Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 2
,
A
p
r
il
201
5, p
p
.
21
3
~
22
0
I
S
SN
: 208
8-8
7
0
8
2
13
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
A
Power
System Stabilizer
fo
r
Multi Machine-Based on
Hyb
r
id BF0A-P
SO
M
a
ry
S
a
ra
nya
T*
,
R
a
ja
pa
nd
iy
an
A
*
*
,
Fat
h
ima K*
,
H
e
ma
S*
, G
e
et
ha
P
r
iy
a S*
,
S
a
ra
va
na
n S*
* Depart
em
ent o
f
El
ectr
i
c
a
l
and
Electronics Eng
i
neering
,
Vel
Tech, Anna Univers
i
ty
, India
** Depart
em
ent
of El
ectr
i
c
a
l
and
El
ectron
i
cs
Eng
i
neer
ing,
M
Z
CE
T, Anna
Univers
i
t
y
,
India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 19, 2014
Rev
i
sed
Jan
7, 2
015
Accepte
d
Fe
b 8, 2015
Bact
eria
l Swarm
Optim
ization
(BSO)
is u
s
ed to design power s
y
stem
stabili
zers in a
m
u
lti m
achine p
o
wer s
y
stem
. In
BSO, the search
direc
tions of
tumble beh
a
vior
for each b
a
cterium are or
iented b
y
th
e
indiv
i
dual’s b
e
st
location and th
e global best locat
ion of PSO. The h
y
brid
BFOA-PSO
algorithm
has been appl
ied to I
EEE 14 bus test
sy
st
em
under norm
a
l, light
and heav
y
lo
ad
conditions
. Simulations r
e
sults
have r
e
vealed
th
e strength of
the BSO in tuning Power Sy
stem Stab
ilizers under normal, ligh
t
and heav
y
load conditions. The results pr
esent th
e effectiveness of the controller to
im
prove the po
wer s
y
stem
sta
b
ilit
y
over
a d
i
fferen
t
rang
e
of loadin
g
conditions
.
Keyword:
Bacteria fora
ging
Mu
lti m
ach
in
e
Particle swarm op
ti
m
i
zatio
n
Power system
Stabilizer
Copyright ©
201
5 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
:
T. M
a
ry
Sara
n
y
a
,
Vel Tech
,
An
na Un
iv
ersity
Depa
rtem
ent of Electrical a
n
d
El
ect
ro
ni
cs E
n
gi
nee
r
i
n
g,
A
v
ad
i, C
h
en
n
a
i-
60
0 062
,
I
n
d
i
a
Em
a
il: saran
17.t@g
m
ail.co
m
1.
INTRODUCTION
Stab
ility o
f
p
o
wer system
s
is
o
n
e
of th
e
mo
st i
m
p
o
r
tan
t
asp
ects in
electric syste
m
o
p
e
ratio
n. Th
is
arises from
the fact that the powe
r sy
st
em
m
u
st
m
a
i
n
t
a
i
n
fre
que
ncy
an
d
vol
t
a
ge i
n
t
h
e
desi
re
d l
e
vel
,
un
de
r
any
di
st
u
r
banc
e, t
h
e
de
vel
o
p
m
ent
of i
n
t
e
rc
on
nect
i
o
n
of
la
rge
electric power syste
m
s;
there
ha
ve
been natural
syste
m
o
s
cillat
i
o
n
s
at
v
e
ry low frequ
e
n
c
ies i
n
th
e
o
r
d
e
r of
0
.
2
to
3
.
0Hz.
Mo
reo
v
e
r, l
o
w freq
u
en
cy
o
s
ci
llatio
n
s
are ob
serv
ed
wh
en
larg
e
power
syste
m
s are in
terco
n
n
ect
ed
b
y
weak
tie lin
es. Th
ese
o
s
cillatio
n
s
m
a
y
su
stai
n
an
d gro
w
, cau
s
in
g
system
sep
a
ratio
n if
no
ad
equ
a
te
d
a
m
p
in
g is av
ailab
l
e.Low freq
u
e
n
c
y
o
s
cillatio
n
s
presen
t
li
mitatio
n
s
on
th
e power t
r
ansfer cap
a
b
ility. Power sy
stem stab
ilizers (PSSs) are
no
w
rou
tin
ely u
s
ed
in
th
e
industry to da
m
p
out oscillations
. An
a
p
propriate selection of PSS
param
e
te
rs results in
suitable performance
during system
conflict. T
h
e
problem
of
PSS
param
e
ter tuning is a
com
p
lex exe
r
cise.
A
num
ber
of
co
nv
en
tio
n
a
l t
ech
n
i
q
u
e
s h
a
ve b
een
repo
rted
in
th
e literatu
re
p
e
rtain
i
n
g
to
d
e
sign
pro
b
le
m
s
o
f
co
nv
en
tio
n
a
l
PSSs
nam
e
ly: the Eige
n
value assignm
e
nt, m
a
them
atical
program
m
i
ng, gra
d
ient pr
oce
d
ure for optim
ization
and also the m
ode
rn c
ontrol t
h
eory.
