Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 10
74
~1
081
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
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p
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1081
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Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Op
timal placement of wind turb
ine
in a r
a
d
i
al
distribution
network using PSO m
e
thod
Y
a
h
i
ao
u
i
Merzo
ug
,
B
o
ua
n
a
ne Ab
delkrim,
Bo
u
m
edien
e
La
rbi
L.G
.
E L
a
bo
ra
to
ry
, D
e
p
a
rte
m
en
t
o
f
El
ectr
i
cal
Eng
i
neer
ing
,
Dr. M
o
ulay
Tahe
r
Univ
ers
i
ty o
f
S
a
id
a,
Algeria
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Au
g 2
3
, 2
019
Re
vise
d N
o
v
9
,
20
19
A
c
ce
p
t
ed
Jan
22
, 20
20
Th
e a
i
m of
th
is
ar
t
i
c
le
is
t
o
ap
pl
y
th
e P
a
r
t
i
c
le
S
w
ar
m O
p
t
i
mi
z
a
t
i
o
n
(
P
S
O
)
meth
od
to
f
i
nd
t
h
e
b
e
st
lo
ca
ti
on
f
o
r
th
e
wi
nd
t
u
r
b
i
n
e in
th
e
r
a
d
i
al
di
st
r
i
b
u
ti
on
net
w
o
r
k.
T
h
e
o
p
t
ima
l
lo
cat
io
n
i
s
f
o
un
d u
s
i
n
g
th
e
lo
ss
sen
s
i
tiv
it
y
f
act
or
.
By
resp
ecting th
e
co
n
s
train
t
s
of
th
e a
c
tiv
e
pow
er
t
r
an
smitted
in
th
e
b
r
an
ches
and
t
h
e limits of t
h
e
voltages modules for
al
l t
h
e nodes. T
h
e
v
a
lidit
y
of
this
met
h
od
i
s
t
e
s
t
ed on
a 33-IEEE tes
t
net
w
ork and
the
resul
t
s
obtai
n
e
d
are
comp
ar
e
d
w
i
th
t
h
e res
u
lts
of b
a
sic
lo
ad f
l
ow.
Ke
yw
ords:
P
a
r
t
i
c
le
sw
a
r
m op
tim
iz
at
io
n
Ra
dia
l
di
strib
u
t
i
on s
y
ste
m
Di
strib
u
t
e
d ge
nerat
i
o
n
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
Yahi
a
oui
M
e
rz
ou
g,
L.G
.
E L
a
b
o
rat
o
ry,
De
part
em
ent
o
f
El
ec
t
r
i
c
a
l
E
ngi
nee
r
i
n
g,
Dr.
Mo
ul
ay
Ta
her U
n
i
v
e
r
si
ty
of Sai
d
a
,
A
l
ge
ri
a,B
P
1
3
8
E
n
-
N
asr,
(2
00
0
0
S
a
i
d
a), Al
ge
ri
a.
Emai
l:
mya
h
ia
oui
20
0
1
@
y
a
h
oo
.fr
1.
IN
TR
O
DUCTION
Elec
tr
ic
pow
e
r
, wor
l
dw
i
d
e,
h
a
s
b
e
c
o
me
a con
s
ume
r
g
ood
fo
r
b
o
t
h
ev
e
r
yda
y
l
i
f
e
an
d
the
e
c
o
n
o
m
y of
t
h
e
c
o
unt
ri
e
s
, a
nd
t
h
e
s
m
al
l
e
st
probl
e
m
s of el
ec
tric
al
o
r
i
g
i
n
ha
ve
a
g
r
ea
t i
n
fl
ue
nce
on
t
h
e c
ont
in
u
i
t
y
of
ec
onomi
c
ac
ti
vi
ti
e
s
. T
h
ere
f
o
r
e, t
h
e
p
o
sses
s
i
on o
f
re
li
abl
e
a
n
d
ec
o
n
o
mi
ca
l el
e
c
t
r
i
c
i
t
y net
w
o
r
ks
ope
ra
t
i
ng
pro
p
erly
a
n
d e
n
su
ri
n
g
a c
onti
nui
ty
of servi
c
e
and a
g
o
o
d
q
u
al
it
y o
f
ene
r
gy
has
bec
o
me
essent
ia
l
in
or
der t
o
cont
ri
b
u
te
p
o
si
ti
ve
ly to t
h
e
de
vel
o
pme
n
t
of o
u
r
m
ode
rn
soc
i
e
t
ie
s.
