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20
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p
p
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p
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d
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m
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rm
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l,
win
d
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a
n
d
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p
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P
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to
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s we
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tes
ted
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lu
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p
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d
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lo
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d
e
two
o
th
e
r
tec
h
n
i
q
u
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s:
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c
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p
ti
m
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ti
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lg
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m
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d
t
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rm
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m
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th
sy
st
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m
s
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p
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ll
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2
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se
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a
c
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ted
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s.
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ro
m
t
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lt
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m
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th
o
d
wa
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b
le
t
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c
h
iev
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r
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p
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a
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ll
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c
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m
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d
a
s
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ffe
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ti
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ti
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iza
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o
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d
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re
ss
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n
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rtain
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o
c
iate
d
with
so
lar ra
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a
n
d
win
d
s
p
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d
.
K
ey
w
o
r
d
s
:
E
lk
h
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d
o
p
tim
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Hy
d
r
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p
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lan
t
So
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la
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h
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al
p
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lan
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W
in
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p
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p
lan
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h
is i
s
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c
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a
rticle
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n
d
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CC B
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SA
li
c
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se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Hu
n
g
Du
c
Ng
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Dep
ar
tm
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t o
f
Po
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Deliv
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y
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o
f
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d
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l
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n
ics E
n
g
in
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r
in
g
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C
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C
ity
Un
iv
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s
ity
o
f
T
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h
n
o
lo
g
y
(
HC
MU
T
)
2
6
8
L
y
T
h
u
o
n
g
Kiet
Stre
et,
Dien
Ho
n
g
W
ar
d
,
Ho
C
h
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in
h
C
ity
,
Vietn
am
E
m
ail:
h
u
n
g
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d
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h
cm
u
t.e
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v
n
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CL
A
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a
d
,
a
p
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d
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m
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max
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
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E
n
g
I
SS
N:
2252
-
8
7
9
2
E
lk
h
erd
o
p
timiz
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r
co
s
t
-
eff
icien
t h
yb
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y
s
ystems
u
n
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er ren
ewa
b
le
u
n
ce
r
ta
in
ty
(
L
y
Hu
u
P
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a
m
)
431
1.
I
NT
RO
D
UCT
I
O
N
In
c
o
n
tem
p
o
r
ar
y
p
o
wer
s
y
s
t
em
s
,
ef
f
ec
tiv
ely
d
is
p
atch
in
g
av
ailab
le
p
o
wer
r
eso
u
r
ce
s
to
m
ee
t
t
h
e
in
cr
ea
s
in
g
d
em
a
n
d
is
cr
u
cia
l
f
o
r
im
p
r
o
v
in
g
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o
n
o
m
ic
e
f
f
icien
cy
.
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d
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g
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o
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a
g
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ea
t
o
p
p
o
r
tu
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ity
f
o
r
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teg
r
atio
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with
th
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m
al
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o
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p
lan
ts
(
T
PP
s
)
.
B
y
u
tili
zin
g
h
y
d
r
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e
n
er
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ca
n
ac
h
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n
er
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d
m
o
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en
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ess
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im
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ee
d
s
lik
e
f
lo
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co
n
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o
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d
ir
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ig
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.
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h
er
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r
e,
ef
f
ec
tiv
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en
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ed
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al
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tem
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lay
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o
le
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en
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e
e
f
f
icien
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o
f
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tr
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p
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tili
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s
y
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tem
s
.
Giv
en
th
e
n
o
n
-
o
p
er
atio
n
al
co
s
ts
ass
o
ciate
d
with
h
y
d
r
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p
o
wer
p
lan
ts
(
HPPs
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,
th
e
f
o
cu
s
s
h
if
t
s
to
o
p
tim
izin
g
t
h
e
f
u
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s
ts
f
o
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PP
s
[
1
]
.
T
h
e
h
y
d
r
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-
th
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m
al
s
ch
e
d
u
lin
g
(
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T
S)
p
r
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as
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ee
n
a
f
o
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s
o
f
r
esear
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f
o
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m
an
y
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ec
ad
es,
lead
in
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to
th
e
d
ev
elo
p
m
e
n
t
o
f
v
ar
i
o
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s
ef
f
ec
t
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e
tech
n
iq
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HT
S
p
r
o
b
lem
s
ar
e
co
n
s
id
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as
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g
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ter
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a
n
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s
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r
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ter
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HT
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p
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s
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ased
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n
th
e
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ch
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]
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r
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t
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ter
m
HT
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ch
ed
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SHTS)
p
r
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lem
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a
v
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o
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class
ical
tech
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iq
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ca
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f
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tiv
ely
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h
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itio
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d
in
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m
eth
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s
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a
n
d
New
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n
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s
m
eth
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Ho
wev
e
r
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ese
m
eth
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d
s
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ac
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u
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x
p
r
o
b
lem
an
d
m
u
ltip
le
co
n
s
tr
ain
ts
,
th
ey
also
o
p
en
th
e
d
o
o
r
to
n
ew
p
o
s
s
ib
ilit
ies
an
d
in
n
o
v
ativ
e
s
o
lu
tio
n
s
.
T
h
e
e
m
er
g
en
ce
o
f
m
eta
-
h
eu
r
is
tic
m
eth
o
d
s
h
ig
h
lig
h
ts
th
e
p
o
ten
tial
o
f
tech
n
o
lo
g
y
-
d
r
i
v
en
ap
p
r
o
ac
h
es
to
tack
le
th
e
c
h
allen
g
es
p
r
esen
t
in
r
ea
l
-
wo
r
ld
p
r
o
b
lem
s
.
T
h
ese
m
eth
o
d
s
wer
e
e
f
f
icien
t
m
eth
o
d
(
E
M)
[
3
]
,
g
en
etic
alg
o
r
ith
m
(
GA)
an
d
m
o
d
if
ied
GA
(
MG
A)
[
4
]
,
c
u
ck
o
o
s
ea
r
ch
alg
o
r
ith
m
(
C
SA)
[
5
]
,
s
elf
-
a
d
ap
tiv
e
GA
[
6
]
,
b
ac
k
tr
ac
k
in
g
s
ea
r
ch
(
B
A)
[
7
]
,
s
lim
e
m
o
u
ld
alg
o
r
ith
m
(
SMA)
[
8
],
clu
s
ter
ed
ad
a
p
tiv
e
t
ea
ch
in
g
-
lear
n
in
g
-
b
ased
o
p
tim
izatio
n
(
C
AT
L
B
O)
alg
o
r
ith
m
[
9
]
,
h
y
b
r
id
b
at
alg
o
r
ith
m
with
an
ar
tific
ial
b
ee
co
lo
n
y
(
B
A
-
AB
C
)
[
1
0
]
,
n
o
n
-
d
o
m
in
ated
s
o
r
tin
g
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
NSPS
O)
[
1
1
]
,
im
p
r
o
v
ed
teac
h
in
g
-
lear
n
in
g
-
b
ased
o
p
tim
iz
atio
n
(
I
T
B
L
O)
[
1
2
]
an
d
a
n
o
n
-
d
o
m
in
ated
s
o
r
tin
g
d
is
r
u
p
tio
n
-
b
ased
o
p
p
o
s
itio
n
al
g
r
av
itatio
n
al
s
ea
r
c
h
alg
o
r
ith
m
(
NSDOGSA)
[
1
3
]
.
Am
o
n
g
m
eth
o
d
s
,
NSDOGSA
was
s
u
g
g
ested
b
y
Nad
ak
u
d
it
i
et
a
l
.
[
1
3
]
in
2
0
2
3
.