T
h
e
conventional tec
h
niques a
r
e tim
e
cons
um
ing as
they are iterati
ve a
nd
requ
ire
h
eav
y
co
m
p
u
t
atio
n
bu
rd
en
and
slow con
v
e
rg
en
ce. In
ad
d
ition
,
t
h
e search
pro
c
ess is su
scep
ti
b
l
e to
b
e
t
r
ap
ped i
n
l
o
ca
l
m
i
nim
a
and t
h
e sol
u
t
i
o
n o
b
t
a
i
n
ed m
a
y
not
be o
p
t
i
m
al
. A no
vel
ev
ol
ut
i
o
nary
al
g
o
ri
t
h
m
base
d
ap
pro
ach
t
o
op
ti
m
a
l d
e
sig
n
o
f
m
u
lti
m
ach
i
n
e PSSs is
d
e
v
e
lop
e
d. Th
is
ap
pro
ach
em
p
l
o
y
s a particle swarm
o
p
tim
izat
io
n
(PSO) techn
i
que to
search fo
r op
ti
m
a
l settin
g
s
o
f
PSS p
a
ra
m
e
ters. Th
e
desig
n
prob
lem
o
f
t
h
e
co
n
t
ro
ller is tran
sform
e
d
in
to
an
o
p
tim
iza
tio
n
p
r
ob
lem
.
PSO b
a
sed
opti
m
a
l
tu
n
i
ng
alg
o
rith
m
is u
s
ed
to
o
p
tim
all
y
tu
n
e
th
e p
a
ram
e
ters o
f
th
e
PSS.
GA
h
a
s attract
ed
th
e atten
tion
in
th
e
field
of con
t
ro
ller p
a
ra
m
e
ter
o
p
tim
izat
io
n
.
Th
is is v
e
ry suitab
l
e in
fin
d
i
ng
g
l
ob
al or n
e
ar g
l
ob
al op
timal resu
lt o
f
th
e prob
lem
;
it
n
eeds a
v
e
r
y
l
o
ng
ru
n
ti
m
e
th
at
m
a
y
b
e
sev
e
ral m
i
n
u
tes
o
r
ev
en
sev
e
r
a
l
ho
ur
s
dep
e
nd
ing on
t
h
e size of
t
h
e syste
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Po
wer S
y
stem
S
t
ab
ilizer for Mu
lti Ma
ch
i
n
e - Ba
sed
on
Hyb
r
id BF0
A
-PSO
(
T
. M
a
ry
S
a
r
any
a)
21
4
un
de
r st
u
d
y
.
H
o
we
ve
r,
PS
O s
u
f
f
ers
f
r
om
t
h
e
pa
rt
i
a
l
opt
i
m
is
m
,
wh
ich
cau
s
es th
e less deman
d
at th
e regulatio
n
of
i
t
s
spee
d a
n
d t
h
e
di
rect
i
o
n
.
In a
d
di
t
i
on,
t
h
e al
go
ri
t
h
m
suffe
rs f
r
om
sl
ow co
n
v
er
ge
nce
in re
fine
d sea
r
ch stage
,
weak local searc
h
ab
ility an
d
al
g
o
rith
m
m
a
y l
ead
to po
ssi
b
l
e en
trap
m
e
n
t
in
lo
cal m
i
n
i
m
u
m
so
lu
tio
ns. A relativ
ely n
e
wer
evol
ut
i
ona
ry
c
o
m
put
at
i
on al
go
ri
t
h
m
,
cal
l
e
d B
act
eri
a
Fo
ragi
ng
(B
F)
s
c
hem
e
has be
en p
r
op
ose
d
.
The B
F
algorithm
depends on ra
ndom search
di
rec
tions whic
h may lead to del
a
y in reachi
n
g the
global sol
u
tion.
Co
m
b
in
ed
BFOA and
PSO ai
m
s
to
m
a
k
e
u
s
e o
f
PSO ab
ility to
ex
ch
an
g
e
so
cial in
form
at
io
n
and
BF ab
i
lity i
n
find
ing
a n
e
w
so
lu
tion
b
y
elimin
atio
n
an
d
disp
ersal. An
inn
o
v
a
tiv
e op
timizatio
n
alg
o
rithm k
n
o
wn
as BSO is
in
trodu
ced
for o
p
tim
al d
e
sig
n
i
ng
of th
e PSSs con
t
ro
ller in
a m
u
lt
i-
mach
in
e
p
o
wer
syste
m
. Th
e desig
n
pr
o
b
l
e
m
of t
h
e pro
p
o
se
d co
nt
rol
l
e
r i
s
fo
rm
ul
at
ed as an o
p
t
i
m
i
zat
i
on pro
b
l
e
m
and B
S
O i
s
em
pl
oy
ed t
o
searc
h
fo
r o
p
t
i
m
al
cont
r
o
l
l
e
r pa
ram
e
t
e
rs. A
n
Ei
ge
n val
u
e base
d
ob
ject
i
v
e f
u
n
c
t
i
on re
fl
ect
i
ng t
h
e com
b
i
n
a
t
i
on o
f
d
a
m
p
in
g
fact
o
r
an
d
d
a
m
p
in
g
ratio
is op
timi
zed
fo
r
d
i
ff
eren
t op
erating
con
d
ition
s
.
Sim
u
latio
n
s
resu
lts assure
th
e effecti
v
eness of con
t
ro
l i
n
p
r
ov
id
ing
goo
d d
a
m
p
in
g characteristics to
syste
m
o
s
cillat
i
o
n
s
.
2.
