Indonesian Journal of
Electrical
Engineer
ing and
Computer Science
V
o
l.11
,
No
.1
, Ju
ly 20
18
, pp
. 18
7
~
19
4
ISSN: 2502-4752,
DOI: 10.
11591/ij
eecs.v11
.i1.pp187-194
1
87
Jo
urn
a
l
h
o
me
pa
ge
: http://iaescore.c
om/jo
urnals/index.php/ijeecs
Gbest Artificial Bee Colony fo
r Non-Convex Optimal Economic
Dispatch in Power Gen
e
ration
M.
N. Ab
dulla
h
1
, A.F.
A.
Ma
nan
2
, J.
J. J
a
m
i
an
3
, S.
A. Jum
a
at
4
,
N.
H.
R
a
dzi
5
1,2,4,5
F
acult
y
of
Ele
c
tri
cal
and
E
l
ectron
i
c
Engin
e
e
r
ing, Univ
ers
iti
Tun Hus
s
e
in On
n M
a
la
ys
i
a
,
86400 Parit Raja, Batu Pah
a
t, Joh
o
r, Malay
s
ia
3
Facult
y
of
Ele
c
t
r
ica
l
Eng
i
ne
erin
g, Universi
ti
Tek
nologi Ma
la
ysia
,
81310 UTM Johor Bahru, Johor,
Malay
s
ia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Ja
n
9, 2018
Rev
i
sed
Mar
23
, 20
18
Accepted Apr 13, 2018
Non-convex Optimal Economic Dispat
ch (OED) problem is
a complex
optimization pr
oblem in power
s
y
stem
oper
a
tion that must be optimized
economically
to
meet
the power dema
nd
and s
y
stem
constrain
t
s. The non-
convex OED is due to the generator
char
acteristic such
as prohibited
operat
i
on zon
e
s,
valve
point
eff
ects (VPE) or
m
u
ltiple fu
el op
tions. Th
is
paper proposes a Gbest Artificial Bee Colon
y
(
GABC) algorithm based on
global best particle (gbe
st) guided of Particle
Swarm
Optim
ization
(PSO)
inArtificial bee
colon
y
(ABC) algorithm for solving non-convex OED with
VPE. In order to investiga
t
e th
e e
ffectiv
eness and performance of GABC
algorithm,
the IEEE 14-bus 5 unit g
e
ner
a
tors and I
E
EE 30-bus 6
unitgen
erators
t
e
s
t
s
y
s
t
em
s
are
cons
idered
. T
h
e com
p
aris
on
of optim
a
l
solution, conver
g
ence char
acteristic
a
nd
robustn
ess are also hig
h
lighted
to
revea
l
the
advan
t
ages
of GABC.
M
o
re
over, the optimal
results
obtain
e
d b
y
proposed GABC are compared
with oth
e
r repor
ted r
e
sults of
meta-h
euristic
algorithms. It f
ound that
the
GABC cap
able to obtain low
e
st cost
as
compared to others. Thus, it
has gr
eat pot
en
tial
to be im
pl
em
ented in
differen
t
ty
p
e
s o
f
power s
y
s
t
em
optimization pro
b
lem.
K
eyw
ords
:
Artificial Bee
Co
lon
y
Algo
rith
m
Po
wer Dis
p
atch
Valve Poi
n
t
Effect
Copyright ©
201
8 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
:
M.N
.
Ab
du
llah,
Faculty of Elec
trical an
d
El
ect
ro
ni
c E
ngi
neer
i
ng,
Un
i
v
ersiti Tu
n
Hu
ssein
On
n
Malaysia, 8
640
0 Parit Raj
a
,
Batu
Pah
a
t, Joh
o
r, Malaysia.
Em
ail: m
noor@ut
h
m
.
edu.m
y
1.
INTRODUCTION
Po
wer
di
spat
c
h
i
s
one
of t
h
e opt
i
m
i
z
at
i
on pr
obl
em
i
n
powe
r
sy
st
em
p
l
anni
n
g
a
nd
o
p
erat
i
o
n.
It
i
s
im
port
a
nt
t
o
e
n
su
re t
h
at
t
o
t
a
l
cost
o
f
po
we
r ge
ne
rat
i
o
n
c
a
n
be m
i
nim
i
ze as m
u
ch as
pos
si
bl
e t
o
gai
n
hi
g
h
p
r
o
f
it to
po
w
e
r co
m
p
an
y as kn
own
as
op
ti
mal eco
no
m
i
c
di
spat
ch (
O
ED
) pr
o
b
l
e
m
.
