TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 16, No. 3, Dece
mbe
r
2
015, pp. 389
~ 400
DOI: 10.115
9
1
/telkomni
ka.
v
16i3.885
2
389
Re
cei
v
ed Au
gust 19, 20
15
; Revi
sed
No
vem
ber 1
3
, 2015; Accepte
d
No
vem
ber
28, 2015
Optimal Coordination of Overcurrent and Distance
Relays Using Cuckoo Optimization Algorithm
Farhad
Nam
d
ari*, Sajad Samadinasa
b, Nader Sh
ojaei, Mohammad Bakh
shipour
Dep
a
rtement o
f
Electrical Eng
i
ne
erin
g,
Engi
n
eeri
ng F
a
cult
y,
Lorestan U
n
iv
ersit
y
,
Dan
e
shg
ah Str
eet, 712
34-9
8
6
53, Khorram
a
b
ad, Loresta
n, Iran
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: namdar
i.f@lu
.ac.ir
A
b
st
r
a
ct
The duty of protective system
s is the tim
e
ly det
ection of
fault and remo
ving
it from
the power
netw
o
rk. T
he a
ccuracy of th
e
results a
nd r
e
d
u
cin
g
the
exec
ution ti
me of th
e opti
m
i
z
i
n
g a
l
gorith
m
are tw
o
cru
c
i
a
l el
em
ents i
n
se
l
e
ctin
g
o
p
t
im
i
z
ing a
l
g
o
ri
th
m
s
i
n
pr
ote
c
tive functi
ons.
T
he
mo
st i
m
p
o
rtant pr
otectiv
e
ele
m
ents th
at
are
use
d
i
n
p
o
w
e
r netw
o
rks
are
d
i
stanc
e
and
ov
ercurre
nt rel
a
ys. In t
h
is
article,
a
n
e
w
alg
o
rith
m is
pr
esente
d
to s
o
lv
e the
opti
m
i
z
a
t
i
on
prob
le
m of coord
i
nati
on of
over
curr
ent
an
d dist
ance
rel
a
ys
by us
ing
C
u
ck
oo Opti
mi
z
a
ti
o
n
Al
gorith
m
w
h
ich
cons
id
ers
the
no
n-li
ne
ar
mod
e
l
overc
u
rrent re
lays
at
al
l
stages of setti
ng. The pr
op
o
s
ed
meth
od is
tested on
a stand
ard 8-
bus
pow
er syste
m
netw
o
rk. Also th
e
results obta
i
n
ed hav
e be
e
n
compar
ed
w
i
th other ev
oluti
onary a
l
g
o
rith
ms. T
he results show
tha
t
the prop
ose
d
a
ppro
a
ch ca
n
b
e
prov
ide
more
effective an
d
practica
l sol
u
ti
ons
to
min
i
mi
ze the ti
me
fu
nc
tion
of the
rel
a
ys
a
nd ac
hi
evin
g
opti
m
a
l
co
or
din
a
tion
in
c
o
mparis
on
w
i
th prev
io
us studi
es o
n
o
p
ti
ma
l
coordination of
overcurre
nt and distanc
e relays in
power system
networks.
Ke
y
w
ords
: Cu
ckoo Opti
mi
z
a
t
i
on Al
gorith
m
,
Optimi
z
a
t
i
o
n
methods, Overcu
rrent relay, Dist
ance re
lay,
optim
al coordination of rela
ys, Power system
protection.
Copy
right
©
2015 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
One of the
m
a
inly com
m
o
n
prote
c
tive relays
us
ed
in p
o
w
e
r
s
y
s
t
ems
fr
om va
r
i
ou
s
fa
u
l
ts
is the ove
r
cu
rre
nt rel
a
y. Overcu
rrent rel
a
y (O
CR) is
a type of pr
o
t
ective rel
a
y whi
c
h o
perates
w
h
en
th
e
lo
ad
c
u
rr
en
t e
x
c
e
ed
s
a
pr
es
e
t
va
lu
e
[1, 2]. Overcurrent relays a
r
e use
d
as b
o
th
prima
r
y and backu
p prote
c
tion for he
a
v
ily meshed
and multi-sou
r
ce p
o
wer ne
twork. Low
cost
and si
mplicit
y to impleme
n
t are the m
e
rits of
ove
r
current rel
a
y appli
c
ation fo
r Powe
r sy
stem
prote
c
tion [3]
.
The issue o
f
coordination
of over
cu
rr
e
n
t
relay
s
in
cl
ude
s
time setting multipliers
(TSM) a
nd p
l
ug setting
(PS) with ap
plying relate
d con
s
traints on ope
ratin
g
time difference
betwe
en b
a
ckup
and
prim
ary rel
a
ys [4]. Over the
pa
st five Deca
de
s, seve
ral
stu
d
ies
have b
e
en
carrie
d out o
n
optimal
co
ordin
a
tion of
overcurrent
relays. T
h
e
s
e studi
es
ca
n be divid
e
d
into
three
categ
o
r
ies: 1
)
T
r
ial
and e
r
ror
method 2
)
S
t
ructu
r
al a
nal
ysis meth
od
3) Optimi
za
tion
method [5
-8].
In re
ce
nt yea
r
s, a
r
tificial
in
te
lligen
ce m
e
thods an
d nat
ure
-
in
spired
a
l
gorithm
s
su
ch
as Evolutio
n
Programmin
g
[9], Geneti
c
Algorithm
(G
A) [10-12], P
a
rticle
Swarm
Algorithm
(P
SO)
[13, 14] amo
ng othe
rs
are
used to
solv
e the iss
ue
of optimal coordination of ov
ercurrent
rela
ys.
The pi
ckup
value of
an
overcurrent
rela
y must b
e
se
t betwe
en th
e maximum
l
oad
cu
rre
nt a
nd
the minim
u
m
fault current
experi
e
n
c
ed
by the
re
lay
.
In high
voltage
and
extra-hig
h
voltag
e
netwo
rks, the
s
e pa
ram
e
ters are often n
o
t well def
ine
d
, for a safe
sele
ction of a
pickup setting.
For
su
ch
ca
se
s, the
dist
ance relay f
u
rni
s
he
s
excellent p
r
ote
c
tion u
nde
r all
circu
m
sta
n
ces.