PROBLEM STATEMENT
2.1. Power System Model
A
po
wer
sy
st
e
m
can be m
ode
l
e
d by
a
set
of
no
nl
i
n
ea
r
di
ffe
rent
i
a
l
eq
uat
i
o
ns a
r
e:
,
(1
)
Whe
r
e X is the vector
of t
h
e
state variables
and
U is the
vecto
r
of inpu
t v
a
riab
les. In
this stu
d
y
U is th
e PSS
out
put
si
gnal
a
nd
X
=
,
,
′
,
,
. Here,
and
are the rot
o
r a
ngle a
nd s
p
ee
d,
res
p
ectively. Also,
′
,
and
are t
h
e internal, t
h
e
field, and
ex
citatio
n vo
ltag
e
s
resp
ectiv
ely.
In th
e
d
e
sign
o
f
PSS, the lin
earized
in
cremen
tal
m
o
d
e
ls aro
und
an
equ
ilib
riu
m
p
o
i
nt are
u
s
u
a
lly
use
d
. T
h
e
r
efore, the
state equa
t
i
on
of
a
po
w
e
r sy
st
em
wi
t
h
m
m
achines a
n
d
n
PSSs can
be written
as:
(2
)
Whe
r
e
A
is a
5
m×
5
m
m
a
trix
an
d equ
a
ls
⁄
while
B
is a 5
m×
n ma
trix
an
d e
q
ual
s
⁄
. Both
A
an
d
B
are e
v
aluated a
t
a certain
operating
poi
nt.
X
is a
5
m×
1 state
vector a
n
d
U
is
a
n×
1
inpu
t vecto
r
.
2.
2. Stru
cture
of
PSS
The
o
p
erat
i
n
g
fu
nct
i
o
n
of a
P
SS i
s
t
o
pr
od
uc
e a p
r
ope
r t
o
r
q
ue
on
t
h
e
r
o
t
o
r
of
t
h
e m
achi
n
e
occ
upi
e
d
in s
u
ch a
way that the
phase l
a
g
betwee
n the
exciter i
n
put a
n
d the m
achine
electrical
to
rqu
e
is co
m
p
en
sated
.
Th
e sup
p
l
em
en
tary stab
ilizin
g sign
al con
s
id
ered is on
e
propo
rtion
a
l to speed
.
Th
e
transfer fun
c
tio
n of t
h
e
jth
PSS:
∆
1
1
1
1
1
∆
(3
)
Whe
r
e
∆
i
s
t
h
e d
e
vi
at
i
on i
n
spe
e
d f
r
om
t
h
e sy
nch
r
on
o
u
s s
p
e
e
d. T
h
i
s
t
y
pe
o
f
st
abi
l
i
zer co
n
s
i
s
t
s
of a
was
h
out
filter, a
d
y
n
a
m
i
c co
m
p
en
sator. Th
e
o
u
t
p
u
t
sig
n
a
l is fed
as a supp
lem
e
n
t
ary in
pu
t sign
al,
to
th
e regu
lator
o
f
th
e ex
citation
syste
m
. Th
e wash
ou
t
filter,
which
b
a
sically is
a h
i
g
h
p
a
ss
filter, is
u
s
ed
to reset th
e stead
y
state
of
fset
i
n
t
h
e
ou
t
put
o
f
t
h
e P
S
S
.
T
h
e
val
u
e
of
t
h
e t
i
m
e const
a
nt
is
u
s
u
a
lly no
t critical an
d i
t
can rang
e
fro
m
(0.5-20) s. Th
e d
y
n
a
m
i
c co
mp
ensato
r is m
a
d
e
up
to
two
lead
lag
circu
its, li
miters an
d
an
add
itio
n
a
l g
a
in
. The
ad
ju
stab
le PSS p
a
ram
e
ters are th
e g
a
in
of th
e PSS,
and t
h
e t
i
m
e
const
a
nt
s,
T
1j
–
T
4j
.
The lead la
g bloc
k
p
r
esen
t in
th
e
syste
m
p
r
o
v
i
des p
h
a
se lead
co
m
p
en
satio
n
for th
e ph
ase l
a
g
th
at is in
trod
u
c
ed
in
th
e circu
it
b
e
tween
th
e exciter in
pu
t an
d
th
e electrical to
rqu
e
.
A st
a
nda
rd
IE
EE1
4
bu
s sy
st
e
m
i
s
sho
w
n i
n
fi
g
u
re
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
21
3 – 2
2
0
2
15
Fi
gu
re
1.
IEE
E
1
4
Sy
st
em
B
u
s
2.
3. Ob
jecti
v
e
Functi
on
To m
a
intain stability and
provide
greater
da
m
p
ing, the
pa
ra
m
e
ters of the
PSSs
m
a
y be selected to
min
i
mize th
e fo
llo
wi
n
g
obj
ectiv
e fu
n
c
tion
:
(4
)
It will
place the system
closed l
o
op ei
genva
l
ues in the
D-shape
sect
or c
h
aracterized by
and
as s
h
o
w
n i
n
Fi
gu
re
2.
Wh
ere,
Np
is th
e nu
m
b
er of
o
p
e
rating
po
int
s
conside
r
ed i
n
the desi
gn
process,
and
are the real
part
a
n
d t
h
e
da
m
p
i
ng rat
i
o
o
f
t
h
e ei
ge
nval
u
e o
f
t
h
e
op
erat
i
n
g
p
o
i
n
t
.
I
n
t
h
i
s
st
u
d
y
,
and
chosen to be
-
0.
5 an
d 0.
1 res
p
ect
i
v
el
y
.