R
e
duct
i
on of fo
ssi
l
fuel
s
resources an
d
h
i
gh
fu
el
p
r
ices en
co
urag
e u
t
i
lity to
o
p
e
ra
te t
h
e system
at
min
i
m
u
m
co
st as well as satisfi
ed
all
t
h
e sy
st
em
an
d o
p
e
r
at
i
onal
con
s
t
r
ai
nt
s. C
o
m
m
onl
y
,
t
h
e cost
f
u
nct
i
on
of t
h
erm
a
l
gen
e
rat
o
r
i
s
m
odel
l
e
d a
s
qua
d
r
at
i
c
funct
i
on t
h
at
can b
e
sol
v
e effi
ci
e
n
t
l
y
by
m
o
st of t
h
e con
v
e
n
t
i
onal
m
e
t
hods suc
h
l
a
m
bda i
t
erat
i
o
n
m
e
t
hod [
1
]
,
l
i
n
ear
pr
og
ram
m
i
ng [2]
,
qua
d
r
at
i
c
pr
og
ram
m
i
ng [3]
an
d ot
he
r m
e
t
hod
st
hat
can be
fo
u
nd i
n
[
4
]
[5,
6]
.
Ho
we
ver
,
t
h
e
s
e
m
e
t
hods s
h
o
w
s
di
ffi
c
u
l
t
y
t
o
obt
ai
n
opt
i
m
al
resul
t
s
whe
n
t
h
e
no
n
-
l
i
n
ea
r
ch
aracteristic are tak
e
n
i
n
to
acco
un
t in co
st m
o
d
e
llin
g
su
ch
v
a
lv
e po
in
t effect (VPE), p
r
oh
ib
ited
op
erating
zo
n
e
(POZ)
or m
u
ltip
le fu
els o
p
t
i
o
n
(MFO)
[7
]. In
p
r
actical, g
e
n
e
rato
rs u
s
ed
m
u
lti-v
a
lv
e tu
rb
in
e th
at
p
r
od
u
c
ed
sev
e
ral ripp
les i
n
h
eat-rate
ch
aracteristic as
we
ll as cost-power c
h
aracteristi
c that contri
butes a
com
b
i
n
at
i
on
of
si
nus
oi
dal
a
n
d
qua
d
r
at
i
c
cost
fu
nct
i
o
n. T
h
er
efo
r
e, i
t
chal
l
e
nge
s m
o
st
opt
i
m
i
zat
i
on al
gori
t
hm
s
to
ob
tain
ed
op
ti
m
a
l so
lu
tio
n
i
n
OED pro
b
l
em
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
250
2-4
7
5
2
I
ndo
n
e
sian
J Elec Eng
& Com
p
Sci, V
o
l. 11
,
No
.
1
,
Ju
ly
20
18
:
1
87–
194
18
8
Due t
o
t
h
i
s
pr
obl
em
,
m
o
st
of researc
h
e
r
s use t
h
e m
e
ta-
h
euristics alg
o
rith
m
s
that can searc
h
the
opt
i
m
al
sol
u
t
i
on wi
t
h
out
depe
ndi
ng t
o
t
h
e co
nve
xi
t
y
of t
h
e
cost
fu
nct
i
o
n s
u
ch as
Genet
i
c
Al
go
ri
t
h
m
,
Part
i
c
l
e
Swarm
Op
timizatio
n
(PSO) [8, 9
]
,
Cu
ck
oo
Se
a
r
ch
(CS
)
[10
]
,
Artif
icial Bee
Co
lon
y
(ABC) [11
]
,
B
ackt
r
acki
n
g Searc
h
Al
go
ri
t
h
m
(B
SA) [
1
2]
and R
oot
e
d
Tr
ee Alg
o
rithm
(TRO)
[1
3]
. H
o
weve
r, in
som
e
cases
these algorithm
s
are suffere
d
and c
o
n
v
er
g
e
d at
l
o
cal
opt
im
al
sol
u
t
i
on.
As a res
u
l
t
s
, m
a
ny
im
prove
m
e
nt
of
ori
g
i
n
al
al
g
o
ri
t
h
m
have bee
n
pr
o
pose
d
by
re
searche
r
s t
o
i
m
prove t
h
e
pe
rf
orm
a
nce of
o
r
i
g
i
n
al
al
g
o
ri
t
h
m
[14]
[15
]
[7
]. To
hav
e
b
a
lan
ce exp
l
oratio
n
an
d
ex
p
l
o
itati
o
n
cap
a
b
ility o
f
orig
in
al A
BC, the Gb
est Artificial Bee
Colony (GAB
C) [16] has be
en intr
oduce
d
and s
u
ccess
f
ul
ly solve num
er
ical function optim
i
zation problem
.
The
GAB
C
i
s
gui
ded
t
h
e
AB
C
al
go
ri
t
h
m
based
on
t
h
e
gl
o
b
al
best
s
o
l
u
t
i
o
n
(
g
best
) i
n
PS
O al
g
o
ri
t
h
m
i
n
or
de
r
to enha
nce the
exploitation c
a
pability
of
ABC. It also
prom
ises a good
result for
finding optim
al econom
ic-
em
i
ssi
on co
nsi
d
eri
n
g
wi
nd
i
n
[1
7]
an
d
o
p
t
i
m
a
l
po
we
r fl
ow
[
18]
.
