Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
9,
No.
2,
Februa
ry 20
18,
pp.
365
~
372
IS
S
N: 25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v9.i
2.pp
365
-
372
365
Journ
al h
om
e
page
:
http:
//
ia
es
core.c
om/j
ourn
als/i
ndex.
ph
p/ij
eecs
Activ
e an
d Reactive Po
wer Sch
eduli
ng Opti
mizati
on
using
Firefly
Algorith
m to Im
prove V
oltage St
ability U
nd
er
L
oad
Demand
Variatio
n
Moham
ad K
h
airuz
z
ama
n
Moham
ad Z
ama
ni
1
, Ism
ail
Mus
ir
in
2
, Hali
m H
as
san
3
,
Sha
ri
fah A
z
w
a
S
haa
ya
4
,
Shahril
Irwa
n Sul
aima
n
5
, Nor
A
z
ura Md
. Ghani
6
, Sai
fu
l I
z
w
an
Su
li
man
7
1,2,3,5,7
Facult
y
of
Elec
tr
ical Engi
n
ee
ring
,
Univ
ersiti
T
eknol
ogi
MA
RA,
40000
Shah
Alam,
Se
la
ngor
,
Malay
si
a
4
Depa
rtment of
El
e
ct
roni
cs
&
C
om
m
uni
ca
ti
on
E
ngine
er
ing, Univ
ersit
i
Te
n
aga Na
sional
,
43000
Ka
ja
ng,
Sel
angor
,
Malay
s
ia
6
Facul
t
y
of
Com
pute
r & Ma
the
m
at
i
ca
l
Sci
enc
es,
Univer
siti
Te
kno
logi
MA
RA,
400
00
Shah
Alam,
Sela
ngor
,
Ma
lay
si
a
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
J
un
9
, 201
6
Re
vised
N
ov
2
0
, 2
01
6
Accepte
d
Dec
11
, 201
6
Thi
s
pap
er
pre
sents
active
an
d
react
iv
e
pow
er
sche
du
li
ng
u
sing
firef
l
y
al
gorit
hm
(FA
)
to
improve
voltage
stab
il
i
t
y
un
der
loa
d
deman
d
var
iation
.
The
stud
y
involves
the
develop
m
ent
of
fire
fl
y
o
pti
m
iz
ation
engine
for
power
sche
duli
ng
p
roc
ess
invol
ving
t
he
a
ct
iv
e
and
rea
c
ti
ve
power
for
wind
gene
ra
tor.
Th
e
sche
dul
ing
opti
m
iz
a
ti
on
of
wind
gene
ra
tor
is
te
st
ed
b
y
usin
g
IEE
E
30
-
Bus
Re
li
ability
T
est
S
y
stem
(RTS).
Vol
ta
ge
stabilit
y
of
the
s
y
s
te
m
is
assess
ed
base
d
in
a
pre
-
deve
l
oped
volt
age
sta
bil
ity
indica
tor
t
ermed
as
fast
volt
ag
e
stabilit
y
inde
x
(FV
SI).
Thi
s
stud
y
al
so
conside
rs
the
ef
fec
ts
on
th
e
loss
and
voltage
profile
of
the
s
y
stem
r
esult
ed
f
rom
the
opti
m
i
z
at
ion
,
wher
e
the
FV
SI
val
ue
a
t
the
observe
d
line,
m
ini
m
um
vo
lt
ag
e
of
the
s
y
st
e
m
and
loss
were
m
onit
ore
d
during
the
lo
ad
inc
rement
.
R
esult
s
obtained
f
ro
m
the
stud
y
are
convi
n
ci
ng
in
addr
essing
th
e
sche
duli
ng
of
power
in
wind
gene
rat
o
r.
Im
ple
m
ent
at
ion
of
FA
appr
oac
h
to
solve
po
wer
sche
duli
ng
rev
ea
l
ed
it
s
fle
xibilit
y
an
d
f
ea
sibl
e
for
solvi
ng
la
rge
r
s
y
st
e
m
withi
n
diffe
r
e
nt
objecti
v
e
func
ti
ons.
Ke
yw
or
d
s
:
Fast V
oltage
S
ta
bili
ty
I
nd
e
x
Firefly
A
l
gorithm
Power Sch
ed
ul
ing
Copyright
©
201
8
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Moh
am
ad
K
ha
iruzzam
an
Mo
ham
ad
Zam
ani
,
Faculty
of Elec
tric
al
Engineer
ing
,
Un
i
ver
sit
i Te
knol
og
i M
ARA
,
40000 S
hah A
l
a
m
, S
el
ango
r,
Ma
la
ysi
a
Em
a
il
:
m
oh
d_kh
ai
ru
zzam
an@
ya
hoo.com
1.
INTROD
U
CTION
Most
cu
rr
e
nt
powe
r
syst
em
network
s
ha
ve
been
de
velo
pe
d
to
s
upplem
e
nt
the
fa
st
-
gr
owin
g
dem
and
for power
. As
a res
ult, the
de
sign
of these
pow
e
r
syst
em
b
ecom
e co
m
plica
te
d
an
d
a
n
e
w
appr
oac
h
to
optim
iz
e
the po
wer sy
stem
is n
eede
d
t
o
e
nsure
t
he
sy
stem
can
oper
a
te
at it
s b
est
.
