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iate
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term
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a
p
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d
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a
l
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n
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car
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s
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is
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y
d
e
m
o
n
stra
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th
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p
o
ten
t
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f
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sin
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iza
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R
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T
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a
rticle
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d
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CC B
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SA
li
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.
C
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r
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s
p
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A
uth
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:
Olu
m
u
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Ajib
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Awo
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Dep
ar
tm
en
t o
f
E
lectr
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an
d
E
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g
in
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Facu
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in
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,
Un
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s
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f
Ab
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Ab
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Nig
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m
ail:
awo
n
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i.o
lu
m
u
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iwa@
y
ah
o
o
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
I
n
d
y
n
am
ic
ec
o
n
o
m
ic
d
is
p
atch
(
DE
D)
o
p
tim
izatio
n
,
g
e
n
er
a
tin
g
u
n
its
co
n
tr
ib
u
tin
g
th
e
s
a
m
e
am
o
u
n
t
o
f
p
o
wer
d
o
n
o
t
n
ec
ess
ar
ily
in
cu
r
th
e
s
am
e
o
p
e
r
atio
n
al
co
s
t.
I
n
f
ac
t,
s
o
m
e
u
n
its
m
ay
b
e
m
o
r
e
ex
p
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n
s
iv
e
to
o
p
er
ate
d
esp
ite
d
eliv
er
in
g
id
e
n
tical
elec
tr
ical
o
u
tp
u
t
[
1
]
,
[
2
]
.
C
o
n
s
eq
u
en
tly
,
it
b
ec
o
m
es
ess
en
tial
to
o
p
tim
ally
allo
ca
te
p
o
r
tio
n
s
o
f
th
e
to
tal
l
o
ad
d
em
a
n
d
am
o
n
g
th
e
av
ail
ab
le
u
n
its
to
m
in
im
ize
f
u
el
c
o
s
ts
ef
f
ec
tiv
ely
[
3
]
.
T
h
is
en
s
u
r
es th
at
p
o
wer
g
en
er
atio
n
ef
f
icien
tly
m
ee
ts
th
e
l
o
a
d
-
s
id
e
d
em
an
d
r
eq
u
ir
em
en
ts
[
4
]
.
Ho
wev
er
,
th
e
in
te
g
r
atio
n
o
f
d
is
tr
ib
u
ted
en
er
g
y
r
eso
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r
ce
s
(
DE
R
s
)
in
tr
o
d
u
ce
s
ad
d
itio
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al
ch
allen
g
es
an
d
co
n
s
tr
ain
ts
,
m
a
k
in
g
d
y
n
a
m
ic
ec
o
n
o
m
ic
l
o
ad
d
is
p
atch
(
DE
L
D)
m
o
r
e
co
m
p
lex
to
s
o
lv
e
[
5
]
.
T
h
e
p
r
esen
ce
o
f
d
ec
e
n
tr
alize
d
e
n
er
g
y
s
o
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r
c
es
an
d
tim
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-
s
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s
itiv
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p
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eq
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ir
em
en
ts
f
u
r
th
er
co
m
p
licates
th
e
DE
L
D
p
r
o
b
lem
[
5
]
.
W
ith
in
m
icr
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g
r
id
s
,
th
e
en
er
g
y
m
a
n
ag
em
en
t
s
y
s
tem
(
E
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p
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s
a
cr
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cial
r
o
le
in
m
in
im
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g
o
p
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al
co
s
ts
,
tak
in
g
in
to
ac
co
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n
t
c
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s
tr
ain
ts
s
u
ch
as
s
tar
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p
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t
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d
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wn
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f
DE
R
s
,
as
well
as th
e
ch
ar
g
in
g
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d
d
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ch
ar
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in
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b
eh
a
v
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r
o
f
b
atter
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g
y
s
to
r
ag
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s
y
s
tem
s
(
B
E
S)
[
6
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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I
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N:
2088
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8
6
9
4
P
erfo
r
ma
n
ce
o
p
timiz
a
tio
n
o
f h
yb
r
id
r
en
ewa
b
le
en
erg
y
s
ystems
w
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…
(
Olu
mu
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A
jib
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la
A
w
o
n
iyi)
1383
I
n
th
e
co
n
tex
t
o
f
m
o
d
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n
p
o
w
er
s
y
s
tem
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,
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ar
ticu
lar
ly
m
icr
o
g
r
id
s
,
o
p
tim
al
d
is
p
atch
h
as
em
er
g
ed
as
a
c
r
i
t
i
c
al
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p
t
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m
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z
at
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o
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s
t
r
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g
y
t
o
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s
u
r
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a
f
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,
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e
li
a
b
l
e
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a
n
d
c
o
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t
-
e
f
f
e
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t
i
v
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a
ti
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n
.
A
m
i
c
r
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g
r
i
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c
a
n
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v
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s
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a
s
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wo
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k
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o
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s
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D
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a
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w
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t
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n
a
s
p
e
c
i
f
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c
a
r
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a
[
5
]
,
[
7
]
.
DE
R
s
aim
to
co
m
p
en
s
ate
f
o
r
t
h
e
s
h
o
r
tf
all
ca
u
s
ed
b
y
th
e
lim
i
ted
av
ailab
ilit
y
o
f
f
o
s
s
il
f
u
el
-
b
ased
eq
u
ip
m
en
t
i
n
m
icr
o
g
r
id
ap
p
licatio
n
s
.
T
ec
h
n
o
lo
g
ies
s
u
ch
as
f
u
el
ce
lls
,
m
ic
r
o
tu
r
b
i
n
es,
an
d
o
th
er
r
en
ewa
b
le
o
r
in
ex
h
au
s
tib
le
s
o
u
r
ce
s
ar
e
p
ar
ticu
lar
ly
well
-
s
u
ited
f
o
r
u
s
e
in
m
icr
o
g
r
id
e
n
v
ir
o
n
m
en
ts
[
8
]
.
E
n
er
g
y
s
to
r
ag
e
s
y
s
tem
s
(
E
SS
)
,
in
clu
d
in
g
b
atter
ies
an
d
f
ly
w
h
e
els,
ar
e
also
in
teg
r
al
co
m
p
o
n
e
n
ts
o
f
DE
R
s
[
9
]
.
Giv
en
th
e
u
n
iq
u
e
ch
ar
ac
ter
is
tics
o
f
ea
ch
m
icr
o
g
r
i
d
an
d
t
h
e
s
p
e
cif
ic
co
n
s
tr
ain
ts
th
ey
im
p
o
s
e,
ec
o
n
o
m
ic
d
is
p
atch
b
ec
o
m
es a
h
ig
h
ly
co
m
p
lex
a
n
d
d
em
an
d
in
g
task
f
o
r
elec
tr
ica
l
en
g
in
ee
r
s
[
1
0
]
-
[
1
2
]
.
Mic
r
o
g
r
id
o
p
er
atio
n
s
g
en
er
ally
f
all
in
to
two
p
r
im
ar
y
ca
teg
o
r
ies:
is
lan
d
ed
m
o
d
e
an
d
g
r
id
-
c
o
n
n
ec
te
d
(
u
tili
ty
-
c
o
n
n
ec
ted
)
m
o
d
e
.
T
h
e
g
r
id
-
c
o
n
n
e
cted
m
o
d
e
is
o
f
te
n
r
eg
ar
d
e
d
as
m
o
r
e
ef
f
icien
t
an
d
r
o
b
u
s
t,
as
it
allo
w
s
f
o
r
en
er
g
y
ex
c
h
an
g
e
b
ased
o
n
th
e
s
u
r
p
lu
s
o
r
d
ef
icit
p
r
o
d
u
ctio
n
o
f
in
d
i
v
id
u
al
DE
R
u
n
its
.
Mo
r
eo
v
er
,
in
th
e
ev
en
t
o
f
a
DE
R
m
alf
u
n
ctio
n
,
th
e
r
elian
c
e
o
n
th
e
m
ain
u
tili
ty
g
r
id
in
th
is
m
o
d
e
en
h
an
ce
s
s
y
s
tem
r
eliab
ilit
y
an
d
p
r
e
v
en
ts
u
n
in
ten
ti
o
n
al
n
et
wo
r
k
s
h
u
td
o
wn
s
.
I
n
a
g
r
id
-
c
o
n
n
ec
ted
m
ic
r
o
g
r
i
d
s
y
s
tem
,
C
h
en
et
a
l.
[
1
3
]
em
p
l
o
y
ed
th
e
m
atr
ix
r
ea
l
-
c
o
d
ed
g
e
n
etic
alg
o
r
ith
m
(
MRC
GA)
to
m
in
im
ize
g
en
er
atio
n
co
s
ts
.
T
h
e
alg
o
r
ith
m
'
s
ef
f
ec
ti
v
en
ess
was
a
s
s
e
s
s
ed
u
n
d
er
v
ar
io
u
s
o
p
er
atin
g
co
n
d
itio
n
s
,
i
n
clu
d
in
g
f
l
u
ctu
atin
g
lo
ad
s
an
d
d
y
n
am
ic
elec
tr
icity
p
r
icin
g
.
Kasaei
[
1
4
]
u
tili
ze
d
th
e
i
m
p
er
ialis
t
co
m
p
etitiv
e
a
lg
o
r
ith
m
(
I
C
A)
to
d
ev
elo
p
an
d
m
an
ag
e
a
v
ir
t
u
al
p
o
wer
p
lan
t,
f
o
c
u
s
in
g
o
n
b
o
th
o
p
er
atio
n
al
co
n
tr
o
l
an
d
ec
o
n
o
m
ic
o
p
tim
izatio
n
.
B
asu
an
d
C
h
o
wd
h
u
r
y
[
1
5
]
a
p
p
lied
th
e
cu
ck
o
o
s
ea
r
c
h
alg
o
r
ith
m
(
C
SA)
to
ad
d
r
ess
b
o
th
s
tatic
an
d
DE
L
D
p
r
o
b
lem
s
,
an
d
s
u
b
s
eq
u
e
n
tly
co
m
p
ar
ed
th
e
r
esu
lts
with
th
o
s
e
o
b
tain
ed
u
s
in
g
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
an
d
d
if
f
e
r
en
tial
ev
o
l
u
tio
n
(
DE
)
.
T
h
eir
a
n
aly
s
is
in
v
o
l
v
ed
two
win
d
tu
r
b
i
n
es
o
p
er
at
in
g
u
n
d
er
v
ar
iab
le
win
d
s
p
ee
d
co
n
d
itio
n
s
.
Ad
d
it
io
n
ally
,
Mo
g
h
ad
d
am
a
n
d
co
ll
ea
g
u
es
[
1
6
]
a
d
o
p
ted
a
n
ad
ap
t
iv
e
m
o
d
if
ied
PS
O
(
AM
PS
O)
,
as
p
r
o
p
o
s
ed
b
y
R
ab
iee
et
a
l.
[
1
7
]
,
to
p
er
f
o
r
m
ec
o
n
o
m
ic
-
em
is
s
io
n
d
is
p
atc
h
u
s
in
g
th
e
Par
eto
-
o
p
tim
al
f
r
o
n
t
ap
p
r
o
ac
h
.
R
ab
iee
et
a
l.
[
1
7
]
p
r
o
p
o
s
ed
th
at
th
e
m
o
d
if
ied
im
p
e
r
ialis
t
co
m
p
etitiv
e
alg
o
r
ith
m
(
MI
C
A)
was
ap
p
lied
to
a
u
tili
ty
-
co
n
n
ec
te
d
m
icr
o
g
r
id
s
y
s
tem
.
