I
A
E
S
I
n
t
e
r
n
at
io
n
al
Jou
r
n
al
of
A
r
t
if
ic
ia
l
I
n
t
e
ll
ig
e
n
c
e
(
I
J
-
AI
)
V
ol
.
11
, N
o.
1
,
M
a
r
c
h
2022
, pp.
22
1
~
228
I
S
S
N
:
2252
-
8938
,
D
O
I
:
10.11591/
ij
a
i.
v
11
.i
1
.pp
22
1
-
228
221
Jou
r
n
al
h
om
e
page
:
ht
tp
:
//
ij
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.
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E
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e
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t
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ha
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c
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U
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, I
ndone
s
i
a
2
E
ne
r
gy P
ow
e
r
P
l
a
nt
S
t
udy
P
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ogr
a
m
, D
e
pa
r
t
m
e
nt
of
M
e
c
ha
ni
c
a
l
E
ngi
ne
e
r
i
ng,
S
t
a
t
e
P
ol
yt
e
c
hni
c
of
U
j
ung P
a
nda
ng
, M
a
ka
s
s
a
r
, I
ndone
s
i
a
A
r
t
ic
le
I
n
f
o
A
B
S
T
R
A
C
T
A
r
ti
c
le
h
is
to
r
y
:
R
e
c
e
iv
e
d
A
pr
4
, 2021
R
e
vi
s
e
d
N
ov 4, 2021
A
c
c
e
pt
e
d
N
ov 20
,
2021
In
this
study,
a
particle
swarm
optimization
(PSO)
is
proposed
to
op
timize
the
cost
of
generating
thermal
plants
in
the
South
Sulawesi
syste
m.
The
study
was
con
ducted
by
analyzing
several
methods
using
the
lagrange
and
ant
colony
optimization
(ACO).
P
SO
algorithm
converges
on
th
e
11
th
iteration
algorithm
with
the
lowest
generatio
n
cost
obtained,
wh
ich
is
Rp12968796
2.17/hour
.
While
the
ACO
algorithm
conver
ges
on
t
h
e
34
th
iteration
with
a
generatio
n
cost
of
Rp131,473,269.3
9/hour.
The
res
ults
of
optimization
using
PSO
produce
a
total
thermal
power
of
400.75
MW
and
losses
of
26.15
MW.
The
PSO
method
is
able
to
reduce
the
c
ost
of
generating
the
South
Sulawesi
system
by
Rp11,118,31
2.07/hour
or
7.9%.
While
using
the
ACO
method
generates
a
generation
co
st
of
Rp131,473,2
69.39/hour
to
genera
te
power
of
400,812
MW
with
los
ses
of
26,219
MW.
The
ACO
method
is
able
to
reduce
the
cost
of
generati
ng
the
South
Sulawesi
system
by
Rp
9,333,004.9/hour
or
6.62%.
PSO
alg
orithm
provides
the
lowest
cost
calculation
of
generato
r
compared
with
conventi
onal
methods
and
ACO
smart
methods
.
This
is
also
shown
in
the
calculati
on
process,
the
PSO
method
completes
calculati
ons
faster
th
an
the
ACO me
thod.
K
e
y
w
o
r
d
s
:
A
nt
c
ol
ony opti
m
iz
a
ti
on
E
c
onomi
c
di
s
pa
tc
h
L
a
gr
a
nge
L
os
s
e
s
P
a
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
This is an
open
acce
ss artic
le unde
r the
CC BY
-
SA
license.
C
or
r
e
s
pon
di
n
g A
u
th
or
:
M
a
r
ha
ta
ng
E
ne
r
gy
C
onve
r
s
io
n
S
tu
dy
P
r
ogr
a
m
,
D
e
pa
r
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e
nt
o
f
M
e
c
ha
ni
c
a
l
E
ngi
ne
e
r
in
g
,
S
ta
te
P
ol
yt
e
c
hni
c
of
U
ju
ng
P
a
nda
ng
J
l.
P
e
r
in
ti
s
K
e
m
e
r
de
ka
a
n K
M
.
10,
M
a
ka
s
s
a
r
90245, I
ndone
s
ia
E
m
a
il
:
m
a
r
ha
ta
ng@
pol
iu
pg.a
c
.i
d
1.
I
N
T
R
O
D
U
C
T
I
O
N
I
n
a
pow
e
r
pl
a
nt
c
e
nt
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,
good
m
a
na
ge
m
e
nt
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ne
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de
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in
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gul
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ti
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a
m
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e
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a
t
m
us
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be
s
e
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ge
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th
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y
s
te
m
.
O
pe
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ti
ona
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m
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na
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m
e
nt
a
t
th
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pow
e
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pl
a
nt
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ve
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im
por
ta
nt
,
e
s
pe
c
ia
ll
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in
th
e
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m
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nt
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th
a
t
ope
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te
w
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f
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l
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bi
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s
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C
ha
nge
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e
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a
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e
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le
c
tr
ic
pow
e
r
s
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te
m
w
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l
e
nc
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a
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a
ddi
ti
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ue
l
c
on
s
um
pt
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pe
r
uni
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m
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r
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pow
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nt
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pr
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om
m
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r
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f
e
r
r
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to
a
s
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in
pu
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out
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s
of
th
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e
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e
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T
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e
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c
r
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s
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xpe
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in
th
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opt
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us
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,
s
o
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a
t
m
in
im
um
c
os
ts
a
r
e
obt
a
in
e
d
[
1]
.
T
he
S
ul
s
e
lr
a
b
a
r
s
ys
te
m
ope
r
a
te
s
a
t
150
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a
nd
c
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of
46
tr
a
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m
is
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.
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hi
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c
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c
ts
lo
a
d
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e
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s
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r
s
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lr
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ba
r
s
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m
ha
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37 bus
e
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a
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is
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s
of
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r
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r
m
a
l
a
nd
non
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r
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s
.
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or
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m
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[
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
11
, N
o.
1
,
M
a
r
c
h
2022
:
221
-
228
222
I
n
th
is
r
e
s
e
a
r
c
h,
a
s
tu
dy
on
th
e
S
out
h
S
ul
a
w
e
s
i
e
le
c
tr
ic
it
y
s
ys
te
m
w
il
l
be
pr
opo
s
e
d,
na
m
e
ly
e
c
onomi
c
di
s
pa
tc
h
.
I
n
pr
e
vi
ous
s
tu
di
e
s
,
pr
e
vi
ous
e
c
onomi
c
di
s
pa
tc
h
s
tu
di
e
s
ha
v
e
be
e
n
c
onduc
te
d.
S
om
e
of
th
e
s
e
s
tu
di
e
s
pr
oduc
e
a
c
om
bi
na
ti
on
of
e
c
onomi
c
l
oa
di
ng
f
or
g
e
ne
r
a
ti
ng
uni
ts
in
th
e
S
out
h
S
ul
a
w
e
s
i
s
y
s
te
m
.