Power
sc
hedul
ing
com
pr
ise
s
of
tw
o
ta
sk
s
w
hich
are
un
it
com
m
itm
ent
and
powe
r
dis
patch
to
fu
l
fil
the
powe
r
de
m
and
an
d
thes
e
ta
sk
s
are
to
be
pe
rfor
m
ed
eff
ect
ively
wit
hin
the
ge
ner
a
ti
on
’s
c
onstrai
nts
a
nd
lim
it
s.
The
power
dis
patch
w
il
l
ensu
re
t
he
ge
ner
at
io
n
c
os
t
to
be
at
t
he
m
i
nim
u
m
.
Me
anw
hile,
react
ive
powe
r
sche
du
li
ng is
s
uggeste
d
to
r
e
duce the
po
wer
syst
e
m
loss.
[1
]
.
Loa
d
Dem
and
var
ie
s
t
hro
ughout
t
he
ti
m
e
thu
s
t
he
syst
em
will
nee
d
to
ha
ve
th
e
a
bili
ty
to
s
us
ta
in
a
sta
ble
conditi
on.
A
s
the
loa
d
dem
and
increa
sed
to
wards
th
e
lim
it
wh
ic
h
it
can
sta
nd,
th
e
syst
e
m
is
at
risk
of
colla
ps
e
[2
]
.
T
he
Fa
st
V
oltag
e
Stabil
it
y
Ind
ex
(F
V
SI)
is
a
m
et
ho
d
t
o
dete
rm
ine
the
sta
bi
li
ty
of
the
syst
e
m
a
s
the li
ne
ind
e
x
s
hows 0 to
1
w
he
re 1
s
howing
the syst
e
m
is a
t t
he
verge of c
ollapse [3]
–
[5
]
. Volta
ge
sta
bili
ty
i
s
the
te
rm
us
ed
wh
e
n
a
syst
em
is
in
equ
il
ibri
um
du
rin
g
no
m
inal
op
e
ra
ti
on
[
6]
–
[
7].
Be
sides
im
pr
ov
in
g
the
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
9
,
No.
2
,
Fe
bruary
2
01
8
:
365
–
372
366
sta
bili
ty
of
the
syst
e
m
,
this
st
ud
y
al
so
will
be
lookin
g
at
the
reacti
on
of
th
e
syst
e
m
loss
and
volt
age
pro
file
of
the syst
em
.
FA
is
us
e
d
to
op
ti
m
iz
e
the
IEEE
30
-
bus
s
yst
e
m
with
va
ryi
ng
l
oa
ds
.
T
he
F
A
is
us
e
d
as
it
has
t
he
abili
ty
to
so
lv
e
m
ult
i
-
obj
ect
ive
an
d
al
s
o
fast
co
nver
ge
nc
e
rate
[
8]
–
[9]
.
The
sche
du
li
ng
is
done
to
al
l
gen
e
rato
rs
an
d
synch
r
onou
s
conde
ns
ers
.
This
pap
e
r
pr
ese
nts
act
iv
e
and
reacti
ve
power
sc
he
du
l
in
g
op
ti
m
iz
ation
usi
ng
fi
ref
ly
al
gorithm
to
i
m
pr
ov
e
vo
lt
a
ge
sta
bili
ty
con
sideri
ng
loa
d
dem
and
.
Re
su
lt
s
f
rom
this
stud
y
re
vealed
that
the
syst
e
m
sta
bility
i
mp
r
oved
base
d
on
the
reducti
on
of
the
val
ue
of
F
VSI.
Be
sides
tha
t
,
the bus
volt
age
profil
e an
d
t
he
sy
stem
loss
w
ere also
im
pr
oved
after
the
optim
iz
at
ion
.
2.
RESEA
R
CH MET
HO
D
2.1. Pro
blem
Formul
at
i
on
In
this
pa
per,
the
m
a
in
obj
ect
ive
of
the
opti
m
iz
at
ion
pr
oce
ss
is
to
i
m
pr
ove
the
vo
lt
age
sta
bili
ty
in
the
syst
e
m
.
Vo
lt
ag
e
sta
bili
ty
is
rep
rese
nted
by
usi
ng
FVSI
val
ue.
T
he
obj
ect
i
ve
f
unct
ion
of
the
opti
m
iz
at
io
n
a
nd
the form
ula of
FV
S
I
ca
n be
re
pr
ese
nted
as:
=
min
(
)
(1
)
=
4
2
2
(2
)
wh
e
re
is t
he
F
VS
I
v
al
ue of
li
ne
c
onnecti
ng
s
th
bus to
r
th
bu
s,
is t
he
reacti
ve power
f
l
ow
i
ng
into
r
th
bus,
is
the
volt
age
va
lue
at
s
th
bu
s,
and
are
the
im
ped
a
nce
a
nd
re
act
ance
of
the
li
ne
wh
il
e
s
and
r
a
re th
e
se
nd
i
ng bus
num
ber an
d recei
vi
ng bus n
um
ber
r
es
pecti
vely
.
Durin
g
the
op
tim
iz
at
ion
pro
cess
,
the
re
are
sever
al
var
i
ous
w
hic
h
nee
ds
to
be
sat
isfi
ed.