An
d
t
o
reduce t
h
e c
o
m
put
at
i
onal
b
u
r
d
e
n
i
n
t
h
i
s
st
udy
, t
h
e
val
u
e of t
h
e was
h
o
u
t
t
i
m
e
constant
is f
i
xed
to
10
second
, th
e
v
a
lu
es
of
and
are
kept
consta
nt at a reasona
b
le val
u
e of 0.05
secon
d
an
d tun
i
ng
of
an
d
are c
h
osen to
achieve
the
ne
t phase
l
ead
re
qui
red
by
t
h
e
sy
st
em
. Ty
pi
cal
ranges of
the optim
i
zed
pa
r
a
meter
s
ar
e [1
-
1
0
0
]
fo
r
K
an
d [0
.0
6-
1
.
0]
fo
r
and
.
Based on
th
e obj
ective
fu
nct
i
o
n
op
timizatio
n
p
r
ob
le
m
can
b
e
stated as: Minim
i
ze
subjected to:
(5
)
Figure
2. D-s
h
ape sect
or i
n
t
h
e s-plane
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Po
wer S
y
stem
S
t
ab
ilizer for Mu
lti Ma
ch
i
n
e - Ba
sed
on
Hyb
r
id BF0
A
-PSO
(
T
. M
a
ry
S
a
r
any
a)
21
6
2.
4. T
h
e B
a
c
t
e
r
i
a
l
Sw
arm
O
p
ti
mi
z
a
ti
on
Al
gori
t
hm
B
S
O c
o
m
b
i
n
es b
o
t
h
al
go
ri
t
h
m
s
B
F
OA an
d
PS
O t
h
us
usi
n
g a
dva
nt
age
s
o
f
b
o
t
h
t
ech
ni
q
u
e
s. T
h
e ai
m
is to
m
a
k
e
u
s
e o
f
PSO ab
ility
to
ex
ch
ang
e
social in
fo
rm
atio
n
and
BFOA ab
ility in
fin
d
i
ng
a n
e
w so
lu
ti
o
n
b
y
el
im
i
n
at
i
on a
n
d
di
spe
r
sal
.
I
n
B
F
OA
, a
uni
t
l
e
ngt
h
di
rect
i
o
n
of
t
u
m
b
l
e
beh
a
vi
o
r
i
s
ra
n
d
o
m
l
y
generat
e
d
whi
c
h
may
lead to delay in reach
ing the global sol
u
tion. In
the B
S
O, technique
the unit lengt
h random
direction of
t
u
m
b
l
e
behavi
or can
be o
b
t
a
i
n
ed
by
t
h
e gl
o
b
al
best
po
si
t
i
on a
nd t
h
e b
e
s
t
posi
t
i
on o
f
ea
ch bact
eri
u
m
b
y
PSO
alg
o
rith
m
.
PSO i
s
a st
oc
hast
i
c
opt
i
m
i
z
at
i
on t
ech
ni
q
u
e
t
h
at
draw
s i
n
spi
r
at
i
on
fr
o
m
t
h
e behavi
o
r
of a fl
ock
of
b
i
rd
s
o
r
th
e collectiv
e in
tellig
en
ce
o
f
a
group
o
f
so
cial in
sects with li
m
i
t
e
d
i
n
d
i
v
i
du
al cap
a
b
ilities. In
PSO a
p
opu
latio
n of
p
a
rticles is i
n
itialized
with ran
d
o
m
p
o
s
itions
and
v
e
lo
cities
, and a
f
itn
ess fun
c
tio
n
u
s
i
ng
th
e p
a
rticle’s
po
sitio
n
a
l coordin
a
tes as in
pu
t v
a
lu
es. Po
sition
s
and
v
e
l
o
cities are adj
u
sted, an
d
t
h
e fu
n
c
ti
o
n
is
evaluate
d with the ne
w coordinates at
each ti
m
e
step. The
velocity and
po
sition update equations for
the
d-th
di
m
e
nsi
on
of t
h
e i
-
t
h
part
i
c
l
e
i
n
t
h
e
swa
r
m
m
a
y
be gi
ve
n
a
s
f
o
l
l
o
ws:
))
(
(
))
(
(
)
(
)
1
(
2
2
1
1
t
X
P
C
t
X
V
C
t
V
t
V
id
gd
id
lid
id
id
(6
)
)
1
(
)
(
)
1
(
t
V
t
X
t
X
id
id
id
(7
)
In
add
itio
n
,
the BF is b
a
sed
u
pon
search
an
d
op
tim
a
l
fo
rag
i
ng
d
ecisio
n
m
a
k
i
n
g
cap
a
bilit
ies o
f
the
Esche
r
ichia coli bacteria. The coordinates of a bacter
i
u
m
here repre
s
ent
an i
ndi
vi
d
u
al
sol
u
t
i
o
n o
f
t
h
e
o
p
tim
izat
io
n
prob
lem
.
Su
ch
a set o
f
trial so
lu
tion
s
co
nv
erg
e
s toward
s t
h
e
o
p
tim
al so
l
u
tio
n fo
llo
wi
ng
the
forag
i
n
g
group d
y
n
a
m
i
cs o
f
th
e b
acteria pop
u
l
ation
.
C
h
em
o
tac
tic
m
o
v
e
m
e
n
t
is co
n
tin
uou
s un
til a bacteriu
m
g
o
e
s in
th
e d
i
rectio
n
of po
sitiv
e nu
trien
t
g
r
ad
ien
t
.
