Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 2, No. 1,
April 201
6, pp. 132 ~ 14
4
DOI: 10.115
9
1
/ijeecs.v2.i1.pp13
2-1
4
4
132
Re
cei
v
ed
Jan
uary 24, 201
6
;
Revi
sed Ma
rch 8, 2
016;
Acce
pted Ma
rch 1
9
, 2016
Automatic Voltage Generation Control for Two Are
a
Power System Based on Particle Swarm Optimization
Ali M Ali*
1
, M
A
Ebrahim
2
, MA Moustafa Hassan
3
1
Cairo Nort
h Po
w
e
r Statio
n, Ministr
y
of Elec
tricit
y
an
d Ener
g
y
, Eg
ypt
2
Electrical En
gi
neer
ing D
e
p
a
rtment, F
a
cult
y
of
Engin
eer
ing
(Shou
bra), Ben
ha Un
iversit
y
, Eg
ypt
3
Departme
n
t of Electrical Po
wer and Mac
h
in
es, F
a
cult
y
of
Engi
neer
in
g, Cairo U
n
ivers
i
t
y
,
Eg
ypt
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: eng.al
i_mo
ha
mmed@h
o
tmai
l.com
A
b
st
r
a
ct
This artic
l
e
presentes
a PID c
ontroller for
tw
o ar
ea power
system
equi
pped with
both automatic
gen
eratio
n co
n
t
rol an
d a
u
to
matic volta
ge r
e
gul
ator lo
ops.
T
he rese
arch
h
a
s be
en
do
ne t
o
contro
l tw
o a
r
ea
power systems with PSO
optim
i
z
ed s
e
lf
-tuning PID
c
ontroller. The com
p
arison
between differ
ent
control
l
ers
an
d
the s
u
g
geste
d
PSO
bas
ed
c
ontrol
l
er
ill
ustrates that
the
p
r
opos
ed c
ontro
ller c
a
n
g
ener
a
t
e
the best dyn
a
m
ic res
p
o
n
se for a step loa
d
chan
ge. F
o
r this purpos
e, MAT
L
AB-Simuli
nk
softw
are is used
.
T
he obtai
ne
d results are pr
o
m
is
ing.
Ke
y
w
ords
: a
u
tomatic ge
ne
ration co
ntrol
(AGC), automat
ic vo
ltag
e
regul
ator (AVR), evoluti
o
n
a
ry
computation (
E
C), particle s
w
arm
optim
i
z
a
t
ion (PSO), two area
power system
,
lo
ad frequ
ency co
ntro
l
(LFC)
Copy
right
©
2016 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1
.
Introduc
tion
The g
r
o
w
ing
on ele
c
tri
c
ity deman
d will
cause
incre
a
si
ng loa
d
chan
ge. Wh
en the
load
o
n
the grid raise
d
, the spee
d of turbine is
decrea
s
e
d
be
fore the gove
r
no
rs
can ta
ke an adju
s
tm
ent
action to
adj
ust the i
nput
of steam
to
the ne
w lo
a
d
. As the
ch
ange i
n
the
value of
spe
ed
decrea
s
e
d
, the error si
gnal
become
s
sm
aller an
d the
positio
n of the govern
o
r flyballs g
e
ts cl
o
s
er
to the point nece
s
sary to
maintain a co
nstant spee
d.
There a
r
e t
w
o re
ason
s a
g
a
inst
allo
wing
the
freque
ncy to deviate
extremely mu
ch f
r
om
its stan
dard
value. A non
–stan
dard fre
quen
cy in
th
e system
ca
use
s
a p
o
o
r
er qu
ality of the
delivere
d
el
e
c
tri
c
al p
o
wer.
Many of th
e
device
s
that
are
co
nne
cte
d
to the
syste
m
wo
rk bette
r at
nominal frequ
ency a
s
expla
i
ned in [1].
Many di
scussion
s h
a
ve b
een
ca
rrie
d
out in
the
p
a
st to treat
with Lo
ad F
r
eque
ncy
Control
(LFC) pro
b
lem. In
literature,
so
me
co
ntrol p
o
licie
s have
been di
scu
s
sed ba
sed
on
the
conve
n
tional l
i
near
cont
rol theory [2].