T
h
is
m
eth
o
d
r
e
p
r
esen
ts
a
s
ig
n
if
ican
t
ad
v
a
n
ce
m
en
t
in
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
p
a
r
ticu
lar
ly
f
o
r
c
o
m
p
le
x
m
u
lti
-
o
b
j
ec
tiv
e
p
r
o
b
lem
s
in
en
er
g
y
s
ch
ed
u
lin
g
.
I
ts
co
m
b
in
atio
n
o
f
n
o
n
d
o
m
in
ated
s
o
r
tin
g
,
o
p
p
o
s
itio
n
al
lear
n
i
n
g
,
an
d
d
i
s
r
u
p
tio
n
s
tr
ateg
ies
m
ak
es
it
a
p
o
we
r
f
u
l
to
o
l
f
o
r
r
esear
ch
er
s
an
d
p
r
ac
titi
o
n
er
s
in
th
e
f
ield
.
I
n
g
en
e
r
al,
th
e
m
en
t
io
n
ed
s
tu
d
ies
f
o
cu
s
o
n
d
ea
lin
g
with
th
e
f
u
el
co
s
t a
n
d
n
o
t
co
n
s
id
er
in
g
th
e
h
ea
t a
n
d
em
is
s
io
n
g
en
er
atio
n
o
f
T
PP
s
[
1
4
]
,
[
1
5
]
.
W
in
d
an
d
s
o
lar
p
o
wer
ar
e
cl
ea
n
en
er
g
y
s
o
u
r
ce
s
th
at
o
f
f
e
r
a
p
r
o
m
is
in
g
s
o
lu
tio
n
to
m
e
et
en
er
g
y
d
em
an
d
s
in
a
co
s
t
-
ef
f
ec
tiv
e
m
an
n
er
wh
ile
g
en
er
atin
g
n
o
h
ar
m
f
u
l
em
is
s
io
n
s
.
Giv
en
th
ese
s
ig
n
if
ican
t
b
en
ef
its
,
m
an
y
r
esear
ch
er
s
ar
e
ac
tiv
ely
ex
p
lo
r
in
g
th
e
ch
allen
g
es o
f
i
n
teg
r
atin
g
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
lik
e
win
d
a
n
d
s
o
lar
with
tr
ad
itio
n
al
p
o
wer
p
lan
ts
[
1
6
]
.
Dam
o
d
ar
a
n
an
d
K
u
m
ar
[
1
7
]
d
escr
ib
ed
f
o
u
r
m
et
h
o
d
s
,
in
clu
d
in
g
GA,
PS
O,
h
ar
m
o
n
y
s
ea
r
ch
(
HS)
,
a
n
d
J
AYA
alg
o
r
ith
m
s
ar
e
ap
p
l
ied
f
o
r
s
ea
r
ch
in
g
s
o
lu
tio
n
to
h
y
d
r
o
-
th
er
m
al
-
win
d
g
en
er
atio
n
s
ch
ed
u
lin
g
(
HT
W
GS)
co
n
s
id
er
in
g
ec
o
n
o
m
ic
an
d
em
is
s
io
n
f
ac
to
r
s
.
Similar
to
s
tu
d
y
in
[
1
7
]
,
Ph
am
et
a
l
.
[
1
8
]
h
av
e
in
te
g
r
ated
wi
n
d
en
er
g
y
in
to
tr
a
d
itio
n
al
h
y
d
r
o
th
er
m
al
p
o
wer
s
y
s
tem
to
m
in
im
ize
th
e
co
s
t
o
f
T
PP
s
b
y
th
e
u
s
e
o
f
im
p
r
o
v
ed
C
SA
(
I
C
SA)
.
T
h
e
a
u
th
o
r
s
of
[
1
9
]
-
[
2
2
]
h
a
v
e
co
n
s
id
er
e
d
win
d
an
d
s
o
lar
en
er
g
ies
as
alter
n
ativ
e
s
o
u
r
ce
s
to
r
ed
u
c
e
f
u
el
co
s
ts
f
r
o
m
T
PP
s
.
I
n
th
e
s
e
s
tu
d
ies,
th
e
u
n
ce
r
tain
ty
an
d
ce
r
tain
ty
o
f
win
d
s
p
ee
d
an
d
s
o
lar
ir
r
ad
iatio
n
ar
e
in
v
esti
g
ated
.
Fo
r
th
e
ce
r
tain
ty
ca
s
e,
th
e
p
o
wer
o
u
tp
u
t
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
ca
n
b
e
ca
lcu
lated
as
[
2
2
]
.
Fo
r
a
n
o
th
er
,
win
d
s
p
ee
d
an
d
s
o
lar
ir
r
ad
iatio
n
ar
e
m
o
d
eled
b
y
u
s
in
g
p
r
o
b
a
b
ilit
y
d
e
n
s
ity
f
u
n
ctio
n
s
(
PDF)
s
u
ch
as
W
eib
u
ll,
B
eta,
a
n
d
L
o
g
n
o
r
m
al
o
n
es.
I
n
th
e
a
b
o
v
e
s
tu
d
ies,
d
ata
o
n
r
en
ewa
b
le
en
er
g
y
r
eso
u
r
ce
s
wer
e
cited
b
y
p
r
ev
i
o
u
s
r
esea
r
ch
an
d
n
o
t
c
h
o
s
en
f
r
o
m
s
p
ec
if
ic
lo
ca
tio
n
s
f
o
r
in
s
tallin
g
p
lan
ts
.
I
n
ad
d
itio
n
,
ac
co
r
d
in
g
to
t
h
e
No
Fre
e
L
u
n
ch
th
eo
r
em
,
n
o
s
in
g
le
o
p
tim
izatio
n
ap
p
r
o
ac
h
is
o
p
tim
al
f
o
r
ev
er
y
p
o
ten
tial
is
s
u
e.
C
lear
ly
,
th
ese
ar
e
th
e
o
p
p
o
r
tu
n
ities
f
o
r
r
esear
ch
e
r
s
to
co
n
tin
u
e
th
e
d
ee
p
ex
p
lo
r
atio
n
.
In
th
e
p
ap
er
,
th
e
HT
S
p
r
o
b
l
em
with
th
e
ex
is
ten
ce
o
f
wi
n
d
an
d
s
o
lar
en
er
g
ies,
ca
lled
W
SHT
S
p
r
o
b
lem
,
will
b
e
s
o
lv
ed
,
tak
i
n
g
u
n
ce
r
tain
co
s
ts
lik
e
d
ir
ec
t,
p
en
alty
,
an
d
r
eser
v
e
co
s
ts
in
to
ac
co
u
n
t
b
y
th
e
ap
p
licatio
n
o
f
elk
h
er
d
o
p
tim
i
ze
r
(
E
HO)
[
2
3
]
.
I
n
ad
d
itio
n
t
o
E
HO,
th
e
co
o
t
o
p
tim
izatio
n
alg
o
r
ith
m
(
C
OOT
)
p
r
o
p
o
s
ed
b
y
Qin
et
a
l
.
[
2
4
]
i
n
2
0
2
2
a
n
d
tu
n
icate
s
war
m
alg
o
r
ith
m
(
T
SA)
p
r
o
p
o
s
ed
b
y
Kau
r
et
a
l
.
[
2
5
]
in
2
0
2
0
ar
e
ap
p
lied
to
g
et
r
esu
lts
f
o
r
c
o
m
p
ar
is
o
n
.