T
h
e
p
r
o
b
lem
a
d
d
r
ess
ed
in
th
at
s
tu
d
y
is
clo
s
ely
r
elate
d
to
th
e
o
n
e
d
is
cu
s
s
ed
i
n
th
is
p
ap
er
;
h
o
wev
er
,
th
e
p
r
esen
t
r
esear
ch
u
n
iq
u
ely
in
v
esti
g
ates
s
ce
n
ar
io
s
in
wh
ich
th
e
u
tili
ty
g
r
i
d
b
ec
o
m
es
u
n
av
ailab
le,
eith
e
r
d
u
e
to
u
n
i
n
ten
tio
n
al
f
ailu
r
e
o
r
in
te
n
tio
n
a
l
d
is
co
n
n
ec
tio
n
,
a
n
asp
ec
t n
o
t e
x
p
lo
r
ed
in
p
r
ev
i
o
u
s
liter
atu
r
e.
Fu
r
th
er
m
o
r
e
,
th
is
s
tu
d
y
ex
am
i
n
es
s
ix
p
o
s
s
ib
le
g
r
id
in
ter
ac
ti
o
n
s
ce
n
ar
io
s
with
in
a
lo
w
-
v
o
l
tag
e
(
L
V)
m
icr
o
g
r
id
ar
ch
itectu
r
e
.
R
esear
ch
er
s
in
[
1
7
]
-
[
1
9
]
u
s
ed
t
h
e
wh
ale
o
p
tim
izatio
n
alg
o
r
ith
m
(
W
OA)
,
m
o
d
if
ied
h
ar
m
o
n
y
s
ea
r
ch
alg
o
r
ith
m
(
MH
SA)
,
an
d
in
ter
io
r
s
ea
r
ch
alg
o
r
ith
m
to
s
o
lv
e
ec
o
n
o
m
ic
d
is
p
atch
(
E
D)
,
co
m
b
in
ed
ec
o
n
o
m
ic
an
d
em
is
s
io
n
d
is
p
atch
(
C
E
E
D)
,
a
n
d
ec
o
n
o
m
ic
l
o
ad
d
is
p
atch
(
E
L
D)
p
r
o
b
lem
s
in
a
th
r
ee
-
u
n
it
is
lan
d
ed
m
icr
o
g
r
id
s
y
s
tem
co
m
p
r
is
in
g
p
h
o
to
v
o
ltaic
an
d
win
d
en
er
g
y
s
o
u
r
ce
s
.
Similar
ly
,
s
tu
d
ies
in
[
2
0
]
an
d
[2
1
]
ap
p
lied
th
e
m
e
m
o
r
y
-
b
ased
g
en
etic
alg
o
r
ith
m
,
ar
tifi
cial
f
is
h
s
war
m
alg
o
r
ith
m
,
a
n
d
m
o
d
if
ie
d
p
er
s
o
n
al
b
est
p
ar
ticle
s
war
m
o
p
tim
iz
atio
n
(
MPB
PS
O)
to
im
p
r
o
v
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
an
is
lan
d
ed
m
icr
o
g
r
id
.
R
am
li
[
2
2
]
ex
am
in
ed
two
ad
d
itio
n
al
o
p
er
atin
g
co
n
d
itio
n
s
b
y
in
cr
ea
s
in
g
th
e
lo
ad
d
em
a
n
d
o
f
a
test
s
y
s
tem
b
y
1
0
%
an
d
co
n
s
id
er
in
g
a
g
r
id
-
c
o
n
n
ec
ted
m
icr
o
g
r
id
e
q
u
ip
p
e
d
with
a
b
atter
y
en
er
g
y
s
to
r
ag
e
s
y
s
tem
(
B
E
S
S)
to
s
u
p
p
o
r
t o
n
e
-
way
p
o
wer
f
lo
w.
T
h
e
s
tu
d
y
in
[2
3
]
f
o
c
u
s
ed
o
n
m
in
im
izin
g
th
e
o
p
e
r
atin
g
c
o
s
t o
f
a
g
r
id
-
c
o
n
n
ec
te
d
m
icr
o
g
r
id
u
s
in
g
th
e
im
p
r
o
v
ed
b
at
alg
o
r
ith
m
(
I
B
A)
.
Dey
et
a
l.
[2
4
]
s
u
cc
ess
f
u
lly
r
ed
u
ce
d
th
e
o
p
er
atin
g
co
s
t
o
f
b
o
th
s
m
all
an
d
lar
g
e
r
en
ew
ab
le
-
in
teg
r
ated
m
icr
o
g
r
id
s
b
y
ap
p
ly
in
g
th
e
r
ec
e
n
tly
d
e
v
elo
p
e
d
cr
o
w
s
ea
r
ch
alg
o
r
ith
m
(
C
SA)
.
T
h
e
o
b
jecti
v
e
f
u
n
ctio
n
s
co
n
s
id
er
e
d
in
th
o
s
e
m
icr
o
g
r
id
s
tu
d
ies
in
clu
d
ed
b
o
th
u
n
im
o
d
al
a
n
d
m
u
ltimo
d
al
f
o
r
m
s
.
T
h
e
C
SA
d
em
o
n
s
tr
ated
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
o
v
er
s
ev
er
al
m
etah
e
u
r
is
tic
an
d
co
n
v
e
n
tio
n
al
o
p
tim
izatio
n
m
eth
o
d
s
in
te
r
m
s
o
f
g
en
er
atio
n
c
o
s
t
r
ed
u
ctio
n
.
I
n
a
n
o
th
er
s
tu
d
y
,
Pap
a
r
i
et
a
l.
[2
5
]
e
m
p
lo
y
e
d
C
SA
f
o
r
en
e
r
g
y
m
an
a
g
em
en
t
in
AC
-
DC
h
y
b
r
id
m
icr
o
g
r
id
s
,
with
em
p
h
asis
o
n
r
ed
u
cin
g
co
n
v
er
ter
-
r
elate
d
p
o
wer
lo
s
s
es.
Dey
et
a
l.
[2
4
]
p
r
o
p
o
s
ed
an
o
p
tim
al
d
is
p
atch
s
tr
ateg
y
f
o
r
a
r
esid
en
tial
m
icr
o
g
r
id
u
s
in
g
a
h
y
b
r
id
o
p
tim
izatio
n
ap
p
r
o
ac
h
an
d
ex
am
in
ed
th
e
in
f
lu
en
ce
o
f
ac
tiv
e
g
r
id
p
a
r
ticip
atio
n
.
Fu
r
th
er
m
o
r
e
,
Dey
et
a
l.
[2
6
]
ev
alu
ated
d
if
f
er
en
t
elec
tr
icity
p
r
icin
g
s
tr
u
ctu
r
es
u
s
in
g
th
e
MG
W
OS
C
A
C
SA
alg
o
r
ith
m
to
lo
wer
o
p
er
atin
g
co
s
ts
in
t
wo
lo
w
-
v
o
ltag
e
m
icr
o
g
r
id
co
n
f
ig
u
r
atio
n
s
.
Un
lik
e
ea
r
lier
s
tu
d
ies,
th
e
p
r
esen
t
w
o
r
k
in
v
esti
g
ates
b
o
th
in
ten
tio
n
al
an
d
u
n
in
ten
tio
n
al
g
r
id
f
ai
lu
r
es
an
d
ex
am
in
es
th
eir
ef
f
ec
t
o
n
elec
tr
icity
g
e
n
er
atio
n
co
s
t.
T
h
e
p
r
o
p
o
s
ed
h
y
b
r
id
alg
o
r
ith
m
,
wh
ich
is
b
as
ed
o
n
th
e
W
OA,
is
ev
alu
ated
a
g
ain
s
t
d
if
f
e
r
en
tial
ev
o
lu
tio
n
(
DE
)
,
co
n
v
en
tio
n
al
W
OA,
an
d
th
e
s
in
e
co
s
in
e
al
g
o
r
ith
m
(
SC
A)
.
I
n
ad
d
itio
n
,
th
is
s
tu
d
y
in
tr
o
d
u
ce
s
n
o
n
-
p
ar
am
etr
ic
s
tatis
tical
an
a
ly
s
is
to
v
alid
ate
th
e
r
esu
lts
,
a
f
ea
tu
r
e
th
at
is
r
ar
ely
ad
d
r
ess
ed
in
t
h
e
ex
is
tin
g
lite
r
atu
r
e.
Pre
v
iew
s
tu
d
y
[2
7
]
,
a
d
ay
-
a
h
ea
d
p
r
icin
g
m
ec
h
a
n
is
m
,
an
d
an
en
er
g
y
co
n
s
u
m
p
tio
n
g
am
e
wer
e
u
s
ed
to
d
ev
elo
p
a
n
ad
v
a
n
ce
d
d
em
an
d
-
s
id
e
m
an
a
g
em
en
t
(
DSM)
s
tr
ateg
y
b
ased
o
n
g
am
e
th
eo
r
y
,
wh
er
e
a
s
in
g
le
u
tili
ty
p
r
o
v
id
er
in
te
r
ac
ts
with
m
u
ltip
le
r
esid
en
tial
co
n
s
u
m
e
r
s
.
T
o
ad
d
r
ess
th
e
m
u
lti
-
o
b
jectiv
e
d
y
n
am
ic
ec
o
n
o
m
ic
an
d
em
is
s
io
n
d
is
p
atch
(
MO
DE
E
D)
p
r
o
b
lem
,
[
28
]
em
p
lo
y
ed
th
e
m
u
lti
-
o
b
jectiv
e
p
ar
ticle
s
war
m
o
p
t
im
izatio
n
(
MO
PS
O)
alg
o
r
ith
m
.
R
esear
ch
er
s
in
[
29
]
p
r
o
p
o
s
ed
a
co
o
p
er
ativ
e
o
p
tim
izatio
n
f
r
am
ewo
r
k
f
o
r
th
e
d
esig
n
an
d
m
an
ag
e
m
en
t
o
f
d
em
an
d
-
s
id
e
-
m
an
ag
e
d
g
r
id
-
c
o
n
n
ec
ted
r
esid
en
tial
m
icr
o
g
r
id
s
.
T
h
e
s
y
s
tem
co
n
s
id
er
ed
m
u
ltip
le
d
is
tr
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
,
in
clu
d
i
n
g
s
o
lar
p
an
els,
win
d
tu
r
b
in
es,
g
r
id
s
u
p
p
ly
,
d
iesel
en
g
in
e
u
n
its
(
DE
s
)
,
an
d
B
E
SS
s
.
Fo
r
ec
asti
n
g
m
o
d
els
wer
e
u
s
ed
to
p
r
e
d
ict
s
h
o
r
t
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
1
3
8
2
-
1395
1384
ter
m
v
ar
iatio
n
s
in
d
e
m
an
d
a
n
d
s
o
lar
ir
r
a
d
ian
ce
,
allo
win
g
th
e
g
r
ey
w
o
lf
o
p
tim
izer
(
G
W
O)
alg
o
r
ith
m
to
o
p
tim
ize
g
en
er
atio
n
s
ch
ed
u
lin
g
,
s
to
r
ag
e
o
p
er
atio
n
,
an
d
p
o
we
r
d
is
p
atch
d
y
n
am
ically
.
B
y
in
t
eg
r
atin
g
p
r
ed
ictiv
e
m
o
d
els
with
m
etah
eu
r
is
tic
o
p
t
im
izatio
n
,
th
e
f
r
am
ewo
r
k
r
e
d
u
ce
s
o
p
er
atin
g
co
s
t,
im
p
r
o
v
es
p
o
wer
b
alan
ce
,
an
d
en
h
an
ce
s
s
y
s
tem
r
eliab
ilit
y
u
n
d
er
v
ar
ia
b
le
lo
ad
a
n
d
wea
th
er
co
n
d
itio
n
s
.