Th
e
d
i
str
i
b
u
t
i
o
n
n
e
twor
k mu
st
evo
l
v
e
t
o
w
a
rd
s a
f
l
e
x
ib
le an
d in
te
ll
ig
en
t
n
e
two
r
k th
a
t
be
st in
t
e
gr
a
t
e
s
l
o
cal
a
n
d /
or
rene
w
a
bl
e e
n
e
r
gi
es.
The
ope
nin
g
u
p
of t
h
e
el
ect
ric
i
t
y
market
a
nd
t
h
e
g
r
owi
ng e
nvi
ron
m
ent
a
l
conc
e
r
ns li
n
k
e
d
t
o
gl
o
b
al
cl
ima
t
e
c
h
a
nge
are l
eadi
n
g
to
sig
n
i
f
i
c
a
n
t
c
h
a
nge
s,
pa
rti
c
ula
r
l
y
i
n
dist
ri
b
u
t
i
on
net
w
orks,
w
i
t
h
t
h
e
massi
ve
i
n
flu
x
of
de
ce
nt
ra
l
i
z
e
d p
r
od
uct
s
. T
h
i
s
e
v
ol
ut
io
n c
a
n
be
e
nvi
s
a
ge
d
by
de
vel
opi
ng
i
n
te
ll
i
g
ent
s
y
s
t
ems,
ca
pa
b
l
e
o
f
mi
ni
miz
i
ng
the
i
m
pac
t
s ge
nera
te
d
by
t
h
e
i
n
se
rt
i
o
n
of
d
e
ce
nt
r
a
l
i
z
e
d
p
r
od
u
c
tion
s
and
/
o
r
by
t
h
e
sear
c
h
f
o
r
n
e
w
arc
h
it
ec
tu
r
e
s. Th
ese
t
w
o
so
lu
t
i
on
s
sh
ou
ld
al
low
t
h
e
in
cre
a
s
e
o
f
the
dec
e
nt
ral
i
zed
p
r
o
d
u
ct
i
o
n
ra
te
i
n
t
h
e
di
st
ri
but
i
o
n
net
w
o
r
k
unde
r
the
best
e
c
o
n
o
mic
a
n
d se
c
u
ri
ty
co
n
d
i
t
i
ons.
The
di
stri
but
i
o
n net
w
o
r
k
wa
s
not
o
r
i
g
i
n
a
l
l
y
de
si
gne
d
t
o
h
o
u
se
pro
d
u
c
t
ion
u
n
it
s,
b
u
t t
o
p
r
ovi
de
uni
di
re
ct
i
o
nal
e
l
e
c
t
r
i
c
i
t
y
f
r
o
m
t
h
e
dist
ri
b
u
t
i
on
net
w
o
r
k t
o
me
di
u
m
a
n
d l
o
w
vol
t
a
g
e
c
o
nsu
m
ers.
Th
e
use
o
f
D
i
st
ri
bu
te
d
i
n
t
e
l
lig
e
n
t s
y
stems
alo
n
e
wi
ll
n
o
t
b
e
eno
ugh
to
e
l
i
m
in
a
t
e
all
th
e
p
r
ob
le
ms t
h
at
th
e
d
i
strib
u
t
i
o
n
net
w
ork
wi
ll
fa
ce
i
n
c
a
se
o
f
si
gni
fi
ca
n
t
penet
r
a
t
i
o
n
o
f
dec
e
n
t
r
a
l
i
z
e
d
p
r
od
uc
ti
ons
[1
].
Di
strib
u
t
i
on ne
t
w
o
r
ks a
r
e
b
r
a
n
c
h
e
d
radi
al
t
o
pol
og
y
net
w
orks a
n
d ha
v
e
se
ve
ral
l
o
a
d
no
d
e
s. The
pro
b
le
m t
h
at
arises
i
s
ho
w t
o
c
h
o
o
se
t
h
e
b
e
st
l
o
ca
ti
on
o
f
GED
(dec
e
n
t
r
a
l
i
z
e
d
ene
r
g
y
ge
nera
t
o
r
)
i
n
a
di
st
ri
buti
o
n
ne
tw
or
k.