He
r
e
ar
e
s
o
m
e
c
o
n
tr
ib
u
tio
n
s
:
i)
I
t
f
o
r
m
u
lat
es
a
r
o
b
u
s
t
o
p
ti
m
a
l
s
c
h
ed
u
l
in
g
p
r
o
b
l
em
s
p
ec
i
f
i
ca
lly
d
es
ig
n
ed
f
o
r
a
n
ew
c
o
m
p
l
ex
i
n
t
e
g
r
ati
o
n
s
tr
u
ct
u
r
e
t
h
at
i
n
c
o
r
p
o
r
a
tes
f
o
u
r
d
is
ti
n
c
t t
y
p
es
o
f
p
o
we
r
p
l
an
ts
.
ii)
I
t
i
d
en
ti
f
ies
a
n
d
s
el
ec
ts
s
u
it
ab
l
e
d
e
cisi
o
n
v
a
r
i
ab
les
t
ail
o
r
ed
f
o
r
t
h
e
m
e
th
o
d
o
l
o
g
ies
e
m
p
lo
y
ed
i
n
t
h
e
an
al
y
s
is
.
iii)
I
t
c
o
n
d
u
c
ts
a
t
h
o
r
o
u
g
h
e
v
a
lu
ati
o
n
o
f
th
e
p
er
f
o
r
m
a
n
ce
o
f
E
HO
,
C
O
OT
,
a
n
d
T
SA,
p
r
o
v
i
d
i
n
g
v
a
lu
a
b
le
in
s
i
g
h
ts
i
n
t
o
t
h
ei
r
ef
f
e
cti
v
e
n
es
s
.
iv
)
I
t
t
h
o
u
g
h
t
f
u
ll
y
co
n
s
i
d
er
s
t
h
e
u
n
c
er
tai
n
ti
es
ass
o
ci
at
ed
wi
th
s
o
lar
r
a
d
i
ati
o
n
,
t
h
e
r
e
b
y
im
p
r
o
v
i
n
g
th
e
r
eli
ab
ilit
y
o
f
t
h
e
s
c
h
ed
u
l
in
g
s
o
lu
ti
o
n
s
.
T
h
e
r
est
o
f
th
e
p
ap
er
is
co
n
s
tr
u
cted
as
f
o
ll
o
ws:
S
ec
tio
n
2
s
h
o
ws
p
r
o
b
lem
f
o
r
m
u
latio
n
.
S
ec
tio
n
3
p
r
esen
ts
th
e
s
tr
u
ctu
r
e
o
f
th
e
ap
p
lied
m
eth
o
d
.
S
ec
tio
n
4
d
i
s
cu
s
s
es
an
d
an
aly
ze
s
th
e
r
esu
lts
o
b
tain
ed
b
y
th
e
m
eth
o
d
s
.
Fin
ally
,
s
ec
tio
n
5
g
i
v
es a
co
n
clu
s
io
n
a
n
d
f
u
tu
r
e
r
e
s
ea
r
ch
.
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.
15
,
No
.
1
,
Ma
r
ch
20
26
:
430
-
4
3
9
432
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
2
.
1
.
T
he
o
bje
ct
iv
e
f
un
ct
io
n
T
o
s
u
p
p
ly
elec
tr
icity
to
u
r
b
a
n
co
n
s
u
m
er
s
,
c
o
m
m
er
cial
ce
n
ter
s
,
an
d
in
d
u
s
tr
ial
zo
n
es,
a
win
d
-
s
o
lar
-
h
y
d
r
o
th
er
m
al
p
o
wer
s
y
s
tem
is
d
esig
n
ed
.
T
h
is
s
y
s
tem
in
clu
d
es
T
PP
s
,
h
y
d
r
o
elec
tr
ic
p
o
wer
p
lan
ts
(
HPPs
)
,
win
d
p
o
wer
p
la
n
ts
(
W
PP
s
)
,
an
d
s
o
lar
p
o
wer
p
lan
ts
(
SP
Ps
)
,
all
s
ch
ed
u
led
f
o
r
o
p
tim
izatio
n
d
u
r
i
n
g
s
p
ec
if
ic
p
er
io
d
s
.
Sin
ce
h
y
d
r
o
p
o
wer
p
lan
ts
h
av
e
ze
r
o
f
u
el
co
s
ts
,
th
e
m
ain
g
o
al
is
to
m
in
im
ize
th
e
co
s
ts
(
F
C
)
o
f
T
PP
s
,
W
PP
s
,
an
d
SP
Ps
.
T
h
e
o
b
jectiv
e
is
in
d
icate
d
in
(
1
)
.
=
∑
{
(
)
+
(
)
+
(
)
}
2
4
=
1
(
1
)
W
h
er
e,
(
)
,
(
)
,
an
d
(
)
ar
e
th
e
co
s
ts
o
f
N
t
th
er
m
al
p
o
wer
p
lan
ts
,
N
w
win
d
p
o
wer
p
la
n
ts
,
an
d
N
s
s
o
la
r
p
o
wer
p
lan
ts
.
T
h
e
f
u
el
c
o
s
t f
u
n
ctio
n
f
o
r
th
e
t
th
T
PP
is
r
ep
r
esen
ted
o
v
er
2
4
in
ter
v
als as
(
2
)
.
(
)
=
∑
(
a
t
+
b
t
+
c
(
)
2
+
|
d
×
s
in
(
e
×
(
,
-
)
)
|
)
t
=1
(
2
)
T
h
e
to
tal
o
p
e
r
atin
g
co
s
t
o
f
a
WPP
in
clu
d
es
th
r
ee
c
o
m
p
o
n
en
ts
:
d
ir
ec
t
co
s
t
(
C
dwpp
)
,
p
en
a
lty
co
s
t
(
C
pwpp
)
f
o
r
u
n
d
er
esti
m
atin
g
p
o
wer
p
r
o
d
u
ctio
n
(
wh
en
p
lan
n
ed
p
o
wer
is
less
th
an
ac
tu
al
o
u
tp
u
t)
,
an
d
r
eser
v
e
co
s
t
(
C
rwpp
)
f
o
r
o
v
er
esti
m
atin
g
p
r
o
d
u
ctio
n
(
wh
en
p
lan
n
ed
p
o
wer
ex
c
ee
d
s
ac
tu
al
o
u
tp
u
t)
as g
iv
en
by
(
3
)
[
2
6
]
.
(
)
=
∑
(
C
+
C
+
C
)
=
1
(
3
)
C
=
a
d
.
P
w
;
C
=
a
.
∫
(
p
-
P
w
)
.
f
w
(
)
.
dp
P
P
w
;
C
=
a
.
∫
(
P
w
-
p
)
.
f
w
(
)
.
dp
P
w
0
(
4
)
I
n
(
4
)
,
P
is
th
e
r
ated
p
o
wer
o
u
tp
u
t
o
f
t
h
e
w
th
WPP
;
f
w
(
)
in
d
icate
s
th
e
p
r
o
b
a
b
ilit
y
d
e
n
s
ity
f
u
n
ctio
n
.
Similar
to
WPP
,
th
e
to
tal
o
p
er
atin
g
co
s
t o
f
SP
P
is
p
r
esen
ted
u
n
d
er
d
i
r
ec
t c
o
s
t (
C
dspp
)
,
p
en
alty
co
s
t (
C
pwpp
)
,
an
d
r
eser
v
e
co
s
t (
C
rwpp
)
as sh
o
wn
in
(
5
)
.
(
)
=
∑
(
+
+
)
=
1
(
5
)
C
=
d
.
P
;
C
=
.
∫
(
p
-
P
)
.
f
(
)
.
d
p
P
P
;
C
=
.
∫
(
P
-
p
)
.
f
(
)
.
d
p
P
0
(
6
)
I
n
(
6
)
,
P
is
th
e
r
ated
p
o
wer
o
u
tp
u
t o
f
th
e
s
th
S
P
P
;
f
s
(
)
in
d
icate
s
th
e
p
r
o
b
a
b
ilit
y
d
en
s
ity
f
u
n
ctio
n
.
2
.
2
.
