Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol.
4, No. 6, Decem
ber
2014, pp. 858~
867
I
S
SN
: 208
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Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Applications of Particle Swar
m Optimization Algorithm to
Solving the Economic Load Dispat
ch of Units in Power Systems
with Valve-Point Effects
Hossein
Sh
ahi
n
z
a
deh
1
, S
a
ye
d Mohse
n
Nas
r
-Az
a
d
a
ni
2
, Naz
ereh
Janne
s
a
ri
3
1,2
Department of
Electr
i
cal
Engin
eeing
,
Amirkabir
University
of Technolog
y
(Tehr
a
n Poly
technic),
Tehran
, Ir
an
3
Department of Engineering,
SepahanInstitueof
Higher
Edu
c
atio
n, Isfah
a
n, Iran
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 19, 2014
Rev
i
sed
No
v
21
, 20
14
Accepted Nov 30, 2014
Reduction o
f
o
p
erating costs
in power s
y
stem in order to
return th
e
investment costs and more pr
ofitabi
lit
y h
a
s vital im
port
a
nc
e in power
industr
y
.
Econo
mic Load
Dispatch (ELD)
is on
e
of the most important issues
in reducing op
er
ating cos
t
s
.
EL
D is
form
ulated as
a nonlinear
optim
izat
ion
problem with continuous variables w
ithin
the power plan
ts. The main
purpose of this problem is optimal pl
anning of
power generation in power
pl
a
n
t
s
wi
t
h
mi
nimum c
o
st
by
t
o
ta
l
unit
s
,
re
ga
rded t
o
e
qual
i
t
y
a
n
d i
n
e
quality
constrain
t
s inclu
d
ing load deman
d
and the rang
e of units'
power p
r
oductiv
ity
.
In this article,
Economic Lo
ad
Disp
atch problem has been
modeled b
y
considering th
e valve-poin
t
loading e
ffects with power plants' constraints
such as: the balance of productio
n and
consumption in sy
st
em, the forbidden
zones, rang
e o
f
production
,
increasi
ng and decreasing
ra
tes, reliability
constrain
t
s and network security
. To solve th
e problem, Particle Swarm
Optim
izatio
n (P
S
O
) Algorithm
s
has
been
em
plo
y
ed. To evalu
a
te t
h
e
effectiven
ess of
the proposed
method,
the p
r
oblem has been
implemented on
a power
s
y
stem with 15 g
e
ne
r
a
ting units
and
the
results hav
e
b
e
en evaluated.
Keyword:
Econom
ic Loa
d
Dispatc
h
O
p
er
ating
Particle Swarm Op
ti
m
i
zatio
n
Power System
Valv
e-Po
in
t Effects
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Hos
s
ein Sha
h
i
n
zade
h
,
IEEE Mem
b
er, De
partm
e
nt of
Electrical Engineeing,
Am
i
r
kabi
r
Uni
v
ersi
t
y
o
f
Tec
h
nol
ogy
,
Te
hra
n
, I
r
an
.
Em
a
il: H.S.Shah
in
zad
e
h@ieee.o
rg, Sh
ah
in
zad
e
h@au
t.ac.ir.
1.
INTRODUCTION
Mo
st of
op
timizatio
n
p
r
oble
m
s in
po
w
e
r
syst
em
s are Econom
i
c L
o
ad Dis
p
atch (EL
D
) wit
h
co
m
p
licated
a
n
d
n
o
n
lin
ear ch
aracteristics,
eq
u
a
lity an
d
in
equ
a
lity co
n
s
train
t
s, th
at
mak
e
s th
em
d
i
fficu
lt to
so
lv
e m
a
th
em
a
tically. ELD is on
e of t
h
e main
issu
es in
t
e
rm
s o
f
m
a
n
a
g
e
m
e
n
t
an
d
operatio
n
of th
e
p
o
wer
syste
m
th
at
its
p
u
rp
o
s
e
was to d
e
term
in
e th
e
p
r
od
u
c
tion
rate p
e
r un
it po
wer p
l
an
t in
a
way th
at syste
m
's
lo
ad
is p
r
ov
id
ed
wi
th
th
e m
i
n
i
m
u
m
co
st, wh
ile all co
n
s
t
r
aints are respecte
d
.ELD
has
been com
p
licated
by the
enlargem
ent of powe
r systems and it
became difficult to fi
nd the
best
of
many local opt
i
m
u
m
points.
In
ge
neral
,
t
h
e
m
e
t
hods
p
r
o
p
o
se
d t
o
s
o
l
v
e
ELD,
can
be
di
vi
de
d i
n
t
o
t
w
o c
a
t
e
g
o
ri
es,
t
h
e cl
assi
c
m
e
t
hods an
d t
h
e sm
art
m
e
t
h
ods
. G
r
adi
e
nt
m
e
t
hod,
rep
e
titio
n
,
n
o
n
lin
ear p
r
og
ramm
i
n
g, and
d
y
n
a
mic
pr
o
g
ram
m
i
ng
are t
h
e
fi
rst
m
e
t
h
o
d
s
pr
o
p
o
s
e
d
t
o
s
o
l
v
e t
h
e
Eco
nom
i
c
Loa
d
Di
spat
c
h
pr
o
b
l
e
m
;
ho
wev
e
r
t
h
ese
m
e
thods woul
d not be use
f
ul
whe
n
the cost functions ar
e nonlinea
r. S
o
in som
e
cases, it
will be very di
fficult
to
ach
iev
e
o
p
t
i
m
al
so
lu
tio
ns. Fo
r th
is reaso
n
, in
recen
t
years, th
e sm
a
r
t alg
o
r
it
h
m
s
h
a
v
e
b
een
u
s
ed
fo
r
heu
r
i
s
t
i
c
o
p
t
i
m
i
zat
i
on
m
e
t
hods
t
o
o
v
erc
o
m
e
t
h
i
s
pr
o
b
l
e
m
.
Theref
ore i
n
rece
nt
y
ears
,
di
f
f
ere
n
t
sm
art
an
d
in
no
v
a
tiv
e algo
rith
m
s
su
ch
as: Gen
e
tic Algo
rith
m
(GA)
, Particle Swarm Op
ti
m
i
za
tio
n
(PSO), Evo
l
u
tio
n
a
ry
Pro
g
r
am
m
i
ng
Al
g
o
ri
t
h
m
(EP
)
,
Gra
v
i
t
a
t
i
ona
l
Searc
h
Al
g
o
r
i
t
h
m
(GS
A
)
,
… ha
ve
bee
n
pr
o
pose
d
t
o
s
o
l
v
e t
h
i
s
pr
o
b
l
e
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE Vol. 4, No. 6, D
ecem
ber 2014
:
858 – 867
8
59
In
referen
ce [1-2
]
o
f
t
h
e classi
c
m
e
th
o
d
,
Lag
r
ang
e
m
u
ltip
l
i
er
b
a
sed
on
no
n
lin
ear p
r
og
ra
mmin
g
h
a
s
been
use
d
t
o
sol
v
e EL
D i
ssu
e. In re
fere
nce
s
[3-
5
]
,
t
y
pes o
f
cl
assi
c al
gori
t
hm
s and de
vel
ope
d pa
rt
i
c
l
e
swarm
s
have
been
use
d
t
o
sol
v
e t
h
e p
r
obl
em
.
