TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 13, No. 2, Februa
ry 20
15, pp. 247 ~ 256
DOI: 10.115
9
1
/telkomni
ka.
v
13i2.702
6
247
Re
cei
v
ed
No
vem
ber 1
4
, 2014; Re
vi
sed
De
cem
ber 2
9
,
2014; Accep
t
ed Jan
uary 1
2
, 2015
Optimal Placement and Sizing of Distributed
Generation Units Using Co-Evolutionary Particle Swarm
Optimization Algorithms
Alireza Kav
i
ani-Ar
ani
Dep
a
rtment of Electrical E
ngi
nee
ing, Maj
l
es
i
Branch, Islami
c Azad Univ
ers
i
t
y
, Isfahan, Ira
n
Shah
id Ra
ja
ee
Center, Dep
a
r
t
ment of
T
e
chnica
l a
nd Voc
a
ti
ona
l Educ
ation
in Isfahan Pro
v
ince
E-mail: A.Kaviani@
i
aumajlesi.
ac.ir, A.Kavian
i@etvto.ir
A
b
st
r
a
ct
Today, w
i
th the incr
ease
of
dist
rib
u
ted
gen
eratio
n so
urce
s in p
o
w
e
r systems, it
’
s
i
m
p
o
rtant t
o
opti
m
a
l
l
o
cati
o
n
of th
ese
so
ur
ces. Deter
m
ine
the
nu
m
ber, l
o
catio
n
, si
z
e
a
nd typ
e
of distr
i
bute
d
gen
erati
o
n
(DG) on Pow
e
r Systems, cau
s
es the reduc
i
ng loss
es
and
improvi
ng rel
i
a
b
ility of the system. In this pa
per
is use
d
Co-ev
o
luti
onary
p
a
rticle sw
ar
m o
p
ti
mi
z
a
t
i
o
n
a
l
gor
ithm (CPSO) to
deter
mi
ne th
e
opti
m
a
l
va
lues
o
f
the l
i
sted
par
a
m
eters.
Obtain
ed r
e
sults
thro
ugh
si
mu
la
ti
on
s are
d
one
i
n
MAT
L
AB softw
are
is pr
ese
n
te
d i
n
the form
of fig
u
re an
d tab
l
e i
n
this pa
per.
T
hese
tab
l
es
and fi
gures, s
how
how
to chan
ges the sy
stem
losses
an
d
improvi
ng r
e
li
ab
ili
ty by ch
an
gin
g
par
a
m
eters
s
u
ch
as l
o
cati
o
n
, si
z
e
,
nu
mb
e
r
an
d type
of
DG.
F
i
nally, th
e res
u
lts of this
met
hod
are c
o
mpa
r
ed w
i
th t
he r
e
sults of the Ge
netic a
l
gor
ith
m
(GA) meth
od,
to
deter
mi
ne the
perfor
m
a
n
ce of
each of these
meth
ods.
Ke
y
w
ords
:
opti
m
a
l
si
z
e
and
loc
a
tio
n
, distrib
u
ted
g
ener
ation
(DG
)
, co-evo
lutio
n
a
ry p
a
rticle
s
w
arm
optim
i
z
at
ion (CPSO), system
losses
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
The
simpl
e
st
and th
e m
o
st
gen
eral d
e
finition of
di
stri
buted
gen
era
t
ion sou
r
ces i
n
clu
de
the sou
r
ce t
hat is
conn
e
c
ted
directly
to dist
ribute
d
(the
cli
ent).
Usua
lly the
s
e resource
s
are
referred
to a
s
small
-
scal
e
power pl
ants.
There
a
r
e v
a
riou
s d
e
finitions fo
r di
stri
buted g
ene
ra
tion
sou
r
ce in vie
w
of different
institutes. From t
he pe
rsp
e
ctive of the Inte
rnation
a
l Energy
Age
n
cy
(IEA), DG refers to the s
o
urc
e
that c
a
n
me
et
cu
stome
r
re
quire
ment
s
on-site, an
d
help
distrib
u
tion
n
e
twork in
ene
rgizi
ng. In
th
e view of
CI
GRE,
DG
ref
e
rs
to
a
re
so
urc
e
th
at is
f
a
cin
g
feature
s
: It’s
not e
s
tabli
s
h
ed a
cent
rali
zed,
it’s not ce
ntralized disp
atchin
g,
it’s u
s
ually co
nne
cted
to the distri
b
u
tion net
work and its valu
e is u
s
ua
lly l
e
ss than 5
0
M
W to 10
0M
W. In the vie
w
of
Powe
r Re
se
a
r
ch In
stitute, DG is the p
o
w
er of a fe
w KW to 50MW.