T
h
is
f
o
r
ec
ast
-
awa
r
e
GW
O
f
r
am
ewo
r
k
en
s
u
r
es
r
ea
l
-
tim
e
ad
ap
tab
ilit
y
an
d
im
p
r
o
v
ed
p
er
f
o
r
m
an
ce
co
m
p
ar
ed
to
co
n
v
en
tio
n
al
s
tatic
o
r
n
o
n
-
f
o
r
ec
asti
n
g
o
p
tim
i
za
tio
n
ap
p
r
o
ac
h
es
in
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
.
T
h
e
k
ey
i
n
n
o
v
ativ
e
co
n
t
r
ib
u
ti
o
n
s
p
r
esen
ted
in
th
is
s
tu
d
y
to
ac
co
m
p
lis
h
th
e
o
u
tlin
ed
o
b
jectiv
es a
r
e
as f
o
llo
ws:
−
T
h
is
r
esear
ch
p
r
esen
ts
a
n
o
v
e
l
in
teg
r
atio
n
o
f
th
e
GW
O
wit
h
r
ea
l
-
tim
e
lo
ad
f
o
r
ec
asti
n
g
m
o
d
els,
en
ab
lin
g
m
o
r
e
ac
cu
r
ate
a
n
d
ad
a
p
tiv
e
en
er
g
y
d
is
p
atch
s
tr
ateg
ies
in
h
y
b
r
id
r
en
ewa
b
le
en
e
r
g
y
s
y
s
tem
s
(
HR
E
S),
wh
ich
is
n
o
t w
id
ely
ad
d
r
ess
ed
in
ex
is
tin
g
liter
atu
r
e.
−
A
h
y
b
r
id
m
o
d
el
is
d
ev
elo
p
ed
th
at
co
m
b
in
es
s
o
lar
PV,
g
r
id
,
win
d
,
b
atter
y
s
to
r
ag
e
,
an
d
p
o
s
s
ib
ly
d
iesel
b
ac
k
u
p
,
o
p
tim
ize
d
d
y
n
am
icall
y
in
th
e
p
r
esen
ce
o
f
u
n
ce
r
tain
lo
ad
an
d
g
e
n
er
atio
n
p
r
o
f
iles
.
T
h
e
p
r
o
p
o
s
ed
f
r
am
ewo
r
k
in
co
r
p
o
r
ates f
o
r
ec
asti
n
g
u
n
ce
r
tain
ty
d
ir
ec
tly
in
to
th
e
o
p
tim
izatio
n
l
o
o
p
.
−
T
h
e
s
tu
d
y
in
tr
o
d
u
ce
s
a
m
u
lti
-
o
b
jectiv
e
GW
O
m
o
d
el
th
at
s
i
m
u
ltan
eo
u
s
ly
m
in
im
izes
o
p
er
atio
n
al
co
s
t
an
d
ca
r
b
o
n
em
is
s
io
n
s
,
o
f
f
e
r
in
g
a
m
o
r
e
b
alan
ce
d
p
er
f
o
r
m
an
ce
o
p
tim
izatio
n
s
tr
ateg
y
co
m
p
ar
ed
to
tr
ad
itio
n
al
s
in
g
le
-
o
b
jectiv
e
m
eth
o
d
s
.
−
Un
lik
e
m
an
y
s
tatic
o
p
tim
izati
o
n
m
o
d
els,
th
is
r
esear
ch
p
r
o
p
o
s
es a
r
ea
l
-
tim
e
p
r
ed
ictiv
e
en
er
g
y
m
an
ag
em
e
n
t
ap
p
r
o
ac
h
th
at
d
y
n
am
ically
u
p
d
ates
o
p
er
atio
n
al
d
ec
is
io
n
s
b
ased
o
n
f
o
r
ec
asted
d
em
a
n
d
an
d
av
aila
b
le
g
en
er
atio
n
,
im
p
r
o
v
in
g
s
y
s
tem
r
eliab
ilit
y
an
d
r
esp
o
n
s
iv
en
ess
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
is
s
ec
tio
n
o
u
tlin
es
th
e
co
m
p
r
eh
en
s
iv
e
m
eth
o
d
o
lo
g
ical
f
r
a
m
ewo
r
k
em
p
lo
y
ed
in
th
e
s
im
u
latio
n
an
d
an
aly
s
is
o
f
an
HR
E
S
f
o
r
th
e
APO
c
o
m
m
u
n
ity
,
with
a
f
o
cu
s
o
n
p
h
o
to
v
o
ltaic
(
PV)
s
o
lar
en
er
g
y
,
win
d
,
b
atter
y
en
er
g
y
s
to
r
ag
e
,
an
d
g
r
id
in
teg
r
atio
n
.
T
h
e
m
eth
o
d
o
l
o
g
y
in
teg
r
ates
s
y
s
tem
m
o
d
elin
g
,
d
ata
ac
q
u
is
itio
n
,
s
im
u
latio
n
d
esig
n
,
o
p
tim
izatio
n
th
r
o
u
g
h
GW
O,
an
d
p
er
f
o
r
m
an
ce
e
v
alu
atio
n
b
ased
o
n
tim
e
-
s
er
ies
o
u
tp
u
ts
.
T
h
is
f
r
am
ewo
r
k
e
n
s
u
r
es
a
r
o
b
u
s
t,
r
ep
r
o
d
u
ci
b
le,
an
d
a
n
al
y
tical
ap
p
r
o
ac
h
to
ass
ess
in
g
th
e
r
eliab
ilit
y
an
d
ef
f
icien
cy
o
f
t
h
e
p
r
o
p
o
s
ed
en
e
r
g
y
s
y
s
tem
.
R
ea
l h
is
to
r
ical
d
ata
o
n
lo
ad
d
e
m
an
d
a
n
d
r
en
ewa
b
le
en
er
g
y
a
r
e
u
s
ed
f
o
r
th
e
f
o
r
ec
asti
n
g
m
o
d
els.
Sen
s
itiv
ity
an
aly
s
is
is
also
p
er
f
o
r
m
ed
t
o
d
eter
m
in
e
th
e
r
o
b
u
s
tn
ess
o
f
th
e
s
y
s
tem
u
n
d
er
v
ar
io
u
s
o
p
er
atio
n
al
c
o
n
d
itio
n
s
,
s
u
ch
as
v
ar
y
in
g
e
n
er
g
y
d
e
m
an
d
,
wea
th
e
r
co
n
d
it
io
n
s
,
an
d
av
ailab
le
r
en
ewa
b
le
en
er
g
y
r
eso
u
r
ce
s
.
F
ig
u
r
e
1
s
h
o
ws
a
s
ch
em
atic
d
esig
n
o
f
t
h
e
h
y
b
r
id
m
icr
o
g
r
id
en
er
g
y
s
y
s
tem
.
T
h
is
wo
r
k
in
tr
o
d
u
ce
s
a
m
u
lti
-
o
b
je
ctiv
e
o
p
tim
izatio
n
f
r
am
ewo
r
k
th
at
s
im
u
ltan
eo
u
s
ly
tar
g
ets
t
h
e
m
in
im
izatio
n
o
f
o
p
er
atio
n
al
co
s
t
an
d
g
r
ee
n
h
o
u
s
e
g
as
em
is
s
io
n
s
in
h
y
b
r
id
r
e
n
ewa
b
le
en
er
g
y
s
y
s
tem
s
.
B
y
b
alan
cin
g
ec
o
n
o
m
ic
an
d
e
n
v
ir
o
n
m
en
tal
o
b
jectiv
e
s
,
th
e
ap
p
r
o
ac
h
e
n
s
u
r
es
o
p
tim
al
en
er
g
y
d
is
p
atch
,
s
to
r
a
g
e
s
ch
ed
u
lin
g
,
a
n
d
r
eso
u
r
ce
u
tili
za
tio
n
.
T
h
e
o
p
tim
izatio
n
em
p
lo
y
s
ad
v
an
ce
d
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
to
id
en
tify
Par
eto
-
o
p
tim
al
s
o
lu
tio
n
s
th
at
tr
ad
e
o
f
f
c
o
s
t
an
d
em
is
s
io
n
p
er
f
o
r
m
an
ce
u
n
d
er
v
ar
y
in
g
lo
ad
a
n
d
r
en
ewa
b
le
g
en
er
atio
n
co
n
d
itio
n
s
.
T
h
is
d
u
al
-
o
b
jectiv
e
s
tr
ateg
y
p
r
o
m
o
tes
s
u
s
tain
ab
le
an
d
co
s
t
-
ef
f
ec
tiv
e
o
p
er
atio
n
o
f
m
o
d
er
n
m
icr
o
g
r
id
s
,
en
a
b
lin
g
im
p
r
o
v
e
d
en
er
g
y
ef
f
icien
c
y
,
r
ed
u
ce
d
ca
r
b
o
n
f
o
o
tp
r
in
t,
an
d
en
h
a
n
ce
d
d
ec
is
io
n
-
m
ak
i
n
g
f
o
r
r
ea
l
-
tim
e
e
n
er
g
y
m
an
a
g
em
en
t in
r
en
ewa
b
le
-
in
teg
r
ated
p
o
wer
s
y
s
tem
s
.
2
.
1
.
Sy
s
t
em
c
o
m
po
nent
mo
delin
g
2
.
1
.
1
.
M
a
t
hem
a
t
ic
a
l pho
t
o
v
o
lt
a
ic
s
y
s
t
em
mo
delin
g
Ph
o
to
v
o
ltaic
(
PV)
m
o
d
u
les
co
n
s
is
t
o
f
a
s
er
ies
o
f
in
ter
co
n
n
e
cted
s
o
lar
ce
lls
d
esig
n
ed
to
p
r
o
d
u
ce
th
e
r
eq
u
ir
ed
o
u
tp
u
t
v
o
ltag
e
an
d
c
u
r
r
en
t
lev
els
[
3
0
]
.
PV
s
y
s
tem
s
h
av
e
b
ec
o
m
e
o
n
e
o
f
th
e
m
o
s
t
wid
ely
ad
o
p
ted
r
en
ewa
b
le
e
n
er
g
y
tech
n
o
lo
g
ie
s
,
p
r
im
ar
ily
d
u
e
to
th
eir
m
in
i
m
al
o
p
e
r
atin
g
a
n
d
m
ain
ten
a
n
ce
co
s
ts
,
ze
r
o
f
u
el
co
n
s
u
m
p
tio
n
,
an
d
ab
s
en
ce
o
f
ca
r
b
o
n
e
m
is
s
io
n
s
.
T
h
e
p
o
wer
o
u
tp
u
t
o
f
PV te
ch
n
o
l
o
g
y
ca
n
b
e
ca
lcu
lated
as
(
1
)
.
=
(
1
)
W
ith
r
ep
r
esen
ts
th
e
s
u
r
f
ac
e
ar
ea
o
f
th
e
PV
m
o
d
u
le,
d
en
o
tes
th
e
co
n
v
er
s
io
n
ef
f
icien
cy
,
wh
ich
is
d
ef
in
ed
b
y
(
2
)
.
