Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 1, No. 2,
February 20
1
6
, pp. 255 ~
263
DOI: 10.115
9
1
/ijeecs.v1i2.
pp25
5-2
6
3
255
Re
cei
v
ed O
c
t
ober 1
1
, 201
5; Revi
se
d Ja
nuar
y 8, 201
6
;
Accepte
d
Ja
nuary 23, 20
1
6
Tuning of PID Controller for Load Frequency Control
Problem via H
a
rmony Search
Algorithm
M. Omar*, M. A. Ebrahim,
A. M. abdelG
han
y
, F. Bendar
y
F
a
cult
y
of Engi
neer
ing at Sh
o
ubra, Un
iversi
t
y
of Ben
ha, Sh
oubr
a, Cairo 1
08, Eg
ypt
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: engma
h
mou
domar
_10
@
y
a
hoo.com
A
b
st
r
a
ct
In this
pa
per,
a n
e
w
artifici
al
inte
lli
genc
e te
chni
que,
Har
m
ony S
earch
(H
S), w
ill b
e
us
e
d
for th
e
opti
m
i
z
at
ion
of a classic
a
l o
r
der PID for a tw
o-
area lo
ad freq
uency
control (LF
C
)
mo
de
l usi
ng t
h
e
partici
patio
n fa
ctor conce
p
t. T
he HS
has f
our
ma
in v
a
ri
ants, these v
a
riants h
ad
be
en us
ed for
th
e
o
p
t
im
i
z
a
t
i
o
n o
f
cl
a
ssi
ca
l
o
r
d
e
r
PID
co
n
t
rol
l
e
rs i
n
ca
se
o
f
cen
t
ra
l
i
z
e
d
co
n
t
ro
l
schem
e
,
th
e re
su
l
t
s
h
a
d
b
een
compar
ed to
s
e
lect
and
rec
o
mme
n
d
the
be
st HS var
i
ant.
T
hen, this
b
e
st HS v
a
ria
n
t h
a
d
b
een
us
ed
fo
r the
tunin
g
of PID control
l
ers in ca
se of dece
n
trali
z
e
d
sche
m
e.
Ke
y
w
ords
: loa
d
freque
ncy co
ntrol, har
mo
ny search, fitness
function
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 p
r
o
b
lem
of LFC is con
s
ide
r
ed
a
s
o
n
e
of the
main
and
mo
st im
portant to
pics in the
power
syste
m
. The mai
n
purp
o
se of L
F
C i
s
to
mai
n
tain the
syste
m
frequ
en
cy
of each a
r
ea
and
the inter-are
a
tie line powe
r
within tole
ra
ble limit
s. Thi
s
impo
rtant functio
n
is aut
hori
z
ed to LF
C
due to
the
fact that a
reli
abl
e po
we
r
syst
em
sho
u
ld m
a
intain volta
g
e an
d frequ
e
n
cy at
sch
e
d
u
led
rang
e while p
r
oviding
an
a
c
ceptabl
e lev
e
l of po
we
r
quality [1]. Us
ually LFC is
c
l
ass
i
fied to three
levels:
a)
Primary
cont
rol: is do
ne b
y
governo
rs
of the gen
era
t
ors,
whi
c
h p
r
ovide imm
e
d
i
ate
action to sud
den chan
ge o
f
load.
b)
Secon
d
a
r
y control:
ke
ep
s freq
uen
cy at
its
nomin
al v
a
lue
by adj
usting the
outp
u
t of
s
e
lec
t
e
d
ge
ne
r
a
tor
s
(
c
on
tro
lle
r
is
ne
e
ded
)
.
c)
Tertiary
co
ntrol: is a
n
e
c
o
nomic di
spat
ch th
at is
used to o
p
e
r
at
e the
system
as
eco
nomi
c
ally
as po
ssible
[2]. Several
co
ntrol
tech
nique
s
had
been
ap
plied
to LF
C
pro
b
lem
durin
g th
e p
a
st yea
r
s, which
ha
s gre
a
tly improve
d
the
re
spo
n
se of
po
wer
system to
a l
a
rge
extent. A ro
bust
LFC u
s
i
ng LMI
co
ntrol techniqu
e
for
singl
e a
r
ea
po
we
r system ha
s
b
een
desi
gne
d in [3]. The disa
dvantage of
this metho
d
rep
r
e
s
ent
s in
the compl
e
xity of controll
er
desi
gn and i
m
pleme
n
tatio
n
, which in tu
rn makes the
process very
complex esp
e
cially for large
scale inte
rco
nne
cted po
wer sy
stem
s. In [4] LF
C
with fuzzy logic
controller (FLC) including
nonlin
earitie
s and
b
o
iler dy
namics is introdu
ced
wh
ich ha
s greatly
improve
d
the
perfo
rman
ce
of
the controller.