Use the
DG
in po
wer
syst
em ca
n have
advant
ag
es
su
ch a
s
: re
d
u
ce l
o
sse
s
; improve
voltage profil
es, increa
se
d reliability, lowe
r TH
D a
nd power sy
stem im
provement qualit
y. In
addition, the
small si
ze
of this re
sou
r
ce i
s
an
oth
e
r advant
age
that it’s a very sh
ort time of
installatio
n
a
nd be
in pl
ace. A numb
e
r
of ava
ilable
d
i
stribute
d
p
o
w
er ge
neratio
n tech
nolo
g
ie
s in
the worl
d are
:
fuel cells, wind turbine
s
, sola
r po
we
rhou
se
s, geot
herm
a
l po
we
rhou
se
s, micro-
turbine
s
an
d so on.
Therefore, it l
ooks e
s
sentia
l to determini
ng di
stribute
d
gene
ra
tion
u
n
its to a
c
hiev
e these
benefits. So
far, seve
ral
method
s h
a
ve bee
n p
r
op
ose
d
such a
s
minimi
zin
g
co
sts, im
prove
voltage p
r
ofil
es, lo
w T
H
D,
increa
sed
sy
stem reli
ability,
minimi
zing system
lo
sses and etc.
to DG
determi
ne th
e optimal l
o
cation
and
size. In ea
ch
of these m
e
thod
s, seve
ral o
p
timizati
on
algorith
m
s
are used to
ach
i
eve the d
e
s
i
red goal. In [1] to [7] refere
nc
es
, it is
us
ed G
A
to
impr
o
v
e
the voltage p
r
ofile an
d mi
nimizin
g
the l
o
sse
s
, in ref
e
ren
c
e [1
2], redu
ce th
e cost ha
s b
een
to
bas
is
of ac
counting, in [8],[9] references
,
it is
us
ed A
C
O algorithm to reduce losses
and improv
e
voltage, in re
feren
c
e [1
3], it is u
s
ed
GA
in o
r
de
r to e
liminate the
shor
tcomin
gs system
volta
g
e
with DG, in [1
0, 11] refe
ren
c
e
s
, it has
used fuzz
y logi
c for mi
nimizi
ng lo
sses, a
n
d
finally, in [14]
referen
c
e, it’
s
u
s
e
d
T
abu
Search
Algo
rithm fo
r thi
s
pu
rpo
s
e
(de
t
erminin
g
the
optimal
lo
ca
tion
and
size of
DG). In thi
s
p
a
per, it i
s
p
r
e
s
ented a
meth
od to d
e
termi
ne the
num
b
e
r, lo
cation
a
n
d
size of DG
wi
th the goal of
minimizin
g
l
o
sse
s
and im
proving
relia
b
ility systems t
hat in whi
c
h i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 247 – 256
248
use
d
Co-evolutiona
ry P
a
rticle
Swarm Optimi
zat
i
on alg
o
rith
m (CPSO) for o
p
timi
zation
pro
c
ed
ure.
2. Ev
aluation and Selection of I
ndica
tors for DG I
n
stalla
tion
Installation of
DG witho
u
t the study will
hav
e a negat
ive effect in distributio
n net
works,
so to avoid th
e negative im
pact of DG o
n
system
parameters; it sh
ould
be exist
comp
re
hen
si
ve
and total
standa
rd
s for
control, insta
llation an
d p
l
acem
ent of
these
units [15]. Howe
ver,
according to
whi
c
h choose of following purp
oses, it will be specif
ied target
function:
2.1. Losses
Redu
ction In
dicator
Line
s a
r
e im
portant i
n
condition
s of
heavy l
oad
s,
so th
at its co
st will
im
pose to
con
s
um
er’
s
form of ene
rg
y by higher p
r
ice
s
. It is ob
vious that losse
s
in line a
r
e effects of p
o
we
r
transmissio
n in transmi
ssi
on lines. Thu
s
by us
ing DG, we can redu
ce the a
m
ount of po
wer
transmission in lines and therefor
e it will be reduced losses. In any
case, accordi
n
g to the power
and lo
cation
of DG there is also the po
ssi
bility of increa
sing the lo
sses lin
es.
2.2. Voltage of Profile Improv
ement Indicato
r
One of the a
d
vantage
s of
usin
g DG is i
m
prove th
e voltage p
r
ofile
and mai
n
tain
voltage
in acceptabl
e
range in the
consume
r
’s
terminal
. By
usin
g DG, be
cau
s
e am
oun
t of active an
d
rea
c
tive p
o
wer l
oad
s i
s
provide
d
by
voltage
pro
f
ile, it will
b
e
redu
ced
e
l
ectri
c
ity in t
he
transmissio
n line and the
r
ef
ore st
ren
g
the
n
of voltage range for
con
s
umer.
2.3. Increase
in S
y
stem L
o
ading Indic
a
tor
One othe
r ad
vantage
s of usin
g DG i
s
redu
ct
ion of a
c
tive and re
a
c
tive power transitio
n
from the tra
n
smi
ssi
on li
nes
(Ove
rall
appa
rent
p
o
we
r). T
h
is
works le
ads to increa
se
of
transmissio
n
lines capa
city and
therefore it will
be
preventing co
n
s
tru
c
tion and
develo
p
ment
of
new li
ne
s an
d
other i
n
stall
a
tions
su
ch
as tran
smissio
n
and
distri
buti
on sub
s
tation
s an
d the
r
efo
r
e
redu
ce
s cost
s the relate
d to them.