B
ut
th
e
de
ve
lo
pm
e
nt
of
th
e
s
ys
te
m
a
nd
a
ls
o
th
e
e
m
e
r
ge
nc
e
of
s
e
ve
r
a
l
ne
w
opt
im
iz
a
ti
on
m
e
th
ods
,
w
e
ne
e
d
a
f
ur
th
e
r
s
tu
dy of
e
c
onomi
c
di
s
pa
tc
h.
P
a
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
(
PSO
)
m
e
th
od
is
a
n
unde
t
e
r
m
in
i
s
ti
c
m
e
th
od
or
s
m
a
r
t
m
e
th
od.
P
S
O
is
a
n
e
vol
ut
io
na
r
y
c
om
put
a
ti
ona
l
te
c
hni
que
,
in
w
hi
c
h
th
e
popula
ti
on i
n t
he
P
S
O
i
s
ba
s
e
d on a
n a
lg
or
it
hm
s
e
a
r
c
h
a
nd
be
gi
ns
w
it
h
a
r
a
ndom
popula
ti
on
c
a
ll
e
d
a
pa
r
ti
c
le
.
T
he
a
ppl
ic
a
ti
on
of
P
S
O
a
s
a
n
e
c
onomi
c
di
s
pa
tc
h
opt
im
iz
a
ti
on
m
e
th
od
ha
s
be
e
n
in
ve
s
ti
ga
te
d
by
[
3]
–
[
7]
.
T
he
s
t
udy
di
s
c
us
s
e
s
th
e
im
pl
e
m
e
nt
a
ti
on
of
th
e
P
S
O
a
lg
or
it
hm
to
s
ol
ve
e
c
onomi
c
di
s
pa
tc
h
pr
obl
e
m
s
.
P
r
e
vi
ous
r
e
s
e
a
r
c
h
on
e
c
onomi
c
di
s
pa
tc
h
in
th
e
S
out
h
S
ul
a
w
e
s
i
s
ys
t
e
m
ha
s
b
e
e
n
c
onduc
t
e
d.
I
n
r
e
s
e
a
r
c
h
[
8]
di
s
c
u
s
s
e
s
e
c
onomi
c
di
s
pa
tc
h
u
s
in
g
th
e
P
S
O
m
e
th
od.
F
r
om
th
e
r
e
s
ul
ts
of
th
e
s
tu
dy
th
e
ge
ne
r
a
to
r
da
ta
us
e
d
di
d
n
ot
c
ove
r
a
ll
of
th
e
ge
ne
r
a
to
r
s
in
th
e
s
ys
te
m
,
e
s
pe
c
ia
ll
y
th
e
r
m
a
l
pl
a
nt
s
.
T
he
S
ul
s
e
lr
a
ba
r
s
ys
te
m
ha
s
now
de
ve
lo
pe
d
w
it
h
th
e
a
ddi
ti
on
of
s
e
ve
r
a
l
th
e
r
m
a
l
pl
a
nt
s
.
I
n
r
e
s
e
a
r
c
h
[
9]
,
th
e
im
pl
e
m
e
nt
a
ti
on
of
th
e
a
nt
c
ol
on
y
a
lg
or
it
hm
is
e
xpl
a
in
e
d
a
s
a
n
opt
im
iz
a
ti
on
m
e
th
od.
F
r
om
th
e
r
e
s
ul
ts
of
th
is
s
tu
dy
obt
a
in
e
d
th
e
ol
d
a
nt
c
ol
ony
c
om
put
in
g
pr
oc
e
s
s
.
I
n
a
ddi
ti
on,
th
e
opt
im
iz
a
ti
on
r
e
s
ul
ts
obt
a
in
e
d
a
r
e
not
s
o
s
ig
ni
f
ic
a
nt
w
it
h
th
e
c
a
lc
ul
a
ti
on
pr
oc
e
s
s
us
in
g
th
e
c
onve
nt
io
na
l
l
a
gr
a
nge
m
e
th
od.
I
n
[
4]
,
[
6]
di
s
c
us
s
e
s
th
e
im
pl
e
m
e
nt
a
ti
on
of
th
e
P
S
O
in
c
a
lc
ul
a
ti
ng
th
e
c
o
s
t
of
ge
n
e
r
a
ti
on
in
a
m
ul
ti
-
e
ngi
ne
s
ys
te
m
,
a
nd
s
how
s
opt
im
a
l
r
e
s
u
lt
s
in
tu
ni
ng.
I
n
r
e
s
e
a
r
c
h
[
5]
di
s
c
us
s
e
s
th
e
opt
im
iz
a
ti
on
of
ge
ne
r
a
ti
on
c
os
ts
in
s
m
a
ll
s
ys
te
m
s
w
it
h
a
c
a
s
e
s
tu
dy
of
a
9
bu
s
s
ys
te
m
a
nd
3
ge
ne
r
a
to
r
s
.
R
e
s
e
a
r
c
h
on
s
m
a
ll
s
c
a
le
s
y
s
te
m
s
h
a
s
a
l
s
o
be
e
n
c
a
r
r
ie
d
out
by
[
10]
,
w
ho
di
s
c
us
s
e
s
th
e
im
pl
e
m
e
nt
a
ti
on
of
e
c
onomi
c
di
s
pa
tc
h
in
m
ic
r
ogr
id
s
ys
te
m
s
.
T
hi
s
r
e
s
e
a
r
c
h
w
il
l
pr
opos
e
a
n
e
w
a
ppr
oa
c
h
f
or
opt
im
iz
a
ti
on
of
ge
ne
r
a
ti
on
c
os
t
s
in
la
r
ge
m
ul
ti
na
ti
ona
l
s
ys
te
m
s
, e
s
pe
c
ia
ll
y i
n t
he
S
out
h S
ul
a
w
e
s
i
s
y
s
te
m
.
I
n t
hi
s
s
tu
dy, we
c
ons
id
e
r
t
r
a
ns
m
is
s
io
n l
o
s
s
e
s
a
nd
th
e
e
qua
li
ty
a
nd
in
e
qua
li
ty
li
m
it
s
of
th
e
ge
ne
r
a
to
r
[
3]
.
T
he
f
in
a
l
r
e
s
ul
t
of
th
is
r
e
s
e
a
r
c
h
is
th
e
opt
im
iz
a
ti
on
of
opt
im
a
l
pow
e
r
ge
ne
r
a
ti
on s
o t
ha
t
th
e
c
he
a
pe
s
t
ge
ne
r
a
ti
on c
os
ts
a
r
e
obt
a
in
e
d.
2.
R
E
S
E
A
R
C
H
M
E
T
H
O
D
O
pt
im
a
l
ope
r
a
ti
on
of
th
e
ge
n
e
r
a
t
or
m
us
t
pa
y
a
tt
e
nt
io
n
to
e
qua
li
ty
c
on
s
tr
a
in
ts
a
nd
in
e
qua
li
ty
c
ons
tr
a
in
ts
.