In [5] another techni
que h
ad been
sug
geste
d for tuning the pa
ra
meters of a PID
controlle
r for
LFC in
a
sin
g
le a
r
ea
po
wer
system
by
usi
ng
pa
rticl
e
swa
r
m
opti
m
ization
(PS
O
).
Ant Colony
Optimiz
a
tion
(ACO) [2] also used in
thi
s
field for th
e purpo
se of
tuning of a
PID
para
m
eters f
o
r
singl
e a
r
ea
with
reh
eat t
herm
a
l mo
del
incl
uding
no
nlinea
rities. B
a
cteri
a
F
o
ra
gi
ng
Optimizatio
n
(BFO) te
ch
nique ha
s be
e
n
applie
d to a two area
system with di
fferent step l
oad
cha
nge
s in [6]. The pap
er is o
r
gani
zed as follo
ws: a brief de
scription fo
r HS variant
s is
illustrate
d in
Section 2. S
e
ction
3 will
focu
s on the
modellin
g of
the pro
p
o
s
e
d
LFC
model
. In
Section 4, a
brief di
scussi
on of cla
s
sica
l orde
r PI
D
wi
ll be intro
d
u
c
ed. This
se
cti
on contain
s
a
l
so
the fitness fu
nction a
nd d
e
sig
n
criteria
to be us
e
d
i
n
the optimization process. Simulation and
results obtai
n
ed after the appli
c
ation of
PID C
ontroll
er had be
en
introdu
ce
d in
section 5. T
h
e
main co
ncl
u
si
ons a
r
e d
r
ive
n
in se
ction 6
.
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ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 255 – 263
256
2. Harmon
y
Search Alg
o
r
ithm
HS was pro
posed by Z
o
ng
Woo
Gee
m
in 20
01 [
7
]. It is well
kno
w
n
that
HS is a
phen
omen
on
-mimickin
g
al
gorithm in
spi
r
ed by the i
m
provi
s
ation
pro
c
e
ss
of musi
cian
s. In this
se
ction, a
b
r
ief review o
f
HS al
gorit
hm a
nd it
s
variants i
s
g
i
ven. The
a
nalogy
between
improvi
s
ation
and optimiza
t
ion is likely a
s
follows [2]:
1) Each musi
cian
corre
s
p
o
nds to ea
ch d
e
ci
sion vari
ab
le.
2) Mu
sical instrument’
s
pitch rang
e co
rre
s
po
nd
s to the deci
s
ion vari
able’
s value range.
3) Mu
sical h
a
rmo
n
y at a certain time
corr
e
s
pon
ds to the solution vector at
certain
iteration.
4) Audi
en
ce’
s
ae
stheti
c
s
corre
s
p
ond
s
to the obj
ect
i
ve function
to be mini
mi
zed
or
maximized.
In this se
ction
,
a brief revie
w
of HS algo
rithm and its variant
s is give
n.
2.1. The Basi
c Harmony
Search
Algori
t
hm
Before the
di
scussion of
the
HS al
gorit
hm, th
is secti
on
will identify
the mai
n
parameters
of the algorith
m
as follows:
HM: ha
rmo
n
y
memory, it is the
soluti
on matrix, e
a
ch
ro
w in t
he HM re
pre
s
ent
s a
s
o
lution vec
t
or.
HMS: harm
o
ny memory size, it represents t
he num
ber of availa
ble sol
u
tion vectors in
the harm
ony memory (nu
m
ber of rows).
HMCR: ha
rm
ony memo
ry con
s
id
eratio
n rate
, it is
a numb
e
r
which
determi
nes th
e
probability of selecting
a
solution from the existing HM
solutions.
PAR: pitch adjustment rat
e
, it is a num
ber
whi
c
h determines the probability of adjusting
the sele
cted
solutio
n
withi
n
a cert
ain ra
nge.
