I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t
201
9
,
p
p
.
2
7
9
4
~2
8
0
2
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v9
i
4
.
p
p
2
7
9
4
-
2802
2794
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e
.
co
m/
jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JE
C
E
An
i
nt
eg
ra
ted
O
P
F
d
ispa
tch
ing
m
o
del w
ith
w
ind
p
o
w
er and
d
e
m
a
nd
r
espo
nse
for
d
ay
-
a
hea
d
m
a
rkets
Rica
rdo
M
o
re
no
,
J
o
ha
n O
ba
nd
o
,
G
a
briel
G
o
nza
lez
En
e
rg
y
a
n
d
M
e
c
h
a
n
ica
l
De
p
a
rtm
e
n
t,
Un
iv
e
rsid
a
d
A
u
tó
n
o
m
a
d
e
Oc
c
id
e
n
te,
Ca
li
,
C
o
lo
m
b
ia
Art
icle
I
nfo
AB
ST
RAC
T
Ar
ticle
his
to
r
y:
R
ec
eiv
ed
Au
g
22
,
2
0
1
8
R
ev
i
s
ed
Mar
1
2
,
2
0
1
9
A
cc
ep
ted
A
p
r
3
,
2
0
1
9
In
t
h
e
d
a
y
-
a
h
e
a
d
d
isp
a
tch
in
g
o
f
n
e
t
w
o
rk
-
c
o
n
stra
in
e
d
e
lec
tri
c
it
y
m
a
r
k
e
ts,
re
n
e
wa
b
le
e
n
e
rg
y
a
n
d
d
istri
b
u
te
d
re
so
u
rc
e
s
a
re
d
isp
a
tch
e
d
to
g
e
th
e
r
w
it
h
c
o
n
v
e
n
ti
o
n
a
l
g
e
n
e
ra
ti
o
n
.
T
h
e
u
n
c
e
rtain
ty
a
n
d
v
o
latil
it
y
a
s
so
c
iate
d
to
re
n
e
wa
b
le
re
so
u
rc
e
s
re
p
re
se
n
ts
a
n
e
w
p
a
ra
d
ig
m
to
b
e
fa
c
e
d
f
o
r
p
o
w
e
r
s
y
ste
m
o
p
e
ra
ti
o
n
.
M
o
re
o
v
e
r,
in
v
a
rio
u
s
e
lec
tri
c
it
y
m
a
rk
e
ts
th
e
re
a
re
m
e
c
h
a
n
ism
s
to
a
ll
o
w
th
e
d
e
m
a
n
d
p
a
rti
c
ip
a
ti
o
n
th
ro
u
g
h
d
e
m
a
n
d
re
sp
o
n
se
(DR)
stra
t
e
g
ies
.
Un
d
e
r
o
p
e
ra
ti
o
n
a
l
a
n
d
e
c
o
n
o
m
ic
re
strictio
n
s,
th
e
o
p
e
ra
to
r
e
a
c
h
d
a
y
,
o
r
e
v
e
n
in
i
n
tra
-
d
a
y
m
a
rk
e
ts
,
d
isp
a
tch
s
a
n
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
to
f
in
d
a
f
e
a
sib
le
sta
te
o
f
o
p
e
ra
ti
o
n
.
T
h
e
o
p
e
ra
ti
o
n
d
e
c
isi
o
n
s
i
n
p
o
w
e
r
m
a
rk
e
ts
u
se
a
n
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
c
o
n
sid
e
rin
g
u
n
it
c
o
m
m
it
m
e
n
t
to
d
isp
a
tc
h
e
c
o
n
o
m
ica
ll
y
g
e
n
e
ra
ti
o
n
a
n
d
DR
re
so
u
rc
e
s
u
n
d
e
r
se
c
u
rit
y
re
s
tri
c
ti
o
n
s.
T
h
is
p
a
p
e
r
c
o
n
stru
c
ts
a
m
o
d
e
l
to
in
c
lu
d
e
d
e
m
a
n
d
re
sp
o
n
se
in
th
e
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
u
n
d
e
r
win
d
p
o
w
e
r
u
n
c
e
rtain
ty
.
T
h
e
m
o
d
e
l
is
f
o
r
m
u
late
d
a
s
a
m
ix
e
d
-
in
teg
e
r
li
n
e
a
r
q
u
a
d
ra
ti
c
p
ro
b
lem
a
n
d
e
v
a
lu
a
ted
th
ro
u
g
h
M
o
n
te
-
Ca
rl
o
sim
u
latio
n
s.
A
larg
e
n
u
m
b
e
r
o
f
sc
e
n
a
rio
s
a
ro
u
n
d
a
traje
c
to
ry
b
i
d
c
a
p
tu
re
s
th
e
u
n
c
e
rtain
ty
in
win
d
p
o
w
e
r
f
o
re
c
a
stin
g
.
T
h
e
p
ro
p
o
se
d
i
n
teg
ra
ted
OPF
m
o
d
e
l
is
tes
ted
o
n
th
e
sta
n
d
a
rd
IEE
E
3
9
-
b
u
s sy
ste
m
.
Ke
ywo
r
d
s
:
De
m
a
n
d
r
esp
o
n
s
e
E
lectr
icit
y
m
ar
k
et
s
Mo
n
te
-
C
ar
lo
s
i
m
u
latio
n
s
Op
ti
m
al
p
o
w
er
f
lo
w
(
OP
F)
W
in
d
p
o
w
er
Co
p
y
rig
h
t
©
2
0
1
9
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
R
icar
d
o
Mo
r
en
o
,
E
n
er
g
y
a
n
d
Me
ch
a
n
ical
Dep
ar
t
m
e
n
t,
Un
i
v
er
s
id
ad
Au
tó
n
o
m
a
d
e
Oc
cid
en
te
,
C
ali,
C
o
lo
m
b
ia
.
E
m
ail:
r
m
o
r
e
n
o
@
u
ao
.
ed
u
.
co
1.
I
NT
RO
D
UCT
I
O
N
No
w
ad
ay
s
,
th
e
p
o
w
er
s
y
s
tem
o
p
er
ati
o
n
in
v
o
lv
es
th
e
c
o
m
p
etit
iv
e
p
a
r
ti
ci
p
at
i
o
n
o
f
r
en
ew
ab
le
g
en
er
a
ti
o
n
an
d
DR
r
eso
u
r
c
es.
W
in
d
p
o
w
er
g
en
e
r
at
o
r
s
a
r
e
p
ar
t
i
ci
p
a
tin
g
in
el
ec
t
r
i
city
m
ar
k
ets
u
n
d
e
r
d
if
f
e
r
en
t
in
ce
n
tiv
es
an
d
th
e
p
o
w
er
s
y
s
te
m
o
p
er
at
o
r
f
ac
es
an
im
p
o
r
t
an
t
ch
a
llen
g
e
r
el
ate
d
w
ith
th
e
w
in
d
p
o
w
er
in
ter
m
itten
cy
an
d
u
n
p
r
ed
ict
a
b
il
ity
[1
-
3]
.
I
n
th
is
c
o
n
t
ex
t,
th
e
in
t
eg
r
a
ti
o
n
o
f
d
em
an
d
r
es
p
o
n
s
e
r
es
o
u
r
ce
s
r
e
p
r
es
en
ts
a
n
ew
r
eso
u
r
ce
t
o
b
e
all
o
c
ate
d
in
th
e
p
o
w
er
s
y
s
tem
o
p
e
r
a
ti
o
n
[
4
]
.
T
h
e
in
teg
r
a
ti
o
n
o
f
DR
r
es
o
u
r
ce
s
in
th
e
m
ar
k
ets
lea
d
s
t
o
te
ch
n
ic
al
an
d
ec
o
n
o
m
ic
ch
al
len
g
es
as
s
o
ci
at
ed
w
ith
th
e
in
teg
r
at
io
n
o
f
DR
r
eso
u
r
ce
s
in
to
th
e
r
es
er
v
e
m
ar
k
ets.
T
h
e
f
o
c
u
s
o
f
th
is
p
a
p
e
r
is
o
n
th
e
f
o
r
m
u
lati
o
n
o
f
an
in
teg
r
ate
d
m
o
d
el
t
o
d
is
p
a
tch
ec
o
n
o
m
ically
a
p
o
w
er
s
y
s
tem
u
n
d
er
w
in
d
p
o
w
er
in
t
eg
r
a
ti
o
n
an
d
DR
p
a
r
t
ici
p
a
ti
o
n
.