T
he
fi
rst
const
raint
is
to
ens
ur
e
t
hat
the
real
and
r
eact
ive
power
gen
e
rated
by
the
gen
e
rati
on
unit
s
and
t
he
wind
gen
e
rato
r
s
houl
d
be
withi
n
th
e
range
of
it
s
m
ini
m
u
m
and
m
axi
m
u
m
op
e
rati
on
lim
it
.
T
he
c
on
st
raints
can
be
expresse
d
as:
≤
≤
(3
)
≤
≤
(4
)
wh
e
re
P
g
is
th
e
act
ive
po
wer
outp
ut
of
th
e
gen
e
rati
on
un
it
,
Q
g
is
the
rea
ct
ive
powe
r
outp
ut
of
t
he
gen
e
rati
on
unit
,
an
d
is
the
m
ini
m
u
m
power
ou
t
pu
t
li
m
i
t
and
m
axim
u
m
powe
r
outp
ut
lim
i
t
of
the
gen
e
rati
on
un
it
w
hile
an
d
ar
e
the
m
ini
m
um
reacti
ve
power
outp
ut
li
m
it
and
m
axim
u
m
reacti
ve
powe
r ou
t
pu
t l
i
m
it
o
f
the
ge
ne
rati
on unit
.
The
next
con
stra
int
wh
i
ch
s
ho
uld
be
consid
er
e
d
i
s
t
he
p
ower
bal
ance
co
n
stra
i
nts.
In
thi
s
co
n
stra
i
nt,
tot
al
power
ge
n
er
ated
in
a
p
ow
e
r
syste
m
sh
o
uld
cat
er
the
load
dem
and
a
s
we
ll
a
s
the
losse
s
in
the
system.
T
hi
s
con
stra
i
nt
hold
s
tru
e
fo
r
both
ac
tiv
e
and
re
a
ctive
power
bala
n
ce
.
In
ac
tiv
e
power
balan
ce,
po
we
r
g
ene
ra
te
d
by
the
gene
ra
tion
u
nit
and
power
p
roduc
ed
by
the
wind
generato
r,
P
Gw
sh
ould
ca
te
r
the
ac
tiv
e
p
ow
e
r
d
eman
d
,
P
de
m
an
d
and
re
al
po
we
r
lo
ss
,
P
loss
.
In
r
e
ac
tiv
e
power,
the
p
ow
e
r
ge
nerat
ed
by
the
ge
ner
atio
n
unit
s
as
w
ell
as
inj
ec
ted
re
a
ctive
power,
Q
inj
sh
o
uld
ca
ter
th
e
reactiv
e
po
wer
deman
d,
Q
de
m
and
and
the
losse
s,
Q
l
oss
.
Thes
e
constr
aints
can
be
expre
ssed a
s:
+
=
∑
+
(5
)
+
=
∑
+
∑
(6
)
Gr
i
d
co
nn
ect
e
d
wi
nd
tu
r
bin
e
s
produce
real
powe
r
w
hich
de
pends
on
t
he
wind
sp
ee
d,
V
w
.
The
wi
nd
tur
bin
e
will
on
ly
sta
rt
to
generate
at
a
c
ut
i
n
wind
s
pee
d
and
the
m
axi
m
um
po
we
r
ge
ne
rated
is
in
be
tween
15
m
s
-
1
and
c
ut
-
out
sp
ee
d
[10
]
.
The
cut
i
n
wind
s
peed
is
5
ms
-
1
and
the
cut
-
ou
t
s
peed
is
25
m
s
-
1
.
The
cut
-
ou
t
sp
ee
d
is
set
to
reduce
the
ris
k
of
the
tur
bine
to
ro
ta
te
too
fast
and
e
xp
e
rience
m
echan
ic
al
fail
ur
e,
th
us
th
e
br
a
ke
is
a
ppli
ed
to
the
wind
r
otors.
T
he
pow
er
cu
r
ve
of
t
he
m
od
el
le
d
wind
tu
rb
i
ne
us
e
d
in
this
s
t
ud
y
c
an
be
expresse
d
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Act
iv
e a
nd
Rea
ct
iv
e Po
we
r
Sc
hedulin
g Op
ti
miza
ti
on
us
in
g Fi
ref
ly
Algo
rit
hm
…
(
Mo
ham
ad Z
ama
ni
)
367
=
{
0
0
.
017
×
3
60
0
<
5
−
1
5
−
1
≤
<
15
−
1
15
−
1
≤
≤
25
−
1
>
25
−
1
(7)
Figure
1
sho
w
s
the
pr
oce
ss
of
act
ive
and
re
act
ive
power
s
cheduli
ng
opti
m
iz
at
ion
by
us
ing
F
A.
The
process
sta
rts
by
determ
ining
the
le
ast
loada
bl
e
bu
s
a
nd
t
he
weak
e
st
li
ne
in
the
syst
e
m
.
Load
i
ncr
em
ent
at
the
sel
ect
ed
loa
d
bu
s
will
be
do
ne
a
nd
t
he
un
-
op
ti
m
iz
ed
FVSI
of
t
he
wea
kest
li
ne,
m
inim
u
m
bu
s
volt
age
a
nd
transm
issi
on
loss
a
re
m
on
it
ored
.