Therefore, in
transmissio
n and subtran
s
missi
on
syste
m
s, the coordinat
ion of O/
C and
dista
n
c
e
relays
sho
u
ld
be con
s
id
ere
d
[15-18].
Today’s p
o
wer
system
s a
r
e ve
ry
comp
lex,
large an
d interconn
e
c
ted. Beca
use of the
increa
sing
de
pend
en
ce o
n
ele
c
tricity, e
n
su
ring
it
s d
e
livery
in a secu
re and
rel
i
able
m
ann
er
is
very importan
c
e to both cu
stome
r
s a
nd
sup
p
liers.
On
the other ha
nd, sho
r
t circuit conditio
n
s
can
occur
unexp
e
ctedly in a
n
y
part of a p
o
we
r sy
stem
.
The in
cide
n
c
e of the fau
l
t is harmful
and
must be i
s
ola
t
ed by a set of prote
c
tive device
s
. The
s
e lea
d
to the need fo
r a large n
u
mb
er of
prote
c
tive rel
a
ys coop
erating with
one
a
nother
to a
s
sure th
e secure and
reli
able
ope
ration
of a
whol
e [19]. Relay Coord
i
nation in a
meshe
d
po
wer n
e
two
r
k in highly tediou
s an
d time
con
s
umi
ng a
ffair. If any r
e
lay fails to respon
d
the fault it is backed by ano
ther rel
a
y. The
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 389 – 400
390
operation of p
r
imary relay is qui
ck a
nd b
a
ck up rel
a
y operates afte
r a ce
rtain time margi
n
[20]. In
fact relay
co
ordin
a
tion p
r
oblem i
s
to
determi
ne th
e se
quen
ce
of relay op
erations fo
r ea
ch
possibl
e fault
locatio
n
so t
hat the faulte
d se
cti
on i
s
i
s
olate
d
with
sufficie
n
t margins
and
with
out
exce
ssive ti
me delays [2
1]. This stud
y is a novel appro
a
ch b
a
se
d on Cu
ckoo O
p
timiza
tion
Alg
o
r
ith
m
(CO
A
)
w
h
ic
h is
pr
es
en
te
d
to
s
o
lve
the
optimal
coo
r
dinatio
n of
overcurrent
and
distan
ce rela
ys to improve the accura
cy of t
he results and re
du
cing the exe
c
ution time of
the
optimizin
g al
gorithm. Wh
e
n
the network is protecte
d with distan
ce
relays, each line is prote
c
t
ed
by
the main
and b
a
ckup
relay of
its li
ne. By pl
aci
ng overcu
rre
n
t relays
alo
ng with
dista
n
ce
relays, protective territory of the transmissi
on network
will expand. If
a disturbance
occurred,
initially main distan
ce rel
a
y will opera
t
es and if
it fails to clea
r fault, overcurrent
relay
will
operates. If
main relay fa
ils to o
perate
,
the ba
ck
up
distan
ce
rel
a
y will ope
rate
and if it fails to
operate ultim
a
tely backup
overcurrent relay
must isol
ate the faulted se
ction [22]
.
This
a
r
ticle prop
oses an
intelligent O/C-
O/C an
d O/C-dista
n
ce relays
co
ordin
a
tion
method ba
se
d on Cu
ckoo
Optimization
Algorithm
(COA). The dist
ance relay is con
s
ide
r
ed
as
the main rel
a
y and the overcurrent rela
y (O/C) is
a
s
the backup
relay. In this method, fro
m
multiple
zon
e
s
of p
r
ote
c
tio
n
are u
s
ed
to cove
r the
entire li
ne d
e
pend
ably an
d
se
cu
rely. Also,
from 50 to 2
00% in step
s of 25%, the
curre
n
t se
ttin
g
multipliers
(PS) is chan
ged to make the
investigatio
n more
pra
c
tica
l COA which
has th
e
adva
n
tage
s of three well kn
own algo
rithms
DE,
GA and
PSO
. Sharin
g info
rmation
bet
ween
sol
u
tion
s
is
one
of the
GA's featu
r
e
s
[23]. In PS
O,
from ea
ch ite
r
ation to the
next, solution
s are sa
ve
d
but each saved sol
u
tion i
s
capa
ble to le
arn
from its neig
hbors an
d si
multaneo
usly
with the pr
o
g
re
ssi
on of the algo
rith
m, adapt itself [24].
Therefore,
co
ntaining the
s
e feat
ure
s
si
multaneo
usly
, causes the
sup
e
rio
r
pe
rforma
nce of COA
algorith
m
. Th
is novel evol
utionary al
go
rithm, is
suitable for
conti
nuou
s no
nlin
ear o
p
timizati
on
probl
em
s. Application of
the
propo
se
d algo
rithm t
o
so
me b
e
n
c
hma
r
k fun
c
tions
and
a real
probl
em has proven
its ca
pability to deal with difficul
t
optimiz
ation problem
s
. The key features of
COA a
r
e th
e
faster
co
nvergen
ce
rate a
nd redu
ce
co
mputational
complexity [25
]. Results
sh
ow
whi
c
h th
e p
r
o
posed m
e
tho
d
ha
s
signifi
cantly red
u
ced
the exe
c
utio
n time of th
e
algorith
m
whi
l
e
improvin
g the accu
ra
cy of the
output
results in compa
r
ison wi
th the other nature
-
in
spired
algorith
m
s
su
ch a
s
PSO
and GA tho
s
e previo
usly
have bee
n a
pplied to the
probl
em whi
c
h
demonstrate the ability of
COA
to
solve non-linear opti
m
ization problems.
All
the simulations are
carrie
d o
u
t i
n
MATLAB
software.
The
re
st of
t
he
pape
r i
s
org
anized
as fol
l
ows: sectio
n
s
2
explain
s
prob
lem formul
ation setting overcurrent
a
n
d
distan
ce
rel
a
ys, re
spe
c
ti
vely. Section 3
explain
s
cu
ckoo o
p
timiza
tion algorith
m
(COA
).
Section 4 rep
r
esents u
s
e
of the Cuckoo
Optimizatio
n
Algorithm (COA) for optim
al coo
r
di
n
a
tio
n
of overcu
rrent and dista
n
ce relays. T
he
simulation results
are illustrat
ed and di
scussed in
section
5 an
d finally
concluding remarks
are
dra
w
n in secti
on 6.