In refe
r
e
nces [
6
-
1
4]
, o
t
her ty
pes o
f
s
m
art algorithms such as the
genetic
al
go
ri
t
h
m
and
m
odi
fi
cat
i
o
n
of i
t
s
ext
e
n
d
ed
versi
o
n
,
evol
ut
i
ona
ry
p
r
o
g
ram
m
i
ng al
go
ri
t
h
m
,
di
fferent
i
a
l
evol
ut
i
o
n
,
gra
v
i
t
a
t
i
onal
searc
h
al
go
ri
t
h
m
and
hy
b
r
i
d
al
g
o
ri
t
h
m
s
have
bee
n
use
d
t
o
s
o
l
v
e
t
h
e Ec
on
om
i
c
Loa
d
Di
spat
c
h
pr
obl
em
.
In
th
is article, p
a
rticle swarm
o
p
timizatio
n
(PSO)
al
go
ri
t
h
m
has been us
ed t
o
sol
v
e t
h
e
Econ
om
i
c
Loa
d
Dis
p
atch problem
. To s
o
lve m
o
re real
istic
m
odel of
ELD iss
u
e, the
effect of
th
e stea
m
in
let v
a
lv
e h
a
s
b
een con
s
i
d
ered
in th
e co
st
fun
c
tio
ns related
to
th
e
po
we
r
pl
ants'
fuel.
Fina
lly, in orde
r to
show t
h
e e
ffici
ency
of
t
h
e
pr
o
p
o
s
e
d
al
g
o
r
i
t
h
m
,
a po
we
r sy
st
em
wi
t
h
15
ge
ne
ra
t
i
ng
uni
t
s
a
n
d i
t
s res
u
l
t
s
ha
ve
been
eval
uat
e
d
.
2.
FOR
M
ULAT
ION OF
T
H
E ECON
O
M
IC
LOAD
D
I
SP
A
T
CH
P
R
OBL
E
M
2.
1.
Th
e Cos
t
Functi
on by
C
o
nsiderin
g
the
V
a
lve
-
Poin
t Effect
s
The E
L
D
det
e
r
m
i
n
es a m
e
t
hod
wi
t
h
t
h
e
m
o
st
effi
ci
ency
, t
h
e l
o
west
c
o
st
a
n
d
t
h
e
rel
i
a
bl
e
ope
rat
i
o
n
of
a po
wer system
with
p
r
op
er Disp
atch
o
f
en
erg
y
g
e
n
e
ratin
g sources to
su
pp
ly th
e
syste
m
's lo
ad
.
Its
p
r
im
ary
p
u
rp
o
s
e is t
o
min
i
mize th
e to
tal co
st of produ
ctio
n
w
ith reg
a
rd
t
o
o
p
eratio
n
a
l limit
atio
n
s
o
f
g
e
neratin
g
reso
u
r
ces. T
h
e
ELD i
ssue
de
t
e
rm
i
n
es t
h
e am
ount
of l
o
a
d
for
p
o
we
r pl
a
n
t
s
i
n
o
r
de
r t
o
red
u
ce t
h
e co
st
s. It
s
fo
rm
ul
at
i
on i
s
im
pl
em
ent
e
d as an opt
i
m
i
zation
pr
obl
em
t
o
m
i
nim
i
ze
t
h
e t
o
t
a
l
cost
of f
u
el
of p
o
w
er
pl
ant
s
wh
ich
p
r
ov
id
e
lo
ad
and
loss.
So
t
h
e ELD issu
e can
b
e
ex
pressed
with
t
h
e fo
llowing
ob
j
e
ctiv
e
fu
n
c
tion
:
2
11
mi
n
NN
ii
l
i
D
L
o
s
s
ii
FP
K
P
P
P
(1
)
In
t
h
e a
b
ove
eq
uat
i
on:
ii
FP
: is fu
el co
st
o
f
th
e
th
i
po
we
r pl
ant
,
N
: is nu
m
b
er of
g
e
n
e
rators
op
eratin
g system
,
i
P
: is ou
tpu
t
power
o
f
t
h
e
th
i
gene
r
a
t
o
r;
D
P
: is lo
ad d
e
m
a
n
d
;
Lo
s
s
P
: is tran
sm
issio
n
n
e
two
r
k
'
s lo
ss.
ii
FP
: as a
qua
dratic
equation ca
n
be expres
sed as
follows:
2
ii
i
i
i
i
i
F
Pa
b
P
c
P
(2
)
In e
quatio
n
(2
),
a
i
,
b
i
a
nd
c
i
are cost coefficients of t
h
e
th
i
g
e
n
e
r
a
to
r
.
T
o
co
n
s
id
e
r
th
e
v
a
lv
e
-
p
o
i
n
t
effects, sin
e
fun
c
tio
ns
g
e
t in
t
o
th
e obj
ectiv
e
fun
c
tion
as
fo
llo
ws:
2m
i
n
ii
i
i
i
i
i
i
i
i
i
FP
a
b
P
c
P
e
S
i
n
h
P
P
(3
)
Th
at in
th
e abo
v
e
equ
a
tio
n,
i
e
and
i
h
are co
efficien
ts co
rrespo
nd
ing
to
t
h
e
p
o
s
ition
o
f
the
th
i
gene
rat
o
r'
s st
eam
val
v
es, t
h
e cost
fu
nct
i
o
n o
f
eq
uat
i
o
n
(1) c
h
a
nges
i
n
t
o
a n
o
n
-
co
nve
x an
d
pol
y
nom
i
a
l
com
posi
t
e
fun
c
t
i
on. Fi
g
u
r
e
1 sh
ows t
h
e
v
a
l
v
e-
poi
nt
effe
ct
s on t
h
e n
o
n
l
i
n
eari
t
y
of t
h
e cost
f
unct
i
on
. In
ad
d
ition
to
th
e effects of v
a
lve's p
o
s
itio
n
,
any o
t
h
e
r co
st
s su
ch
as m
a
in
ten
a
n
ce co
sts or po
llu
tio
n
can
b
e
ad
ded
to
th
e co
st
fu
nctio
n
.
Th
e
o
b
t
ain
e
d obj
ective fu
n
c
tion subj
ect to th
e fo
llo
wi
n
g
limitat
i
o
n
s
wou
l
d resu
lt the
form
u
l
atio
n
of
th
e ELD issu
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
App
lica
tio
ns
o
f
Pa
rticle S
w
a
r
m
Op
timiza
tion
Al
g
o
r
ithm t
o
S
o
l
ving
t
h
e Eco
nomic … (Hossein
S
hah
in
zad
e
h
)
86
0
$/MW
Fig
u
re
1
.
Th
e
v
a
lv
e-po
in
t effects on
th
e co
st
fu
n
c
tion
o
f
power p
l
an
t un
it.
2.2. I
ssue B
o
n
d
s:
2.
2.
1. T
h
e Bal
a
nce
of Pr
odu
c
tion
and
Con
s
umpti
o
n
of P
o
wer in
the
System
Th
e to
tal po
wer g
e
n
e
rated
by all u
n
its in
t
h
e circu
it m
u
st
b
e
equ
a
l to
the to
tal co
n
s
u
m
p
tio
n
o
f
the
syste
m
.
