In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
6
9
4
~1
7
0
4
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1694-1704
1694
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Application of artificial intel
ligence techniques for LFC and
AVR systems u
s
ing
PID contro
ller
Ghassan
Abdullah
Salman,
A
s
sama
S
ah
i
b
Jafar,
Ammar Issa
Ismael
Depart
m
e
nt
o
f Elect
rical Po
w
er a
n
d
M
ach
in
es
E
n
gineerin
g, Co
l
l
e
ge o
f
En
g
i
neerin
g
, Un
i
v
e
rsity
o
f
Di
y
a
la, D
i
y
a
la
,
I
r
a
q
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
No
v
1
9
,
2
018
Re
vise
d F
e
b 11,
201
9
Ac
ce
p
t
ed
Ap
r
2
2
,
2
019
Dev
e
lo
pm
ent
o
f
e
lect
ri
cal
p
o
w
er
s
ys
tems
l
ed
t
o
search
f
or
a
n
ew
m
a
th
ematical
m
eth
ods
t
o
f
i
n
d
t
he
v
alu
e
s
of
P
ID
(
P
r
op
ort
i
onal-In
tegral
-
Deri
vati
ve)
co
ntroll
er.
T
h
e
go
al
o
f
th
e
pap
e
r
is
t
o
i
m
pro
v
e
th
e
p
erf
o
rman
ce
of
t
he
o
veral
l
s
ys
tem,
t
hro
ugh
i
m
p
rov
e
d
t
h
e
f
r
eq
uency
d
e
v
i
ation
a
n
d
t
h
e
vo
lt
age
dev
i
ati
o
n
char
acteri
s
ti
cs
u
sin
g
P
ID
c
on
tro
l
l
e
r,
s
o
i
n
t
h
i
s
paper
ar
e
pro
p
o
s
ed
t
h
r
ee
m
e
t
hod
s
o
f
a
rtif
icial
i
n
t
e
llig
ence
t
echn
i
q
u
es
f
o
r
de
s
i
g
n
i
n
g
t
h
e
op
tim
al
v
a
l
ues
o
f
P
ID
c
on
tro
l
ler
o
f
L
oad
-
Fre
q
uen
c
y-Con
t
ro
l
(LF
C
)
and
Automa
tic-Voltage-Regul
ator
(
A
V
R),
t
h
e
f
i
r
s
t
i
s
t
he
F
i
r
e
f
l
y
A
l
g
orithm
(
F
A)
,
th
e
s
e
co
nd
i
s
t
h
e
Genet
i
c
Alg
o
rith
m
(GA
)
a
nd
t
h
e
t
hi
rd
i
s
th
e
P
arti
c
l
e
S
w
arm
Op
ti
mizati
o
n
(PS
O
),
i
n
ad
dit
i
o
n
t
o
thes
e
three
m
e
th
od
s
u
s
e
t
h
e
conventional
(Zie
g
l
e
r
–N
ic
h
o
l
s
,
Z-
N).
Th
e
F
A
,
GA
a
nd
P
SO
a
re
u
se
d
to
o
bta
i
n
t
he
o
p
t
im
al
param
e
ters
o
f
PI
D
controller
base
d
on
m
inimized
d
i
f
f
e
rent
v
ar
i
o
us
i
n
d
i
c
es
a
s
a
f
i
t
n
ess
f
u
nction
,
t
h
es
e
f
i
t
n
ess
f
u
n
c
ti
on
s
n
a
mely
I
nteg
ral-T
i
m
e-Absolu
t
e
-
Error
(ITAE)
and
Integral-T
i
m
e-
Squa
re-E
rror
(IT
SE).
C
om
pari
s
o
n
b
e
tween
th
e
res
u
lts
o
bt
a
i
ned
sho
w
t
h
a
t
F
A
h
as
b
ett
e
r
perf
orm
a
nce
to
c
on
tr
o
l
o
f
fre
q
ue
n
c
y
d
e
viatio
n
a
n
d
te
rm
in
a
l
v
o
l
ta
ge
t
ha
n
GA
a
n
d
PSO,
s
o
th
e
resul
t
s
ob
serv
ed
t
he
F
A
is
m
ore
eff
e
ct
ual
and
reli
abl
e
t
o
det
e
rmine
the
o
p
t
i
m
a
l
val
u
es
o
f
P
I
D
co
n
t
ro
ller.
K
eyw
ord
s
:
AVR
Fitne
ss F
unct
i
o
n
LFC
O
p
t
i
m
i
za
t
i
o
n
Te
c
hn
i
que
PID
c
o
ntro
ller
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
G
h
assan
A
b
du
lla
h S
a
lma
n
,
Depa
rtem
ent o
f
E
lectr
i
c
a
l P
o
wer
and Ma
chi
n
s En
gi
neer
in
g
,
Col
l
a
g
e
of
E
n
g
i
ne
er
in
g,
Un
iv
ersit
y
of
Di
y
a
l
a
,
Ba
qu
ba
h,
D
iyala,
Ir
a
q.
Em
ail:
gha
ssan
pow
er
z@
gm
ai
l.
com
1.
I
N
TR
OD
U
C
TI
O
N
Both
L
F
C
a
nd
A
V
R
p
la
ys
a
n
i
m
portant
a
nd e
s
se
nt
ial
role in
t
h
e
c
ont
r
o
l
of pow
er
g
ener
ati
on
syste
m
s
in
o
r
d
er
t
o
be
s
uit
a
ble
for
the
c
onsu
m
er
,
through
the
control
o
f
(a
ctive
pow
er
-
f
re
quency)
a
nd
(re
active
pow
er
-
voltage)
r
e
spec
t
i
vely,
so
t
hat
the
de
vi
a
t
ion
values
m
us
t
be
w
ith
in
a
c
cepta
bl
e
lim
i
t
s
[1,
2].
F
i
rst
of
a
l
l
influence
be
tween
t
he
m
ec
h
a
nical
a
nd
ele
c
trical
p
ar
t
s
p
re
cisely
,
int
e
rconne
ction
e
quations
b
e
t
w
e
en
L
F
C
a
nd
A
V
R
h
ave
be
en
p
roposed
by
[3,
4].
The
coordination
betw
ee
n
LF
C
and
A
V
R
w
i
t
h
the
ne
w
mode
l
ha
s
be
en
proposed
by
[5].
T
he
o
sc
il
la
t
i
on
of
L
F
C
a
nd
A
V
R
a
r
e
s
tudied
w
it
h
P
I
D
c
ont
r
o
l
l
e
r
i
n
[6,
7]
t
o
improve
t
he
perform
ance
o
f
tw
o
control
loops.
To
m
ore
e
fficient
results
t
he
a
r
t
ific
i
a
l
intelli
ge
nce tec
h
nique
s
w
a
s used
f
or
tuni
ng
the
gains
of
P
ID
c
ont
r
o
l
l
e
r
f
or
L
F
C
w
ith
A
V
R
l
oops,
t
h
e
appli
c
ations
o
f
a
r
tificial
int
e
ll
igenc
e
technique
b
a
s
ed
on
opti
m
iza
t
ion
of
P
ID
c
ont
r
o
l
l
e
r
f
or
L
F
C
a
re
p
r
e
sented
i
n
[8-
12],
w
h
e
r
ea
s
t
h
e
opti
m
al
design
of
P
I
D
c
ontroller
by
using
ar
t
i
fic
i
a
l
i
ntelligence
t
echn
ique
f
or
A
V
R
s
yste
m
a
r
e
pr
esented
in
[
13-
1
7
]
.
The
LF
C
and
A
V
R
c
ontrol
loop
s
w
i
th
t
uning
P
I
D
pa
ram
e
ter
s
by
opt
i
m
iza
t
ion
tec
hnique
a
re
s
tudied
indi
vidually
i
n
[18,
19],
w
h
ile
t
he
i
nt
e
r
ac
ti
on
effec
t
a
mong
th
e
LFC
w
ith
A
V
R
c
ontrol
loo
p
s
w
ith
o
ptim
i
z
ed
the P
I
D
controller
gains ar
e pr
esented
in [20-22]
.
