I
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rna
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l J
o
urna
l o
f
Appl
ied P
o
wer
E
ng
i
neer
ing
(
I
J
AP
E
)
Vo
l.
14
,
No
.
4
,
Dec
em
b
er
20
25
,
p
p
.
7
8
3
~
7
9
3
I
SS
N:
2252
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8
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.
v
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4
.
i
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.
pp
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793
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:
h
ttp
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//
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p
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M
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bje
ctive e
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ma
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nv
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ntal inde
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d
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d
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lar
e
n
e
rg
y
i
n
re
c
e
n
t
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e
a
rs
h
a
s
b
e
c
o
m
e
m
o
re
wid
e
sp
re
a
d
m
a
in
l
y
.
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th
is
wo
r
k
,
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e
o
f
th
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m
o
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n
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ra
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f
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ll
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telli
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m
s
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a
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iza
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is
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p
ti
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a
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d
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m
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tal
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p
ti
m
iza
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O)
p
ro
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lem
s
o
f
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icro
-
g
rid
(M
G
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p
e
ra
ti
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g
b
y
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n
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b
le
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n
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in
a
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ra
ti
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s
te
m
s
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G
S
).
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p
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s
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a
m
in
e
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s
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s
(W
T),
p
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v
o
lt
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sy
ste
m
s
(P
V),
f
u
e
l
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ll
s
(F
C),
m
icro
tu
rb
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n
e
(M
T),
a
n
d
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l
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tri
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ra
to
r
(DEG
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with
e
n
e
rg
y
sto
ra
g
e
sy
ste
m
s
(ES
S
).
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e
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su
lt
s
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re
p
ro
m
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a
n
d
sh
o
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n
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ro
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t
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h
e
re
su
lt
s
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tai
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re
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re
d
with
so
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s
.
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e
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lt
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o
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t
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E
n
v
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n
m
en
tal
in
d
e
x
o
p
tim
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Mic
r
o
-
g
r
id
s
Op
tim
al
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g
y
m
an
ag
em
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t
Par
ticle
s
war
m
o
p
tim
izatio
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R
en
ewa
b
le
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g
y
s
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s
T
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s
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p
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n
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c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
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-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
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r
:
Ah
m
ed
B
ah
r
i
Dep
ar
tm
en
t o
f
Au
to
m
atics a
n
d
E
lectr
o
m
ec
h
a
n
ics,
Facu
lty
o
f
Scien
ce
an
d
T
ec
h
n
o
lo
g
y
Ma
ter
ials
,
E
n
er
g
y
Sy
s
tem
s
T
e
ch
n
o
lo
g
y
an
d
E
n
v
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o
n
m
en
t L
a
b
o
r
ato
r
y
(
ME
STE
)
,
U
n
iv
er
s
ité
d
e
Gh
ar
d
aia
Gh
ar
d
aia,
Alg
er
ia
E
m
ail:
b
ah
r
i.a
h
m
e
d
@
u
n
iv
-
g
h
ar
d
aia.
ed
u
.
d
z
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
r
is
e
in
elec
tr
icity
d
em
an
d
is
r
elate
d
b
y
p
o
p
u
latio
n
g
r
o
wth
,
d
ig
itizatio
n
,
an
d
in
d
u
s
tr
ial
d
ev
elo
p
m
e
n
t.
R
en
ewa
b
le
en
er
g
y
r
esear
ch
a
n
d
ad
o
p
tio
n
h
av
e
in
cr
ea
s
ed
s
ig
n
if
ican
tl
y
,
esp
ec
ially
win
d
en
er
g
y
[
1
]
.
Ho
wev
e
r
,
th
e
f
lu
c
tu
atio
n
s
o
f
t
h
is
en
er
g
y
d
u
e
to
f
lu
ctu
atin
g
win
d
s
p
ee
d
s
ca
n
a
f
f
ec
t
th
e
q
u
ality
o
f
v
o
ltag
e
an
d
cu
r
r
en
t in
th
e
g
r
id
[
2
]
.
E
s
o
ter
ic
-
f
u
el
p
o
wer
p
lan
ts
ar
e
m
ajo
r
air
p
o
llu
tio
n
s
o
u
r
ce
s
,
em
itti
n
g
h
ar
m
f
u
l
g
ases
f
r
o
m
b
u
r
n
in
g
co
al,
g
as,
an
d
o
il
[
3
]
.
C
o
al
co
m
b
u
s
tio
n
r
elea
s
es
h
ig
h
lev
els
o
f
C
O₂,
SOx
,
an
d
NOx
,
with
em
is
s
io
n
s
v
ar
y
in
g
b
y
f
u
el
ty
p
e
an
d
q
u
ality
[
4
]
,
[
5
]
.
E
n
v
ir
o
n
m
en
tal
co
n
ce
r
n
s
lik
e
p
o
llu
tio
n
a
n
d
g
r
ee
n
h
o
u
s
e
g
ases
h
av
e
d
r
iv
e
n
ef
f
o
r
ts
to
en
h
an
ce
e
n
er
g
y
s
y
s
tem
ef
f
icien
cy
,
lead
in
g
to
v
ar
i
o
u
s
em
is
s
io
n
r
ed
u
ctio
n
s
tr
ateg
ies
[
6
]
.
Fo
llo
win
g
th
e
1
9
9
0
C
lean
Air
Act
am
en
d
m
en
t
an
d
r
is
in
g
en
v
ir
o
n
m
en
t
al
awa
r
en
ess
,
elec
tr
icity
p
r
o
d
u
ce
r
s
wer
e
r
eq
u
ir
ed
to
m
o
d
if
y
th
eir
d
esig
n
s
an
d
s
tr
ateg
ies to
r
ed
u
ce
p
o
wer
p
la
n
t
em
is
s
io
n
s
[
4
]
.
Dis
tr
ib
u
ted
g
en
er
atio
n
(
DG)
h
as
s
tead
ily
g
r
o
wn
o
v
e
r
th
e
p
ast
two
d
ec
ad
es.
Geo
g
r
a
p
h
ical
an
d
m
eteo
r
o
lo
g
ical
f
ac
t
o
r
s
in
f
lu
en
ce
h
o
w
r
en
ewa
b
le
DG
s
o
u
r
ce
s
s
u
ch
as
PV
an
d
W
T
ar
e
in
teg
r
ated
in
m
ain
g
r
i
d
.