=
[
1
−
(
−
)
]
(
2
)
W
h
er
e
r
ep
r
esen
ts
th
e
r
ef
er
en
ce
ef
f
icien
cy
o
f
th
e
s
o
lar
m
o
d
u
le,
d
en
o
tes
th
e
tem
p
er
atu
r
e
co
ef
f
icien
t
o
f
s
ilico
n
-
b
ased
p
h
o
to
v
o
ltaic
ce
l
ls
,
r
ef
er
s
to
th
e
s
tan
d
a
r
d
o
p
er
atin
g
tem
p
er
atu
r
e
o
f
s
o
lar
ce
l
ls
(
°C
)
,
is
th
e
g
lo
b
al
s
o
lar
ir
r
a
d
ian
ce
(
W
/m
²)
,
is
th
e
tem
p
e
r
atu
r
e
o
f
th
e
p
h
o
t
o
v
o
ltaic
ce
ll,
in
d
ica
tes
th
e
am
b
ie
n
t
tem
p
er
atu
r
e
(
°C
)
,
an
d
NOCT
s
tan
d
s
f
o
r
th
e
n
o
m
in
al
o
p
er
ati
n
g
ce
ll tem
p
er
at
u
r
e
(
°C
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
erfo
r
ma
n
ce
o
p
timiz
a
tio
n
o
f h
yb
r
id
r
en
ewa
b
le
en
erg
y
s
ystems
w
ith
…
(
Olu
mu
yiw
a
A
jib
o
la
A
w
o
n
iyi)
1385
=
+
(
−
20
800
)
(
3
)
=
[
1
+
0
.
0539
l
og
(
(
)
)
]
+
(
(
)
)
+
0
.
02
(
)
(
4
)
α
r
ep
r
esen
ts
th
e
am
b
ien
t
tem
p
er
atu
r
e
c
o
ef
f
icien
t,
G
tt
is
th
e
r
ad
iatio
n
p
r
ed
ictio
n
f
ac
to
r
(
i
n
k
W
/m
2
)
,
G
st
is
th
e
s
tan
d
ar
d
r
ad
iatio
n
co
ef
f
icien
t
(
in
u
n
its
o
f
1
k
W
/m
²)
,
T
a
in
d
i
ca
tes
th
e
tem
p
er
atu
r
e
p
ar
am
et
er
(
in
Kelv
in
)
,
an
d
V
mppt
r
ef
er
s
to
th
e
v
o
ltag
e
m
ea
s
u
r
ed
at
th
e
m
a
x
im
u
m
p
o
wer
p
o
in
t.
T
h
e
(
5
)
was u
s
ed
to
d
eter
m
in
e
th
e
cu
r
r
e
n
t o
u
t
p
u
t (
I
PV
)
o
f
a
s
o
lar
PV m
o
d
u
le
.
=
ℎ
(
)
−
(
)
[
e
xp
(
(
)
)
−
1
]
(
5
)
W
h
er
e
I
Ph
s
tan
d
s
f
o
r
th
e
p
h
o
to
cu
r
r
en
t,
I
rs
f
o
r
s
atu
r
atio
n
cu
r
r
e
n
t,
q
f
o
r
elec
tr
o
n
c
h
ar
g
in
g
,
N
s
f
o
r
s
er
ies
ce
ll
to
tal
v
ar
iab
le,
K
f
o
r
B
o
ltzm
an
n
'
s
co
n
s
tan
t,
an
d
A
i
f
o
r
th
e
id
ea
l
d
io
d
e
r
atio
.
T
h
e
(
6
)
esti
m
ated
th
e
to
tal
en
er
g
y
g
en
er
ated
b
y
s
o
lar
PV (
p
h
o
to
v
o
ltaic)
p
an
els (
E
PV
).
(
)
=
(
×
(
)
×
×
∆
)
1000
(
6
)
W
h
er
e
t
is
th
e
s
tep
d
u
r
atio
n
o
f
1
5
m
in
u
tes
,
an
d
N
PV
is
th
e
n
u
m
b
er
o
f
PV m
o
d
u
les.
Fig
u
r
e
1
.
Sch
em
atic
d
esig
n
o
f
th
e
h
y
b
r
id
m
icr
o
g
r
id
e
n
er
g
y
s
y
s
tem
2
.
1
.
2
.
B
a
t
t
er
y
ba
nk
m
a
t
hema
t
ica
l mo
delin
g
T
h
e
co
n
n
e
cted
b
atter
ies
an
d
th
eir
r
esp
ec
tiv
e
s
tate
o
f
ch
ar
g
e
at
an
y
g
iv
en
m
o
m
en
t
a
r
e
u
s
ed
to
ev
alu
ate
th
e
to
tal
e
n
er
g
y
g
en
er
ated
an
d
co
n
s
u
m
e
d
.
T
h
e
n
u
m
b
er
o
f
av
ailab
le
b
atter
ies
at
a
s
p
ec
if
ic
tim
e
is
ex
p
r
ess
ed
b
y
(
7
)
[3
1
]
,
[
3
2
]
.
(
)
=
(
−
1
)
+
(
)
×
×
(
7
)
T
h
e
q
u
a
n
tity
o
f
g
r
ee
n
en
e
r
g
y
th
at
is
p
r
esen
tly
ac
ce
s
s
ib
le
i
s
E
Em
(
t)
.
T
h
e
m
ec
h
an
is
m
'
s
ch
ar
g
in
g
c
o
n
tr
o
ller
is
in
d
icate
d
b
y
α
CC
,
wh
ile
b
atter
y
ch
ar
g
i
n
g
p
e
r
f
o
r
m
an
ce
is
d
ep
icted
b
y
σ
CHG
.
State
o
f
ch
ar
g
e
(
SOC
)
is
th
e
b
atter
y
'
s
ch
ar
g
e
lev
el,
an
d
th
e
SOC
m
ax
im
u
m
p
ar
am
eter
is
ca
lled
SOC
max
.
T
h
e
SO
C
m
in
im
al
p
ar
am
eter
is
ca
lled
SOC
min
.
T
h
e
m
in
im
al
SOC
p
ar
am
eter
is
as (
8
)
.
=
1
−
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
1
3
8
2
-
1395
1386
T
h
e
d
is
ch
ar
g
e
b
atter
ies'
in
ten
s
ity
is
in
d
icate
d
b
y
DOD
(
%).
≤
(
)
≤
2
.
1
.
3
.
Wind
-
po
wer
ed
t
urbi
n
e
s
y
s
t
em
A
m
o
d
el
o
f
t
h
e
win
d
g
e
n
er
at
o
r
s
y
s
tem
was
d
ev
elo
p
ed
b
ased
o
n
th
e
win
d
tu
r
b
in
e
p
o
wer
p
r
o
f
ile.
Acc
o
r
d
in
g
to
[
3
0
]
,
th
e
win
d
en
er
g
y
eq
u
atio
n
is
g
o
v
er
n
ed
u
s
in
g
a
cu
r
v
e
-
f
itti
n
g
tech
n
iq
u
e.
T
h
e
p
o
wer
o
u
t
p
u
t o
f
win
d
tu
r
b
in
es (
PW
T
)
ca
n
b
e
c
alcu
lated
u
s
in
g
(
9
)
an
d
(
1
0
)
.
(
)
=
0
≤
>
0
(
)
=
1
1
+
1
+
1
<
<
1
(
)
=
2
2
+
2
+
1
1
<
<
2
(
)
=
3
2
+
3
+
3
2
<
<
0
}
(
9
)
W
h
er
e
B
,
Y,
an
d
K
ar
e
th
e
p
a
r
am
eter
s
o
f
th
e
d
is
tin
ctiv
e
eq
u
atio
n
s
,
X
is
th
e
win
d
e
n
er
g
y
t
u
r
b
in
e'
s
o
p
er
atio
n
a
l
s
p
ee
d
,
is
it
s
cu
t
-
in
s
p
ee
d
,
an
d
0
is
th
e
cu
t
-
o
u
t
s
p
ee
d
.
T
h
e
(
1
0
)
ca
n
b
e
u
s
ed
to
ex
p
r
ess
th
e
e
n
er
g
y
p
r
o
d
u
ce
d
b
y
th
e
win
d
tu
r
b
i
n
e
s
y
s
tem
(
E
WT
).
=
×
(
)
×
∆
1000
(
1
0
)
W
h
er
e
th
e
to
tal
am
o
u
n
t o
f
win
d
tu
r
b
in
es is
d
en
o
ted
b
y
K
WT
.
2
.
1
.
4
.
Diesel
g
ener
a
t
o
r
s
y
nchro
no
us
m
o
delin
g
T
h
r
o
u
g
h
th
e
aid
o
f
in
(
11
)
,
th
e
f
u
el
u
tili
za
tio
n
f
o
r
s
y
n
ch
r
o
n
o
u
s
d
iesel
g
en
er
ato
r
s
(
DGs)
is
ev
alu
ated
h
o
u
r
ly
[
2
8
].
(
)
=
(
)
+
(
1
1
)
W
h
er
e
α
D
an
d
β
D
ar
e
th
e
f
u
el
u
s
ag
e
cu
r
v
e
p
ar
am
ete
r
s
,
L
/k
W
h
,
P
Dg
is
th
e
ty
p
ical
p
o
wer
c
o
n
s
u
m
ed
p
er
h
o
u
r
o
f
th
e
en
g
i
n
e
in
k
W
,
P
Dgr
is
th
e
n
o
m
in
al
s
y
n
c
h
r
o
n
o
u
s
d
iesel
en
g
in
e
in
k
W
,
a
n
d
D
f
(
t
)
is
th
e
h
o
u
r
ly
f
u
el
u
tili
za
tio
n
o
f
th
e
s
y
n
c
h
r
o
n
o
u
s
g
e
n
er
ato
r
i
n
L
/h
.
2
.
2
.
O
bje
c
t
iv
e
f
un
ct
io
n
T
h
e
m
ain
o
b
jectiv
e
o
f
th
is
p
r
o
b
lem
is
to
m
in
im
ize
b
o
th
th
e
g
en
er
atio
n
co
s
t
an
d
em
is
s
io
n
s
o
f
th
e
m
icr
o
g
r
id
[
2
1
]
,
wh
ich
ca
n
b
e
m
ath
em
atica
lly
f
o
r
m
u
lated
as
(
1
2
)
.
(
)
=
∑
(
)
+
∑
(
)
=
=
1
(
1
2
)
W
h
er
e
F(E
i
)
r
ep
r
esen
ts
th
e
g
en
er
atio
n
c
o
s
t
ass
o
ciate
d
with
th
e
m
icr
o
g
r
id
,
wh
er
e
n
d
is
tr
ib
u
ted
g
e
n
er
atio
n
(
DG)
u
n
its
ar
e
co
n
n
ec
ted
.
T
h
e
g
en
er
atio
n
co
s
t
is
r
ep
r
esen
ted
b
y
(
)
,
wh
ile
th
e
em
is
s
io
n
co
s
t
is
d
en
o
ted
as
(
)
.
T
h
e
p
o
wer
o
u
t
p
u
t
f
r
o
m
th
e
i
th
d
is
tr
ib
u
ted
g
en
er
atio
n
(
DG)
u
n
it
is
Pi.
an
d
th
e
tim
e
i
n
d
ex
t
s
p
an
s
f
r
o
m
1
t
o
2
4
h
o
u
r
s
.
T
h
e
to
tal
g
en
er
atio
n
co
s
t
[
3
0
]
,
wh
ich
in
clu
d
es
f
u
el
ex
p
e
n
s
es,
o
p
er
atio
n
an
d
m
ain
te
n
an
ce
(
O&
M)
co
s
ts
,
an
d
d
e
p
r
ec
iatio
n
,
ca
n
b
e
m
ath
em
atica
lly
f
o
r
m
u
lated
as
(
1
3
)
.