The
pa
per
pro
b
lem
li
e
s
i
n
t
u
ni
n
g
t
he
opt
im
al
v
a
l
ues
of
t
h
e
P
ID
contro
ll
er
on
the
LF
C
a
n
d
A
V
R
syste
m
s
a
nd
thus
i
m
p
ro
v
i
n
g
the
gener
a
l
p
e
rform
ance
o
f
the
s
y
s
t
e
m
b
y
i
mpr
o
v
i
n
g
f
r
e
que
nc
y
a
nd
vo
l
t
ag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
pplication of ar
tif
icial intell
igence
t
e
chnique
s for L
F
C
and
AVR syst
ems
…
(
G
hassan A
b
dullah
Salman)
1
695
dev
i
a
t
i
o
ns,
F
i
na
lly,
f
o
r th
is pa
p
e
r
t
he perf
o
rm
ance
of
LF
C w
i
t
h
A
V
R
l
oo
ps for si
n
gle ar
e
a
po
w
er syste
m
have
bee
n
s
tu
d
i
ed
a
nd
i
t
is
i
mp
le
m
e
nta
t
i
o
n
F
A
,
G
A
and
P
S
O
for
tu
ni
n
g
t
h
e
p
a
r
amet
e
r
s
o
f
P
ID
b
a
s
ed
t
o
mi
n
i
mize
tw
o d
i
ffe
r
en
t
fi
t
n
e
s
s
fu
nc
ti
o
n
s.
F
irst
i
s
ITA
E
and
se
c
o
n
d
is I
T
SE.
2.
MODELING OF LFC
AND
AVR
S
Y
STEM
S
The
e
f
fec
t
o
f
cou
p
l
i
n
g
a
nd
coor
di
na
ti
o
n
b
e
t
w
een
L
F
C
a
nd
A
V
R
ar
e
s
t
u
d
i
ed
i
n
this
p
ape
r
,
a
fu
ll
descr
i
pt
i
on
of
t
he
t
rans
fe
r
fu
nc
ti
on
m
ode
l
f
o
r
LF
C
an
d
A
V
R
l
oo
p
s
a
r
e
pr
esen
ted
i
n
[
2,
6
]
and
s
h
ow
n
in
F
i
gure
1.
F
i
gure
1.
M
A
TLA
B/S
i
m
u
l
i
n
k
mode
l
from
LF
C
and
A
V
R
sys
t
e
m
A
c
c
o
rdi
n
g
t
o
[
2,
5
]
fr
om
t
he
i
n
t
era
c
t
i
o
n
a
m
ong
LF
C
w
ith
A
V
R
l
oo
p
s
o
bt
ain
th
e
fol
l
o
w
i
ng
equa
t
i
o
n
s
:
∆P
K
∆
δ
K
∆E
(
1)
∆E
′
∆E
∆δ
(
2)
∆V
K
∆δ
K
∆E
(3)
3.
MODELING OF THE
PID CONTRO
LLER
The
P
I
D
c
o
n
t
r
o
ller
st
ill
t
h
e
d
o
mina
n
t
p
l
a
y
a
n
i
mp
orta
nt
r
ole
i
n
p
ower
s
y
s
t
e
ms,
f
o
r
e
a
s
e
of
repr
esenta
t
i
o
n
and
im
p
l
e
m
e
n
ta
t
i
o
n
,
as
w
e
l
l
a
s
t
o
its
e
ffec
t
i
ve
n
es
s
in
e
nha
nc
em
ent
th
e
per
f
orm
a
nce
o
f
elec
tr
ical p
ow
e
r
s
ystem
s
. A
ccord
ing
t
o
[7,
21]
F
igure
2 sho
w
s t
he
ty
p
i
c
a
l
struc
t
ure
of P
I
D
c
on
tr
ol
ler
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
169
4
– 1
704
1
696
F
i
gur
e 2.
Bl
o
c
k
dia
gra
m
o
f
t
h
e
P
I
D c
ontro
lle
r
The
P
I
D
contr
o
l
l
er
t
ransfe
r f
unc
t
i
o
n
m
ode
l
in term
s
of Lap
l
ac
e
doma
i
n
i
s
qua
l
i
f
i
e
d
a
s
fol
l
ow
:
G
s
k
k
s
(
4
)
W
h
e
r
e
,
E
(
s
)
w
i
t
h
U
(
s
)
a
r
e
t
h
e
e
r
r
o
r
s
i
g
n
a
l
a
n
d
t
h
e
c
o
n
t
r
o
l
s
i
g
n
a
l
t
h
a
t
re
pr
esen
ted
t
h
e
varia
t
i
o
n
am
o
n
g
i
np
ut
and
fe
e
d
bac
k
i
n
e
x
pressi
on
o
f
L
ap
lac
e
d
om
ain
on
the
o
t
he
r;
k
r
e
p
rese
nt
t
h
e
p
r
o
p
o
rtio
na
l
ga
in,
k
r
e
p
r
e
s
e
n
t
the
in
tegr
a
tio
n
gai
n
a
n
d
k
r
eprese
n
t
t
he
d
eri
v
a
t
i
v
e
ga
in.
The
P
I
D
c
ontro
l
l
e
r
out
pu
t
i
n
t
e
rm
o
f
t
i
me
dom
ai
n
is
repr
esente
d
as fo
llow
:
u
t
k
et
k
e
t
dt
k
(5)
Whe
r
e,
e(
t
)
and
u(t)
a
re
trac
k
ing
er
ror a
nd the
con
t
ro
l si
gn
als
t
hat r
e
pre
s
e
n
t
i
n
t
he
f
orm
of
t
i
m
e
doma
i
n
.
Fi
n
a
lly
,
in
t
hi
s
p
a
p
e
r
th
e
e
ffec
t
o
f
t
w
o
d
i
f
f
e
r
e
n
t
o
b
j
e
c
t
i
v
e
f
u
nc
ti
o
n
s
is
s
t
u
d
i
e
d
f
or
o
p
tim
izat
io
n
to
d
e
t
e
rmin
e
t
h
e p
a
r
amet
ers o
f
PI
D
co
n
t
rol
l
er. Fi
rst
i
s
ITAE
an
d
sec
ond
is
I
TS
E.
H
as be
e
n de
fi
ne
d
as fol
l
o
w
s
:
IT
AE
|
e
t
|
|
e
t
|
dt
(
6
)
IT
S
E
e
t
e
t
dt
(
7)
M
i
n
i
m
i
z
e
I
TA
E
and I
T
S
E
subjec
te
d t
o
:
k
k
k
,
k
k
k
a
nd
k
k
k
(8)
4.
CONT
ROL S
T
RATEG
Y
OF PID
C
O
N
TROLLER
4.1.
C
o
n
v
en
t
i
on
al
(
Z
-
N
)
M
e
t
h
o
d
[20,
23-25]
I
n
t
he
f
o
u
rt
h
d
e
c
a
de
o
f
the
l
a
st
c
ent
u
ry,
Zi
e
g
l
e
r
and
N
i
c
hols
p
rese
nt
e
d
t
he
v
a
l
u
e
s
of
K
,
T
a
n
d
T
ac
cord
in
g t
o
th
e
r
ules show
n
in
T
ab
le
1
.
B
y
t
his
me
th
o
d
,
the
dy
na
mi
c
pr
oper
t
y
of
t
he
p
roc
e
dure
i
s
r
epre
s
en
te
d
by
the
fi
na
l
gai
n
f
r
o
m
a
con
s
is
t
e
nt
c
o
n
t
r
ol
ler
and t
h
e
f
i
na
l
pu
lse
pe
ri
od
of
t
h
e
l
o
o
p.
T
he
f
i
n
a
l
gai
n
and
a
pe
rio
d
o
f
ac
t
u
al
o
per
a
t
i
on
ar
e
usu
a
l
l
y
deter
m
ine
d
b
y the
fo
l
l
ow
i
ng pr
o
c
ess
:
a.