T
he
co
ns
t
ra
ints
Po
wer
s
y
s
tem
b
alan
ce
co
n
s
tr
ain
t:
Po
wer
g
en
er
ated
b
y
p
lan
ts
m
u
s
t
m
atch
lo
ad
d
e
m
an
d
(
P
d
)
p
lu
s
tr
an
s
m
is
s
io
n
lin
e
lo
s
s
es (
P
l
)
,
as st
ated
in
(
7
)
[
2
1
]
.
∑
,
+
=
1
∑
ℎ
,
ℎ
ℎ
=
1
+
∑
,
=
1
+
∑
,
=
1
−
,
−
,
=
0
;
=
1
,
…
,
24
(
7
)
W
h
er
e
,
P
t
,
P
h
,
P
w
,
an
d
P
s
ar
e
p
o
wer
o
u
t
p
u
ts
o
f
th
e
tth
th
er
m
al
p
o
wer
p
lan
t,
t
h
e
h
th
h
y
d
r
o
elec
tr
ic
p
o
we
r
p
lan
ts
,
th
e
w
th
win
d
p
o
wer
p
la
n
t
,
an
d
t
h
e
s
th
s
o
lar
p
o
wer
p
la
n
t,
r
esp
ec
tiv
ely
.
Dis
ch
ar
g
e
co
n
s
tr
ain
t:
T
h
e
w
ater
d
is
ch
ar
g
e
o
f
th
e
h
t
h
HP
P
(
wQ
h
)
th
r
o
u
g
h
tu
r
b
in
es
u
s
ed
f
o
r
elec
tr
icity
g
en
er
atio
n
is
lim
ited
to
s
p
ec
if
ic
p
ar
am
eter
s
(
i
.
e
.
,
lo
wer
wate
r
d
is
ch
ar
g
e
(
wQ
h,
m
in
)
an
d
u
p
p
e
r
wate
r
d
is
ch
ar
g
e
(
wQ
h,
max
)
)
as
(
8
)
.
w
Q
h
,
mi
n
≤
w
Q
h
≤
w
Q
h,
max
(
8
)
W
h
er
e,
wQ
h
in
d
icate
s
a
q
u
ad
r
atic
f
u
n
ctio
n
as d
e
f
in
ed
b
y
(
9
)
.
w
Q
h
=
h
+
h
h
+
h
P
h
2
(
9
)
W
ater
av
ailab
ilit
y
co
n
s
tr
ain
t
:
T
h
e
to
tal
wate
r
d
is
ch
ar
g
e
ac
r
o
s
s
th
e
2
4
in
ter
v
als
m
u
s
t
b
e
p
r
ec
is
ely
m
atch
ed
to
th
e
av
ailab
le
am
o
u
n
t (
WV
h,
av
)
as sp
ec
if
ied
b
y
(
1
0
)
.
∑
w
Q
h,
p
24
=
1
=
WV
h,
av
ai
;
p
=1
,
…,
2
4
(
1
0
)
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
E
lk
h
erd
o
p
timiz
er fo
r
co
s
t
-
eff
icien
t h
yb
r
id
en
erg
y
s
ystems
u
n
d
er ren
ewa
b
le
u
n
ce
r
ta
in
ty
(
L
y
Hu
u
P
h
a
m
)
433
Po
wer
g
en
er
atio
n
lim
its
:
Po
wer
g
en
er
atio
n
f
r
o
m
TPP
s
,
HP
P
s
,
WPP
s
,
an
d
S
P
P
s
m
u
s
t
ad
h
er
e
s
tr
ictly
to
th
eir
estab
lis
h
ed
ca
p
ac
ity
lim
its
.
,
≤
≤
,
;
ℎ
,
≤
ℎ
≤
ℎ
,
(
1
1
)
,
≤
≤
,
;
,
≤
≤
,
(
1
2
)
2
.
3
.
So
la
r
un
ce
rt
a
inties m
o
delin
g
T
o
ef
f
ec
tiv
ely
ass
ess
th
e
u
n
ce
r
tain
ty
o
f
s
o
lar
ir
r
ad
ian
ce
,
it
is
ad
v
is
ab
le
to
u
tili
ze
a
lo
g
n
o
r
m
al
p
r
o
b
a
b
ilit
y
d
is
tr
ib
u
tio
n
(
PDF)
as sh
o
wn
in
(
1
3
)
.
P
DF
(
A
)
=
(
1
A
.
.
√
(
2.
π
)
)
×
exp
.
[
-
(
ln
(
A
)
-
)
2
2.
2
]
w
ith
A
> 0
(1
3)
W
h
er
e,
an
d
ar
e
th
e
s
ca
le
an
d
lo
ca
tio
n
p
a
r
am
eter
s
.
W
h
en
s
o
lar
ir
r
ad
ian
ce
is
a
k
n
o
w
n
f
ac
to
r
,
we
ca
n
d
eter
m
in
e
th
e
p
o
wer
o
u
tp
u
t
o
f
S
P
P
b
y
a
p
p
ly
in
g
th
e
p
r
i
n
cip
les
o
f
en
e
r
g
y
c
o
n
s
er
v
ati
o
n
r
elate
d
t
o
s
o
lar
r
ad
iatio
n
as
in
(
1
4
)
.
P
(
A
)
=
{
P
×
A
2
A
s
td
+
R
c
if
0<
A
<
R
c
P
×
A
A
s
td
if
A
>
R
c
(
1
4
)
In
(
1
4
)
,
R
c
i
s
r
a
d
iatio
n
in
ten
s
it
y
in
W
/m
2
.
2
.
4
.
Wind
un
ce
rt
a
inties m
o
delin
g
T
o
ef
f
ec
tiv
ely
ass
ess
th
e
u
n
c
er
tain
ty
o
f
win
d
s
p
ee
d
,
it
is
a
d
v
is
ab
le
to
u
tili
ze
a
W
eib
u
ll
p
r
o
b
a
b
ilit
y
d
is
tr
ib
u
tio
n
(
PDF)
as sh
o
wn
i
n
(
1
6
)
.
PDF
(
V
w
)
=
(
k
w
c
w
)
×
(
V
w
c
w
)
k
w
-
1
×
ex
p
[
-
(
V
w
c
w
)
k
w
]
,
V
w
> 0
(
1
5
)
W
h
en
win
d
s
p
ee
d
is
a
k
n
o
wn
f
ac
to
r
,
we
ca
n
d
eter
m
in
e
t
h
e
p
o
wer
o
u
tp
u
t o
f
WPP
b
y
a
p
p
ly
i
n
g
(
1
6
)
.
P
w
=
{
0
,
(
V
w
<
V
w
,
c
i
,
V
w
>
V
w
,
c
o
)
P
wr
×
(
V
w
-
V
w
,
c
i
)
(
V
wr
-
V
w
,
c
i
)
,
(
V
w
,
c
i
≤
V
w
≤
V
wr
)
P
w
i,
r
,
(
V
wr
≤
V
w
≤
V
w
,
c
o
)
(
1
6
)
I
n
(
1
6
)
,
V
w,
V
wr,
V
w,
ci,
an
d
V
w
,
co
d
e
n
o
te
win
d
s
p
ee
d
,
r
ated
win
d
s
p
ee
d
,
c
u
t
-
in
win
d
s
p
ee
d
,
an
d
cu
t
-
o
u
t
win
d
s
p
ee
d
o
f
th
e
wth
WPP
.
3.
M
E
T
H
O
D
T
h
e
elk
h
er
d
o
p
tim
izer
(
E
HO
)
[
2
3
]
is
an
ad
v
a
n
ce
d
m
etah
e
u
r
is
tic
alg
o
r
ith
m
th
at
d
r
aws
i
n
s
p
ir
atio
n
f
r
o
m
th
e
n
atu
r
al
b
e
h
av
io
r
s
e
x
h
ib
ited
b
y
elk
h
e
r
d
s
,
p
ar
tic
u
lar
ly
d
u
r
in
g
th
e
c
r
itical
p
er
i
o
d
s
o
f
r
u
ttin
g
an
d
ca
lv
in
g
.