Thi
s
pape
r
pr
o
pos
es a
GAB
C
al
go
ri
t
h
m
for
sol
v
i
ng t
h
e
no
n-c
o
nve
x
OE
D
pr
o
b
l
e
m
consi
d
eri
n
g
t
h
e
no
n
-
l
i
n
ear c
o
st
fu
nct
i
o
n d
u
e
VPE.
The
p
ro
p
o
se
d G
A
B
C
h
a
s bee
n
val
i
d
at
edo
n
t
w
o
di
ffe
rent
t
e
st
sy
st
em
s. The
effective
n
ess
of GABC has c
o
m
p
ared
with
o
r
i
g
in
al ABC i
n
term
s o
f
op
timal cost, converge
n
ce
performance
and
r
o
b
u
st
ne
ss
aft
e
r
40 t
r
i
a
l
s
.
M
o
re
ove
r, t
h
e
obt
ai
ned
o
p
t
i
m
al
resul
t
s
al
so com
p
are
d
wi
t
h
t
h
e s
o
m
e
repo
rt
ed
resu
lt
foun
d in literatu
re. It
fo
und
t
h
at,
p
r
op
o
s
ed GABC
p
r
ov
id
ed
si
g
n
i
fican
t co
st
redu
ctio
n for
OED
with
VPE.
2.
PROBLEM FORMUL
ATION: OPTIMA
L ECONOMIC DISPAT
CH
(OE
D
)
This section explains the m
a
them
ati
cal
form
ul
at
i
on of OE
D
p
r
obl
em
such
as objective function a
nd
co
nstrain
t
s as fo
llo
ws:
2.
1. Ob
jecti
v
e
Functi
on o
f
O
E
D
The m
a
i
n
ob
je
ct
i
v
e of
OE
D i
s
t
o
det
e
rm
i
n
e
t
h
e best
po
we
r
out
put
of t
h
e s
c
hed
u
l
e
d
ge
ner
a
t
o
r s
o
t
h
at
t
h
e po
we
r de
m
a
nd an
d sy
st
em
const
r
ai
nt
s
can be m
eet
in econom
i
cal way. Th
e co
s
t
funct
i
o
n co
m
m
onl
y
fo
rm
ul
at
ed as
qua
d
r
at
i
c
funct
i
on.
Ho
we
ver,
t
h
e pract
i
cal
cost
fu
nct
i
o
n be
com
e
non-l
i
n
e
a
r du
e t
o
val
v
e
poi
n
t
ef
f
ect
(
V
PE) as show
n in
Figu
r
e
1. Th
er
efor
e, t
h
e
ob
ject
i
v
e f
unct
i
o
n
o
f
OED
pr
obl
em
fo
r m
i
nim
i
zi
ng
t
o
t
a
l
cost (
F
c
) of
i
th
g
e
n
e
rator as follo
ws:
2
1
mi
n
si
n
N
c
i
ii
ii
i
i
FF
P
aP
b
P
c
e
f
P
P
ii
i
i
(
1
)
whe
r
e
a
i
,b
i
and
c
i
are qua
dratic cost coefficients,
e
i
and
f
i
are non-linear c
o
st coe
fficient
s
due t
o
valve
poi
nt
effect,
P
i
min
a
n
d
P
i
min
are t
h
e m
i
nim
u
m
and m
a
xim
u
m
pow
er o
u
t
p
ut
l
i
m
i
t of t
h
e
i
th
un
it g
e
n
e
ratin
g,
P
i
is th
e
po
we
r out
put
o
f
i
th
un
it
and
N
is th
e
nu
m
b
er o
f
th
e co
mmitt
ed
g
e
n
e
rators.
…
Fi
gu
re
1.
C
o
st
and
P
o
we
r
O
u
t
put
R
e
l
a
t
i
o
ns
hi
p
wi
t
h
a
n
d
wi
t
h
o
u
t
VPE
Evaluation Warning : The document was created with Spire.PDF for Python.
In
d
onesi
a
n
J
E
l
ec En
g& C
o
m
p
Sci
ISS
N
:
2
5
0
2
-
47
52
Gb
est
Artificia
l Bee Co
lon
y
fo
r N
o
n-co
n
vex
OED i
n
Po
wer Gen
e
ra
tio
n (M.N. Abd
u
llah)
18
9
2.
2. C
o
ns
trai
n
t
s
T
h
e
mi
n
i
mi
z
a
t
i
o
n
o
f
F
c
i
n
(1) i
s
subjected t
o
t
h
e system
a
nd
ope
rat
i
o
nal
co
nst
r
ai
nt
s
as
fol
l
ows:
2.
2.
1.