T
h
is
p
a
p
e
r
p
r
o
v
id
es
a
d
ay
-
ah
ea
d
d
is
p
at
ch
in
g
f
r
am
e
w
o
r
k
i
n
clu
d
in
g
th
e
in
t
eg
r
ati
o
n
o
f
w
in
d
p
o
w
er
g
en
er
a
ti
o
n
an
d
d
em
an
d
r
esp
o
n
s
e
r
es
o
u
r
ce
s
in
th
e
O
PF
f
o
r
m
u
latio
n
.
S
p
ec
if
ica
lly
,
th
e
m
o
d
el
p
r
o
p
o
s
ed
in
th
is
p
a
p
e
r
is
f
o
r
m
u
late
d
as
a
m
ix
ed
-
in
teg
e
r
lin
e
ar
q
u
ad
r
a
tic
o
p
ti
m
izatio
n
p
r
o
b
l
em
,
an
d
th
e
ev
a
lu
ati
o
n
is
p
er
f
o
r
m
ed
th
r
o
u
g
h
M
o
n
te
-
C
a
r
l
o
s
im
u
latio
n
s
t
o
c
ap
tu
r
e
th
e
u
n
ce
r
t
a
in
ty
r
elate
d
w
ith
th
e
w
in
d
p
o
w
er
g
en
e
r
at
io
n
.
DR
r
es
o
u
r
c
es
a
r
e
m
o
d
e
le
d
as
d
is
p
a
tch
a
b
l
e
lo
a
d
s
,
w
h
ich
in
d
ica
tes
th
e
d
em
an
d
ten
d
en
cy
to
s
h
e
d
its
co
n
s
u
m
p
tio
n
at
d
et
er
m
in
ed
p
r
i
ce
.
T
h
e
w
in
d
p
o
w
er
o
u
t
p
u
t
h
as
an
in
ter
m
itten
t
n
a
tu
r
e,
s
o
,
th
e
in
teg
r
ati
o
n
o
f
w
in
d
p
o
w
er
g
en
er
a
ti
o
n
r
e
q
u
i
r
es
an
ci
lla
r
y
s
er
v
ices
s
u
ch
as
r
eg
u
lat
io
n
,
c
o
n
tin
g
en
cy
r
ese
r
v
e
an
d
o
th
e
r
s
t
o
c
o
m
p
en
s
ate
w
in
d
p
o
w
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
in
teg
r
a
ted
OP
F
d
is
p
a
tch
in
g
mo
d
el
w
ith
w
in
d
p
o
w
er a
n
d
d
ema
n
d
r
esp
o
n
s
e
fo
r
d
ay
...
(
R
ica
r
d
o
Mo
r
en
o
)
2795
r
am
p
s
.
T
h
e
g
en
e
r
a
ti
o
n
s
y
s
te
m
r
el
ia
b
il
ity
o
f
th
e
s
y
s
tem
m
a
y
b
e
r
ed
u
c
e
d
in
c
ase
o
f
u
n
p
r
e
d
ic
te
d
d
e
cr
ea
s
es
in
w
in
d
p
o
w
er
b
e
ca
u
s
e
th
e
av
ail
ab
l
e
r
am
p
in
g
ca
p
a
b
i
lity
o
f
th
e
s
y
s
tem
m
a
y
n
o
t
b
e
s
u
f
f
ici
e
n
t
to
ac
co
m
m
o
d
ate
th
o
s
e
ch
an
g
es.
T
h
e
d
ay
-
ah
ea
d
d
is
p
a
tch
in
g
w
ith
w
in
d
p
o
w
er
h
as
b
ee
n
ad
d
r
ess
ed
w
id
ely
.
T
h
e
o
p
tim
al
p
o
w
er
f
lo
w
(
OP
F)
f
o
r
m
u
lati
o
n
h
av
e
b
ee
n
ex
ten
d
e
d
t
o
ac
co
u
n
t
f
o
r
th
e
v
a
r
ia
b
l
e
n
atu
r
e
o
f
w
in
d
p
o
w
er
g
en
e
r
at
io
n
.
Fo
r
in
s
tan
c
e,
in
[5
-
8]
,
th
e
i
n
ter
m
itten
t
n
atu
r
e
o
f
w
in
d
p
o
w
er
g
en
er
a
ti
o
n
is
ca
p
tu
r
e
d
u
s
in
g
p
r
o
b
a
b
ilis
tic
tech
n
i
q
u
es.
A
s
to
ch
ast
ic
u
n
it
co
m
m
it
m
en
t
m
o
d
e
l
is
p
r
esen
t
ed
in
[
9
]
,
w
h
er
e
au
th
o
r
s
p
r
o
p
o
s
e
a
f
r
am
e
w
o
r
k
t
o
q
u
an
tif
y
th
e
im
p
ac
t
o
f
la
r
g
e
-
s
ca
l
e
w
in
d
p
o
w
er
in
teg
r
ati
o
n
i
n
to
p
o
w
er
s
y
s
te
m
s
.
T
h
e
u
n
ce
r
ta
in
ty
in
th
e
w
in
d
g
en
er
a
ti
o
n
is
a
d
d
r
ess
e
d
b
y
m
e
an
s
o
f
s
ce
n
ar
io
s
an
d
d
em
an
d
s
ar
e
c
o
n
s
id
e
r
e
d
t
o
b
e
f
ix
e
d
.
O
th
er
s
au
th
o
r
s
h
av
e
s
u
g
g
ested
s
to
ch
ast
ic
o
p
tim
izat
io
n
(
SO
)
b
as
ed
o
n
s
c
en
ar
io
s
t
o
co
p
e
w
ith
w
in
d
p
o
w
er
u
n
ce
r
ta
in
ty
in
th
e
u
n
it
co
m
m
it
m
en
t
p
r
o
b
lem
[
1
0
-
1
2
]
.
SO
em
p
lo
y
s
s
ev
er
al
s
c
en
a
r
io
s
al
o
n
g
w
ith
th
eir
ass
o
ci
at
ed
p
r
o
b
a
b
il
iti
es
to
s
im
u
late
p
o
s
s
i
b
le
u
n
ce
r
ta
in
ties
d
u
r
in
g
th
e
p
e
r
i
o
d
.
I
n
[
1
3
]
,
an
o
p
tim
al
g
en
er
a
ti
o
n
s
ch
ed
u
lin
g
m
eth
o
d
in
c
lu
d
in
g
r
en
ew
ab
le
en
e
r
g
y
,
d
is
t
r
i
b
u
te
d
r
es
o
r
u
es
an
d
s
t
o
r
ag
e
s
y
s
tem
s
is
s
o
lv
e
d
u
s
in
g
a
p
a
r
ti
cl
e
s
w
an
o
p
t
im
izati
o
n
alg
o
r
ith
m
.
I
n
a
d
d
iti
o
n
,
in
[
1
4
]
,
th
e
au
h
o
r
s
p
r
o
p
o
s
e
an
en
h
an
ce
d
g
en
eti
c
a
lg
o
r
ith
m
to
s
o
lv
e
th
e
o
p
tim
al
p
o
w
er
f
lo
w
.
On
th
e
o
th
er
h
an
d
,
th
e
in
t
eg
r
a
t
io
n
o
f
d
em
an
d
s
i
d
e
r
es
o
u
r
ce
s
i
n
to
el
ec
tr
i
city
m
ar
k
ets h
as d
r
a
w
n
a
lo
t o
f
atten
t
io
n
.
DR
is
a
s
tr
a
te
g
y
to
u
tili
ze
e
le
ctr
ici
ty
d
em
an
d
as
a
d
is
t
r
i
b
u
te
d
r
eso
u
r
c
e
w
ith
r
ea
l
p
o
s
s
ib
ilit
ies
t
o
im
p
r
o
v
e
ef
f
icien
cy
an
d
r
el
ia
b
i
lity
o
f
elec
tr
ici
ty
n
et
w
o
r
k
s
.
Us
u
ally
,
th
e
d
em
an
d
in
p
o
w
er
s
y
s
tem
is
co
n
s
id
er
e
d
in
elast
ic
to
th
e
p
r
i
ce
s
.
Ho
w
ev
er
,
a
s
u
b
s
tan
ti
al
am
o
u
n
t
o
f
el
e
ctr
ici
ty
d
em
an
d
is
el
asti
c
s
u
ch
as
p
lu
g
-
in
e
lec
tr
ic
v
eh
icle
(
PEV)
[
1
5
]
ch
a
r
g
in
g
b
atte
r
i
es,
h
e
atin
g
v
en
ti
lat
io
n
,
ai
r
c
o
n
d
iti
o
n
in
g
,
an
d
th
is
r
e
p
o
r
t
[
1
6
]
in
d
ic
ates
th
at
o
n
e
th
ir
d
o
f
r
esi
d
en
t
ial
d
em
an
d
in
U
.