The
der
i
va
tive
a
nd
in
te
gra
t
e
d
m
odes
o
f
t
he
f
e
e
dbac
k
c
on
t
r
oller
s
a
re
t
ur
ned
(off
)
f
o
r
this
r
eason
t
h
e
y
have
a
rela
t
i
ve
c
on
tr
ol.
b.
For
the
a
u
tom
a
tic
c
o
n
t
ro
l,
t
he
r
elat
ive
ga
i
n
-
r
elat
ive
range
r
e
d
u
c
ti
on
-
i
s
i
nc
rea
s
e
d
i
n
t
o
th
e
l
o
op
f
lu
ct
u
a
te
s
for
a
cons
tan
t
ca
p
ac
it
y.
c.
For
the
he
lp
o
f
t
i
m
e
r
egis
ter
fo
r
th
e
co
nt
roll
ed
v
ari
a
bl
e
,
t
he
p
u
l
s
e
p
e
r
i
o
d
i
s
m
e
a
s
u
r
e
d
a
n
d
r
e
g
i
s
t
e
r
e
d
a
s
t
h
e
fi
na
l T
per
i
o
d
.
Tab
l
e
1.
Z
-N
T
un
ing
Ru
les
T
ype
o
f C
ontro
l
l
e
r
K
p
T
i
T
d
P
T/
L
∞
0
PI
0
.9*T
/L
L
/0.3
0
P
I
D
1
.
2
*
T
/L
2
L
0
.5
L
Not
e
:
k
p
=
K
p
, k
i
=
K
p
/ T
i
a
nd
k
d
=
K
p
*
T
d
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
pplication of ar
tif
icial intell
igence
t
e
chnique
s for L
F
C
and
AVR syst
ems
…
(
G
hassan A
b
dullah
Salman)
1
697
4.2.
Int
e
llige
n
ce
tech
niqu
es
The
m
odern
a
rti
f
i
c
ia
l
in
t
e
lli
genc
e
a
nd
heu
r
istic
s
t
e
c
h
ni
q
u
es
p
l
ay
a
n
im
porta
nt
r
o
l
e
to
c
on
tro
l
o
f
elec
tr
ic
pow
er
s
ys
tem
t
h
ere
f
ore
,
t
he
m
a
i
n
ob
j
e
c
t
i
v
e
o
f
t
h
i
s
pa
p
e
r
f
o
r
c
o
n
t
r
o
l
t
h
e
f
r
e
q
u
e
n
c
y
d
e
v
i
a
t
i
o
n
a
n
d
term
ina
l
v
o
l
tag
e
d
e
v
i
a
tio
n
o
f
s
ing
l
e
ar
ea
po
w
e
r
system
.
A
t
f
irs
t
co
nt
roll
er
p
a
r
amet
e
r
s
t
u
n
i
ng
i
s
a
cco
mpl
i
shed
by
c
o
n
v
e
n
t
i
o
n
a
l
(Z-N
)
proc
edure.
B
u
t
,
th
i
s
m
eth
od
is
not
f
eas
i
b
l
e
i
n
p
r
a
c
ti
cal
s
yst
e
ms
t
h
a
t
n
eed
f
ast
proce
ssi
ng
a
n
d
t
h
i
s
i
s
n
o
t
a
va
ila
b
l
e
in
t
h
i
s
me
th
od.
C
on
seq
u
e
n
t
ly,
m
u
c
h
p
ow
er
fu
l
m
a
t
h
e
m
atica
l
o
p
t
imi
z
a
tio
n
tech
n
i
q
u
es
a
re
u
t
iliz
in
g
to
t
u
n
e
t
h
e
para
me
te
rs
o
f
P
I
D
a
n
d
m
o
st
r
e
l
ia
bl
e
ar
e
po
p
u
l
at
i
o
n
ba
se
d
op
t
i
miz
a
tio
n
proce
dures
e
sp
ecia
l
l
y
F
A,
G
A
and P
S
O
.
F
A
i
s
a
Meta
h
eur
i
st
ic
s
ea
rch
tec
h
n
i
que
b
a
s
ed
o
n
o
p
tim
iz
ati
o
n
a
l
gor
ith
m
;
i
t
is
p
r
o
p
o
s
e
d
i
n
200
7
b
y
X
i
n S
h
e Y
a
ng [26]
.
The F
A
i
s de
sc
ribe
d
in
t
he fo
llow
i
n
g
rule
s
.
a.
Ea
ch
f
i
r
efly
h
as t
h
e
abi
lit
y
to
a
t
t
r
act
o
th
e
r
f
i
r
ef
li
es of
t
h
e
sa
m
e
s
ex or of
t
h
e
opp
os
i
t
e se
x.
b.
F
i
re
fly
bri
ght
n
e
ss
is
p
r
opor
ti
ona
l
to
t
h
e
a
t
t
r
acti
o
n
an
d
i
n
v
e
rs
ely
prop
ort
i
ona
l
to
t
h
e
d
i
s
t
a
nc
e,
t
h
u
s
the
l
o
w
bri
g
h
t
ne
ss
o
f
the
fire
fl
y m
o
v
e
s to
a
hi
gh-br
i
g
h
t
ness fire
fl
y ne
ar
i
t.
c.
The
o
p
tim
um
v
al
ue
f
or
t
he
fi
t
ne
ss fu
n
c
tio
n
repre
s
ente
d
by
the b
r
i
ghtnes
s
of firef
l
ies.
The
fo
l
l
ow
in
g e
qua
t
i
o
n
s
be
l
o
w
de
sc
ribe
t
he
F
A
:
X
X
β
X
X
α
rand
(9)
β
β
e
γ
m
1
(
10)
r
X
X
∑
X
,
X
,
(
11)
Where
(9)
represent
s
t
h
e
m
ovem
e
nt
o
f
the
Firef
lies,
w
here
t
he
f
i
r
st
e
x
p
r
e
s
si
on
i
s
th
e
cu
rre
n
t
po
siti
on
of
a
f
ire
f
l
y
,
t
h
e
ne
xt
e
xpre
s
s
i
o
n
i
s
ap
p
lie
d
for
c
onsi
d
er
in
g
a
f
i
r
e
fl
y’s
a
t
trac
tio
ns
t
o
l
i
g
h
t
i
n
te
nsit
y
se
e
n
b
y
adjac
e
n
t
firefli
e
s,
t
he
n
t
h
e
t
h
i
r
d
expre
ssio
n
i
ssue
d
for
the
ra
nd
om
m
ove
me
nt
o
f
a
firefl
y
in
c
ase,
t
here
a
re
no
any
br
ig
h
t
er
o
nes.
T
he
c
oe
fficie
n
t
i
s
a
in
di
sc
ri
mi
n
a
t
e
p
a
r
amet
er
d
et
ermi
n
e
d
by
t
h
e
p
robl
e
m
o
f
i
n
t
ere
s
t
,
w
h
i
l
s
t
r
and is a
r
andom
numb
e
r ge
nera
to
r
re
gu
larl
y d
i
str
i
bu
ted
i
n
t
he
s
pa
c
e
[
0,
1].
Where
β
0
c
o
n
s
i
de
r
t
h
e
fore
mos
t
a
ttra
c
t
i
ve
n
e
ss
a
t
r
equa
l
0,
γ
i
s
an
a
b
so
rpt
i
o
n
c
o
effi
ci
e
n
t
t
h
at
c
an
c
o
n
t
r
o
l
s
t
h
e
d
e
c
r
e
a
s
e
f
r
o
m
t
h
e
l
i
g
h
t
i
n
t
e
n
s
i
t
y
a
n
d
r
c
o
n
s
i
d
e
r
t
he
d
ime
n
sion
a
m
o
n
g
a
ny
tw
o
fire
fl
ies.