W
h
ile
n
o
n
-
r
en
ewa
b
le
s
o
u
r
ce
s
lik
e
f
u
el
ce
lls
(
FC
)
,
m
icr
o
tu
r
b
in
e
(
MT
)
,
an
d
d
iesel
elec
tr
ic
g
en
er
ato
r
(
DE
G
)
p
r
o
v
id
e
s
tab
le
p
o
wer
a
n
d
ca
n
b
e
attac
h
ed
to
a
n
y
p
o
in
t w
ith
i
n
th
e
g
r
i
d
[
6
]
.
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.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
7
8
3
-
793
784
E
f
f
ec
tiv
e
DG
m
an
ag
em
en
t
im
p
r
o
v
es
p
o
wer
q
u
ality
,
r
eliab
ili
ty
,
an
d
ef
f
icien
c
y
wh
ile
r
ed
u
c
in
g
lo
s
s
es
an
d
em
is
s
io
n
s
.
T
h
e
co
n
ce
p
t
o
f
m
icr
o
g
r
id
s
(
MG
s
)
[
2
]
,
[
7
]
is
th
e
co
o
r
d
in
ated
o
p
er
atio
n
a
n
d
co
n
tr
o
l
o
f
s
to
r
a
g
e
d
ev
ices
an
d
co
n
tr
o
llab
le
lo
ad
s
.
T
h
e
latter
ca
n
o
p
er
ate
in
d
e
p
en
d
en
tly
o
r
with
t
h
e
m
ai
n
g
r
i
d
[
8
]
.
E
n
s
u
r
in
g
MG
s
tab
ilit
y
with
v
ar
y
in
g
lo
a
d
s
p
r
ev
en
ts
v
o
ltag
e
d
is
tu
r
b
a
n
ce
s
at
th
e
p
o
in
t
o
f
c
o
m
m
o
n
c
o
u
p
lin
g
(
PC
C
)
[
9
]
.
As
a
r
esil
ien
t a
n
d
in
tellig
en
t e
n
er
g
y
s
o
lu
tio
n
,
MG
s
ar
e
k
ey
to
m
o
d
er
n
p
o
wer
s
y
s
tem
s
[
1
0
]
.
Mic
r
o
g
r
id
s
ar
e
ce
n
tr
al
to
m
o
d
er
n
p
o
wer
d
is
tr
ib
u
tio
n
n
etw
o
r
k
s
.
I
n
te
g
r
atin
g
R
E
S
in
MG
s
an
d
th
e
m
ain
g
r
id
o
p
tim
izes
s
y
s
tem
p
er
f
o
r
m
an
ce
,
e
n
h
an
cin
g
p
r
o
f
itab
ilit
y
an
d
r
ed
u
cin
g
d
ep
en
d
en
ce
o
n
th
e
m
ain
n
etwo
r
k
[
1
1
]
,
[
1
2
]
.
E
n
er
g
y
m
an
ag
em
en
t
aim
s
to
m
a
x
im
i
ze
ef
f
icien
cy
an
d
m
in
im
ize
l
o
s
s
es,
m
ak
in
g
it
a
co
m
p
lex
o
p
tim
izatio
n
c
h
allen
g
e
with
co
n
s
tr
ain
ts
.
Nu
m
er
o
u
s
m
ath
em
atica
l
an
d
ar
tific
ial
in
tellig
en
ce
-
b
ased
m
eth
o
d
s
h
av
e
b
ee
n
u
s
ed
to
a
d
d
r
ess
E
MO
an
d
en
v
ir
o
n
m
e
n
tal
in
d
ex
o
p
tim
izatio
n
(
E
I
O
)
ch
al
len
g
es.
R
ec
en
tly
,
p
o
p
u
latio
n
-
b
ased
m
eth
o
d
s
an
d
ev
o
lu
ti
o
n
ar
y
alg
o
r
i
th
m
s
h
av
e
b
ee
n
wid
ely
u
s
ed
f
o
r
o
p
tim
al
en
er
g
y
m
an
a
g
em
en
t
(
OE
M
)
o
p
tim
izatio
n
.
Gen
etic
alg
o
r
ith
m
s
(
GA)
ar
e
f
r
eq
u
en
tly
e
m
p
l
o
y
ed
,
as
h
ig
h
lig
h
ted
in
[
1
3
]
,
wh
ile
ev
o
l
u
tio
n
ar
y
p
r
o
g
r
a
m
m
in
g
a
n
d
d
if
f
er
e
n
tial
e
v
o
l
u
t
i
o
n
(
D
E
)
p
r
o
p
o
s
e
d
i
n
[
1
4
]
a
n
d
[
1
5
]
a
r
e
d
e
v
e
l
o
p
e
d
t
o
i
m
p
r
o
v
e
t
h
e
p
e
r
f
o
r
m
a
n
c
e
o
f
O
E
M
.
S
i
m
i
l
a
r
l
y
,
b
ac
k
t
r
a
c
k
i
n
g
s
ea
r
c
h
o
p
t
i
m
iz
a
t
i
o
n
(
B
T
A
)
w
a
s
a
p
p
l
i
ed
i
n
[
1
6
]
f
o
r
t
h
e
s
a
m
e
p
u
r
p
o
s
e
.
Swar
m
in
tellig
en
ce
m
et
h
o
d
s
h
av
e
b
ee
n
ap
p
lied
to
o
p
tim
al
e
n
er
g
y
m
an
a
g
em
en
t.
P
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PSO
)
[
1
0
]
,
[
1
7
]
,
ar
tific
ial
b
ee
co
lo
n
y
(
AB
C
)
[
1
8
]
,
a
n
d
a
n
t
co
lo
n
y
o
p
tim
izatio
n
(
AC
O)
[
1
9
]
aim
to
m
in
im
ize
t
h
e
en
er
g
y
m
an
a
g
em
en
t in
MG
an
d
d
is
tr
ib
u
te
d
n
etwo
r
k
s
.
Ph
y
s
ic
al
al
g
o
r
i
th
m
s
s
u
c
h
as g
r
av
i
tat
io
n
al
s
ea
r
c
h
a
lg
o
r
it
h
m
s
(
GSA)
[
2
0
]
,
[
2
1
]
,
b
la
ck
h
o
l
e
o
p
tim
i
za
t
i
o
n
(
B
HO
)
[
2
2
]
,
a
n
d
wi
n
d
-
d
r
i
v
e
n
o
p
ti
m
i
za
t
io
n
(
W
DO
)
[
2
3
]
al
s
o
t
ar
g
et
O
E
M
in
el
ec
tr
i
ca
l
m
ic
r
o
-
g
r
i
d
.