Pow
er B
a
l
a
nce
C
o
n
s
tr
ai
nt
Th
e to
tal power produ
ced
b
y
th
e sch
e
du
lled
g
e
n
e
rator m
u
st
m
eet th
e to
tal
p
o
wer
d
e
m
a
n
d
(
P
D
) an
d
tran
sm
isisio
n
lo
ss
(
P
Loss
) as fo
llo
ws:
1
N
iDL
o
s
s
i
PP
P
(
2
)
The
P
Loss
ca
n
be calculated
by
Kron'
s
loss
form
ula as follows:
00
0
11
1
()
(
)
()
NN
N
Lo
s
s
i
i
j
j
i
i
ij
i
PP
t
B
P
t
B
P
t
B
(3
)
whe
r
e
ij
B
,
0
B
and
00
B
are t
h
e loss c
o
efficients
obtaine
d
from
the power
flow calculation.
…
………
2.
2.
2. Pow
er Outp
ut
L
i
mi
ts
For
st
abl
e
o
p
e
r
at
i
on,
t
h
e real
po
we
r pr
od
uce
d
by
eac
h ge
ne
rat
o
r
m
u
st
be wi
t
h
i
n
al
l
o
wa
b
l
e
m
i
nim
u
m
(
P
i
min
)
an
d
ma
x
i
mu
m
P
i
max
) li
mits as fo
llows:
max
min
i
i
i
P
P
P
(
4
)
.
3.
PROPOSE
D
GBEST
ARTIFICIAL
BEE
COLONY (GABC) FOR OED
Art
i
f
i
c
i
a
l
B
ee C
o
l
o
ny
(AB
C
)
i
s
a po
pul
at
i
o
n base
d al
g
o
r
i
t
h
m
i
n
spi
r
ed
b
y
beha
vi
o
u
r
of
ho
ney
bee
s
col
o
ni
es f
o
r fi
ndi
ng
fo
o
d
so
urces
. It
co
nsi
s
t
s
of t
h
ree m
a
i
n
bees i
n
or
der t
o
sea
r
c
h
opt
i
m
al
food
sou
r
ce
(sol
ut
i
o
n
)
whi
c
h
are
em
pl
oy
ed bees, o
n
l
o
o
k
er bees an
d
s
c
out
bees.
T
h
e
bri
e
f
w
o
rki
n
g
pri
n
ci
pl
e of A
B
C
as
fo
llows[19
]
:
Artificial
Bee
Col
o
n
y
Alg
o
rithm
Step 1
Initia
liza
t
io
n
Det
e
rm
i
n
e t
h
e
num
ber
of
f
o
o
d
s
o
u
r
ce
(
SN
)
C
a
l
c
ul
at
e vect
or
o
f
pos
si
bl
e s
o
l
u
t
i
o
n
X
i
=
X
1
,
X
2
…
X
SN
;
X
i
is rep
r
esen
t
b
y
th
e lo
cati
o
n of
fo
od
sou
r
ce.
The fitness of each possible
s
o
lution
ca
n be
calculate
using
the following form
ula:
otherwise
F
abs
F
if
F
Fitness
i
i
i
i
),
(
1
0
,
1
1
(
5
)
Step 2
Employe
d
Bee
s
Em
ployed Bees find t
h
e
new
food s
o
urce
position
V
ij
usi
n
g:
kj
ij
ij
ij
ij
X
X
X
V
*
(
6
)
whe
r
e
ϕ
ij
i
s
a r
a
nd
om
num
ber
bet
w
e
e
n
[
-
1
,
1]
, a
n
d
k
∈
{
1,
2,
.
.
.N
s
} a
n
d
j
∈
{
1, 2
,
…D
} are i
n
de
x
r
a
ndo
m
l
y ch
o
s
en
.
D
is nu
m
b
er
o
f
pr
ob
lem
v
a
r
i
ab
les.
If t
h
e
n
e
w po
si
tio
n
is
foun
d better th
an th
e
old
po
sition
,
a new
p
o
s
ition
is
me
m
o
rized
and
o
t
h
e
rwise
it is rem
o
v
e
d
.
Th
e
g
r
eed
y
sel
ectio
n
m
e
th
o
d
is u
s
ed
to d
e
termin
e th
e best so
lu
tion
.
……
…..
Step 3
Onlooker
Bee
s
In
this pha
se, onlooke
r bees will
search
t
h
e
best results accordi
n
g to t
h
e
proba
bility (
P
i
) as fo
llo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
250
2-4
7
5
2
I
ndo
n
e
sian
J Elec Eng
& Com
p
Sci, V
o
l. 11
,
No
.
1
,
Ju
ly
20
18
:
1
87–
194
19
0
S
N
j
j
i
i
Fitness
Fitness
P
(
7
)
Th
e so
lu
tion
with
b
e
tter
fitness v
a
lu
e
h
a
s
h
i
gh
prob
ab
ility o
f
b
e
i
n
g
selected
b
y
an
o
n
l
o
o
k
e
r b
ee in
o
r
d
e
r to
exp
l
o
i
t th
e so
lu
tion
near to g
l
o
b
a
l
op
ti
m
a
l v
a
lu
e.