S.
is
f
lex
i
b
l
e.
Sev
er
al
s
tu
d
ies
a
r
e
r
ese
ar
ch
in
g
ab
o
u
t
th
e
p
a
r
ti
ci
p
at
io
n
o
f
d
em
an
d
s
id
e
r
eso
u
r
c
es
in
th
e
p
r
o
cu
r
em
en
t
o
f
en
er
g
y
an
d
r
es
e
r
v
e
s
e
r
v
ices
.
S
em
in
al
s
tu
d
ies
[
1
7
-
19]
h
av
e
d
e
v
elo
p
e
d
p
o
o
l b
as
e
d
m
ar
k
et
s
tr
u
ctu
r
es
co
n
s
i
d
e
r
in
g
th
e
p
ar
tic
ip
ati
o
n
o
f
d
em
an
d
s
id
e
r
es
o
u
r
ce
s
in
to
th
e
en
er
g
y
an
d
r
es
er
v
e
m
ar
k
e
ts
.
T
h
e
d
e
m
an
d
s
id
e
r
es
o
u
r
ce
s
(
i
.
e
.
,
DR
r
eso
u
r
c
es)
ar
e
te
c
h
n
ically
ca
p
ab
le
o
f
p
r
o
v
i
d
in
g
an
cilla
r
y
s
er
v
ices
g
iv
en
t
h
e
f
lex
ib
i
lity
an
d
th
e
p
o
s
s
i
b
ili
ty
to
allev
i
ate
l
a
r
g
e
an
d
u
n
ex
p
ec
te
d
w
in
d
r
am
p
ev
en
ts
[
2
0
,
2
1
]
.
D
is
tr
ib
u
tio
n
c
o
m
p
an
ies
o
r
ag
g
r
eg
at
o
r
s
u
s
u
ally
m
an
ag
e
DR
r
es
o
u
r
ce
s
[
2
2
]
.
T
h
e
ag
g
r
eg
a
to
r
s
r
e
p
r
esen
t
t
ec
h
n
ic
ally
an
d
f
in
an
cially
v
ar
i
o
u
s
u
s
er
s
in
o
r
d
e
r
t
o
b
i
d
DR
r
e
d
u
ctio
n
s
in
e
lec
tr
ici
ty
m
ar
k
ets.
T
h
is
p
a
p
er
a
d
d
r
ess
es
th
e
d
a
y
-
ah
ea
d
d
is
p
atch
in
g
in
clu
d
in
g
w
in
d
p
o
w
er
b
id
s
an
d
DR
b
i
d
s
.
T
h
e
p
ap
e
r
is
o
r
g
an
iz
e
d
as
f
o
l
l
o
w
s
.
T
h
e
p
r
o
b
lem
f
o
r
m
u
latio
n
is
p
r
esen
t
ed
in
Se
cti
o
n
I
I
.
I
n
Secti
o
n
I
I
I
,
th
e
p
r
o
p
o
s
ed
p
r
o
c
ed
u
r
e
is
tes
t
ed
u
s
in
g
th
e
I
E
E
E
3
9
-
b
u
s
test
s
y
s
te
m
.
T
h
e
r
esu
lts
ar
e
an
a
ly
ze
d
an
d
d
is
cu
s
s
e
d
.
Secti
o
n
I
V
p
r
o
v
i
d
es
s
o
m
e
co
n
clu
d
in
g
r
em
ar
k
s
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
T
h
e
n
o
tatio
n
f
o
r
th
e
OP
F
d
is
p
atch
i
n
g
m
o
d
el
i
n
cl
u
d
in
g
w
i
n
d
p
o
w
er
g
e
n
er
atio
n
s
a
n
d
DR
r
eso
u
r
ce
s
i
s
ex
p
r
ess
ed
i
n
ter
m
s
o
f
p
o
w
e
r
g
en
er
atio
n
f
o
r
ea
ch
u
n
it,
t
h
e
lo
ad
f
o
llo
w
in
g
r
eser
v
es
a
n
d
t
h
e
b
in
ar
y
co
m
m
i
t
m
en
t
v
ar
iab
le
f
o
r
th
er
m
al
u
n
it
s
.
T
h
e
co
m
p
lete
s
et
o
f
v
ar
iab
le
s
ar
e
d
escr
ib
ed
as f
o
llo
w
s
:
2
.
1
.
No
t
a
t
io
n
t
I
n
d
ex
o
v
er
ti
m
e
p
er
io
d
s
.
T
Set o
f
in
d
ice
s
o
f
ti
m
e
p
er
io
d
s
in
th
e
p
la
n
n
i
n
g
h
o
r
izo
n
,
t
y
p
ical
l
y
1
.
.
.
t
n
.
i
I
n
d
ex
o
v
er
in
j
ec
tio
n
s
(
g
en
er
at
i
o
n
u
n
its
,
d
is
p
atc
h
ab
le
o
r
cu
r
tailab
le
lo
ad
s
)
.
j
I
n
d
ex
o
v
er
s
ce
n
ar
io
s
.
t
I
I
n
d
ices o
f
all
u
n
i
ts
(
g
e
n
er
ato
r
s
)
av
ailab
le
f
o
r
d
is
p
atch
in
an
y
ti
m
e
t
.
f
I
n
d
ex
o
f
w
i
n
d
f
ar
m
s
.
F
N
Set o
f
in
d
ice
s
o
f
all
u
n
i
ts
(
w
i
n
d
f
ar
m
s
a
n
d
g
e
n
er
ato
r
s
)
av
ail
a
b
le
f
o
r
d
is
p
atch
in
a
n
y
ti
m
e
t
b
I
n
d
ex
o
f
lo
ad
s
.
M
A
X
D
P
Ma
x
.
,
p
o
w
er
d
e
m
a
n
d
f
o
r
u
n
it
i
at
ti
m
e
t
.
B
N
Set o
f
in
d
ice
s
o
f
all
lo
ad
s
at
ti
m
e
t
.
ti
F
L
o
ad
f
le
x
ib
ilit
y
o
f
d
e
m
a
n
d
f
o
r
u
n
it
i
at
ti
m
e
t
.
tij
p
A
cti
v
e
i
n
j
ec
tio
n
f
o
r
u
n
it
i
o
f
s
ce
n
ar
io
j
at
ti
m
e
t
.
tf
w
p
W
in
d
p
o
w
er
f
o
r
ec
ast as o
f
f
er
e
d
in
th
e
m
ar
k
et
f
o
r
u
n
it
f
at
ti
m
e
t
ti
D
P
R
ea
l p
o
w
e
r
d
e
m
a
n
d
f
o
r
u
n
it
i
o
f
s
ce
n
ar
io
j
at
ti
m
e
t
.
ti
P
C
C
o
s
t
f
u
n
ctio
n
f
o
r
ac
tiv
e
i
n
j
ec
tio
n
i
at
ti
m
e
t
.
ti
D
C
C
o
s
t
f
u
n
ctio
n
o
f
u
p
w
ar
d
an
d
d
o
w
n
w
ar
d
r
eg
u
latio
n
o
f
t
h
e
d
em
an
d
f
r
o
m
u
n
it
i
at
ti
m
e
t
.
tb
D
De
m
a
n
d
p
o
w
er
at
ti
m
e
t
.
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.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
7
9
4
-
2802
2796
,
ti
ti
Up
w
ar
d
/d
o
w
n
w
ar
d
lo
ad
-
f
o
ll
o
w
i
n
g
r
a
m
p
i
n
g
r
eser
v
e
s
n
ee
d
ed
f
r
o
m
u
n
it
i
at
tim
e
t
f
o
r
tr
an
s
it
io
n
to
ti
m
e
1
t
.
ti
C
,
ti
C
C
o
s
t o
f
u
p
w
ar
d
an
d
d
o
w
n
w
ar
d
lo
ad
-
f
o
llo
w
i
n
g
r
a
m
p
.
R
e
s
er
v
e
f
o
r
u
n
it
i
at
ti
m
e
t
.
tij
M
I
N
P
,
tij
M
A
X
P
L
i
m
it
s
o
n
ac
ti
v
e
in
j
ec
tio
n
f
o
r
u
n
i
t
i
in
t
h
e
s
ce
n
ar
io
j
at
ti
m
e
t
.