2.4. Reliability
Indicator
Improving th
e reliability o
f
the system
is
one of the obje
c
tives of using di
stributed
gene
ration.
But this d
o
e
s
not
mea
n
that we
sh
o
u
ld loo
k
to it
as
an i
nde
pend
ent obj
e
c
tive
because if we use
DG to
any reason, i
t
will affe
ct reliability. Of course
maybe
we can know i
n
total, all these objectives for a dist
ributi
on net
work as subset of the system's rel
i
ability.
2.5. Voltage Stabilit
y
Indi
cator
In the network, voltage
stability is a
s
sociate
d
with
the syste
m
's
ability to pro
v
ide the
need
ed rea
c
tive
power of
netwo
rk.
In o
t
her words,
most
of rea
c
t
i
ve
power re
serve
in syst
em
resulted a hig
her de
gree of
vo
ltage stabil
i
ty in the system.
2.6. En
v
i
ron
m
ental Indic
a
tor
With utili
zatio
n
of
DG
an
d
electri
c
al
en
e
r
gy p
r
od
uctio
n
, it will
be
m
o
re
le
ss the
e
m
issi
on
s
of
green
hou
se ga
se
s and othe
r environ
menta
l
polluta
nts co
mpa
r
ed
with
tradit
i
onal
techn
o
logie
s
.
We can u
s
e
resource
s th
at are o
p
ti
mal in this respect a
c
cordin
g to percent
of
emission
s of DG. But it is not con
s
id
ere
d
as impo
rtan
t indicators in
our co
untry.
No
w, with re
gard
s
to the
material
s ab
o
v
e by
targetin
g the two ta
rgets to redu
ce losse
s
and i
m
prove
reli
ability, al
l indi
cato
rs
are
pr
ovided.
Becau
s
e
re
duced l
o
sse
s
and
imp
r
ov
ed
reliability a
r
e
more
co
nsi
s
t
ent with th
e p
h
ilosophy
of
usin
g di
strib
u
t
ed gen
eratio
n. The
obje
c
tive
function i
s
d
e
fined a
s
th
e
sum
of this
two indi
ca
to
rs (Re
d
u
c
e lo
sses
and
im
prove
relia
bili
ty)
.
Thus our obj
e
ctive function is
a m
u
lti-objective
fu
ncti
on (Multi-p
urpose) th
at is
major differe
nce
with the singl
e
indicator objective function
that we will
discuss them
in the following.
3. Model of L
o
sses
Redu
ction Indica
tor
We n
eed
re
ductio
n
in p
o
we
r lo
sse
s
for op
eratio
n
efficiently of
netwo
rk. Lo
sses i
n
distrib
u
tion sy
stem are cal
c
ulat
ed from th
e Equation (1
), (2).
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Optim
a
l Placem
ent and Sizing of Di
strib
u
ted Ge
n
e
rati
on Unit
s Usin
g… (Alire
z
a
Kaviani
-Arani
)
249
nn
Li
j
i
j
i
j
i
j
i
j
i
j
i1
j
1
P A
(
P
P
Q
Q
)
B
(
Q
P
P
Q
)
(1)
i
j
ij
i
j
ij
ij
ij
ij
ij
Rc
o
s
(
δδ
)R
s
i
n
(
δδ
)
A,
B
VV
VV
(2)
P
L
: Power los
s
es
P
i
: Ac
tive po
wer at bus
i
Q
i
: Reactive
power at bu
s i
V
i
: Bus volta
ge i
i
: Phase angl
e
of bus i
The o
b
je
ctive of solving th
e problem
is
minimi
zi
ng th
e total po
we
r
losse
s
so that
the first
part of the obj
ective f
unc
tion is
as
follows
:
sc
N
1L
k
i1
FP
L
o
s
s
(3)
The co
nst
r
ain
t
s governi
ng i
s
sue is a
s
foll
ows:
Powe
r bala
n
ce con
s
trai
nt
sc
sc
NN
DGi
Di
L
i1
i1
PP
P
(4)
Ran
ge of acti
ve and rea
c
ti
ve powe
r
pro
duced by the DG
max
DGi
DGi
min
DGi
Q
Q
Q
(5)
max
DGi
DGi
min
DGi
P
P
P
(6)
Ran
ge of net
work lo
sses
kk
L
o
s
s
(
w
i
t
hDG)
L
o
ss
(
w
i
t
hout
DG)
(7)
Ran
ge of line
loading
max
ij
ij
I
I
(8)
4. Calculate the Reliability
Index
4.1. Unit Unav
a
ilabilit
y
It is defined the probability
of failure in
some
time int
e
rvals
duri
n
g
the work in t
he next
as th
e u
navai
lability of unit
and it i
s
kno
w
n a
s
the
unit f
o
rced
rem
o
va
l rate
(
FO
R
) i
n
ap
plicatio
n
s
of po
wer sy
stems [1
6]. Thi
s
p
a
ra
meter i
s
d
e
fined
based
on
the
ra
tio of the t
w
o
units value
as
follows
:
(9)
[d
o
w
n
ti
m
e
]
FOR
[down
ti
m
e
]
[
up
tim
e]
rr
f
mr
T
That
λ
is
expec
ted failure rate,
μ
is expecte
d rep
a
ir rate
s,
m
is mean time
to failure
(
MTTF = 1/
λ
),
r
i
s
me
an tim
e
to repai
r (
M
TTR =
1/
μ
),
m+
r
is m
ean
time bet
wee
n
f
a
ilure
s
(
MTB
F
=
1/f
), f is frequency pe
riod a
nd
T
is si
nce
perio
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 247 – 256
250
(10
)
MTT
R
FO
R
M
T
T
R
M
TTF
In co
nne
ctio
n with
the
p
r
odu
ction
eq
uipment
with relatively lo
ng d
u
ty cycl
e, FO
R
parameter i
s
a probabili
stic estim
a
tes
whi
c
h show
s that the production unit will not be able to
next time load servi
c
e un
d
e
r simil
a
r ci
rcumstan
ce
s.