2. Problem Formulation
2.1. Setting
ov
ercurrent rela
y
s
The
obje
c
tive functio
n
a
nd
con
s
trai
nts
of
the p
r
o
b
lem,
to obtai
n the
pa
ramete
rs
of TMS
and
set
I
is
defined as
follows
[
26]:
seti
I
sci
I
i
TMS
i
set
I
i
TMS
f
n
i
opi
t
Minimize
log
3
)
,
(
opi
t
(1)
1
:
Whe
r
e
n is
the num
ber
of overcurre
n
t rela
y
s
. Constraint o
p
timization
pro
b
lem a
s
follows
:
(2)
i
max
i
min
TMS
i
TMS
TMS
(3)
)
(
)
(
CTI
m
z
m
op
t
m
z
b
op
t
(4)
Min
i
fault
I
i
set
I
Max
i
ioad
I
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Optim
a
l Coordination of O
v
ercu
rrent an
d Dista
n
ce Relays Usin
g Cu
ckoo … (F
arha
d Nam
d
a
r
i)
391
Whe
r
e
i
op
t
is op
erating tim
e
th
i
relay, and
b
op
t
a
r
e op
erating
time of prima
r
y and
backu
p relay
s
re
spe
c
tively and CTI is th
e Coo
r
din
a
tio
n
Time Interv
al.
Con
s
trai
nt (3) is used fo
r each p
a
ir main
and backu
p relay
b)
,
(
m
and for errors relatin
g
to zo
ne
of protection
m
z
. With
re
spe
c
t to th
e Figu
re
1, th
e failures are
identified
by
the F1
and
F2 poi
nts. Ta
king i
n
to a
ccount Con
s
trai
nt (4),
th
e pi
ckup val
ue
of an ove
r
curre
n
t relay m
u
st
be
set between t
he maximum
load current a
nd the mini
m
u
m fault curre
n
t experien
c
e
d
by the relay.
2.2. Coordin
a
tion b
y
taking the dis
t
a
n
ce rela
y
s
Whe
n
the
n
e
twork is protected
with
dista
n
ce
rel
a
ys, ea
ch
lin
e is p
r
ote
c
te
d by
the
main
and
ba
ckup
relay of
its line. By placi
ng
ove
r
current
rel
a
ys
along with distan
ce rela
ys,
prote
c
tive territory of the tran
smi
ssi
on
netwo
rk
will expand. If a disturban
ce
occurre
d
, initiall
y
main di
stance relay will
operates
and i
f
it fails to clear fault,
overcurrent rel
a
y
will operates.
If
main relay f
a
ils to
ope
ra
te, the ba
ckup di
stan
ce
relay
will op
erate
and if
it fails to o
p
e
rate
ultimately ba
ckup ove
r
current relay mu
st isol
ate
the
faulted
se
ction. As
sho
w
n in Fig
u
re 2
in
orde
r to
e
s
ta
blish
the m
e
n
t
ioned
se
que
nce
protectio
n
, two
other
con
s
trai
nt sh
ould
be a
dde
d to
the con
s
trai
nts of coo
r
din
a
tion pro
b
lem
s
:
(5)
'
2
)
3
(
CI
z
t
F
b
t
(6)
'
)
4
(
2
CI
F
m
t
z
t
In (5) a
nd (
6
)
m
t
is ope
rating t
i
me of overcu
rre
nt relay a
n
d
2
z
t
is op
eratin
g time of the
s
e
c
o
nd
z
o
ne
o
f
d
i
s
t
an
ce
r
e
la
y. In
th
is con
d
i
tio
n
,
a n
e
w
c
o
or
d
i
na
tion
time
in
te
r
v
al (
'
CI
) bet
wee
n
distan
ce a
nd
overcurrent relays shoul
d be defin
e
d
, which d
o
e
s
not
have the sa
me value as
CI
that is use
d
in coo
r
din
a
tio
n
of overcu
rrent relays p
a
i
r
s.
t
(
B
ack
u
p
)
b
(M
a
i
n
)
F1
F2
>C
I
>CI
t
b
t
m
m
Figure 1. Coo
r
dinatio
n of overcu
rrent rel
a
ys
t
(
B
ack
u
p
)
b
(M
a
i
n
)
F4
F
3
<C
I
`
>C
I
`
t
b
t
m
m
t
z2
t
z2
Figure 2. Coo
r
dinatio
n bet
wee
n
dista
n
ce and
overcurrent relays
3. The propo
sed Cu
ckoo
Optimiza
tion
Algorithm (CO
A
)
This optimization algorithm
is inspired by t
he life of a
bird family, called Cucko
o
.
Special
lifestyle of th
ese
birds an
d their chara
c
teri
stic
s in
e
gg laying
an
d
bre
edin
g
ha
s b
een th
e b
a
si
c
motivation for develo
p
me
nt of this new evolut
io
n
a
ry optimization algo
rith
m. This nov
el
evolutiona
ry algorith
m
, is
suitabl
e for
continuo
us
no
nlinea
r optimi
z
ation
pro
b
le
ms. The effort to
survive amo
ng cu
ckoo
s con
s
titutes th
e basi
s
of Cuckoo O
p
timization Algo
rithm. Durin
g
the
survival com
petition som
e
of the cucko
o
s or
thei
r eg
gs, demi
s
e. T
he su
rvived cuckoo
so
cieti
e
s
immigrate to
a better env
ironm
ent and
start re
pro
d
u
cin
g
and la
ying egg
s. Cuckoo
s’ survi
v
al
effort hopeful
ly converge
s to a st
ate th
at there i
s
o
n
ly one cuckoo society, al
l with the sa
me
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5 : 389 – 400
392
profit value
s
. Applicatio
n
of the propo
sed
algo
rith
m to som
e
b
enchma
r
k fu
nction
s a
nd
a real
probl
em ha
s
proven its
ca
pability to deal with difficul
t
optimization
proble
m
s [25
]
.
Figure 3
sho
w
s a
flowch
a
r
t of th
e p
r
o
posed
algo
rithm. Similar t
o
othe
r
evol
utionary
method
s, Cu
ckoo Optimi
zation Algorith
m
(COA
) st
a
r
ts with an in
itial populatio
n. These initi
a
l
cu
ckoo
s have some e
g
g
s
to lay in some host birds’
nest
s
. Some of these egg
s which a
r
e m
o
re
simila
r to
the
ho
st bi
rd’
s
e
ggs have
the
opp
ortu
nity to g
r
o
w
u
p
a
n
d be
co
me
a
mature
cucko
o
.