B
ut
X
i,
k
con
s
i
d
er
t
he
k
t
h
c
om
po
ne
nt
o
f
t
h
e
l
o
c
a
t
i
v
e
X
i
o
f
t
he
i
t
h
f
ire
f
l
y
w
h
i
le
d
i
s
the
d
i
me
n
s
i
ons
num
ber
.
G
A
i
s
i
n
t
r
o
d
u
c
e
d
by
Jo
hn
Hol
l
a
nd
i
n
1
970
;
it
i
s
a
st
o
c
h
a
st
i
c
g
lo
b
a
l
s
ea
rch
m
e
th
o
d
u
se
d
for
o
p
timiza
tio
n
[27]
.
The
G
A
ope
rators
a
re
usuall
y
do
n
e
b
y
fo
l
low
i
n
g
s
t
a
ges [
28]
-[29]
.
a.
Se
lecti
o
n
:
O
pe
rator
se
lec
t
ion
is
a
p
p
lie
d
m
u
ltip
le
t
i
m
es
b
ec
a
u
se
t
here
a
re
m
em
ber
s
i
n
th
e
p
o
p
u
l
a
t
i
on.
A
n
y
in
d
i
v
i
dua
l
is
it
e
r
a
ti
v
e
a
t t
h
i
s
s
t
e
p
to
ge
ther
w
i
t
h a e
v
e
n
tua
l
i
t
y pro
por
ti
o
n
al
to
the
r
e
la
tive
f
i
t
n
ess
fu
nct
i
on of
t
h
e
pop
ul
ati
o
n
.
b.
Crosso
ve
r:
T
h
e
c
ross
over
o
p
e
r
ator
i
s
a
p
p
l
i
e
d
to
p
rod
u
ce
t
w
o
n
ew
i
nd
ivid
u
a
l
s
,
b
y
c
hoi
ce
a
nd
c
o
m
bi
ni
ng
tw
o
in
d
i
vi
d
u
al
s
(
p
are
n
t
s
).
T
h
e
c
o
llec
tio
n
pr
ocess
is
d
o
n
e
by
r
a
n
d
o
m
s
e
l
e
c
t
i
on
o
f
th
e
c
u
t
poi
nt
a
n
d
then
di
v
i
d
i
ng
the
p
a
re
nt
s
in
to
t
w
o
p
arts,
so
t
h
a
t
t
h
e
pare
n
t
s
are
re
place
d
by
the
o
f
fspr
ing,
f
or
me
d
i
n
t
he
p
opu
l
a
t
i
o
n
.
c.
Mu
t
a
tio
n
:
T
he
v
al
ues
i
n
a
s
i
t
e
ar
e
random
l
y
s
e
l
e
c
t
e
d
f
or
i
n
d
i
v
i
dua
l
c
h
a
nge
s
by
t
h
e
m
u
t
a
t
i
o
n
opera
t
o
r,
aft
e
r
t
h
e
n
u
m
b
er
o
f
iter
a
t
i
ons
t
ha
t
t
h
e
a
l
gor
it
hm
h
as
b
een
c
omp
le
te
d
,
w
hile
r
un
n
i
n
g
t
he
a
l
gor
it
hm
re
presents t
he
b
es
t in
d
i
v
i
dua
l
sol
u
t
i
on cr
eate
d
.
In 19
95 the P
S
O
is
de
veloped by K
e
nne
dy
a
nd Eber
hart, it is one
of the
m
oder
n
heur
i
stic algorithms
used
f
or
optim
i
z
ation
[30].
I
n
P
S
O
m
e
t
hod,
s
et
o
f
indi
viduals
t
hat
m
a
ke
up
the
sw
a
r
m
c
a
lled
par
t
ic
l
e
s,
e
a
c
h
particle
h
a
s
positi
on
and
veloc
i
ty.
To
r
e
ach
t
he
optima
l
v
alue
s
t
he
posit
ion
and
velocity
a
re
upda
te
u
sing
the
follow
i
ng
e
qua
t
i
ons:
X
X
V
(
12)
V
w
V
c
r
p
,
X
c
r
g
,
X
(
13)
w
(14)
Whe
r
e
X
i
k+1
is
posi
tion
of
p
article
a
t
k+1
iter
a
tion
,
X
i
k
i
s
posit
ion
of
p
article
a
t
k
itera
t
i
on,
V
i
k+1
repr
esent
veloc
i
ty
f
or
m
pa
rticle
a
t
k+1
itera
t
i
on,
V
i
k
r
epre
sent
v
elocity
o
f
pa
rti
c
le
a
t
k
itera
ti
on,
w
r
e
p
resent
inertia
w
eight par
am
eter,
c
1
with
c
2
a
re
lea
rning fa
ctors,
r
1
w
ith
r
2
a
re
ra
ndom
numbe
r in the
interva
l
[0,
1].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
169
4
– 1
704
1
698
The
fl
ow
chart
of
F
A
,
G
A
a
nd
P
S
O
based
on
ITA
E
a
nd
ITS
E
a
s
a
fit
ness
functions
t
o
determ
ine
opti
m
al
v
alue
s
of
P
ID
c
ontroll
e
r
a
s
show
n
a
t
F
igure
3,
w
hi
le
t
h
e
para
me
t
e
rs
f
rom
these
te
chnique
a
r
e
g
iven
in Table 2.
F
i
gure
3.
F
l
ow
c
h
art
of i
n
t
e
l
l
i
ge
nce
t
e
ch
n
i
q
u
e
s for P
I
D
cont
rol
l
e
r
Ta
ble
2.
P
aramete
r
s of
F
A
, GA
and
PS
O
FA
G
A
PS
O
Popul
a
tion
S
i
ze
(
Pop
)
=
30
A
b
sorp
t
i
on C
o
e
ffic
i
e
n
t (
) =
0.5
A
t
t
r
act
io
n
Co
ef
f
i
ci
e
n
t
(
0
)
=
0
.
2
Muta
tion C
o
e
ffic
i
e
n
t (
)
=
0.
3
m
=
3
Popul
a
tion
S
i
ze
(
Pop
)
=
30
C
r
oss
o
ve
r F
a
c
t
or
(
)
=
0
.
5
C
r
ossove
r
Pe
r
c
e
n
ta
g
e
(
p
c
) =
0.8
M
u
ta
t
i
on
P
e
rce
n
tage
(
p
m
) = 0
.3
Muta
tion Ra
te (
mu
)
=
0.
1
Popula
tion
S
i
ze
(
Pop
)
=
30
1
= 2
,
2
=
2.
1 a
nd
2
1
I
n
er
t
i
a
W
eig
h
t (
w
)
=
E
q
.
(
14)
Pe
rsona
l Lea
r
ning
C
o
e
f
f
i
c
i
e
n
t
(
1
c
) =
1
*
w
G
l
oba
l
L
e
a
r
ning
Coe
f
fic
i
e
n
t
(
2
c
)
=
2
*
w
5.
SIMU
L
A
TION
R
ESULT
S
AN
D
DIS
CUSS
ION
Th
e
i
m
pl
e
m
e
n
ta
t
i
on
c
ou
pl
i
n
g
b
e
t
w
een
L
FC
w
i
t
h
A
V
R
l
oop
s
fo
r
si
ng
le
a
re
a
pow
er
s
yste
m
and
P
I
D
con
t
ro
l
l
er
t
ha
t
sh
ow
n
at
F
igur
e
4,
t
he
L
F
C
w
ith
A
V
R
c
o
n
tr
ol
l
oo
ps
a
s
pr
esente
d
i
n
d
i
v
i
dua
lly
i
n
the pa
pers
[
1
8
,
19].
Table
3 gi
ves t
h
e
P
I
D
gain,
w
h
ich
i
s
s
et
i
n t
h
e
co
nve
n
t
i
ona
l (Z-
N
) me
t
h
o
d
.