Fire
fly
al
gorithm
op
ti
m
izati
on
is
the
n
c
ondu
ct
ed,
an
d
the
opti
m
iz
ed
value
s
are m
on
it
or
e
d for a
ny ch
a
nge
s.
T
he pr
ocess
is rep
eat
e
d un
ti
l t
he
m
axi
m
u
m
load
a
bili
ty
o
f
t
he bus i
s
reach
ed.
Figure
1. Acti
ve
and
Re
ac
a
ti
ve
Powe
r
Sc
he
duli
ng
Op
ti
m
iz
ation
P
ro
ces
s
Figure
2. Flo
w
Chart
t
o
Deter
m
ine
W
orst
Pe
rfor
m
ing
Line
2.2. Alg
orit
h
m for we
akest
li
ne identific
ati
on
The
w
eakest
bus
of
the
syst
e
m
need
ed
t
o
be
identifie
d
be
fore
the
weak
e
st
li
ne
of
the
s
yst
e
m
can
be
sel
ect
ed
f
or
ob
serv
at
io
n.
The
weake
st
bus
i
s
determ
ined
by
so
rtin
g
the
l
east
m
axi
m
u
m
loada
bili
ty
of
each
bu
s
. T
he st
eps t
o
dete
rm
ine the w
ea
kest
bu
s:
In
c
rease l
oad a
t sel
ect
ed
bus
.
Exec
ute loa
d flow analy
sis
In
c
rease l
oad a
t sel
ect
ed
bus
unti
l l
oad
flo
w d
iver
ges.
The
l
oad at b
us i
s r
ec
orde
d when the
loa
d flo
w dive
rg
e
d.
Pr
oc
eed
step i
un
ti
l i
v f
or
t
he next
bus.
So
rt
the
bus
with the least
m
axim
u
m
b
us
loa
dab
il
it
y when
al
l bu
sse
s ar
e
don
e
.
Determ
ine w
ea
kest
bu
s
w
it
h l
ow
est
m
axi
m
u
m
loadab
il
it
y.
Figure 2
s
hows
the steps
in d
e
te
rm
ining
the
weak
e
st l
ine w
hich
will
b
e ob
serv
e
d
f
or
this
stud
y. L
oad
will
be
increas
ed
at
the
sel
ect
ed
loa
d
bus
gr
adu
al
ly
an
d
F
VS
I
of
eac
h
li
ne
is
determ
ined
f
or
eac
h
inc
rem
ent
.
The
increm
ent
is
do
ne
unti
l
a
li
ne’
s
FV
S
I
re
aches
ab
ove
1.
This
li
ne
is
con
side
red
as
the
weak
est
li
ne
in
the
syst
e
m
d
ur
i
ng
load
i
ncr
em
ent at t
he
sel
ec
te
d b
us
. Afte
r dete
rm
ining
the
w
eakest l
ine,
the
optim
iz
ation
i
s done
and the
FVSI
of the
li
ne wil
l b
e m
on
it
or
ed
.
S
T
A
R
T
E
N
D
D
e
t
e
r
m
i
n
e
m
a
x
i
m
u
m
l
o
a
d
a
b
i
l
i
t
y
a
n
d
w
e
a
k
e
s
t
l
i
n
e
Load
i
n
c
r
e
a
s
e
d
u
p
t
o
m
a
x
i
m
u
m
l
o
a
d
a
b
i
l
i
t
y
?
I
n
c
r
e
a
s
e
l
o
a
d
a
t
t
h
e
c
h
o
s
e
n
bus
A
n
a
l
y
s
e
p
r
e
-
o
p
t
i
m
i
s
e
d
F
V
S
I
,
m
i
n
i
m
u
m
b
u
s
v
o
l
t
a
g
e
a
n
d
r
e
a
l
p
o
w
e
r
l
o
s
s
O
p
t
i
m
i
s
e
F
V
S
I
u
s
i
n
g
F
A
A
n
a
l
y
s
e
t
h
e
o
p
t
i
m
i
s
e
d
FV
S
I
,
m
i
n
i
m
u
m
b
u
s
v
o
l
t
a
g
e
a
n
d
r
e
a
l
p
o
w
e
r
l
o
s
s
R
e
c
o
r
d
a
n
d
t
a
b
u
l
a
t
e
t
h
e
r
e
s
u
l
t
s
Y
e
s
No
S
T
A
R
T
E
N
D
L
o
a
d
i
n
c
r
e
m
e
n
t
a
t
t
h
e
s
e
l
e
c
t
e
d
l
o
a
d
b
u
s
D
o
e
s
F
V
S
I
>
1
.
0
0
?
C
a
l
c
u
l
a
t
e
FV
S
I
v
a
l
u
e
f
o
r
a
l
l
l
i
n
e
s
R
a
n
k
t
h
e
FV
S
I
v
a
l
u
e
s
D
e
t
e
r
m
i
n
e
t
h
e
w
o
r
s
t
p
e
r
f
o
r
m
i
n
g
l
i
n
e
Y
e
s
No
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on
esi
a
n
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c Eng &
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m
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Sci,
Vo
l.
9
,
No.
2
,
Fe
bruary
2
01
8
:
365
–
372
368
2.3. Fi
refly
Al
go
ri
th
m
FA
ha
s
bee
n
f
ounded
by
Dr.
