
b
)
Fig
u
r
e
6
.
Op
tim
izatio
n
m
ac
h
i
n
e
s
ch
em
atic
f
o
r
(
a)
ca
s
e
1
a
n
d
(
b
)
c
ase
2
3
.
3
.
1
.
Ca
s
e
1
T
h
e
o
p
tim
izatio
n
v
ar
ia
b
le
v
ec
to
r
is
d
iv
id
ed
in
to
two
s
tag
es
.
T
h
e
f
ir
s
t
s
tag
e
in
clu
d
es
o
n
ly
th
e
f
ix
e
d
v
ar
iab
les to
b
e
o
p
tim
ized
,
wh
i
ch
r
em
ain
c
o
n
s
tan
t th
r
o
u
g
h
o
u
t
th
e
s
im
u
latio
n
h
o
r
izo
n
[
4
]
,
[
1
7
]
.
1
=
[
,
,
,
0
]
(
24
)
T
h
e
s
ec
o
n
d
s
tag
e
in
clu
d
es
all
tim
e
-
d
ep
en
d
en
t
v
ar
ia
b
les,
wh
ich
v
ar
y
th
r
o
u
g
h
o
u
t
th
e
s
im
u
latio
n
h
o
r
izo
n
an
d
ar
e
ev
alu
ated
at
ea
ch
tim
e
s
tep
.
2
,
=
[
,
,
,
,
,
]
(
25
)
T
h
u
s
,
th
e
co
m
p
lete
o
p
tim
izati
o
n
v
ar
iab
le
v
ec
to
r
is
co
n
s
tr
u
cted
b
y
co
m
b
i
n
in
g
th
e
f
ix
e
d
v
ar
iab
les f
r
o
m
th
e
f
ir
s
t
s
tag
e
with
th
e
tim
e
-
d
ep
en
d
en
t
v
ar
iab
les f
r
o
m
th
e
s
ec
o
n
d
s
tag
e,
ev
alu
ated
ac
r
o
s
s
th
e
en
tire
s
im
u
latio
n
h
o
r
izo
n
.
=
[
1
2
,
1
⋯
2
,
…
2
,
]
(
26
)
I
n
th
is
s
tag
e,
th
e
co
s
t
v
ec
to
r
i
s
d
ef
in
ed
b
ased
o
n
th
e
u
n
it
in
s
tallatio
n
co
s
ts
o
f
th
e
win
d
p
o
wer
p
lan
t
a
n
d
t
h
e
B
E
SS
.
T
h
ese
co
s
ts
ar
e
tr
ea
ted
as
f
ix
ed
p
ar
a
m
eter
s
an
d
ar
e
u
s
ed
to
ev
al
u
ate
th
e
to
tal
in
v
es
tm
en
t
r
eq
u
ir
ed
f
o
r
th
e
s
y
s
tem
co
n
f
ig
u
r
atio
n
.
=
[
0
…
0
]
(
27
)
I
n
th
e
ca
s
e
o
f
th
e
m
atr
ix
,
a
s
im
ilar
ap
p
r
o
ac
h
is
tak
en
.
0
=
[
0
0
0
0
0
0
−
0
0
0
0
−
1
0
−
1
−
1
0
−
1
−
1
0
1
]
;
1
=
[
1
0
−
,
0
0
0
0
1
,
0
0
0
0
0
0
1
0
0
0
0
0
−
1
0
0
0
0
0
1
0
0
0
0
0
−
1
0
0
0
0
0
0
0
0
]
(
28
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
744
-
759
752
2
=
[
0
0
0
0
0
0
−
0
0
0
0
−
1
0
0
−
1
0
0
]
;
3
=
[
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
−
1
0
0
0
0
0
1
0
0
]
(
1
)
Acc
o
r
d
in
g
ly
,
m
atr
ix
is
co
n
s
tr
u
cted
b
ased
o
n
th
e
d
e
f
in
ed
ti
m
e
win
d
o
w
o
v
er
wh
ich
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
is
ex
ec
u
ted
.
T
h
is
m
atr
ix
in
co
r
p
o
r
ates
th
e
s
y
s
tem
co
n
s
tr
ain
ts
an
d
v
ar
iab
le
r
elatio
n
s
h
ip
s
ac
r
o
s
s
all
t
im
e
s
tep
s
with
in
th
e
s
im
u
latio
n
h
o
r
izo
n
.
=
0
1
2
⋯
⋯
⋯
[
0
1
∅
⋯
⋯
⋯
∅
2
3
4
∅
⋯
⋯
∅
2
∅
3
4
∅
⋯
∅
⋮
⋮
⋮
⋮
⋮
⋮
⋮
2
∅
⋯
⋯
∅
3
4
]
;
=
[
1
2
⋮
2
]
1
2
⋮
(
30
)
0
,
1
=
[
0
0
0
0
0
−
1
]
;
1
=
[
−
1
1
0
0
−
1
−
1
−
1
0
1
0
0
]
(
31
)
0
,
=
[
0
0
0
0
0
]
;
2
=
[
0
0
0
0
0
0
0
0
0
−
1
0
0
]
(
32
)
=
0
1
2
⋯
⋯
⋯
[
0
,
1
1
∅
⋯
⋯
⋯
∅
0
,
2
2
1
∅
⋯
⋯
∅
0
,
3
∅
2
1
∅
⋯
∅
⋮
⋮
⋮
⋮
⋮
⋮
⋮
0
,
∅
⋯
⋯
∅
2
3
]
;
=
[
1
1
⋮
1
]
1
2
⋮
(
33
)
3
.
3
.
2
.
Ca
s
e
2
I
n
th
is
ca
s
e,
th
e
v
ec
to
r
o
f
v
ar
iab
les
to
b
e
o
p
tim
ized
in
th
e
f
ir
s
t
s
tag
e
r
em
ain
s
u
n
ch
an
g
ed
f
r
o
m
th
e
p
r
ev
io
u
s
s
ce
n
ar
i
o
.
1
=
[
,
,
,
0
]
(
34
)
T
h
e
s
ec
o
n
d
s
tag
e
in
co
r
p
o
r
ates
th
e
p
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3
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3
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3
.
Sequ
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s
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p
r
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in
Fig
u
r
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7
.
Evaluation Warning : The document was created with Spire.PDF for Python.