(
)
=
,
(
)
+
&
,
(
)
+
,
(
)
+
×
(
1
3
)
W
h
er
e
,
(
)
,
&
,
(
)
an
d
,
(
)
ar
e
th
e
co
s
t
o
f
o
p
er
atin
g
f
u
el,
o
p
e
r
atio
n
-
m
ain
ten
an
ce
co
s
t
,
an
d
d
ep
r
ec
iatio
n
c
o
s
t,
r
esp
ec
tiv
ely
,
f
o
r
th
e
ith
DG
u
n
it.
d
en
o
tes
th
e
m
ar
k
et
-
b
ased
elec
tr
icity
p
r
ice
at
h
o
u
r
t
,
as
d
eter
m
in
ed
b
y
g
r
id
tr
an
s
ac
tio
n
s
.
2
.
3
.
P
r
o
ba
bil
is
t
ic
f
o
re
ca
s
t
mo
del
L
et
̂
+
ℎ
b
e
th
e
p
o
in
t
f
o
r
ec
ast
at
tim
e
t
f
o
r
h
o
r
izo
n
h
.
R
ep
r
esen
t
u
n
ce
r
tain
ty
b
y
a
p
r
ed
i
ctiv
e
d
is
tr
ib
u
tio
n
+
ℎ
(
)
o
r
m
ea
n
+
ℎ
an
d
s
tan
d
ar
d
d
e
v
iatio
n
+
ℎ
.
̂
+
ℎ
=
(
+
ℎ
,
2
+
ℎ
)
,
(
∈
[
+
ℎ
±
∝
2
⁄
+
ℎ
]
)
=
1
−
∝
(
1
4
)
T
h
e
L
STM
to
o
u
t
p
u
t
,
o
r
q
u
an
t
iles
∝
2
⁄
is
th
e
Gau
s
s
ian
v
alu
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
erfo
r
ma
n
ce
o
p
timiz
a
tio
n
o
f h
yb
r
id
r
en
ewa
b
le
en
erg
y
s
ystems
w
ith
…
(
Olu
mu
yiw
a
A
jib
o
la
A
w
o
n
iyi)
1387
2.
4
.
L
o
a
d pro
f
ile
m
o
delin
g
T
h
e
elec
tr
ical
lo
ad
d
em
an
d
was
r
ep
r
esen
ted
as
a
tim
e
-
d
ep
en
d
en
t
f
u
n
ctio
n
s
im
u
latin
g
ty
p
ical
h
o
u
s
eh
o
ld
o
r
in
s
titu
tio
n
al
u
s
e
p
atter
n
s
.
L
o
ad
d
ata
f
ea
tu
r
ed
p
ea
k
d
em
a
n
d
d
u
r
in
g
m
o
r
n
in
g
an
d
ev
e
n
in
g
h
o
u
r
s
,
co
n
s
is
ten
t w
ith
r
ea
l
-
wo
r
ld
en
er
g
y
u
s
e
in
h
ea
lth
ca
r
e
f
ac
ilit
ies.
T
h
e
d
aily
lo
ad
p
r
o
f
ile
was e
it
h
er
m
ea
s
u
r
ed
f
r
o
m
ac
tu
al
f
ac
ilit
ies
o
r
ap
p
r
o
x
im
a
ted
b
ased
o
n
s
tan
d
ar
d
c
o
n
s
u
m
p
tio
n
d
ata
(
e.
g
.
,
lig
h
tin
g
,
r
e
f
r
ig
er
atio
n
,
m
ed
ical
d
ev
ices,
HVAC sy
s
tem
s
)
.
Fig
u
r
e
2
s
h
o
ws
th
e
l
o
ad
p
r
o
f
ile
o
f
th
e
s
tu
d
y
ar
ea
.
Fig
u
r
e
2
.
L
o
ad
p
r
o
f
ile
o
f
th
e
s
tu
d
y
ar
ea
2.
5
.
G
rid
i
nte
g
ra
t
io
n
T
h
e
g
r
i
d
was
m
o
d
eled
as
a
n
in
f
in
itely
a
v
ailab
le
p
o
wer
s
o
u
r
ce
with
a
d
e
f
in
ed
c
o
s
t
f
u
n
ctio
n
an
d
em
is
s
io
n
p
r
o
f
ile.
I
t
s
er
v
e
d
as
a
last
-
r
eso
r
t
en
er
g
y
s
o
u
r
ce
a
ctiv
ated
o
n
ly
w
h
en
r
e
n
ewa
b
l
e
an
d
s
to
r
ed
e
n
er
g
y
wer
e
in
s
u
f
f
icien
t.
Gr
id
u
s
ag
e
was
m
in
im
ized
as
p
ar
t
o
f
t
h
e
s
y
s
tem
’
s
o
b
jectiv
e
to
r
ed
u
ce
r
elian
ce
o
n
f
o
s
s
il
-
b
ased
o
r
ex
p
en
s
iv
e
elec
tr
icity
.
2.
6
.
G
re
y
wo
lf
o
ptim
iza
t
i
o
n
Gr
ey
wo
lf
o
p
tim
izatio
n
(
G
W
O)
is
a
b
io
-
in
s
p
ir
ed
m
etah
eu
r
is
tic
tech
n
iq
u
e
m
o
d
ele
d
o
n
th
e
co
o
p
er
ativ
e
h
u
n
tin
g
s
tr
ateg
y
o
f
g
r
ey
w
o
lv
es.
I
t
h
as
g
ain
ed
s
ig
n
if
ican
t
atten
tio
n
in
o
p
tim
izatio
n
ap
p
licatio
n
s
d
u
e
to
its
s
tr
u
ctu
r
al
s
im
p
licit
y
,
ad
ap
ta
b
ilit
y
,
an
d
s
tr
o
n
g
c
o
n
v
er
g
e
n
ce
ch
ar
ac
te
r
is
tics
.
I
n
th
is
wo
r
k
,
GW
O
is
u
tili
ze
d
to
o
p
tim
ize
th
e
o
p
er
at
io
n
al
p
er
f
o
r
m
an
ce
o
f
t
h
e
h
y
b
r
i
d
en
er
g
y
s
y
s
tem
,
with
p
ar
ticu
l
ar
em
p
h
asis
o
n
th
e
s
ch
ed
u
lin
g
o
f
p
o
wer
f
r
o
m
r
e
n
ewa
b
le
g
en
e
r
atio
n
u
n
its
an
d
en
er
g
y
s
to
r
a
g
e
s
y
s
tem
s
.
T
h
e
o
b
jectiv
e
o
f
th
e
o
p
tim
izatio
n
is
to
r
ed
u
ce
o
v
er
all
o
p
er
atio
n
al
co
s
t
wh
ile
s
atis
f
y
in
g
th
e
f
o
r
ec
asted
lo
ad
d
em
an
d
an
d
m
ain
tain
in
g
ef
f
icien
t
ch
ar
g
e
–
d
is
ch
ar
g
e
co
o
r
d
in
atio
n
o
f
th
e
s
to
r
ag
e
u
n
its
.
T
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
is
g
u
id
ed
b
y
th
e
f
o
llo
win
g
o
b
jectiv
es
:
−
Min
im
izin
g
en
e
r
g
y
co
s
t
:
T
h
e
co
s
t
o
f
en
e
r
g
y
g
e
n
er
atio
n
an
d
s
to
r
ag
e
is
m
in
im
ized
b
y
ef
f
icien
tly
d
is
p
atch
in
g
th
e
a
v
ailab
le
r
en
e
wab
le
en
er
g
y
an
d
o
p
tim
izin
g
t
h
e
u
s
e
o
f
e
n
er
g
y
s
to
r
ag
e
s
y
s
te
m
s
.
−
Min
im
izin
g
en
er
g
y
lo
s
s
es
:
T
h
e
GW
O
alg
o
r
ith
m
en
s
u
r
es
th
at
th
e
en
er
g
y
l
o
s
s
es
d
u
r
in
g
t
r
an
s
m
is
s
io
n
an
d
s
to
r
ag
e
ar
e
m
in
im
ize
d
,
im
p
r
o
v
in
g
th
e
o
v
er
all
s
y
s
tem
ef
f
icien
cy
.
−
Me
etin
g
lo
ad
d
em
a
n
d
:
T
h
e
s
y
s
tem
m
u
s
t
m
ee
t
th
e
f
o
r
ec
asted
lo
ad
d
em
an
d
wh
ile
m
ain
tain
i
n
g
th
e
r
eq
u
ir
ed
r
eliab
ilit
y
an
d
s
tab
ilit
y
.
−
E
n
er
g
y
s
to
r
ag
e
m
a
n
ag
em
e
n
t
:
GW
O
h
elp
s
in
m
an
ag
in
g
t
h
e
en
er
g
y
s
to
r
ag
e
u
n
its
b
y
o
p
tim
izin
g
th
eir
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
cy
cl
es
to
av
o
id
u
n
d
er
c
h
ar
g
in
g
o
r
o
v
er
ch
ar
g
in
g
.
T
h
e
d
ec
is
io
n
v
ar
iab
les
in
cl
u
d
e
th
e
p
o
wer
o
u
tp
u
t
f
r
o
m
ea
ch
r
en
ewa
b
le
s
o
u
r
ce
(
s
o
lar
an
d
win
d
)
an
d
th
e
p
o
wer
in
p
u
t/o
u
tp
u
t
f
r
o
m
e
n
er
g
y
s
to
r
a
g
e
s
y
s
tem
s
.
T
h
e
co
n
s
tr
ain
ts
o
f
th
e
o
p
tim
izatio
n
i
n
clu
d
e
th
e
ca
p
ac
ity
lim
its
o
f
th
e
en
er
g
y
s
o
u
r
ce
s
an
d
s
to
r
ag
e
s
y
s
tem
s
,
as
well
as
th
e
f
o
r
ec
asted
lo
ad
d
em
a
n
d
.
T
h
e
r
ea
l
-
tim
e
f
ea
s
ib
ilit
y
o
f
GW
O
d
ep
en
d
s
o
n
its
p
o
p
u
latio
n
s
ize
an
d
iter
atio
n
co
u
n
t,
wh
ich
in
f
lu
en
ce
co
m
p
u
tatio
n
al
lo
a
d
.
W
ith
ad
ap
tiv
e
p
o
p
u
latio
n
co
n
tr
o
l,
war
m
-
s
tar
t
in
itializatio
n
,
an
d
p
ar
allel
f
itn
ess
ev
alu
atio
n
,
GW
O
ac
h
iev
es
n
ea
r
r
ea
l
-
tim
e
p
er
f
o
r
m
a
n
ce
.
I
ts
O(
N×
D×
T
)
co
m
p
le
x
ity
r
e
m
ain
s
m
an
ag
ea
b
le
f
o
r
o
n
lin
e
HR
E
S
o
p
tim
izatio
n
with
m
o
d
er
ate
d
im
e
n
s
io
n
s
an
d
f
o
r
ec
ast h
o
r
izo
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
1
3
8
2
-
1395
1388
2.
6
.
1
.
G
WO
a
lg
o
rit
hm
i
m
plem
ent
a
t
io
n
T
h
e
GW
O
alg
o
r
ith
m
(
Alg
o
r
ith
m
1
)
f
o
llo
ws a
s
tr
u
ctu
r
ed
s
eq
u
en
ce
o
f
o
p
e
r
atio
n
s
:
−
I
n
itializatio
n
:
T
h
e
p
r
o
ce
s
s
b
eg
in
s
with
th
e
r
an
d
o
m
g
en
er
ati
o
n
o
f
a
p
o
p
u
latio
n
o
f
g
r
e
y
wo
lv
es
with
in
th
e
d
ef
in
ed
s
ea
r
ch
s
p
ac
e,
wh
er
e
e
ac
h
wo
lf
r
e
p
r
esen
ts
a
ca
n
d
id
at
e
s
o
lu
tio
n
to
th
e
o
p
tim
izatio
n
p
r
o
b
lem
.