After
a certain
nu
m
b
er o
f
co
m
p
lete s
w
im
s
th
e b
e
st h
a
lf of
th
e p
opu
latio
n
u
n
d
e
r
g
o
e
s r
e
p
r
o
d
u
c
tion
,
elimi
n
atin
g
th
e
r
e
st o
f
th
e popu
latio
n. I
n
o
r
d
e
r
to
escap
e lo
cal opti
m
a,
an elim
ination dispe
r
sion eve
n
t is ca
rried out where
,
som
e
bacteria are liq
ui
dat
e
d at
ra
nd
om
wi
t
h
a very
sm
al
l
probability and the
new
re
place
m
e
nts are initialized at ra
ndom
locations of t
h
e searc
h
space. The
propose
d
BSO al
g
o
rith
m to
search op
ti
mal v
a
lu
es
o
f
param
e
ters is d
e
scrib
e
d
as fo
llows:
Step 1
:
In
itialize p
a
ram
e
ters i
,
S,
N
C
,
N
Re
,
N
Ed
,
P
Ed
C(l
)(l
=1,
2
,…
……,
N
)
,
∅
.
Whe
r
e,
i
: Dim
e
nsion of the
searc
h
s
p
ace.
S
:
T
h
e num
ber of bact
eri
a
i
n
po
p
u
l
a
t
i
on,
N
C
: The
num
b
er
of c
h
em
otactic steps,
N
Re
:
The num
ber of re
pr
od
uct
i
on st
eps,
N
Ed
: Th
e
n
u
m
b
e
r of elim
in
at
io
n-d
i
sp
ersal ev
en
ts to
b
e
im
p
o
s
ed
o
v
e
r th
e bacteria,
P
Ed
: Th
e
p
r
ob
ab
ility with
wh
i
c
h
th
e elim
in
atio
n
and
d
i
sp
ersal will co
n
t
i
n
ue
C
(
l
) : Th
e size
o
f
th
e step
tak
e
n
in th
e
ra
ndom
direction s
p
ecified
by the t
u
m
b
le,
: In
ertia wei
ght
C
1
: The s
w
arm
confi
d
ence
,
,
: Po
sitio
n v
e
cto
r
o
f
th
e l
-
th
bacteriu
m
,
in
m
-
th
ch
em
o
t
actic step
an
d n-th
rep
r
od
u
c
tion
.
l
V
: Velo
city
v
ecto
r
of th
e l-th bacteriu
m
.
Step 2:
Upd
a
te
th
e fo
llowing
J
(
l
,
m
,
n
): C
o
st
or fitn
ess
v
a
lue of th
e l-th
b
a
cteriu
m
in
th
e
m
-
th
ch
em
o
t
ax
is, and
t
h
e
n
-
th rep
r
o
d
u
c
tion
l
o
op
.
best
g
_
: Po
sition
v
ecto
r
of th
e b
e
st po
sitio
n fo
und
by all b
acteria.
best
J
(l
,,m
,n):
Fi
t
n
es
s val
u
e
of t
h
e
b
e
st
p
o
si
t
i
on
f
o
un
d s
o
fa
r.
Step 3:
R
e
pr
o
duct
i
o
n l
o
o
p
:
n
=
n+1
Step 4:
C
h
em
ot
axi
s
l
o
op:
m
=
m
+
1
Sub
ste
p
(i
)
:
F
o
r
l=1,
2, …
., S
take a
che
m
otaxis
step for
bacterium
l as follows
.
Sub
ste
p
(ii)
:
Co
m
p
u
t
e fitness
fu
nctio
n,
)
,
,
(
n
m
l
J
.
Sub
ste
p
(iii
):
Let
)
,
,
(
n
m
l
J
J
last
t
o
save t
h
i
s
val
u
e si
nce
one
m
a
y
fi
nd a
bet
t
e
r c
o
st
vi
a
a r
u
n
.
Sub
ste
p
(i
v):
Tu
m
b
le: g
e
ner
a
te a rando
m v
ector
k
R
l
)
(
with ea
ch elem
ent
a
p
k
l
k
.
,....,
2
,
1
),
(
ran
d
o
m
num
ber
on
[
-
1
,
1]
.
Sub
ste
p
(
v
)
:
Mov
e
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
21
3 – 2
2
0
2
17
Let
)
(
)
(
)
(
)
(
)
,
,
(
)
,
1
,
(
l
l
l
l
C
n
m
l
n
m
l
T
Sub s
t
ep
(vi):
C
o
m
put
e J(l
,
m
+
1,
n)
.
Sub s
t
ep
(vii):
Swim
: o
n
e
con
s
id
ers
on
ly the l-th
b
acteri
u
m
is swimmin
g
wh
ile th
e o
t
hers are
n
o
t
m
o
v
i
ng
th
en
a)
Let k
=
0
(cou
n
t
er for swim
len
g
th)
b)
Wh
ile k
<
N
S
(
h
ave
n
o
t
cl
i
m
bed
do
w
n
t
o
o l
o
ng
)
Let
k=
k+1
If
last
J
n
m
l
J
)
,
1
,
(
(if d
o
in
g better),
Let
)
,
1
,
(
n
m
l
J
J
last
and
let
)
(
)
(
)
(
)
(
)
,
,
(
)
,
1
,
(
l
l
l
l
C
n
m
l
n
m
l
T
An
d use
t
h
i
s
)
,
1
,
(
n
m
l
to com
pute the
new
)
,
1
,
(
n
m
l
as sh
ow
n i
n
[su
b
st
e
p
6]
.