Xin
-
She
Ya
ng
at
Cam
br
idg
e
Un
i
ver
sit
y
in
2007
[
11]
.
Firef
ly
al
go
rithm
is
based
on
fir
efli
es
li
vin
g
in
natu
re
w
hich
usual
ly
found
in
the
woo
ds
of
t
ropical
area.
T
he
al
gorithm
will
be
us
in
g
the
at
tra
ct
iveness
of
a
so
luti
on,
t
he
sa
m
e
te
chn
iqu
e
us
e
d
by
fire
flie
s
in
the
nat
ur
e
to
at
tract
the
opposit
e
sex
f
or
repr
oduction
[12].
T
he
firef
li
es
are
draw
n
to
the
m
or
e
at
tract
ive
or
flashy
li
gh
ts
e
m
itted
by
the
ot
her
s
reg
a
rd
le
ss
the
sex
or
ie
ntati
on.
T
her
e
are
se
ve
ral
va
riables
that
need
to
be
consi
der
e
d
be
f
or
e
a
firef
ly
ca
n
see
the
li
gh
ts
em
itted.
The
em
itt
ed
li
gh
ts
will
be
le
ss
at
tract
i
ve
due
to
natu
re’
s
co
ns
t
raint
s
su
ch
as
ai
r
m
ist
and
water c
onte
nts
in the ai
r
ca
us
e
d by rai
n
as
we
ll
as b
y a
n
inc
r
ease i
n dist
anc
e [
12
]
.
The
known
ad
van
ta
ge
of
FA
ov
e
r
the
existi
ng
cl
assic
al
op
tim
iz
at
ion
m
eth
od
is
it
s
fa
st
conve
rg
e
nce
sp
ee
d
[13].
As
sta
te
d
in
[1
4]
and
[
15
]
,
it
ha
s
a
bette
r
perform
ance
co
m
par
e
d
to
ot
her
popula
r
opti
m
i
zat
ion
al
gorithm
s
su
ch
as
pa
rtic
le
swar
m
op
tim
izati
on
an
d
arti
f
ic
ia
l
bee
colony
.
Firefly
al
gorithm
a
lso
has
oth
er
adv
a
ntage
s
w
he
n
so
l
ving
pro
blem
s;
the
so
luti
on
or
t
he
at
tract
iveness
of
the
firef
ly
is
no
t
gender
s
pe
ci
fic.
Attract
ion
le
ve
l
is
pr
opor
ti
on
al
to
the
le
vel
of
bri
ghtnes
s
wh
il
e
the
br
i
ghtness
of
the
s
olu
ti
on
is
base
d
on
the
obj
ect
ive
fun
ct
ion
[
11
]
. T
he
optim
iz
at
ion
p
r
oc
ess u
si
ng F
A
i
s briefly
d
isc
usse
d
as
in Fi
gur
e 3
[
16
]
.
1.
Defin
e ob
ject
ive fu
n
ctio
n
2.
Pop
u
la
tio
n
of firefl
y initia
lized
,
n
.
3.
Defin
e ligh
t red
u
cin
g
facto
r a
n
d
pa
rameters.
4.
w
hile
itera
tio
n
< max itera
tio
n
5.
for
i = 1
:
n
6.
for
j = 1
:
n
7.
Lig
h
t br
ig
h
tn
es
s d
etermin
ed
by o
b
jective fun
ctio
n
8.
if
(I
i
<
I
j
)
9.
Firefly i
flies tow
a
rd
s firefly j
10.
Attra
ctio
n
cha
n
g
es
beca
u
se o
f cha
n
g
e
in d
ista
n
ce
11.
Retrieve
so
lu
tio
n
12.
else
13.
Firefly i
flies to a
n
ywh
ere
14.
end if
15.
end f
o
r
j
16.
end f
o
r
i
17.
Fireflies so
rted
fro
m bes
t to wo
rs
t
18.
end w
hile
Figure
3. Pse
udo
Co
de
of F
A
The
at
tract
ive
ne
ss of a
f
ire
fly
can be
def
i
ned
as in t
he
f
unct
ion bel
ow
:
(
)
=
0
×
(
−
2
)
(8)
wh
e
re
β(
j)
is
t
he
at
tract
ive
ne
ss
of
j
th
firef
ly
wh
il
e
β
0
is
th
e
init
ia
l
at
tractiven
ess
of
the
firef
ly
at
dista
nce
0,
wh
ic
h
ca
rr
ie
s
t
he
value
of
1.
The
a
bsor
ptio
n
coe
ff
ic
ie
nt
γ
with
the
va
lue
of
0.1
an
d
r
ij
is
the
distance
be
twee
n
i
th
firef
ly
and
j
th
firef
ly
a
nd it
can
be
e
xpress
ed
as:
=
|
−
|
(9)
Fr
om
(8)
a
nd
(
9),
it
show
s
th
at
the
at
tract
iv
eness
of
a
fire
f
ly
is
dep
e
nd
i
ng
on
t
he
distan
ce
betwee
n
the
tw
o
fire
flie
s,
r
ij
a
nd
t
he
li
gh
t
abs
orptio
n
coeffic
ie
nt,
γ
.
The
m
or
e
at
tra
ct
ive
j
th
fire
fly
,
will
at
tract
the
ot
he
r
firef
li
es
or
in
this
case
i
th
firef
ly
to
fly
towar
ds
it
.