Th
is
p
r
ob
le
m is
th
e
sub
j
ec
t o
f
r
e
s
ear
c
h
t
h
e
m
a
t
ic
o
f
t
h
is
a
r
t
i
c
l
e,
for
this
w
e
h
a
v
e
u
s
e
d
th
e
sof
t
w
a
re
fo
r
ca
lc
ula
t
i
ng t
h
e
po
we
r
fl
ow
an
d cal
cul
a
t
e
s
o
me
pa
ramet
e
rs t
o
det
e
rmine
t
h
e b
e
st
n
ode
of GED
c
o
n
n
ec
t
i
on
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Opt
i
m
a
l
plac
e
m
ent
of
wi
n
d
t
u
rbi
n
e i
n
a r
a
d
i
al
dist
rib
u
t
i
o
n
net
w
ork
u
s
i
n
g
PS
O
m
e
t
h
od
(
Y
a
h
i
a
oui
Merz
ou
g
)
1
075
S
e
ve
r
a
l
me
th
o
d
s
ha
ve
bee
n
use
d
t
o
c
h
o
o
s
e
the
o
p
t
i
m
a
l
l
o
ca
ti
on of
t
h
e wi
n
d
t
u
rbi
n
e in t
h
e d
i
st
ri
buti
o
n
ne
tw
or
k i
n
o
r
der
t
o
r
e
d
u
ce
t
h
e
ac
t
i
ve
los
s
e
s.
[
2
]
,
T
r
y t
o
pr
o
v
i
d
e
a
co
mp
re
he
nsive
a
p
p
r
oa
ch t
o
s
o
l
v
e
t
h
e
p
r
o
b
l
em
of
p
l
a
c
e
m
e
n
t
a
nd de
ter
m
i
n
ing th
e c
a
p
a
c
ity
of
win
d
un
i
t
s i
n
t
h
e ne
two
r
k
.
[
3
],
p
r
e
s
en
ts a vo
lt
age
sen
s
itiv
ity
an
aly
s
is
w
i
t
h
resp
ec
t to
th
e
r
e
a
l
po
w
e
r
in
je
ct
e
d
w
i
th
ren
e
w
a
b
l
e e
n
erg
i
es to
det
e
r
m
i
n
e th
e
op
t
i
ma
l
i
n
t
e
gra
t
i
o
n
of
di
str
i
but
e
d
ge
n
e
rat
i
o
n
(
D
G
)
i
n
di
st
ri
b
u
ti
on
s
y
st
ems
(
D
S)
.
I
n
t
h
is ar
tic
le
,
a
te
chn
i
qu
e u
s
ed
is b
a
se
d
on
t
h
e
par
t
i
c
le
s
w
a
r
m o
p
t
i
m
iza
t
i
o
n
me
tho
d
(PS
O
)
t
o
de
te
rmi
n
e
a
n
o
p
t
i
m
a
l
al
l
o
ca
ti
on
of
wi
nd
-ba
s
e
d
di
st
ri
b
u
te
d
gene
rat
o
rs i
n
o
r
de
r t
o
red
u
c
e
t
h
e
r
eal
po
wer
l
o
ss
o
f
th
e
d
i
s
t
ribu
tio
n
sy
st
em
.
Th
e
d
e
v
e
lop
e
d
meth
od
i
s
i
m
p
l
eme
n
te
d on
th
e I
EEE 3
3
bu
s te
st
sy
ste
m
. Th
e
w
o
rk
pl
an
f
o
r
thi
s
a
r
t
i
c
l
e
ha
s
bee
n
or
ga
ni
ze
d
a
s
f
o
l
l
ow
s:
T
h
e
basi
c
ma
the
m
a
t
ic
al
mo
del
o
f
radi
a
l
dist
ri
b
u
t
i
on
syst
ems i
s
pre
s
ent
e
d i
n
the
S
ect
i
on 2
.