E
qua
li
ty
c
on
s
tr
a
in
t
is
th
e
pow
e
r
li
m
it
ge
ne
r
a
te
d
by e
a
c
h
ge
n
e
r
a
to
r
w
hi
c
h
i
s
e
qu
a
l
to
th
e
to
ta
l
lo
a
d
r
e
qui
r
e
m
e
nt
a
nd t
r
a
ns
m
is
s
io
n l
os
s
e
s
, e
xpr
e
s
s
e
d by the
f
ol
lo
w
in
g (
1)
[
11]
.
L
os
s
c
oe
f
f
ic
ie
nt
s
c
a
n be
c
ons
id
e
r
e
d
c
ons
ta
nt
f
or
c
ha
nge
s
i
n t
he
out
put
pow
e
r
of
e
a
c
h g
e
ne
r
a
to
r
i
n t
he
s
ys
te
m
.
∑
=
+
=
1
(
1)
W
he
r
e
:
Pi
=
G
e
ne
r
a
to
r
out
put
pow
e
r
(
M
W
)
PR
=
T
ot
a
l
lo
a
d (
M
W
)
PL
=
T
r
a
ns
m
i
s
s
io
n l
os
s
e
s
(
M
W
)
w
hi
le
th
e
i
ne
qu
a
li
ty
c
ons
tr
a
in
t
i
s
th
e
out
put
pow
e
r
pr
oduc
e
d
by
th
e
ge
n
e
r
a
to
r
th
a
t
m
us
t
be
gr
e
a
te
r
th
a
n
or
e
qua
l
to
t
he
m
in
im
um
pe
r
m
it
te
d powe
r
a
nd l
e
s
s
t
ha
n or
e
qua
l
to
t
he
m
a
xi
m
um
pe
r
m
it
te
d powe
r
[
12]
≤
≤
(
2)
=
∑
∑
+
=
1
=
1
∑
0
+
00
=
1
(
3)
w
he
r
e
:
P
L
:
L
os
s
e
s
.
B
ij
:
L
os
s
e
s
c
oe
f
f
ic
ie
nt
s
.
P
i
, P
i
:
G
e
ne
r
a
to
r
out
put
B
i
0
, B
00
:
L
os
s
e
s
c
on
s
ta
nt
2.1.
P
ar
t
ic
le
s
w
ar
m
op
t
im
iz
at
io
n
P
a
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
(
PSO
)
is
a
n
a
r
ti
f
ic
ia
l
in
te
ll
ig
e
nc
e
m
e
th
od
th
a
t
w
a
s
di
s
c
ov
e
r
e
d
in
1995
[
13]
,
[
14
]
.
T
hi
s
a
lg
or
it
hm
w
or
ks
by
a
dopt
in
g
th
e
m
ove
m
e
nt
b
e
ha
vi
or
of
a
f
lo
c
k
of
bi
r
ds
or
f
is
h
in
s
e
a
r
c
h
of
f
ood
s
o
th
a
t
it
c
a
n
be
a
ppl
ie
d
to
s
c
ie
nt
if
ic
a
nd
e
ngi
n
e
e
r
in
g
r
e
s
e
a
r
c
h
m
e
th
od
s
.
T
h
e
m
a
in
a
dv
a
nt
a
ge
s
of
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
O
pt
imal
e
c
onomic
di
s
pat
c
h u
s
in
g par
ti
c
le
s
w
ar
m
opt
imi
z
at
io
n
in
Sul
s
e
lr
abar
s
y
s
te
m
(
M
ar
hat
ang
)
223
P
S
O
a
lg
or
it
hm
a
r
e
s
im
pl
e
a
lg
or
it
hm
s
tr
uc
tu
r
e
,
e
a
s
y
to
u
s
e
,
e
a
s
y
to
s
e
t
pa
r
a
m
e
te
r
s
,
a
nd
v
e
r
y
good
e
f
f
ic
ie
nc
y
[
10]
, [
15]
. T
he
w
e
ig
ht
i
m
pr
ove
m
e
nt
f
unc
ti
on i
s
de
te
r
m
in
e
d by t
he
f
ol
lo
w
in
g
(
4)
.
(
)
=
(
−
min
)
−
(
)
+
(
4)
W
he
r
e
:
W
(
t)
:
W
e
ig
ht
W
m
a
x
:
M
a
xi
m
um
w
e
ig
ht
va
lu
e
W
min
:
M
in
im
um
w
e
ig
ht
va
lu
e
I
te
r
m
a
x
:
M
a
xi
m
um
I
te
r
a
ti
on
I
te
r
(
t)
:
I
te
r
a
ti
on
I
ne
r
ti
a
w
e
ig
ht
va
lu
e
s
a
r
e
us
u
a
ll
y
s
e
t
be
twe
e
n
0.4
a
nd
0.9.
T
he
c
on
c
e
pt
of
in
e
r
ti
a
w
e
ig
ht
w
a
s
de
ve
lo
pe
d
by
S
hi
a
nd
E
be
r
ha
r
t
in
1998
w
hi
c
h
in
s
pi
r
e
d
th
e
m
odi
f
ic
a
ti
on
of
pa
r
ti
c
le
ve
lo
c
it
y
a
nd
pos
it
io
n
us
in
g t
he
a
dj
us
ta
bl
e
i
ne
r
ti
a
w
e
ig
ht
pa
r
a
m
e
te
r
. V
e
lo
c
it
y a
nd pa
r
t
ic
le
pos
it
io
n e
qua
ti
on
[
16]
, [
17]
:
=
−
1
+
1
1
(
−
1
−
−
1
)
+
2
2
(
−
−
−
1
)
(
5
)
F
or
I
=
1,2,…, N
D
;
j
=
1,….,N
pa
r
.
W
he
r
e
:
t
:
C
a
lc
ul
a
te
i
te
r
a
ti
on
:
T
he
i
j
di
m
e
ns
io
n of
t
he
pa
r
ti
c
le
ve
lo
c
it
y a
t
it
e
r
a
ti
on t
.
:
T
he
i
j
di
m
e
ns
io
n of
t
he
pa
r
ti
c
le
pos
it
io
n i
n t
he
i
te
r
a
ti
on t
.
:
W
e
ig
ht
of
i
ne
r
ti
a
c
1
, c
2
:
P
os
it
iv
e
a
c
c
e
le
r
a
ti
on c
oe
f
f
ic
ie
nt
−
1
:
T
he
i
j
di
m
e
ns
io
n f
r
om
t
he
be
s
t
pos
it
io
n i
s
r
e
a
c
he
d unti
l
it
e
r
a
ti
on
t
-
1
−
1
:
D
im
e
ns
io
n I
of
a
ll
be
s
t
pos
it
io
ns
i
s
a
c
hi
e
ve
d unti
l
t
-
1 i
te
r
a
ti
on
N
D
:
N
um
be
r
of
de
c
is
io
n va
r
ia
bl
e
s
N
par
:
N
um
be
r
of
s
w
a
r
m
r
1
, r
2
:
R
a
ndom
num
be
r
s
a
r
e
e
ve
nl
y
di
s
tr
ib
ut
e
d
in
th
e
r
a
nge
[
0,1]
;
th
e
la
te
s
t
va
lu
e
is
ge
ne
r
a
te
d
a
t
a
ny t
im
e
.