−
Fit
n
ess
e
v
alu
atio
n
:
E
ac
h
ca
n
d
id
ate
s
o
lu
tio
n
is
ass
ess
ed
u
s
in
g
th
e
d
ef
in
e
d
o
b
jectiv
e
f
u
n
ctio
n
s
,
s
u
ch
as
en
er
g
y
c
o
s
t,
p
o
wer
l
o
s
s
es,
an
d
s
y
s
tem
co
n
s
tr
ain
ts
,
to
d
eter
m
i
n
e
its
s
u
itab
ilit
y
.
−
Po
s
itio
n
u
p
d
ate:
T
h
e
p
o
s
itio
n
s
o
f
t
h
e
wo
lv
es
ar
e
iter
ativ
ely
r
ef
in
ed
b
ased
o
n
th
e
lea
d
in
g
s
o
lu
tio
n
s
,
n
am
ely
th
e
alp
h
a,
b
eta,
a
n
d
d
elta
wo
l
v
es,
wh
ich
g
u
id
e
th
e
s
ea
r
ch
p
r
o
ce
s
s
ac
co
r
d
in
g
to
t
h
e
s
o
cial
h
ier
ar
ch
y
a
n
d
co
o
p
er
ativ
e
h
u
n
tin
g
m
ec
h
an
is
m
.
−
T
er
m
in
atio
n
c
o
n
d
itio
n
:
T
h
e
iter
ativ
e
p
r
o
ce
s
s
co
n
tin
u
es
u
n
til
a
p
r
ed
ef
in
ed
s
to
p
p
in
g
co
n
d
it
io
n
is
s
atis
f
ied
,
s
u
ch
as
r
ea
ch
in
g
t
h
e
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
o
r
ac
h
iev
in
g
c
o
n
v
er
g
en
ce
to
an
o
p
tim
al
o
r
n
ea
r
-
o
p
tim
al
s
o
lu
tio
n
.
Alg
o
r
ith
m
1
.
P
s
eu
d
o
co
d
e
f
o
r
GW
O
I
n
itialize
th
e
g
r
ey
w
o
lf
p
o
p
u
la
tio
n
(
X_
i)
,
wh
e
r
e
(
i =
1
,
2
,
\
d
o
ts
,
n
)
.
Def
in
e
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
(
Ma
x
_
iter
)
.
E
v
alu
ate
th
e
f
itn
ess
o
f
all
ca
n
d
id
ate
s
o
lu
tio
n
s
.
Dete
r
m
in
e
th
e
to
p
t
h
r
ee
s
o
lu
ti
o
n
s
,
d
en
o
ted
as Alp
h
a
(
b
est),
B
eta
(
s
ec
o
n
d
b
est),
an
d
Delta
(
th
ir
d
b
est).
Fo
r
ea
ch
iter
atio
n
(
t =
1
)
to
(
Ma
x
_
iter
)
:
Fo
r
ev
e
r
y
wo
lf
(
X_
i)
:
Fo
r
ea
ch
d
im
en
s
io
n
(
j
)
:
C
o
m
p
u
te
th
e
co
e
f
f
icien
t v
ec
to
r
s
(
A)
a
n
d
(
C
)
.
Up
d
ate
t
h
e
p
o
s
itio
n
o
f
th
e
wo
lf
u
s
in
g
th
e
in
f
lu
e
n
ce
o
f
Alp
h
a,
B
eta,
an
d
Delta
wo
lv
e
s
:
,
=
∝
+
+
3
Up
d
ate
th
e
co
n
tr
o
l p
ar
am
et
er
(
a)
,
d
ec
r
ea
s
in
g
it lin
ea
r
ly
f
r
o
m
2
to
0
.
Re
-
ev
alu
ate
th
e
f
it
n
ess
o
f
all
wo
lv
es.
Up
d
ate
Alp
h
a
,
B
eta,
an
d
De
lta
b
ased
o
n
th
e
n
ew
f
itn
ess
v
a
lu
es.
Af
ter
co
m
p
letin
g
all
iter
atio
n
s
,
r
etu
r
n
th
e
Alp
h
a
wo
l
f
as th
e
o
p
tim
al
s
o
lu
tio
n
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Gr
id
im
p
o
r
t
an
d
ex
p
o
r
t
lev
els
ar
e
p
r
esen
ted
to
illu
s
tr
ate
h
o
w
th
e
s
y
s
tem
ex
ch
a
n
g
es
p
o
wer
with
th
e
u
tili
ty
n
etwo
r
k
to
m
ain
tain
th
e
s
u
p
p
ly
–
d
em
a
n
d
b
ala
n
ce
.
T
h
e
elev
ated
p
h
o
t
o
v
o
ltaic
g
en
er
atio
n
r
esu
lts
f
r
o
m
s
tr
o
n
g
y
ea
r
-
r
o
u
n
d
s
o
lar
av
ail
ab
ilit
y
.
W
in
d
g
en
er
atio
n
r
em
ain
s
r
elativ
ely
s
tab
le
b
ec
au
s
e
o
f
p
er
s
is
ten
t
win
d
p
atter
n
s
th
at
s
u
s
tain
tu
r
b
in
e
o
p
er
atio
n
a
n
d
co
n
tin
u
o
u
s
en
er
g
y
p
r
o
d
u
ctio
n
.
T
h
e
u
tili
ty
g
r
id
f
u
n
ctio
n
s
as
a
b
u
f
f
er
,
tak
in
g
in
s
u
r
p
lu
s
en
e
r
g
y
wh
en
r
e
n
ewa
b
le
o
u
tp
u
t
ex
ce
ed
s
d
em
an
d
an
d
s
u
p
p
ly
i
n
g
elec
tr
icity
wh
en
g
en
er
atio
n
f
alls
s
h
o
r
t.
B
atter
y
s
to
r
ag
e
o
p
er
ates
in
a
lim
ited
s
u
p
p
o
r
t
r
o
le,
m
ai
n
ly
d
u
r
i
n
g
in
ter
v
als
o
f
r
ed
u
ce
d
r
en
ewa
b
le
o
u
t
p
u
t,
to
p
r
eser
v
e
o
v
er
all
s
y
s
tem
r
eliab
ilit
y
.
Fig
u
r
e
3
illu
s
tr
ates
th
e
g
en
er
at
io
n
an
d
allo
ca
tio
n
o
f
p
o
wer
wi
th
in
th
e
r
en
ewa
b
le
e
n
er
g
y
s
y
s
tem
u
n
d
er
th
e
co
n
d
itio
n
wh
er
e
r
en
ewa
b
le
o
u
t
p
u
t
e
x
ce
ed
s
g
r
id
g
en
er
atio
n
(
PR
en
ewa
b
le>
PGr
id
)
.
Du
r
in
g
th
e
r
ain
y
s
ea
s
o
n
,
p
h
o
t
o
v
o
ltaic
o
u
tp
u
t
d
e
clin
es
b
ec
au
s
e
o
f
r
ed
u
ce
d
s
u
n
s
h
in
e
d
u
r
atio
n
a
n
d
lo
we
r
ir
r
a
d
ian
ce
lev
els.
W
in
d
g
en
er
atio
n
also
f
l
u
ctu
ates
with
wea
th
er
co
n
d
itio
n
s
,
y
et
it
p
ar
tially
o
f
f
s
ets
th
e
d
r
o
p
in
P
V
p
r
o
d
u
ctio
n
.
As
a
r
esu
lt,
g
r
id
im
p
o
r
ts
in
cr
ea
s
e
d
u
r
in
g
th
is
in
ter
v
al
to
s
atis
f
y
l
o
ad
r
e
q
u
ir
em
e
n
ts
.
L
o
wer
s
o
la
r
in
s
o
latio
n
d
ir
ec
tly
s
u
p
p
r
ess
es
PV
co
n
tr
ib
u
tio
n
,
wh
ich
m
ak
es
ad
d
itio
n
al
g
r
id
s
u
p
p
o
r
t
n
ec
ess
ar
y
to
co
v
er
th
e
d
em
an
d
.
Var
iatio
n
s
in
win
d
o
u
t
p
u
t
a
r
e
d
r
iv
en
b
y
s
ea
s
o
n
al
atm
o
s
p
h
e
r
ic
ch
a
n
g
es.
C
o
n
s
eq
u
en
tly
,
t
h
e
s
y
s
tem
d
ep
en
d
s
m
o
r
e
o
n
g
r
id
s
u
p
p
ly
d
u
r
in
g
th
ese
lo
w
g
en
er
atio
n
in
ter
v
als,
as
in
d
icate
d
in
Fig
u
r
e
3
.
B
atter
y
s
to
r
ag
e
p
r
o
v
id
es
au
x
iliar
y
s
u
p
p
o
r
t
d
u
r
in
g
p
ea
k
lo
a
d
p
e
r
io
d
s
o
r
wh
en
b
o
th
r
en
ewa
b
le
s
o
u
r
ce
s
d
eliv
er
i
n
s
u
f
f
icie
n
t
p
o
wer
,
th
er
eb
y
m
ain
tain
in
g
co
n
tin
u
ity
o
f
s
u
p
p
ly
.
Fig
u
r
e
4
in
d
icate
s
a
m
o
d
est
r
is
e
in
g
r
id
im
p
o
r
ts
to
o
f
f
s
et
th
e
d
r
o
p
in
PV
g
e
n
er
atio
n
.
I
n
th
e
f
all
s
ea
s
o
n
,
PV
o
u
tp
u
t
d
ec
r
ea
s
es
b
ec
au
s
e
o
f
s
h
o
r
ter
d
ay
lig
h
t
d
u
r
atio
n
a
n
d
l
o
wer
s
u
n
an
g
les,
wh
ich
r
e
d
u
ce
p
an
el
co
n
v
er
s
io
n
ef
f
icien
cy
.
W
in
d
g
en
er
atio
n
r
em
ain
s
an
im
p
o
r
ta
n
t
co
n
tr
ib
u
to
r
b
y
d
eliv
er
in
g
c
o
m
p
ar
ativ
ely
s
tab
le
p
o
wer
.
T
h
e
ad
d
itio
n
al
g
r
id
p
u
r
ch
ases
m
ak
e
u
p
f
o
r
th
e
PV
d
ef
icit
an
d
k
ee
p
d
e
m
an
d
f
u
ll
y
s
u
p
p
lied
.
B
atter
y
s
to
r
ag
e
m
ay
b
e
d
is
p
atch
ed
in
t
er
m
itten
tly
to
h
an
d
le
b
r
ief
s
h
o
r
tag
es,
b
u
t
it
p
lay
s
a
s
u
p
p
o
r
tin
g
r
o
le
r
elativ
e
t
o
th
e
g
r
id
.
PV
r
em
ain
s
th
e
d
o
m
in
an
t
en
er
g
y
co
n
tr
ib
u
to
r
d
u
e
to
a
s
y
s
tem
co
n
f
ig
u
r
atio
n
t
h
at
p
r
io
r
itizes
s
o
lar
r
eso
u
r
ce
u
tili
za
tio
n
.
W
in
d
en
e
r
g
y
,
wh
ile
r
e
p
r
esen
tin
g
a
s
m
al
ler
f
r
ac
tio
n
o
f
to
tal
g
en
er
atio
n
,
o
f
f
er
s
d
e
p
en
d
a
b
le
an
d
c
o
m
p
lem
en
ta
r
y
o
u
tp
u
t,
p
ar
ticu
lar
ly
wh
e
n
s
o
lar
p
r
o
d
u
c
tio
n
wea
k
en
s
.