M
A
X
i
,
M
A
X
i
Up
w
ar
d
/d
o
w
n
w
ar
d
lo
ad
-
f
o
llo
w
i
n
g
r
a
m
p
i
n
g
r
eser
v
e
li
m
its
f
o
r
u
n
it
i
.
ti
u
B
in
ar
y
co
m
m
it
m
e
n
t state
f
o
r
u
n
it
i
in
p
er
io
d
t
.
,
t
i
t
i
vw
B
in
ar
y
s
tar
t
u
p
an
d
s
h
u
td
o
w
n
s
tates f
o
r
u
n
it
i
in
p
er
io
d
t
.
,
t
i
t
i
vw
CC
Star
tu
p
an
d
s
h
u
td
o
w
n
co
s
ts
f
o
r
u
n
it
i
at
ti
m
e
t
,
ti
ti
Star
tu
p
an
d
s
h
u
td
o
w
n
co
s
ts
f
o
r
u
n
it
i
at
ti
m
e
t
2
.
2
.
F
o
r
m
ula
t
io
n
T
h
e
p
r
o
b
lem
f
o
r
m
u
la
tio
n
i
s
ex
p
r
ess
ed
as
a
m
ix
ed
-
in
teg
er
lin
ea
r
q
u
ad
r
atic
o
p
ti
m
izatio
n
p
r
o
b
le
m
(
MI
L
P
)
,
w
h
er
e
t
h
e
o
p
ti
m
izati
o
n
v
ar
iab
le
x
is
co
m
p
r
is
ed
o
f
all
t
h
e
,
p
,
ti
-
,
ti
,
u
v
an
d
w
v
ar
iab
les
co
r
r
esp
o
n
d
in
g
to
p
o
w
er
g
e
n
e
r
atio
n
f
o
r
ea
ch
u
n
it,
th
e
lo
ad
f
o
llo
w
in
g
r
eser
v
es
a
n
d
th
e
b
in
ar
y
co
m
m
it
m
e
n
t
v
ar
iab
le
f
o
r
th
er
m
al
u
n
it
s
.
Ob
jective
F
u
n
ctio
n
:
T
h
e
o
b
j
ec
tiv
e
is
e
x
p
r
ess
ed
as t
h
e
m
in
i
m
izatio
n
()
fx
m
i
n
(
)
x
fx
(
1
)
Su
b
j
ec
t to
(
)
0
gx
(
2
)
(
)
0
hx
(
3
)
m
i
n
m
a
x
x
x
x
(
4
)
w
h
er
e
()
fx
is
co
m
p
r
is
ed
o
f
t
h
r
ee
co
m
p
o
n
en
t
s
.
(
)
(
)
(
,
)
(
,
)
(
,
)
p
l
f
u
c
d
r
f
x
f
p
f
f
u
w
f
u
w
(
5
)
C
o
s
t o
f
ac
ti
v
e
p
o
w
er
d
is
p
at
ch
(
)
(
)
t
ti
tij
p
P
t
T
i
I
f
p
C
p
(
6
)
C
o
s
t o
f
lo
ad
-
f
o
llo
w
i
n
g
r
a
m
p
r
eser
v
es
(
,
)
t
t
i
t
i
t
i
ti
lf
t
T
i
I
f
C
C
(
7
)
Star
tu
p
an
d
s
h
u
td
o
w
n
co
s
t
(
,
)
t
t
i
t
i
t
i
t
i
uc
vw
t
T
i
I
f
v
w
C
v
C
w
(
8
)
C
o
s
t o
f
d
e
m
a
n
d
r
esp
o
n
s
e
(
,
)
t
tij
ti
dr
DD
t
T
i
I
f
v
w
C
P
(
9
)
T
h
is
m
i
n
i
m
izatio
n
i
s
s
u
b
j
ec
t to
th
e
f
o
llo
w
i
n
g
co
n
s
tr
ai
n
ts
,
f
o
r
all:
a
l
l
a
n
d
a
l
l
:
Tt
t
T
j
J
i
I
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
in
teg
r
a
ted
OP
F
d
is
p
a
tch
in
g
mo
d
el
w
ith
w
in
d
p
o
w
er a
n
d
d
ema
n
d
r
esp
o
n
s
e
fo
r
d
ay
...
(
R
ica
r
d
o
Mo
r
en
o
)
2797
C
o
n
s
tr
a
in
ts
:
P
o
w
er
b
alan
ce
co
n
s
tr
ai
n
ts
,
TT
FB
t
i
j
t
f
j
t
i
j
t
b
w
D
i
I
i
I
f
N
b
N
p
P
p
D
(
1
0
)
No
n
li
n
ea
r
tr
an
s
m
is
s
io
n
f
lo
w
a
n
d
v
o
ltag
e
l
i
m
its
as
i
n
eq
u
a
lit
y
co
n
s
tr
ain
t
s
,
(
,
)
0
t
j
t
j
t
j
h
V
p
(
1
1
)
L
o
ad
-
f
o
llo
w
i
n
g
r
a
m
p
i
n
g
li
m
it
s
an
d
r
eser
v
es,
m
a
x
0
t
i
t
i
(
1
2
)
m
a
x
0
ti
ti
(
1
3
)
I
n
j
ec
tio
n
li
m
it
s
an
d
co
m
m
i
t
m
en
ts
,
m
a
x
m
i
n
t
i
j
t
i
j
t
i
t
i
j
t
i
u
P
p
u
P
(
1
4
)
Star
tu
p
an
d
s
h
u
td
o
w
n
ev
e
n
t
s
,
(
1
)
t
i
t
i
t
i
t
i
u
u
v
w
(
1
5
)
I
n
teg
er
co
n
s
tr
ain
t
s
,
0
,
1
,
0
,
1
,
0
,
1
t
i
t
i
t
i
u
v
w
(
1
6
)
Flex
ib
ili
t
y
i
n
ter
v
al
o
f
t
h
e
d
e
m
an
d
m
a
x
0
t
i
D
FP
(
1
7
)
3.
SI
M
UL
AT
I
O
N
S RE
SU
L
T
S
T
h
e
I
E
E
E
3
9
-
b
u
s
test
s
y
s
tem
is
ex
am
in
ed
in
th
is
s
e
cti
o
n
t
o
test
th
e
in
teg
r
at
ed
m
o
d
el
th
at
co
n
s
i
d
e
r
s
w
in
d
p
o
w
er
g
en
er
ati
o
n
DR
r
e
s
o
u
r
ce
s
.
T
h
e
d
ay
-
ah
ea
d
d
is
p
at
ch
in
g
f
r
am
e
w
o
r
k
p
r
o
p
o
s
ed
as
a
MI
L
P
p
r
o
b
lem
is
s
o
lv
e
d
u
s
in
g
G
UR
OB
I
7
.
5
.
1
[
2
3
]
u
n
d
e
r
th
e
M
at
p
o
w
er
p
l
atf
o
r
m
[
2
4
]
.
T
h
e
ca
s
e
I
E
E
E
3
9
-
b
u
s
t
est
s
y
s
tem
in
clu
d
es
1
0
g
en
e
r
at
or
s
;
th
e
d
at
a
is
lis
te
d
in
T
ab
le
1
.
T
h
e
co
s
t
d
at
a
ar
e
e
q
u
al
t
o
r
e
p
o
r
t
in
[
2
5
]
an
d
[
2
6
]
.
T
a
b
l
e
2
lis
ts
th
e
q
u
a
d
r
ati
c
c
o
s
t
f
u
n
cti
o
n
s
f
o
r
e
ac
h
g
en
e
r
at
o
r
in
th
e
I
E
E
E
3
9
-
b
u
s
s
y
s
tem
ac
co
r
d
in
g
to
[
2
7
]
.
T
h
e
s
y
s
tem
d
ai
ly
lo
a
d
cu
r
v
e
is
s
h
o
w
n
in
Fig
u
r
e
1
w
ith
a
m
ax
im
u
m
p
ea
k
o
f
4
5
3
1
M
W
a
t
h
o
u
r
2
0
an
d
a
m
in
i
m
u
m
o
f
1
8
4
0
at
h
o
u
r
3
.
T
ab
le
1
.
Gen
er
ato
r
d
ata
f
o
r
t
h
e
I
EEE
3
9
b
u
s
s
y
s
te
m
G
e
n
.
#
C
C
v
C
w
C
m
i
n
P
m
ax
P
1
6
.
9
6
.
9
9
2
0
7
3
6
0
2
5
0
2
6
.
9
6
.
9
9
2
0
7
3
6
0
6
7
8
3
6
.
9
6
.
9
9
2
0
7
3
6
0
6
5
0
4
6
.
9
6
.
9
9
2
0
73
6
0
6
3
2
5
6
.
9
6
.
9
9
2
0
7
3
6
0
5
0
8
6
6
.