The
flig
ht
path
of
the
f
irefly
can
be
s
how
n
in
the
f
unct
ion
belo
w:
=
+
0
×
(
−
2
)
×
(
−
)
+
×
(
−
0
.
5
)
(10)
Fr
om
(10),
the
init
ia
l
po
sit
io
n
of
the
fire
fly
is
m
ov
ed
base
d
on
t
he
at
tract
iveness
of
the
oth
e
r
fire
fly
and
α
,
is
t
he
pa
rt
w
he
re
the
f
irefly
is
m
ov
e
d
in
a
ra
ndom
m
ann
er
.
T
he
α
hel
ps
th
e
al
go
rithm
to
searc
h
a
nd
exp
l
or
e
any
possible
ne
w
a
tt
racti
on
,
m
eanwhil
e
γ
c
ontrols
t
he
s
pee
d
of
co
nver
ge
nc
e
of
the
al
gorithm
.
Coef
fici
ent
r
and
is a
r
a
ndom
n
um
ber
i
n
the
ra
ng
e
0 up t
o 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
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J
E
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c Eng &
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m
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Sci
IS
S
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02
-
4752
Act
iv
e a
nd
Rea
ct
iv
e Po
we
r
Sc
hedulin
g Op
ti
miza
ti
on
us
in
g Fi
ref
ly
Algo
rit
hm
…
(
Mo
ham
ad Z
ama
ni
)
369
3.
RESU
LT
S
AND A
N
ALYSIS
The
res
ults
of
t
he
st
ud
y
a
re
presented
to
a
ddr
ess
the
FVSI,
bu
s
volt
age
an
d
the
po
wer
lo
ss
pro
file
of
the
syst
e
m
befor
e
a
nd
after
t
he
opti
m
iz
a
ti
on
.
Fi
gure
4
il
lustrate
s
the
te
st
syst
e
m
wh
ic
h
is
us
e
d
in
this
s
tud
y
.
The
te
st
syst
em
us
ed
is
IEE
E
30
-
bu
s
syst
e
m
and
sli
gh
t
m
od
i
ficat
ion
has
been
done
w
he
re
a
ge
ner
at
or
wh
ic
h
represe
nts
a
w
ind
gen
e
rato
r
is
connecte
d
at
bu
s
7
of
the
s
yst
e
m
.
Fr
om
T
able
1,
bus
26,
bu
s
30
an
d
bus
29
hav
e
the
le
ast
m
axi
m
u
m
load
abili
ty
resp
ect
ively
w
hich
ca
n
af
fect
the
sta
bili
ty
of
the
sy
stem
.
Ther
e
for
e,
this
stud
y
im
ple
m
e
nts
load
var
ia
t
ion
at
bus
26.
By
increasing
Q
d
at
bu
s
26
with
5
MV
A
inter
val;
FV
S
I
at
the
weak
e
st l
ine,
bus
vo
lt
a
ge
a
nd
loss a
re
ob
se
r
ve
d
th
r
oughout t
he pr
ocess
.
Table
1.
T
hree
Buses
with t
he
Least
Maxim
um
Bus
Load
a
bi
li
ty
Bu
s Nu
m
b
e
r
Maxi
m
u
m
Bu
s Lo
ad
ab
ility
(
MVA
r)
26
3
3
.5
30
3
5
.1
29
3
8
.2
Figure
5
s
how
s
the
F
VSI
rankin
g
of
t
he
li
ne
s
in
the
po
we
r
syst
em
du
rin
g
loa
d
i
ncr
em
ent
at
bus
26.
The
fig
ur
e
s
ho
ws
li
ne
34
w
hi
ch
c
onnecti
ng
bu
s
25
a
nd
26
is
the
wea
kest
li
ne
w
hich
s
ho
ws
the
F
VS
I
of
the
li
ne
reache
d
the
value
a
bove
1
at
32
.
4
MVAR.
T
hus,
this
stud
y
w
il
l
ob
serv
e
li
ne
34
f
or
t
he
FV
S
I
op
ti
m
iz
ation
.
Figure
4: Mo
di
fied IEEE
30
-
Bus S
yst
em
with
W
i
nd G
e
ne
r
at
or
C
onnecte
d
at
Bus
7
Figure
5: Sta
bili
ty
I
nd
ic
es
of
the
Weak
e
st B
us i
n
T
he Sy
ste
m
0
0,
2
0,
4
0,
6
0,
8
1
1,
2
30
30
,
5
31
31
,
5
32
32
,
5
33
33
,
5
34
FVSI
Qd
at
b
u
s
26
(M
VA
R
)
line 3
4 (25-
26)
line 3
3 (24-
25)
line 3
5 (25-
27)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
9
,
No.
2
,
Fe
bruary
2
01
8
:
365
–
372
370
3.1.
FA
for
vo
l
tage st
ab
il
ity
i
mpro
vemen
t
FV
S
I
val
ues
s
hows
the
sta
bi
li
ty
of
a
power
syst
e
m
.
Re
du
ced
val
ue
of
t
he
in
dex
s
how
s
there
is
a
n
i
m
pr
ovem
ent
on
the
sta
bili
ty
of
the
netw
or
k.