Natu
r
e
-
in
s
p
ir
ed
an
d
b
io
-
in
s
p
ir
e
d
m
et
h
o
d
s
,
in
clu
d
in
g
f
ir
e
f
ly
alg
o
r
ith
m
(
FF
A)
[
2
4
]
,
[
2
5
]
,
g
r
ey
wo
lf
o
p
tim
izatio
n
[
2
6
]
,
[
2
7
]
,
b
ac
ter
ial
f
o
r
a
g
in
g
[
2
8
]
,
cu
ck
o
o
s
ea
r
c
h
[
2
9
]
,
s
h
u
f
f
led
f
r
o
g
-
leap
i
n
g
al
g
o
r
ith
m
[
3
0
]
,
an
d
m
o
th
-
s
war
m
alg
o
r
ith
m
[
3
1
]
,
ar
e
u
s
ed
f
o
r
o
p
tim
al
en
er
g
y
m
a
n
ag
em
e
n
t.
I
n
th
is
wo
r
k
,
th
e
PS
O
ap
p
r
o
ac
h
is
u
s
ed
to
s
o
lv
e
th
e
OE
M
an
d
E
I
O
p
r
o
b
lem
s
.
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
T
h
e
OE
M
an
d
th
e
E
I
O
p
r
o
b
lem
s
,
g
en
er
ally
e
x
p
r
ess
ed
as
(
1
)
-
(
4
)
[
2
7
]
.
T
h
ese
f
o
r
m
u
latio
n
s
r
ep
r
esen
t
th
e
s
tan
d
ar
d
e
x
p
r
ess
io
n
s
f
o
r
b
o
th
p
r
o
b
lem
s
.
(
,
)
(
1
)
Su
b
ject
to
(
2
)
-
(
4
)
.
ℎ
(
,
)
=
0
(
2
)
(
,
)
≤
0
(
3
)
≤
x
≤
an
d
≤
u
≤
(
4
)
(
,
)
is
th
e
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
e
co
n
s
tr
ain
ts
ar
e
d
en
o
ted
as
ℎ
(
,
)
f
o
r
eq
u
ality
an
d
(
,
)
f
o
r
in
eq
u
ality
.
T
h
e
s
tate
an
d
co
n
tr
o
l v
ar
iab
les ar
e
r
esp
ec
tiv
el
y
,
an
d
.
2
.
1
.
O
bje
c
t
iv
e
f
un
ct
io
ns
2
.
1
.
1
.
E
nv
iro
nm
ent
a
l index
o
ptim
iza
t
io
n
Gen
er
ally
,
th
e
E
I
O
p
r
o
b
lem
ca
n
b
e
e
x
p
r
ess
ed
as
(
5
)
.
I
t
s
h
o
ws
th
e
g
en
e
r
al
f
o
r
m
u
latio
n
u
s
ed
in
th
e
liter
atu
r
e.
(
,
)
=
∑
10
−
2
(
=
1
+
+
2
)
+
e
xp
(
)
(
5
)
α
i
,
β
i
,
γ
i
,
ζ
i
,
an
d
λ
i
ar
e
th
e
em
is
s
io
n
co
ef
f
icien
ts
o
f
g
en
er
ato
r
i
.
Hen
ce
,
an
d
ca
n
b
e
ex
p
r
ess
ed
as g
iv
en
in
(
6
)
an
d
(
7
)
,
r
esp
ec
tiv
ely
.
=
{
1
,
|
|
,
…
|
|
,
+
1
,
…
,
1
,
…
}
(
6
)
T
h
e
s
ch
ed
u
led
ac
tiv
e
p
o
wer
at
s
lack
b
u
s
,
th
e
r
ea
ctiv
e
p
o
wer
s
ch
ed
u
led
b
y
all
g
en
er
at
o
r
s
,
th
e
m
ag
n
itu
d
e
v
o
ltag
e
o
f
all
lo
ad
b
u
s
es
,
an
d
th
e
ap
p
a
r
en
t
p
o
wer
f
lo
w
i
n
all
lin
es
ar
e
r
ep
r
esen
ted
,
r
esp
ec
ti
v
ely
,
b
y
,
,
,
an
d
S
i
.
T
h
e
to
tal
n
u
m
b
er
o
f
g
e
n
er
ato
r
s
,
o
f
l
o
ad
b
u
s
es
,
an
d
b
r
an
ch
es
ar
e,
r
esp
ec
tiv
ely
,
d
en
o
ted
b
y
,
,
an
d
.
T
h
e
co
n
tr
o
l v
a
r
iab
le
v
ec
to
r
is
p
r
esen
ted
as
(
7
)
[
2
5
]
,
[
2
7
]
.
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
Mu
lti
-
o
b
jective
en
erg
y
ma
n
a
g
eme
n
t a
n
d
e
n
viro
n
men
ta
l in
d
e
x
o
p
timiz
a
tio
n
o
f
…
(
A
h
med
B
a
h
r
i
)
785
=
{
2
,
…
,
|
1
|
,
…
|
|
,
1
,
…
,
1
,
…
}
(
7
)
T
h
e
ac
tiv
e
p
o
wer
g
e
n
er
atio
n
ex
clu
d
in
g
s
lack
b
u
s
,
th
e
m
ag
n
itu
d
es
v
o
ltag
es
o
f
g
en
er
a
to
r
s
,
th
e
r
atio
n
o
f
tr
an
s
f
o
r
m
er
s
,
an
d
th
e
co
m
p
e
n
s
ated
r
ea
ctiv
e
p
o
wer
a
r
e
d
e
n
o
ted
,
r
esp
ec
tiv
ely
,
b
y
,
,
T
,
an
d
.
T
h
e
tr
an
s
f
o
r
m
er
s
an
d
co
m
p
en
s
ato
r
s
n
u
m
b
er
s
ar
e
n
o
ted
,
r
esp
ec
tiv
ely
b
y
an
d
.
−
E
q
u
ality
co
n
s
tr
ain
ts
T
h
e
n
o
n
lin
ea
r
lo
a
d
f
lo
w
eq
u
a
tio
n
s
ar
e
p
r
esen
ted
as
eq
u
alit
y
co
n
s
tr
ain
ts
as
g
iv
en
in
(
8
)
.
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
g
e
n
er
atio
n
s
,
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
in
jectio
n
s
,
an
d
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
lo
ad
s
ar
e
p
r
esen
ted
,
r
esp
ec
tiv
e
ly
,
by
an
d
,
,
,
an
d
.
{
=
+
−
=
+
(
8
)
−
E
q
u
ality
co
n
s
tr
ain
ts
T
h
e
in
eq
u
ality
c
o
n
s
tr
ain
ts
ar
e
p
r
esen
ted
b
y
(
9
)
-
(
1
3
)
[
2
5
]
.