These two control si
gnal
s (
C
tie
Pa
n
d
P
) are imp
r
o
v
ed, mixed and tran
sform
ed to a
real po
wer
signal, which then controls
the
g
o
vern
or p
o
sitio
n
.
Dep
endin
g
o
n
the
governo
r
positio
n, the
turbine
ch
an
ges it
s outp
u
t
powe
r
to e
s
tabli
s
h the
real po
we
r b
a
lan
c
e [1]. The
automatic
co
ntrol system
consi
s
ts of two ma
jor p
a
rts, the pri
m
ary and se
con
dary cont
rol.
Tern
ary co
ntrol is manually
activated clo
s
e to t
he electricity produ
ct
ion acco
rdin
g
to generatio
ns
sched
ule
s
(di
s
pat
ch) a
s
di
scusse
d in [3].
The mo
st co
mmon
ways
use
d
to a
c
hi
eve freq
uen
cy control are
gene
rato
r g
o
verno
r
respon
se
(pri
mary frequ
e
n
cy reg
u
latio
n
) and L
F
C.
The task of LFC is to restore prim
a
r
y
freque
ncy re
gulation
cap
a
c
ity, bringin
g
again the
fre
quen
cy to its pred
efined v
a
lue an
d re
d
u
ce
unsch
edule
d
tie-line
po
wer flo
w
s bet
wee
n
n
e
ighb
oring
control are
a
s.
Fro
m
the me
ch
ani
sm
s
use
d
to han
d
l
e the econo
mic of this
service i
n
add
itional market
s, the co
mm
on co
ntra
cts
or
comp
etitive offers sta
nd o
u
t [4]. The normal
spe
e
d
will not be the set poi
nt due to prim
a
r
y
controller, and there
will
be an
offset. One method to
restore
the speed or fr
equency t
o
its
sup
p
o
s
ed val
ue is to ad
d
an integ
r
ato
r
. The inte
gral part o
b
serv
es the
avera
ge e
rro
r ove
r
a
period of tim
e
and will
defeat the off
s
et. Thi
s
scheme i
s
done manu
ally through the
Load
Freq
uen
cy Control (LFC)
or Automatic
Gene
ration
Control (A
GC) [5, 6] as sho
w
n on Fig
u
re 1.
In general AGC is a
cont
rol system
with three mai
n
items a
s
ment
ioned b
e
low:
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IJEECS
Vol.
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144
133
1)
AGC is a
co
ntrol sy
stem
with thre
e majo
r thing
s
a
s
mentio
ned
belo
w
: Prese
r
ving sy
stem
freque
ncy in i
t
s sup
p
o
s
ed
value or a val
ue clo
s
e to it.
2)
Preserving ev
ery unit gene
ration in an co
st-effe
ctively prop
er valu
e.
3)
Preserving
co
rre
ct value of
power tra
n
sfe
r
betwe
en a
r
e
a
s.
Comm
on LF
C system
s are
de
sig
ned
with
Prop
orti
onal-Integral (PI) c
ont
rollers [7]. However,
sin
c
e the “I” control parameters a
r
e
usually tun
ed; it is incapabl
e of ob
taining go
od
dynamic
perfo
rman
ce
for variou
s lo
ad and
syste
m
chan
ge
s.
Figure 1. Sch
e
matic Di
ag
ram of LFC an
d AVR of a Synchrono
us
Gene
rato
r
In the integ
r
al co
ntrolle
r,
if the integ
r
al gai
n
i
K
is
very high
un
accepta
b
le l
a
rge
overshoot
s
will be o
c
cu
rre
d. Thou
g
h
, adju
s
ting
the maxim
u
m and
mi
nimum valu
e
s
o
f
prop
ortio
nal (
p
K
), integral (
i
K
) and de
rivative (
d
K
) gain
s
re
spe
c
tively, the outputs of
th
e
system (volta
ge, freque
ncy
)
coul
d be im
proved a
s
sta
t
ed in [8].