Step 4
Scout
Bees
After sev
e
ral trials, u
n
i
m
p
roved
fo
od
lo
cation
(so
l
u
tion
)
will ex
p
l
o
r
e
o
t
h
e
r p
o
ssi
b
l
e lo
catio
n
in
o
r
d
e
r
to
im
p
r
o
v
e
th
e
cu
rren
t
so
l
u
tion
u
s
ing
t
h
e fo
llo
wi
n
g
equ
a
tion
:
mi
n
m
ax
mi
n
[0
,1
]
*
ij
j
j
j
XX
r
a
n
d
X
X
(
8
)
The good position re
placed
t
h
e unim
prove
d
solution.
Repeat
Ste
p
s 2
– 4
un
til satisfied
th
e
stop
p
i
ng
criteria
Th
e
d
e
tails wor
k
i
n
g pr
in
cip
l
e of
A
CB
algo
r
i
th
m
can
b
e
f
oun
d in
[2
0
]
[
1
1
]
.
3.
1. Wor
k
i
n
g
Pri
n
ci
pl
e
o
f
G
A
B
C
To
im
p
r
o
v
e
the ex
p
l
o
itation
cap
ab
ility o
f
ABC, th
e g
l
obal b
e
st so
lu
tion
(g
b
e
st
) in
PSO algo
rith
m
[21
]
is u
s
ed
to
up
d
a
te th
e
so
lu
tion
in
ABC. Th
er
efore, Gb
est Artificial Bee
C
o
l
ony
(G
AB
C
)
m
odi
fi
ed
so
lu
tion
i
n
(6)
as fo
llo
ws [16
]
:
…
)
(
*
*
ij
j
ij
kj
ij
ij
ij
ij
X
gbest
X
X
X
V
(9
)
whe
r
e
ij
i
s
an un
i
f
orm
rand
om
num
ber i
n
[
0
,
C
]
, where C
i
s
a no
n-
negat
i
v
e
const
a
nt
an
d
gbest
j
r
e
p
r
es
en
ts
th
e
j
th elem
ent of the
gbest
ve
ctor.
3.2. I
m
plementation
Pr
ocedures of GAB
C
for Solving
OED Pr
oblem
Th
e
d
e
tails imp
l
em
en
tatio
n
of GABC al
g
o
rith
m
fo
r
s
o
l
v
i
n
g
OED
p
r
obl
e
m
i
s
descri
bed
as f
o
l
l
o
w
s
:
GABC for
Sol
v
ing OE
D Pr
oblem
Step 1
Inpu
t d
a
ta: C
o
st an
d system
d
a
ta.
…..
Step 2
Param
e
t
e
r set
t
i
ng
f
o
r
G
A
B
C
.
The
n
u
m
b
er o
f
ge
nerat
o
r i
s
de
fi
ne
d as
p
r
o
b
l
e
m
vari
abl
e
s.
……
…
Step 3
Calculate the fitness value in (5
) according to objective func
tion in
(1). Set the iteration equal to
1.
……
…
Step 4
Em
pl
oy
ed bees
det
e
rm
i
n
e new
can
di
dat
e
fo
o
d
s
o
u
r
ce
base
d
on
(
9
)
.
……
…..
Step 5
Ap
pl
y
t
h
e con
s
t
r
ai
nt
s ha
ndl
i
ng i
n
or
der t
o
sat
i
s
fy
t
h
e const
r
ai
nt
s i
n
(
2
)–
(4
). T
h
e det
a
i
l
s
of
con
s
t
r
ai
nt
s ha
n
d
l
i
n
g
m
e
t
hod
ol
ogy
ca
n be f
o
u
n
d
i
n
[
22]
.
Step 6
Calculate the fi
tness
value.
If t
h
e
ne
w fi
t
n
ess val
u
e i
s
bet
t
er t
h
an t
h
e ol
d
one
, t
h
e
ne
w f
o
o
d
s
o
urce
po
s
i
t
i
on i
s
rem
e
m
b
ere
d
;
o
t
h
e
rwise, th
e
o
l
d
on
e is
rem
a
in
in
t
h
e m
e
m
o
ry.
Step 7
On
l
o
ok
er b
ees d
e
term
in
e
th
e b
e
tter
so
lu
tion
u
s
ing
(7).
Step 8
Ap
pl
y
g
r
ee
dy
s
e
l
ect
i
on
pr
oces
s an
d st
ore
t
h
e
best
s
o
l
u
t
i
o
n.
Step 9
Sco
u
t
be
e
pr
o
duce
s
a
ne
w
r
a
nd
om
sol
u
t
i
o
n acc
or
di
n
g
t
o
(
8
)
f
o
r
u
n
i
m
pr
o
v
ed
sol
u
t
i
o
n a
f
t
e
r
certain
limits.
…………
Step 10
Sto
r
e
th
e b
e
st
so
lu
tion
(fo
o
d
so
urce po
sitio
n)
ob
tain
ed so
far an
d in
crease i
t
eratio
n
nu
m
b
er
b
y
1.