Her
e,
is
th
e
m
ax
im
u
m
ap
p
ar
en
t
p
o
wer
ex
c
h
an
g
e
b
etwe
en
b
u
s
es
i
an
d
j
.
≤
≤
and
≤
≤
wh
er
e
=
1
,
…
,
(
9
)
≤
≤
an
d
≤
≤
wh
er
e
=
1
,
…
,
(
1
0
)
≤
≤
wh
er
e
=
1
,
…
,
(
11
)
≤
≤
wh
er
e
=
1
,
…
,
(
12
)
≤
wh
er
e
=
=
1
,
…
,
(
1
3
)
2
.
1
.
2
.
E
nerg
y
m
a
na
g
em
ent
o
ptim
iza
t
io
n
T
h
e
OE
M
p
r
o
b
lem
is
d
ef
in
e
d
in
th
is
s
tu
d
y
b
ased
o
n
th
e
f
ir
s
t
m
ar
k
et
p
o
licy
,
an
d
th
e
p
r
im
a
r
y
g
o
al
o
f
OE
M
is
to
r
ed
u
ce
th
e
MG
'
s
o
p
er
atio
n
al
ex
p
e
n
s
es,
th
o
u
g
h
ad
d
itio
n
al
g
o
als
ca
n
b
e
in
clu
d
ed
.
T
h
e
OE
M
p
r
o
b
lem
g
en
er
ally
ca
n
b
e
ex
p
r
ess
ed
as g
iv
en
in
(
1
4
)
.
min
(
,
)
=
∑
(
,
)
=
=
1
∑
∑
[
(
)
+
]
=
1
=
1
(
1
4
)
W
h
er
e
(
,
)
is
th
e
co
s
t
f
u
n
ctio
n
th
r
o
u
g
h
o
u
t
th
e
p
lan
n
in
g
h
o
r
iz
o
n
.
T
h
e
ac
tiv
e
p
o
we
r
ex
ch
a
n
g
ed
with
th
e
g
r
id
at
tim
e
t
is
d
en
o
ted
b
y
.
NT
an
d
N
G
ar
e
th
e
to
tal
co
u
n
t
o
f
tim
e
a
n
d
DGs,
in
cl
u
d
in
g
s
to
r
ag
e;
,
(
)
,
an
d
ar
e,
r
esp
ec
tiv
ely
,
th
e
ac
tiv
e
p
o
wer
o
u
tp
u
t,
t
h
e
b
id
o
f
i
th
DG
,
an
d
th
e
elec
tr
ic
ity
ex
ch
an
g
e
p
r
ice
b
etwe
en
th
e
MG
an
d
g
r
id
at
tim
e
t
[
3
2
]
,
[
3
3
]
.
T
h
e
s
tate
an
d
co
n
tr
o
l
v
ar
iab
les,
x
an
d
u
,
ar
e
d
ef
in
ed
as
(
1
5
)
a
n
d
(
1
6
)
.
=
≤
(
1
5
)
=
[
1
,
2
,
…
,
]
(
1
6
)
−
C
o
n
s
tr
ain
ts
i)
C
o
n
s
tr
ain
t o
f
b
alan
ce
p
o
wer
(
C
B
P)
T
h
e
p
o
wer
b
alan
ce
c
o
n
s
tr
ain
t
,
w
h
en
th
e
a
ctiv
e
lo
s
s
in
th
e
MG
is
ig
n
o
r
ed
,
is
r
e
p
r
esen
te
d
as
(
1
7
)
.
Her
e,
ND
r
ep
r
esen
ts
th
e
to
tal
lo
ad
lev
els an
d
is
th
e
ten
th
lo
a
d
lev
el'
s
q
u
an
tity
.
∑
=
1
+
=
∑
=
1
(
1
7
)
ii)
C
o
n
s
tr
ain
ts
o
f
p
o
wer
g
e
n
er
ati
o
n
ca
p
ac
ity
(
C
PGC
)
T
h
e
a
cti
v
e
p
o
we
r
o
u
t
p
u
t
li
m
i
ts
f
o
r
e
v
er
y
DG
i
n
t
h
e
MG
a
r
e
p
r
es
en
te
d
as
(
1
8
)
an
d
(
1
9
)
.
−
,
−
,
−
,
a
n
d
−
a
r
e
,
r
e
s
p
e
c
ti
v
e
l
y
,
t
h
e
DG
a
n
d
u
t
i
l
it
y
a
c
t
i
v
e
p
o
we
r
l
i
m
its
a
t
ti
m
e
t
.
−
≤
≤
−
(
1
8
)
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.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
7
8
3
-
793
786
−
≤
≤
−
(1
9)
iii)
C
o
n
s
tr
ain
ts
o
f
s
p
in
n
in
g
r
eser
v
e
(
C
SR
)
Du
e
to
lo
ad
an
d
r
en
ewa
b
le
e
n
er
g
y
f
lu
ct
u
atio
n
s
,
SC
is
im
p
o
r
tan
t
to
m
ain
tain
s
y
s
tem
r
eliab
ilit
y
.
Fo
r
th
is
,
th
e
co
n
s
tr
ain
t lis
ted
in
(
2
0
)
m
u
s
t b
e
s
atis
f
ied
[
3
3
]
.
is
t
h
e
r
es
er
v
e
s
p
i
n
n
in
g
at
t
im
e
t
.
−
−
−
=
∑
+
=
1
(
2
0
)
iv
)
L
im
its
o
f
en
er
g
y
s
to
r
ag
e
(
L
E
S)
T
h
e
(
2
1
)
r
ep
r
esen
ts
th
e
co
n
s
t
r
ain
ts
f
o
r
a
ty
p
ical
b
atter
y
d
u
r
in
g
ea
c
h
tim
e
p
er
io
d
t
[
3
2
]
.
_
an
d
_
−
1
d
en
o
te
b
atter
y
ca
p
ac
ity
.
T
h
e
p
er
m
itted
c
h
ar
g
e/d
is
ch
ar
g
e
r
ate
f
o
r
is
ℎ
(
ℎ
)
,
_
,
a
n
d
_
ar
e
t
h
e
s
to
r
ag
e
lim
its
.
T
h
e
ch
ar
g
e/d
is
ch
ar
g
e
r
ate
p
er
an
d
b
atter
y
ef
f
icien
cy
a
r
e
d
en
o
ted
b
y
ℎ
−
_
ℎ
_
an
d
ℎ
(
ℎ
)
.