BW: band
width, the available ra
nge of
adju
s
ting
the sele
cted solut
i
on.
In the ba
sic
HS algo
rithm
each sol
u
tio
n
is
called
a
harm
ony and
rep
r
e
s
ente
d
by an n-
dimen
s
ion re
al vector. An initial population of
harmony vectors is ran
doml
y
generate
d
and
store
d
in
a
h
a
rmo
n
y mem
o
ry (HM
)
. Th
en a
ne
w
can
d
idate h
a
rm
o
n
y is g
ene
rat
ed fro
m
all
of the
solutio
n
s i
n
th
e HM
by usi
n
g a mem
o
ry
consi
der
ation
rule, a pitch a
d
justme
nt rul
e
and
a rand
om
re-i
nitializatio
n. Finally, the HM is u
p
d
a
ted
by com
parin
g the ne
w ca
ndid
a
te harm
ony and
the
worst ha
rmo
n
y vector in
the HM. The
above pr
ocess is
repe
ated until a
ce
rtain termi
nat
ion
crite
r
ion i
s
m
e
t. The ba
sic HS algo
rith
m con
s
i
s
ts
of
three b
a
si
c
pha
se
s, nam
ely, initialization,
improvi
s
ation
of a harmo
ny vector a
n
d
upd
ati
ng t
he HM [8].
The st
eps
of the sol
u
tion
are
illustrated in the flow chart
gi
ven in Figure 1 as follows:
Step 1: initialize the HS pa
rameters.
Step 2: gene
rate ran
dom
vectors (X1,
…., XH
MS) as many as HMS then store them in
HM in matrix
form, and eva
l
uate the fitness
fun
c
tion
co
rre
sp
ondi
ng to each sol
u
tion vector:
Step 3: Improvise a new harmony from the HM with
probability HMCR
(0
≤
HMC
R
≤
1),
pick the
sto
r
e
d
value from
HM, after th
a
t, and with
probability of P
A
R (0
≤
PA
R
≤
1)
, a
d
j
us
t th
e
sele
cted
solut
i
on with the b
and wi
dth value acco
rdin
g to the followin
g
relation:
Xi’=
Xi’ +
rand* BW
(1)
Step 4: If Xi'
is better than
the worst vector
X wors
t in HM, replace Xwors
t
with Xi'.
Step 5:
Rep
eat from
Ste
p
2
to Step
4
until termination
criterion
(e.g.
maximum
iterations) i
s
satisfied.
2.2. The Improv
ed Harmon
y
Search (IHS)
The IHS
algo
rithm ad
dresse
s the
sh
ort
c
omin
gs
of the ba
si
c HS
algorith
m
whi
c
h u
s
e
s
fixed values
for PAR a
n
d
BW p
a
ram
e
ters [4]. Th
e
IHS algo
rith
m appli
e
s th
e sa
me m
e
mory
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Tuning of PID Controll
er for Load Frequ
e
n
cy Co
ntrol P
r
oblem
via
Harm
ony Sea
r
ch…
(M.Om
a
r)
257
con
s
id
eratio
n
,
pitch adju
s
tment and
rando
m
se
lection a
s
the ba
sic
HS algorithm,
but
dynamically update
s
value
s
of PAR and
BW as sho
w
n belo
w
:
PA
R
i
P
A
R
∗i
(
2
)
BW
i
B
W
∗e
∗
(
3
)
Figure 1. Optimization p
r
o
c
edure of the Harmony Sea
r
ch al
go
rithm
In Equation
(2), PAR (i
) i
s
the
pitch a
d
just
me
nt rate in
gen
erati
on i, PARmi
n is the
minimum a
d
j
u
stment
rate,
PARmax is t
he maximum
adju
s
tment ra
te. In Equation (3
), BW (i
)
is
the distan
ce
band
width in
generation i, BW
min and
BWmax are
the minimu
m and maxi
mum
band
width
s
, resp
ectively.