1
0
N
iD
L
o
s
s
i
PP
P
(4
)
Transm
ission network'
s loss
(
L
os
s
P
)
d
e
pend
s
o
n
th
e ph
ysical stru
ctur
e of
th
e
netw
or
k
and
th
e r
a
te of
pr
o
duct
i
o
n, a
n
d i
s
cal
cul
a
t
e
d by
usi
n
g l
o
ad fl
ow cal
c
u
l
a
t
i
ons o
r
B
lo
ss co
efficien
ts
with
th
e
fo
ll
owing
fo
rm
ula:
00
,
0
11
1
NN
N
Lo
s
s
i
j
i
j
i
i
ij
i
P
BP
P
B
P
B
(5
)
Th
at in
th
e
abo
v
e
equ
a
tion
,
,
ij
B
is
th
i
,
th
j
lo
ss ele
m
e
n
t of a lo
ss
squ
a
re m
a
trix
,
0,
i
B
is
th
e
th
i
loss
v
ector
an
d
0,0
B
is th
e loss co
nstant.
2.
2.
2. Pow
er Genera
tio
n
Limita
tions
The o
u
t
p
ut
p
o
w
er
of eac
h ge
nerat
o
r m
u
st
not
be hi
ghe
r t
h
an t
h
e n
o
m
i
nal
and i
t
sh
oul
d
not
be l
e
ss
t
h
an t
h
e am
ount
w
h
i
c
h i
s
nec
e
ssary
f
o
r t
h
e s
t
abl
e
o
p
erat
i
o
n
of t
h
e b
o
i
l
e
r.
Th
us, t
h
e
p
r
o
d
u
ct
i
o
n
i
s
so l
i
m
i
t
e
d t
o
be
bet
w
ee
n
p
r
edet
erm
i
ned
m
i
nim
u
m
and m
a
xim
u
m
range
. Eac
h
pr
od
uct
i
v
i
t
y
u
n
i
t
wi
t
h
a
n
est
i
m
a
t
e
d
p
r
od
u
c
tion
can b
e
exp
r
essed by th
e fo
llowing equ
a
tio
n in the circu
it:
mi
n
m
a
x
ii
i
PP
P
(6
)
Abov
e estim
at
i
o
n
s
, in add
ition
to b
e
i
n
g cau
sed
b
y
tech
n
i
cal con
s
train
t
s
of
p
e
r
un
it, will l
ead
th
at t
h
e
u
n
it with
lo
wer co
st d
o
e
s n
o
t
p
r
odu
ce m
o
re th
an
its
m
a
x
i
m
u
m al
lo
wab
l
e p
o
wer and
the u
n
it with
m
o
re co
st
doe
s
not
pr
o
d
u
ce l
o
we
r t
h
an
i
t
s
al
l
o
wa
bl
e p
o
w
er
.
2.2.3. Limitati
on
of In
cre
asi
n
g and Decre
asing
Rate
of Power
Ge
neration
For technical reasons, the
r
m
a
l po
wer
plants
cannot inc
r
ea
se or
dec
r
ease
their power i
mmediately
and this
gain or loss is associ
ated
with a pa
use. In this wa
y, each powe
r plant has lim
itations in gra
d
ient
of
in
creasing
o
r
decreasing
of its p
r
o
d
u
c
tiv
ity p
o
wer th
at v
i
olatio
n
o
f
these restrictio
n
s
will resu
lt in
d
a
mag
e
t
o
th
e ro
tor an
d it cau
ses m
o
re op
eration
co
sts,
th
at th
es
e con
s
train
t
s are expressed
b
y
th
e follo
wing
relatio
n
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE Vol. 4, No. 6, D
ecem
ber 2014
:
858 – 867
8
61
mi
n
m
a
x
mi
n
m
i
n
ma
x
m
ax
max
1
,
mi
n
1
,
ii
i
ii
i
i
ii
i
i
Pt
P
t
P
t
Pt
P
t
R
D
R
P
Pt
P
t
R
U
R
P
(7
)
In
ab
o
v
e e
quat
i
on,
i
RD
R
i
s
t
h
e
red
u
ced
rat
e
o
f
pl
ant
'
s po
wer
ge
nerat
i
o
n a
n
d
i
RU
R
is the i
n
creas
e
d
rat
e
o
f
pl
ant
'
s po
we
r ge
ne
rat
i
o
n
.
I
n
or
de
r t
o
enf
o
rce
t
h
es
e
co
n
s
t
r
ain
t
s, it is n
ecessary to
ascertain
th
e statu
s
of
pri
m
ary
pr
od
u
c
t
i
on
of
pe
r
po
wer
pl
a
n
t
.
2.
2.
4. E
n
vi
r
o
n
ment
a
l
C
o
s
t
s
Red
u
c
tion
o
f
air po
llu
tion
is
certain
ly on
e
o
f
t
h
e m
o
st i
m
p
o
rtan
t ch
alleng
es
facing
h
u
man
ity n
o
w
and
i
n
t
h
e c
o
m
i
ng
deca
des.
E
l
ect
ri
ci
t
y
gener
a
t
e
d f
r
om
fossi
l
fuel
s,
sp
rea
d
s
seve
ral
di
ffe
re
nt
su
bst
a
nces s
u
ch
as sul
f
u
r
di
o
x
i
de, ni
t
r
o
g
e
n
oxi
de an
d car
bo
n di
oxi
de i
n
t
h
e ai
r. Tw
o m
o
st
im
port
a
nt
sam
p
l
e
s of t
h
ese
com
pou
nd
s t
h
at
pr
od
uce
d
i
n
t
h
e m
o
st
pow
er pl
a
n
t
s
are
N
i
t
r
oge
n
Oxi
d
e
(
X
NO
) and
sul
f
u
r
d
i
oxi
de
(
X
SO
). I
n
th
is article, th
e co
sts cau
sed
by th
e sp
read
ing p
r
ev
en
tion
o
f
these com
pounds in the ai
r
,
h
a
ve bee
n
co
nsi
d
ere
d
in
th
e
ob
j
e
ctive fu
n
c
tion
.
Di
ff
usi
on e
q
ua
t
i
on i
s
co
nsi
d
er
ed as a
q
u
ad
rat
i
c
fu
nc
tion wit
h
consta
nt coe
f
ficients for eac
h unit. T
h
e
to
tal d
i
ffu
s
ion
co
st is u
s
ed
as
th
e ob
j
ectiv
e
fu
n
c
tion
(co
s
t fu
n
c
tion) to
b
e
min
i
mized
. Of co
urse, t
h
e
g
factor
is conside
r
ed a
s
a
price e
r
ror
factor.
g
factor's u
n
it is
$/
K
G
an
d
co
nve
rt
s t
h
e
di
ff
usi
o
n
fu
nct
i
o
n
t
o
t
h
e
cost
fu
nct
i
o
n:
11
nn
o
b
j
ii
ii
ii
F
CP
EP
(8
)
2.
2.