_
=
−
1
+
ℎ
ℎ
∆
−
ℎ
ℎ
∆
(
2
1
)
ℎ
{
=
−
1
ℎ
_
≤
ℎ
_
ℎ
_
≤
ℎ
_
v)
Activ
e
p
o
wer
ca
lcu
latio
n
f
o
r
g
r
id
ex
ch
a
n
g
e
Acti
v
e
p
o
we
r
e
x
ch
a
n
g
e
is
t
r
e
a
ted
as
a
d
e
p
e
n
d
e
n
t
v
a
r
i
a
b
le
,
w
ith
g
r
i
d
p
o
w
er
d
e
te
r
m
in
e
d
b
y
(
2
2
)
.
is
ch
ec
k
ed
wh
eth
er
it satis
f
ies
co
n
s
tr
ain
t (
1
9
)
o
r
n
o
t.
T
h
u
s
,
th
e
v
ar
iab
le
_
is
d
ef
in
ed
as
(
2
3
)
.
=
∑
−
=
1
∑
=
1
(
2
2
)
_
=
{
_
>
_
_
<
_
_
≤
<
_
(
2
3
)
T
h
e
n
ew
o
b
jec
ti
v
e
f
u
n
ct
io
n
t
o
b
e
o
p
t
im
ize
d
a
f
te
r
a
d
d
e
d
t
h
e
d
ep
e
n
d
e
n
t
v
a
r
i
a
b
le
,
i
.
e
.
,
as
a
q
u
ad
r
a
tic
p
e
n
a
lt
y
t
e
r
m
is
d
ef
in
e
d
as
(
2
4
)
.
Her
e,
r
ep
r
esen
t th
e
p
en
alty
f
ac
to
r
.
=
∑
(
,
)
+
=
1
(
−
_
)
2
(
2
4
)
−
Dis
tr
ib
u
ted
g
en
er
atio
n
b
id
ca
l
cu
latio
n
As
p
e
r
(
2
5
)
,
D
G
b
i
d
s
a
r
e
q
u
ad
r
atic
.
T
h
e
y
ca
n
b
e
e
x
p
r
ess
e
d
as
:
=
2
+
+
(
2
5
)
i)
Fu
el
ce
ll a
n
d
m
icr
o
-
tu
r
b
in
e
T
h
e
b
i
d
s
o
f
FC
a
n
d
MT
i
n
(
$
/
h
)
ar
e
d
ete
r
m
in
e
d
as
(
2
6
)
[
3
4
]
.
I
t r
ep
r
esen
ts
th
eir
b
id
d
in
g
f
o
r
m
u
latio
n
.
=
+
(
2
6
)
is
th
e
elec
tr
ical
p
o
wer
s
u
p
p
lied
b
y
DGs
(
MT
o
r
FC
)
in
(
k
W
)
,
an
d
ar
e
th
e
ef
f
icien
cy
a
n
d
th
e
DG
f
u
el
(
g
as)
p
r
ice
(
$
/
k
W
h
)
.
r
ep
r
esen
ts
th
e
h
o
u
r
ly
r
ate
(
$
/h
)
.
=
_
=
(
+
1
)
(
+
1
)
−
1
(
2
7
)
T
h
e
i
n
s
t
all
ati
o
n
c
o
s
t
of
DG
is
r
e
p
r
es
en
te
d
b
y
IC
,
n
a
n
d
i
ar
e
t
h
e
a
m
o
r
ti
za
ti
o
n
p
e
r
i
o
d
(
y
e
a
r
s
)
,
an
d
th
e
i
n
te
r
est
r
at
e,
r
es
p
e
cti
v
e
ly
.
ii)
Ph
o
to
v
o
ltaic
an
d
w
in
d
tu
r
b
in
e
s
W
T
a
n
d
P
V
b
i
d
s
c
o
n
s
id
e
r
A
P
(
k
W
h
/
k
W
)
a
n
d
AC
(
$
/
k
W
)
r
ep
r
esen
te
d
b
y
(
2
7
)
.
T
h
es
e
s
o
u
r
ce
s
a
r
e
u
n
c
o
n
tr
o
l
la
b
le
,
r
el
y
i
n
g
o
n
p
r
i
m
a
r
y
s
o
u
r
ce
a
v
ail
ab
ilit
y
.
T
h
e
PV
o
u
tp
u
t
p
o
we
r
d
e
p
e
n
d
s
o
n
s
o
la
r
ir
r
a
d
i
ati
o
n
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Mu
lti
-
o
b
jective
en
erg
y
ma
n
a
g
eme
n
t a
n
d
e
n
viro
n
men
ta
l in
d
e
x
o
p
timiz
a
tio
n
o
f
…
(
A
h
med
B
a
h
r
i
)
787
am
b
ie
n
t
te
m
p
e
r
a
tu
r
e
,
an
d
c
h
a
r
a
cte
r
is
tics
o
f
m
o
d
u
l
e.
T
h
e
(
2
8
)
is
u
s
e
d
t
o
ca
l
c
u
la
te
t
h
e
PV
o
u
tp
u
t
p
o
wer
[
3
4
]
-
[
3
7
]
.
=
1000
[
1
+
(
−
25
)
]
(
2
8
)
is
t
h
e
PV
m
ax
im
u
m
p
o
w
er
u
n
d
e
r
STC
i
n
(
W
)
;
is
th
e
s
o
la
r
ir
r
a
d
i
ati
o
n
o
f
P
V
in
(
W
/m
2
)
;
an
d
is
t
h
e
PV
m
o
d
u
l
e
te
m
p
er
at
u
r
e
c
o
e
f
f
ic
ie
n
t
f
o
r
p
o
we
r
i
n
(
°C
-
1
)
.
T
h
e
te
m
p
e
r
a
tu
r
e
o
f
PV
ce
ll
i
n
(
C
)
,
is
d
e
n
o
te
d
b
y
C
T
an
d
d
et
e
r
m
i
n
ed
b
y
t
h
e
m
o
d
u
l
e'
s
n
o
m
i
n
al
o
p
er
ati
n
g
ce
ll
te
m
p
e
r
at
u
r
e
(
NOCT
)
[
3
2
]
,
[
3
4
]
g
iv
e
n
b
y
(
2
9
)
.
=
+
800
(
−
20
)
(
2
9
)
an
d
ar
e,
r
esp
ec
tiv
ely
,
th
e
a
m
b
ien
t
tem
p
er
atu
r
e
an
d
t
h
e
m
o
d
u
le'
s
NO
C
T
(
°C
)
.
As
p
e
r
[
3
3
]
,
[
3
4
]
,
t
h
e
WT
p
o
w
er
c
u
r
v
e
is
p
r
es
en
te
d
b
y
(
3
0
)
.