2.3. Global Best Harmon
y
Search (G
HS)
Inspired by th
e parti
cle
swarm o
p
timizat
i
on [5
], a GHS algorithm t
hat modifie
s
the pitch
adju
s
tment rule ha
s
bee
n propo
se
d [6]. Unlike th
e ba
sic HS
algorith
m
, the G
H
S algo
rithm
gene
rate
s a
n
e
w
harmony
vector XB
= {
x
B(1), xB(2
),…., xB(n)
} in
the
HM. Th
e
pitch
adju
s
tm
ent
rule is give
n as bel
ow [11]
:
X
j
X
k
j
1,2,
…
n
(
4
)
Whe
r
e
k is a
rand
om inte
ger b
e
twe
en
1 and n. In
addition, the
GHS alg
o
rith
m employs t
he
dynamic up
d
a
ting p
r
o
c
ed
u
r
e fo
r the
PAR p
a
ra
meter,
Equation
(4
).
It is cl
aimed
that the m
odifi
ed
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ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 255 – 263
258
pitch adju
s
tm
ent allows the GHS algo
ri
thm to
work
more effici
en
tly on both continuo
us an
d
discrete p
r
ob
lems. The ad
vantage of this algo
rith
m is that it selects the glob
a
l
best solutio
n
every gene
rat
i
on as it is wit
hout any adju
s
tment to the values of the
variable
s
.
2.4. Self Adaptiv
e
GHS (SGHS)
An extensio
n
of the GHS al
gorithm, a
sel
f
-
adaptive G
H
S (SG
H
S) a
l
gorithm i
s
p
r
ese
n
ted
in this
section. Unli
ke the GHS
algorithm,
the SG
HS algorith
m
employs a
n
e
w im
provi
s
a
t
ion
scheme
an
d
an ad
aptive p
a
ram
e
ter tu
ni
ng meth
od.
T
he G
H
S alg
o
r
ithm takes a
d
vantage
of the
best h
a
rm
ony
vector XB to
prod
uce a n
e
w
vecto
r
Xne
w
. Ho
weve
r, the modifie
d
p
i
tch adj
ustme
n
t
rule m
a
y bre
a
k the
buildi
n
g structu
r
e
s
i
n
XB, so that
Xnew
may b
e
com
e
worse
than Xb
with
a
high proba
bili
ty when solvi
ng pro
b
lem
s
with a gl
ob
al optimum havi
ng different n
u
meri
cal valu
es
for differe
nt d
i
mensi
o
n
s
. T
herefo
r
e, to b
e
tter inhe
rit g
ood info
rmati
on from XB,
a modified
pitch
adju
s
ting rul
e
is pre
s
ente
d
belo
w
:
1
,2,
…
(
5
)
It should b
e
noted that, according to
the modi
fie
d
pitch a
d
ju
stment rule
xnew(j
),is
assign
ed to the corre
s
p
o
nding de
ci
sio
n
variable x
B
(j) in XB,
while in the
GHS algo
rith
m,
xnew(j
) i
s
det
ermin
ed
rand
omly by sel
e
cting
a
m
ong
st any one
of the de
cisi
on
variable
s
of
XB
[9].
In addition, in
the memo
ry con
s
id
eratio
n
pha
se
, the e
quation in
G
H
S is repla
c
e
d
by Eq.
(6) in o
r
de
r to
avoid getting
trapped in a l
o
cally optimal
solution.
∗
B
W
(
6
)
In the SGHS algorith
m
, four cont
rol pa
ra
meters HMS,
HMCR, PAR and BW are clo
s
ely
related
to the
pro
b
lem b
e
i
ng solved a
n
d
the p
has
e
of the search
pro
c
e
s
s that
may be eith
er
exploratio
n o
r
exploitation.
These fou
r
types
of
HS a
r
e the mo
st p
opula
r
an
d
commonly u
s
e
d
in
the
different optimizatio
n probl
em
s, al
so, there a
r
e
o
t
her type
s
not
listed
he
re,
h
ad b
een
worke
d
out by rese
arche
r
s, all the
s
e types d
eal
with the para
m
eters settin
g
and form
ula
t
ion.
3. Modeling of Sy
stem u
nder Study
Figure 2..Two
area po
we
r system model
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Tuning of PID Controll
er for Load Frequ
e
n
cy Co
ntrol P
r
oblem
via
Harm
ony Sea
r
ch…
(M.Om
a
r)
259
The sy
stem i
n
vestigatio
n is carried o
u
t on an inte
rco
nne
cted
com
b
ined p
o
wer
system
as
sho
w
n i
n
Figure 2 [10].