Else let k
=
S
N
. This is th
e en
d of
th
e wh
ile statemen
t.
Step 5:
Mu
tati
o
n
with PSO
op
erat
o
r
For i=1,
2…S
Upd
a
te th
e
best
g
_
and
)
,
,
(
k
j
i
J
best
Upd
a
te th
e p
o
sitio
n
an
d
v
e
lo
city o
f
th
e
d
-
th
coo
r
d
i
n
a
te o
f
th
e i-th
b
acteriu
m
acc
o
r
d
i
ng
to
the
fo
llowing
ru
le:
))
,
1
,
(
(
.
_
.
1
1
n
m
l
C
V
V
old
d
best
g
new
id
new
id
d
new
id
old
d
new
d
V
n
m
l
n
m
l
)
,
1
,
(
)
,
1
,
(
Step 6:
Let S
_
r
=
S/
2. T
h
e S_r
bact
eri
a
wi
t
h
hi
g
h
est
c
o
st
fu
nct
i
o
n(J
)
val
u
es di
e a
n
d ot
he
r hal
f
b
act
eri
a
population
wit
h
the
be
st val
u
es split (a
nd the copies ar
e
made
placed at the sam
e
location as t
h
eir
pare
nt).
Step 7:
If
m
<
Re
N
, go to
(step
1). One
has not reached the
num
b
er of s
p
ecified re
producti
on
steps, so
one
starts th
e
n
e
x
t
g
e
n
e
ration
in th
e ch
em
o
t
ax
is lo
op
.
3.
SIMULATION RESULT
This deals wit
h
testing of hy
bri
d
BFOA-P
S
O
algo
rithm
for IEEE
14 Bus
test syste
m
s.
The standard
IEEE
14 syste
m
s are considered t
o
investi
g
ate the e
ff
ect
iveness
of the
propose
d
m
e
thodology.
The t
e
st is
carried
with a 2.20-GHz Intel Core
2 Duo CPU T6600 PC
. The IEEE
14-bus
system
has 5 gene
rators a
nd
16
tran
sm
issio
n
lin
es.
3.
1.
Resp
onse
f
o
r
Hea
v
y
L
o
ad
Co
ndi
ti
on
Fi
gu
re
3.
R
o
t
o
r
an
gl
es
of
ge
ne
rat
o
r
s
un
der
he
avy
l
o
a
d
c
o
n
d
i
t
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Po
wer S
y
stem
S
t
ab
ilizer for Mu
lti Ma
ch
i
n
e - Ba
sed
on
Hyb
r
id BF0
A
-PSO
(
T
. M
a
ry
S
a
r
any
a)
21
8
The
resp
o
n
se
o
f
t
h
e
rot
o
r a
n
gl
e of
ge
nerat
o
rs
un
de
r
heavy
l
o
ad
co
n
d
i
t
i
on i
s
sh
ow
n i
n
fi
g
u
re
3.
U
n
der
h
eav
y l
o
ad con
d
ition
,
t
h
e averag
e p
e
ak
ov
ershoo
t of a
ll the g
e
n
e
rat
o
rs reach
u
p
t
o
1
.
0
035
P.U and
t
h
e
mean
settlin
g
ti
m
e
o
f
th
e
o
s
cillatio
ns is abou
t 90
t
o
11
0 seco
nd
s.
3.
2.
Resp
onse
f
o
r
Nor
m
al L
o
a
d
Co
nditi
on
The r
e
sp
o
n
se
of t
h
e r
o
t
o
r a
n
gl
e o
f
ge
ne
rat
o
rs
u
nde
r
heav
y
no
rm
al
cond
i
t
i
on i
s
sh
o
w
n
i
n
fi
g
u
r
e 4
.
Und
e
r no
rm
al lo
ad
con
d
ition
,
th
e av
erag
e peak
ov
ershoo
t
o
f
all th
e
g
e
n
e
rato
rs reach
u
p
to
1
.
00
1 P.U an
d
t
h
e
mean
settlin
g
t
i
m
e o
f
th
e o
s
cillatio
n
s
is ab
o
u
t 6
0
to
80
secon
d
s
. As co
m
p
ared
to
u
n
d
e
r
h
e
av
y lo
ad
cond
itio
n,
b
o
t
h
th
e p
e
ak ov
ersho
o
t
and
mean
settlin
g
t
i
m
e
o
f
th
e o
s
cillatio
n
s
are redu
ced.
Fi
gu
re
4.
R
o
t
o
r
an
gl
e o
f
ge
ner
a
t
o
rs
u
nde
r
n
o
r
m
al
l
o
ad c
o
n
d
i
t
i
o
n
3.
3.
Resp
onse
f
o
r
L
i
ght L
o
ad
C
o
ndi
ti
on
Fig
u
re
5
.
Ro
tor ang
l
e of
g
e
n
e
rato
rs
un
d
e
r ligh
t
lo
ad
co
nd
itio
n
Und
e
r lig
h
t
l
o
ad
co
nd
itio
n, t
h
e av
erag
e
p
e
ak
o
v
e
rsh
o
o
t
o
f
all th
e g
e
n
e
rat
o
rs reach
u
p
t
o
1
.