Wi
nd
gene
r
a
t
i
on
syst
em mo
del
i
n
g
i
s
give
n i
n
Se
ct
i
on 3
.
I
n
sec
t
i
on
4
Lo
ss
sens
itiv
i
t
y
fa
ct
o
r
an
d
P
S
O
me
thod
i
s
u
s
e
d
fo
r op
t
i
ma
l a
l
l
o
ca
tio
n
o
f
w
i
n
d
.
Resu
lts
a
nd D
i
s
c
u
s
s
i
on
e
xpla
i
ne
d i
n
se
ct
ion5
.
F
i
na
ll
y,
co
nc
lu
de
s t
h
is
pa
per
a
nd
pr
o
pos
es
pe
rs
pec
t
i
v
es
fo
r
c
o
nt
inu
a
ti
on
w
o
r
k
.
2.
Mat
h
e
m
at
ical m
o
de
l
2.
1. Po
wer fl
o
w
f
o
rm
u
l
at
i
o
n
Th
e go
a
l
of th
i
s
ar
tic
le
is to
f
i
n
d
t
h
e
op
t
i
ma
l lo
c
a
tion of t
h
e w
i
nd
t
u
rb
in
e in th
e
n
e
two
r
k
i
n
or
d
e
r
t
o
mi
nimi
ze
ac
ti
ve los
s
es.
T
h
e
te
chni
que p
r
o
pos
ed
f
o
r
c
a
l
c
ul
at
i
ng
t
h
e po
we
r f
l
o
w
in
the
ra
dia
l
dist
ri
but
io
n
ne
tw
or
k i
s
ba
sed
ma
inl
y
o
n
kn
owl
e
d
g
e
o
f
t
h
e
to
pol
og
y
or
a
r
c
h
i
t
ect
ur
e
of
t
h
e
net
w
or
k.
The
si
n
g
l
e
-l
i
n
e
d
i
a
g
ra
m is
show
n in
F
i
gu
r
e
1.
Th
e pow
er
f
l
ow
e
q
u
a
ti
on
s are
g
i
v
e
n
by
[
4
-
6
].
F
i
gu
re
1.
S
i
n
g
l
e
l
i
ne
di
a
g
ra
m
of
ra
di
al
fee
d
er
,
.
|
|
(1
)
,
.
|
|
(2
)
|
|
|
|
2
,
.
,
.
.
|
|
(3
)
Whe
r
e ,
an
d
are
t
h
e
re
al
a
n
d
rea
c
t
i
v
e po
w
e
r
fl
o
w
in
g
o
u
t o
f
bus
;
an
d
a
r
e
the
real
an
d
r
e
a
c
t
i
v
e
l
o
ad
p
o
w
e
r
s
at
bu
s
1
.l
i
n
e
se
ct
io
n
bet
w
ee
n b
u
ses
and
1
has
resistance
,
and
reac
ta
nce
,
.
vol
t
a
ge
ma
g
n
i
t
ude
of
b
u
s
is
|
|
.f
o
r
c
o
n
v
e
r
ge
nce
of
po
we
r fl
ow
,
t
h
e
p
o
we
r ba
la
nc
e (
1
)a
nd
(
2
) m
u
st
be
sat
i
sf
ie
d i
n
a
d
dit
i
o
n
,
ma
g
n
it
ud
es
of
se
ndi
ng
a
n
d
re
ce
ivi
n
g
e
n
d
bus
v
o
l
t
a
ges
must
sa
ti
sf
y
(3
).
Th
e w
e
ll
kno
wn
g
e
n
e
r
a
li
ze
d
fo
rmu
l
a
s
fo
r
real
a
n
d r
e
a
c
tiv
e
p
o
w
e
r
lo
ss
in
th
e
lin
e s
e
c
tio
n
b
e
tw
een
b
u
s
e
s
and
1
a
r
e ca
lc
ula
t
ed by
usi
n
g the
f
o
l
l
o
wi
n
g
e
qua
ti
ons
.