4.2. Energ
y
I
ndex Reliabilit
y
(EIR)
Area und
er th
e load cu
rve sho
w
s the co
nsum
ed en
ergy during a specifi
c
peri
o
d
and can
be u
s
e
d
to
cal
c
ulate
not
feedin
g
en
ergy
due
de
ficien
cy in
manufa
c
turi
n
g
capa
city.
This
para
m
eter i
s
defined the ratio of energy
lost due
to m
anufa
c
turin
g
defect
s
and t
o
tal requi
rem
ent
energy for fe
eding
the n
e
twork. It’s i
n
d
epen
dent of
t
i
me to d
e
fine
this p
a
ra
mete
r for the
defin
ed
perio
d in th
e load
cu
rve
and i
s
u
s
u
a
lly con
s
id
ered for a
da
y, a month
or a yea
r
.
An
y
manufa
c
turi
n
g
defect ca
u
s
ing lo
ss of
load pow
e
r
still be obtained its pro
bability from th
e
followin
g
equ
ation:
(11
)
Pr
(
)
(
)
1
n
n !
m
(n
-
m
)
!
m!
mn
m
n
ob
U
A
m
AU
That m is
nu
mber
of units that have be
en dam
age
d,
n
is the total
numbe
r of u
n
its,
U
isunit not
ava
ilable and
A
i
s
avail
ability
of units.
Probable
energy l
o
ss in a Power fail
ure is
E
k
P
k
.
The total od this multiplie
s
is the total en
ergy lost o
r
h
ope lo
st energy.
(12
)
1
n
kk
k
L
OE
E
E
P
That
P
k
is possi
bility of exi
t
produ
ction
unit with a capacity of
Q
k
and
E
k
is en
ergy lost
due to
the
p
r
odu
ction
unit
failure
with
a capa
city of
Q
k
. Thi
s
pa
rameter can
b
e
no
rmali
z
e
d
b
y
usin
g the total energy un
de
r the
load curve that is defined by
E
.
(13
)
..
1
n
kk
pu
k
E
P
LO
E
E
E
The amou
nt of
LOEE
p.u.
is the
ratio
b
e
tween potential
energy
lo
st d
ue to
corrupti
on u
n
it
and the total
requi
re
d ene
rgy to feed the netwo
rk loa
d
. Index of reliability energ
y
EIR
is defined
as
follows
:
(14
)
..
1
p
u
E
IR
L
O
E
E
5. Objectiv
e
Function
the
Problem
By combini
n
g
the phrase a
bove, obje
c
tive func
tio
n
to
determi
ne the
size an
d location of
DG resource
s are p
r
ovid
e
d
as follo
ws:
11
2
2
,1
n
To
t
a
l
i
i
Fw
F
w
F
w
(15
)
11
,
2
2
,
To
t
a
l
p
u
p
u
Fw
F
w
F
(16
)
w
1
and
w
2
p
a
r
amete
r
s are
weig
hting
co
efficients th
at are
an in
dication of thei
r
relative
importa
nce.
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n
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-Arani
)
251
6. Particle Sw
arm Optimi
z
a
tion (PSO)
PSO
is an evolutiona
ry comp
utation tec
hni
que
wi
th the m
e
ch
anism
of i
n
d
i
vidual
improvem
ent,
pop
ulation coo
peration and com
petit
ion, which
is ba
sed
on t
he
simulatio
n
of
simplified
so
cial model
s, su
ch a
s
bird flo
cki
ng, fish schoolin
g and the swarming
theory (Ken
n
edy
and Eb
erh
a
rt
, 1995
). In P
S
O, it start
s
with the
ran
d
o
m initiali
zati
on of a
po
pul
ation (swarm
) o
f
individual
s
(p
article
s
) in
th
e search
spa
c
e
and
wo
rks on th
e
so
cia
l
beh
avior
of
the pa
rticle
s i
n
the swarm. T
herefo
r
e, it finds the glo
b
a
l
best solu
tio
n
by simply adjustin
g
the trajecto
ry of each
individual
toward
s it
s o
w
n
best l
o
cation
and to
wa
rd
s t
he b
e
st
pa
rticle of th
e
swarm at e
a
ch tim
e
step
(g
ene
rat
i
on).