T
h
e
p
r
o
ce
s
s
o
f
E
HO
b
eg
in
s
with
th
e
in
itializatio
n
o
f
th
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p
o
p
u
latio
n
a
n
d
t
h
e
estab
lis
h
m
en
t
o
f
p
r
o
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lem
p
ar
a
m
eter
s
.
I
t
th
en
p
r
o
g
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ess
es
in
to
t
h
e
r
u
ttin
g
s
ea
s
o
n
,
wh
er
e
th
e
p
o
p
u
latio
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is
o
r
g
an
ized
in
to
f
am
ilies
led
b
y
th
e
s
tr
o
n
g
est
b
u
lls
.
I
n
th
e
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lv
in
g
s
ea
s
o
n
,
th
ese
f
am
ilies
g
en
er
ate
n
ew
s
o
l
u
tio
n
s
b
ased
o
n
th
e
ch
ar
ac
ter
is
tics
o
f
ea
c
h
b
u
ll
a
n
d
its
h
ar
em
s
.
F
i
n
a
l
l
y
,
d
u
r
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n
g
t
h
e
s
e
l
e
c
ti
o
n
s
e
a
s
o
n
,
a
l
l
s
o
l
u
t
i
o
n
s
a
r
e
a
s
s
es
s
e
d
,
a
n
d
o
n
l
y
t
h
e
f
i
t
t
e
s
t
i
n
d
i
v
i
d
u
a
ls
a
r
e
c
h
o
s
e
n
t
o
f
o
r
m
t
h
e
n
e
x
t
g
e
n
e
r
a
t
i
o
n
.
T
h
e
d
e
t
a
i
l
e
d
s
t
e
p
s
o
f
t
h
e
E
H
O
a
r
e
p
r
e
s
e
n
t
e
d
a
s
f
o
l
l
o
ws
:
−
I
n
itializatio
n
:
Similar
to
m
et
ah
eu
r
is
tic
m
eth
o
d
s
,
t
h
e
p
o
p
u
latio
n
(
)
o
f
E
HO
is
g
e
n
er
ate
d
r
an
d
o
m
ly
with
in
estab
lis
h
ed
p
ar
am
eter
s
,
en
s
u
r
in
g
v
ar
iab
ilit
y
wh
ile
m
ain
tain
in
g
co
n
tr
o
l
with
in
d
ef
in
ed
lim
its
(
an
d
)
as sh
o
wn
in
(
1
8
)
.
=
+
×
(
−
)
,
d
=1,2
…
(
1
8
)
Af
ter
th
e
in
itializatio
n
,
th
e
f
itn
ess
f
(
x
d
)
o
f
s
o
lu
tio
n
s
will
b
e
ca
lcu
lated
a
n
d
s
o
r
ted
t
o
f
in
d
th
e
to
p
b
est
s
o
lu
tio
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.
15
,
No
.
1
,
Ma
r
ch
20
26
:
430
-
4
3
9
434
−
R
u
ttin
g
p
h
ase:
T
h
e
p
o
p
u
latio
n
is
d
iv
id
ed
in
to
d
if
f
er
e
n
t
f
am
ilies
b
ased
o
n
th
e
n
u
m
b
er
o
f
b
u
lls
(
Nb
)
.
E
ac
h
f
am
ily
h
as
o
n
e
b
u
ll
a
n
d
m
an
y
h
ar
em
s
,
i
n
wh
ich
th
e
h
ar
em
s
ar
e
ass
ig
n
ed
b
y
ap
p
ly
in
g
th
e
r
o
u
lette
-
wh
ee
l
s
elec
tio
n
as g
iv
en
in
(
1
9
)
.
=
(
)
∑
(
)
;
=
1
,
2
…
,
(
1
9
)
−
C
alv
in
g
p
h
ase:
New
s
o
lu
tio
n
s
ca
lled
ca
lv
es
ar
e
g
en
er
ated
b
ased
o
n
th
e
g
en
etics
o
f
th
e
f
ath
er
b
u
ll
o
r
m
o
th
er
h
a
r
em
.
I
f
th
e
ca
lf
h
as
g
en
etic
tr
aits
f
r
o
m
th
e
f
at
h
er
b
u
ll
(
i
.
e
.
,
th
e
i
n
d
ex
o
f
th
e
ca
lf
is
th
e
in
d
ex
o
f
th
e
f
ath
er
)
,
th
e
g
e
n
er
atio
n
is
cr
ea
ted
b
y
(
2
0
)
.
Oth
er
wis
e,
(
2
1
)
is
ap
p
lied
.
=
+
×
(
−
)
,
d
=1,2
…
(
2
0
)
=
ℎ
+
×
(
−
ℎ
)
+
×
(
,
−
ℎ
)
,
d
=1
,
2
…
(
2
1
)
I
n
(
2
0
)
an
d
(
2
1
)
,
is
a
s
o
lu
tio
n
s
elec
ted
f
r
o
m
th
e
p
o
p
u
latio
n
;
,
is
a
s
o
lu
tio
n
s
elec
ted
f
r
o
m
b
u
l
ls
.
−
Selectio
n
p
h
ase:
I
n
th
is
p
h
ase
,
n
ew
s
o
lu
tio
n
s
in
th
e
ca
lv
in
g
p
h
ase
ar
e
co
m
b
i
n
ed
to
th
e
o
ld
s
o
lu
tio
n
s
to
f
o
r
m
a
n
ew
g
r
o
u
p
with
2
.
Np
z.
T
h
e
f
itn
ess
o
f
ea
ch
s
o
lu
tio
n
in
th
e
n
ew
g
r
o
u
p
is
ca
lcu
lated
an
d
s
o
r
ted
.
Fro
m
th
e
r
an
k
e
d
s
o
lu
tio
n
s
in
th
e
n
ew
g
r
o
u
p
,
th
e
b
est
s
o
lu
tio
n
g
r
o
u
p
with
Np
z
is
s
elec
t
ed
f
o
r
th
e
n
e
x
t
iter
atio
n
.
Fo
r
s
o
lv
in
g
th
e
W
SHTS
p
r
o
b
lem
,
th
e
f
itn
ess
f
u
n
ctio
n
o
f
s
o
lu
tio
n
s
,
wh
ich
ar
e
in
itialized
o
r
u
p
d
ated
b
y
th
e
m
eth
o
d
,
is
f
ir
s
t
estab
lis
h
ed
.
T
h
en
,
th
e
s
o
lu
tio
n
s
-
d
eter
m
in
i
n
g
m
e
ch
an
i
s
m
o
f
E
HO
is
im
p
lem
en
ted
b
y
u
s
in
g
(
1
8
)
‒
(
2
1
)
.
T
h
is
cy
cle
co
n
tin
u
es
u
n
til
th
e
alg
o
r
ith
m
co
n
v
er
g
es
o
r
r
ea
ch
es
th
e
p
r
ed
eter
m
in
e
d
iter
atio
n
lim
it.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
s
tu
d
y
em
p
lo
y
s
E
HO
,
C
O
OT
,
an
d
T
SA
m
eth
o
d
s
to
ad
d
r
ess
th
e
o
p
tim
al
g
en
er
atio
n
p
r
o
b
lem
f
o
r
a
h
y
b
r
id
p
o
we
r
s
y
s
tem
.
T
o
f
in
d
th
e
id
ea
l
p
ar
am
eter
s
f
o
r
th
e
p
r
o
b
lem
,
two
test
s
y
s
tem
s
wer
e
u
s
ed
.