P
S
O
w
a
s
de
ve
lo
pe
d ba
s
e
d on the
f
ol
lo
w
in
g m
ode
l
[
18]
:
a.
W
he
n a
bi
r
d a
ppr
oa
c
he
s
a
f
ood s
our
c
e
, i
t
w
il
l
qui
c
kl
y s
e
nd i
nf
o
r
m
a
ti
on t
o ot
he
r
bi
r
ds
.
b.
A
f
te
r
r
e
c
e
iv
in
g t
he
i
nf
or
m
a
ti
on, t
he
ot
he
r
bi
r
ds
f
ol
lo
w
i
n gr
oup
s
.
P
S
O
pa
r
a
m
e
te
r
s
us
e
d i
nc
lu
de
[
19]
:
−
N
um
be
r
of
s
w
a
r
m
s
=
30
−
N
um
be
r
of
va
r
ia
bl
e
s
=
16
−
M
a
xi
m
um
i
te
r
a
ti
on=
50
−
S
oc
ia
l
c
ons
ta
nt
=
0.5
−
C
ogni
ti
ve
c
ons
ta
nt
=
0.01
−
I
ne
r
ti
a
(
w
)
=
0.01
W
hi
le
t
he
a
nt
c
ol
ony opti
m
iz
a
ti
on (
A
C
O
)
pa
r
a
m
e
te
r
s
i
nc
lu
de
[
20]
, [
21]
:
−
N
um
be
r
of
a
nt
s
=
10
−
M
a
x I
te
r
a
ti
on=
100
−
A
lp
ha
=
0.9
R
e
s
e
a
r
c
h
b
e
gi
ns
by
c
ol
le
c
ti
ng
s
y
s
te
m
da
ta
.
T
he
n
m
a
k
e
a
m
ode
li
ng
of
th
e
S
ul
s
e
lr
a
ba
r
s
ys
te
m
to
be
in
te
gr
a
te
d
w
it
h
th
e
PSO
a
lg
or
it
hm
.
T
he
n
m
a
ke
PSO
m
ode
li
ng
in
M
A
T
L
A
B
s
of
twa
r
e
.
F
ig
ur
e
1
s
how
s
th
e
f
lo
w
c
ha
r
t
of
t
he
r
e
s
e
a
r
c
h
c
onduc
te
d
.
3.
R
E
S
U
L
T
S
A
N
D
A
N
A
L
Y
S
I
S
I
n
th
is
s
tu
dy,
th
e
c
om
pl
e
ti
on
of
e
c
onomi
c
di
s
pa
tc
h
us
e
s
s
e
ve
r
a
l
m
e
th
ods
in
c
lu
di
ng
th
e
c
onv
e
nt
io
na
l
L
a
gr
a
nge
m
e
th
od,
th
e
a
nt
c
ol
ony
opt
im
iz
a
ti
on
(
A
C
O
)
m
e
th
o
d,
a
nd
th
e
pr
opos
e
d
m
e
th
od,
na
m
e
ly
pa
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
(
P
S
O
)
.
T
he
c
a
s
e
s
tu
dy
us
e
d
is
th
e
S
ul
s
e
lr
a
ba
r
s
ys
t
e
m
.
T
he
a
lg
or
it
hm
pe
r
f
or
m
s
c
om
put
a
ti
ons
t
o c
a
lc
ul
a
te
t
he
c
he
a
pe
s
t
c
om
bi
na
ti
on of
t
he
r
m
a
l
ge
ne
r
a
ti
on. I
n t
hi
s
s
tu
dy, 4 non
-
th
e
r
m
a
l
pow
e
r
pl
a
nt
s
w
e
r
e
m
a
xi
m
iz
e
d.
T
he
P
S
O
a
lg
or
it
hm
w
or
ks
w
it
h
th
e
lo
w
e
s
t
c
os
t
ge
ne
r
a
ti
on
obj
e
c
ti
ve
f
unc
ti
on.
T
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
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8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
11
, N
o.
1
,
M
a
r
c
h
2022
:
221
-
228
224
s
ol
ut
io
n
be
gi
ns
by
c
a
lc
ul
a
ti
ng
th
e
in
put
-
out
put
c
ha
r
a
c
te
r
is
ti
c
s
of
th
e
ge
ne
r
a
to
r
w
it
h
th
e
f
ol
lo
w
in
g
(
6)
[
22]
,
[
23]
.
F
ig
ur
e
1. P
a
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on f
lo
w
c
ha
r
t
=
∑
=
1
+
+
2
(
6)
T
o
obt
a
in
s
ta
bl
e
ge
ne
r
a
to
r
pe
r
f
or
m
a
nc
e
,
th
e
ope
r
a
ti
on
of
th
e
ge
ne
r
a
to
r
s
houl
d
not
e
xc
e
e
d
or
be
le
s
s
th
a
n
th
e
ge
ne
r
a
to
r
c
a
pa
c
it
y
[
24]
.
T
he
r
e
f
or
e
,
th
e
g
e
ne
r
a
to
r
pow
e
r
pr
oduc
ti
on
m
us
t
be
li
m
it
e
d
by
th
e
e
qu
a
li
ty
c
ons
tr
a
in
t
a
s
s
how
n
in
(
7)
.
I
n
a
ddi
ti
on,
it
m
us
t
a
ls
o
pa
y
a
tt
e
nt
io
n
to
th
e
l
im
it
s
of
th
e
in
e
qua
li
ty
c
ons
tr
a
in
t
a
s
s
how
n
in
(
8)
[
25]
.
∑
=
1
=
(
7)
≤
≤
(
8)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
A
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f
I
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e
ll
I
S
S
N
:
2252
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8938
O
pt
imal
e
c
onomic
di
s
pat
c
h u
s
in
g par
ti
c
le
s
w
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m
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at
io
n
in
Sul
s
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lr
abar
s
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s
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m
(
M
ar
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ang
)
225
3.1. T
h
e
r
m
al
ge
n
e
r
at
or
i
n
p
u
t
-
ou
t
p
u
t
a
n
d
f
u
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l
c
os
t
c
h
ar
ac
t
e
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is
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ic
s
T
he
c
om
put
a
ti
ona
l
pr
oc
e
s
s
be
gi
ns
by
c
a
lc
ul
a
ti
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th
e
in
put
-
out
put
c
ha
r
a
c
te
r
is
ti
c
s
of
th
e
th
e
r
m
a
l
ge
ne
r
a
to
r
[
26]
. T
he
n de
te
r
m
in
e
t
he
f
ue
l
c
os
t
e
qua
ti
on by mul
ti
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he
i
nput
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out
put
e
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ti
on b
y t
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e
o
f
th
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f
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r
e
s
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t
he
c
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a
ti
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f
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i
npu
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a
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t
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r
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s
how
n i
n
T
a
b
le
1
[
9]
.