5. For
b
i
d
d
e
n
z
o
nes
For tec
hnical
reasons
,
plants
can
no
t pr
oduce p
o
w
e
r
i
n
so
m
e
areas between t
h
e minim
u
m
and
m
a
xim
u
m
of t
h
ei
r
ow
n
pr
od
uct
i
o
n
.
T
h
ese
areas nam
e
d a
s
fo
r
b
i
d
den z
o
nes a
nd
defi
ne
d as
,,
[]
ij
L
i
j
U
PP
. So
the possi
ble tas
k
a
r
eas
of the
th
i
pr
o
duct
i
o
n
u
n
i
t
are s
p
eci
fi
e
d
a
ccor
d
i
n
g t
o
e
q
uat
i
o
n
9:
mi
n
,1
,j
1
,
j
max
,
,
j
2
,
3
,
...
,
i
L
ii
i
UL
ii
i
i
U
iz
i
i
PP
P
PP
P
z
PP
P
(9
)
That
i
z
i
s
t
h
e
n
u
m
ber of
f
o
r
b
i
d
den
zo
nes
o
f
t
h
e
th
i
un
it.
2
.
2
.
6
.
Relia
bility
Co
nstra
i
nts
a
n
d Netwo
r
k Security
Oth
e
r co
n
s
t
r
ain
t
s
d
u
e
to
stan
d
a
rd
s
o
f
reliab
ility a
n
d
n
e
t
w
ork secu
rity
can
also
b
e
co
n
s
i
d
ered
as
t
echni
cal
c
onst
r
ai
nt
s
of
ELD
i
ssue.
I
n
m
o
st cases, thes
e limitations are
cons
i
d
ere
d
i
n
ot
he
r st
u
d
i
e
s
or
pl
a
nni
n
g
an
d
ELD
is reso
lv
ed
with
ou
t co
ns
ideration of these
constrai
nts.
3.
PARTICLE SWARM OPTIMIZ
A
TION ALGO
RITH
M (PSO
)
For t
h
e fi
rst
t
i
m
e, Kenne
dy
and
Ay
b
r
ha
rt
, i
n
t
r
o
d
u
ced
par
t
i
c
l
e
swarm
opt
im
i
zat
i
on algo
ri
t
h
m
as a
new
m
e
t
hod i
n
1
9
9
5
[1
5]
. T
h
e m
a
i
n
p
u
r
p
o
s
e
of
t
h
ei
r
resea
r
ch
was t
o
si
m
u
l
a
t
e
t
h
e soci
al
beha
vi
o
r
of
fl
o
c
k a
n
d
fi
sh. B
y
de
vel
opi
ng t
h
ei
r res
earch
, t
h
ey
di
s
c
ove
re
d t
h
at
t
h
e
m
odel
of t
h
e
s
e gr
o
ups'
m
e
m
b
ers'
soci
al
b
e
havi
or
can al
s
o
act
as
a p
o
we
rf
ul
opt
i
m
i
zat
i
on m
e
t
hod
wi
t
h
som
e
m
odi
fi
cat
i
ons.
The
fi
rst
versi
o
n
of t
h
i
s
m
e
t
hod
was
ju
st
use
d
t
o
s
o
l
v
e n
o
n
l
i
n
ear c
ont
i
n
u
o
u
s
o
p
t
i
m
i
zat
i
on pr
obl
em
s. Ho
we
ver,
m
a
ny
adva
nce
s
i
n
o
r
de
r t
o
de
vel
o
p
th
is field
,
h
a
v
e
u
p
g
r
ad
ed
its ab
ilities to
so
lv
e a larg
e rang
e o
f
co
m
p
lex
op
ti
m
i
zatio
n
p
r
o
b
l
em
s in
scie
n
ce and
engi
neeri
n
g
.
The
key
an
d at
t
r
act
i
v
e aspect
of
PS
O i
s
i
t
s
si
m
p
li
ci
t
y
, so t
h
at
i
t
onl
y
has t
w
o m
odel
s
of
equat
i
o
n.
I
n
this
m
e
thod, ea
ch particle'
s
coordinates re
pre
s
ent a po
ssi
ble answe
r
associ
ated w
ith two
vectors, position (
X
i
)
and vel
o
city (
i
V
)
vectors, i
n
the
N-dim
e
nsional searc
h
s
p
ace i
n
clude:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Applications
of Particle Sw
arm
Op
timization Al
gorithm t
o
Solving t
h
e Ec
o
nomic … (Hossein
S
hah
in
zad
e
h
)
86
2
12
,,
.
.
.
,
ii
i
i
N
XX
X
X
That
,
,
k
in
n
n
X
lu
,
1
nN
suc
h
that
n
u
and
n
l
are respectively the upper lim
it and
lo
wer limit fo
r t
h
e
th
n
di
m
e
nsi
o
n a
n
d
12
,,
.
.
.
,
ii
i
i
N
VV
V
V
, th
at is limited
b
y
a
v
e
lo
cit
y
v
ector
ma
x
m
a
x
,
1
ma
x
,
n
m
a
x
,
N
,
...
,
,
..
.
,
kk
k
k
VV
V
V
, t
h
at
t
w
o
vect
ors a
r
e de
pe
nd
ent
an
d ass
o
ciated with eac
h particle
i
.
An
assem
b
l
y
of
pa
rt
i
c
l
e
s ha
s bee
n
m
a
de f
r
om
num
ber
o
f
p
a
rt
i
c
l
e
s (
p
o
ssi
bl
e an
swe
r
s
)
t
h
at
pr
o
g
res
s
t
o
fi
n
d
optim
al answers in a spac
e of
possible
answe
r
s. Position of
each pa
rticle ba
sed
on its best search, and t
h
e best
o
v
e
r
a
ll exp
e
r
i
en
ce
o
f
gr
oup f
ligh
t
and
p
r
ev
iou
s
v
e
lo
cit
y
v
ector
of
t
h
e p
a
r
ticle itself
,
is acco
r
d
i
n
g
to
th
e
fol
l
o
wi
n
g
m
o
d
e
l
.
I
n
fi
gu
re
2,
t
h
e pa
rt
i
c
l
e
s m
ovi
ng
i
n
t
e
ract
i
o
n
ha
s
been
sh
ow
n
by
t
h
e
f
o
l
l
o
wi
ng
eq
uat
i
o
ns:
1
11
2
2
k
k
kk
kk
ii
i
i
i
v
w
v
c
r
p
be
st
x
c
r
g
be
st
x
(1
0)
11
kk
k
ii
i
x
xv
(1
1)
In
w
h
ich:
1
c
and
2
c
are t
w
o positive constants
whic
h
k
nown a
s
acceleration
coefficients.
1
r
and
2
r
are t
w
o
ra
n
dom
num
bers i
n
t
h
e
ra
n
g
e [
0
,
1
]
.
W
i
s
t
h
e i
n
e
r
t
i
a
w
e
i
ght
t
h
at
l
i
n
ea
rl
y
decrea
ses
fr
om
0.9 t
o
0.
4
d
u
ri
ng
t
h
e
pr
oce
ss.
k
i
p
best
is th
e
b
e
st po
si
tio
n
o
f
p
a
rticle
i
th
at ob
tain
ed
b
a
sed
o
n
p
a
rticle's ex
p
e
rien
ce.
k
p
be
s
t
pbe
s
t
p
b
e
s
t
ii
1
i
2
i
N
P
b
e
s
t
[
x,
x,
.