Sy
s
tem
1
in
clu
d
es
h
y
d
r
o
an
d
th
er
m
al
p
o
wer
p
lan
ts
,
an
d
Sy
s
tem
2
co
n
s
is
ts
o
f
h
y
d
r
o
p
o
wer
,
th
er
m
al
e
n
er
g
y
,
s
o
lar
p
o
wer
,
an
d
win
d
p
o
wer
p
lan
ts
.
T
h
e
an
aly
s
is
s
p
an
s
a
2
4
-
h
o
u
r
p
er
io
d
d
i
v
id
ed
i
n
to
twen
ty
-
f
o
u
r
in
ter
v
als
.
T
h
ese
alg
o
r
ith
m
s
ar
e
p
r
o
g
r
a
m
m
ed
b
y
MA
T
L
AB
s
o
f
twar
e
with
v
er
s
io
n
2
0
1
9
,
a
n
d
ex
ec
u
ted
o
n
a
co
m
p
u
ter
with
8
GB
o
f
R
AM
an
d
a
2
.
4
GHz
p
r
o
ce
s
s
o
r
.
4
.
1
.
T
he
s
im
ula
t
io
n r
esu
lt
s
f
o
r
Sy
s
t
em
1
T
h
e
co
m
b
in
atio
n
o
p
e
r
atio
n
o
f
TPP
s
an
d
HP
P
s
to
f
o
r
m
Sy
s
tem
1
is
ap
p
lied
to
in
v
e
s
tig
ate
th
e
p
ar
am
eter
s
o
f
E
HO,
C
OOT
,
an
d
T
SA m
eth
o
d
s
b
ased
o
n
m
i
n
im
u
m
co
s
t (
Mi.c
)
,
av
er
a
g
e
co
s
t (
A
v.
c
)
,
m
ax
im
u
m
co
s
t
(
Ma
.
c
)
,
an
d
s
tan
d
ar
d
d
ev
i
atio
n
(
ST
d
)
.
T
h
e
d
ata
o
f
Sy
s
tem
1
is
cited
f
r
o
m
[
8
]
.
B
ased
o
n
p
r
ev
i
o
u
s
s
tu
d
ies,
th
r
ee
m
eth
o
d
s
id
en
tify
th
e
o
p
t
im
al
co
s
t
b
y
ex
am
in
in
g
th
e
p
o
p
u
latio
n
s
ize
(
)
,
n
u
m
b
er
o
f
h
i
g
h
est
iter
atio
n
s
(
H
iter
)
,
an
d
tr
ial
r
u
n
s
.
C
o
n
s
eq
u
en
tly
,
o
f
3
0
an
d
H
iter
o
f
4
0
0
ar
e
ch
o
s
en
f
o
r
E
HO,
C
OOT
,
an
d
T
SA.
Fig
u
r
e
1
s
h
o
ws
th
e
r
esu
lt
o
f
t
h
r
ee
m
et
h
o
d
s
ac
r
o
s
s
5
0
in
d
e
p
en
d
en
t
r
u
n
s
,
in
w
h
ich
t
h
e
cu
r
v
es
ar
e
c
o
lo
r
-
c
o
d
ed
:
b
lack
f
o
r
T
SA,
b
l
u
e
f
o
r
C
OOT
,
an
d
r
e
d
f
o
r
E
HO.
Fro
m
Fig
u
r
e
1
,
t
h
e
cu
r
v
e
o
f
C
OOT
an
d
E
HO
is
s
tr
aig
h
tf
o
r
war
d
,
wh
ile
th
at
o
f
T
SA
h
as
s
o
m
e
h
ig
h
f
lu
ctu
ati
o
n
s
.
Ou
t
o
f
5
0
r
u
n
s
,
we
will
s
h
o
wca
s
e
th
e
m
o
s
t
s
u
cc
ess
f
u
l
r
u
n
to
h
ig
h
lig
h
t
th
e
p
r
o
ce
s
s
o
f
id
e
n
tify
in
g
t
h
e
o
p
tim
al
s
o
lu
tio
n
with
th
e
lo
we
s
t
co
s
t
o
f
th
e
th
r
ee
m
eth
o
d
s
,
as
illu
s
tr
ated
in
Fig
u
r
e
2
.
As
s
ee
n
in
th
e
f
i
g
u
r
e,
E
HO
r
ea
ch
es
th
e
o
p
tim
al
s
o
lu
tio
n
s
f
aster
th
an
C
OOT
,
wh
ile
T
SA
ca
n
n
o
t
r
ea
ch
th
e
b
est
s
o
lu
tio
n
.
T
h
e
m
etr
ics
o
f
E
HO,
C
OOT
,
an
d
T
SA
f
r
o
m
th
e
b
est
-
r
u
n
,
s
u
ch
as
Mi.c
,
A
v.
c
,
Ma
.
c
,
an
d
ST
d
,
a
r
e
co
llected
a
n
d
p
r
esen
ted
in
T
ab
le
1
.
Ob
s
er
v
in
g
th
ese
co
s
ts
o
f
th
e
th
r
ee
ap
p
lied
m
eth
o
d
s
,
we
s
ee
th
at
th
e
Mi.c
o
f
E
HO
is
$
9
6
0
2
4
.
3
4
an
d
less
th
a
n
C
OOT
an
d
T
SA
b
y
$
0
.
1
0
2
an
d
$
6
4
.
1
5
4
.
Oth
er
c
o
s
ts
o
f
E
HO
ar
e
$
9
6
0
2
4
.
3
7
4
an
d
$
9
6
0
2
4
.
4
3
1
,
c
o
m
p
ar
e
d
to
(
$
9
6
0
2
4
.
7
3
an
d
$
9
6
0
2
5
.
0
7
6
)
o
f
C
OOT
an
d
(
$
1
3
1
3
6
6
.
5
an
d
$
7
1
1
4
2
1
.
2
3
)
o
f
T
SA.
T
h
e
ST
d
is
t
h
e
s
m
allest
f
r
o
m
E
HO
(
0
.
0
0
8
9
)
,
wh
ile
th
e
ST
d
is
th
e
b
ig
g
est
f
r
o
m
T
SA
(
1
3
9
7
5
3
.
8
7
)
.
Fro
m
t
h
ese
an
aly
s
es,
E
HO
is
m
o
r
e
e
f
f
ec
tiv
e
th
an
C
OOT
an
d
T
SA.
I
n
co
m
p
ar
is
o
n
to
o
th
er
m
eth
o
d
s
,
th
e
Mi.c
o
f
E
HO
d
em
o
n
s
tr
ates
a
n
o
tab
le
im
p
r
o
v
em
en
t
o
v
er
th
e
v
alu
es
d
ec
lar
ed
b
y
E
M
[
3
]
(
$
9
6
0
2
4
.
3
7
)
,
GA
[
4
]
(
$
9
6
0
2
8
.
6
5
)
,
SMA
[
8
]
(
$
9
6
0
2
4
.
3
5
)
,
C
SA
[
5
]
(
$
9
6
0
2
4
.
6
8
)
,
an
d
eq
u
als
MG
A
[
4
]
(
$
9
6
0
2
4
.
3
4
)
.
Ho
wev
e
r
,
MG
A
d
id
n
o
t
s
h
o
w
ST
d
,
N
pz
,
an
d
H
iter
,
m
ak
in
g
it
d
if
f
icu
lt
t
o
co
n
clu
d
e
th
at
th
e
MG
A
m
eth
o
d
is
m
o
r
e
e
f
f
ec
tiv
e
th
an
E
HO.
R
eg
ar
d
in
g
ST
d
,
E
HO
is
0
.
0
0
8
9
,
C
SA
[
5
]
is
0
.