,
,
.
|
|
(
4)
,
,
.
|
|
(5
)
Th
e
to
ta
l a
c
tiv
e
a
n
d
re
ac
ti
v
e
l
o
sse
s
i
n
t
h
e
d
i
s
t
r
i
b
u
tion
n
e
twor
k c
a
n
b
e
e
a
s
ily
f
oun
d by
addin
g
all
t
h
e
po
we
r
l
o
ss
es i
n
al
l b
r
a
n
ches
a
n
d
t
h
e
y
a
r
e
e
xpress
e
d
as foll
ows
.
∑
,
1
(6
)
∑
,
1
(7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 10
74
–
1
0
81
1
076
Whe
r
e,
is t
h
e
t
o
ta
l r
e
a
l
pow
er
l
o
ss a
nd
is t
h
e l
o
ss i
n
c
u
r
r
e
d du
e
t
o
re
a
c
t
i
ve
p
o
w
e
r t
h
ro
ug
hou
t
t
h
e
net
w
ork.
In
t
h
i
s
st
u
d
y
w
e
c
o
n
s
i
d
er
wi
n
d
su
p
p
l
y
in
g
rea
l
po
wer
wi
t
h
u
n
i
t
y
po
we
r fa
ct
or.
2.2. El
ec
tri
c
al
gri
d
oper
a
t
i
n
g c
o
ns
tr
ai
n
t
s
To
en
su
r
e
t
h
e sta
b
ili
ty
o
f
th
e
ne
tw
or
k and
t
h
e
sa
f
e
t
y
of
e
q
u
i
p
m
en
t,
v
o
l
t
a
g
e
must b
e
ma
in
tai
n
ed
w
ith
in
li
mit
s
se
t
b
y
t
h
e
ru
le
s of
op
era
tio
n
o
f
t
h
e pow
er
gri
d
s.
(8
)
Whe
r
e
a
nd
are
t
h
e mi
ni
m
u
m
and
ma
xi
m
u
m
val
u
es
of bu
s v
o
l
t
age a
m
pl
it
u
d
es,
re
spe
c
t
i
ve
l
y
.
An
d t
h
e
po
we
r
t
r
ansi
t
e
d
i
n
a
l
i
ne
must
not
,
u
nde
r
a
n
y c
i
rc
u
m
sta
n
ces,
e
x
c
e
ed
t
h
e
ma
xi
m
u
m
l
i
mi
t.
(9
)
W
ith
(1
0)
Whe
r
e
: Apparen
t
power transmitt
ed i
n
l
i
n
e
i -
j
.
A
nd
:
Ma
xi
mu
m a
p
pare
nt
po
wer
t
r
ansi
t
e
d i
n
l
i
ne
i -
j
.
3.
WIND
G
E
N
E
RA
T
I
ON SY
STEM
MO
DELL
IN
G
The
p
o
we
r ge
nera
te
d by
t
h
e
wi
n
d
t
u
rbi
n
e
d
e
pe
n
d
s on
th
e
i
r
t
y
pe a
nd
l
o
ca
ti
on,
a
s
w
e
l
l
a
s
t
h
e w
i
n
d
spee
d [7
-1
2].
T
h
e
e
l
e
c
t
r
i
c
a
l
o
u
t
put
po
we
r
of
a
wi
n
d
t
u
rbi
n
e
is det
e
rmi
n
e
d
by
usin
g
(1
1
)
.
W
ith
,
,
are
di
ffe
r
ent
s
p
ee
ds c
o
r
r
esp
o
n
d
i
n
g
t
o
t
h
e
wi
n
d
tur
b
in
e
a
n
d
is r
a
t
e
d
o
u
t
pou
t
p
o
wer
of wi
nd
tur
b
in
e
a
nd i
t
ca
n
be
det
e
rmi
n
ed
fro
m
(1
2).
0
(1
1)
0.
5
(1
2)
4.
LO
SS SE
NSITIVITY FACTO
R
The
Ac
ti
ve
p
o
w
er
l
o
sse
s
i
n
e
l
e
c
t
r
i
c
a
l
net
w
orks a
r
e
gi
ve
n
by
(12
)
.
∑∑
(1
3)
Whe
r
e,
co
s
(1
4)
si
n
(1
5)
An
d
Are
t
h
e
of
ma
trix
An
d
&
:
Ac
ti
ve
a
n
d
rea
c
t
i
ve
p
o
w
e
r
of
t
h
e
ge
nerat
o
r.