The mo
del i
s
about 2
ar
ea
symmetri
c
al
model a
s
sh
o
w
n in th
e figu
re;
every area
consi
s
ts
of three ty
pes of
plants, the
r
m
a
l with
reh
e
a
t, hydro an
d
gas
plant. T
he
sha
r
ing
facto
r
s are 0.6,
0.3 an
d 0.1
re
spe
c
tively
. T
he p
h
ysi
c
al
meanin
g
of
the va
rian
ce
of the
sha
r
ing
facto
r
s i
s
th
at, the
steam
pla
n
t
in ge
neral h
a
s
g
r
eate
r
rati
ng rathe
r
tha
n
the
other two
types, so it
must work a
s
ba
se u
n
it with gr
eate
r
sha
r
ing fa
cto
r
for o
peratio
nal and
econ
omic
crite
r
ia. In co
ntrast, the
ga
s pla
n
t usuall
y
operate
s
a
s
pea
king
unit
due to the
hi
gh ru
nnin
g
cost
for thi
s
type
of gen
eratio
n
station
s
. In
this p
ape
r
we p
r
opo
se
d t
o
in
sert
the
boiler dyna
mi
cs
model to th
e
thermal
plan
ts to ma
ke t
he mo
del mo
re reali
s
tic. T
he Boile
r dyn
a
mics mo
del
is
sho
w
n in Fig
u
re 3 [11].
Figure 3. Boiler Dyna
mics
model
4. Classical
Order PID
In this
section, a brief
discussi
on
of both
the classical order
PI
D cont
rollers
will be
introdu
ce
d.Also, the obje
c
tive functio
n
and de
sig
n
crite
r
ia u
s
ed in this re
sea
r
ch wo
rk will
illustrate
d. Th
e PID cont
rol
is a wid
e
ly used a
p
p
r
oa
ch for de
signi
ng a sim
p
le feedb
ack cont
rol
system [12]. It has the sim
p
le co
nstructi
on given in Equation (7).
()
/
pi
d
ks
k
k
s
k
s
(
7
)
Whe
r
e
kp, ki
and kd are
proportio
nal, integral a
nd de
rivative gains
respe
c
tively. The fun
c
tion
o
f
each part of a PID controlle
r can be d
e
scribed a
s
fo
llo
ws, the pro
p
o
r
tional pa
rt re
duces the error
respon
se
s
of
the sy
stem to
distu
r
ba
nces, the integ
r
al
part
eliminate
s
the
ste
ady-state e
r
ror,
a
nd
finally the derivative part d
a
mpen
s
the d
y
namic re
spo
n
se and
im
prov
es the
syst
em stability [1
3].
The input to the controller is the area
control er
ro
r (ACE), an
d the output is
u(s) a
s
sho
w
n in
Equation (8).
()
()
*
A
CE
us
k
s
(8)
These gain
s
have bee
n minimize
d su
bje
c
ted to the followin
g
inequ
a
lities:
mi
n
m
a
x
ii
i
kk
k
mi
n
m
a
x
dd
d
kk
k
mi
n
m
a
x
pp
p
kk
k
Whe
r
e
max
a
nd mi
n refers to the
pe
rmi
ssi
ble
upp
er
and l
o
wer val
ues for ea
ch
gain. In
additi
on
,
the cont
rolle
r has b
een o
p
timized a
c
co
rd
ing to the followin
g
fitness function:
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260
j
i
i
p
f
t
J
ij
tie
i
,...,
3
,
2
,
1
0
(9)
5. Simulation and Re
sults
In this pape
r the re
sea
r
ch
work ha
s be
e
n
orga
nized a
s
follows:
a)
The cl
assi
cal
PID cont
rolle
r had
bee
n tuned
wi
th the four m
entione
d HS varia
n
ts in
ca
se
of cent
ralize
d
control
(a controller for
ea
ch are
a
)
(2 co
ntrolle
rs) schem
e
a
nd
the
b
e
st HS
variant had b
een sele
cted
to complete t
he re
sea
r
ch
work with thi
s
one.
b)
With the
be
st HS vari
ant, PID controlle
rs ha
d b
een
tuned
for
ea
ch
plant in
e
a
ch
area
(6
controllers) to a
c
hi
ev the con
c
e
p
t of dec
e
n
tralize
d
co
ntrol
sch
eme. Th
en, a com
p
a
r
ison
betwe
en the
centralized a
nd de
ce
ntrali
zed
schem
es had b
een
do
ne to sele
ct and recomm
en
d
the best on
e for the control
appli
c
ation
s
.