0
005
P.U
an
d th
e m
ean
settlin
g
ti
m
e
o
f
th
e o
s
cillatio
n
s
is abo
u
t
30
to
4
0
second
s. As co
m
p
ared to
bo
th
t
h
e cases heav
y
lo
ad
cond
itio
n
an
d
n
o
rm
al
lo
ad
con
d
ition
,
both
th
e p
eak
o
v
ershoo
t an
d
mean
settlin
g
time o
f
th
e o
s
cillatio
n
s
are redu
ced und
er th
e ligh
t
load
co
nd
ition
.
4.
CO
NCL
USI
O
N
Th
is
p
a
p
e
r in
ten
d
s
a
n
e
w
op
timizatio
n
alg
o
rith
m
k
nown as BSO,
wh
ich
syn
e
rg
istically
co
up
les t
h
e
B
F
OA
wi
t
h
t
h
e PS
O f
o
r
opt
i
m
al
desi
gni
ng
of
PSS
s c
ont
r
o
l
l
e
r. The
de
si
g
n
pr
obl
em
of t
h
e
pr
o
pose
d
c
o
nt
r
o
l
l
e
r
is form
ulated as an optimization pr
obl
em
and B
S
O i
s
em
pl
oy
ed t
o
sea
r
c
h
f
o
r
o
p
t
i
m
al
cont
r
o
l
l
e
r
param
e
t
e
rs
.
The potential of the propose
d desi
gn approach
has bee
n
dem
onstrat
ed by applying it to IEEE 14
bus
5
g
e
n
e
rator syste
m
s with
d
i
fferen
t
lo
ad
ing
co
nd
itio
ns. Si
m
u
la
tio
n
s
results assu
re th
e effectiv
en
ess o
f
t
h
e
co
n
t
ro
ller in
prov
id
i
n
g
g
ood d
a
m
p
in
g
ch
aracteristic to
syste
m
o
s
cilla
ti
o
n
s
ov
er a
w
i
d
e
ran
g
e
o
f
l
o
ad
ing
co
nd
itio
ns.
Our fu
ture wo
rk
i
n
clud
es th
e com
p
ariso
n
of
the p
r
op
o
s
ed
al
go
rith
m
with
the latest o
p
timi
zatio
n
techniques
as c
u
koo sea
r
ch,
NSGA-II.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
21
3 – 2
2
0
2
19
ACKNOWLE
DGE
M
ENTS
W
e
th
ank
all o
u
r
fr
iend
s and
co
lleg
u
e
s f
o
r
th
eir
en
cou
r
g
e
men
t
an
d
suppo
r
t
to
d
e
si
g
n
an
d
sim
u
late
th
is p
a
p
e
r and also
th
ank
the research
scho
lars t
o
g
e
t an id
ea abou
t this research
and
also th
an
k
go
d
fo
r
success
f
ully com
p
le
ting this
work
REFERE
NC
ES
[1]
P. Kundur. “
Po
wer System
Stab
ilit
y and
Control
”. McGr
aw-Hill. 1994.
[2]
P. Kundur, M.
Klein, G
.
J. Rog
e
rs, a
nd M.S. Z
y
wno. “Applicat
ion of Power
S
y
stem
Stabilizers f
o
r Enhancem
ent
of
Overall
S
y
s
t
em
S
t
abili
t
y
”
.
I
EEE
Transactions on. Power S
y
stem
.
Vol. 4
,
No. 2, 19
89.
[3]
K.M
.
P
a
s
s
i
no. “
B
iom
i
m
i
cr
y
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eria
l F
o
ragi
ng for Distributed Optimization
and Control”.
IEEE.
Control Sy
ste
m
Magazine
. Vol.
22, No. 3, June 2
002.
[4]
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A.
Abido.
“
O
ptimal Design
of Power S
y
stem
Stabili
zers
Using Partic
l
e
Swarm
Optim
ization
”
.
IE
EE
Transactions on
Energy Con
version
. Vol. 17
, No.
3, September 20
02, pp
. 406-413
.
[5]
S.
Mishra
,
M.
Tripathy
,
a
nd J. Na
nda
.
"Multima
c
h
ine
Po
wer S
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stem
Stabili
z
e
r Design b
y
R
u
le Based Bac
t
e
r
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Foraging".
Int. J.
of Ele
c
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r Sy
ste
m
s
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searc
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[6]
S. Panda, and N.P. Padh
y
.
“Robust Power
Sy
st
em
Stabilizer Design using
Particle Swarm
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ization
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i
qu
e”.
Int.
J. of Elec
trical and
Electroni
cs Engin
eering
.
Vol.1, No.1, 200
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[7]
E.S. Al
i,
and
S.
M. Abd-Ela
z
im
.
“
B
acte
r
ia
Forag
i
ng Optim
iz
atio
n Algorithm
Ba
sed Load
Frequ
e
nc
y Con
t
roll
er
for
Interconn
ect
ed P
o
wer S
y
s
t
em
”.
I
n
t.
J. of Electrical
Pow
e
r and
En
ergy Systems
. V
o
l. 33
, No
. 3
,
M
a
rch 2011
.
[8]
H. Shay
eghi, H
.
A. Shay
anf
a
r, A. Sa
fari,
and R
.
Aghmasheh. “A Robust
PSSs De
sign Using
PSO
in a Multimachine
Environment”.
I
n
t. J.