T
a
bl
e
1. I
O
c
ha
r
a
c
t
e
r
is
ti
c
s
a
nd c
o
s
t
f
unc
ti
on
No
U
ni
t
I
nput
-
O
ut
put
E
qua
t
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on
(
L
i
t
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r
/
J
a
m
)
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nput
-
O
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put
E
qua
t
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on
(
L
i
t
e
r
/
J
a
m
)
1
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L
T
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P
a
r
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-
P
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r
e
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3.2941P
2
6211800+4936380P
-
28658.67P
2
2
P
L
T
D
S
uppa
2070+178.6P
+0.4P
2
18009000+1553820P
+3480P
2
3
P
L
T
U
B
a
r
r
u
2805.6+251.6P
-
0.11976P
2
17675280+1585080P
+754.488P
2
4
P
L
T
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T
e
l
l
o
558+174.5P
+1.375P
2
3515400+1099350P
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2
5
P
L
T
D
A
gr
e
kko/
T
.L
a
m
a
771.975+160P
+2.7397P
2
6716182.5+1392000P
+23835.39P
2
6
P
L
T
D
S
gm
ns
a
617.625+477.25P
-
4.1667P
2
5373337.5+4152075P
-
36250.29P
2
7
P
L
T
D
A
r
e
na
/
J
e
ne
pont
o
629.475+176.3P
+4.8052P
2
5476432.5+1533810P
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2
8
P
L
T
D
M
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t
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kko/
B
ul
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506.25+124.9P
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2
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2
9
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L
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P
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11
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a
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2
12
P
L
T
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P
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2
3.2
.
A
n
al
ys
is
an
d
d
is
c
u
s
s
io
n
T
he
c
a
s
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s
tu
dy
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s
e
d
is
b
a
s
e
d
on
pr
e
vi
ous
r
e
s
e
a
r
c
h,
in
w
h
ic
h
th
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s
e
tt
le
m
e
nt
m
e
th
od
us
e
s
a
n
in
te
ll
ig
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nt
a
nt
c
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opt
im
iz
a
ti
on
(
A
C
O
)
a
lg
or
it
hm
a
nd
th
e
c
onve
nt
io
na
l
L
a
gr
a
nge
.
T
a
bl
e
2
s
how
s
th
e
r
e
a
l
ge
ne
r
a
ti
on
pow
e
r
a
nd
c
os
ts
f
or
th
e
th
e
r
m
a
l
uni
t
of
th
e
S
out
h
S
ul
a
w
e
s
i
s
ys
t
e
m
a
t
pe
a
k
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v
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ni
ng
lo
a
d
be
f
or
e
opt
im
iz
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ti
on
a
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th
e
c
om
pa
r
is
on
of
th
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r
e
s
ul
t
s
of
s
im
ul
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ti
ons
c
a
r
r
ie
d
out
us
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g
th
e
pr
opos
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d
m
e
th
od
na
m
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ly
pa
r
ti
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le
s
w
a
r
m
opt
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iz
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ti
on
(
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S
O
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lg
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,
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A
C
O
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,
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L
a
gr
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a
ph of
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onve
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opt
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iz
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ti
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ge
ne
r
a
ti
on c
o
s
ts
us
in
g P
S
O
i
s
s
how
n i
n F
ig
ur
e
2.
T
a
bl
e
2.
T
he
c
om
pl
e
te
opt
im
iz
a
ti
on r
e
s
ul
t
s
U
ni
t
R
e
a
l
L
a
gr
a
nge
A
nt
C
ol
ony
PSO
P
(
M
W
)
C
os
t
(
R
p/
hr
)
P
(
M
W
)
C
os
t
(
R
p/
hr
)
P
(
M
W
)
C
os
t
(
R
p/
hr
)
P
(
M
W
)
C
os
t
(
R
p/
hr
)
1
20.1
9385464.873
19.40
9119159.49
18.50
8772640.01
10.50
5488737.86
2
62.2
12812016.72
31.98
7125923.05
60.03
12382534.57
59.73
12323912.16
3
44.7
10360370.52
44.00
10202568.76
41.40
9622921.45
33.55
7935567.73
4
29.7
4380719.96
19.80
2867857.65
17.80
2582845.65
28.38
4169183.92
5
19.3
4246022.69
19.00
4176875.82
21.88
4858396.36
18.39
4036545.83
6
12.3
5095955.36
27.60
9235658.65
29.20
9570548.02
19.08
7140357.97
7
19.6
5159900.95
23.86
6587284.55
13.36
3342993.46
18.66
4864960.35
8
9.0
2083951.36
6.30
1451132.36
11.94
2909265.78
9.35
2175760.65
9
15.1
3725118.15
14.56
3519839.04
11.52
2482548.48
11.24
2395951.36
10
192.9
79268321.18
184.38
76780078.63
166.10
71509642.44
188.35
77937456.65
11
3.5
1452615.24
3.730
1542902.63
3.520
1460445.24
2.02
885723.75
12
6.9
2835817.20
6.060
2280116.88
5.560
1978487.88
1.50
333803.93
T
ot
a
l
435.3
140806274.24
400.67
134889397.56
400.81
131473269.39
400.75
129687962.17
F
ig
ur
e
2. G
r
a
ph of
c
onve
r
ge
nc
e
opt
im
iz
a
ti
on us
in
g pa
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
11
, N
o.
1
,
M
a
r
c
h
2022
:
221
-
228
226
T
a
bl
e
2
is
a
pr
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li
m
in
a
r
y
s
tu
dy
o
f
th
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c
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lc
ul
a
ti
on
o
f
ge
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r
a
to
r
c
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ts
be
f
or
e
be
in
g
opt
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d
in
a
c
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of
pe
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k
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ve
ni
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ds
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th
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r
a
ti
on
lo
a
d
c
ha
r
ge
d
to
th
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th
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r
m
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l
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435.3
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W
,
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M
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ta
l
s
ys
te
m
lo
a
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is
532.3
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.
4
H
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o
pow
e
r
pl
a
nt
uni
ts
be
a
r
r
e
s
pe
c
ti
ve
ly
:
B
a
ka
r
u
126
M
W
,
P
in
r
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ng
0.3
M
W
,
S
in
ja
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3.5
M
W
,
B
il
i
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B
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7.1
M
W
.
F
u
r
th
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r
m
or
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,
by
us
in
g
th
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pr
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d
m
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th
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th
a
t
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us
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t
m
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s
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d
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th
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r
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ti
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d
th
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T
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pl
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te
opt
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ti
on r
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s
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ts
a
r
e
s
how
n i
n
Ta
bl
e
2.