.
.
,
x
]
(1
2)
k
g
best
i
s
t
h
e
best
p
o
si
t
i
on
of
t
h
e
pa
rt
i
c
l
e
based
o
n
g
r
o
u
p
e
xpe
ri
enc
e
.
12
[,
,
.
.
.
,]
g
be
st
g
b
e
s
t
gbe
st
N
gb
e
s
t
x
x
x
(1
3)
K
is fre
quency i
n
dicator.
k
i
P
1
k
i
X
k
g
P
k
i
X
11
kk
ii
cr
P
X
22
kk
g
i
cr
P
X
k
i
V
1
k
i
V
Fi
gu
re
2.
Part
i
c
l
e
s'
m
ovi
ng i
n
t
e
ract
i
on i
n
t
h
e
PS
O al
g
o
r
i
t
h
m
Som
e
of t
h
e a
d
vant
a
g
es
of
PS
O i
n
com
p
ari
s
on
wi
t
h
ot
her
s
i
m
i
l
a
r o
p
t
i
m
i
zat
i
on m
e
t
hods
a
r
e:
This
m
e
thod does not
nee
d
di
ffe
rentia
tion unlike m
a
ny tr
aditional m
e
thods.
It h
a
s flex
ib
ility to
in
tegrate
with
o
t
h
e
r
o
p
t
i
m
izatio
n
tech
niq
u
e
s in
o
r
d
e
r t
o
d
e
v
e
l
o
p co
m
p
lex
t
o
o
l
s.
It h
a
s less sen
s
itiv
ity to
th
e obj
ectiv
e
fun
c
tion
'
s n
a
ture,
wh
ich
m
ean
s it h
a
s con
v
e
x
ity or co
n
tinu
ity.
Unlike
m
a
ny other e
v
olutiona
ry
com
putational
m
e
thods
, it
needs fe
we
r
pa
ram
e
ter settings.
It h
a
s th
e ab
ility to
escap
e
from
lo
cal min
i
mu
m
.
It
can
easi
l
y
be
im
pl
em
ent
e
d
and
pl
a
nne
d
wi
t
h
ba
sic m
a
the
m
atical and logical operations.
It
can be use
d
fo
r t
h
e o
b
j
e
c
t
i
v
e fu
nct
i
ons
wi
t
h
ran
dom
nat
u
re
. Sim
i
lar t
o
t
h
e case t
h
at
one of t
h
e
o
p
tim
izat
io
n
variab
les
is rando
m
.
It do
es
no
t n
e
ed
a
prop
er in
itial res
pon
se t
o
start th
e freq
u
e
ncy p
r
o
cess.
PSO a
l
go
rith
m
ad
van
t
ag
es
in
comparison wi
th the
genetic algorithm (GA)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE Vol. 4, No. 6, D
ecem
ber 2014
:
858 – 867
8
63
As
o
n
e
of
t
h
e
ev
ol
ut
i
o
nary
com
put
at
i
onal
m
e
t
hods,
PS
O,
si
m
i
l
a
r t
o
genet
i
c
al
go
ri
t
h
m
(GA
)
i
s
started
fro
m
se
ries of in
itial po
pu
latio
n as
ran
d
o
m
resp
o
n
s
es and
d
e
v
e
l
o
ps th
e pro
cess
o
f
search
ing
throu
g
h
a
repetition
proc
ess. By the developm
ent and applicati
on
of PSO al
gori
thm
in r
ecent
years, resea
r
chers
concl
ude
d that
PSO algorithm
can be
used
to s
o
lve
sim
ila
r
p
r
o
b
l
em
s in
GA. Fro
m
th
e
stan
dpo
in
t
o
f
practical
cases, a
dva
nta
g
es
of PSO a
r
e
summ
arized as follows
.
In
add
itio
n
t
o
t
r
ad
ition
a
l op
timizatio
n
alg
o
rith
m
s
b
a
sed
o
n
g
r
ad
ien
t
, th
ere
are m
a
n
y
o
t
h
e
r in
nov
ativ
e
m
e
t
hods
t
h
at
c
o
m
p
et
e wi
t
h
P
S
O
suc
h
a
s
G
e
net
i
c
Al
go
ri
t
h
m
,
evol
ut
i
o
nar
y
pr
o
g
ram
m
i
n
g a
n
d m
o
re r
e
cent
l
y
Ant
O
p
t
i
m
i
zat
ion
Al
go
ri
t
h
m
.
Gene
ral
l
y
, as
m
o
st
of t
h
ese
m
e
t
hods
w
h
i
c
h
use
d
t
o
s
o
l
v
e
di
ffe
re
nt
o
p
t
i
m
i
zat
i
on
p
r
ob
lem
s
, th
e ab
ov
e m
e
th
o
d
is also
ab
le t
o
so
lv
e
d
i
fferen
t
op
ti
m
i
zatio
n
issu
es.
Howev
e
r, so
m
e
o
f
th
ese
com
p
et
i
ng m
e
tho
d
s,
h
a
ve
so
m
e
deficiencie
s
and
wea
k
poi
nts s
u
ch as
foll
owi
n
g cases:
They
need
m
o
re pa
ram
e
ter settings.
Ab
o
v
e m
e
t
hod
s nee
d
t
o
o
com
put
at
i
o
nal
t
i
m
e.
Dev
e
l
o
p
m
en
t
an
d m
o
d
i
ficatio
n of t
h
e ab
ov
e algorith
m
s
n
eeds m
a
n
y
prog
ramm
in
g
sk
ills, in
o
r
d
e
r
to
adapt
t
h
em
t
o
di
ffe
re
nt
ki
nds
of
o
p
t
i
m
i
zat
i
on p
r
o
b
l
e
m
s
.
Som
e
of t
h
ese
t
echni
q
u
es
nee
d
t
o
c
o
n
v
ert
t
o
bi
na
ry
fi
el
d i
n
s
t
ead of
w
o
r
k
i
n
g
with
t
h
e actual v
a
lu
es of
vari
a
b
l
e
s'
sy
st
em
. In spi
t
e
of s
i
m
p
l
e
concept
and ea
sy
im
pl
em
ent
a
t
i
on o
f
p
r
esent
e
d m
e
t
hod, i
t
s
su
peri
ori
t
y
i
n
m
a
ny
di
ffe
re
nt
ap
pl
i
cat
ory
fi
el
ds
has
been
p
r
ove
d i
n
c
o
m
p
ari
s
o
n
wi
t
h
ot
he
r m
e
t
hods.
4.
N
U
M
E
RICAL STUD
Y AND
R
E
SU
LTS'
A
N
A
L
YSIS
In
t
h
is sectio
n, th
e propo
sed
alg
o
rith
m
h
a
s been
im
p
l
e
m
en
t
e
d
on
a
po
wer
syste
m
with
1
5
g
e
n
e
rating
uni
t
s
,
whi
c
h h
a
s been st
udi
e
d
i
n
seve
ral
p
a
pers
. Al
l
i
n
f
o
rm
at
i
on has
been
gi
ve
n i
n
t
a
bl
es 1 an
d
2 fo
r
sim
u
l
a
t
i
on o
f
t
h
e
desi
re
d t
e
st
net
w
or
k.