Ho
weve
r, the t
r
aje
c
to
ry of e
a
ch in
dividual i
n
th
e sea
r
ch
spa
c
e i
s
adju
s
te
d by
dynamically a
l
tering th
e vel
o
city of e
a
ch
particl
e,
a
c
co
rding
to it
s o
w
n flying
exp
e
rien
ce
an
d t
he
flying experie
nce of the oth
e
r pa
rticle
s in
the sea
r
ch
space.
The po
sition
and the velo
city of the ith
particl
e in the
dimen
s
ion
a
l sea
r
ch spa
c
e
can b
e
r
e
pr
es
e
n
t
ed
a
s
X
i
=
[
X
i1
, X
i2
, …, X
iN
]
T
and
V
i
= [V
i1
, V
i2
, …, V
iN
]
T
, res
p
ec
tively. Eac
h
partic
le has
its own
be
st positio
n (
pb
es
t
)
P
i
= [
P
i1
, P
i2
, …, P
iN
]
T
corre
s
p
ondin
g
to the personal be
st obj
ective
value obtai
n
ed so far
at time
t
. The
global
be
st parti
cle (
gb
est
) i
s
d
enot
ed by
P
g
, whic
h
rep
r
e
s
ent
s th
e be
st
parti
cl
e foun
d
so
fa
r at tim
e
t in
t
he e
n
tire
swa
r
m. Th
e n
e
w
velocity of
ea
ch
particl
e is cal
c
ulate
d
as foll
ows:
(17
)
(
)
()
()
,1
,
1
1
,
,
2
2
,
(
,)
,
1
,
2
,
,
ij
t
i
j
t
ij
i
j
t
g
j
i
j
t
vw
v
c
r
p
x
c
r
p
x
j
d
Whe
r
e
c
1
and
c
2
are con
s
tants calle
d
accele
ration coeffici
ents,
w
is called th
e inertia
fac
t
or,
r
1
and
r
2
are two in
d
epen
dent ra
n
dom num
bers uniformly distributed in the
range of [0, 1].
Thus, the
po
sition of ea
ch parti
cle i
s
update
d
in e
a
ch
gene
rati
on a
c
cordi
n
g
to the
followin
g
equ
ation:
(18
)
,1
,
,
()
(
)
(
1
)
,
1
,
2
,
,
ij
t
i
j
t
ij
t
x
xv
j
d
In the
stand
ard PSO, Equat
ion (17
)
is u
s
ed to
cal
c
ulat
e the
new vel
o
city a
c
cordi
n
g to its
previou
s
velo
city and to the dista
n
ce of its cu
rrent
position fro
m
both its own be
st hist
orical
positio
n and i
t
s neighb
ors’
best positio
n
.
G
enerally, the value of each
comp
one
nt in
V
i
can be
clamp
ed to th
e ran
ge [
V
i,m
i
n
, V
i,
m
a
x
] to control excessiv
e roa
m
ing of
particl
es
outside the sea
r
ch
spa
c
e [
X
i,m
i
n
, X
i,
m
a
x
] Then the particle f
lies toward a
new po
sition
accordi
ng to
Equation (1
8).
The process i
s
rep
eated u
n
t
il a user-defi
ned sto
ppin
g
crite
r
ion i
s
re
ach
ed [17].
6.1. Co-ev
o
lutionary
Particle S
w
arm Optimiz
a
tion (CPSO)
6.1.1. Mecha
n
ism of Co-e
v
o
lution
Due to the simpli
city of
prin
ciple a
n
d
easin
ess to implement, the penalty functio
n
method is the
most popul
ar techniq
ue to handl
e con
s
tr
aints. With re
spe
c
t to the main difficulty of
setting ap
pro
p
riate p
enalty
factor
s, Michale
w
icz an
d
Attia (1994)
indicated that
a self-a
dapti
v
e
scheme
is
a
promi
s
in
g direction. In th
e
previou
s
wo
rk by Coello
(2000
), a n
o
tion of
co-evol
u
tion
wa
s p
r
op
ose
d
an
d in
co
rp
orated
into
a
GA
to solve
co
nstraine
d optimizatio
n probl
em
s.
In this
pape
r, we
will make
so
me modifi
cat
i
ons
on
co
evolution a
n
d
incorp
orate
it into
PSO
for
con
s
trai
ned o
p
timization p
r
oblem
s [17].