5.1. Centralized PID Tuni
ng
v
i
a all HS Variants
In this se
ctio
n, 2 PID cont
rolle
rs
(on
e
for ea
ch a
r
e
a
) had be
en tu
ned with th
e previou
s
ly
mentioned fitness
func
tion for the four type
s of
HS alg
o
rithm
via MATLA
B
softwa
r
e.
The
resulted
valu
es of controll
er gain
s
had
bee
n
li
st
ed i
n
Ta
ble
1. T
he
re
spon
se
of the
syste
m
in
ca
se
of ap
plying the
p
r
op
o
s
ed
techniq
u
e
PID
contro
llers ha
d
bee
n comp
are
d
with a
nothe
r
PID
tuned via BFO algotithm a
s
given in [10
]
for
the same
model exclu
d
ing the boil
e
r dynami
cs.
Table 1. Valu
es of PID gai
ns for
centrali
zed
control
The sy
stem had be
en te
sted for 1%
load in
cre
m
e
n
t in area 1.
Maximum o
v
ersh
oot
(%Mp), pe
ak
time (tp) and
settling time (ts) had
been
recorded in T
able 2.
Table 2. System perfo
rma
n
ce eval
uatio
n for all varia
n
ts
The freq
uen
cy deviation and tie line po
wer
re
spo
n
se
s are
sho
w
n i
n
Figure 4-6.
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Tuning of PID Controll
er for Load Frequ
e
n
cy Co
ntrol P
r
oblem
via
Harm
ony Sea
r
ch…
(M.Om
a
r)
261
Figure 4. Fre
quen
cy devia
tion respon
se
in
area 1 fo
r all variants
Figure 5. Fre
quen
cy devia
tion respon
se
in
area 2 fo
r all variants
Figure 6. Tie line po
wer d
e
v
iation respo
n
se for
all variants
From the p
r
e
v
ious figures
and result
s li
sted in
Ta
ble
1, it is shown that all HS variants
based PID controlle
rs hav
e better effect than BFO
base
d
PID in spite of existi
ng of the boli
e
r
dynamics. It is al
so
clea
r
that the SGHS base
d
PID is the m
o
st
effective one
among
all HS
types, so this
type will be re
comm
end
ed for the next st
age (De
c
ent
ralize
d
Co
ntrol
)
.
5.2. Decen
tr
alized PID T
uning
v
i
a SG
HS Variant
In this se
ctio
n, 6 PID con
t
rollers (one f
o
r ea
ch pl
ant
) had b
een t
uned
with th
e sam
e
fitness fu
ncti
on to a
c
hieve
the co
ncept
of decentra
lized control. In this case, th
e co
ntrolle
rs
had
been
tune
d
with the
be
st
HS va
riant
resulted
abo
ve (SG
H
S).
Re
sults from
ce
ntrali
zed
and
decentrali
ze
d
co
ntrol
sch
e
m
es ha
d b
e
e
n
comp
are
d
t
o
evalu
a
te a
nd
re
comme
nd the
be
st a
nd
most a
ppli
c
a
b
le sch
e
me i
n
the
control
appli
c
at
ion
s
.
The valu
es
o
f
controllers’
gain
s
ha
d be
en
listed in Tabl
e 3.
Table 3. Valu
es of PID gai
ns for d
e
ce
ntralize
d
co
ntrol
.
0
1
2
3
4
5
6
7
8
9
10
-2
.
5
-2
-1
.
5
-1
-0
.
5
0
0.
5
x 10
-3
ti
m
e
(s
ec
)
P
ti
e
HS
IH
S
GH
S
SGH
S
BF
O
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IJEECS
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6 : 255 – 263
262
The sy
stem
had be
en te
sted for th
e
same l
oad d
i
sturb
a
n
c
e v
a
lue 1% in
area
1.
Maximum overshoot (%M
p
), pea
k time (tp) and se
ttl
ing time (ts)
had bee
n re
corde
d
in Tabl
e 4
for both centralize
d
and d
e
c
entralized S
G
HS ba
sed
controlle
rs.