Other eggs are detected by host bi
rds and are kill
ed. T
he grown eggs
reveal the
suitability of th
e
nest
s
in
that
area.
The
mo
re
egg
s
su
rvive in a
n
a
r
ea, th
e
mor
e
p
r
o
f
it is
ga
in
ed
in
th
a
t
ar
ea
.
So
the positio
n in whi
c
h mo
re
eggs
survive
will be t
he term that COA i
s
goin
g
to poi
nt optimize.
Figure 3. Flowchart of Cu
ckoo O
p
timizat
i
on Algorithm
3.1. Genera
ti
ng initial cuckoo habitat
In ord
e
r to
solve an o
p
timization
pro
b
lem, it’s n
e
c
e
s
sary that
the value
s
of
pro
b
lem
variable
s
be
formed as an array.
In GA and
PSO terminologi
es this array is called
“Ch
r
om
osom
e” and “Pa
r
ticle Position”, resp
ective
ly. But here in Cuckoo Optimi
zation Algo
rithm
(COA) it is called “habitat
”
. In a
var
N
dimen
s
i
onal optimiza
t
ion proble
m
, a habitat is an array of
var
1
N
, repre
s
e
n
ting
current living
position of cu
ckoo. Thi
s
a
rray is d
e
fine
d as follo
ws:
Start
Initialize
Cuckoos w
i
th
e
gg
s
La
y
eggs in
different nests
Some of eggs ar
e
detected and
killed
Check Survival o
f
eggs in nests
(get pro
f
it values)
Population is
less than
max value?
Yes
Kill cuckoos
in w
o
rst area
Stop condition
Satisfied?
E
nd
Yes
No
Let eggs gro
w
Find nests
w
i
th best
s
u
rv
i
v
al
rate
Determine
cuckoo
societies
Move all cuckoos
toward b
e
st
environment
Determine eg
g
lay
i
ng radius
for
each cuckoo
No
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Optim
a
l Coordination of O
v
ercu
rrent an
d Dista
n
ce Relays Usin
g Cu
ckoo … (F
arha
d Nam
d
a
r
i)
393
(7)
1
[
]
var
...,
,
2
,
N
x
x
x
Habital
Each of the
variable valu
es
)
,...,
,
(
var
2
1
N
x
x
x
is floatin
g point num
ber. The p
r
of
it of a
habitat is obt
ained by eval
uation of profi
t
function
p
f
at a habitat of
)
,...,
,
(
var
2
1
N
x
x
x
.
So
(8)
(habital)
)
var
,...,
2
,
1
(
N
x
x
x
p
f
p
f
profit
As it is seen
COA is an al
gorithm that
maximi
ze
s a
profit function
. To use CO
A in cost
minimization
probl
em
s, on
e can e
a
sily
maximize
the following p
r
o
f
it function:
(9)
(habital)
)
var
,...,
2
,
1
(
N
x
x
x
c
f
Cost
profit
To sta
r
t the optimizatio
n
algorithm, a
candi
date h
abitat matrix
of size
var
N
N
pop
is
gene
rated. T
hen some ra
ndomly produ
ced n
u
mbe
r
of eggs i
s
su
ppo
sed for
e
a
ch of the
s
e i
n
itial
cu
ckoo ha
bitats. In nature
,
each
cu
cko
o
lays from 5
to 20 egg
s. These value
s
are u
s
ed a
s
the
uppe
r a
nd lo
wer limits
of
egg d
edi
catio
n
to ea
ch
cuckoo
at differe
nt iteration
s
.
Another
habit
of
real cucko
o
s
is that they lay eggs within
a maximum distan
ce fro
m
their habitat. From no
w o
n
,
this maximu
m rang
e will
be call
ed “Eg
g
Laying Ra
d
i
us (EL
R
)”. In an optimizati
on pro
b
lem
with
uppe
r limit
of
hi
var
and l
o
wer lim
it of
low
var
for
vari
a
b
les, ea
ch
cu
ckoo ha
s an egg
l
a
ying ra
dius
(ELR) which is propo
rtiona
l to the total numbe
r
of eg
gs, num
ber
o
f
current cuckoo’
s eg
gs
a
nd
also vari
able l
i
mits of
hi
var
and
low
var
.
So ELR is def
ined a
s
:
(10)
eggs
of
number
total
eggs
s
cuckoo'
current
of
number
)
var
(var
low
hi
ELR
Whe
r
e
α
i
s
a
n
integer, sup
posed to han
dle the maximum value of
ELR.
3.2. Cucko
o
s
’ st
y
l
e for e
gg la
y
i
ng
Each cucko
o
starts laying
eggs rando
mly in some
other ho
st birds’ n
e
st
s wi
thin her
ELR. Figure 4 gives a cl
ea
r view of this
con
c
e
p
t.
Figure 4. Ran
dom egg layi
ng in ELR, ce
ntral re
d star i
s
the initial ha
bitat of the cuckoo
with 5 egg
s; pink
stars are
the eggs’ n
e
w
ne
st.
After all cu
ckoos’ e
g
g
s
are
laid in ho
st b
i
rds’
ne
sts, so
me of them that are le
ss similar to
host bi
rd
s’ o
w
n e
g
g
s
, are
detecte
d by h
o
st bi
rd
s an
d
though
are
th
rown out
of the ne
st. So after
egg laying p
r
oce
s
s, p% of all eggs (usually 10%),
with less profit values, will
be killed. Th
ese
egg
s have
n
o
ch
an
ce to
gro
w
. Re
st of
the egg
s g
r
o
w
in h
o
st n
e
sts, hatch
and
are fe
d by h
o
st
bird
s. Anothe
r interestin
g
point ab
out l
a
id cuck
o
o
e
ggs i
s
th
at o
n
ly one
egg i
n
a n
e
st
has the
cha
n
ce to
grow. T
h
is is
becau
se
wh
e
n
cucko
o
eg
g hat
che
s
a
nd the
chi
c
ks
com
e
o
u
t,
she
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394
throws the
ho
st bird’
s
o
w
n
egg
s out of the ne
st. In case that h
o
st
bird’
s
egg
s
hatch
earli
er
and
cu
ckoo
egg
hatch
es later, cu
ckoo’
s
ch
ick eat
s mo
st
of the foo
d
ho
st bird b
r
i
ngs to the
n
e
st
(be
c
au
se
of
her
3 time
s
b
i
gger bo
dy, she p
u
she
s
ot
her
chi
c
ks an
d eat
s m
o
re
).