Then,
for
enhanc
i
ng
the
term
inal
vol
ta
ge
a
nd
the
fre
quency
osci
llati
on
of
s
ingle
are
a
pow
er
s
ystem
,
the optim
al va
l
ue
s of P
I
D
controller
ar
e obt
a
i
ne
d by F
A
,
G
A
and
P
S
O
w
ith I
TA
E a
nd ITS
E
fi
t
ness functions,
the
I
T
A
E
t
ake
a
s
a
f
it
ne
ss
f
unc
t
i
on
to
obt
a
i
ne
d
the
opt
im
al
v
a
l
ues
of
P
I
D
c
ontroller
is
s
how
n
in
F
igure
5,
w
h
er
eas F
igure 6 show
s the
I
T
S
E
takes as
a
fi
tne
s
s function t
o
obtained t
h
e
optima
l
v
alue
s of P
ID
c
on
tr
o
ller
.
The
low
e
r
bound
of
P
ID
g
a
i
n
is
c
hosen
a
s
0
a
nd
the
uppe
r
bou
nd
is
c
hosen
a
s
3.
T
here
fore
,
the
opti
m
al
values
o
f the P
I
D
ga
i
n
s t
o
m
i
n
im
ize
t
h
e
I
T
A
E
a
nd ITS
E
a
re com
pu
t
e
d by
F
A
,
G
A
and P
S
O
, also
these values
of
P
ID
controller
are
given
at Ta
b
le 4.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
pplication of ar
tif
icial intell
igence
t
e
chnique
s for L
F
C
and
AVR syst
ems
…
(
G
hassan A
b
dullah
Salman)
1
699
F
i
gur
e 4.
MA
TLA
B/
si
m
u
la
tio
n
mode
l
o
f
L
FC w
it
h A
V
R
sys
tem
w
ith P
ID
c
ontro
l
le
r
Ta
b
l
e 3.
G
a
i
ns
o
f P
I
D
Con
t
ro
l
l
er
by Z-N
Metho
d
k
p1
k
i1
k
d1
k
p2
k
i2
k
d2
1.
6028
2
.
0254
1
.
3137
0
.
9523
0
.
3515
0
.
2018
F
i
gure
5.
MATLAB/
s
i
m
u
la
t
i
on
m
od
e
l
for
m
LF
C w
ith A
VR
s
ys
tem
ba
sed on
ITA
E
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
169
4
– 1
704
1
700
F
i
gure
6.
MATLAB
/
sim
u
la
t
i
on
mode
l
from
LF
C
w
ith A
VR sys
tem
ba
se
d on I
T
S
E
T
a
b
l
e 4.
O
ptima
l
gai
ns o
f P
I
D c
ont
r
o
ller
by
F
A
, G
A
and P
S
O
k
p1
k
i1
k
d1
k
p2
k
i2
k
d2
F
A
-ITA
E
2
.
9931
2.
9972
2.
486
2
2.
6
872
0
.
571
7
0
.
7283
FA
-I
T
S
E
2.
9850
2.
9916
2.
423
8
2.
8
715
0
.
582
1
0
.
7764
GA
-I
T
A
E
2.
6959
2.
9638
2.
235
9
2.
3
915
0
.
598
4
0
.
6293
G
A
-
IT
SE
2
.
6231
2.
4978
2.
350
9
2.
4
868
0
.
644
1
0
.
6637
PS
O-IT
AE
2
.
7789
2.
9868
2.
359
2
2.
5
751
0
.
580
3
0
.
6883
PSO
-I
T
S
E
2.
8192
2.
7951
2.
402
6
2.
7
821
0
.
620
2
0
.
7518
F
i
gure
s
7
a
nd
8
show
s
t
h
e
freque
ncy
deviation
r
e
sponse
t
o
a
djus
t
the
P
I
D
controll
e
r
by
F
A
,
G
A
and
P
S
O
on the basis of
I
TA
E and ITS
E
com
par
e
d
to the
c
onventional
(
Z
-N)
me
thod
,
w
h
i
l
e the char
acte
r
istics
of
the
fr
equenc
y
deviation
(m
aximum
-de
v
i
a
t
i
on,
p
eak-
t
im
e,
t
h
e
n
s
ett
l
i
ng-tim
e
and
fin
a
ly
s
t
e
ady-state-
err
o
r)
a
r
e
given a
t
Table
5 c
ompa
red
w
i
t
h
r
esults ar
e
pr
e
sented
i
n pape
rs
[1
8,
19].
F
i
gure
7.
F
reque
nc
y D
e
vi
a
t
io
n
and P
I
D
t
u
ni
ng us
i
n
g
F
A
, G
A
w
ith P
S
O
b
ased
o
n ITA
E
c
om
pare
d
w
ith
Z
-N
F
i
gur
e 8.
Repr
e
sen
t
fr
e
que
nc
y
dev
i
a
t
i
o
n an
d
P
I
D
t
uning us
i
ng F
A
,
GA
with P
S
O
b
ased
on ITSE
com
p
ar
ed wit
h
Z-
N
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
pplication of ar
tif
icial intell
igence
t
e
chnique
s for L
F
C
and
AVR syst
ems
…
(
G
hassan A
b
dullah
Salman)
1
701
Tab
l
e 5.
F
reque
ncy de
v
i
a
tio
n
char
acter
ist
i
cs a
nd P
I
D
t
u
ni
n
g
usi
ng Z-N
,
F
A, G
A
and P
S
O
M
d
(
p.
u)
t
p
(s
e
c
.
)
t
s
(se
c.)
E
ss
(
p.
u)
Z
-
N
-
8
.
5
9
7x1
0
–3
0.
9976
9
.
441
-3.
8
1
6
x
1
0
-
4
FA-
I
TA
E
-
6
.6
66
x
1
0
-3
0.
7040
8
.
726
-2.
6
2
7
x
1
0
-
4
FA
-ITS
E
-
6.
91
7x
1
0
-3
0.
6893
8
.
671
-2.
6
0
8
x
1
0
-
4
GA
-I
T
A
E
-7.19
4
x
1
0
-3
0.
7363
8
.
993
-2.
6
6
2
x
1
0
-
4
G
A
-
IT
SE
-
7.
18
6x
1
0
-3
0.
7239
9
.
012
-3.
1
5
1
x
1
0
-
4
P
S
O
-
IT
AE
-
6.
99
7x
1
0
-3
0.
7166
8
.
695
-2.
6
3
6
x
1
0
-
4
PS
O-ITS
E
-
7.
06
1x
1
0
-3
0.
6968
8
.
738
-2.
8
2
5
x
1
0
-
4
Re
f.
[
18]
-
7.
6x
10
-3
None
10.
42
N
one
Re
f.
[
19]
-
9.
3x
10
-3
None
9
.
5
N
one
F
i
gure
s
9
a
nd
10
show
s
t
h
e
term
inal
volt
a
ge
r
esponse
to
t
he
P
I
D
c
ontroller
a
d
j
u
stm
e
nt
by
F
A
,
G
A
and
P
S
O
based
o
n
I
TA
E
a
nd
ITS
E
c
om
par
e
d
w
ith
c
onventi
ona
l
(Z-N
)
m
ethod,
w
hile
t
he
c
ha
rac
t
e
r
isti
c
s
o
f
the te
rm
i
n
a
l
volt
a
ge (m
a
ximum
-
pe
ak, pea
k
-ti
m
e,
t
he
n
settli
ng-
t
i
m
e
and finaly
s
tea
dy-state-e
rror)
a
re given
i
n
Table
6 c
o
mpa
r
ed
w
i
t
h
results ar
e
pr
e
sented
i
n
pape
rs [18,
19].
F
i
gure
9.
Termina
l
V
ol
ta
ge
w
ith
P
I
D
tun
i
n
g
by F
A
,
G
A
a
n
d
PS
O ba
sed o
n
I
TA
E com
p
are
d
w
it
h
Z-
N
F
i
gure
1
0
.
Terminal
V
o
l
t
a
ge
w
it
h P
I
D
t
u
n
i
n
g
by
F
A
,
G
A
and
PS
O base
d o
n
I
TS
E
c
o
m
p
are
d
w
it
h Z-
N
Table 6.