The Gen
e
ration Rate Con
s
traint (GRC) is tak
en into
account by addin
g
a limiter to the
turbine
and
al
so by
addin
g
to the integ
r
al
cont
rol
p
a
rt t
o
prevent excessive control
action
[9]. It is
assume
d tha
t
gene
rating
units
belon
gi
ng to the
sa
me type of
g
eneration
will
have the
sa
me
GRC. The
re
sults i
n
refe
rences [1
0-1
1
]
indicate
th
at the GRC
wo
uld si
gnifica
n
t
ly influence t
h
e
dynamic resp
onses of
po
wer
system
s. In the
ca
se
w
h
er
e GR
C is
pr
es
en
te
d
,
th
e
s
y
s
t
e
m
will
sho
w
l
a
rg
er overshoot
s a
nd
lo
nge
r set
t
ling
time
s,
compa
r
ed
with
the
ca
se
wh
ere
G
R
C is
not
c
o
ns
idered [12].
Stability and
reliability of
n
o
minal volta
g
e
level in
an
ele
c
tric po
wer g
r
id i
s
on
e of the
main pro
b
lem
s
for an ele
c
tric po
wer
syst
em cont
rol.
It
is po
ssi
ble to minimize the real line lo
sse
s
by controllin
g the nomin
al voltage le
vel. No
wa
da
ys, Automatic Voltage
Control (AV
R
) is
gene
rally a
p
p
lied to
the
power
gen
eration u
n
its i
n
o
r
de
r to
solve this con
t
rol p
r
obl
em
as
discu
s
sed in [13-1
4
].
The aim
of thi
s
control is to
maintain th
e
system volta
g
e
between
li
mits by adj
usting the
excitation of t
he ma
chi
n
e
s
. The AVR se
nse
s
the
vari
ation bet
wee
n
a rectified
voltage de
riv
e
d
from the
stator voltage
an
d a refere
nce voltage.
Th
e error sig
n
a
l
is am
plified
and fed to t
h
e
excitation
sy
stem. Th
e
consta
nt VAR bala
n
ce in
the
net
work is
offe
red by
the cha
nge
in
excitation sy
stem. Thi
s
tech
niqu
e is
also
referre
d
as Me
ga
wa
tt Volt Amp
Rea
c
tive (M
VAr)
control or
Re
active-Volta
g
e
(QV)
contro
l [15].
The voltag
e
of the ge
nerator i
s
p
r
op
o
r
tional
to
excitation (flux)
of the ge
nerator. The
excitation is
use
d
to cont
rol the voltage
. Therefo
r
e, the voltage co
ntrol sy
stem i
s
also call
ed
as
excitation co
ntrol system or
AVR.
F
o
r the
gen
er
ators, the ex
citation is
provid
ed by a
devi
c
e
(anoth
e
r
ma
chine or
a sta
t
ic
devi
c
e
)
called ex
cite
r.
De
pen
ding
on
the
way
t
he DC suppl
y
is
given to the fi
eld wi
ndin
g
of
altern
ator
(which i
s
o
n
the rotor), the ex
c
i
ters
ar
e
c
l
as
s
i
fied
as
D
i
re
c
t
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
AVG Control for Two a
r
ea
Powe
r Syste
m
Including GRC nonli
n
e
a
rity ba
se
d o
n
PSO
(Ali M. Ali)
134
Current (DC)
exc
i
ters
, Alternating
Curre
n
t
(AC)
exciters an
d stati
c
e
x
citers as discu
s
sed in [1
6-
17]. This
re
search u
s
e
s
A
C
po
we
r sou
r
ce via
so
lid
-state re
ctifiers,
the
output v
o
ltage of ex
ci
ter
is a nonli
nea
r function of field voltage d
ue to the satu
ratuin effect
s
in the magnet
ic circuit.
The rest of article is o
r
ga
ni
zed a
s
follo
w:
Section 2 di
scue
sses the
AGC in
cludi
ng AVR
sy
st
em mo
de
l.
Section
3 pre
s
ent
s mo
deli
ng of AG
C fo
r two
-
a
r
ea po
wer
sy
stem. Furthe
rmo
r
e Section 4
illustrates Evolutionary
Computation while Sections
5, 6,
7 and
8 present
s di
fferent types
of
Particle
Swa
r
m O
p
timization te
chni
qu
es. Se
ction
9 p
r
e
s
ent
s t
he
simulatio
n
results
an
d
discu
ssi
on; the con
c
lu
sio
n
s were d
r
iven i
n
se
ction 10.