After coupl
e
of
days the ho
st
bird’s o
w
n
ch
icks die fro
m
hung
er an
d o
n
ly cucko
o
ch
ick
remai
n
s in
the nest.
3.3. Immigra
t
ion of cu
ck
oos
Whe
n
young
cu
ckoo
s gro
w
and be
com
e
mature, the
y
live in
their own a
r
ea an
d
soci
ety
for
some
tim
e
. But when t
he time fo
r
e
gg layin
g
ap
p
r
oa
che
s
th
ey immigrate to
ne
w a
nd
bet
ter
habitats
with more
simila
rity of eggs to host birds a
n
d
also
with more food fo
r new you
ngst
e
rs.
After the cu
ckoo
gro
u
p
s
are fo
rmed i
n
different
a
r
eas, the
so
ci
ety with be
st profit value
is
sele
cted a
s
the goal p
o
int for other
cu
ckoos to immig
r
ate.
3.4. Conv
ergence
After some iteration
s
, all the cuckoo
population
moves to one best ha
b
i
tat with
maximum si
milarity of eggs to the ho
st birds a
nd al
so with the
maximum foo
d
re
sou
r
ces.
This
habitat will produ
ce the m
a
ximum profit
ever. There
will be lea
s
t e
gg losse
s
in this be
st habit
a
t.
Conve
r
ge
nce
of mo
re
tha
n
95%
of all
cu
ckoo
s to
the same
ha
bitat puts an
end
to
Cu
ckoo
Optimization Algorithm (COA).
4. Apply
COA Algorithm in order to O
p
timal Coor
dination of
Rela
y
s
Relay co
ordi
nation pro
b
le
ms,
i
s
a
n
op
timization problem with constraints
an
d
man
y
local o
p
timu
m points. In the usu
a
l
method
s, su
ch a
s
lin
ear p
r
og
ram
m
ing, non
-li
near
prog
ram
m
ing
and inte
ge
r pro
g
ra
mmin
g
, sin
c
e o
p
timization
sta
r
t with initial
point, the fin
a
l
answe
r de
pe
nds h
eavily on that point a
nd may lead
t
o
a local opti
m
ization.
Ho
wever
COA
starts
the sea
r
ch from a populati
on of initial points, ther
efo
r
e in the local
optimum poin
t
s the possibil
i
ty
of stoppin
g
this alg
o
rithm
is very low.
COA alg
o
rit
h
m, probl
em's varia
b
le
s a
r
e en
co
ded i
n
to
string
s, so ea
ch st
ring represe
n
ts an
a
n
s
wer to the problem of co
ordination.
4.1. Encode
d
v
a
riables
In the relays coordinatio
n
proble
m, the deci
s
ion v
a
riabl
es a
r
e
the TMS and
I
set
variable
s
fo
r
each rel
a
y. Therefo
r
e, in t
he COA met
hod a
habitat
is defin
ed in
the form of
a
string
whi
c
h
contai
ns b
o
th TMS and
I
set
para
m
eters a
s
discrete va
riable
s
. Figu
re 5 sh
ows
stru
cture of the habitat wh
e
n
the netwo
rk
con
s
ist
s
of n overcurrent relays.
set
1
I
1
TM
S
se
t
2
I
2
TM
S
…
se
tn
I
n
TM
S
Figure 5. Structure of the h
abitat in the COA metho
d
.
4.2. Ne
w
method
In the pro
p
o
s
ed
co
ordi
na
tion method
for the ove
r
curre
n
t and
distan
ce
rela
ys, the
obje
c
tive function optimizati
on pro
b
lem i
s
formulated a
s
[18]:
(11)
1
F
2
1
2
2
)
2
2
(
3
1
1
1
2
)
1
1
(
2
1
2
)
(
.
P
k
K
mbDISOC
t
K
mbDISOC
t
P
k
K
mb
t
K
mb
t
N
i
i
t
O
Whe
r
e
3
2
1
,
,
are
t
he weightin
g factors,
i
is th
e num
ber of
overcurrent
relays that
cha
nge
s from
1
to
N,
1
k
is the
numbe
r of
m
a
in an
d b
a
ckup ove
r
curre
n
t relay
s
that
cha
nge
s fro
m
1 to
1
P
, k
2
is the
numb
e
r of m
a
in di
stan
ce
and
ba
ckup
o
v
ercu
rrent
rel
a
ys
cha
ngin
g
from
1
to
2
P
,
1
K
mb
t
is the
di
scrimi
nation time
b
e
twee
n the
m
a
in a
nd
ba
ckup ove
r
curre
n
t rel
a
ys.
2
K
mbDISOC
t
is the
discrim
i
nation time
betwe
en the
main di
stan
ce and
ba
cku
p
overcu
rrent
relay
s
which
is
obtaine
d from
the equation
(12
)
:
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TELKOM
NIKA
ISSN:
2302-4
046
Optim
a
l Coordination of O
v
ercu
rrent an
d Dista
n
ce Relays Usin
g Cu
ckoo … (F
arha
d Nam
d
a
r
i)
395
'
t
t
t
C
T
I
(
1
2
)
m
b
DI
S
O
C
K
b
o
c
k
m
DI
S
k
22
2
Whe
r
e
2
k
boc
t
is the operating tim
e
of ba
cku
p o
v
ercu
rrent
rel
a
y for the faul
t at the end of
the first
zon
e
of main
distan
ce rel
a
y (critical faul
t location
s),
2
k
mDIS
t
is the ope
rati
ng time of the se
con
d
zon
e
of main distan
ce rela
y and CTI is the co
ordi
nati
on time interv
al that is equ
al to 0.3(se
c).