T
e
rm
in
a
l
V
o
l
ta
g
e
C
h
a
r
acte
r
ist
i
cs
w
ith
P
ID
T
un
ing
by Z-
N
, F
A, GA
and P
S
O
M
p
(p
.
u
)
t
p
(s
e
c
.
)
t
s
(
sec
.
)
E
ss
(
p.
u)
Z
-
N
1.
029
1
.
625
1
.
933
5
.
3x10
–
3
FA
-
I
T
A
E
1.
013
0
.
7
849
1
.
422
-
1x
10
–
3
F
A
-ITS
E
1
.
015
0
.
7
679
1
.
383
0
G
A
-ITA
E
1
.
027
0
.
8
218
1
.
439
-
3x
10
–
3
GA
-I
T
S
E
1.
028
0
.
8
085
1
.
396
-
5x
10
–
3
P
S
O
-
IT
A
E
1
.
019
0
.
7
995
1
.
432
-
2x
10
–
3
PS
O-IT
SE
1
.
019
0
.
7
766
1
.
385
-
3x
10
–
3
Re
f.
[
18]
1
.
204
N
one
9
.
3
N
one
Re
f.
[
19]
1
.
0
N
one
4
.
9
N
one
F
i
gure
11
ill
ustra
t
es
t
he
c
onverge
n
ce
in
r
educ
ing
the
IT
A
E
i
nde
x
using
F
A
,
G
A
a
nd
P
S
O
t
o
deter
m
ine
t
h
e
opti
m
al
v
a
l
ue
s
for
a
P
I
D
c
o
ntroller
.
W
hi
le,
F
i
gur
e
12
illustra
tes
the
c
onverge
n
ce
i
n
r
educing
the
ITS
E
i
ndex
using
F
A
,
G
A
,
a
nd
P
S
O
to
d
eterm
i
ne
t
he
opt
im
al
v
alues
f
o
r
a
P
I
D
controller.
T
herefore;
these
conver
g
ence
cur
ves show
t
ha
t
F
A
h
as
b
e
t
t
e
r pe
rfor
ma
nce
th
an GA
and
PS
O.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
169
4
– 1
704
1
702
F
i
gur
e 1
1
.
Con
v
erge
nc
e
curve
of
F
A, GA
then P
SO
for
op
t
i
ma
l
ga
i
n
s for
PI
D w
ith m
ini
m
i
z
e
ITA
E
F
i
gure
1
2
.
Con
v
erge
nc
e
curve
of
F
A, GA
then P
SO
for
op
tim
al ga
i
ns
f
or
P
ID
w
ith m
i
n
im
iz
e
ITSE
In
a
ll
the
results
a
bove
,
th
e
ove
rall
c
h
ara
c
ter
i
stics
of
t
he
f
r
equenc
y
de
v
i
a
t
ion
and
t
h
e
ter
m
inal
volt
a
ge
a
r
e
r
educ
ed
by
F
A
,
G
A
a
nd
P
S
O
for
tuni
ng
of
t
he
P
ID
c
on
troller
w
h
e
n
c
om
p
a
red
w
ith
c
onventional
(Z-N
)
P
I
D
controller,
t
he
d
a
m
ping
char
acte
r
istics
of
s
ing
l
e
a
r
e
a
pow
e
r
s
yste
m
w
ith
t
uning
the
P
I
D
controller
by
F
A
a
re
i
mprove
d
mor
e
e
ffe
ctively
com
p
are
d
w
ith
G
A
and
P
S
O
.
A
lso,
s
tabilit
y
of
s
ingl
e
are
a
pow
e
r
syst
e
m
i
s
conser
ved a
nd re
duced
f
or
pow
er
s
yst
e
m
oscill
a
t
ions.
6.
CONCL
U
S
ION
Th
is
p
ape
r
s
t
u
die
d
t
he
P
ID
c
ontr
o
l
pe
rform
a
nc
e
tak
i
ng
t
h
e
c
o
u
p
l
i
n
g
e
f
f
e
c
t
b
e
t
w
e
e
n
L
F
C
a
n
d
A
V
R
,
a
t
f
i
r
st
u
si
ng
t
h
e
c
onv
e
n
ti
ona
l
PID
c
o
n
t
rolle
r
(
Z-
N)
m
et
ho
d
to
impr
ove
t
he
p
e
rform
anc
e
o
f
the
s
e
l
o
o
p
s,
a
nd
the
n
f
or
f
as
te
r
tune
o
f
P
I
D
c
o
n
t
r
o
ller
a
n
d
for
o
b
ta
i
n
t
he
r
e
s
ul
ts
m
or
e
a
ccur
a
te,
we
u
se
d
t
h
e
m
oder
n
in
t
e
l
l
i
g
e
n
ce
t
e
c
hn
i
que
s
suc
h
a
s
FA
,
G
A
and
P
S
O.
D
e
m
onstra
t
e
d
b
y
t
he
r
esul
ts
t
ha
t
w
e
re
obta
i
ne
d
an
d
com
p
are
d
b
e
t
w
een
t
he
t
hr
ee
t
ec
hn
iq
ues
m
e
nt
ione
d
pre
v
ious
l
y
,
o
b
s
erve
d
t
h
a
t
F
A
has
a
clea
r
p
r
o
g
res
s
ove
r
tha
n
G
A
a
nd
P
S
O
for
tun
i
n
g
t
he
P
ID
g
ains
t
o
en
hanc
e
d
t
he
ove
ral
l
c
h
ara
c
t
eris
tic
s
of
t
he
t
erm
i
na
l
v
o
l
t
a
g
e
an
d
fre
que
nc
y
osc
illa
ti
on f
o
r sin
g
l
e
a
r
ea pow
e
r
sys
tem
.
REFE
RENCES
[1]
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u
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f
r
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n
a
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“
Ef
f
ects
of
M
od
ern
Ampli
d
y
ne
V
o
l
ta
g
e
R
e
g
ula
t
o
r
i
n
Un
de
re
xc
ite
d
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pe
r
a
tion
o
f
Large Turbine
Generators,”
AI
E
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Tr
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F.
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D
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a
n
d
C
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Co
nco
r
dja,
“
C
o
n
cepts
o
f
Sy
nch
r
on
ou
s
Mac
hi
ne
S
tabi
li
ty
a
s
Af
f
ect
ed
by
Ex
cit
a
tio
n
Con
t
ro
l,
”
IEE
E
T
r
ans
.
,
P
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88
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[5]
E
.
Rakh
sh
an
i
,
K
.
Rou
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b
e
hi
a
nd
S
.
Sad
e
h,
“
A
New
Co
mbin
ed
M
o
d
e
l f
o
r
S
i
mu
lat
i
o
n
o
f
M
u
t
u
al Ef
f
ects
bet
w
een
L
F
C
and
AV
R
Loops,”
Pro
ceedi
ng
on
As
ia
-Paci
f
i
c
Po
wer a
n
d
En
erg
y
En
gi
neeri
n
g
Con
f
er
e
n
ce, (
A
PPE
E
C 2
0
0
9
)
,
W
u
han,
C
hi
na,
200
9.
[6]
B.
U.
M
usa,
B
.
M.
K
all
i
a
n
d
K
.
Shett
i
ma,
“Mo
d
e
l
i
ng
a
n
d
S
i
m
ul
at
io
n
of
L
F
C
a
n
d
A
V
R
w
it
h
P
I
D
Cont
rol
l
er,
”
Int
e
rna
t
i
o
n
a
l
Jou
r
n
a
l of
En
gi
neeri
n
g
Sci
e
nce In
venti
on
,
v
o
l
.
2
,
Iss
u
e 7
,
p
p.
5
4
-5
7,
J
ul
y 201
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[7]
S.
Saty
anaray
ana
,
R
.
K.