=
{
0
≤
≥
2
−
2
2
−
2
_
<
≤
<
≤
(
3
0
)
_
a
n
d
a
r
e
t
h
e
o
u
t
p
u
t
p
o
w
er
a
n
d
r
a
te
d
p
o
we
r
o
f
WT
.
,
,
an
d
a
r
e
,
r
esp
ec
t
iv
el
y
,
th
e
r
at
e
d
win
d
s
p
ee
d
,
s
wit
c
h
-
i
n
win
d
s
p
ee
d
,
a
n
d
s
wi
tc
h
-
on
win
d
s
p
ee
d
o
f
WT
[
3
3
]
.
iii)
Diesel e
lectr
ic
g
en
er
ato
r
s
(
DE
G)
T
h
e
D
E
G
f
u
el
c
o
n
s
u
m
p
ti
o
n
ca
n
b
e
m
o
d
el
ed
as
a
q
u
ad
r
at
ic
f
u
n
ct
io
n
i
n
(
3
1
)
.
is
f
u
el
co
n
s
u
m
p
t
io
n
(
L
/
h
)
;
is
DE
G
o
u
t
p
u
t
p
o
we
r
(
k
W
)
;
a
n
d
,
,
a
n
d
a
r
e
f
u
el
c
o
n
s
u
m
p
t
io
n
c
o
e
f
f
ici
en
ts
.
DE
G
b
id
s
(
$
/h
)
a
r
e
c
alc
u
l
ate
d
as
(
3
2
)
.
=
2
+
+
(
3
1
)
=
+
(
3
2
)
W
h
e
r
e
,
is
t
h
e
d
iese
l
f
u
el
p
r
ic
e
in
(
$
/
L
)
.
is
t
h
e
i
n
v
est
m
e
n
t
co
s
t
d
et
er
m
i
n
e
d
b
y
(
2
7
)
.
iv
)
E
lectr
ic
g
r
id
T
h
e
e
n
er
g
y
m
a
r
k
et
c
o
s
ts
(
$
/
h
)
ar
e
r
e
p
r
ese
n
t
e
d
b
y
t
h
e
f
o
ll
o
w
in
g
q
u
a
d
r
ati
c
f
u
n
cti
o
n
.
r
ep
r
esen
t
th
e
elec
tr
ic
p
o
wer
(
k
W
)
,
w
h
ile
a
,
b
,
an
d
c
ar
e
co
s
t c
o
e
f
f
icien
ts
.
=
+
+
2
(
3
3
)
3.
P
ARTI
C
L
E
SWA
RM
O
P
T
I
M
I
Z
AT
I
O
N
PS
O,
d
ev
elo
p
ed
b
y
Ken
n
ed
y
an
d
E
b
er
h
a
r
t
[
3
8
]
,
is
an
ev
o
lu
tio
n
ar
y
o
p
tim
izatio
n
m
eth
o
d
i
n
s
p
ir
ed
b
y
th
e
m
o
v
em
en
t
o
f
b
ir
d
f
lo
ck
s
an
d
f
is
h
s
ch
o
o
ls
.
I
t
u
s
es
a
s
war
m
o
f
p
ar
ticles
th
at
ex
p
lo
r
e
a
s
ea
r
ch
s
p
ac
e,
ad
ju
s
tin
g
p
o
s
itio
n
s
b
ased
o
n
p
er
s
o
n
al
an
d
n
eig
h
b
o
r
ex
p
er
i
en
ce
s
to
f
in
d
th
e
o
p
tim
al
s
o
lu
tio
n
in
n
o
n
lin
ea
r
s
y
s
tem
s
[
3
9
]
.
I
n
PS
O,
p
ar
ticles
n
av
ig
ate
a
m
u
ltid
im
en
s
io
n
al
s
p
ac
e,
an
d
t
h
e
m
o
v
em
e
n
t
o
p
tim
izatio
n
is
in
f
lu
en
ce
d
b
y
p
ast
b
est
p
o
s
itio
n
s
an
d
th
e
s
war
m
'
s
co
llectiv
e
h
is
to
r
y
[
4
0
]
,
[
4
1
]
.
E
ac
h
p
ar
ticle'
s
b
est
p
ast
p
o
s
itio
n
is
r
ec
o
r
d
e
d
an
d
d
en
o
ted
as
p
b
e
s
t
,
wh
ile
am
o
n
g
all
th
e
p
ar
ticles,
t
h
e
b
est
p
ar
ticle
p
o
s
itio
n
is
r
ep
r
esen
ted
as
.
T
h
e
v
elo
city
an
d
p
o
s
itio
n
ar
e
u
p
d
ated
ac
co
r
d
i
n
g
ly
u
s
in
g
(
3
4
)
an
d
(
3
5
)
,
r
esp
ec
tiv
ely
.
(
+
1
)
=
(
.
(
)
+
1
.
(
−
(
)
)
+
2
2
.
(
−
(
)
)
)
(
3
4
)
(
+
1
)
=
(
)
+
(
+
1
)
∀
=
1
,
2
,
3
,
…
,
(
3
5
)
T
h
e
cu
r
r
en
t
p
o
s
itio
n
an
d
p
ar
ti
cle
v
elo
city
o
f
at
th
e
ℎ
g
en
er
atio
n
ar
e
r
ep
r
esen
ted
,
r
esp
ec
tiv
ely
,
b
y
an
d
.
w
,
1
an
d
2
ar
e
in
er
tia
we
ig
h
t
f
ac
to
r
an
d
th
e
ac
ce
ler
ati
o
n
co
n
s
tan
ts
,
wh
ile,
an
d
ar
e
th
e
n
u
m
b
er
o
f
s
war
m
s
,
an
d
r
an
d
o
m
n
u
m
b
er
s
b
etwe
en
0
an
d
1
.
Gen
er
ally
,
ww
is
ex
p
r
ess
ed
as
(
3
6
)
[
4
1
]
-
[
4
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
7
8
3
-
793
788
=
−
−
.
(
3
6
)
Her
e,
an
d
r
ep
r
esen
t
th
e
cu
r
r
en
t
an
d
m
a
x
im
u
m
iter
atio
n
s
,
wh
ile
an
d
d
ef
in
e
th
e
weig
h
t
lim
its
[
4
1
]
-
[
4
3
]
.
K
is
a
co
n
s
tr
ictio
n
f
ac
to
r
en
s
u
r
in
g
co
n
v
er
g
en
ce
with
o
u
t
p
r
e
m
atu
r
e
s
tab
ilit
y
lo
s
s
an
d
is
ex
p
r
ess
ed
as
(
3
7
)
.