0
0
3
,
an
d
is
less
t
h
an
th
e
o
th
er
s
;
h
o
we
v
er
,
C
SA
u
s
es
1
0
0
0
iter
atio
n
s
,
b
u
t
o
th
e
r
s
u
s
e
f
r
o
m
2
0
0
t
o
4
0
0
iter
atio
n
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
E
lk
h
erd
o
p
timiz
er fo
r
co
s
t
-
eff
icien
t h
yb
r
id
en
erg
y
s
ystems
u
n
d
er ren
ewa
b
le
u
n
ce
r
ta
in
ty
(
L
y
Hu
u
P
h
a
m
)
435
T
ab
le
1
.
C
o
s
ts
o
f
th
r
ee
a
p
p
ied
m
eth
o
d
s
an
d
p
r
e
v
io
u
s
m
eth
o
d
s
M
e
t
h
o
d
EM
[
3
]
G
A
[
4
]
M
G
A
[
4
]
C
S
A
[
5
]
S
M
A
[
8
]
TSA
C
O
O
T
EH
O
M
i
.
c
(
$
)
9
6
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9
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6
5
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0
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3
4
9
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.
6
8
9
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3
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.
4
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9
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4
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3
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A
v
.
c
(
$
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3
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a
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(
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1
1
4
2
1
.
2
3
9
6
0
2
5
.
0
7
6
9
6
0
2
4
.
4
3
1
ST
d
-
-
-
0
.
0
0
3
0
.
0
3
6
1
3
9
7
5
3
.
8
7
0
.
1
5
3
3
0
.
0
0
8
9
N
pz
-
-
-
20
50
30
30
30
H
iter
-
-
-
1
0
0
0
2
0
0
4
0
0
4
0
0
4
0
0
Fig
u
r
e
1
.
R
esu
lts
o
f
5
0
r
u
n
s
o
b
tain
ed
b
y
th
e
m
eth
o
d
s
Fig
u
r
e
2
.
C
o
n
v
er
g
e
n
ce
f
ea
tu
r
e
s
o
b
tain
ed
b
y
th
e
m
eth
o
d
s
4
.
2
.
T
he
s
im
ula
t
io
n r
esu
lt
s
f
o
r
Sy
s
t
em
2
Sy
s
tem
2
is
m
o
r
e
co
m
p
licated
th
an
Sy
s
tem
1
b
ec
au
s
e
o
f
th
e
ad
d
itio
n
o
f
win
d
an
d
s
o
lar
p
o
wer
p
lan
ts
.
W
h
er
e
th
e
d
ata
o
f
TPP
is
cited
f
r
o
m
[
8
]
,
an
d
th
e
d
ata
o
f
S
P
P
an
d
WPP
a
r
e
cited
f
r
o
m
[
2
7
]
.
Fu
r
th
er
m
o
r
e,
we
tak
e
in
to
ac
co
u
n
t
th
e
u
n
ce
r
tai
n
ties
ass
o
ciate
d
wi
th
s
o
lar
r
ad
iatio
n
an
d
win
d
s
p
ee
d
.
T
o
e
f
f
e
ctiv
ely
ev
alu
ate
th
e
im
p
ac
t
o
f
th
e
u
n
ce
r
tain
c
o
s
ts
o
f
S
P
P
an
d
WPP
o
n
to
tal
c
o
s
t
o
f
th
e
s
y
s
tem
,
d
ir
ec
t
co
s
ts
,
p
en
alty
c
o
s
ts
,
an
d
r
eser
v
e
co
s
ts
o
f
th
em
ar
e
ad
d
e
d
in
to
th
e
f
u
el
co
s
t
o
f
TPP
.
T
h
er
ef
o
r
e
,
t
h
r
e
e
c
o
s
ts
m
en
tio
n
e
d
ar
e
v
ital
elem
e
n
ts
o
f
th
e
f
u
n
ctio
n
al
o
b
jectiv
e
o
f
t
h
e
p
r
o
b
lem
.
L
ik
e
in
s
y
s
tem
1
,
N
pz
an
d
H
iter
f
o
r
e
x
ec
u
tin
g
th
e
th
r
ee
m
eth
o
d
s
ar
e
3
0
an
d
4
0
0
,
an
d
th
e
r
esu
lts
f
o
u
n
d
b
y
E
HO,
C
OOT
,
an
d
T
S
A
ar
e
s
h
o
wn
in
T
a
b
le
2
.
T
ab
le
2
.
C
o
s
ts
o
f
th
r
ee
a
p
p
lied
m
eth
o
d
s
M
e
t
h
o
d
TSA
C
O
O
T
EH
O
M
i
.
c
(
$
)
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1
7
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4
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8
.
1
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9
3
.
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v
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(
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0
6
7
7
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1
.
7
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5
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5
3
M
a
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c
(
$
)
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4
.
6
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6
.
8
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5
7
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2
.
8
1
4
ST
d
7
0
7
.
4
3
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3
6
5
.
7
1
5
5
3
6
0
.
5
6
1
8
T
ab
le
2
s
h
o
ws
th
at
Mi.c
,
A
v.
c
,
an
d
Ma
.
c
o
f
E
HO
ar
e
$
7
1
5
9
3
.
3
1
,
$
7
1
8
7
5
.
2
5
3
,
a
n
d
$
7
2
8
2
2
.
8
1
4
,
r
esp
ec
tiv
ely
,
an
d
a
r
e
less
th
an
th
o
s
e
f
r
o
m
C
OOT
(
$
7
1
6
9
8
.
1
3
1
,
$
7
2
1
3
1
.
7
7
2
,
a
n
d
$
7
3
4
1
6
.
8
8
5
)
,
a
n
d
T
SA
(
$
7
1
7
4
4
.
9
3
8
,
$
7
2
3
5
0
.
0
6
7
,
an
d
$
7
4
1
4
4
.
6
1
6
)
.
C
o
m
p
a
r
in
g
ST
d
o
f
th
r
ee
m
eth
o
d
s
,
we
s
ee
t
h
at
E
HO
h
as
ST
d
o
f
3
6
0
.
5
6
1
8
an
d
is
s
m
aller
th
an
C
OOT
an
d
T
SA
b
y
5
.
1
5
3
7
an
d
3
6
4
.
8
6
8
6
.
Fig
u
r
e
3
illu
s
tr
ates
th
e
co
s
ts
o
f
f
if
ty
s
o
lu
tio
n
s
ac
h
iev
ed
th
r
o
u
g
h
E
HO,
C
OOT
,
an
d
T
SA
m
eth
o
d
s
.
C
o
s
t
v
alu
es
o
f
th
e
th
r
ee
m
e
th
o
d
s
also
f
lu
ctu
ate
b
etwe
en
ea
ch
r
u
n
;
h
o
we
v
er
,
E
HO
h
as
th
e
s
m
allest
f
lu
ctu
a
tio
n
am
o
n
g
t
h
e
th
r
ee
.
B
esid
es,
E
HO
h
as
th
e
b
est
s
o
lu
tio
n
s
as
th
ey
ar
e
b
e
n
ea
th
th
o
s
e
o
f
C
OOT
an
d
T
SA
.
F
ig
u
r
e
4
s
h
o
ws
c
o
n
v
er
g
en
ce
f
ea
tu
r
es
o
b
tain
ed
b
y
m
eth
o
d
s
,
in
wh
ich
E
HO
ten
d
s
to
r
ea
ch
s
o
lu
tio
n
s
b
etter
th
a
n
C
OOT
an
d
T
SA
f
r
o
m
2
0
0
to
th
e
en
d
iter
atio
n
.
All
d
is
cu
s
s
io
n
s
m
en
tio
n
ed
p
r
o
v
e
th
at
E
HO
h
as
v
er
y
p
o
t
en
tial
in
d
ea
lin
g
with
th
e
p
r
o
b
lem
with
m
o
r
e
ch
allen
g
es.