S
h
a
rm
a
an
d
Mu
k
t
a,
“
Mu
t
u
al
E
f
f
ect
b
et
w
e
e
n
L
F
C
a
n
d
A
V
R
L
o
o
p
s
i
n
P
o
w
e
r
P
l
a
n
t
,
”
El
ectri
cal
an
d
Elect
ro
nics
E
ngi
neer
in
g:
A
n
In
ter
nat
io
na
l Jo
ur
na
l
(
E
L
E
L
I
J)
,
v
o
l
.
3
,
no
.
1
,
pp
.
6
1
-69
,
F
eb
ruary
201
4.
[8]
M.
Naj
eeb
,
et
a
l
.,
“An
Opti
mal
L
F
C
in
T
wo
-Area
Po
wer
Systems
U
s
i
n
g
a
M
eta-h
e
uris
ti
c
Op
ti
m
i
zati
o
n
A
l
go
rit
h
m
,
”
Int
e
rna
t
i
o
n
a
l
Jou
r
n
a
l
of
El
ectri
cal
an
d
Comp
ut
er
E
n
g
i
neer
in
g
(
I
JE
CE
)
,
vo
l/issue
:
7
(6)
,
p
p.
3
2
1
7
-
32
2
5
,
20
17
.
[9]
B.
M.
H
u
s
sein,
“A
n
ew
s
cal
ed
f
uzzy
m
et
h
o
d
usi
n
g
PSO
s
eg
men
t
a
ti
on
(
S
e
P
S
O
)
ap
pli
e
d fo
r
t
w
o area
po
wer
s
y
s
t
em
,
”
Int
e
rna
t
i
o
n
a
l
Jou
r
n
a
l
of
El
ectri
cal
an
d
Comp
ut
er
E
n
g
i
neer
in
g
(
I
JE
CE
)
,
vo
l/issue
:
9
(2), p
p.
8
1
5
-
82
5,
2
0
1
9
.
[10]
K.
N
aid
u
,
H.
M
o
khl
is
a
and
A.
H
.
Bak
a
r,
“
Ap
pli
cati
o
n
of
F
iref
l
y
Algo
rith
m
(FA)
b
a
s
e
d
o
ptimiz
a
t
io
n
in
l
oa
d
f
r
equ
e
ncy
con
t
rol
f
o
r
in
tercon
nect
ed
r
eh
eat
t
herm
al
p
o
w
er
s
ys
te
m,”
IEE
E
Jo
rd
an
Con
f
eren
ce
o
n
A
p
p
lied
E
l
ectr
i
ca
l
En
gi
neeri
n
g
an
d
Co
mp
ut
ing
T
echn
o
l
o
g
i
es
(
A
EE
CT)
,
2
013
.
[11]
G.
K
o
n
ar,
K.
K
.
M
a
n
d
al
,
an
d
N.
C
hak
r
abo
r
t
y
,
“
T
w
o
A
rea
Lo
ad
F
re
q
u
e
nc
y
Co
ntro
l
Usin
g
GA
T
u
n
e
d
P
ID
Co
ntro
lle
r
i
n
De
re
gu
la
te
d
En
viron
m
e
n
t,”
P
r
o
ceedin
gs
o
f
t
h
e
Inter
n
a
t
i
ona
l M
u
lti
Con
f
eren
ce o
f
E
n
g
i
n
eers an
d
Co
mp
u
t
e
r
S
c
ie
ntists
20
14
,
vol
.
II,
I
ME
CS
2
0
1
4
,
M
arch
12
-
14
,
H
ong
Ko
n
g
,
2
01
4.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
pplication of ar
tif
icial intell
igence
t
e
chnique
s for L
F
C
and
AVR syst
ems
…
(
G
hassan A
b
dullah
Salman)
1
703
[12]
G.
A
.
S
a
lm
an,
“
A
ut
om
at
ic
G
en
eratio
n
Co
ntro
l
i
n
M
ul
ti
A
rea
Int
e
r
con
n
ected
P
ower
S
y
s
t
e
m
U
s
i
ng
P
I
D
Con
t
rol
l
er
Ba
se
d
on
G
A
a
n
d
PSO,”
Seco
nd E
ngi
neer
ing
Scien
t
i
f
i
c
Con
f
er
ence, Col
l
eg
e
o
f
En
gin
eeri
n
g
,
Un
iv
e
r
s
i
ty
o
f
Diya
la
,
pp
.
2
97-3
1
0
,
2
01
5.
[13]
Z.
L
.
G
a
in
g,
“
A
P
a
rti
c
le
S
warm
O
p
t
i
m
i
zati
on
A
p
p
r
oach
f
or
O
p
t
i
m
u
m
Des
i
gn
o
f
PID
Cont
rol
l
er
i
n
AVR
S
ys
tem
,
”
IEE
E
T
r
ans
act
i
o
n
s on
En
erg
y
Con
versi
on
,
vo
l.
1
9,
n
o
. 2
,
Ju
ne
2
00
4,
p
p
.
38
4
-
39
1.
[14]
N.
R
.
Raj
u
,
et
a
l.
,
“
R
ob
ust
n
es
s
St
ud
y
of
F
ract
ion
a
l
Ord
e
r
P
I
D
C
ont
rol
l
er
O
pt
im
ized
b
y
Part
icl
e
S
warm
O
p
t
i
m
i
z
a
t
io
n
in
A
VR
S
ys
te
m,
”
In
ter
n
a
tio
na
l Jou
r
n
a
l
o
f
E
l
ectr
i
ca
l an
d Com
p
u
t
er E
n
g
i
neer
in
g (
I
JECE)
,
vol
/issue:
6
(
5),
pp
.
20
33
-20
4
0
,
20
16
.
[15]
A
.
K
u
m
a
r
a
n
d
R
.
G
u
p
t
a
,
“
C
o
m
p
a
r
e
t
h
e
r
e
s
u
l
t
s
o
f
T
u
n
i
n
g
o
f
P
I
D
c
o
ntrolle
r
by
u
sin
g
PSO
a
n
d
GA
Te
c
h
niq
u
e
fo
r
AV
R
system
,”
In
ter
n
a
tio
na
l Jo
ur
nal
of
Ad
van
ced
R
e
sear
ch i
n
Co
mp
uter
En
gi
neeri
n
g
&
T
echno
lo
gy
(
I
JAR
C
ET
)
,
v
o
l.
2
, I
ssue
6
,
p
p
.2
13
0-2
1
3
8
,
J
un
e
20
13
.
[16]
S
.
A
.
H
a
sh
emi
Z
ad
eh
a
n
d
H
.
F
.
M
arj
,
“
T
h
e
a
n
aly
s
i
s
a
n
d
c
om
pari
so
n
o
f
P
S
O
and
BG
A
al
go
rit
h
m
s
f
or
d
esi
g
n
o
f
P
ID
c
o
ntrolle
r
in
A
utom
a
t
ic
V
olta
g
e
R
e
g
ula
t
io
n
(AVR)
sy
ste
m
,”
Ad
vances
in
Na
tu
ral
an
d Ap
pl
ied S
c
iences
,
8
(
11
)
Sp
e
c
i
a
l
2
0
1
4
,
pp
. 5
6-7
0
,
2
01
4.
[17]
N.
N
ayak,
S.
K
.
Rou
t
ray
an
d
S
.
P
radh
an,
“
O
pt
im
al
D
es
ig
n
o
f
P
ID
Co
nt
roll
er
f
or
A
V
R
i
n
a
m
u
l
t
i
Mach
in
e
Po
wer
S
y
s
t
em
u
si
ng
M
od
if
i
e
d
P
S
O
and
F
i
re
F
l
y
O
pt
im
izat
io
n
Techn
i
q
u
e,”
IEEE Po
we
r,
Co
mmun
ic
atio
n an
d
In
fo
rma
t
ion
T
echn
o
lo
gy Co
nf
erence
(
P
CIT
C
)
,
Siksha
‘
O’ An
u
sa
nd
ha
n
Un
ive
r
sity
,
Bh
ub
a
n
e
swa
r,
I
n
d
ia
,
20
15
.