9
6
.
9
9
2
0
7
3
6
0
6
5
0
7
6
.
9
6
.
9
9
2
0
7
3
6
0
5
6
0
8
6
.
9
6
.
9
9
2
0
7
3
6
0
5
4
0
9
6
.
9
6
.
9
9
2
0
7
3
6
0
8
3
0
10
6
.
9
6
.
9
9
2
0
7
3
6
0
1
0
0
0
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.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
7
9
4
-
2802
2798
T
ab
le
2
.
C
o
s
t
f
u
n
ctio
n
s
G
e
n
.
C
o
st
F
u
n
c
t
i
o
n
[
$
]
1
2
1
0
.
0
0
1
9
4
7
.
8
5
3
1
0
C
P
P
2
2
2
0
.
0
0
3
5
8
.
5
2
6
0
C
P
P
3
2
3
0
.
0
0
4
8
2
7
7
8
C
P
P
4
2
4
0
.
0
0
1
2
8
6
.
4
4
5
9
C
P
P
5
2
5
0
.
0
0
2
4
6
8
0
C
P
P
6
2
6
0
.
0
0
3
2
5
.
8
4
0
0
C
P
P
7
2
7
0
.
0
0
5
3
6
.
2
4
1
2
0
C
P
P
8
2
8
0
.
0
0
1
8
5
8
.
4
6
0
C
P
P
9
2
9
0
.
0
0
2
5
5
.
7
5
4
5
0
C
P
P
10
2
10
0
.
0
0
1
4
2
8
.
2
5
1
0
C
P
P
F
ig
u
r
e
1
.
S
y
s
te
m
d
ail
y
lo
ad
cu
r
v
e
T
h
is
m
o
d
e
l
co
n
s
i
d
er
s
a
w
in
d
p
o
w
er
in
teg
r
a
ti
o
n
lev
el
o
f
2
0
%
w
ith
r
es
p
e
ct
t
o
th
e
p
e
ak
lo
a
d
lev
el.
A
lar
g
e
n
u
m
b
er
o
f
s
c
en
a
r
i
o
s
ar
o
u
n
d
a
tr
a
ject
o
r
y
b
id
c
a
p
tu
r
es
th
e
u
n
ce
r
t
ain
ty
in
w
in
d
p
o
w
er
f
o
r
ec
asti
n
g
b
y
th
e
w
in
d
p
o
w
e
r
g
en
e
r
a
to
r
as
s
h
o
w
n
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
W
in
d
p
o
w
er
g
en
e
r
a
ti
o
n
p
r
o
f
il
e
DR
o
f
f
er
s
in
ce
n
tiv
es
d
es
ig
n
ed
to
in
d
u
ce
l
o
w
er
elec
tr
ici
ty
u
s
e
at
tim
es
o
f
h
ig
h
m
ar
k
et
p
r
ic
e.
Fo
r
th
is
s
im
u
latio
n
,
f
o
u
r
l
o
ad
s
p
r
o
v
i
d
e
d
em
an
d
r
es
p
o
n
s
e
s
e
r
v
ic
es,
a
n
d
th
e
p
o
w
er
q
u
an
tity
,
w
h
ich
th
ey
ar
e
w
illi
n
g
to
r
e
d
u
ce
in
a
ce
r
t
ain
tim
e,
is
1
2
9
5
MW.
T
h
e
in
c
en
tiv
es
r
e
p
r
ese
n
ted
as
c
o
s
t
f
u
n
cti
o
n
s
a
r
e
s
h
o
w
n
in
T
a
b
l
e
3
.
T
ab
le
3
.
L
o
ad
d
ata
f
o
r
t
h
e
d
e
m
an
d
r
esp
o
n
s
e
L
o
a
d
B
u
s
D
e
man
d
P
o
w
e
r
[
M
W
]
C
o
st
F
u
n
c
t
i
o
n
[
$
]
1
8
522
2
1
0
.
0
0
1
2
8
6
.
4
4
5
9
C
P
P
2
15
320
2
2
0
.
0
0
1
2
8
6
.
4
4
5
9
C
P
P
3
23
2
4
7
.
5
2
3
0
.
0
0
1
2
8
6
.
4
4
5
9
C
P
P
4
28
206
2
4
0
.
0
0
1
2
8
6
.
4
4
5
9
C
P
P
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
in
teg
r
a
ted
OP
F
d
is
p
a
tch
in
g
mo
d
el
w
ith
w
in
d
p
o
w
er a
n
d
d
ema
n
d
r
esp
o
n
s
e
fo
r
d
ay
...
(
R
ica
r
d
o
Mo
r
en
o
)
2799
Fo
r
f
iv
e
h
u
n
d
r
ed
(
5
0
0
)
s
c
e
n
ar
i
o
s
,
th
is
p
a
p
e
r
q
u
an
tif
ies
th
e
d
em
an
d
r
es
p
o
n
s
e
f
r
eq
u
en
cy
an
d
h
e
m
ag
n
itu
d
e
in
MW
f
o
r
ea
ch
lo
a
d
.
E
a
ch
s
ce
n
a
r
i
o
r
u
n
s
o
v
e
r
2
4
h
o
u
r
s
ac
c
o
r
d
in
g
to
th
e
s
y
s
tem
d
aily
lo
ad
an
d
it
co
n
s
i
d
e
r
s
a
f
o
r
e
ca
s
te
d
tr
a
ject
o
r
y
f
o
r
th
e
w
in
d
in
teg
r
a
ti
o
n
.
I
n
Fig
u
r
e
3
,
c
an
o
b
s
e
r
v
e
th
e
f
r
eq
u
en
cy
an
d
q
u
an
tity
o
f
f
lex
ib
i
lity
f
o
r
th
e
lo
a
d
in
th
e
b
u
s
8
.
I
t is o
b
ese
r
v
e
d
th
e
d
e
m
an
d
r
esp
o
n
s
e
is
m
ax
i
m
u
m
al
l
th
e
tim
e.
E
ac
h
tim
e
th
at
th
is
lo
ad
is
s
h
e
d
,
it
is
s
h
e
d
at
5
2
2
MW.
W
h
i
le
th
at
f
o
r
t
h
e
lo
a
d
in
th
e
b
u
s
1
5
,
Fig
u
r
e
4
s
h
o
w
s
s
o
m
eti
m
es
th
e
q
u
an
tity
o
f
DR
r
e
q
u
ir
ed
i
s
ar
o
u
n
d
2
7
0
M
W
,
2
9
5
MW,
an
d
3
0
5
MW,
alth
o
u
g
h
th
e
7
5
%
o
f
t
im
e
th
e
DR
r
e
q
u
i
r
e
d
i
s
at
th
e
m
ax
im
u
m
v
alu
e.
T
h
e
r
esu
lts
f
o
r
d
em
an
d
r
esp
o
n
s
e
in
th
e
b
u
s
2
3
,
s
ee
Fig
u
r
e
5
,
a
r
e
s
im
ilar
t
o
th
e
r
esu
lts
in
th
e
Fig
u
r
e
4
,
al
m
o
s
t
all
th
e
tim
e
th
e
D
R
is
d
is
p
at
ch
e
d
a
t
m
ax
im
u
m
.
I
n
Fig
u
r
e
6
,
t
he
l
o
ad
in
th
e
b
u
s
2
8
ex
h
ib
i
t
a
s
im
ila
r
d
is
p
at
ch
in
g
t
o
th
e
l
o
a
d
s
in
th
e
b
u
s
es
1
5
an
d
2
3
.
Fig
u
r
e
3
.
De
m
an
d
r
esp
o
n
s
e
in
th
e
b
u
s
8
Fig
u
r
e
4
.
De
m
an
d
r
esp
o
n
s
e
in
th
e
b
u
s
1
5
Fig
u
r
e
5
.
De
m
an
d
r
esp
o
n
s
e
in
th
e
b
u
s
2
3
Fig
u
r
e
6
.
De
m
an
d
r
esp
o
n
s
e
in
th
e
b
u
s
2
8
No
w
,
in
Fig
u
r
e
7
s
h
o
w
s
th
e
p
er
ce
n
tag
e
o
f
DR
w
i
th
r
esp
ec
t
to
th
e
av
ail
ab
le
c
ap
ac
i
ty
.
I
t
is
o
b
s
er
v
e
d
th
at
in
th
e
h
o
u
r
3
,
1
3
,
1
6
a
n
d
1
7
f
o
r
th
e
2
4
h
o
r
i
zo
n
p
l
an
n
in
g
,
th
e
D
R
is
n
o
t
d
is
p
at
ch
ed
at
m
ax
i
m
u
m
.