Table 4. System perfo
rma
n
ce eval
uatio
n
for ce
ntrali
zed and d
e
cen
t
ralize
d
sche
mes
The freq
uen
cy deviation and tie line po
wer
re
spo
n
se
s are
sho
w
n i
n
Figure 7-9.
Figure 7. Fre
quen
cy devia
tion respon
se
in area 1
Figure 8. Fre
quen
cy devia
tion respon
se
in area 2
Figure 9. Tie line po
wer d
e
v
iation respo
n
se
0
1
2
3
4
5
6
7
8
9
10
-10
-8
-6
-4
-2
0
2
x 10
-3
ti
m
e
(
s
ec
)
f
1
(H
Z
)
C
e
n
t
r
a
liz
e
d
D
e
c
e
n
t
r
a
l
i
zed
0
1
2
3
4
5
6
7
8
9
10
-6
-5
-4
-3
-2
-1
0
1
x 1
0
-3
ti
m
e
(s
ec
)
f
2
(H
Z
)
C
e
n
t
r
a
liz
e
d
D
e
c
e
n
t
r
a
liz
e
d
0
2
4
6
8
10
12
14
16
18
20
-1
4
-1
2
-1
0
-8
-6
-4
-2
0
2
x 10
-4
ti
m
e
(s
e
c
)
P
ti
e
C
e
n
t
r
a
l
i
zed
D
e
c
e
n
t
r
a
l
i
zed
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IJEECS
ISSN:
2502-4
752
Tuning of PID Controll
er for Load Frequ
e
n
cy Co
ntrol P
r
oblem
via
Harm
ony Sea
r
ch…
(M.Om
a
r)
263
From the
pre
v
ious figu
re
s
and results listed in
Table
4
,
it is sho
w
n t
hat the de
cen
t
ralize
d
control sche
me is better
than the cent
ralized on
e. From the pra
c
tical
side, the decentrali
zed
control i
s
mo
re a
ppli
c
able
and
widely u
s
ed
be
cau
s
e
it is not lo
gic
in re
alisti
c m
odel to
give the
same
control
signal to all the plants in the same a
r
e
a
(ce
n
trali
z
e
d
sch
eme
)
a
nd force all the
plants in thi
s
area to respo
nd with the same value an
d profile.
6. Conclusio
n
In this pape
r a new a
r
tifici
al intelligen
ce optimizatio
n techni
que (HS) ha
d bee
n applied
for the
tunin
g
of
cla
ssi
cal
PID orde
r
co
ntrolle
r in
ca
se
of
centrali
zed
an
d d
e
centrali
zed
co
ntrol
scheme
s
. T
h
e re
sult
s h
a
d
prove
n
the
e
ffectiveness
of this
optimi
z
ation
techni
que in
tunin
g
this
type of
contro
llers for thi
s
model. It al
so
proved
th
e
wellne
s
s of d
e
c
entralized
control
sch
e
m
e
in
comp
ari
s
o
n
with the ce
ntralize
d
one.
Referen
ces
[1]
M Soro
ush, M
Ali, S M
o
h
a
mmad, A Mo
h
a
mmad.
T
unin
g
of PID
Co
ntroller
for Mu
lti
Area
Lo
a
d
F
r
eque
nc
y C
o
ntrol
b
y
Usi
n
g
Imper
ia
list C
o
m
petitive
Alg
o
rit
h
m.
Jour
nal
of Basic and
Ap
pl
ied Scie
ntific
Research
. 20
1
2
: 2090-
43
04.
[2]
M Omar, M Solimn, AM Ab
de
l gh
an
y, F
Be
n
dar
y
.
Optimal t
uni
ng
of PID control
l
ers for
h
y
dr
otherm
a
l
loa
d
frequ
enc
y control usi
ng
ant colo
n
y
opti
m
izatio
n.
Internatio
nal j
our
na
l on el
ectrical
eng
ine
e
ri
n
g
and i
n
for
m
atics
. 2013; 5(3): 34
8-35
6.
[3]
A Bensen
ouci,
AM Abdel Ghan
y. Perform
anc
e An
al
ysis
and Comp
ar
ative Stud
y
of
LMI-Based
Iterative PID L
oad-F
r
e
que
nc
y Contro
llers
of a Sin
g
le-Ar
e
a
Po
w
e
r S
y
ste
m
.