T
h
e
g
r
id
f
u
n
ctio
n
s
b
id
ir
ec
tio
n
ally
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
erfo
r
ma
n
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o
p
timiz
a
tio
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f h
yb
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id
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(
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jib
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w
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1389
b
o
th
s
u
p
p
l
y
in
g
p
o
wer
d
u
r
in
g
d
ef
icits
an
d
ab
s
o
r
b
in
g
s
u
r
p
lu
s
en
er
g
y
,
t
h
er
eb
y
m
ain
tain
in
g
o
p
er
atio
n
al
s
tab
ilit
y
.
B
atter
y
s
to
r
ag
e
p
r
o
v
id
es
co
n
tin
g
en
cy
s
u
p
p
o
r
t
d
u
r
in
g
ex
tr
em
e
ev
en
ts
o
r
u
n
ex
p
ec
ted
r
e
n
ewa
b
le
s
h
o
r
tf
alls
.
Ov
er
all,
th
e
r
esu
lts
em
p
h
asize
PV
as
th
e
p
r
im
ar
y
en
e
r
g
y
s
o
u
r
ce
in
th
e
h
y
b
r
id
a
r
ch
itectu
r
e
,
with
win
d
s
er
v
in
g
as
a
s
tead
y
au
x
iliar
y
c
o
n
tr
ib
u
to
r
an
d
th
e
g
r
id
e
n
s
u
r
in
g
d
e
m
an
d
s
atis
f
ac
tio
n
wh
en
r
en
e
wab
le
g
en
er
atio
n
is
in
s
u
f
f
icien
t.
Fig
u
r
e
3
.
Po
wer
g
en
er
ate
d
f
r
o
m
th
e
r
en
ewa
b
le
e
n
er
g
y
r
eso
u
r
ce
s
wh
en
P
Renewa
ble
>P
G
rid
Fig
u
r
e
4
.
Po
wer
g
en
er
ate
d
f
r
o
m
th
e
r
en
ewa
b
le
e
n
er
g
y
r
eso
u
r
ce
s
wh
en
P
Renewa
ble
<P
G
rid
B
atter
y
s
to
r
ag
e
s
y
s
tem
s
ar
e
c
en
tr
al
to
th
e
o
p
er
ati
o
n
o
f
HR
E
S
,
ac
tin
g
as
b
u
f
f
er
s
t
h
at
s
tab
ilize
th
e
s
u
p
p
ly
-
d
em
an
d
m
is
m
atch
.
T
h
e
SOC
cu
r
v
e
r
ev
ea
ls
wh
en
t
h
e
b
atter
y
is
ch
ar
g
in
g
(
d
u
r
i
n
g
ex
ce
s
s
g
en
er
atio
n
)
an
d
d
is
ch
ar
g
in
g
(
d
u
r
i
n
g
g
en
e
r
atio
n
d
ef
icits
o
r
p
ea
k
d
em
a
n
d
)
.
A
well
-
b
eh
av
ed
SOC
cu
r
v
e
s
h
o
u
ld
s
h
o
w
a
r
eg
u
lar
ch
ar
g
e
-
d
is
ch
ar
g
e
cy
cl
e
with
o
u
t
r
ea
ch
in
g
d
an
g
er
o
u
s
ly
lo
w
o
r
ex
ce
s
s
iv
ely
h
ig
h
lev
els.
E
x
ce
s
s
iv
ely
lo
w
SOC
v
alu
es m
ay
d
am
ag
e
th
e
b
atter
y
o
r
r
esu
lt in
in
s
u
f
f
icien
t
b
ac
k
u
p
p
o
wer
,
wh
ile
co
n
tin
u
o
u
s
h
ig
h
SOC
co
u
ld
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
6
9
4
I
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t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
2
,
J
u
n
e
20
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6
:
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lead
to
e
n
er
g
y
s
p
illag
e
o
r
cu
r
tailed
g
en
er
atio
n
.
I
d
ea
lly
,
t
h
e
b
atter
y
o
p
er
ates
with
in
a
n
o
p
tim
al
SOC
win
d
o
w
(
e.
g
.
,
2
0
–
9
0
%)
to
e
n
s
u
r
e
lo
n
g
ev
ity
an
d
ef
f
icien
cy
.
Fro
m
th
e
g
r
a
p
h
,
we
ca
n
in
f
e
r
p
er
io
d
s
o
f
en
er
g
y
s
u
r
p
lu
s
(
r
is
in
g
SOC
)
an
d
d
ef
icit
(
f
all
in
g
SOC
)
,
lin
k
in
g
th
em
t
o
th
e
ea
r
lier
d
is
cu
s
s
ed
Fig
u
r
es
3
an
d
4
.
I
f
th
e
SOC
in
cr
ea
s
es
d
u
r
in
g
d
ay
lig
h
t
h
o
u
r
s
,
it
co
n
f
ir
m
s
th
at
th
e
PV
s
y
s
tem
i
s
ef
f
ec
tiv
ely
ch
ar
g
in
g
th
e
b
atter
y
.
A
co
n
s
is
ten
t
d
ec
lin
e
in
SOC
d
u
r
in
g
n
o
n
-
s
o
lar
h
o
u
r
s
in
d
icate
s
p
r
o
p
er
u
tili
za
tio
n
o
f
s
to
r
ed
en
er
g
y
.
T
h
is
b
eh
a
v
io
r
r
ein
f
o
r
ce
s
th
e
n
ee
d
f
o
r
b
atter
y
m
an
ag
em
en
t sy
s
tem
s
(
B
MS)
th
at
ca
n
o
p
tim
ize
ch
a
r
g
e
-
d
is
ch
ar
g
e
cy
cles,
en
s
u
r
e
s
af
ety
lim
its
,
an
d
ex
ten
d
b
atter
y
life
.
Mo
r
eo
v
e
r
,
in
teg
r
atin
g
SOC
m
o
n
ito
r
in
g
with
p
r
ed
ictiv
e
co
n
tr
o
l
ca
n
p
r
ee
m
p
tiv
ely
a
d
ju
s
t lo
ad
s
o
r
g
en
er
atio
n
s
ch
ed
u
les to
m
ain
tai
n
s
y
s
tem
b
alan
ce
.
Fig
u
r
e
5
d
em
o
n
s
tr
ates
th
at
win
d
g
e
n
er
atio
n
r
em
ain
s
s
tab
le
wh
ile
g
r
id
ex
ch
a
n
g
es
ar
e
r
ed
u
ce
d
,
in
d
icatin
g
ef
f
icien
t
u
tili
za
tio
n
o
f
r
en
ewa
b
le
r
eso
u
r
ce
s
to
s
atis
f
y
th
e
lo
ad
d
em
an
d
.
Hig
h
e
r
PV
o
u
tp
u
t
d
u
r
in
g
th
e
d
r
y
s
ea
s
o
n
r
esu
lts
f
r
o
m
ex
ten
d
ed
d
ay
lig
h
t
h
o
u
r
s
an
d
in
cr
ea
s
ed
s
o
lar
elev
atio
n
,
wh
ich
im
p
r
o
v
e
p
an
el
co
n
v
er
s
io
n
p
e
r
f
o
r
m
an
ce
.
W
in
d
p
o
wer
co
n
tin
u
es
to
s
u
p
p
ly
a
d
ep
en
d
ab
le
b
aselin
e
c
o
n
tr
ib
u
tio
n
,
f
u
r
th
er
l
o
w
e
r
i
n
g
t
h
e
r
e
q
u
i
r
e
m
e
n
t
f
o
r
g
r
i
d
i
m
p
o
r
t
s
.
U
n
d
e
r
t
h
es
e
c
o
n
d
i
t
i
o
n
s
,
r
e
n
ew
a
b
l
e
s
o
u
r
c
es
l
a
r
g
ely
m
e
e
t
d
e
m
a
n
d
,
s
o
d
e
p
e
n
d
e
n
c
e
o
n
t
h
e
g
r
i
d
i
s
m
i
n
i
m
i
z
e
d
.
B
at
t
e
r
y
s
t
o
r
a
g
e
p
a
r
t
i
cip
a
t
i
o
n
i
s
l
i
m
it
e
d
b
e
c
a
u
s
e
r
e
n
ew
a
b
l
e
g
en
er
atio
n
is
s
u
f
f
icien
t
f
o
r
m
o
s
t
o
p
er
atin
g
in
ter
v
als.
W
in
d
o
u
tp
u
t
s
tay
s
r
elativ
ely
u
n
if
o
r
m
,
an
d
g
r
i
d
ex
p
o
r
ts
in
cr
ea
s
e,
r
ef
lectin
g
ex
ce
s
s
g
e
n
er
atio
n
d
eliv
er
ed
b
ac
k
to
th
e
u
tili
ty
n
et
wo
r
k
.
Peak
PV
p
r
o
d
u
ctio
n
in
th
e
s
u
m
m
er
p
er
io
d
is
d
r
iv
en
b
y
m
a
x
im
u
m
s
o
lar
e
x
p
o
s
u
r
e
an
d
s
tr
o
n
g
er
ir
r
ad
ian
c
e
lev
els.
W
in
d
en
er
g
y
c
o
m
p
le
m
en
ts
th
is
elev
ate
d
s
o
lar
o
u
tp
u
t
with
s
tead
y
p
r
o
d
u
ctio
n
.
T
h
e
s
u
r
p
l
u
s
en
er
g
y
is
ex
p
o
r
ted
to
th
e
g
r
id
,
im
p
r
o
v
in
g
o
v
er
all
s
y
s
tem
ec
o
n
o
m
ics
an
d
o
p
e
r
atio
n
al
ef
f
icien
cy
.
I
n
th
is
o
p
er
atin
g
r
e
g
im
e,
th
e
g
r
id
ef
f
ec
tiv
ely
a
b
s
o
r
b
s
ex
ce
s
s
p
o
wer
,
wh
ile
b
atter
y
s
to
r
ag
e
r
em
ain
s
m
o
s
tly
id
le
s
in
ce
r
en
ewa
b
le
g
en
er
atio
n
f
u
lly
co
v
er
s
th
e
lo
ad
.
Fig
u
r
e
5
.
E
lectr
ical
lo
a
d
d
em
a
n
d
Fig
u
r
e
6
f
u
r
th
er
ela
b
o
r
ates
o
n
b
atter
y
o
p
er
atio
n
b
y
p
r
esen
tin
g
b
o
t
h
th
e
d
is
ch
ar
g
e
cu
r
r
en
t
an
d
SOC
o
v
er
tim
e.
T
h
e
d
is
ch
ar
g
e
cu
r
r
en
t
cu
r
v
e
p
r
o
v
id
es
a
q
u
an
titativ
e
m
ea
s
u
r
e
o
f
h
o
w
m
u
ch
p
o
wer
th
e
b
atter
y
is
s
u
p
p
ly
in
g
to
th
e
lo
ad
,
wh
ile
th
e
SOC
tr
ac
e
co
m
p
le
m
en
ts
th
is
b
y
s
h
o
win
g
th
e
av
ailab
le
en
er
g
y
.
A
h
ig
h
d
is
ch
ar
g
e
cu
r
r
e
n
t
ty
p
ically
co
r
r
esp
o
n
d
s
with
p
ea
k
d
e
m
an
d
p
er
io
d
s
o
r
tim
es
wh
en
r
en
ew
ab
le
g
en
er
atio
n
is
lo
w.