Fo
r
in
s
tan
ce
,
in
th
e
h
o
u
r
1
3
,
t
h
e
lo
a
d
in
th
e
2
8
r
es
p
o
n
d
s
at
4
0
%
f
o
r
th
e
m
ax
i
m
u
m
v
alu
e
av
aila
b
l
e.
A
t
th
e
p
ea
k
d
em
an
d
f
o
r
th
e
s
y
s
tem
,
at
h
o
u
r
2
0
,
all
l
o
a
d
s
a
r
e
d
is
p
atch
ed
as
DR
r
eso
u
r
c
es.
Fig
u
r
e
7
.
De
m
an
d
r
esp
o
n
s
e
f
o
r
all
lo
ad
s
in
th
e
p
o
w
er
s
y
s
te
m
I
n
o
r
d
e
r
t
o
q
u
an
tif
y
th
e
b
en
ef
i
ts
f
o
r
DR
p
a
r
t
ici
p
ati
o
n
in
th
e
p
o
w
er
s
y
s
tem
o
p
er
ati
o
n
,
th
e
p
r
o
b
ab
ilit
y
de
n
s
ity
f
u
n
cti
o
n
f
o
r
th
e
p
o
w
er
g
en
er
a
ti
o
n
c
o
s
t
is
ca
lcu
l
ate
d
in
th
e
2
4
-
h
o
u
r
h
o
r
i
z
o
n
.
T
h
e
r
ea
l
i
za
ti
o
n
s
c
o
r
r
es
p
o
n
d
to
th
e
tr
a
ject
o
r
ies
g
en
er
ate
d
a
r
o
u
n
d
th
e
b
i
d
m
ad
e
b
y
th
e
w
in
d
p
o
w
er
g
en
e
r
at
o
r
.
F
ig
u
r
e
8
s
h
o
w
s
th
e
p
o
w
er
g
en
er
a
ti
o
n
c
o
s
t
u
n
d
e
r
5
0
0
s
ce
n
ar
i
o
s
w
ith
DR
av
ail
ab
le
f
o
r
d
is
p
at
ch
in
g
w
h
ile
th
e
Fig
u
r
e
9
s
h
o
w
s
th
e
p
o
w
er
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.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
7
9
4
-
2802
2800
g
en
er
a
ti
o
n
co
s
t
w
ith
o
u
t
DR
av
ail
ab
le
.
I
n
o
r
d
e
r
t
o
c
o
m
p
ar
e
th
e
r
esu
lts
f
o
r
b
o
th
c
ases
,
m
ea
n
an
d
s
tan
d
a
r
d
d
ev
i
ati
o
n
f
o
r
e
ac
h
ca
s
e
a
r
e
ca
l
cu
lat
e
d.
T
h
e
s
av
in
g
s
f
o
r
th
e
p
o
w
er
g
en
er
ati
o
n
c
o
s
t
is
$
8
2
71
.
T
h
e
r
esu
lt
r
e
p
r
esen
ts
th
e
s
av
in
g
s
ca
n
b
e
m
ad
e
in
th
e
p
o
w
er
g
en
er
at
io
n
co
s
t
if
th
e
d
em
an
d
is
f
lex
ib
le
.
T
a
b
l
e
4
c
o
m
p
ar
e
s
th
e
m
ea
n
an
d
v
a
r
i
an
ce
p
a
r
am
eter
s
f
o
r
b
o
th
c
ases
,
w
ith
DR
an
d
w
ith
o
u
t D
R
.
Fig
u
r
e
8
.
C
o
s
t
o
b
j
e
c
tiv
e
f
u
n
cti
o
n
w
ith
D
R
Fig
u
r
e
9
.
Co
s
t
o
b
j
e
c
tiv
e
f
u
n
cti
o
n
w
ith
o
u
t D
R
T
ab
le
4
.
Gau
s
s
ian
p
ar
a
m
e
ter
s
f
o
r
th
e
c
o
s
t
o
b
j
e
c
tiv
e
f
u
n
ctio
n
w
it
h
D
R
an
d
w
it
h
o
u
t D
R
P
a
r
a
me
t
e
r
Est
i
m
a
t
e
w
i
t
h
o
u
t
D
R
Est
i
m
a
t
e
w
i
t
h
D
R
D
i
f
f
e
r
e
n
c
e
M
e
a
n
$
5
7
7
,
4
0
0
$
5
6
9
,
1
2
0
$
8
,
2
7
1
st
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
$
3
,
1
9
0
$
3
,
3
6
0
-
I
n
o
r
d
er
to
q
u
an
tif
y
DR
b
en
ef
its
,
o
th
e
r
s
c
o
s
t
f
u
n
cti
o
n
s
ar
e
s
et
u
p
t
o
p
r
o
v
i
d
e
in
s
ig
h
t
ab
o
u
t
th
e
d
is
p
at
ch
in
g
co
s
t
.
T
ab
le
5
p
r
o
v
i
d
es
s
ix
c
o
s
t
f
u
n
ctio
n
s
f
o
r
d
em
an
d
r
es
p
o
n
s
e
.
T
h
is
c
o
s
t
f
u
n
ctio
n
s
r
ep
r
es
en
ts
th
e
w
illi
n
g
o
f
ea
ch
l
o
a
d
t
o
p
r
o
v
id
e
DR
.
T
h
e
p
l
o
t
f
o
r
th
o
s
e
co
s
t f
u
n
cti
o
n
s
a
r
e
s
h
o
w
n
in
Fig
u
r
e
1
0
.
T
ab
le
5
.
I
n
ce
n
tiv
e
b
ased
d
e
m
a
n
d
r
esp
o
n
s
e
R
e
f
.
C
o
st
F
u
n
c
t
i
o
n
[
$
]
A
2
0
.
0
0
0
1
2
8
1
.
4
4
3
9
A
C
P
P
B
2
0
.
0
0
2
4
8
2
.
4
4
4
9
B
C
P
P
C
2
0
.
0
0
1
2
8
6
.
4
4
5
9
C
C
P
P
D
2
0
.
0
0
5
2
8
6
.
4
4
6
9
D
C
P
P
E
2
0
.
0
0
9
2
8
6
.
4
4
7
9
E
C
P
P
F
2
0
.
0
1
5
2
2
1
6
.
4
4
8
9
F
C
P
P
Fig
u
r
e
1
0
.
C
o
s
t
f
unc
t
io
n
s
f
o
r
d
em
a
n
d
r
esp
o
n
s
e
T
h
e
p
o
w
er
g
en
er
ati
o
n
c
o
s
t
v
a
r
ies
a
cc
o
r
d
in
g
t
o
d
if
f
er
en
t
in
c
en
tiv
es
f
o
r
DR
as
s
h
o
w
n
in
Fig
u
r
e
1
1
.
Fo
r
in
s
tan
c
e,
th
e
ca
s
e
F,
in
Fig
u
r
e
1
0
,
s
h
o
w
s
a
co
s
t
f
u
n
cti
o
n
w
ith
h
ig
h
b
id
f
o
r
DR
.
T
h
e
ca
s
e
A
co
r
r
es
p
o
n
e
d
s
to
a
s
itu
ati
o
n
w
ith
a
lo
w
er
co
s
t
f
u
n
ctio
n
,
h
o
w
ev
er
,
th
e
d
is
p
a
t
ch
in
g
is
n
o
t
th
e
lo
w
er
.
F
o
r
t
h
e
ca
s
es
ev
a
lu
at
ed
,
th
e
o
p
tim
al
s
o
lu
ti
o
n
co
r
r
es
p
o
n
d
s
to
th
e
c
ase
C
,
th
e
c
o
s
t
f
u
n
cti
o
n
C
is
b
e
tw
ee
n
th
e
ca
s
es
A
an
d
F
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
in
teg
r
a
ted
OP
F
d
is
p
a
tch
in
g
mo
d
el
w
ith
w
in
d
p
o
w
er a
n
d
d
ema
n
d
r
esp
o
n
s
e
fo
r
d
ay
...
(
R
ica
r
d
o
Mo
r
en
o
)
2801
Fig
u
r
e
1
1
.
Co
s
t o
b
j
ec
tiv
e
f
u
n
c
tio
n
f
o
r
d
if
f
er
en
t i
n
ce
n
ti
v
es to
DR
4.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
er
,
p
r
es
en
te
d
an
in
t
eg
r
a
te
d
O
P
F
m
o
d
e
l
th
a
t
ex
p
li
c
itly
in
clu
d
es
w
in
d
p
o
w
er
g
en
e
r
at
io
n
an
d
d
em
an
d
r
es
p
o
n
s
e
r
eso
u
r
c
es
f
o
r
d
ay
-
ah
ea
d
d
is
p
a
tch
in
g
in
c
o
n
s
tr
ain
ed
ele
ct
r
i
city
m
ar
k
ets
.