Two first term
s of (11
)
are the sa
me a
s
the OF in [10]. The third term is add
ed to
OF for
the Coo
r
di
na
tion of overcurrent and
di
stan
ce rela
ys. To descri
b
e the rol
e
of this ne
w term,
assume that
2
K
mbDISOC
t
is po
sitive (f
ully coordinat
ed), then the
relative term
in (11) b
e
co
mes
zero
a
nd OF also
ha
s a small
value. Howeve
r
if
2
K
mbDISOC
t
is negative (mi
s
coo
r
din
a
tion)
the
mentione
d te
rm will b
e
eq
ual to
2
3
mb
D
I
S
O
C
k
2t
and ob
viously for p
o
s
itive values
of
3
the
new term
will
have large value
s
, that COA algorit
hm
removes it from the sele
ction then, based
on the co
nce
p
t of the evaluation an
d se
lection, th
os
e va
l
u
e
s
th
a
t
ha
ve
mo
r
e
op
ti
ma
l
O
F
va
l
u
e
s
(less value
)
i
n
the
ha
bitat, are g
r
a
n
ted
more
op
po
rtu
n
ities to
b
e
selecte
d
fo
r th
e next ite
r
ati
on.
By s
o
lving COA,
se
t
I
and TMS
for all relays
will be
determined in
a m
anne
r that th
e relay
s
have
a least op
erat
ion time and
will sati
sfy all con
s
trai
nts.
5. Simulation Resul
t
s an
d Discus
s
io
n
Th
e
pr
op
os
ed
me
th
od
is
a
p
p
l
i
e
d
to
an 8
-
bu
s
,
9
-
b
r
an
c
h
n
e
t
w
o
rk
s
h
ow
n i
n
Figu
r
e
. 6
.
At
bus
4, there
is a lin
k to a
nother
netwo
rk
whi
c
h
i
s
modele
d
by
a sh
ort ci
rcui
t capa
city of 400
MVA. The p
a
ram
e
ters u
s
ed in th
e ne
twork i
s
p
r
ov
ided in
refe
rence [27]. T
he tra
n
smi
s
si
on
netwo
rk
co
nsists of 14
rel
a
ys whi
c
h th
eir lo
cation a
r
e indi
cate
d in Figure. 6. The TMS val
u
e
s
can
ra
nge
co
ntinuou
sly fro
m
0.1 to 1.1,
while
seve
n
available
discrete pi
ckup ta
p setting
s
(0.
5
,
0.6, 0.8, 1.0,
1.5, 2.0
an
d 2.
5) a
r
e
consi
dered. T
he g
ene
ratio
n
si
ze
and
p
opulatio
n si
ze is
dire
ctly relate
d to the h
abit
a
t length; for
longe
r len
g
th
s, more h
abitats shoul
d be
pro
d
u
c
ed. T
h
e
gene
ration
si
ze an
d the po
pulation
size are con
s
ide
r
e
d
to be 300 a
nd 100, re
sp
e
c
tively.
r
1
r
8
1
65
7
23
4
r
13
r
6
r
12
r
5
r
11
r
4
r
10
r
7
r
3
r
9
r
2
r
14
2
1
8
6
7
3
4
5
Figure 6. 8-b
u
sb
ars test system
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Vol. 16, No. 3, Dece
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396
This pa
per i
s
solve th
e
opti
m
al
coo
r
din
a
tion
di
stan
ce
and overcu
rrent
relays
to verify
the
effectivene
ss of the p
r
op
o
s
ed
Cu
ckoo
Optimizati
o
n
Algorithm
(COA). Fo
r com
pari
s
on
pu
rp
ose
s
Geneti
c
Algo
rithm (GA
)
, P
a
rticle
Swarm
Optimiza
tion
(PSO), Differential
Evoluti
onary (DE) a
n
d
Cu
ckoo O
p
timization Al
g
o
rithm (COA
) we
re
use
d
in the
system. Tabl
e
1 sh
ows t
h
e
prima
r
y/backup (P/B)
relay
pairs a
nd
correspon
ding
fa
ult cu
rre
nts p
a
ssing th
rough them for fault
in front of the main rel
a
y an
d fault on bus away
the main relay in the studied
system. This matrix
contai
ns 20
rows and two
column
s. Th
e first colu
m
n
is the num
ber of the main relay and
the
se
con
d
colu
mn is the
nu
mber
of ba
ckup rel
a
y. The
n
, for a sho
r
t circuit in front
of the main
relay
the fault
currents
pa
ssi
ng
throu
gh th
e
prim
ary/ba
ckup
(P/B)
rel
a
y pairs, i
s
calcul
ated a
n
d
is
store
d
in the
IP and IB matrix resp
ectiv
e
ly, as
sh
own in Table
1. Obviously,
whe
n
the sy
stem
topology is
ch
ange
d the prese
n
ted data
in Table 1 sh
ould be u
pdat
ed.
Table 1. P/B Relay pai
rs a
nd the fault currents in the
main network topology
P/B pair
Near-En
d
Fault
Curre
nts(A)
primar
y
rel
a
y
s
backup
rel
a
y
s
IP IB
2
14
3
4
5
6
7
1
2
8
13
8
14
9
10
11
7
12
6
12
1
1
2
3
4
5
5
6
7
7
8
9
9
10
11
12
13
13
14
14
5910
5190
3550
3780
2400
6100
5210
3230
5910
6080
2980
6080
5190
2480
3880
3700
5210
5890
6100
5890
993
993
3550
2240
2400
1200
1200
3230
1880
1880
2980
1160
1160
2480
2340
3700
985
985
1870
1870
Initially, the setting pa
ram
e
ters for th
e
ca
se th
at onl
y the overcu
rrent
relays a
r
e u
s
ed i
n
the net
work
have be
en i
d
entified. The
setting
cu
rre
n
t of rel
a
ys i
s
o
b
tained
by
usi
ng the
po
wer
flow. Th
en
se
t
I
a
nd TMS
ove
r
curre
n
t relays have
bee
n
o
b
tained
u
s
ing
COA,
DE-G
A, GA, PSO
and
DE algo
rithms, as
sh
o
w
n in th
e tab
l
e 2. Also, th
e ratio
s
of th
e cu
rrent tran
sform
e
rs (CT
s
)
are indi
cate
d
in Table 2. It is obvious that
the Cuckoo Optimization Algorithm
(COA) have the
operation tim
e
an
d the
fitn
ess valu
e le
ss
com
pared
t
o
the
othe
r al
gorithm
s. In
o
t
her
wo
rd
s, COA
gave the be
st result
s wh
en
compa
r
e
with three well known algo
rith
ms DE, GA a
nd PSO.