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.
15
,
No
.
1
,
Ma
r
ch
20
26
:
430
-
4
3
9
436
Fig
u
r
e
3
.
R
esu
lts
o
f
5
0
r
u
n
s
o
b
tain
ed
b
y
th
e
m
eth
o
d
s
Fig
u
r
e
4
.
C
o
n
v
er
g
e
n
ce
f
ea
tu
r
e
s
o
b
tain
ed
b
y
th
e
m
eth
o
d
s
4
.
3
.
Dis
cus
s
io
n o
n t
he
re
s
ult
s
o
f
t
he
t
wo
s
y
s
t
em
s
Fig
u
r
e
5
s
h
o
ws
th
r
ee
c
o
s
ts
o
f
E
HO
f
o
r
Sy
s
tem
s
1
an
d
2
,
in
wh
ich
b
l
u
e
co
lo
r
b
a
r
s
ar
e
f
o
r
Sy
s
tem
1
an
d
o
r
a
n
g
e
co
l
o
r
b
a
r
s
ar
e
f
o
r
Sy
s
tem
2
.
As
s
ee
n
in
th
e
f
ig
u
r
e,
Mi.c
,
A
v.
c
,
an
d
Ma
.
c
f
o
r
S
y
s
tem
1
ar
e
$
9
6
0
2
4
.
3
4
,
$
9
6
0
2
4
.
3
7
,
an
d
$
9
6
0
2
4
.
4
3
,
an
d
th
ese
co
s
ts
ar
e
less
th
an
th
o
s
e
f
r
o
m
S
y
s
te
m
2
b
y
$
2
4
4
3
1
.
0
3
,
$
2
4
1
4
9
.
1
2
,
an
d
$
2
3
2
0
1
.
6
2
,
r
e
s
p
ec
tiv
ely
.
T
h
e
co
s
t
r
ed
u
ctio
n
o
f
Sy
s
tem
2
co
m
p
ar
ed
t
o
Sy
s
tem
1
is
s
h
o
wn
to
b
e
th
e
co
n
tr
ib
u
tio
n
o
f
r
e
n
ewa
b
le
en
er
g
y
r
eso
u
r
ce
s
.
T
o
m
ee
t
th
e
lo
ad
d
em
an
d
o
f
1
3
9
0
4
(
MW)
in
2
4
h
o
u
r
s
,
Sy
s
tem
1
r
eq
u
ir
es
two
p
o
wer
p
lan
ts
to
s
u
p
p
ly
5
9
2
8
.
0
8
(
M
W
)
f
o
r
HP
P
an
d
8
3
9
8
.
2
5
(
M
W
)
f
o
r
TPP
,
with
a
p
o
wer
lo
s
s
o
f
4
2
2
.
3
3
(
MW)
a
s
p
r
esen
ted
in
T
ab
le
3
.
W
ith
t
h
e
s
am
e
lo
ad
d
em
a
n
d
,
Sy
s
te
m
2
r
e
q
u
ir
es
p
o
wer
p
lan
ts
to
s
u
p
p
ly
5
9
2
9
.
7
8
(
M
W
)
f
o
r
HP
P
,
5
2
8
4
.
7
8
(
MW)
f
o
r
TPP
,
9
8
9
.
0
4
(
MW)
f
o
r
S
PP
,
an
d
2
0
1
2
.
3
8
(
MW)
f
o
r
W
PP
,
with
a
p
o
wer
lo
s
s
o
f
3
1
1
.
9
8
(
MW)
.
T
ab
le
3
.
C
o
n
tr
ib
u
tio
n
p
o
wer
o
u
tp
u
t o
f
p
o
wer
p
lan
ts
v
s
lo
ad
d
em
an
d
a
n
d
p
o
wer
lo
s
s
S
y
st
e
m
P
d
(
M
W
)
P
h
(
M
W
)
P
t
(
M
W
)
P
s
(
M
W
)
P
w
(
M
W
)
P
l
(
M
W
)
1
1
3
9
0
4
5
9
2
8
.
0
8
8
3
9
8
.
2
5
N
/
A
N
/
A
4
2
2
.
3
3
2
1
3
9
0
4
5
9
2
9
.
7
8
5
2
8
4
.
7
8
9
8
9
.
0
4
2
0
1
2
.
3
8
3
1
1
.
9
8
Fig
u
r
e
5
.
C
o
s
ts
o
f
E
HO
to
Sy
s
tem
s
1
an
d
2
Fig
u
r
es
6
an
d
7
s
h
o
w
th
e
d
is
tr
ib
u
tio
n
o
f
p
o
wer
o
u
tp
u
t g
en
er
ated
b
y
v
a
r
io
u
s
p
o
wer
p
lan
ts
a
cr
o
s
s
ea
ch
h
o
u
r
in
2
4
in
ter
v
als
as
in
d
icate
d
b
y
E
HO.
I
n
t
h
e
f
ig
u
r
es,
t
h
e
p
o
wer
o
u
t
p
u
ts
f
r
o
m
HP
P
,
T
P
P
,
S
P
P
,
an
d
WPP
ar
e
r
ep
r
esen
ted
b
y
d
i
f
f
er
en
t
co
lo
r
ed
b
ar
s
.
Fro
m
an
aly
s
es,
it
c
an
b
e
s
ee
n
th
at
th
e
p
r
esen
ce
o
f
r
en
ewa
b
le
e
n
er
g
y
r
eso
u
r
ce
s
p
lay
s
an
im
p
o
r
tan
t
r
o
le
in
r
ed
u
cin
g
th
e
f
u
el
co
s
t
o
f
T
PP
,
lead
in
g
to
s
ig
n
if
ican
t
c
o
s
t
s
av
in
g
s
f
o
r
th
e
s
y
s
tem
.
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
E
lk
h
erd
o
p
timiz
er fo
r
co
s
t
-
eff
icien
t h
yb
r
id
en
erg
y
s
ystems
u
n
d
er ren
ewa
b
le
u
n
ce
r
ta
in
ty
(
L
y
Hu
u
P
h
a
m
)
437
Fig
u
r
e
6
.
Op
tim
al
o
b
tain
ed
b
y
E
HO
f
o
r
Sy
s
tem
1
Fig
u
r
e
7
.
Op
tim
al
o
b
tain
ed
b
y
E
HO
f
o
r
Sy
s
tem
2
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
ex
p
lo
r
es
s
o
m
e
ex
citin
g
o
p
tim
izatio
n
m
eth
o
d
s
p
ec
if
ically
th
e
elk
h
er
d
o
p
ti
m
izer
,
co
o
t
o
p
tim
izatio
n
alg
o
r
ith
m
,
a
n
d
t
u
n
icate
s
war
m
alg
o
r
ith
m
,
to
f
in
d
th
e
b
est
o
p
er
atio
n
al
p
ar
a
m
eter
s
f
o
r
v
a
r
io
u
s
ty
p
es
o
f
p
o
wer
p
lan
ts
,
in
clu
d
in
g
th
er
m
al,
h
y
d
r
o
,
win
d
,
an
d
s
o
lar
.
T
h
ese
m
eth
o
d
s
ar
e
in
v
esti
g
ated
o
n
two
d
if
f
er
en
t
s
y
s
tem
s
.
T
h
e
s
ec
o
n
d
s
y
s
tem
b
u
ild
s
o
n
th
e
f
ir
s
t
o
n
e,
m
ak
in
g
th
i
n
g
s
a
b
it
m
o
r
e
ch
allen
g
in
g
b
y
in
clu
d
in
g
S
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DATA AV
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[
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,
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RE
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[
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Evaluation Warning : The document was created with Spire.PDF for Python.