2. AGC inclu
d
ing AVR Sy
stem
Mod
e
l
Small cha
nge
s in real po
wer a
r
e e
s
senti
a
lly depen
de
nt on ch
ang
e
s
in rotor a
ngl
e
δ
and,
therefo
r
e th
e
freq
uen
cy f. The
rea
c
tive po
we
r i
s
m
a
inly dep
end
e
n
t on
the vol
t
age m
agnitu
de
(i.e. on the
gene
rato
r ex
citation) [1
5]. Cha
nge i
n
angle
δ
is
d
ue to mom
e
ntary chan
ge
in
gene
rato
r sp
eed. Thu
s
, lo
ad freq
uen
cy
and excitatio
n
voltage co
ntrols
are no
n- inte
ra
cting
for
small ch
ang
e
s
and ca
n be
modeled an
d analyze
d
separately [1
5]. Moreover, excitation
cont
rol
is fast acting
at the same time as
the
power
frequ
e
n
cy control is slow acting sin
c
e, the
m
a
jor
time con
s
tant
sha
r
ed
by the turbi
ne a
nd ge
nerator
moment of i
nertia
-
time consta
nt is m
u
ch
large
r
than th
at of the gene
rator field [
15].
Since the
r
e i
s
a wea
k
co
upling b
e
twe
en LF
C and
AVR system
s, the freq
ue
ncy an
d
voltage
were
co
ntrolle
d
separately. Th
e AG
C a
nd
AVR loo
p
s a
r
e
con
s
id
ere
d
ind
epe
nde
ntly,
sin
c
e
excitati
on
control of
gen
erato
r
h
a
ve sm
all
ti
me con
s
tant
co
ntribute
d
by field wi
nd
ing,
whe
r
e A
G
C l
oop i
s
slo
w
acting
loop
h
a
ving maj
o
r t
i
me con
s
tant
co
ntribute
d
by turbin
e a
nd
gene
rato
r mo
ment of i
nerti
a. Thu
s
tran
sient in
excitat
i
on
control lo
op a
r
e
scatte
r mu
ch
fast
a
nd
doe
s n
o
t affe
ct the
AGC l
oop. T
he i
n
te
ractio
n
exists but i
n
o
ppo
site directio
n.
Since
AVR l
o
op
affect the
ma
gnitude
of g
e
nerate
d
e.m.f
,
this e.m.f d
e
t
ermine
s th
e
magnitud
e
of
re
al p
o
wer
a
n
d
hen
ce AVR lo
op felt in AGC loop. When
includ
ed the
small effect o
f
voltage on real po
wer [23
]
.
The followi
ng
lineari
z
ied e
quation i
s
obt
ained:
'
es
1
PP
K
E
(2)
W
h
er
e
s
P
is synchro
n
izing po
wer
co
efficient.
is cha
nge in
the power an
gle.
1
K
is the cha
n
g
e
in the electrical po
we
r for small ch
ang
e in the stator emf.
'
t2
3
VK
K
E
(3)
W
h
er
e
K
2
is the cha
nge in termi
n
al voltage for small c
han
ge
in rotor an
gle
at consta
nt stator emf.
K
3
is chan
ge i
n
terminal vol
t
age for sm
all
chan
ge in st
ator emf at co
nstant rotor a
ngle.
Modifying the gene
rato
r field transfe
r function to inclu
de effect of rotor an
gle may
expre
s
sed th
e stator emf a
s
'
G
f4
G
K
E(
V
K
)
1s
(4)
The above
co
nstant
s dep
e
nd upo
n the n
e
twor
k pa
ram
e
ters a
nd op
e
r
ating conditi
on.
3. Modelling of AG
C inclu
d
ing AVR for
T
w
o
-
Area P
o
w
e
r Sy
tem
The system studie
d
con
s
i
s
ts of
two po
wer
c
ontrol
a
r
ea
s
with the
r
mal
reh
eat u
n
it type
c
o
nn
ec
te
d
by tie
-
lin
es
tha
t
a
llow
s
pow
e
r
e
x
c
h
an
ge
b
e
t
w
e
en
a
r
e
a
s [1
8
]
as
pr
es
en
te
d in
Figure 2.
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ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 1, April 2016 : 132 –
144
135
Figure 2. Two
Area Interco
nne
cted Power System.
The propo
se
d work inve
stigates the effe
ct of coupli
n
g
betwee
n
AGC and AVR.
The main aim
s
of the multi-area p
o
wer
system are
a)
Red
u
ce po
we
r system freq
uen
cy deviation
b)
Interch
ang
e p
o
we
r within th
e fixed range.
c)
Co
ntrol the tie-line p
o
wer f
l
ow at the sch
edule
d
value
determi
ned [1
9].