De
m
an
d
r
es
p
o
n
s
e
is
in
teg
r
ate
d
in
to
th
e
m
o
d
el
as f
l
e
x
ib
le
l
o
a
d
s
w
it
h
w
illi
n
g
to
b
i
d
d
ay
-
ah
ea
d
.
O
b
s
er
v
ed
th
at
c
o
n
s
id
e
r
ab
le
s
av
in
g
s
in
p
o
w
er
g
en
e
r
at
io
n
c
o
s
t
co
u
l
d
b
e
ac
h
i
ev
ed
if
th
e
d
em
an
d
p
a
r
ti
cip
at
es in
th
e
m
ar
k
ets.
T
h
e
n
u
m
er
ical
r
esu
lts
s
h
o
w
th
at
th
e
w
in
d
p
o
w
er
u
n
c
er
tain
t
y
ca
n
b
e
ca
p
tu
r
e
d
u
s
in
g
tr
a
j
e
ct
o
r
ies
f
r
o
m
a
M
o
n
te
-
C
a
r
l
o
s
im
u
lati
o
n
.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
e
au
th
o
r
s
ac
k
n
o
w
led
g
e
th
e
s
u
p
p
o
r
t
o
f
th
e
Un
iv
e
r
s
i
d
a
d
A
u
t
ó
n
o
m
a
d
e
Oc
ci
d
en
t
e
in
C
o
lo
m
b
ia
.
RE
F
E
R
E
NC
E
S
[1
]
J.
M
.
M
o
ra
les
,
e
t
a
l.
,
“
S
h
o
r
t
-
ter
m
trad
in
g
f
o
r
a
w
i
n
d
p
o
w
e
r
p
ro
d
u
c
e
r
,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
S
y
ste
ms
,
v
o
l
/i
ss
u
e
:
25
(
1
),
p
p
.
5
5
4
-
5
6
4
,
2
0
1
0
.
[2
]
S
.
S
.
S
a
k
th
i,
e
t
a
l.
,
“
W
in
d
In
teg
ra
ted
T
h
e
r
m
a
l
Un
it
Co
m
m
it
m
e
n
t
S
o
l
u
ti
o
n
u
sin
g
G
re
y
W
o
lf
Op
ti
m
iz
e
r
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
, v
ol
/i
ss
u
e
:
7
(
5
)
,
p
p
.
2
3
0
9
-
2
3
2
0
,
2
0
1
7
.
[3
]
I.
M
.
W
a
rtan
a
,
e
t
a
l.
,
“
Op
ti
m
a
l
In
teg
ra
ti
o
n
o
f
th
e
Re
n
e
w
a
b
le
En
e
rg
y
to
th
e
G
rid
b
y
Co
n
sid
e
rin
g
S
m
a
ll
S
ig
n
a
l
S
tab
il
it
y
Co
n
stra
in
t
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
ol
/i
ss
u
e
:
7
(
5
)
,
p
p
.
2
3
2
9
-
2
3
3
7
,
2
0
1
7
.
[4
]
C.
L
.
S
u
a
n
d
D.
Kirsc
h
e
n
,
“
Qu
a
n
ti
fy
in
g
th
e
e
ff
e
c
t
o
f
d
e
m
a
n
d
re
sp
o
n
se
o
n
e
lec
tri
c
it
y
m
a
rk
e
ts
,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r S
y
ste
ms
,
v
o
l
/i
ss
u
e
:
24
(
3
),
p
p
.
1
1
9
9
-
1
2
0
7
,
2
0
0
9
.
[5
]
R.
A
.
Ja
b
r
a
n
d
B.
C.
P
a
l,
“
I
n
term
it
ten
t
w
in
d
g
e
n
e
ra
ti
o
n
i
n
o
p
t
ima
l
p
o
w
e
r
f
lo
w
d
isp
a
tch
in
g
,
”
IET
Ge
n
e
r.
T
ra
n
sm
.
Distrib
,
v
o
l
/i
ss
u
e
:
3
(
1
)
,
p
p
.
6
6
-
7
4
,
2
0
0
9
.
[6
]
H.
Zh
a
n
g
a
n
d
P
.
L
i,
“
P
ro
b
a
b
il
isti
c
a
n
a
l
y
sis
f
o
r
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w u
n
d
e
r
u
n
c
e
rtain
ty
,
”
IET
Ge
n
e
r.
T
ra
n
sm
.
Distrib
,
v
o
l
/i
ss
u
e
:
4
(
5
)
,
p
p
.
5
5
3
-
5
6
1
,
2
0
1
0
.
[7
]
R.
En
tr
i
k
e
n
,
e
t
a
l.
,
“
S
to
c
h
a
stic
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
in
sy
ste
m
s
w
it
h
w
in
d
p
o
w
e
r,
”
Pro
c
.
IEE
E
P
o
w
e
r
En
e
rg
y
S
o
c
.
Ge
n
.
M
e
e
ti
n
g
,
S
a
n
Die
g
o
,
CA
,
US
A
,
p
p
.
1
-
5
,
2
0
1
1
.
[8
]
C.
S
.
S
a
u
n
d
e
rs,
“
P
o
in
t
e
stim
a
te
m
e
th
o
d
a
d
d
re
ss
in
g
c
o
rre
late
d
w
in
d
p
o
w
e
r
f
o
r
p
ro
b
a
b
il
ist
ic
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
,
”
IEE
E
T
ra
n
s.
P
o
we
r S
y
st.
,
v
o
l
/i
ss
u
e
:
29
(
3
)
,
p
p
.
1
0
4
5
-
1
0
5
4
,
2
0
1
4
.
[9
]
A
.
P
a
p
a
v
a
sili
o
u
a
n
d
S
.
S
.
Ore
n
,
“
M
u
lt
iare
a
sto
c
h
a
stic
u
n
it
c
o
m
m
it
m
e
n
t
f
o
r
h
ig
h
w
in
d
p
e
n
e
trati
o
n
i
n
a
tran
sm
issio
n
c
o
n
stra
in
e
d
n
e
tw
o
rk
,
”
Op
e
r.
Res
.
,
v
o
l
/i
ss
u
e
:
61
(
3
)
,
p
p
.
5
7
8
-
5
9
2
,
2
0
1
3
.
[1
0
]
F
.
Bo
u
f
f
a
rd
a
n
d
F
.
D.
G
a
li
a
n
a
,
“
S
to
c
h
a
stic
se
c
u
rit
y
f
o
r
o
p
e
ra
ti
o
n
s
p
la
n
n
i
n
g
w
it
h
sig
n
if
ica
n
t
w
in
d
p
o
w
e
r
g
e
n
e
ra
ti
o
n
,
”
IEE
E
T
ra
n
s.
P
o
we
r S
y
st.
,
v
o
l
/i
ss
u
e
:
23
(
2
)
,
p
p
.
3
0
6
-
3
1
6
,
2
0
0
8
.
[1
1
]
J.
M
.
M
o
ra
les
,
e
t
a
l
.
,
“
Eco
n
o
m
ic
v
a
lu
a
ti
o
n
o
f
re
se
rv
e
s
in
p
o
w
e
r
sy
ste
m
s
w
it
h
h
ig
h
p
e
n
e
trati
o
n
o
f
w
in
d
p
o
w
e
r,
”
IEE
E
T
ra
n
s.
P
o
we
r S
y
st.
,
v
o
l
/i
ss
u
e
:
24
(
2
)
,
p
p
.
9
0
0
-
9
1
0
,
2
0
0
9
.
[1
2
]
A
.
P
a
p
a
v
a
sili
o
u
,
e
t
a
l.
,
“
Re
se
rv
e
re
q
u
ire
m
e
n
ts
f
o
r
w
in
d
p
o
w
e
r
in
teg
ra
ti
o
n
:
A
s
c
e
n
a
rio
-
b
a
se
d
sto
c
h
a
stic
p
ro
g
ra
m
m
in
g
f
ra
m
e
w
o
rk
,
”
IEE
E
T
ra
n
s.
Po
we
r S
y
st.
,
v
o
l
/i
ss
u
e:
26
(
4
)
,
p
p
.
2
1
9
7
-
2
2
0
6
,
2
0
1
1
.
[1
3
]
B.
Ba
n
h
tas
it
a
n
d
C.
S
.