&
: A
c
ti
v
e
and
re
ac
tiv
e
lo
ad
p
o
w
e
r
The se
nsit
i
v
i
t
y
fac
t
o
r
of re
al
po
we
r
l
o
ss
wi
t
h
re
spe
c
t
t
o
rea
l
po
we
r i
n
je
ct
ion
fro
m
t
h
e
D
G
is
give
n b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Opt
i
m
al
pl
ace
m
ent
of
w
i
nd t
u
rbi
n
e i
n
a
r
a
d
i
al di
st
ri
b
u
ti
o
n
ne
tw
ork
u
s
i
n
g PS
O
m
e
th
od
(Ya
h
i
a
oui
Merz
ou
g
)
1
077
2
2
∑
(1
6)
Th
e se
nsiti
v
ity
f
a
c
t
o
r
is
c
a
l
cula
te
d
fo
r e
ach
n
o
d
e
using
th
e
v
a
l
u
e
s
ob
ta
in
ed
f
r
o
m
the
ca
l
c
u
l
a
t
io
n
o
f
th
e
b
a
sic
fl
o
w
. T
h
e
n
ode
wi
t
h
t
h
e l
o
wes
t
l
o
ss se
nsi
t
i
v
i
t
y
fa
ct
or
w
i
l
l
be
t
h
e be
st
no
de f
o
r
D
G
pl
ace
me
nt
[1
3-15
].
5.
P
A
RT
IC
LE
SWAR
M
OP
T
I
M
I
ZA
TION
5.1. In
tr
o
d
u
c
ti
on
The
P
S
O
al
g
o
ri
thm is ini
t
i
a
l
iz
ed by
a
po
pul
at
i
on o
f
ra
n
dom
po
t
e
n
t
i
a
l
sol
u
t
i
ons
,
i
n
te
rp
re
te
d
a
s
parti
c
l
e
s mo
vi
ng
i
n
t
h
e
re
sear
ch
s
p
ac
e.
Ea
c
h
pa
rt
ic
le
i
s
a
t
t
r
a
c
t
e
d t
o
i
t
s
bes
t
po
sit
i
on di
sco
v
ere
d
i
n
the
pa
st
as
wel
l
a
s
t
o
t
h
e
b
e
st p
o
sit
i
on di
s
c
ove
re
d by
the
pa
rt
ic
le
s
o
f
i
t
s
vic
i
ni
t
y
(or of t
h
e w
hol
e
s
w
ar
m,
i
n
t
h
e
gl
oba
l
versi
o
n
o
f
t
h
e
al
go
ri
thm). T
h
e
PS
O a
l
go
rit
h
m i
n
cl
u
d
es
se
v
e
ra
l
adj
u
st
me
nt
pa
ra
me
te
rs
w
h
i
c
h ac
t
o
n
t
h
e
expl
orat
i
o
n-ex
pl
oi
ta
t
i
on
co
m
p
romi
se
[16
-
2
2
]
. E
x
pl
o
r
a
t
i
o
n
i
s
t
h
e
a
b
i
l
i
t
y
to
te
st
di
ffe
rent
re
gi
o
n
s
of
spa
ce
i
n
search
of g
o
o
d
c
a
ndi
dat
e
sol
u
t
i
ons
.
E
xpl
oit
a
ti
on
i
s
t
h
e
abi
l
i
t
y
to
foc
u
s
rese
a
r
ch
arou
n
d
promisi
n
g
s
o
l
u
ti
ons
i
n
order
t
o
ge
t as
c
l
o
s
e
t
o
t
h
e
o
p
ti
mum a
s
possi
bl
e. T
h
e c
h
oi
ce o
f
p
a
ra
me
te
rs remai
n
s l
a
rge
l
y em
pi
ri
cal
. A
c
o
mp
le
te
a
n
a
l
ysi
s
o
f
th
e a
l
go
rith
m
w
a
s m
a
d
e
by
K
e
nn
ed
y
In
ge
neral
,
a
P
S
O al
go
ri
t
h
m
has
t
h
re
e ma
in
st
e
p
s:
Fi
rst
st
ep
:
con
s
is
ts
in
a
u
t
h
or
izin
g
a
ll
the
p
a
r
t
ic
le
s a
r
b
i
tr
ari
l
y
d
i
str
i
bu
t
e
d
ac
ro
ss
t
h
e
se
arc
h
sp
ac
e
.