Conve
n
tional
LFC is
dep
e
nding
upo
n ti
e-line
bi
a
s
co
ntrol; where
each a
r
ea
he
ads for
minimize
the area co
ntrol e
rro
r
(A
CE)
to zero.The
i
npu
t to the sup
p
l
e
menta
r
y co
n
t
roller
of the ith
area i
s
the area co
ntrol e
r
ror (ACEi
)
whi
c
h is give
n by:
n
i
tie
(
i
,
j
)
i
i
j1
AC
E
(
P
B
f
)
Whe
r
e
i
B
is freq
uen
cy bias coefficient of
th
i
area,
i
f
is freque
ncy error,
ti
e
P
is tie-line po
we
r
flow error an
d ‘n’ is numb
e
r of intercon
necte
d are
a
s [20-21]. The
area bia
s
i
B
determin
e
s the
amount of i
n
tera
ction d
u
ring l
oad p
e
rturbation i
n
neigh
bo
rin
g
are
a
[22]. To obtain
b
e
tter
perfo
rman
ce,
bias
i
B
is sele
cted as:
ii
i
1
BD
R
Whe
r
e:
R:
is spee
d regul
ation.
D: is Frequ
e
n
cy Sensitivity Load Co
efficient.
4. Ev
olutionar
y
Computi
onal Techni
ques
Evolutionary
Comp
utation
(EC) i
s
dev
elope
d
from
the theory of
the ‘su
r
vival of the
fittest’ obtained by Charl
e
s Da
rwi
n
in 1859 and t
he
expre
ssi
on of
Evolutionary Comp
utation
wa
s
cre
a
ted a
s
re
cently a
s
199
1. It is a meta
heuri
s
tic te
chniqu
e and
a
biologi
cally m
o
tivated se
arch
and optimi
z
a
t
ion method
[24]. An EC tech
niq
u
e
inspi
r
ed the
evolutiona
ry philosophy
into
algorith
m
s th
at are used
to search for optimal
solu
tions to a problem. By th
is algo
rithm, a
numbe
r of po
ssi
ble solutio
n
s to a pro
b
l
e
m are ava
ila
ble and the task is to get the be
st soluti
on.
EC form
s
a
sea
r
ch
spa
c
e whi
c
h
cont
ains th
e
ran
domly ge
nerated
solution
s a
nd find
s
the
optimum solu
tion from the sea
r
ch sp
ace
[17, 24].
One of EC te
chni
que
s is th
e Particle Swarm Optimi
za
tion (PSO).
5. Conv
entional Particle S
w
arm Opti
miz
a
tion
PSO is a
sto
c
ha
stic Evol
u
t
ionary
Comp
ut
ation techni
que b
a
sed
o
n
the move
m
ent and
intelligen
ce of
swarms. The
main advant
age of
PSO
sugge
stion
wh
en
comp
ared
with
GA i
s
th
at
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PSO
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136
PSO doe
s n
o
t have g
ene
tic ope
rato
rs
su
ch a
s
crossover an
d m
u
tation. Parti
c
le
s b
r
ing
up
to
date them
sel
v
es with
the i
n
ternal velo
ci
ty and goes t
o
conve
r
ge to
the best solu
tion quickly [15-
16].
The mai
n
differen
c
e
betwe
en PSO and
other E
C
s p
r
ese
n
ted in h
o
w
it coul
d ch
ange the
popul
ation/swarm from o
n
e
iteration to
the next
in
the sea
r
ch space duri
ng
the whol
e ru
n
,
whe
r
ea
s in E
A
, the individuals a
r
e repla
c
ed in e
a
ch g
eneration [25]
.
In PSO, the coordi
nate
s
of
each pa
rticle
signi
fy a po
ssible
solutio
n
asso
ciated
with two
vectors, the p
o
sition
i
(x
)
and velocity
i
(v
)
v
e
ct
or
s.
In N-di
m
ensi
onal
sea
r
ch space
12
N
ii
i
i
X
[
x
,
x
,
...
..
,
x
]
and
12
N
ii
i
i
V
[
v
,
v
,
..
..,
v
]
are the two v
e
ctors a
s
soci
ated with ea
ch particl
e i.