3.3. An
al
ys
is
I
n
th
e
c
ondi
ti
on
be
f
or
e
opt
im
iz
a
ti
on,
th
e
to
ta
l
c
os
t
of
ge
ne
r
a
ti
on
is
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p140,806,274.24/ho
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it
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a
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of
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of
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.
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he
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ir
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c
onve
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on
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of
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p134,889,397.56/ho
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w
it
h
a
pow
e
r
of
400.67
M
W
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nd
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s
s
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s
of
28.352
M
W
.
F
r
om
th
e
r
e
s
ul
ts
of
th
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s
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c
a
lc
ul
a
ti
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,
th
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ne
r
a
ti
on
c
a
n
be
r
e
duc
e
d
to
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p5,916,876.7/hour
o
r
4.2%
a
t
ni
ght
pe
a
k
lo
a
d.
T
he
m
os
t
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xpe
ns
iv
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ge
ne
r
a
ti
on
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r
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obt
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f
r
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S
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m
bangk
it
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is
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T
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G
as
(
P
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uni
t,
w
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c
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th
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a
s
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la
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,
w
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c
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w
it
h
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of
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M
W
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hi
le
th
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c
he
a
pe
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d
f
r
om
th
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M
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(
P
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uni
t,
w
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c
h
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p1,451,132,365/hou
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h
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of
6.3 M
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N
e
xt
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us
e
th
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a
nt
c
ol
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opt
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(
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th
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F
r
om
th
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c
a
lc
ul
a
ti
on
r
e
s
ul
ts
[
9]
,
C
O
c
onve
r
ge
s
on
th
e
34
th
it
e
r
a
ti
on
w
it
h
a
ge
ne
r
a
ti
on
c
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t
of
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p1
31,473,269.39/hour
.
F
r
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c
om
put
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hour
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of
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p9.333.004.9/hour
or
6.62%
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c
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of
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p7
1,509,642,449/hour
,
w
it
h
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of
166,102
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W
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hi
le
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he
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pe
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it
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(
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W
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ig
ur
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2
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ph
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C
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S
[
1]
M
.
R
.
D
j
a
l
a
l
,
A
.
I
m
r
a
n,
a
nd
I
.
R
oba
ndi
,
“
O
pt
i
m
a
l
pl
a
c
e
m
e
nt
a
nd
t
uni
ng
pow
e
r
s
ys
t
e
m
s
t
a
bi
l
i
z
e
r
us
i
ng
pa
r
t
i
c
i
pa
t
i
on
f
a
c
t
or
a
nd
i
m
pe
r
i
a
l
i
s
t
c
om
pe
t
i
t
i
ve
a
l
gor
i
t
hm
i
n
150
kV
S
out
h
o
f
S
ul
a
w
e
s
i
s
ys
t
e
m
,”
i
n
20
15
I
nt
e
r
nat
i
onal
Se
m
i
nar
on
I
nt
e
l
l
i
ge
nt
T
e
c
hnol
ogy
and
I
t
s
A
ppl
i
c
at
i
ons
(
I
SI
T
I
A
)
, M
a
y 2015, pp. 147
–
152, doi
:
10.1109/
I
S
I
T
I
A
.20
15.7219970.
[
2]
M
.
Y
.
Y
unus
,
M
.
R
.
D
j
a
l
a
l
,
a
nd
M
.
M
a
r
ha
t
a
ng,
“
O
pt
i
m
a
l
de
s
i
gn
pow
e
r
s
ys
t
e
m
s
t
a
bi
l
i
z
e
r
us
i
ng
f
i
r
e
f
l
y
a
l
gor
i
t
hm
i
n
i
nt
e
r
c
onne
c
t
e
d
150
kV
S
ul
s
e
l
r
a
ba
r
S
ys
t
e
m
,
I
ndone
s
i
a
,”
In
t
e
r
nat
i
onal
R
e
v
i
e
w
of
E
l
e
c
t
r
i
c
al
E
ngi
ne
e
r
i
ng
(
I
R
E
E
)
,
vol
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A
.
M
a
hor
,
V
.
P
r
a
s
a
d,
a
nd
S
.
R
a
ngne
ka
r
,
“
E
c
onom
i
c
di
s
pa
t
c
h
us
i
ng
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on:
a
r
e
vi
e
w
,”
R
e
ne
w
abl
e
and
Sus
t
ai
nabl
e
E
ne
r
gy
R
e
v
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e
w
s
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. 13, no. 8, pp. 2134
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H
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Z
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I
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A
.
A
s
hr
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f
,
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.
A
hm
a
d,
“
P
ow
e
r
e
c
onom
i
c
di
s
pa
t
c
h
us
i
ng
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
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J
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S
R
E
T
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M
. M
ur
t
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dha
O
t
hm
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M
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f
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m
a
i
l
S
a
l
i
m
, I
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r
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. A
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da
S
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l
i
m
, a
nd M
.
L
ut
f
i
O
t
hm
a
n, “
D
yna
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i
c
e
c
onom
i
c
di
s
pa
t
c
h
a
s
s
e
s
s
m
e
nt
u
s
i
ng
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on
t
e
c
hni
que
,
”
B
ul
l
e
t
i
n
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E
l
e
c
t
r
i
c
al
E
ngi
ne
e
r
i
ng
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I
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m
at
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c
s
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M
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N
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A
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a
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,
“
S
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a
t
e
-
of
-
t
he
-
a
r
t
e
c
onom
i
c
l
oa
d
di
s
pa
t
c
h
of
pow
e
r
s
y
s
t
e
m
s
us
i
ng
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on,”
D
e
c
.
2018
.
A
r
X
i
v
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[
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V
.
K
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J
a
doun,
N
.
G
upt
a
,
K
.
R
.
N
i
a
z
i
,
a
nd
A
.
S
w
a
r
nka
r
,
“
N
on
c
onve
x
e
c
onom
i
c
di
s
pa
t
c
h
us
i
ng
p
a
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on
w
i
t
h
t
i
m
e
va
r
yi
ng ope
r
a
t
or
s
,”
A
dv
anc
e
s
i
n E
l
e
c
t
r
i
c
al
E
ngi
ne
e
r
i
ng
, vol
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–
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c
t
. 2014, doi
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S
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e
na
,
S
.
M
a
nj
a
ng,
a
nd
I
.
C
.
G
una
di
n,
“
O
pt
i
m
i
z
a
t
i
on
e
c
onom
i
c
pow
e
r
ge
ne
r
a
t
i
on
us
i
ng
m
odi
f
i
e
d
i
m
pr
ove
d
P
S
O
a
l
gor
i
t
hm
m
e
t
hods
,”
J
our
nal
of
T
he
o
r
e
t
i
c
al
and A
ppl
i
e
d I
nf
or
m
at
i
on T
e
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hnol
ogy
, vol
. 93, no. 2, pp. 522
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[
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T
a
s
r
i
f
,
S
uyono,
H
a
di
,
a
nd
R
.