The p
r
in
cipl
e
of co-evol
u
tion mo
del i
n
CPSO
i
s
sho
w
n i
n
Fig
u
re
1. In ou
r
CP
SO
, two
kind
s of
swarms a
r
e u
s
e
d
. In parti
cula
r,
one kind of
a
sin
g
le swarm
(de
noted b
y
Swarm
2
) wi
th
siz
e
M
2
is used adapt suitable pen
alty factors, anot
her ki
nd of multiple swarms (d
enoted
by
Swarm
1,1
,
Swarm
1,2
, …,
Swarm
1,M2
) each
with size
M
1
are used in parall
e
l
to search g
ood
deci
s
io
n solut
i
ons. Each pa
rticle
B
j
in
Swarm
2
repre
s
e
n
ts a set of penalty factors for particle
s
in
Swarm
1,j
, wh
ere
ea
ch
pa
rticle
rep
r
e
s
e
n
ts a
de
ci
sion
solution. In
every ge
ne
ratio
n
of
co
-evolut
i
on
p
r
oc
es
s
,
e
v
ery
Swarm
1,j
will evolve by using
PSO
for a certai
n nu
mber of gen
e
r
ation
s
(
G
1
) with
particl
e
B
j
in Swarm
2
as p
enalty factors for solution
evaluation to get a new
Swarm
1,j
. Then
th
e
fitness of ea
ch pa
rticle
B
j
in
Swarm
2
will be dete
r
mined. After all particl
es in
Swarm
2
are
evaluated,
Sw
a
r
m
2
will also evolve by using
PSO
wit
h
one ge
ne
ra
tion to get a new
Swarm
2
with
adjusted penalty factors.
The above coevolut
ion process will be repe
ated until a pre-defined
stoppi
ng crit
erion i
s
satisfied (e.g., a maximum n
u
mbe
r
of co
-evolution
ge
neratio
ns
G
2
is
rea
c
he
d).
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252
In brief, t
w
o
kind
s
of swa
r
ms evolve i
n
tera
ctively, whe
r
e
Sw
arm
1,j
is used t
o
evolve
deci
s
io
n solut
i
ons
while
Sw
a
r
m
2
is u
s
e
d
to a
dapt
pe
nalty facto
r
s for
solutio
n
ev
aluation.
Du
e
to
the co-evol
u
tion, not
only
deci
s
io
n
solut
i
ons are ex
pl
ored
evolutio
nary, but
also pe
nalty fact
ors
are adju
s
ted
in
a self-tu
n
i
ng way
to avoid
the
di
fficulty of settin
g
suitable
fa
ctors
by trial
and
error.
Figure 1. Graphical illustration fo
r the not
ion of co-evol
u
tion
6.1.2. Ev
alua
tion func
tion
for S
w
a
r
m1,
j
For
co
nstrain
ed optimi
z
ati
on p
r
obl
ems,
we
de
sign
the pe
nalty functio
n
follo
wing t
h
e
guida
nce su
gge
sted by Ri
chardson
et al. (1989
), i.e., not
only how many
con
s
traint
s are
violated b
u
t a
l
so th
e a
m
ou
nts in
which
such
con
s
trai
n
t
s a
r
e viol
ate
d
. In p
a
rticula
r
, the ith
pa
rti
c
le
in
Swarm
1,j
in
CPSO
is eval
uated by usi
n
g the followin
g
formula:
(19
)
12
_
_
ii
F
x
f
x
s
um
v
i
ol
w
num
v
i
ol
w
Whe
r
e
f
i
(x
)
i
s
the o
b
je
ctive value
of the i
t
h parti
cle,
su
m
_
viol
de
not
es th
e
sum
of all the
amount
s by
whi
c
h the
co
nstrai
nts
are
violated,
nu
m
_
viol
de
not
es th
e nu
mb
er of
co
nstra
i
nts
violation,
w
1
and
w
2
a
r
e p
enalty factors corre
s
po
ndin
g
to the particle
B
j
in
Swarm
2
.
The value of
sum
_
viol
i
s
calcul
ated a
s
follows:
(20
)
vi
o
l
1
sum
,
0
N
ii
i
gx
gx
Whe
r
e
N
is t
he num
be
r o
f
inequality constraints
(h
ere it is assu
med that all
equality
con
s
trai
nts h
a
ve been tra
n
s
form
ed to in
equality co
nst
r
aints).
6.1.3. Ev
alua
tion func
tion
for
Swarm
2
Each particle in
Sw
ar
m
2
repre
s
e
n
ts a
set of
facto
r
s (
w
1
and
w
2
).
After
Swarm
1,j
evolves
for a ce
rtain n
u
mbe
r
of gen
eration
s
(
G
1
),
the jth particl
e
B
j
in
Swarm
2
is evaluated
as follows.
a)
If there i
s
at least
one f
easi
b
le
soluti
on in
Sw
ar
m
1,
j
, then pa
rticl
e
B
j
is
evalua
ted usi
n
g
the followin
g
formul
a and i
s
called a valid
particle:
(21
)
fea
s
i
b
le
num
_
f
e
a
sib
l
e
n
u
m
_
feas
i
b
l
e
j
f
PB
W
h
er
e
f
eas
ib
l
e
f
deno
tes the
sum
of obje
c
tive f
unctio
n
valu
e
s
of fe
asi
b
le
solutio
n
s in
Sw
a
r
m
1,j
,
and
num
_fe
a
sibl
e
i
s
th
e
num
ber of
feasi
b
le
sol
u
tions in
Swarm
1,j
. The
re
ason fo
r only
con
s
id
erin
g feasi
b
le sol
u
tions i
s
to bias the
Swarm
1,j
toward
s fea
s
ible regio
n
s.