Fig
ur
e
6
an
d
ta
ble
2
show
the
resu
lt
of
F
VS
I
befor
e
a
nd
after
op
ti
m
iz
ation
.
Fr
om
Figu
re
6,
the
ind
ex
value
after
opti
m
i
zat
ion
(FVS
I
-
FA
)
is
re
du
ce
d
sli
gh
tl
y
wh
e
n
the
load
i
s
le
ss
than
25
M
VA
R.
T
he
im
p
rovem
ent
of
t
he
ind
e
x
on
ly
be
com
es
m
or
e
app
a
re
nt
w
hen
the
loa
d
is
i
ncrea
sed
to
m
or
e
tha
n
25
MV
AR.
Ta
bl
e
2
ta
bu
la
te
s
t
he
detai
ls
of
th
e
res
ults,
wh
il
e
Fig
ur
e
6
sho
w
the
F
VSI
pro
f
il
e
a
t
each
var
ia
ti
on.
Figure
6: F
VSI
W
it
h
a
nd
Without
Op
ti
m
iz
ation
Table
2.
Res
ults o
f Vo
lt
age
St
abili
ty
I
m
pr
ov
e
m
ent
Qd
at
Bu
s 2
6
(
M
V
AR)
Pre
-
o
p
ti
m
iz
ed
FV
SI
(p.u
)
Po
st
-
o
p
ti
m
iz
ed
FV
SI
(p.u
)
I
m
p
rov
e
m
en
t
Per
c
en
tag
e (
%)
5
0
.10
7
9
0
.10
7
8
0
.1
10
0
.22
4
8
0
.22
3
5
0
.6
15
0
.35
1
4
0
.34
9
2
0
.6
20
0
.49
1
9
0
.48
8
4
0
.7
25
0
.65
2
9
0
.64
7
7
0
.8
30
0
.86
5
7
0
.84
3
3
2
.6
32
1
.00
0
4
0
.96
6
7
3
.4
3.
2
.
FA
for mi
nimum b
us
volta
ge
m
ax
im
is
at
i
on
Vo
lt
age
pr
of
il
e
of
a
powe
r
sy
stem
can
be
use
d
to
in
dicat
e
the
healt
h
of
th
e
syst
e
m
.
A
he
al
thy
powe
r
syst
e
m
m
us
t
m
ai
ntain
acce
pta
ble
volt
age
pro
file
to
re
duce
the
ris
k
of
over
loading
a
nd
sy
stem
colla
ps
e
du
e
to
low
bus
vo
lt
a
ge
.
The
f
ollo
wing
fig
ur
e
7
an
d
ta
b
le
3
s
how
the
m
ini
m
u
m
vo
lt
age
pro
file
of
the
syst
em
befor
e
and after
sc
heduling o
ptim
iz
a
t
ion
.
W
it
h
FA,
the
op
ti
m
iz
ed
so
luti
on
m
anag
ed
to
i
m
pr
ove
the
vo
lt
age
pr
of
il
e
of
the
30
-
bu
s
syst
e
m
a
s
dep
ic
te
d
by
Fi
gure
7.
T
he
m
ini
m
u
m
bu
s
volt
age
of
the
s
yst
e
m
was
inc
reased
a
fter
th
e
op
ti
m
iz
ation.
The
nu
m
erical
i
m
pr
ovem
ents
of
the
m
ini
m
u
m
bus
volt
age
wer
e
ta
bu
la
te
d
in
Ta
ble
3.
Fr
om
the
ta
bl
e,
the
m
ini
m
u
m
bu
s
vo
lt
age
dr
op
s
belo
w
0.95
p.
u
wh
e
n
t
he
lo
ad
is
10
MV
A
R.
The
opti
m
i
zed
power
sc
he
du
li
ng
te
chn
iq
ue
had
increase
d
th
e
m
ini
m
u
m
bu
s
vo
lt
age
t
o
0.9
426
w
hic
h
is
cl
os
e
to
the
acc
eptable
ra
nge
of
bus
vo
lt
age
.
T
he
m
ini
m
u
m
bu
s
volt
age
im
pr
ov
em
ent
only
becam
e
app
ar
ent
w
he
n
the
load
is
m
or
e
than
30
MVAR.
Table
3: Result
s of
Mi
nim
u
m
Bus Vo
lt
age
Im
pr
ov
em
ent
Qd
at
Bu
s 2
6
(M
V
AR)
Pre
-
o
p
ti
m
iz
ed
m
in
i
m
u
m
bu
s
v
o
ltag
e (
p
.u)
Po
st
-
o
p
ti
m
iz
ed
m
i
n
i
m
u
m
bu
s
v
o
ltag
e (
p
.u)
I
m
p
rov
e
m
en
t
Percentag
e
(%)
5
0
.98
1
4
0
.98
2
0
0
.1
10
0
.93
9
5
0
.94
2
6
0
.3
15
0
.89
5
3
0
.89
8
7
0
.4
20
0
.84
4
5
0
.84
8
3
0
.5
25
0
.78
3
1
0
.78
7
7
0
.6
30
0
.69
0
7
0
.70
6
5
2
.3
32
0
.62
6
3
0
.64
8
8
3
.6
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Act
iv
e a
nd
Rea
ct
iv
e Po
we
r
Sc
hedulin
g Op
ti
miza
ti
on
us
in
g Fi
ref
ly
Algo
rit
hm
…
(
Mo
ham
ad Z
ama
ni
)
371
3.3. FA
for re
al p
ower l
os
s
mi
nimi
sa
tio
n
Ap
a
rt
f
ro
m
the
FVSI
a
nd
vo
l
ta
ge
pr
of
il
e
im
pro
vem
ent,
the
optim
iz
ed
power
sche
duli
ng
te
ch
nique
had
als
o
im
pr
oved
t
he power l
os
s of the
t
ransm
issi
on
li
ne.