N
ur
,
“
E
c
onom
i
c
di
s
pa
t
c
h
i
n
150
K
V
s
ul
s
e
l
r
a
ba
r
e
l
e
c
t
r
i
c
a
l
s
ys
t
e
m
us
i
ng
a
nt
c
ol
ony
opt
i
m
i
z
a
t
i
on,”
I
O
SR
J
our
nal
of
E
l
e
c
t
r
i
c
al
and
E
l
e
c
t
r
oni
c
s
E
ngi
ne
e
r
i
ng
(
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O
SR
-
J
E
E
E
)
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[
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D
.
M
c
L
a
r
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y,
N
.
P
a
nos
s
i
a
n,
F
.
J
a
bba
r
i
,
a
nd
A
.
T
r
a
ve
r
s
o,
“
D
yna
m
i
c
e
c
o
nom
i
c
di
s
pa
t
c
h
us
i
ng
c
om
pl
e
m
e
nt
a
r
y
qua
dr
a
t
i
c
pr
ogr
a
m
m
i
ng,
”
E
ne
r
gy
, vol
. 166, pp. 755
–
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n. 2019, doi
:
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j
.e
ne
r
gy
.2018.10.087.
[
11]
G
. X
i
ong
e
t
al
.
, “
A
nove
l
m
e
t
hod f
or
e
c
onom
i
c
di
s
pa
t
c
h w
i
t
h a
c
r
os
s
n
e
i
ghbor
hood s
e
a
r
c
h:
a
c
a
s
e
s
t
udy i
n
a
pr
ovi
nc
i
a
l
pow
e
r
gr
i
d,
C
hi
na
,”
C
om
pl
e
x
i
t
y
, vol
. 2018, pp. 1
–
18, N
o
v. 2018, doi
:
10.1155/
2018/
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41.
[
12]
Z
. Y
oune
s
, I
. A
l
ha
m
r
ouni
, S
. M
e
khi
l
e
f
, a
nd M
.
R
e
ya
s
udi
n, “
A
m
e
m
or
y
-
ba
s
e
d
gr
a
vi
t
a
t
i
ona
l
s
e
a
r
c
h a
l
gor
i
t
hm
f
or
s
ol
vi
ng e
c
onom
i
c
di
s
pa
t
c
h
pr
obl
e
m
i
n
m
i
c
r
o
-
gr
i
d,”
A
i
n
Sham
s
E
ngi
ne
e
r
i
ng
J
our
nal
,
vol
.
12,
no.
2,
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1
994,
J
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j
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s
e
j
.2020.10.021.
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M
.
I
m
r
a
n,
R
.
H
a
s
hi
m
,
a
nd
N
.
E
.
A
.
K
h
a
l
i
d,
“
A
n
ov
e
r
vi
e
w
of
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on
va
r
i
a
nt
s
,”
P
r
oc
e
di
a
E
ngi
ne
e
r
i
ng
,
vol
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53, pp. 491
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496, 2013, doi
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.pr
oe
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G
. P
e
r
e
i
r
a
, “
P
a
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on,”
I
N
E
SC
I
D
and I
ns
t
i
t
ut
o Supe
r
i
or
T
e
c
ni
c
o
, vol
. 15, 2011.
[
15]
M
.
F
.
A
r
a
nz
a
,
J
.
K
us
t
i
j
a
,
B
.
T
r
i
s
no,
a
nd
D
.
L
.
H
a
ki
m
,
“
T
unni
ng
P
I
D
c
ont
r
ol
l
e
r
us
i
ng
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on
a
l
gor
i
t
h
m
on
a
ut
om
a
t
i
c
vol
t
a
ge
r
e
gul
a
t
or
s
ys
t
e
m
,”
I
O
P
C
o
nf
e
r
e
nc
e
Se
r
i
e
s
:
M
at
e
r
i
al
s
Sc
i
e
nc
e
and
E
ngi
ne
e
r
i
ng
,
vol
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no.
1,
A
pr
.
2016,
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M
.
S
a
i
ni
,
A
.
M
.
S
hi
ddi
q
Y
unus
,
a
nd
M
.
R
.
D
j
a
l
a
l
,
“
O
pt
i
m
a
l
P
S
S
de
s
i
gn
us
i
n
g
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on
unde
r
l
oa
d
s
he
ddi
ng
c
ondi
t
i
on,”
i
n
P
r
oc
e
e
di
ng
s
-
2020
I
nt
e
r
nat
i
onal
Se
m
i
na
r
on
I
nt
e
l
l
i
ge
nt
T
e
c
hnol
ogy
and
I
t
s
A
ppl
i
c
at
i
on:
H
um
ani
f
i
c
at
i
on
of
R
e
l
i
abl
e
I
nt
e
l
l
i
ge
nt
Sy
s
t
e
m
s
, I
SI
T
I
A
2020
,
J
ul
. 2020, pp. 405
–
410, doi
:
10.1109
/
I
S
I
T
I
A
49792.2020.9163779.
[
17]
Z
. Q
i
, Q
. S
hi
, a
nd
H
. Z
ha
ng,
“
T
uni
ng of
di
gi
t
a
l
P
I
D
c
ont
r
ol
l
e
r
s
u
s
i
ng pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on a
l
gor
i
t
hm
f
or
a
C
A
N
-
ba
s
e
d D
C
m
ot
or
s
ubj
e
c
t
t
o
s
t
oc
ha
s
t
i
c
de
l
a
ys
,”
I
E
E
E
T
r
ans
ac
t
i
ons
on
I
ndus
t
r
i
al
E
l
e
c
t
r
oni
c
s
,
vol
.
67,
no.
7,
pp.
5637
–
5646,
J
ul
.
2020,
doi
:
10.1109/
T
I
E
.2019.2934030.
[
18]
H
.
M
.
S
a
l
m
a
n,
A
.
K
.
M
.
A
l
-
Q
ur
a
ba
t
,
a
nd
A
.
A
.
R
i
ya
dh
F
i
nj
a
n,
“
B
i
gr
a
di
e
nt
ne
ur
a
l
ne
t
w
or
k
-
ba
s
e
d
qua
nt
um
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on f
or
bl
i
nd s
our
c
e
s
e
pa
r
a
t
i
on,”
I
A
E
S I
nt
e
r
nat
i
onal
J
our
nal
of
A
r
t
i
f
i
c
i
al
I
nt
e
l
l
i
ge
nc
e
(
I
J
-
A
I
)
, vol
. 10, no. 2, pp. 355
–
364,
J
un. 2021, doi
:
10.11591/
i
j
a
i
.v10.i
2.pp355
-
364.
[
19]
M
.
I
.
S
ol
i
hi
n,
L
.
F
.
T
a
c
k,
a
nd
M
.
L
.
K
e
a
n,
“
T
uni
ng
of
P
I
D
c
ont
r
ol
l
e
r
us
i
ng
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on
(
P
S
O
)
,”
I
nt
e
r
nat
i
onal
J
our
nal
on A
dv
anc
e
d Sc
i
e
nc
e
, E
ngi
ne
e
r
i
ng and I
nf
or
m
a
t
i
on T
e
c
hnol
ogy
, vol
. 1
, no. 4, 2011, doi
:
10.18517/
i
j
a
s
e
i
t
.1.4.93.