A swarm
co
mposed
of a
numbe
r
of pa
rticle
s
“or po
ssi
ble
sol
u
tions” that p
r
o
g
r
ess
(fly)
throug
h the
feasibl
e
solu
tion sp
ace to explore
op
timal solutio
n
s. Each pa
rticle u
pdate
its
positio
n b
a
se
d on
its hol
d
be
st explo
r
a
t
ion; be
st
swarm
overall e
x
perien
c
e,
a
nd its p
r
evio
us
velocity vecto
r
acco
rdin
g to the following
model
[24]. Equation (5) a
nd (6
) de
scrib
e
s the PSO.
11
1
22
(-
(
-
)
tt
i
tt
t
t
ii
i
i
V
w
V
C
R
P
be
s
t
X
C
R
G
be
s
t
X
(5)
11
tt
t
ii
i
XX
V
(6)
Whe
r
e :-
1
C
and
2
C
are two
positive con
s
tants.
1
R
and
2
R
are two
rand
omly gen
erated n
u
mb
ers
with a ra
n
ge of {0,1}
w is the inertia weight.
t
i
P
be
s
t
is the best p
o
sition p
a
rticl
e
achi
eved b
a
se
d on its o
w
n expe
rien
ce
t
i
Pb
e
s
t
=
p
be
s
t
pb
e
s
t
p
b
e
s
t
i1
i
2
i
N
[
x
,x
,
.
.
.
,x
]
.
k
Gb
e
s
t
is the be
st pa
rticle po
sition
bas
ed on the
whol
e swarm’
s experi
e
n
c
e.
t
gb
e
s
t
=
gbe
s
t
gbe
s
t
gb
e
s
t
12
2
[
x
,
x
,
....,
x
]
.
t is the iteration index.
The term of
p
best
i
s
called
cog
n
itive com
pone
nt whil
e
the term of
g
best
calle
d
so
cial comp
one
nt
so the value
s
of
1
C
and
2
C
co
ntrol the dire
ction of each
par
ticle
s
in both local a
n
d global
comp
one
nts, the term of (
i
wv
) is previo
us ve
locity [16] .
A large
of ine
r
tia weight
w
at initial se
archin
g
then li
n
early d
e
crea
sing with ite
r
at
ion p
r
o
c
eed
e
d
following relat
i
on as
ma
x
mi
n
ma
x
()
_m
a
x
w
w
ite
r
ww
it
e
r
(7)
W
h
er
e
ma
x
w
is
final weight,
mi
n
w
is minimum weight.
_m
a
x
it
e
r
is maximum iteration n
u
mb
er is maximu
m iteration nu
mber
This is
calle
d Time Varying
Ineria Weghi
t (TVIW-PSO
) [27].
6. Cons
tricti
v
e
Particle Sw
a
r
m
Optim
i
zatio
n
(C
- PSO)
The maj
o
r
assumptio
n
of
constri
c
tion
fa
ctor
-PSO i
s
to avoid
pre
m
ature
co
nvergen
ce of
PSO in ea
rly stage
s of
se
arch an
d hel
ps to e
s
cap
e
from lo
cal o
p
timal point
then e
nha
nce
the
conve
r
ge
nce
of PSO algo
rithm [27]. By putting Con
s
trictive fa
ctor
(K) m
u
ltiply o
n
Equatio
n (6)
whe
r
e it equa
ll to
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2
2
K=
a
b
s
(
2
-
C
-
s
q
rt
(
C
-
4
*
C
))
(8)
Whe
r
e C
=
1
C
+
2
C
, C > 4 [28].
7. Adap
tiv
e
Acc
e
lera
tion
Coefficien
ts
Particle S
w
arm
Adaptive Acceleratio
n
Co
e
fficients Parti
c
le
Swarm (AAC-PSO) i
s
cha
r
a
c
teri
ze
d by the
accele
ration
coeffici
ents
1
C
and
2
C
are
cha
nge
d line
a
rly with
tim
e
that the
cog
n
itive
comp
one
nt is red
u
ced
whil
e so
cial
co
m
pone
nt is
in
crea
sed
a
s
se
arch iteration
pro
c
e
e
d
s
. T
h
e
AAC-PSO chang
es
th
e accele
ration
coeffici
ent
s
expone
ntially in time
with re
sp
ect th
eir
minimum a
n
d
maximum
values. Th
e
usin
g of ex
p
onential fu
nction to incre
a
se
or
decre
ase
spe
ed of
su
ch fun
c
tion
to accele
rate
the
convergen
ce p
r
o
c
e
ss to
get b
e
tter search
in
exploratio
n space.