Se
c
o
n
d
st
ep
:
co
n
s
is
ts in
ev
a
l
u
a
tin
g
th
e
f
i
t
n
e
s
s
v
a
l
u
e
o
f
th
e
p
a
rt
ic
le
s in
or
de
r
to
d
e
t
e
rmi
n
e
th
e
b
e
st
posi
t
i
o
n of
e
a
c
h
part
i
c
l
e
an
d
t
o
reve
al
t
h
e
p
a
rt
i
c
l
e
whic
h ha
s the
be
st
ov
e
r
al
l
fit
n
ess
val
u
e
i
n
the
cu
rrent
swarm
.
Thi
r
d st
e
p
:
u
p
d
a
t
es
t
h
e s
p
eed
of
t
h
e
part
i
c
l
e
s
w
h
ic
h
a
r
e t
h
e
n
use
d
as
i
n
fo
rma
t
i
on to
ch
an
ge
t
h
e po
si
t
i
on
o
f
a
ll
th
e
p
a
r
ticle
s.
In
PS
O
,
t
w
o
d
i
ffere
n
t
defi
ni
t
i
ons a
r
e
use
d
:
the
in
di
vi
dua
l
be
st a
n
d
t
h
e
gl
o
b
al
be
st
.
A
s
a
pa
rt
i
c
l
e
mo
v
e
s
thr
oug
h
th
e se
a
r
c
h
sp
ac
e,
i
t
co
mp
ar
es its
f
i
tn
e
s
s v
a
l
u
e
at
t
h
e
cur
r
e
n
t
po
si
tion
to
th
e be
st fi
tn
es
s
v
a
lu
e
i
t
has e
v
e
r
a
t
t
a
i
n
ed
pre
v
io
usl
y
. A
d
just
me
nt
o
f
t
h
e
p
o
si
t
i
on
and
s
p
eed
o
f
e
a
c
h
pa
rt
ic
le
i
s
cal
cul
a
te
d usi
ng t
h
e
c
u
rre
n
t
p
o
s
itio
n
, t
h
e b
e
st p
a
r
tic
le
p
o
s
i
tio
n so
far
a
nd t
h
e be
st o
v
e
r
a
l
l pa
rt
ic
l
e
pos
it
i
on in t
h
e
po
p
u
la
ti
on
.
Ve
loc
i
t
y
of
e
a
c
h
part
i
c
l
e
i
n
t
h
e ne
xt
ge
nerat
i
o
n
ca
n be ca
lc
ula
t
ed
a
s
:
)
(
)
(
2
2
1
1
1
k
i
k
i
k
i
k
i
x
Gbest
r
c
x
Pbest
r
c
wV
V
(1
7)
W
ith
1
r
a
nd
2
r
a
r
e
t
w
o n
u
m
b
ers
b
e
t
w
ee
n 0
a
n
d 1
w
h
il
e
1
c
an
d
2
c
are posi
t
ive
c
onst
a
nt
s,
res
p
e
c
t
i
ve
l
y
.
I
n
ert
i
a w
e
i
g
h
t
w is
is
fo
rm
u
l
at
ed b
y
the
fo
llow
in
g ex
press
i
o
n
:
iter
iter
w
w
w
w
max
min
max
max
(1
8)
Whe
r
e
max
w
an
d
min
w
are
maxi
m
u
m an
d
mi
nimu
m of
i
n
ert
i
a
wei
ght
,
max
iter
and
iter
ar
e maximum iteratio
n
nu
mbe
r
a
n
d
c
u
rre
n
t
it
erat
ion
,
respec
ti
vel
y
.
5.2. PS
O
Pr
o
ced
ur
e
The
c
a
l
c
ul
at
i
o
n
proce
d
u
r
e
fo
r
t
h
e
P
S
O
ca
lc
ula
t
i
on
al
g
o
ri
th
m i
s
a
s
fol
l
o
ws
.