=
2
|
2
−
−
√
2
−
4
|
wh
er
e
=
1
+
2
>
4
(
3
7
)
T
h
e
p
ar
ticle
v
elo
city
is
ca
p
p
ed
b
y
,
ty
p
ically
s
et
f
r
o
m
1
0
–
2
0
%
o
f
t
h
e
v
ar
iab
le'
s
d
y
n
a
m
ic
r
an
g
e
p
er
d
im
en
s
io
n
in
PS
O.
3
.
1
.
I
m
ple
m
ent
a
t
io
n o
f
P
SO
f
o
r
E
M
O
T
h
e
PS
O
alg
o
r
ith
m
f
o
r
s
o
lv
in
g
th
e
OE
M
p
r
o
b
lem
f
o
llo
ws th
ese
s
tep
s
:
Step
1
:
T
h
e
MG
s
y
s
tem
,
in
clu
d
in
g
DG,
s
to
r
ag
e,
an
d
lo
ad
d
ata;
Step
2
: Set
th
e
o
b
jectiv
e
f
u
n
ctio
n
(
1
4
)
an
d
v
ar
iab
le
lim
its
(
1
7
)
-
(
1
8
)
;
Step
3
: I
n
itialize
PS
O
p
ar
am
eter
s
,
in
clu
d
in
g
p
o
p
u
latio
n
s
ize,
in
er
ti
a
weig
h
t,
an
d
co
n
s
tan
ts
;
Step
4
: G
en
er
ate
a
r
an
d
o
m
p
ar
ticle
p
o
p
u
latio
n
;
Step
5
: Co
m
p
u
te
p
o
wer
ex
ch
a
n
g
e
(
2
2
)
an
d
v
er
if
y
co
n
s
tr
ain
ts
(
1
7
)
-
(
1
8
)
;
Step
6
: E
v
alu
ate
f
itn
ess
f
o
r
ea
c
h
p
ar
t
icle
u
s
in
g
(
1
4
)
an
d
(
2
4
)
;
Step
7
: Per
s
o
n
al
an
d
g
l
o
b
al
b
est v
alu
es.
Step
8
: U
p
d
ate
v
elo
city
(
3
4
)
an
d
p
o
s
itio
n
(
3
5
)
o
f
ea
c
h
p
a
r
ticle
;
Step
1
0
: U
n
til th
e
it
max
s
to
p
cr
iter
ia
is
r
ea
ch
ed
,
r
ep
ea
t step
s
5
–
8;
Step
1
1
:
R
etu
r
n
th
e
b
est o
p
tio
n
f
o
u
n
d
;
Sto
p
.
4.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
T
o
d
e
m
o
n
s
tr
ate
h
o
w
to
ascer
tain
th
e
o
f
f
er
s
o
f
th
e
v
ar
io
u
s
DG
u
n
its
,
t
h
e
m
o
d
if
ied
I
E
E
E
-
3
4
b
u
s
s
y
s
tem
as
s
h
o
wn
in
Fig
u
r
e
1
is
u
s
ed
.
T
h
is
s
y
s
tem
co
m
p
r
is
es
o
f
2
6
b
u
s
es,
an
d
2
5
b
r
an
c
h
e
s
,
with
2
3
o
f
th
em
s
er
v
in
g
as
tr
an
s
m
is
s
io
n
lin
es,
2
ar
e
t
h
e
v
o
ltag
e
r
e
g
u
lato
r
s
,
a
n
d
1
as
th
e
ta
p
ch
a
n
g
er
tr
an
s
f
o
r
m
er
.
Fiv
e
d
is
tin
ct
DG
u
n
its
with
o
n
e
SS
E
s
an
d
elec
tr
ical
lo
ad
s
r
e
p
r
esen
t
th
e
MG
s
y
s
tem
s
.
T
h
e
W
T
c
o
n
n
ec
ted
to
b
u
s
4
,
an
MT
co
n
n
ec
ted
to
b
u
s
7
,
a
PV
co
n
n
ec
ted
to
b
u
s
1
1
,
a
DE
G
attac
h
ed
to
b
u
s
1
9
,
an
d
an
FC
co
n
n
ec
ted
to
b
u
s
2
3
.
I
n
ad
d
itio
n
,
th
e
MG
h
as 2
co
m
p
e
n
s
atio
n
ca
p
ac
ito
r
s
p
lace
d
at
b
u
s
es 2
1
an
d
2
4
,
r
esp
ec
tiv
ely
.
T
h
e
r
elev
an
t
d
ata,
in
clu
d
in
g
t
h
e
co
s
t
an
d
em
is
s
io
n
co
ef
f
icie
n
ts
o
f
5
DG
u
n
its
,
wer
e
tak
en
f
r
o
m
[
3
2
]
.
E
ac
h
DG
is
as
s
u
m
ed
to
p
r
o
d
u
ce
ac
tiv
e
p
o
wer
with
a
u
n
if
o
r
m
p
o
wer
f
ac
to
r
.
T
h
e
m
ain
g
r
i
d
an
d
MG
ex
ch
a
n
g
e
p
o
wer
th
r
o
u
g
h
th
e
PC
C
o
v
er
a
o
n
e
-
d
ay
p
er
i
o
d
,
r
eg
u
lated
b
y
th
e
MG
ce
n
tr
al
c
o
n
tr
o
ller
(
MG
C
C
)
[
4
4
]
,
as
illu
s
tr
ated
in
Fig
u
r
e
1
.
Fo
r
s
af
e
o
p
er
atio
n
m
o
d
e
o
f
m
ic
r
o
g
r
id
an
d
en
s
u
r
e
a
h
ar
m
o
n
y
,
an
d
r
eliab
ilit
y
,
if
e
x
is
t
m
o
r
e
th
an
o
n
e
m
icr
o
g
r
id
,
MG
C
C
s
co
m
m
u
n
icate
with
d
is
tr
ib
u
tio
n
m
an
a
g
em
en
t sy
s
te
m
(
D
MS)
.
Fig
u
r
e
1
.
On
e
-
lin
e
d
iag
r
am
o
f
test
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
Mu
lti
-
o
b
jective
en
erg
y
ma
n
a
g
eme
n
t a
n
d
e
n
viro
n
men
ta
l in
d
e
x
o
p
timiz
a
tio
n
o
f
…
(
A
h
med
B
a
h
r
i
)
789
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
im
p
lem
en
ted
a
n
d
th
e
c
o
m
p
u
tat
io
n
s
wer
e
p
e
r
f
o
r
m
ed
u
s
in
g
MA
T
L
AB
s
o
f
twar
e,
R
2
0
2
1
a
an
d
all
ca
s
es
wer
e
r
u
n
o
n
a
d
esk
to
p
co
m
p
u
ter
W
in
d
o
ws
-
1
0
,
6
4
-
b
it,
I
n
te
l(
R
)
C
o
r
e(
T
M)
i5
-
6
5
0
0
C
PU,
3
.