Step 11
Repeat Steps 4 to
10 until m
a
xim
u
m
num
ber of cycles are
reached.
……
..
4.
R
E
SU
LTS AN
D ANA
LY
SIS
The p
r
o
p
o
sed
GAB
C
al
go
ri
t
h
m
has been
t
e
st
ed on t
w
o C
a
se St
udi
e
s
by
usi
ng M
a
t
l
a
b 20
13
b
soft
ware in
order to
validate its perform
ances. The
IEEE
14-bus 5unit gene
rators and IEEE-30 bus
6 unit
gene
rat
o
rs t
e
st
sy
st
em
are co
nsi
d
e
r
ed
i
n
t
h
i
s
pa
per.
To
ev
al
uat
e
t
h
e r
o
bu
st
ness
of
GAB
C
,
4
0
di
ffe
rent
t
r
i
a
l
s
are c
o
nducted
and com
p
are
d
with A
BC al
g
o
rith
m
.
Th
e
o
p
tim
al p
o
w
er ou
tp
ut are
als
o
c
o
m
p
ared
with the
selected
pub
lish
e
d resu
lts.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
d
onesi
a
n
J
E
l
ec En
g& C
o
m
p
Sci
ISS
N
:
2
5
0
2
-
47
52
Gb
est
Artificia
l Bee Co
lon
y
fo
r N
o
n-co
n
vex
OED i
n
Po
wer Gen
e
ra
tio
n (M.N. Abd
u
llah)
19
1
4
.
1
.
Test
Ca
se
1
:
IEEE 14
-B
us 5 Unit
Genera
to
rs
The G
A
B
C
an
d AB
C
al
go
ri
t
h
m
s
have bee
n
use
d
t
o
det
e
rm
i
n
e t
h
e OED f
o
r IE
EE 1
4
b
u
s 5
-
u
n
i
t
g
e
n
e
rator co
nsid
ering
VPE an
d tran
sm
issio
n
losses. Th
e to
tal lo
ad
d
e
m
a
n
d
(
P
D
)
is 25
9 M
W
.
Th
e syste
m
an
d
ope
rat
i
o
nal
dat
a
are t
a
ke
n
fr
o
m
[23]
. T
h
e
o
p
t
i
m
a
l
powe
r
out
put
pr
o
duce
d
by
G
A
B
C
and
AB
C
are
t
a
bul
at
e
d
in
Tab
l
e 1. I
t
sh
ow
s th
at pro
p
o
s
ed
GA
BC
can
ob
tain
ed
lowe
r cost as
well as
si
gni
fi
cant
cost
re
du
ct
i
on
com
p
ared t
o
AB
C
al
go
ri
t
h
m
arou
nd
3.
6
$/
h. M
o
re
o
v
er,
searchi
ng
beh
a
vi
o
u
r
of
GA
B
C
i
s
al
so fast
er t
h
a
n
ABC as sho
w
n in
Fig
u
re 2. It
can
b
e
seen
the GABC
h
a
s cap
ab
ility to
find
m
i
n
i
m
u
m co
st with
10
0
iteratio
n
s
th
at h
i
gh
ligh
t
ed
th
e effectiv
en
ess
o
f
GABC
alg
o
rith
m
.
In
term
o
f
co
nsisten
c
y, it foun
d
t
h
at GABC can
g
i
ve m
i
nim
u
m cost for
every trial as
prese
n
ted i
n
Fig
u
re 3
.
It can
b
e
seen
th
at
GABC h
a
s cap
ab
ility to
o
b
tain
ed
lo
wer co
st with
go
od so
lu
tio
n.Th
e resu
lts
obt
ai
ne
d
f
r
om
t
h
e G
A
B
C
al
g
o
ri
t
h
m
has
bee
n
c
o
m
p
ared
w
i
t
h
t
h
o
s
e
rep
o
r
t
ed res
u
l
t
s
by
GA
[
2
3]
, G
A
_
AP
O
[2
3]
, NS
O
A
[2
3]
, PSO
[2
4]
, M
S
G_
HP
[2
4]
,
PSO
GS
A [7]
and
AB
C
as pr
esent
e
d i
n
Fi
gu
re 4. It
i
s
can b
e
see
n
t
h
at
pr
op
ose
d
GAB
C
ca
n pr
ovi
de l
o
wer c
o
st
as com
p
ared
t
o
ot
he
r al
go
r
i
t
h
m
s
. Thus
, i
t
can gi
ve si
gni
fi
cant
co
st
sav
i
ng
f
o
r
so
lv
i
n
g
O
E
D
pr
ob
lem
.
Tabl
e
1.
O
p
t
i
m
a
l
Po
wer
O
u
t
p
ut
by
AB
C
a
n
d
G
A
B
C
Al
go
ri
t
h
m
(Test
C
a
se 1
)
Generator unit
ABC
GABC
P
1
199.
59
96
199.
59
97
P
2
20.
000
0
20.
000
0
P
3
20.
975
76
21.