Al
s
o
t
h
e ap
pl
i
cat
i
v
e
po
we
r at
di
ffe
r
e
nt
t
i
m
e
s has
b
een
gi
ve
n i
n
t
a
bl
e 3
.
Tab
l
e
1
.
C
h
aracteristics o
f
t
h
e un
its with regard to
po
llu
tion
co
efficien
ts.
P
i,m
a
x
(M
W)
P
i,m
i
n
(M
W)
i
i
i
h
i
e
i
c
i
b
i
a
i
Unit
455
150
0.
09
5.
763
77.
303
0.
0310
357.
95
72
0.
0002
10.
1
671
1
455
150
0.
093
-
5.
48
50
0.
0510
306.
21
07
0.
0002
10.
2
574
2
130
20
0.
054
-
5.
46
57.
254
0.
0910
199.
51
71
0.
0011
8.
8
374
3
130
20
0.
054
-
5.
43
57.
254
0.
0912
199.
51
71
0.
0011
8.
8
374
4
470
150
0.
064
-
5.
93
60.
5
0.
0812
245.
92
88
0.
0002
10.
4
461
5
460
135
0.
094
-
5.
43
75
0.
0612
336.
08
5
0.
0003
10.
1
630
6
465
135
0.
089
-
5.
43
65
0.
0512
292.
34
06
0.
0004
9.
8
548
7
300
60
0.
044
-
4.
43
62
0.
342
121.
09
73
0.
0003
11.
2
227
8
162
25
0.
041
-
4.
02
58.
7
0.
552
92.
29
0.
0008
11.
2
173
9
160
20
0.
041
-
4.
02
57
0.
53
93.
356
93
0.
0012
10.
7
175
10
80
20
0.
042
-
4.
1
69
0.
43
99.
225
08
0.
0036
10.
2
186
11
80
20
0.
045
-
5.
2
69.
5
0.
33
122.
69
77
0.
0055
9.
9
230
12
85
25
0.
045
-
5.
2
69
0.
23
120.
03
03
0.
0004
13.
1
225
13
55
15
0.
051
-
5.
43
55
0.
143
164.
84
17
0.
0019
12.
1
309
14
55
15
0.
054
-
5.
43
57.
84
0.
13
172.
31
02
0.
0044
12.
4
323
15
Tabl
e
2. C
h
ara
c
t
e
ri
st
i
c
s of t
h
e
g
r
adi
e
nt
'
s
rat
e
of
sy
st
em
'
s
15
uni
t
s
.
Unit
UR
i
(M
W)
DR
i
(M
W)
P
io
(MW)
1
80
120
400
2
80
120
300
3
130
130
105
4
130
130
100
5
80
120
90
6
80
120
400
7
80
120
350
8
65
100
95
9
60
100
105
10
60
100
110
11
80
80
60
12
80
80
40
13
80
80
30
14
55
55
20
15
55
55
20
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Applications
of Particle Sw
arm
Op
timization Al
gorithm t
o
Solving t
h
e Ec
o
nomic … (Hossein
S
hah
in
zad
e
h
)
86
4
Tabl
e
3. T
h
e
a
m
ount
o
f
re
q
u
i
r
ed
co
ns
um
pt
ion
p
o
w
er
i
n
a
24
-
h
o
u
r
pe
ri
o
d
.
12
11
10
9
8
7
6
5
4
3
2
1
Ho
ur
3082
3008
2934
2786
2638
2564
2490
2342
2268
2120
1972
1898
Demand (
M
W
)
24
23
22
21
20
19
18
17
16
15
14
13
Ho
ur
2046
2194
2490
2786
2934
2638
2490
2342
2416
2638
2786
2934
Demand (
M
W
)
In
t
h
i
s
pape
r, 2
0
1
0
M
a
tlab
so
ftware
h
a
s
b
e
en u
s
ed
to cod
e
gen
e
tic alg
o
rithm
in
o
r
d
e
r to
si
m
u
late th
e
ELD issue among power pla
n
ts consider
i
ng the valve-poi
nt loading effect
s
and practical constraints of powe
r
syste
m
.
5.
THE RESUL
T
S OF
SIMULATION WI
TH THE P
R
OPOSE
D
AL
GORITHM
Fo
r th
is system
,
th
e nu
m
b
er o
f
p
a
rticles an
d
rep
e
titio
n
s
h
a
s
b
een
selected
equ
a
l to
10
0
fo
r each
o
f
po
p
u
l
a
t
i
ons
. T
h
e res
u
l
t
s
of t
h
e pr
op
ose
d
al
g
o
ri
t
h
m
'
s perf
or
m
a
nce on t
h
i
s
sy
st
em
have b
een p
r
esent
e
d i
n
t
a
bl
e
4.
W
e
see t
h
at
,
t
h
e resul
t
s
obt
ai
ned f
r
om
par
t
i
c
l
e
swar
m
opt
im
i
zat
i
on al
go
ri
t
h
m
for t
h
i
s
sy
st
em
requi
res
l
e
ss
t
i
m
e
t
h
an t
h
e o
t
her m
e
t
hods
.
The
pr
o
pose
d
al
go
ri
t
h
m
has been
al
so
reac
hed
t
o
a
n
a
b
sol
u
t
e
o
p
t
i
m
al
answer
f
o
r
every
10
0 t
i
m
es of
di
f
f
ere
n
t
per
f
o
r
m
a
nces at
t
h
e l
east
fr
eque
ncy
,
whi
c
h i
n
di
cat
es hi
g
h
-
p
owe
r
o
f
pr
op
ose
d
al
go
ri
t
h
m
t
o
achi
eve t
h
e a
b
s
o
l
u
t
e
o
p
t
i
m
al
answ
er a
nd
o
p
t
im
i
zat
i
on of
ELD i
s
s
u
e. Fi
gu
re
3 has
gr
a
phi
cal
l
y
sho
w
n l
o
ad'
s
d
i
spat
ch acc
om
pl
i
s
he
d
by
p
r
o
pos
ed
al
g
o
ri
t
h
m
i
n
2
4
-
h
ou
rs
base
d
on
u
n
i
t
s
' ge
nerat
i
n
g
p
o
w
er
.
Tabl
e
4. R
e
s
u
l
t
s
f
o
r t
h
e
pr
o
p
o
s
ed L
o
a
d
'
s
Di
s
p
at
ch
by
usi
n
g
PSO
al
g
o
ri
t
h
m
o
n
15
u
n
i
t
s
'
sy
st
em
.
12
11
10
9
8
7
6
5
4
3
2
1
Unit
162.
85
251.
38
275.
24
152.
15
256.
97
265.
59
271.
72
304.
25
337.
36
350.
51
365.
76
162.
85
1
454.
84
246.
81
220.
39
305.
84
257.
22
273.
31
270.
66
340.
49
391.
61
347.
91
395.
98
454.
84
2
108.
76
126.
26
127.
32
124.
21
125.
30
121.
85
118.
83
125.
49
125.
59
89.
81
124.
34
108.
76
3
109.
87
126.
21
124.
17
124.
25
127.
21
121.
28
118.
93
125.
54
126.
37
122.
71
125.
58
109.