Also
1
C
and
2
C
are
adapti
v
ely accordin
g to the fitne
s
s value
of
Gb
e
s
t
and
P
be
s
t
[27].
(t)
(
t)
ii
(t)
(
t)
(t)
t
22
(t
1
)
(t
)
(
t
)
(t
)
1
ii
i
(P
b
e
st
X
)
Cr
(
G
b
e
s
t
X
)
wV
C
r
V
(10
)
Whe
r
e
(t
)
w
ww
.
e
x
p
(
α
t)
(11
)
(t
)
(
t
)
cc
11
o
C
c
.
e
xp(
α
tk
)
(12
)
(t)
(
t)
cc
22
o
C
c
.
e
xp(
α
tk
)
(13
)
10
2o
c
ma
x
c
1
α
.l
n
t
c
(14
)
be
s
t
(t
)
(
t
)
(t
)
m
c
(t
)
m
(F
G
)
k
F
(15
)
Whe
r
e
(t
)
i
c
is acceleratio
n
co
efficient at itera
t
ion t, with i=1 or 2.
(t
)
w
is ine
r
tia
wei
ght facto
r
an
d t i
s
ite
r
ation
num
ber.
w
α
is determined
wit
h
respect to i
n
itial
and final values of
w
with the same ma
nner a
s
c
α
and
ln
is nepe
rian
logarithm .
(t
)
c
k
is
determi
ned b
a
se
d on the
fitness valu
e
of
b
es
t
G
and
b
es
t
P
at iteration
t
.
,
oi
c
are
initial
values of ine
r
tia weight fact
or and a
c
cele
ra
tion coeffici
ents re
sp
ecti
vely with i=1o
r 2.
(t
)
m
F
is the
mean value o
f
the best positions rel
a
ted
to all
particle
s
at iteration t as explai
ned i
n
[29].
8. Modified Adap
tiv
e
Accelera
t
ion Coefficients Particle S
w
a
r
m
Modified Ada
p
tive Accele
ration Co
effici
ents Parti
c
le
Swarm
(MAAC-PSO
) equ
ation is
the sam
e
as f
o
r (AAC) but i
t
is assume
d that
12
CC
4
so
2
C
=
1
4C
. It’s
s
u
ppos
ed to
be less calcul
ation for c
1
and
c
2
then getti
ng faste
r
solu
tions than (A
AC) a
s
explai
ned in [30].
9. Simulation results a
n
d discussion
the te
st s
y
stem
The ca
se un
der study
i
s
t
w
o are
a
h
a
ving
two ma
chi
nes (g
ene
rat
o
r a
nd
governor)
with
different sy
stem paramete
r
s u
s
ing PID
controlle
r for
LFC mo
del in
each a
r
e
a
a
nd anoth
e
r P
I
D
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Including GRC nonli
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a
rity ba
se
d o
n
PSO
(Ali M. Ali)
138
for ea
ch AV
R area
with i
n
cluding
GRC,
sud
den
dro
p
in load
(Fin
al
value) in
ea
ch a
r
ea
is
0.01
per unit an
d GRC in ea
ch
area i
s
(-0.1/60)
as presen
ted in Figure 3.
Note
s
:
These value
s
taken with tol
e
ran
c
e
±2% of full scale.
the pso
run si
multaneo
usly
in both area
s which
mean
the gain
s
of one are
a
rel
a
ted to other
area to give the optimum result.
Table (1) di
sp
layes the mo
st optimal gai
ns obtai
ned b
y
different types of PSO.
Area 1 pa
ram
e
ters:
Tg1=0.2, Kg1=1, Kt1=1,
Tt1=0.5, H1=5, D1
=0.6
, B1=20.6, 1/R1
=20, R1
=0.05, Ka
1=10,
Ta
1=0.1, Ke
1=1, Te
1
=
0.4, Kg1=
0.8,
Tg1=1.4, K6=
0
.5, K5=
-0.1, K4=
1
.4, Ps
=
2
=
K
1, K2=
0
.2,
K
r
=1,
Tr
=0.