089
06
P
4
15.
510
43
15.
489
28
P
5
12.
469
85
12.
377
05
T
o
tal power
output (
M
W)
268.
55
56
268.
55
50
P
L
os
s
(M
W)
9.
5556
9.
5550
Fuel cost (
$
/h)
834.
13
830.
53
…………
..
Fi
gu
re
2.
C
o
nv
erge
nce C
h
ara
c
t
e
ri
st
i
c
of
AB
C
an
d
GAB
C
Al
g
o
ri
t
h
m
fo
r
Test
C
a
se 1
Fi
gu
re
3.
R
o
bu
st
ness
of
AB
C
and
G
A
B
C
Al
go
ri
t
h
m
for
Te
st
C
a
se 1
83
0
83
2
83
4
83
6
83
8
84
0
0
2
04
06
0
8
0
1
0
0
Fuel cost
($/
h
)
Iteration
ABC
GABC
83
0
83
1
83
2
83
3
83
4
83
5
83
6
83
7
83
8
01
0
2
0
3
0
4
0
Fuel cost
($/
h
)
No of
trials
ABC
GABC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
250
2-4
7
5
2
I
ndo
n
e
sian
J Elec Eng
& Com
p
Sci, V
o
l. 11
,
No
.
1
,
Ju
ly
20
18
:
1
87–
194
19
2
Fi
gu
re
4.
C
o
m
p
ari
s
on
o
f
O
p
t
i
m
al
C
o
st
of
G
A
B
C
an
d
Ot
he
r Al
g
o
ri
t
h
m
s
(Test
C
a
se 1
)
4
.
2
.
Test
Ca
se
2
:
IEEE 30
B
u
s 6-Unit
Genera
to
rs
The
GAB
C
a
nd
AB
C
al
g
o
r
i
t
h
m
s
have
be
en t
e
st
ed
on t
h
e IE
EE
30
-b
us
6 u
n
i
t
ge
n
e
rat
o
r
s
wi
t
h
VPEa
n
d
t
r
a
n
s
m
i
ssi
on l
o
sse
s.
The
p
o
w
er
de
m
a
nd
of
t
h
i
s
s
y
st
em
i
s
28
3.
4
M
W
.
T
h
e sy
s
t
em
and
o
p
era
t
i
onal
dat
a
are obt
ai
n
e
d fr
om
[23]
. Aft
e
r
40
di
ffe
r
e
nt
ru
ns, t
h
e
b
e
st
resul
t
s
obt
a
i
ned by
G
A
B
C
and AB
C
are
sho
w
n
in Table 2. The GABC can
pr
ovide a better cost as com
p
ared t
o
AB
C
wi
t
h
red
u
ct
i
o
n o
f
0.4
3
$/
h.
Ho
weve
r,
th
e con
v
e
rg
ence b
e
h
a
v
i
our
o
f
G
A
BC algo
r
ith
m
is f
a
ster
th
an
A
BC fo
r
f
i
nd
ing
op
timal co
st w
ith
in
100
i
t
e
rat
i
ons as s
h
o
w
n i
n
Fi
gu
r
e
5. T
h
e m
i
ni
m
u
m
resul
t
s
aft
e
r 4
0
di
f
f
ere
n
t
r
uns a
r
e
pr
esent
e
d i
n
Fi
g
u
re
6
h
i
gh
lig
h
t
ed
t
h
e effectiven
ess
o
f
GABC fo
r ob
tain
ing
lower
cost a
n
d consis
tent res
u
lts com
p
ared to
AB
C.
To val
i
d
at
e t
h
e perf
o
r
m
a
nce of p
r
o
p
o
sed
GAB
C
f
o
r s
o
l
v
i
n
g OE
D p
r
o
b
l
e
m
,
t
h
e com
p
ari
s
on st
udy
has b
een m
a
de wi
t
h
t
h
e
rep
o
r
t
ed res
u
l
t
s
of
GA
[2
3]
,
GA
_
A
P
O
[
23]
,
NS
OA
[2
3]
, P
S
O
[2
4]
, M
S
G
_
H
P
[2
4]
,
PSO
GS
A [
7
]
and
AB
C
as sh
ow
n i
n
Fi
g
u
re
7. It
cl
earl
y
sh
ows t
h
at
p
r
op
o
s
ed G
A
B
C
obt
ai
ned bet
t
e
r r
e
sul
t
s
com
p
ared t
o
t
h
e selected al
gorithm
s
. Thus, it can
gi
ve
a g
o
o
d
pot
e
n
t
i
a
l
cost
savi
n
g
fo
r
opt
i
m
al
po
we
r
gene
rat
i
o
n.
Tabl
e
2.
O
p
t
i
m
a
l
Po
wer
O
u
t
p
ut
by
AB
C
a
n
d
G
A
B
C
Al
go
ri
t
h
m
(Test
C
a
se 2
)
Generator unit
ABC
GABC
P
1
199.
59
96
199.
59
96
P
2
20.