87
4
155.
10
151.
76
218.
46
305.
69
273.
01
305.
09
270.
54
304.
53
389.
21
382.
70
365.
62
155.
10
5
145.
20
188.
50
242.
88
229.
00
340.
87
276.
78
339.
81
339.
75
335.
84
438.
55
389.
90
145.
20
6
144.
21
191.
02
256.
17
229.
56
254.
49
268.
63
383.
57
303.
47
327.
49
349.
04
370.
37
144.
21
7
162.
24
188.
69
218.
11
229.
17
255.
65
287.
19
271.
27
297.
57
298.
76
293.
68
296.
88
162.
24
8
140.
42
157.
00
159.
32
155.
88
127.
51
155.
72
150.
06
156.
54
104.
73
155.
92
157.
83
140.
42
9
138.
42
156.
28
157.
40
156.
32
156.
76
156.
79
148.
77
156.
54
156.
07
152.
75
155.
92
138.
42
10
58.
76
76.
27
78.
32
74.
63
77.
80
78.
44
67.
81
75.
57
78.
31
73.
97
74.
78
58.
76
11
58.
72
75.
89
39.
84
76.
71
77.
62
76.
95
68.
01
75.
54
76.
98
73.
90
76.
92
58.
72
12
65.
02
81.
32
82.
05
79.
30
81.
88
81.
52
72.
05
79.
58
80.
93
78.
93
80.
85
65.
02
13
33.
76
51.
26
52.
32
49.
84
38.
62
52.
06
43.
02
50.
79
53.
15
48.
84
50.
82
33.
76
14
33.
76
51.
27
15.
92
49.
39
39.
02
42.
70
42.
88
50.
29
51.
52
48.
69
50.
38
33.
76
15
24
23
22
21
20
19
18
17
16
15
14
13
Unit
344.
69
317.
88
273.
22
248.
20
263.
76
248.
46
453.
03
334.
16
352.
64
257.
10
454.
51
262.
97
1
340.
23
309.
54
272.
89
234.
01
273.
13
391.
02
268.
51
335.
50
304.
93
256.
55
193.
79
185.
86
2
128.
96
126.
59
117.
99
118.
68
124.
01
120.
34
114.
65
124.
44
125.
87
124.
02
112.
53
124.
08
3
129.
42
122.
86
118.
01
115.
58
123.
58
121.
35
113.
27
123.
50
123.
90
126.
97
112.
57
123.
18
4
346.
32
308.
71
275.
19
266.
39
229.
01
261.
20
270.
84
336.
18
304.
49
265.
71
193.
75
187.
11
5
340.
43
308.
66
443.
50
234.
28
233.
71
392.
25
268.
99
391.
12
318.
26
269.
68
190.
11
186.
85
6
339.
47
323.
28
270.
69
378.
67
229.
85
255.
14
310.
11
346.
69
315.
92
271.
50
191.
42
171.
47
7
298.
98
299.
93
271.
13
236.
75
225.
47
106.
96
270.
71
295.
31
296.
86
289.
25
189.
41
172.
07
8
161.
52
161.
93
150.
01
150.
22
155.
71
151.
26
147.
56
157.
06
156.
23
161.
44
144.
53
155.
95
9
159.
25
159.
94
147.
31
144.
47
156.
18
150.
42
145.
65
155.
58
155.
23
150.
45
143.
60
152.
82
10
78.
42
78.
93
71.
01
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41
75.
72
69.
62
63.
55
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18
74.
82
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32
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56
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38
11
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57
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93
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48
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11
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20
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65
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52
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34
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31
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55
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12
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32
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93
74.
01
70.
076
79.
67
75.
27
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13
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27
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69
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50
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49
77.
90
13
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42
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94
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91
42.
12
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57
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38.
65
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03
50.
47
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61
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53
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10
14
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92
47.
86
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62
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96
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36
39.
16
37.
64
50.
40
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28
38.
51
37.
57
49.
09
15
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65
Figure
3.a. Mesh curve
of th
e accom
p
lished
ELD i
n
24 hours.
Figure
3.b. Contour curve
of
th
e accom
p
lished EL
D i
n
24
hours.
Figure
3. Curve of the
accom
p
lishe
d EL
D i
n
15
units'
system's test by
usi
n
g PSO al
gorithm
.
6.
CO
NCL
USI
O
N
In
th
is article, Econ
o
m
ic Lo
ad
Disp
atch
amo
n
g
pow
er pl
a
n
t
s
was sol
v
ed
by
consi
d
e
r
i
n
g t
h
e val
v
e
-
poi
nt
l
o
adi
n
g
effect
s a
nd
p
r
act
i
cal
const
r
a
i
nt
s of t
h
e
po
wer sy
st
em
usi
ng
part
i
c
l
e
s
w
arm
opt
i
m
i
z
at
i
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
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:
208
8-8
7
0
8
Applications
of Particle Sw
arm
Op
timization Al
gorithm t
o
Solving t
h
e Ec
o
nomic … (Hossein
S
hah
in
zad
e
h
)
86
6
al
go
ri
t
h
m
(PSO). T
h
e
pr
o
p
o
s
ed m
e
t
hod ba
sed o
n
PS
O al
go
ri
t
h
m
i
s
extrem
ely
effi
ci
ent
at
prese
n
t
a
t
i
on
of
o
p
tim
al so
lu
tio
n
s
in pro
p
e
r time. In
t
h
is
p
a
per, in add
ition
to
th
e
v
a
lv
e-p
o
in
t lo
ad
i
n
g effects, o
t
her con
s
train
t
s
and
po
we
r pl
a
n
t
s
'
l
i
m
i
t
a
t
i
ons such as:
t
h
e
b
a
l
a
nce of
pr
o
d
u
ct
i
on a
n
d co
n
s
um
pt
i
on i
n
t
h
e sy
st
em
, forbi
dde
n
zo
n
e
s, th
e
rang
e of produ
ctio
n, in
creasing an
d
d
ecreasing
rates, and
reliab
ility
co
n
s
t
r
ain
t
s and
m
o
d
e
lin
g
net
w
or
k sec
u
ri
t
y
have b
een c
onsi
d
ere
d
.
The
pr
o
pose
d
m
e
tho
d
of E
L
D
w
a
s im
pl
em
ent
e
d o
n
a
15
-
uni
t
s
sy
st
em
and
t
h
e
res
u
l
t
s
have
be
en
sh
o
w
n
g
r
a
phi
cal
l
y
. T
h
e r
e
sul
t
s
i
n
di
cat
e t
h
at
t
h
e
pr
o
pose
d
al
go
r
i
t
h
m
for
EL
D
am
ong
po
we
r
pl
ant
s
h
a
s m
o
re effi
ci
e
n
cy
t
h
a
n
ot
he
r available
algorith
m
s
in
stud
y
r
e
sour
ces.
REFERE
NC
ES
[1]
Sasson, Albert M. "Nonlinear progr
am
m
i
ng so
lutions for load
-flow, m
i
nim
u
m-loss, and econ
o
m
i
c dispatchin
g
problem
s".
Pow
e
r Apparatus an
d Systems, IEEE Transactions on
4 (1969): 399-4
09.
[2]
Sinha, Nidul, R. Chakrabarti, an
d P.