This effect
can
b
e see
n
f
ro
m
f
igure 8
; t
he
l
oss afte
r
op
ti
m
iz
ation
w
as
reduce
d
sig
nificantl
y
on
al
l
load
increm
ent.
P
ow
e
r
loss is
du
e
to h
eat
in
g
of
the
tra
ns
m
issi
on
li
ne
durin
g
power
tra
ns
m
issio
n.
Re
duct
io
n
of
t
he
po
wer
l
os
s
will
i
m
pr
ove
the
e
ff
ic
ie
nc
y
of
the
t
ran
s
m
issi
on
syst
e
m
.
Table
4.
Res
ults o
f
Re
al
P
owe
r
L
os
s Mi
nim
i
zat
ion
Qd
at Bu
s 2
6
(M
V
AR)
Pre
-
o
p
ti
m
iz
ed
r
eal
p
o
wer
lo
ss
(
M
W
)
Po
st
-
o
p
ti
m
iz
ed
r
ea
l po
wer
lo
ss
(
M
W
)
I
m
p
rov
e
m
en
t
Percentag
e
(%)
5
1
7
.71
7
5
9
.96
9
5
44
10
1
8
.22
9
8
1
0
.53
8
1
42
15
1
8
.99
9
7
1
1
.12
6
0
41
20
2
0
.25
1
6
1
2
.26
8
8
39
25
2
2
.26
7
1
1
4
.11
8
4
37
30
2
6
.10
9
4
1
7
.47
2
2
33
32
2
9
.54
4
4
2
0
.35
7
4
31
Table
4
bel
ow
sh
ows
the
lo
ss
i
m
pr
ov
em
ent
in
per
ce
nta
ge.
I
n
Table
4,
the
loss
i
m
pr
ovem
ent
is
betwee
n
44%
and
31%.
T
hes
e
i
m
pr
ovem
ent
s
show
th
at
act
ive
an
d
reacti
ve
power
sche
duli
ng
optim
iz
ation
i
n
this stu
dy g
i
ve
s m
or
e eff
ect
on
reducin
g
t
he powe
r
loss
.
4.
CONCL
US
I
O
N
This
pa
pe
r
ha
s
pr
ese
nted
act
ive
an
d
reacti
ve
powe
r
sche
duli
ng
opti
m
iz
a
ti
on
usi
ng
fire
f
ly
al
go
rithm
to
im
pr
ov
e
vo
lt
age
sta
bili
ty
consi
der
i
ng
lo
ad
dem
and
.
T
he
re
su
lt
s
s
how
that
th
e
vol
ta
ge
sta
bili
ty
of
t
he
syst
e
m
m
easure
d
by
usi
ng
F
VS
I
m
et
ho
d
i
m
pr
ov
e
d
after
the
sche
du
li
ng
te
chn
iq
ue
is
op
tim
iz
ed
us
in
g
FA
.
T
he
Figure
7: Mi
ni
m
u
m
Bus V
oltage
W
it
h
a
nd
W
it
hout
Op
ti
m
iz
at
ion
0,60
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
1,05
5
10
15
20
25
30
35
Min
im
u
m
Vm
(p
.u
)
Qd
(MVAR)
Min
im
u
m
Bu
s
Vo
lta
ge
Vm
in
Vm
in
FA
Figure
8: Real
Power Los
s
W
it
h
an
d
W
it
hout
O
ptim
iz
ation
0
5
10
15
20
25
30
35
5
10
15
20
25
30
35
Lo
s
s
MW
loa
d
M
VAR
Lo
s
s
los
s
los
s
FA
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
9
,
No.
2
,
Fe
bruary
2
01
8
:
365
–
372
372
op
ti
m
iz
ed
sched
ulin
g
te
ch
nique
al
so
increa
s
ed
the
m
ini
m
um
bu
s
vo
lt
a
ge
and
reduce
d
th
e
power
syst
em
loss,
ind
ic
at
in
g
that
the p
e
rfo
rm
ance of th
e
n
et
wor
k was im
pr
ove
d.
ACKN
OWLE
DGE
MENT
The
auth
ors
would
li
ke
to
acknow
le
dg
e
the
In
sti
tute
of
Re
searc
h
Ma
nag
em
ent
and
I
nnovat
io
n
(I
RM
I
)
UiTM
Sh
a
h
Alam
,
Sela
ngor,
Ma
l
ay
sia
for
the
f
inancial
s
uppo
rt
of
this
rese
arch.
T
his
re
s
earch
is
su
pp
or
te
d
by
IRMI
under
the
LE
STA
R
I
Re
searc
h
G
r
ant
Sc
hem
e
with
project
cod
e:
600
-
IR
MI/Dan
a
5/3
/LES
TAR
I (01
17
/
2016).
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