[
20]
Y
.
D
hi
e
b,
M
.
Y
a
i
c
h,
A
.
G
ue
r
m
a
z
i
,
a
nd
M
.
G
h
a
r
i
a
ni
,
“
P
I
D
c
ont
r
ol
l
e
r
t
uni
ng
u
s
i
ng
a
nt
c
ol
ony
opt
i
m
i
z
a
t
i
on
f
or
i
nduc
t
i
on
m
ot
or
,”
J
our
nal
of
E
l
e
c
t
r
i
c
al
Sy
s
t
e
m
s
, vol
. 15, no. 1, pp. 133
–
141
, 2019.
[
21]
I
. C
hi
ha
, N
. L
i
oua
ne
, a
nd
P
. B
or
ne
, “
T
uni
ng P
I
D
c
ont
r
ol
l
e
r
us
i
ng m
ul
t
i
obj
e
c
t
i
v
e
a
nt
c
ol
ony opt
i
m
i
z
a
t
i
on,”
A
ppl
i
e
d C
om
put
at
i
onal
I
nt
e
l
l
i
ge
nc
e
and Sof
t
C
om
put
i
ng
, vol
. 2012, pp. 1
–
7, 2012, doi
:
10.1155/
2012/
536326.
[
22]
K
. M
a
, C
.
W
a
ng, J
. Y
a
ng,
Q
. Y
a
ng, a
nd Y
. Y
u
a
n, “
E
c
onom
i
c
di
s
pa
t
c
h
w
i
t
h de
m
a
nd r
e
s
pons
e
i
n
s
m
a
r
t
gr
i
d:
B
a
r
ga
i
ni
ng m
ode
l
a
nd
s
ol
ut
i
ons
,”
E
ne
r
gi
e
s
, vol
. 10, no. 8, p. 1193, A
ug. 2017, doi
:
10.3390/
e
n10081193.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
11
, N
o.
1
,
M
a
r
c
h
2022
:
221
-
228
228
[
23]
J
.
Z
ha
ng,
J
.
Z
ha
ng,
F
.
Z
ha
ng,
M
.
C
hi
,
a
nd
L
.
W
a
n,
“
A
n
i
m
p
r
ove
d
s
ym
bi
os
i
s
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on
f
or
s
ol
vi
ng
e
c
onom
i
c
l
oa
d
di
s
pa
t
c
h
pr
obl
e
m
,”
J
our
nal
of
E
l
e
c
t
r
i
c
al
and
C
om
put
e
r
E
ngi
ne
e
r
i
ng
,
vol
.
2021,
pp.
1
–
11,
J
a
n.
2021,
doi
:
10.1155/
2021/
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[
24]
N
.
M
.
A
z
ki
ya
,
A
.
G
.
A
bdul
l
a
h,
a
nd
H
.
H
a
s
bul
l
a
h,
“
E
c
onom
i
c
di
s
pa
t
c
h
a
nd
op
e
r
a
t
i
ng
c
os
t
opt
i
m
i
z
a
t
i
on
f
or
t
he
r
m
a
l
pow
e
r
i
n
500
K
V
s
ys
t
e
m
u
s
i
ng
ge
ne
t
i
c
a
l
gor
i
t
hm
(
G
A
)
,”
I
O
P
C
onf
e
r
e
nc
e
S
e
r
i
e
s
:
M
at
e
r
i
al
s
Sc
i
e
nc
e
and
E
ngi
ne
e
r
i
ng
,
vol
.
434,
no.
1,
D
e
c
.
2018, doi
:
10.1088/
1757
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/
434/
1/
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[
25]
B
.
H
ua
ng,
C
.
Z
he
ng,
Q
.
S
un,
a
nd
R
.
H
u,
“
O
pt
i
m
a
l
e
c
onom
i
c
di
s
p
a
t
c
h
f
or
i
nt
e
gr
a
t
e
d
pow
e
r
a
nd
he
a
t
i
ng
s
ys
t
e
m
s
c
ons
i
de
r
i
ng
t
r
a
ns
m
i
s
s
i
on l
os
s
e
s
,”
E
ne
r
gi
e
s
, vol
. 12, no. 13, J
un. 2019, doi
:
10.3390/
e
n12132502.
[
26]
B
.
D
e
y,
B
.
B
h
a
t
t
a
c
ha
r
yya
,
a
nd
F
.
P
.
G
.
M
á
r
que
z
,
“
A
hybr
i
d
opt
i
m
i
z
a
t
i
on
-
ba
s
e
d
a
ppr
oa
c
h
t
o
s
ol
v
e
e
nvi
r
onm
e
nt
c
ons
t
r
a
i
ne
d
e
c
onom
i
c
di
s
pa
t
c
h
pr
obl
e
m
on
m
i
c
r
og
r
i
d
s
ys
t
e
m
,”
J
our
nal
of
C
l
e
ane
r
P
r
oduc
t
i
on
,
vol
.
307,
J
ul
.
2021,
doi
:
10.1016/
j
.j
c
l
e
pr
o.2021.127196.
B
I
O
G
R
A
P
H
I
E
S
O
F
A
U
T
H
O
R
S
Marhatan
g
was
born
in
Soppeng
-
Indonesia
on
N
ovember
17,
1
974.
He
received
bachelor
degree
from
Electronic
Engineering
Polytechnic
Institute
of
Surabaya
(Surabaya,
Indonesia),
majors
in
Electrical
Engineering
in
2002.
Then,
master
degree
from
Hasanuddin
University
(Makassar,
Indonesia)
,
majors
in
Electrical
Engineering
in
2012.
His
research
about,
Power
Electronic,
Renewable
Energy,
and
Electrical
Power
System.
Now,
He
is
lecturer
at
State
Polytec
hnic of
Ujung
Pandan
g (PNU
P).
He can be contacted at email:
marhatang
@
poliupg.ac.id
.
Muhammad
Ruswan
di
Djalal
was
born
in
Makassar
-
Indonesi
a
on
Mar
ch
11,
1990.
He
received
bachelor
degree
from
State
Polytechnic
of
U
jung
Pandang
(Makassar,
Indonesia), m
ajors in E
nergy Generation
engineering
in 2012.
Then,
master degree from
Sepuluh
Nopember
Institute
of
Technology,
(ITS
Surabaya,
Indonesia),
majors
in
Power
System
Engineering
in
2015.
His
research
about,
Power
System
Operation
and
Control,
Renewable
Energy
and
Artificial
Intelligent.
Now,
He
is
lecturer
at
State
Polyt
echnic
of
Ujung
Pandang
(PNUP).
He can be contacted at email:
wandi@
poliupg.ac.id
.
Evaluation Warning : The document was created with Spire.PDF for Python.