K. Chattopadh
y
a
y
.
"Evolutionar
y
progr
am
ming techniqu
es for econom
ic load
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l
u
tionar
y
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[3]
Coelho, Leandr
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ic load di
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l
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[4]
Meng, Ke, Hong Gang W
a
ng, Zhao Yang D
ong, and Kit Po W
o
n
g
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pired particle swarm
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izatio
n
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ic lo
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EEE Transactions on
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[5]
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b
ido, M
.
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"
M
ultiobje
c
tiv
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a
rti
c
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arm
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tim
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zat
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[6]
Yang, Xin-She,
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y
e
d Soheil
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sseini,
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ir Hossein Gandom
i.
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ithm
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ct".
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puting
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[7]
C
h
akrabort
y
,
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.,
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e
nj
yu
, A
.
Y
ona, A
.
Y. Saber
,
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a
shi. "Solvi
ng eco
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int eff
e
cts using a h
ybrid quantum
m
ech
anics
ins
p
i
r
ed part
icl
e
s
w
arm
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is
atio
n".
G
e
ner
a
tion
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ssion &
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. 10
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1): 1042-1052.
[8]
Bhattachar
y
a
, A
n
iruddha,
and P
r
anab Kum
a
r C
h
attop
a
dh
y
a
y
.
"H
y
b
rid differ
e
ntial
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aph
y
-
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e
r System
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r
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[9]
Ravikum
ar Pan
d
i, V., and B
i
jay
a Keta
n Panigrahi. "D
y
n
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ic econom
ic load dispatch usin
g h
y
br
id swarm
intel
ligen
ce
bas
e
d harm
on
y sear
c
h
algor
ithm
"
.
Expert
Systems wi
th Applications
3
8
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. 7
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[10]
H
e
m
a
m
a
lini, S
.
,
and S
i
s
h
aj P
.
Sim
on. "A
rtifici
a
l
bee co
lon
y
a
l
g
o
rithm
for econ
o
m
i
c load dispa
t
ch problem
w
i
t
h
non-sm
ooth cost functions".
Electric
Power Com
ponents and S
y
stems
38, no
. 7
(2
010): 786-803.
[11]
Ham
e
di, Hadi.
"Solving the co
m
b
ined econom
ic load
and em
ission dispatch
probl
em
s using new heuristic
algorithm
"
.
Inter
national Journal
of Electr
ical
Po
wer
&
Energy Systems
46 (2013
): 10-16.
[12]
Zhisheng,
Zhan
g. "Quantum
-behaved pa
r
ticle s
w
arm
optim
ization algorithm
for
econom
ic lo
ad
dispatch of pow
er
sy
s
t
e
m
"
.
Expert
Systems with
Ap
plications
37, no
. 2
(2010): 1800
-
1803.
[13]
Pandit, Manjaree. "Discussion of “Hy
b
ri
d diff
er
ential evolu
tion with biogeogr
ap
h
y
-bas
ed optim
izat
ion for s
o
lution
of econom
ic lo
ad dispatch”.
Pow
e
r Systems, IEEE Transactions
on
27, no. 1 (20
12): 574-575.
[14]
Niknam
,
Taher
,
Hasan Doagou
Moja
rrad, and
Ham
e
d Zeinoddini Mey
m
and
.
"A novel hy
br
id particle swar
m
optim
ization for
econom
ic dispatch w
ith valve-po
int lo
ading ef
fects".
Energy Con
version and Ma
nagement
52
, no
.
4 (2011): 1800
-1
809.
[15]
K
e
nned
y
, J
a
m
e
s. "P
arti
cl
e sw
ar
m
optim
izat
ion".
In
En
cycloped
i
a of Ma
chine Learning
, pp. 760-
766. Springer
U
S
,
2010.
BIOGRAP
HI
ES OF
AUTH
ORS
Hosse
in Sha
hin
z
ade
h
:
H
e
received his B.S
.
an
d M
.
S
c
degrees in Ele
c
tri
c
a
l
En
gineer
ing from
Islam
i
c Azad
University
o
f
Isfahan, Isfah
a
n,
Ir
an and
Am
irkabir University
o
f
Technolo
g
y
(Tehran P
o
l
y
t
e
c
hnic),
Tehr
an, Ir
an. H
e
is a m
e
m
b
er of int
e
rnat
io
nal organ
i
za
tion
s
of IEEE, I
E
T
and Ins
titut
e
of
A
dvanced Eng
i
neer
ing and S
c
ienc
e (IA
ES
) a
nd als
o
an ac
ti
ve m
e
m
b
er of
Isfahan
'
s Young Elites Foundat
i
on and Isfahan
C
onstruction E
ngineer
ing Organiza
tion. His
research
ac
tivi
t
i
e
s focus on th
e S
m
art G
r
id,
Renew
a
bl
e E
n
ergies,
Energ
y
M
a
nagem
e
nt
,
Di
st
ri
but
e
d
Ge
ne
ra
ti
on & Powe
r S
y
st
e
m
Analysi
s.
He has
been a
consultan
t
with utilities of
Esfahan Electr
i
city
Power
Distr
i
bution Com
p
an
y.
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ecem
ber 2014
:
858 – 867
8
67
Say
e
d M
o
hse
n
Nasr
-A
z
a
dani:
He reciv
e
d his
B.S. degree in
electrical
engin
e
ering in 2008
from
Islam
i
c A
z
ad U
n
iversit
y
K
hom
eini S
h
ahr Br
anch, Isfah
a
n, Iran. Now, heis working on the
M
a
ster’s degre
e
in E
l
ec
tri
cal
Engineer
ing from
Am
irkabir University
of
Tech
nolog
y
(Teh
ran
Poly
technic), Tehran, Ir
an. H
e
r
eceived
ETO C
e
rtif
icate (
E
lect
r
o
Techn
i
cal Off
i
cer)
in 2014
From
I
s
lam
i
c Republic of Ira
n Shipping Lines (IRISL Group).
He is working
on m
e
rchant
vessels as el
ec
tric
al eng
i
ne
er.
H
i
s research
inter
e
st inc
l
ude
s Renew
a
ble
E
n
erg
y
, En
er
g
y
Managem
e
nt, Po
wer S
y
stem
Analy
sis
and Distr
i
b
u
ted Gen
e
ration.
Naz
ereh
Jan
n
e
s
a
ri:
She Received her B.S
.
Degree in B
i
o Medical Engin
eer
in
g in 2012 fro
m
Islam
i
c A
zad U
n
iversit
y
K
hom
eini S
h
ahr Bran
ch, Isfahan
,
Ira
n. N
o
w
,
S
h
eis
w
o
rking on the
M
a
s
t
er’s
degree
in Electr
i
c
a
l En
gineer
ing from
S
e
pahan Ins
titue
of H
i
gher Education
,
Is
fahan,
Iran. H
e
r res
ear
ch inter
e
s
t
incl
udes
S
i
gnal P
r
oces
s
i
ng, Inte
llig
ent O
p
tim
izat
io
n A
l
gorithm
s
,
Neural N
e
twork
s
, Advanced Microprocessors and
Sm
art Grid.
Evaluation Warning : The document was created with Spire.PDF for Python.