se
t
I
and T
M
S are the
re
sults of the o
p
tima
l coo
r
dina
tion di
stance
and
overcu
rrent
relays,
whi
c
h
have be
en o
b
tained
usi
n
g
COA, DE
-G
A, GA, PSO and
DE algo
rithms, a
s
sho
w
n
in the table 3.
t
z2
is
sel
e
cte
d
based on
ref
e
ren
c
e
data [11] whi
c
h is
calcul
ated the
se
con
d
zo
ne
of distan
ce
relays. Th
e p
e
rform
a
n
c
e
o
f
a dista
n
ce
relay n
ear its zon
e
b
oun
d
a
rie
s
i
s
not v
e
ry
predi
ctabl
e b
e
ca
use of va
riou
s type
s
of erro
rs. In
thi
s
a
r
ticl
e, fro
m
multiple
zo
nes of p
r
ote
c
tion
are u
s
e
d
to
cove
r the
entire lin
e
depe
nda
bly and
se
cu
rely. Zone 1
relay o
perates
instanta
neo
u
s
ly (n
o inte
ntional d
e
lay –
i.e. in abo
ut
one to t
w
o
cycles)
while
a fault in
Zon
e
2
cau
s
e
s
th
e relay to o
pera
t
e with
an
ad
ded
delay
(g
ener
ally of th
e orde
r of
20
to 30
cy
cle
s
). In
this fashion,
the entire lin
e is
prote
c
te
d even
whe
r
e the
zone
b
ound
ary i
s
n
o
t very preci
s
ely
determi
ned. I
n
ad
dition to
these two
zone
s, oft
en
a
third
zone
(with a
n
a
dditi
onal time
del
ay
about
one
se
con
d
) i
s
provided
at ea
ch
end i
n
o
r
de
r
t
o
provide
re
mote ba
ckup
for the
protection
of the adj
ace
n
t circuit
s
. It sho
u
ld b
e
n
o
t
ed that often
,
due to
syst
em loa
d
, it is not po
ssible
to
obtain
a
se
cu
re Z
one
3
set
t
ing on
high
voltage
networks. It i
s
o
b
vio
u
s th
at COA
have o
peratio
n
time and the fitness value l
e
ss co
mpa
r
e
d
to the other algorithm
s.
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TELKOM
NIKA
ISSN:
2302-4
046
Optim
a
l Coordination of O
v
ercu
rrent an
d Dista
n
ce Relays Usin
g Cu
ckoo … (F
arha
d Nam
d
a
r
i)
397
Table 2. Overcurren
t relay setting
s reg
a
rdle
ss
of distan
ce re
lays
Rrla
y
No.
CT
Ratio
The results of
the prog
ram
GA [2]
F
i
t
ness=
7.63
The results of
the prog
ram
PSO
[13]
F
i
t
ness=
6.847
6
The results of
the prog
ram
DE [9]
F
i
t
ness=
6.29
The results of
the prog
ram
DE-GA
F
i
t
ness=
4.15
The results of
the prog
ram
COA
F
i
t
ness=
4.041
TM
S
se
t
I
TM
S
se
t
I
TM
S
se
t
I
TM
S
se
t
I
TM
S
se
t
I
1
2
3
4
5
6
7
8
9
10
11
12
13
14
240
240
160
240
240
240
160
240
160
240
240
240
240
160
0.25
0.19
0.21
0.17
0.10
0.20
0.20
0.17
0.09
0.16
0.20
0.26
0.18
0.16
0.8000
1.5000
0.6000
0.6000
0.5000
0.8000
0.6000
1.0000
0.6000
0.8000
0.6000
0.8000
0.6000
0.8000
0.1000
0.1000
0.1267
0.1421
0.1000
0.1855
0.1542
0.1624
0.1000
0.1001
0.1821
0.1242
0.1005
0.1625
2.5000
2.0000
1.5000
1.5000
0.8000
0.5000
2.0000
2.5000
0.5000
2.0000
2.5000
1.0000
1.5000
1.5000
0.1000
0.1264
0.1561
0.1271
0.1000
0.2527
0.2297
0.1005
0.1000
0.1944
0.1123
0.1567
0.1424
0.1728
1.0000
1.0000
2.5000
2.0000
0.5000
0.8000
1.0000
2.5000
0.5000
0.6000
2.0000
0.6000
1.5000
2.5000
0.1057
0.1340
0.1520
0.1310
0.1000
0.1904
0.1998
0.2232
0.1000
0.1000
0.1771
0.1511
0.1214
0.1662
2.0000
1.5000
0.5000
0.5000
0.6000
2.0000
1.0000
0.6000
0.5000
0.8000
0.8000
1.0000
1.0000
2.0000
0.1000
0.1000
0.1045
0.1075
0.1010
0.8365
0.7497
0.8015
0.1058
0.1019
0.1000
0.1011
0.1007
0.7484
2.5000
0.5000
2.5000
0.8000
0.6000
2.0000
2.5000
2.5000
0.5000
1.5000
0.8000
2.0000
1.0000
2.5000
Table 3. The
results of the
optimal co
or
d
i
nation of ove
r
cu
rrent and
distan
ce rela
ys
The results of th
e
program
COA
Fitness=18.27
The results of th
e
program
DE-
G
A
Fitness=19.71
The results of th
e
program
DE
Fitness=31.95
The results of th
e
program
PSO
Fitness=67.41
The results of th
e
program
GA
Fitness=49.16
Rela
y
No.