Of Energy Conversion
and Management
. V
o
l. 51
, No
. 4
,
20
10
BIOGRAP
HI
ES OF
AUTH
ORS
MARY SARANYA. T. AS
S
T
. P
R
OF
., EEE -
VEL
TECH Ob
tain
ed Her Bac
h
elor’s Degre
e
(B.E) in
El
ect
ri
cal
and E
l
ec
tro
n
ics
Engin
eerin
g from
Anna Univers
i
t
y
– T
r
ich
y
, Ind
i
a
and
Master’s Degree - In Power
Sy
stems Engin
eering from JJ college of engineer
ing and
Techno
log
y
, An
na University
,
Ch
ennai
,
India
.
S
h
e has
as
pres
ented P
a
p
e
rs
in Conferen
ces
.
Res
earch
Int
e
res
t
s
in R
e
newab
l
e
Energ
y
R
e
s
ourc
e
s
,
P
o
wer S
y
s
t
e
m
.
RAJAPANDI
YAN.A. ASST.PROF., EEE -
Mount Zi
on Colleg
e of Engineering
and Technolo
g
y
Has received
th
e B.E., deg
r
ee
from Mount Zi
on Colleg
e
of
Engineering
an
d Technolog
y
,
Pudukkottai, Tamil Nadu, India in 2011 and recei
v
e
d the M
.
E., degree from J.J Colleg
e
o
f
Engineering
and
Technolog
y
,
Tir
u
ch
irapp
a
lli,
Tamil Nadu, Ind
i
a
in
2014. Ear
lier,
he worked
as a
lecturer in Mah
a
th Am
m
a
Institute of Engi
neeri
ng and Technol
og
y
,
Pudukkottai, Tam
il Nadu
,
India from August 2011 to August 2012. At pres
ent,
His res
earch
inter
e
sts includ
e power s
y
stem
planning
, oper
a
tion and contro
l;
application of
arti
fici
al in
tel
ligen
c
e
te
chniques to
p
o
wer s
y
stem
;
and ren
e
wabl
e
e
n
erg
y
s
y
s
t
em
s
.
K. F
A
THIMA. AS
S
T
. P
R
OF
., EEE -
VEL
T
E
CH
Obtained
Her
Bach
elor’s Degree
(B
.E) i
n
Electronics and
Communicatio
n Engineering
from Kanchipallavan
Engg
Colleg
e
Anna
University
, Chennai, India and
Master’s Degree (M.E) In
Em
bedded S
y
stem Technologies from
Velte
chm
u
ltit
ec
h Anna Universi
t
y
, Ch
ennai
,
Indi
a. She
has prese
n
ted Pap
e
rs in C
onferenc
e
s an
d
journals. She Has 2 Years Of
T
eaching
Experience. R
e
sear
ch In
te
re
sts in Re
ne
wa
ble
Re
source
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Po
wer S
y
stem
S
t
ab
ilizer for Mu
lti Ma
ch
i
n
e - Ba
sed
on
Hyb
r
id BF0
A
-PSO
(
T
. M
a
ry
S
a
r
any
a)
22
0
S
.
HEMA. AS
S
T
. P
R
OF
., EE
E - VEL
TE
CH Ob
tained H
e
r Bach
elor’s
Degree (B
.E)
i
n
Electrical and Electronics Eng
i
n
eering
from
JJ colleg
e
of En
gineer
ing and
technolog
y
and
Master’s Degre
e
(M.E) In A
pplied E
l
e
c
tron
ics from
Sriram
Engineering
coll
ege, Ann
a
University
, Ch
ennai,
India. Sh
e has presented
Papers in Conf
erences
and jour
nals. She Has 6
Years
Of T
e
a
c
hi
ng Exper
i
en
ce.
Res
earch
Int
e
res
t
s
in R
e
newab
l
e
Res
ources
S.
GEETHAPRIYA,
ASST.
PROF.
,
EEE - VEL TEC
H Obtained Her Bach
elor
’s Degree (B
.E)
in El
ec
tric
al
a
nd El
ectron
i
cs
Engin
eering
f
r
om
M
N
M
J
a
in Engin
eering
College
, Ann
a
University
, Chennai, India and Master’s Degree
(M.E) In SSN
College of Engineering
,
Anna
University
, Ch
ennai,
India. Sh
e has presented
Papers in Conf
erences
and jour
nals. She Has 1
Year Of Te
ach
i
ng Experi
enc
e
.
Res
earch
Inter
e
sts in Re
ne
wa
ble
Re
source
s,
Wire
le
ss se
nsor
network
S.
SARAV
ANA
N,
ASST
.
PRO
F
.
,
EE
E
- VE
L
TE
CH
Obtained h
i
s
Bachelor
’s
Degree (B.
E
) in
Electronics and
Communicatio
n Engineering
from
Tagore E
ngineer
ing Coll
ege, M
a
d
r
as
Univers
i
t
y
, Ch
e
nnai, Ind
i
a and
M
a
s
t
er’s
Degree (M
.E)
in S
a
t
h
y
a
b
a
m
a
Unive
r
s
i
t
y
, Chenn
a
i,
India. He has published papers in
journals. He
has 6 Years of
Teaching Experience
and 3.5
y
e
ars
of Industrial
Exp
e
rien
ce. Res
earch
Inter
e
sts in
Applied
Electronics
Evaluation Warning : The document was created with Spire.PDF for Python.