T
h
is
s
itu
atio
n
d
em
an
d
s
atten
tio
n
b
ec
au
s
e
f
r
eq
u
e
n
t
h
ig
h
-
cu
r
r
en
t
d
is
ch
ar
g
es
ca
n
ac
ce
ler
ate
b
atter
y
d
eg
r
ad
atio
n
,
esp
ec
ially
in
lith
iu
m
-
io
n
c
h
em
is
tr
ies.
T
h
e
s
y
s
tem
m
u
s
t
co
n
tr
o
l
lim
it
d
is
ch
ar
g
e
r
ates
with
in
b
atter
y
s
p
ec
if
icatio
n
s
to
p
r
ev
e
n
t
th
er
m
al
an
d
m
ec
h
a
n
ical
s
tr
ess
.
T
h
e
co
o
r
d
in
atio
n
b
etwe
e
n
d
is
ch
ar
g
e
cu
r
r
en
t
an
d
SOC
also
p
o
in
ts
to
th
e
e
f
f
ec
tiv
en
ess
o
f
th
e
e
n
er
g
y
m
a
n
a
g
em
en
t
s
tr
ateg
y
.
I
f
th
e
b
atter
y
d
is
ch
ar
g
es
h
ea
v
ily
d
u
r
in
g
p
ea
k
lo
ad
an
d
s
till
m
ai
n
tain
s
an
ad
eq
u
ate
SOC
,
it
s
u
g
g
ests
th
at
th
e
b
atter
y
was
w
ell
-
p
r
ep
ar
ed
d
u
r
in
g
o
f
f
-
p
ea
k
p
er
io
d
s
.
On
t
h
e
o
th
er
h
an
d
,
a
r
ap
id
d
r
o
p
in
S
OC
d
u
r
in
g
h
ig
h
d
is
ch
ar
g
e
e
v
en
ts
m
ay
in
d
icate
u
n
d
er
c
h
ar
g
in
g
o
r
o
v
er
s
ized
lo
ad
s
.
T
h
is
f
ig
u
r
e
also
en
ab
les
d
iag
n
o
s
tic
ass
es
s
m
en
t.
Sp
ik
es
i
n
d
is
ch
ar
g
e
cu
r
r
en
t
with
o
u
t
co
r
r
esp
o
n
d
in
g
lo
a
d
d
em
an
d
co
u
l
d
in
d
icate
in
v
er
ter
in
ef
f
icien
cies
o
r
an
o
m
alies
in
s
y
s
tem
b
eh
av
io
r
,
war
r
an
tin
g
f
u
r
t
h
er
in
v
esti
g
atio
n
.
He
n
ce
,
c
o
n
tin
u
o
u
s
m
o
n
it
o
r
in
g
an
d
ad
a
p
tiv
e
c
o
n
tr
o
l
o
f
d
is
ch
ar
g
e
b
e
h
av
io
r
ar
e
cr
u
cial
f
o
r
s
y
s
tem
o
p
tim
iz
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
erfo
r
ma
n
ce
o
p
timiz
a
tio
n
o
f h
yb
r
id
r
en
ewa
b
le
en
erg
y
s
ystems
w
ith
…
(
Olu
mu
yiw
a
A
jib
o
la
A
w
o
n
iyi)
1391
Fig
u
r
e
6
.
Dis
ch
ar
g
e
cu
r
r
e
n
t a
n
d
s
tate
o
f
ch
ar
g
e
3
.
1
.
E
nerg
y
ef
f
iciency
a
nd
co
s
t
s
a
v
ing
s
E
n
er
g
y
e
f
f
icien
cy
is
o
n
e
o
f
th
e
m
o
s
t
cr
itical
f
ac
to
r
s
in
o
p
ti
m
izin
g
HR
E
S.
T
h
e
s
tu
d
y
f
o
u
n
d
th
at
th
e
GW
O
-
b
ased
o
p
tim
izatio
n
m
eth
o
d
,
wh
e
n
co
u
p
led
with
ac
c
u
r
ate
f
o
r
ec
asti
n
g
,
s
ig
n
if
ican
tl
y
im
p
r
o
v
ed
en
e
r
g
y
ef
f
icien
cy
co
m
p
ar
ed
to
c
o
n
v
e
n
tio
n
al
en
er
g
y
m
an
a
g
em
en
t
s
tr
ateg
ies.
B
y
u
s
in
g
p
r
ed
ictiv
e
m
o
d
els
to
an
ticip
ate
f
u
tu
r
e
lo
ad
a
n
d
ir
r
a
d
ian
ce
,
th
e
s
y
s
tem
was
ab
le
to
f
in
e
-
tu
n
e
th
e
en
er
g
y
s
to
r
ag
e
an
d
g
e
n
er
atio
n
p
r
o
ce
s
s
es,
r
ed
u
cin
g
waste
an
d
en
h
an
ci
n
g
th
e
o
v
er
all
p
er
f
o
r
m
an
ce
o
f
th
e
HR
E
S.
T
h
e
ap
p
licatio
n
o
f
th
e
o
p
tim
izatio
n
tech
n
iq
u
e
r
esu
lted
in
a
n
o
tic
ea
b
le
r
ed
u
ctio
n
in
en
er
g
y
co
s
ts
.
T
h
is
co
s
t
-
s
av
in
g
p
o
ten
tia
l
is
cr
u
cial
f
o
r
th
e
ec
o
n
o
m
ic
s
u
s
tain
ab
ilit
y
o
f
H
R
E
S,
esp
ec
ially
in
r
eg
io
n
s
with
h
ig
h
e
n
er
g
y
p
r
ices
o
r
wh
er
e
g
r
i
d
ac
ce
s
s
is
lim
ited
o
r
ex
p
en
s
iv
e.
B
y
o
p
tim
izin
g
th
e
u
s
e
o
f
lo
ca
l
r
e
n
ew
ab
le
r
eso
u
r
ce
s
an
d
en
er
g
y
s
to
r
ag
e,
th
e
s
y
s
tem
is
less
r
elian
t
o
n
ex
p
en
s
iv
e
g
r
i
d
p
o
wer
an
d
n
o
n
-
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
th
u
s
im
p
r
o
v
in
g
th
e
f
in
a
n
cial
f
ea
s
ib
ilit
y
o
f
th
e
en
er
g
y
s
y
s
te
m
.
T
h
e
q
u
a
n
titativ
e
p
er
f
o
r
m
an
ce
r
esu
lts
in
Fig
u
r
e
7
clea
r
ly
d
em
o
n
s
tr
ate
th
at
th
e
p
r
o
p
o
s
ed
GW
O
-
p
r
ed
ictiv
e
o
p
tim
izatio
n
m
o
d
el
o
u
tp
er
f
o
r
m
ed
th
e
b
e
n
ch
m
a
r
k
alg
o
r
ith
m
s
ac
r
o
s
s
all
m
etr
ics.
T
h
e
m
o
d
el
ac
h
iev
ed
t
h
e
lo
w
est
f
o
r
ec
asti
n
g
er
r
o
r
s
,
with
a
MA
E
o
f
0
.
1
1
an
d
R
MSE
o
f
0
.
1
5
,
r
ep
r
esen
tin
g
n
ea
r
ly
5
0
%
im
p
r
o
v
em
e
n
t
o
v
e
r
PS
O
an
d
DE
.
T
h
is
co
n
f
ir
m
s
its
s
u
p
er
io
r
p
r
ed
ictio
n
–
o
p
tim
izatio
n
s
y
n
er
g
y
in
ac
cu
r
ately
m
atch
in
g
lo
a
d
an
d
g
en
e
r
atio
n
p
r
o
f
iles
.
I
n
ter
m
s
o
f
en
er
g
y
u
tili
za
tio
n
,
th
e
s
y
s
tem
ef
f
icien
cy
r
ea
ch
ed
9
7
.
6
%,
s
u
r
p
ass
in
g
PS
O
(
9
2
.
1
%)
an
d
DE
(
9
3
.
0
%),
o
win
g
to
GW
O’
s
ad
a
p
tiv
e
ex
p
l
o
r
atio
n
–
ex
p
lo
itatio
n
m
ec
h
a
n
is
m
th
at
m
in
im
izes
tr
an
s
m
is
s
io
n
lo
s
s
e
s
an
d
cu
r
tailm
en
t.
E
co
n
o
m
ically
,
GW
O
d
eliv
er
ed
a
3
1
.
2
%
r
ed
u
ctio
n
in
to
tal
o
p
e
r
atin
g
co
s
t,
co
m
p
ar
ed
with
2
0
–
2
2
%
f
o
r
th
e
o
th
er
alg
o
r
ith
m
s
,
b
y
o
p
tim
ally
s
ch
ed
u
lin
g
r
e
n
ewa
b
le
an
d
s
to
r
ag
e
r
eso
u
r
ce
s
to
r
ed
u
c
e
g
r
id
d
ep
e
n
d
en
ce
d
u
r
i
n
g
p
ea
k
-
tar
if
f
h
o
u
r
s
.
E
n
v
ir
o
n
m
en
tally
,
it
ac
h
iev
ed
2
6
.
8
%
C
O₂
em
is
s
io
n
r
ed
u
ctio
n
,
h
ig
h
lig
h
tin
g
im
p
r
o
v
ed
r
en
ewa
b
le
p
en
etr
atio
n
an
d
r
e
d
u
ce
d
f
o
s
s
il
g
en
er
ato
r
o
p
er
atio
n
.
M
o
r
eo
v
er
,
th
e
G
W
O
-
p
r
ed
ictiv
e
f
r
am
ew
o
r
k
e
x
h
ib
ited
t
h
e
f
astes
t
co
n
v
er
g
en
ce
,
c
o
m
p
letin
g
o
p
ti
m
izatio
n
in
3
.
1
2
s
,
ab
o
u
t
4
0
%
f
aster
th
an
PS
O
an
d
DE
.
Ov
er
all,
th
ese
m
etr
ics
co
n
f
ir
m
th
at
GW
O
-
p
r
ed
ictiv
e
o
f
f
er
s
a
b
alan
ce
d
,
h
ig
h
-
p
er
f
o
r
m
an
ce
s
o
lu
tio
n
f
o
r
r
ea
l
-
tim
e
h
y
b
r
id
r
en
ewa
b
l
e
en
er
g
y
m
an
ag
em
e
n
t,
p
r
o
v
id
in
g
en
h
an
ce
d
ac
cu
r
ac
y
,
ec
o
n
o
m
i
c
s
av
in
g
s
,
em
is
s
io
n
r
ed
u
ctio
n
,
an
d
co
m
p
u
tatio
n
al
ef
f
icien
cy
ess
en
tial
f
o
r
in
tellig
en
t
m
icr
o
g
r
id
c
o
n
tr
o
l
an
d
s
u
s
tain
ab
le
p
o
wer
s
y
s
tem
o
p
er
at
io
n
.
Fig
u
r
e
8
s
h
o
ws
s
ea
s
o
n
al
tim
e
s
er
ies,
an
d
Fig
u
r
e
9
s
h
o
ws m
o
n
th
ly
en
e
r
g
y
p
r
o
d
u
ctio
n
.
3
.
2
.
I
nfe
re
nce
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
is
n
o
v
el
co
m
p
ar
ed
t
o
ex
is
tin
g
GW
O
-
b
ased
HR
E
S
f
r
am
ewo
r
k
s
b
y
i
n
teg
r
atin
g
r
ea
l
-
tim
e
lo
ad
an
d
ir
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ata,
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ates
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ates
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ates
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le
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b
jectiv
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o
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n
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ad
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tiv
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tim
izatio
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.
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h
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p
r
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ed
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jectiv
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GW
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f
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am
ewo
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ated
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lly
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tim
e,
a
d
ap
tiv
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o
p
tim
izatio
n
th
at
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