WSEAS Tr
ansactions o
n
power system
s
.
2010; 2(5).
[4]
A Kumar, A Ahmad, A Grov
er, U Gupta. Load F
r
eq
ue
nc
y Control Us
in
g
F
u
zz
y
Lo
gic,
Internatio
na
l.
Journ
a
l of Scie
ntific and R
e
se
arch Pub
licati
o
ns
. 2012; 2(
7): 225
0-31
53.
[5]
MA Ebrahim,
HE Mostafa, S
A
Ga
w
i
sh, FM
Be
n
dar
y. D
e
si
gn of
dec
entral
i
zed
lo
ad fre
q
u
enc
y B
a
sed-
PID Control
l
er
using Stoc
ha
stic Part
icle S
w
a
rm optim
iza
t
ion tech
niq
ue.
Electric Pow
e
r and En
ergy
Conv
ersio
n
Systems
. 20
09.
[6]
E Salim A
li SM
, Abd-Elaz
im.
Optima
l PID T
uni
ng for
Lo
ad
F
r
eque
ncy C
o
ntrol Us
ing
Bac
t
eria F
o
ra
gi
ng
Optim
i
z
a
t
i
on Algorithm
. Proc
e
edi
ngs
of the
1
4
th Intern
atio
n
a
l Mi
ddl
e E
a
st Po
w
e
r S
y
st
ems Conf
erenc
e
(MEPCON’
1
0
).
Cairo U
n
ivers
i
t
y
, Eg
ypt. 201
0
.
[7]
Z
W
Geem, et al. A ne
w
heur
is
tic optimizati
o
n
al
gor
ithm: har
mon
y
s
earc
h
si
mulati
on. 20
01
; 76: 60-68.
[8]
Geem Z
W
, Ki
m JH, Logan
athan GV. A ne
w
h
eur
istic optimiz
ation al
gor
ithm: Harm
on
y searc
h
.
SIMULATION
.
200
1; 76(2): 60
-68.
[9]
Quan K
Pa
n,
PN Su
ga
ntha
n
,
M F
a
tih
T
a
sgetir
e
n
,
JJ Lia
ng d.
A
s
e
lf-a
daptiv
e glo
bal
best
h
a
rmo
n
y
search
al
gorith
m
for conti
n
u
o
u
s optim
izati
o
n
prob
lems.
Ap
plie
d M
a
the
m
a
t
ics and
Co
mp
utation.
20
10
;
216: 83
0-8
48.
[10]
Ibrahe
em N
a
si
rudd
ina, T
e
rloc
han S
Bh
attib,
Nizamu
d
d
i
n H
a
kimu
ddi
nc. A
u
tomatic Ge
ne
ration
Co
ntro
l
in an Interc
on
nected. Po
w
e
r
S
y
stem Incor
porati
ng Div
er
se Source Po
w
e
r Pla
n
ts Using Bacter
i
a
F
o
ragi
ng Opti
mizatio
n
T
e
chniqu
e.
Electric Pow
e
r Compo
n
e
n
ts and Syste
m
s
. 20
15; 43(
2
)
: 189-19
9.
[11]
FP deMe
llo
w
,
RJ Mil
l
s, WF B’Rel
l
s. Autom
a
tic Gen
e
rati
o
n
C
ontrol:
Part
I- Process
Mo
dell
i
n
g
. IEEE
T
r
ansactio
n
s o
n
Pow
e
r Appar
atus and Syste
m
s
. 19
72; 92(
2
)
: 710-71
5.
[12]
Mu
w
a
ffaq Irsh
eid Al
omous
h. Loa
d frequ
enc
y co
ntrol an
d a
u
tomatic ge
ner
ation co
ntrol us
ing fractio
nal
-
order co
ntroll
er
s.
Electr Eng
. 2010; 91: 3
57-3
68.
[13]
T
an G, Z
eng Q, He S, Cai G. Adaptive an
d Rob
u
st Desi
gn for PID Co
ntroll
er Based
on Ant S
y
st
em
Algorit
hm. Schoo
l of Information Sci
enc
e and En
gi
n
e
e
rin
g
Centra
l South Un
ivers
i
t
y
Ch
an
gsh
a
410
08
3. Huna
n Provinc
e
. P.
R. Chin
a.
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