De
c
h
a
n
u
p
a
p
ri
tt
h
a
,
“
Op
ti
m
a
l
G
e
n
e
ra
ti
o
n
S
c
h
e
d
u
li
n
g
o
f
P
o
w
e
r
S
y
st
e
m
f
o
r
M
a
x
i
m
u
m
Re
n
e
wa
b
le
En
e
rg
y
Ha
r
v
e
stin
g
a
n
d
P
o
w
e
r
L
o
ss
e
s
M
in
im
iza
ti
o
n
,
”
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
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
E
CE)
,
v
o
l
/
issu
e
:
8
(
4
)
,
p
p
.
1
9
5
4
-
1
9
6
6
,
2
0
1
8
.
[1
4
]
S
.
Kim
a
n
d
S
.
R.
S
a
lk
u
t,
“
Op
ti
m
a
l
p
o
w
e
r
f
lo
w
b
a
se
d
c
o
n
g
e
stio
n
m
a
n
a
g
e
m
e
n
t
u
sin
g
e
n
h
a
n
c
e
d
g
e
n
e
ti
c
a
lg
o
rit
h
m
s
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
, v
ol
/i
ss
u
e
:
9
(
2
)
,
p
p
.
8
7
5
-
8
8
3
,
2
0
1
9
.
[1
5
]
M
.
Ke
fa
y
a
ti
a
n
d
R.
Ba
ld
ick
,
“
Ha
rn
e
ss
in
g
d
e
m
a
n
d
f
lex
ib
il
it
y
t
o
m
a
tch
re
n
e
w
a
b
le
p
ro
d
u
c
ti
o
n
u
sin
g
lo
c
a
li
z
e
d
p
o
li
c
ies
,
”
Pro
c
.
5
0
t
h
An
n
u
.
A
ll
e
rto
n
C
o
n
f.
C
o
mm
u
n
.
Co
n
tro
l
Co
mp
u
t.
(
Al
ler
to
n
)
,
M
o
n
ti
c
e
ll
o
,
IL
,
US
A
,
p
p
.
1
1
0
5
-
1
1
0
9
,
2
0
1
2
.
[1
6
]
U.S
.
E
n
e
rg
y
In
f
o
r
m
a
ti
o
n
A
d
m
in
i
stra
ti
o
n
(E
IA
)
,
“
Esti
m
a
ted
U.S
.
R
e
sid
e
n
ti
a
l
El
e
c
tri
c
ty
Co
n
su
m
p
ti
o
n
b
y
En
d
-
Use
,”
2
0
1
0
.
A
v
a
il
a
b
le:
h
tt
p
:/
/w
ww
.
e
i
a
.
g
o
v
/t
o
o
ls/f
a
q
s/f
a
q
.
c
fm
?
id
=
9
6
&
t=3
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.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
7
9
4
-
2802
2802
[1
7
]
M
.
A
rro
y
o
a
n
d
A
.
J.
Co
n
e
jo
,
“
M
u
lt
ip
e
ri
o
d
a
u
c
ti
o
n
f
o
r
a
p
o
o
l
-
b
a
se
d
e
lec
tri
c
it
y
m
a
r
k
e
t,
”
IEE
E
T
ra
n
s.
Po
we
r
S
y
s
t.
,
v
o
l.
1
7
,
p
p
.
1
2
2
5
-
1
2
3
1
,
2
0
0
2
.
[1
8
]
J.
W
a
n
g
,
e
t
a
l.
,
“
De
m
a
n
d
-
sid
e
re
se
rv
e
o
ff
e
rs
in
jo
in
t
e
n
e
rg
y
/re
se
r
v
e
e
lec
tri
c
it
y
m
a
rk
e
ts,”
IEE
E
T
ra
n
s.
Po
we
r
S
y
st.
,
v
o
l.
1
8
,
p
p
.
1
3
0
0
-
1
3
0
6
,
2
0
0
3
.
[1
9
]
A
.
Bo
rg
h
e
tt
i,
e
t
a
l.
,
“
A
u
c
ti
o
n
s
w
it
h
e
x
p
li
c
it
d
e
m
a
n
d
sid
e
b
id
d
i
n
g
in
c
o
m
p
e
ti
ti
v
e
e
lec
tri
c
it
y
m
a
rk
e
ts,”
T
h
e
Ne
x
t
Ge
n
e
ra
ti
o
n
o
f
El
e
c
tric P
o
we
r Un
i
t
Co
mm
it
me
n
t
M
o
d
e
ls.
No
rwe
ll
,
M
A:
Klu
we
r
,
p
p
.
5
3
-
74
,
2
0
0
1
.
[2
0
]
O.
M
a
,
e
t
a
l
.
,
“
De
m
a
n
d
Re
sp
o
n
se
f
o
r
A
n
c
il
lar
y
S
e
rv
i
c
e
s,”
IEE
E
T
ra
n
s.
S
ma
rt
Gr
i
d
,
v
o
l
.
4
,
p
p
.
1
9
8
8
-
1
9
9
5
,
2
0
1
3
.
[2
1
]
U.
He
lma
n
,
e
t
a
l.
,
“
Op
e
ra
ti
o
n
a
l
re
q
u
irem
e
n
ts an
d
g
e
n
e
ra
ti
o
n
f
lee
t
c
a
p
a
b
il
it
y
a
t
2
0
%
R
P
S
,
”
CAI
S
O
,
2
0
1
0
.
A
v
a
il
a
b
le:
h
tt
p
:
//
ww
w
.
u
w
ig
.
o
rg
/
[2
2
]
G.
Laz
a
ro
s,
e
t
a
l.
,
“
T
h
e
ro
le
o
f
a
g
g
r
e
g
a
to
rs
in
sm
a
r
t
g
rid
d
e
m
a
n
d
re
sp
o
n
se
m
a
rk
e
ts
,”
IEE
E
J
o
u
r
n
a
l
o
n
S
e
lec
ted
Are
a
s in
C
o
mm
u
n
ic
a
ti
o
n
s
,
v
o
l
/i
ss
u
e
:
31
(
7
),
p
p
.
1
2
4
7
-
1
2
5
7
,
2
0
1
3
.
[2
3
]
T
h
e
G
URO
BI
M
a
n
u
a
l
,
2
0
1
7
.
A
v
a
il
a
b
le:
h
t
tp
s://
w
ww
.
g
u
ro
b
i.
c
o
m
/d
o
c
u
m
e
n
tatio
n
/7
.
5
/ref
m
a
n
/i
n
d
e
x
.
h
t
m
l.
[2
4
]
M
a
tp
o
w
e
r
Op
ti
m
a
l
S
c
h
e
d
u
li
n
g
T
o
o
l
(M
OST
)
p
a
c
k
a
g
e
,
2
0
1
7
.
A
v
a
il
a
b
le:
h
tt
p
:/
/www
.
p
se
rc
.
c
o
rn
e
ll
.
e
d
u
/
m
a
tp
o
w
e
r/
m
a
n
u
a
l.
p
d
f
[2
5
]
R.
Z
.
Mi
ñ
a
n
o
,
e
t
a
l
.
,
“
A
n
OPF
M
e
th
o
d
o
l
o
g
y
to
En
su
re
S
m
a
ll
-
S
ig
n
a
l
S
tab
il
it
y
,
”
IEE
E
T
ra
n
s.
Po
we
r
S
y
ste
m
,
v
o
l
/i
ss
u
e
:
26
(
3
)
,
2
0
1
1
.
[2
6
]
T
.
Da
i,
e
t
a
l.
,
“
Re
a
l
-
ti
m
e
Op
ti
m
a
l
P
a
rti
c
ip
a
ti
o
n
o
f
W
in
d
P
o
w
e
r
in
a
n
El
e
c
tri
c
it
y
M
a
rk
e
t,
”
IEE
E
In
n
o
v
a
t
ive
S
ma
rt
Gr
id
T
e
c
h
n
o
lo
g
ies
Co
n
f.
,
T
i
a
n
ji
n
,
Ch
in
a
,
2
0
1
2
.
[2
7
]
S
.
Ja
n
g
,
e
t
a
l.
,
“
A
n
e
w
n
e
tw
o
rk
p
a
rti
ti
o
n
m
e
th
o
d
u
sin
g
t
h
e
se
n
sit
iv
e
o
f
m
a
r
g
in
a
l
c
o
st
u
n
d
e
r
n
e
tw
o
rk
c
o
n
g
e
stio
n
,
”
IEE
E
P
o
we
r E
n
g
in
e
e
rin
g
S
o
c
iety
S
u
mm
e
r M
e
e
ti
n
g
,
2
0
0
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.