se
t
I
TM
S
se
t
I
TM
S
se
t
I
TM
S
se
t
I
TM
S
se
t
I
TM
S
0.5000
2.5000
2.0000
0.8000
0.6000
2.0000
2.0000
1.5000
0.8000
0.5000
0.6000
2.0000
2.5000
0.5000
0.1245
0.1548
0.1546
0.1236
0.1002
0.2128
0.2518
0.1945
0.1000
0.1056
0.1549
0.2015
0.1517
0.5482
0.6000
2.5000
1.5000
0.5000
1.0000
0.8000
2.5000
0.5000
2.0000
1.5000
0.8000
0.6000
0.5000
1.0000
0.1471
0.1537
0.1723
0.1541
0.1000
0.2396
0.2455
0.2119
0.1000
0.1006
0.1786
0.1948
0.1465
0.2398
0.5000
0.5000
0.5000
1.5000
0.5000
0.6000
2.5000
1.5000
1.0000
0.5000
0.5000
0.5000
2.5000
2.0000
0.3254
0.6901
0.4214
0.2123
0.1005
0.5566
0.8096
0.5237
0.1001
0.6531
0.5007
1.0000
0.3005
0.4809
0.8000
2.5000
2.0000
0.6000
0.6000
1.5000
1.0000
0.5000
0.5000
0.5000
0.6000
0.8000
0.8000
1.0000
0.5303
0.3158
0.4099
0.5942
0.1002
0.2596
0.5994
0.7668
0.1001
0.5354
0.8850
0.7919
0.4904
0.7844
0.5000
0.5000
0.6000
2.0000
0.5000
0.5000
2.5000
0.6000
0.5000
2.0000
0.8000
0.5000
0.6000
1.0000
0.1257
0.6718
0.5492
0.5672
0.1000
0.1928
0.7362
0.9238
0.1005
0.5289
0.6345
0.7155
0.2886
0.4437
1
2
3
4
5
6
7
8
9
10
11
12
13
14
In orde
r to asse
ss the
validity of
the obtained
setting
s, rela
ys perfo
rma
n
ce
was
evaluated
ca
use
d
by a sh
ort circuit faul
t per 40% of
line the front o
f
relay 7. In th
e ring net
wo
rks,
like
the net
wo
rk
figu
re.6, the relay
s
setti
ng is
compl
e
x in front of ge
nerato
r
bu
s, like relays 5 a
n
d
9 whi
c
h
are b
a
ckup
rel
a
ys
for 6, 7
and
8
,
14 resp
ectiv
e
ly. When
in
the front
of lines
of rel
a
ys
6,
7, 8, 14 a sh
ort ci
rcuit occurs, if the b
a
c
kup rela
ys
5
and 9 a
r
e n
o
t set co
rrect
l
y, it is possi
ble
fault cu
rre
nt
passin
g
throu
gh them
be l
e
ss than
the
curre
n
t set, a
nd thu
s
d
o
e
s
not ope
rate
a
s
a
backu
p of th
e
prim
ary
rela
ys. According
to the
table
s
2
and
3, in
a
ll the
ca
se
s
studied,
relays 5
and 9 are set
at the lowe
st value.
Figure. 7
illu
strated
comp
arative
co
nve
r
gen
ce
p
e
rfo
r
mance
of obj
ective fun
c
tio
n
. It is
obviou
s
that the Cucko
o
O
p
timization
Algorithm
(COA
) gave th
e a
c
curate a
nd
co
nverge
nce wi
th
faster
comp
u
t
ational time
comp
are
d
to other
m
e
th
od. This n
o
vel evolutiona
ry algorith
m, is
suitabl
e
for continuo
us no
nlinea
r
optimi
z
ation proble
m
s
.
The
r
efore, appli
c
ation
of the p
r
opo
se
d
algorith
m
to some be
nchm
ark fu
nctio
n
s
and a real
p
r
oblem h
a
s p
r
oven its capa
bility to deal with
difficult optimization p
r
obl
e
m
s. As a re
sult, COA algo
rithm have o
peratio
n time
and the fitness
value less co
mpared to other alg
o
rithm
s
.
Table
4
sho
w
s that the
op
eration
time
differen
c
e
s
of
all overcu
rre
n
t relay
s
i
s
m
o
re th
an
operation tim
e
zo
ne
2 di
stance relays
which i
ndi
cate
s the corre
c
t coordi
nation
b
e
twee
n di
sta
n
ce
and ove
r
current relay
s
. All
∆
t value
s
are po
sitive an
d most of the
m
are
small t
hat mean
s th
e
setting of ove
r
cu
rrent rel
a
ys is very a
c
cu
rate and the
r
e is no misco
o
rdin
ation.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 389 – 400
398
Figure 7. Compa
r
ison of obje
c
tive
function for 8-b
u
sbars test sy
stem
Table 4. The
operating tim
e
overcurrent
relays fro
m
p
e
rform
a
n
c
e o
f
zone 2 di
sta
n
ce
r
e
lays
primar
y
rela
y
s
backup rela
y
s
∆
t
2
14
3
4
5
6
7
1
2
8
13
8
14
9
10
11
7
12
6
12
1
1
2
3
4
5
5
6
7
7
8
9
9
10
11
12
13
13
14
14
0.6433
0.9101
0.1445
0.0613
0.0162
0.3666
0.9018
0.1991
0.7990
0.3606
0.5632
0.4041
0.1092
0.9236
0.0033
0.0406
0.5249
0.6401
0.1655
0.8158
6. Conclusio
n
Protectio
n
of powe
r
dist
ri
bution, su
b-t
r
an
smi
ssi
on
and tran
smi
s
sion n
e
two
r
ks is a
cru
c
ial
issu
e
in dete
r
mini
n
g
the
stability
and
th
e
reli
ability of a
p
o
we
r
system.
To
have
bet
ter
prote
c
tion it i
s
commo
n to
combi
ne diff
erent type
s o
f
relays, which com
b
inatio
n of overcu
rrent
and dista
n
ce relay
i
s
a well
-kn
o
wn prote
c
tion sche
me
in
tran
smi
ssi
on
lin
es.
A
ppl
ying
optimi
z
in
g
algorith
m
s to
the i
s
sue
s
e
x
isting in
po
wer net
wo
r
ks improve the
se
curity level
of the
netwo
rks.
The executio
n time of the
algorith
m
and
the accu
ra
cy
of the results extracted fro
m
the algorith
m
are two dete
r
mining p
a
ra
m
e
ters i
n
choo
sing the
opti
m
ization
algo
rithm in p
r
ote
c
tive function
s. In
this a
r
ticl
e, a
method
ba
se
d on
Cucko
o
Optimizatio
n
Algorithm
(COA) h
a
s be
e
n
ap
plied
to t
he
optimal
coo
r
d
i
nation of ove
r
cu
rr
ent
a
nd distan
ce rela
ys
problem. The key
feat
ure
s
of COA are
the faste
r
co
nverge
nce ra
te and
re
du
ce computat
io
nal compl
e
xity. Application
of the p
r
op
o
s
ed
algorith
m
to some be
nchm
ark fu
nctio
n
s
and a real
p
r
oblem h
a
s p
r
oven its capa
bility to deal with
difficult optimi
z
ation
p
r
oble
m
s.
Re
sults show the
prop
ose
d
m
e
thod
has si
gnifican
t
ly redu
ce
d th
e
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