Moreove
r
, the
subtractio
n of
num
_feasi
b
l
e
in Eq
uation
(21
)
i
s
to
avo
i
d
Swarm
1,j
stagnatin
g at
certain
regi
on
s in
whi
c
h only ve
ry few parti
cl
es will h
a
ve g
ood obj
ective
values or ev
en be fea
s
ibl
e
. Con
s
eq
ue
ntl
y
,
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TELKOM
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ISSN:
2302-4
046
Optim
a
l Placem
ent and Sizing of Di
strib
u
ted Ge
n
e
rati
on Unit
s Usin
g… (Alire
z
a
Kaviani
-Arani
)
253
Swarm
1,j
will be encouraged to move towa
rds regions includi
ng
a lot of
feasi
b
le sol
u
tions with
good obj
ectiv
e
values. In addition,
nu
m
_
feasible
al
so a
c
ts as a
scali
ng fact
or wh
en u
s
e
d
to
divide
feas
i
b
l
e
f
.
b) If the
r
e i
s
no fea
s
ibl
e
solution i
n
Swarm
1,j
(it can
b
e
con
s
ide
r
ed
that the p
enal
ty is too
low), then p
a
rticle
B
j
in
Swarm
2
is evaluated as follo
ws and i
s
call
e
d
an invalid p
a
rticle.
(22
)
sum
_
v
i
ol
M
a
x
nu
m
_
v
i
ol
nu
m
_
v
i
o
l
jv
a
l
i
d
PB
P
Whe
r
e
Max(P
valid
)
denotes the maximum fitness val
ue of all valid particles in
Swarm
2
,
su
m
_
v
i
o
l
denote
s
the
sum
of co
nstrai
nts viol
ation for all
particl
es i
n
Swarm
1,j
, and
nu
m
_
v
i
ol
count
s the total numbe
r of con
s
trai
nts violation for all
particl
es in
Sw
a
r
m
1,j
.
Obviou
sly, by using
Equ
a
tion (22), th
e pa
rticle i
n
Swarm
2
that re
sults in a
small
e
r
amount of co
nstrai
nts viol
ation of
Swarm
1,j
is consid
ered
better. Con
s
e
quently
, the search
may
bias
Swarm
1,j
to the regio
n
wh
ere
the
sum of
co
nstraints
viol
ation
is sm
all (i.e. the
bo
und
ary
of
the feasible region
). More
over, the addi
tion of item
Max(P
valid
)
is to
assu
re that the valid parti
cle
is alway
s
bet
ter than the invalid one to
guide the
search to the feasibl
e
regi
o
n
. In addition,
nu
m
_
v
i
ol
acts a
s
a scal
ing factor. Fig
u
re 2 sho
w
s t
he flow chart
of a
CPSO
algorithm.
Figure 2. The
process
com
putational al
g
o
rithm (CPSO)
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TELKOM
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KA
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ry 2015 : 247 – 256
254
7. Samples Net
w
o
r
k S
t
u
d
y
The propo
se
d method h
a
s
bee
n appli
ed on a 6
9
buses te
st n
e
twork
samp
les. All
netwo
rk d
a
ta and Algo
rith
m
CPSO
ha
s been give
n re
spe
c
tively in Table 1 an
d 2
.
Table 1. Data
distributio
n n
e
twork
sampl
e
69 bu
se
s
Net
w
ork
A
c
t
i
v
e
po
w
e
r (M
W)
Reacti
v
e
po
w
e
r
(M
v
a
r)
Total
acti
v
e
po
w
e
r
losses (MW)
Total
reacti
v
e
po
w
e
r losses (M
v
a
r
)
69 buses
3.80
2.69
230.0372
104.3791
Table 2. The
CPSO algo
rithm data
CPSO
Popula
t
io
n siz
e
Maximu
m n
u
m
b
er of
repetit
i
on
s Km
a
x
C1 = C2
w
30
100
2
0.4
Figure 3. 69 bus di
strib
u
tion network sample
Table 3.
CPS
O
re
sult
s t
o
t
he sam
p
le
s n
e
t
w
or
k
Total
real p
o
w
e
r
loss(kW
)
Min
A
v
e
.
Max
80.1933
95.4714
203.2326
A
v
e
r
age Time (
S
ec.)
5.6341
Conve
r
ge
nce
ch
ara
c
te
risti
c
of b
e
st th
e
prop
osed alg
o
rithm re
spo
n
s
e
i
s
sho
w
n
i
n
Figu
re
4. Figure
5 shows total a
c
tive power l
o
sse
s
re
sulti
ng from the
100 time
s im
plementatio
n
of
CPSO-OPDG
prog
ram.