2
0
GHz
p
r
o
ce
s
s
in
g
f
r
e
q
u
en
c
y
an
d
8
.
0
GB
R
AM
.
T
h
e
PS
O
ap
p
r
o
ac
h
is
u
s
ed
to
id
en
tify
th
e
b
est
s
o
lu
tio
n
s
o
f
OE
M
an
d
E
I
O
p
r
o
b
lem
s
in
MG
.
Fo
r
estab
lis
h
in
g
th
e
s
u
p
er
io
r
ity
o
f
t
h
e
p
r
o
p
o
s
ed
PS
O,
1
0
in
d
ep
en
d
en
t tr
ial
r
u
n
s
ar
e
p
er
f
o
r
m
ed
f
o
r
all
th
e
test
ca
s
es.
I
n
th
e
MG
,
all
elig
ib
le
DGs
g
en
er
ate
elec
tr
icity
,
with
ex
ce
s
s
o
r
ad
d
itio
n
al
d
e
m
an
d
m
an
ag
ed
th
r
o
u
g
h
th
e
PC
C
to
th
e
m
ain
g
r
id
[
8
]
.
T
h
e
ex
c
h
an
g
e
en
e
r
g
y
with
t
h
e
MG
with
o
u
t
an
y
r
estrictio
n
s
.
I
n
th
is
s
ce
n
a
r
io
,
th
e
im
p
ac
t o
f
en
e
r
g
y
m
ar
k
et
p
r
ice
is
in
v
esti
g
ated
in
th
r
ee
ca
s
es
as sh
o
wn
as:
C
ase
1
: L
o
w
en
er
g
y
m
ar
k
et
p
r
ice;
C
ase
2
: A
v
er
ag
e
en
er
g
y
m
ar
k
et
p
r
ice;
C
ase
3
: G
en
u
in
e
v
alu
e
o
f
en
er
g
y
m
ar
k
et
p
r
ice.
Fig
u
r
e
2
(
a
)
d
is
p
lay
,
r
esp
ec
ti
v
ely
,
f
o
r
ec
ast
d
ata
f
o
r
win
d
s
p
ee
d
,
e
n
er
g
y
m
a
r
k
et
p
r
ice
,
am
b
ien
t
tem
p
er
atu
r
e,
an
d
d
aily
lo
a
d
d
iag
r
am
.
I
t
was
ass
u
m
ed
t
h
at,
in
co
m
p
a
r
is
o
n
to
n
o
m
in
al
v
al
u
es,
th
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
lo
ad
s
v
ar
ies
in
ac
co
r
d
a
n
ce
with
d
aily
lo
a
d
d
iag
r
am
.
Fig
u
r
e
2
is
s
ca
led
f
o
r
a
2
4
-
h
o
u
r
p
er
io
d
.
T
h
e
co
n
v
e
r
g
en
ce
c
h
ar
ac
ter
is
tics
o
f
E
I
O
ar
e
s
h
o
wn
in
Fig
u
r
e
2
(
b
)
.
T
ab
le
1
s
h
o
ws
th
e
o
u
tp
u
t
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
an
d
c
o
n
tr
o
l
v
ar
iab
les
o
f
E
I
O
p
r
o
b
lem
.
T
h
e
co
n
v
er
g
e
n
ce
ch
a
r
ac
ter
is
tics
o
f
to
tal
co
s
t
co
r
r
esp
o
n
d
in
g
to
OE
M
f
o
r
c
ases
1
,
2
,
a
n
d
3
,
r
esp
ec
tiv
ely
,
ar
e
s
h
o
wn
i
n
Fig
u
r
e
3
(
a
)
.
Fo
r
all
ca
s
es,
th
e
o
b
tain
ed
r
esu
lts
o
f
th
e
p
r
o
v
id
ed
DG’
s
p
o
wer
s
,
u
tili
ty
p
o
w
er
,
an
d
d
aily
co
s
t
ar
e
s
h
o
wn
in
Fig
u
r
e
3
(
b
)
an
d
Fig
u
r
e
4
,
r
esp
ec
tiv
el
y
.
Du
e
to
th
e
lo
w
m
ar
k
et
p
r
ice
f
o
r
ca
s
e
1
,
esp
ec
ially
d
u
r
in
g
tim
es
o
f
lo
w
an
d
m
ed
iu
m
l
o
ad
lev
els,
in
th
e
f
ir
s
t
ca
s
e
th
e
u
tili
ty
s
u
p
p
li
es
th
e
lo
ad
in
s
id
e
th
e
MG
o
n
its
o
wn
.
I
n
th
is
ca
s
e,
th
e
o
p
tim
al
o
p
er
atin
g
co
s
t
f
o
u
n
d
is
2
5
7
,
2
8
3
(
$
/h
)
.
I
n
th
e
s
ec
o
n
d
ca
s
e,
wh
ile
th
e
m
ar
k
e
t
p
r
ice
is
m
id
d
le
r
an
g
e,
t
h
e
m
ajo
r
ity
o
f
th
e
lo
a
d
s
p
o
wer
ar
e
p
r
o
v
id
ed
b
y
th
e
MT
an
d
FC
.
Du
r
in
g
p
er
io
d
s
o
f
a
v
er
ag
e
lo
ad
,
c
o
r
r
esp
o
n
d
in
g
to
th
e
av
er
ag
e
m
ar
k
et
p
r
ice
(
5
.
6
$
/k
W
h
)
,
ex
ce
s
s
en
e
r
g
y
is
ex
p
o
r
ted
f
r
o
m
th
e
MG
to
th
e
u
tili
ty
.
T
h
e
b
est
o
p
e
r
atio
n
co
s
t
in
th
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Data
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RE
F
E
R
E
NC
E
S
[
1
]
M
.
F
.
Zi
a
,
E.
El
b
o
u
c
h
i
k
h
i
,
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d
,
a
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d
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M
.
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u
e
r
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o
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E
n
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man
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f
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d
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Ap
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.
[
2
]
H
.
W
u
,
H
.
Li
,
a
n
d
X
.
G
u
,
“
O
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g
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[
3
]
A.
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.
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[
4
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J.
H
.
Ta
l
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-
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a
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[
5
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H
.
Ji
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,
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