000
0
20.
000
0
P
3
23.
978
8
23.
955
2
P
4
18.
822
0
18.
855
9
P
5
18.
231
9
18.
171
4
P
6
13.
871
1
13.
811
3
T
o
tal power
output (
M
W)
294.
50
34
294.
39
34
P
L
os
s
(M
W)
11.
103
4
10.
993
4
Fuel cost (
$
/h)
925.
41
924.
98
Fi
gu
re
5.
C
o
nv
erge
nce C
h
ara
c
t
e
ri
st
i
c
of
AB
C
an
d
GAB
C
Al
g
o
ri
t
h
m
fo
r
Test
C
a
se 2
926,55
926,55
905,54
836,46
834,36
834,13
834,13
830,53
76
0
78
0
80
0
82
0
84
0
86
0
88
0
90
0
92
0
94
0
96
0
GA
GA_APO
NSOA
PSO
MSG_HP
PSOGSA
ABC
GABC
Fuel cost
($/
h
)
Algorithms
92
3
92
5
92
7
92
9
93
1
93
3
93
5
93
7
93
9
0
2
04
06
08
0
1
0
0
Fuel cost
($/
h
Iteration
ABC
GABC
Evaluation Warning : The document was created with Spire.PDF for Python.
In
d
onesi
a
n
J
E
l
ec En
g& C
o
m
p
Sci
ISS
N
:
2
5
0
2
-
47
52
Gb
est
Artificia
l Bee Co
lon
y
fo
r N
o
n-co
n
vex
OED i
n
Po
wer Gen
e
ra
tio
n (M.N. Abd
u
llah)
19
3
Fi
gu
re
6.
R
o
bu
st
ness
of
AB
C
and
G
A
B
C
Al
go
ri
t
h
m
for
Te
st
C
a
se 2
Fi
gu
re
7.
C
o
m
p
ari
s
on
o
f
O
p
t
i
m
al
C
o
st
of
G
A
B
C
an
d
Ot
he
r Al
g
o
ri
t
h
m
s
(Test
C
a
se 2
)
5.
CO
NCL
USI
O
N
Th
e
Gb
est Artificial Bee C
o
lon
y
(GABC) algo
r
ith
m
has b
e
en
p
r
op
osed
for so
lv
i
n
g
th
e OED
pr
o
b
l
e
m
wi
t
h
val
v
e poi
nt
effe
ct
.The OE
D p
r
obl
em
wi
t
h
no
n-c
o
nve
x cost
fu
nct
i
o
n are di
ffi
cul
t
t
o
o
b
t
a
i
n
ed t
h
e
opt
i
m
al
sol
u
t
i
on
by
m
o
st
of
rep
o
r
t
e
d
resul
t
s of
he
uri
s
t
i
c
al
go
ri
t
h
m
.
Theref
ore
,
t
h
i
s
p
a
per i
nve
st
i
g
at
ed t
h
e
effectiv
en
ess
of p
r
op
osed
GABC to
so
lv
e
th
is p
r
o
b
l
em
based o
n
t
h
e t
w
o
di
ffe
re
nt
case st
udi
es w
h
i
c
h are
IEEE 14-bus
5 unit gene
rators a
nd
IEEE
30-bus 6
un
it generat
o
rs c
onsi
d
eri
ng
val
v
e point effec
t
and
tr
an
sm
issio
n
lo
sses. Th
e com
p
ar
iso
n
study h
a
s b
een
co
ndu
cted
in
t
e
r
m
s o
f
o
p
timal co
st, co
nv
erg
e
n
ce
characte
r
istic and
robustne
ss
. It fo
und
th
at
GABC
p
r
ov
id
ed
a
sign
ifican
t co
st redu
ctio
n
as
well as go
od
con
v
e
r
ge
nce
b
e
havi
or as c
o
m
p
ared t
o
AB
C
.
M
o
re
ove
r,
th
e op
ti
m
a
l OED so
l
u
tion
ob
tain
ed
b
y
GABC is
o
u
t
p
e
rform
e
d
co
m
p
ared
t
o
selected
resu
lts rep
o
rted in
literatu
re.
Fro
m
th
is stud
y, it can
b
e
con
c
luded
that
GAB
C
h
a
s g
o
od
p
o
t
e
nt
i
a
l
t
o
be im
pl
em
ent
e
d i
n
ot
her
po
wer sy
st
em
opt
im
i
zat
i
on pr
o
b
l
e
m
s
especi
all
y
i
n
opt
i
m
al
powe
r
di
spat
c
h
are
a
.
ACKNOWLE
DGE
M
ENT
Th
e au
tho
r
s wo
u
l
d
lik
e t
o
than
k Un
iv
ersiti Tun
Hu
ssei
n
Onn
Malaysia (UTHM)
fo
r su
ppo
rting
t
h
e
researc
h
u
nde
r
Sh
ort
Te
rm
Gr
ant
(
U
63
9)
.
REFERE
NC
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