Figure 4. Con
v
ergen
ce
cha
r
acte
ri
stic of
best the p
r
op
ose
d
algo
rith
m respon
se
0
20
40
60
80
100
80
82
84
86
88
90
92
94
96
98
100
Gene
r
a
t
i
on
T
o
t
a
l
Re
al
P
o
w
e
r L
o
s
s
(k
W)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Optim
a
l Placem
ent and Sizing of Di
strib
u
ted Ge
n
e
rati
on Unit
s Usin
g… (Alire
z
a
Kaviani
-Arani
)
255
Figure 5. Total active po
wer losse
s
fro
m
the 100 times imple
m
ent
ation of prog
ram
CPSO-
OPDG
Optimum lo
cation an
d
size of
DG
for
6
9
bu
s
system
by usi
ng
GA
and
CPSO
al
gorithm
s
is sh
own in T
able 4. As it is sh
own in T
able,
loss re
ductio
n
perce
ntage of acti
ve and re
acti
ve
power in ca
se one
DG
by
using the
CPSO
algorith
m
is equal to
63.05% and
60.28%, while,
these t
w
o p
a
rameters a
r
e
equal to
61.6
4
% and 5
8
.4
3% by usin
g
the
GA
algo
ri
thm. In the case
of two
DG
, lo
ss redu
ction
percenta
ge of
active and re
active po
wer
with usi
ng of
CPSO
algo
rithm
is equal to 6
8
.18% and 6
4
.81%, while,
it is
equal to 63.51% an
d 60.43% by using the
GA
algorith
m
. Also in the case
of three
DG
, loss re
du
ction
percenta
ge
of active and
rea
c
tive po
wer
w
i
th
us
in
g o
f
CPSO
algo
rithm is
equ
al
to 69.19%
and
65.81%,
but thi
s
am
ount i
s
eq
ual
to
67.93% and
64.26%
by using the
GA
algorithm. Also
it should be
mentione
d that
CPSO
has
this
advantag
e that it can be achieve
d
true optimal sol
u
tion in the first few repetitio
n, but for
GA
we
need to ru
n the algo
rithm
with many re
petitions
to g
e
t the main optimum and n
on-lo
cal a
n
swer.
Table 4.
DG
Optimal Placement for 69
buses
IEEE
network u
s
ing
GA
and
CPS
O
algorith
m
s
Me
t
h
od
Bus
No.
DG
Size
(MW
)
Bus
No.
DG
Size
(MW
)
Bus
No.
DG
Size
(
MW
)
Ploss
(kW
)
Qloss
(k
v
a
r)
Loss Red
u
cti
o
n
%
Real
Reacti
v
e
Load
Flo
w
An
a
l
ys
i
s
230.0
3
104.3
7
Heuristi
c Searc
h
56 1.807
84.93
41.45
63.08
60.29
GA
61 1.500
88.21
43.39
61.64
58.43
62 0.861
61
0.886
83.91
41.31
63.51
60.43
62 0.736
18
0.519
61
0.809
73.76
37.31
67.93
64.26
CPSO
56 1.808
84.98
41.47
63.05
60.28
56 1.724
53
0.519
73.18
36.74
68.18
64.81
56 1.666
55
0.375
33
0.508
70.87
35.69
69.19
65.81
8. Conclusio
n
In this paper, it has bee
n used a
n
Evolut
ionary Intelligent Method for sol
v
ing the
probl
em of lo
cation
and o
p
t
imized
size o
f
DG
re
so
ur
c
e
s
wit
h
mu
ltiple objectives.
CPSO
method
is very powerful and accu
rate, as well a
s
is sim
p
le o
n
Implementa
t
ion. About the results of the
test netwo
rk
(69 bu
se
s
IEEE
) that is don
e by using two intelligent a
l
gorithm
s
CP
SO
and
GA
, i
t
must be sai
d
that the simulati
on sh
ows that loss re
ductio
n
per
centage of act
i
ve and rea
c
tive
power with
u
s
ing
of
CPSO
algo
rithm i
s
more
an
d b
e
tter of th
e
re
sults o
b
taine
d
of
GA
al
go
rithm.
Of co
urse, t
he mai
n
a
d
vantage
CPS
O
alg
o
rithm
is in
the tim
e
of o
b
tain
s optimal val
ues.
Becau
s
e j
u
st
as me
ntione
d
,
CPSO
in th
e first fe
w re
petition; indi
cates the
right
answe
r. But we
sho
u
ld be i
n
crea
se the
nu
mber
of these rep
e
ti
tions
to find the rig
h
t optimal sol
u
tion in the
GA
.
17
0
18
0
19
0
20
0
21
0
22
0
80
10
0
12
0
14
0
16
0
18
0
20
0
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 247 – 256
256
So in this
c
o
ntext,
CPSO
algorith
m
is more effici
ent
than
genetic algorithm. So in the end, we
can
be
state
d
that
simulat
i
on results
of the
CPSO
m
e
thod i
s
m
o
re effective
co
mpared to
ot
her
method
s use
d
in this field.
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