0
5
Area 2 pa
ram
e
ters:
Tg2=0.3, Kg
2=1, Kt2
=
1,
Tt2=0.6,
H2=4,
D2
=0.9
, B2=16.9,1/
R2
=16,
R2
=0.0625, Ka
2=9,
Ta
2=0.1, Ke2
=
1, Te
2=0.4,
Kg2=1, Tg
2=
1, K8=0.5, Kr2= 1, Tr2=0.0
5
, a12=-1.
Area 1:
Table 1. Perf
orma
nce Evaluation for PID Controll
er tu
nned by Diffe
rent Type
s of PSO for Area
1
The PID co
ntrolle
r of AVR gain
s
are KP
=2; KI=0.13
9
67; KD=1.
KP
KI
KD
Obj. Funct.
Ts (Sec)
Peak Value (
∆
F)
TVIW-PSO 0.05967
100
5.2412
517.181
66.1923
0.0909
C-PSO 6.3119
44.133
8.1723
487.99
75.2692
0.0909
AAC-PSO 0.2396
12.263
10
551.5611
67.2764
0.0909
MAAC-PSO 4.9685
100
4.
6664
487.987
73.2223
0.0909
Figure 3. LFC with AVR usi
ng LFC Integ
r
al Controlle
r.
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Area 2:
Table 2. Perf
orma
nce Evaluation for PID Controll
er Tu
nned by Diffe
rent Type
s of PSO for Area
2
O
p
tm. Technique
KP
KI
KD
O
b
j.
Fun.
Ts (Sec)
Peak Value
TVIW-PSO 9.634
48.26
9.199
517.18
61.59
0.0833
C-PSO 0.5
48.83
8.874
487.99
70.71
0.0833
AAC-PSO 15.25
36.19
7.199
551.56
62.75
0.0833
MAAC-PSO 0.340
23.74
7.312
487.98
68.63
0.0833
The PID- AV
R gain
s
are KP=2; KI=0.13
967; KD=1.
The Figu
re 4
depi
cts the freque
ncy devi
a
tion of
area
1 without u
s
in
g LFC an
d AVR cont
rolle
rs.
Figure 4. Fre
quen
cy Devia
t
ion in Area (1) witho
u
t usi
ng LFC a
nd
AVR Controll
ers
The Figu
re 5
pre
s
ent
s the frequ
en
cy deviation of
Area
2 without usi
ng LFC a
nd
AVR cont
rolle
rs.
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AVG Control for Two a
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Including GRC nonli
n
e
a
rity ba
se
d o
n
PSO
(Ali M. Ali)
140
Figure 5. Fre
quen
cy Devia
t
ion in Area 2
without usi
n
g
LFC and AV
R co
ntrolle
rs
The Figu
re 6
gives the co
mpari
s
o
n
s b
e
t
ween 4
ga
ins
for
freq
uen
cy deviation of Area 1
with PID
-
controlle
r in case of u
s
ing
GRC.
Figure 6. Fre
quen
cy Devia
t
ion of Area 1
with PID con
t
roller in
clu
d
e
d
GRC
The Figure 7
illustrates the
com
pari
s
o
n
s betwe
en 4
ga
in
s
for
frequ
ency d
e
viatio
n of area 2
wi
th
PID- co
ntrolle
r in ca
se of u
s
ing G
R
C.
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Figure 7. Co
mpari
s
o
n
s b
e
t
ween 4 g
a
in
s
for
Frequ
en
cy Deviation
of Area 2
The Figu
re 8
pre
s
ent
s the
freque
ncy d
e
v
iation com
p
arsi
on b
e
twe
en the TVIW
gain an
d with
out
usin
g PID co
ntrolle
r for Area 2.
Figure 8. Fre
quen
cy Devia
t
ion in Area (1) wi
th/with
o
u
t
using LF
C a
nd AVR Co
ntrolle
rs
The Fig
u
re
9
gives the th
e
freque
ncy d
e
v
iation com
p
arsi
on frequ
e
n
cy Are
a
2
with/without u
s
i
n
g
LFC and
AV
R
cont
rolle
rs.
The
Figu
re
1
0
di
splay
s
th
e termi
nal vol
t
age
re
spon
se in A
r
ea
1.
The
Figure 11 di
splays the terminal voltage
resp
on
se in
Area 2.
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