[18]
A.
S
ou
nd
a
rra
ja
n,
S
.
Su
ma
thi
a
n
d
C.
S
undar,
“
Part
icle
S
w
a
rm
O
pt
i
m
i
zat
ion
Based
LF
C
and
A
V
R
o
f
A
ut
on
om
ou
s
Po
we
r
Ge
ne
r
a
ting
S
yste
m
,
”
IAE
N
G
In
tern
at
io
na
l
Jo
ur
nal
o
f
Co
mpu
t
er
Sci
e
nce
(
I
JCS)
,
37
:1
,
F
e
bru
a
ry
2
01
0.
[19]
A.
S
ou
nd
arrajan,
S
.
S
u
m
at
hi
a
nd
G
.
S
ivam
u
r
ug
an,
“
H
y
b
ri
d
Ev
ol
u
ti
on
ary
Al
go
rith
m
s
f
or
F
requ
ency
a
n
d
V
olt
a
ge
Con
t
rol
i
n
P
o
w
er G
enerati
n
g
,
”
ICTACT J
o
u
r
n
a
l
on
So
ft Comp
utin
g
,
Issu
e
:
0
2
Oc
to
be
r
2
0
1
0
,
pp
.88
-
97
.
[20]
A.
M
.
Ham
za,
M
.
S
.
S
aa
d
,
H
.
M
.
R
as
had
and
A
.
B
ah
gat
,
“
D
e
sig
n
o
f
L
F
C
a
n
d
A
V
R
f
or
S
in
gl
e
Area
P
o
w
e
r
S
y
s
t
em
wi
th
P
ID
C
o
n
t
r
oll
e
r
Tu
ni
ng
B
y
BF
O
and
Z
i
egl
e
r
M
e
th
od
s,
”
Inter
n
a
t
i
ona
l Jour
na
l o
f
Comp
ut
er
S
c
ien
ce
an
d
T
e
leco
mmu
ni
cati
on
s
,
vo
l.
4,
Is
su
e 5,
M
ay
2
01
3,
p
p.
1
2
-1
7.
[21]
N.
Y
.
Ko
ub
a,
M
.
M
e
naa,
M
.
H
a
sni
an
d
M
.
B
o
u
d
our,
“
O
p
t
i
m
a
l
C
o
n
t
r
o
l
of
F
requen
c
y
and
Vo
lt
age
Variat
io
ns
U
s
i
n
g
P
I
D
Co
nt
roll
er
B
ased
o
n
P
a
rt
icle
S
warm
O
pti
m
izat
ion
,
”
P
r
o
c
eed
in
gs
of
t
h
e 4
t
h
Int
e
rn
ati
o
n
a
l
Con
f
er
ence
o
n
Sys
t
ems
a
nd
Cont
ro
l
,
S
o
u
sse,
Tu
ni
sia,
A
p
r
il
2
8
-
30
,
20
15
.
[22]
G.
A
.
S
a
lm
an,
H.
I
.
H
u
s
s
ein
and
M.
S
.
Hasan
,
“
En
han
c
em
en
t
Th
e
D
yn
a
m
i
c
S
ta
b
i
li
ty
o
f
Th
e
I
r
a
q'
s
P
o
w
e
r
S
t
a
t
i
o
n
Us
in
g
P
I
D
Con
t
ro
ller
Op
ti
mi
zed
by
F
A
a
nd
P
S
O
B
as
ed
on
Di
f
f
eren
t
O
bj
ecti
v
e
F
u
nct
i
on
s,
”
El
ektr
o
teh
n
i
š
ki
Ves
t
n
i
k
,
vo
l.
85
,
Iss
ue
(
1
-
2),
pp.
42
-4
8,
2
0
1
8
.
[23]
S
.
D
as
,
A
.
Chak
rabo
rty,
J
.
K.
R
ay
,
S
.
Bhatt
acharjee
an
d
B
.
N
e
og
i
,
“
S
tu
dy
o
n
D
i
f
f
e
rent
T
un
ing
App
r
oach
w
it
h
Inco
rporat
io
n
of
S
i
m
u
l
at
io
n
A
s
p
ect
f
o
r
Z
-N
(
Z
i
egl
e
r-Ni
c
h
o
l
s
)
Ru
les,”
In
tern
at
io
nal
Jo
ur
nal
o
f
S
c
ien
t
i
fic an
d
Research Publ
ications
,
V
o
l
u
m
e
2
,
Iss
u
e
8,
A
ug
us
t
2
0
1
2
,
p
p
.
1
-5.
[24]
J.
G
.
Zi
egl
e
r
and
N.B.
N
ichols,
“
O
pt
im
um
S
e
t
ti
ng
s
for
A
u
tom
a
ti
c
C
ontroll
e
rs
,”
Tra
n
s. ASME
,
Vol.
6
4,
p
p
.
75
9-7
6
8
,
19
42
.
[25]
K.
O
gat
a
,
“
M
o
d
ern
Co
nt
rol
En
gi
neerin
g,
” P
r
e
n
ti
ce Hal
l
,
Upp
e
r S
a
d
d
le Ri
v
er,
New
Jersey,
19
97
.
[26]
X. S
.
Yan
g
, “
Natu
re-Ins
p
ired
M
etah
euri
sti
c
A
lgo
r
it
hm
s,
”
Lu
ni
ver
P
re
ss,
20
08
.
[27]
D.
R
erkp
reed
apo
n
g
,
A
.
Has
a
no
vi
c
and
A.
F
eli
achi
,
“
Rob
u
s
t
L
oad
F
r
e
q
u
e
n
c
y
C
o
n
t
r
o
l
U
s
i
n
g
G
e
n
e
t
i
c
A
l
g
o
r
i
t
h
m
s
and
Li
near M
at
ri
x Inequ
a
li
ti
es,”
I
E
E
E
Tran
sacti
o
n
s
o
n Po
wer S
y
s
t
e
ms
,
V
o
l
.
1
8,
N
o.
2,
p
p
.
85
5-86
1,
M
ay 2
00
3.
[28]
G.
A
.
Salman
,
M.
H
.
Ali
an
d
A.
N
.
Ab
du
llah
,
“
Im
pl
em
ent
a
tio
n
Opt
im
al
L
o
cati
on
and
S
i
zi
ng
o
f
UP
F
C
o
n
Iraq
i
Pow
e
r
Sys
t
em
G
rid
(132
k
V)
U
si
ng
G
eneti
c
A
l
g
or
i
t
hm
,
”
I
n
te
r
n
a
t
i
o
na
l
J
o
u
r
na
l o
f
Po
w
e
r
E
l
e
c
tr
on
ic
s
an
d
D
r
i
v
e
Sys
t
em (
I
J
P
ED
S)
,
vo
l/i
ss
ue:
9(4
)
,
p
p.
1
60
7-1
615
,
2
0
1
8
.
[29]
I.
A
zi
m
an
d
F
.
R
ahm
a
n,
“
G
e
neti
c
Alg
o
ri
th
m
Bas
e
d
Reactiv
e
P
o
wer
M
a
nag
e
m
e
nt
b
y
S
V
C,
”
Int
e
rn
at
ion
a
l
Jour
na
l
of
El
ectr
i
cal
a
nd
Comp
ut
er E
n
g
i
n
e
e
r
in
g (
I
JE
CE)
,
vol
/i
ss
ue:
4(2
)
,
pp
.
2
0
0
-
206
,
2
0
1
4
.
[30]
J.
K
e
n
ned
y
a
nd
R
.
E
b
erhart
,
“
P
a
r
t
i
cl
e
S
w
arm
O
p
ti
m
i
zati
o
n
,
”
Pro
ceedi
n
g
o
f
th
e IE
EE
In
tern
at
io
nal
Co
nf
eren
ce o
n
Neur
al Networ
ks,
v
ol.
I
V
,
pp
.19
4
2
-
19
4
8
,
19
95
.
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