St
ep
1:
Int
r
od
u
c
e
da
ta
fo
r a
l
l
no
de
s
an
d
bra
n
che
s
a
s
wel
l
a
s
t
h
e l
i
m
it
s o
f
n
odal
v
o
l
t
a
ges.
St
ep
2:
C
a
l
c
ul
a
t
i
n
g
t
h
e
p
o
w
e
r
fl
ow
i
n
t
h
e
dist
ri
b
u
t
i
on
net
w
o
r
k
a
n
d
de
te
rmi
n
i
n
g t
o
t
a
l
a
c
t
i
ve
l
o
sses
.
S
t
e
p
3
:
g
e
n
e
r
a
te
an
i
n
itia
l p
o
p
u
l
a
tio
n
o
f
p
a
rt
i
c
le
s w
ith
r
a
n
d
o
m
p
o
s
i
tion
s
a
n
d
v
e
lo
c
i
t
y
. S
e
t
th
e
ite
r
a
t
i
o
n
in
d
e
x
t=
0.
S
t
e
p
4
:
F
o
r e
a
c
h
p
a
rti
c
l
e
,
u
p
d
a
t
e
th
e
bu
s da
ta
(for w
i
n
d
t
u
rb
i
n
e
)
b
a
se
d
o
n
i
t
s l
o
c
a
t
ions an
d se
tti
ng val
u
es, if
a
ll
n
o
d
a
l v
o
l
tag
e
s
are
wi
th
in
t
h
e
p
e
rmis
sib
l
e
limi
ts,
e
s
tim
a
t
e
th
e
t
o
tal
lo
ss.
S
t
e
p
5
:
C
o
mp
are
t
h
e
f
i
t
n
ess va
lu
e
of
ea
c
h
p
a
r
t
i
c
l
e
w
i
t
h
th
e
p
e
rson
al
b
e
s
t
,
Pbest
.
If
t
h
e f
i
t
n
ess
v
a
lu
e
is
lo
wer
th
a
n
Pbest,
set th
is
v
a
lu
e
as th
e
cu
rre
n
t
Pbest,
a
nd
r
e
c
o
rd th
e
p
a
rt
ic
le po
sit
i
o
n
c
o
rr
es
po
nd
ing to
t
h
is
Pbest
val
u
e.
St
ep
6:
Se
le
ct
the
mi
nimu
m v
a
lue
of P
b
est
fro
m
al
l pa
rt
ic
le
s
t
o
be t
h
e c
u
rre
n
t
gl
obal
be
st
, G
b
est
, a
n
d
re
co
rd
t
h
e
pa
rt
ic
l
e
p
o
s
i
t
i
on co
rre
s
p
o
ndi
n
g
to
thi
s
G
b
e
s
t val
u
e
.
St
ep
7:
U
p
dat
e
t
h
e ve
l
o
c
i
ty
an
d posi
t
io
n
of
p
a
rt
ic
l
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
In
t
J
Po
w
Ele
c
&
Dri
Sy
st,
Vol.
1
1
,
No
. 2
,
Jun
e
2
020
:
10
74
–
1
081
1
078
Ste
p
8
:
If
t
h
e
ma
x
i
mu
m
n
u
mb
e
r
o
f
ite
ra
ti
ons is r
e
ach
e
d
, t
h
e p
a
r
tic
le
associ
ate
d
w
i
t
h
t
h
e cur
r
e
n
t
Gb
est
is th
e
opt
i
m
a
l
s
o
lut
i
o
n
a
nd t
h
e
n
go
t
o
St
e
p
9.
Ot
he
r
w
i
s
e,
se
t
t=t+1
a
n
d
r
e
tu
rn
to
S
t
e
p
4
.
S
t
ep 9:
D
i
s
p
l
a
ye
d t
h
e be
st
p
o
s
i
t
i
on
f
o
r
ea
c
h
part
i
c
l
e
.
Fi
gu
re
2:
P
S
O
-
O
p
t
i
m
iz
at
i
on
Wi
n
d
c
o
mput
a
t
i
onal
p
r
o
c
ed
u
r
e
6.
RE
SUL
T
S
A
N
D
S
I
MUL
A
TIONS
Opt
i
mi
za
ti
o
n
o
f
t
h
e
loc
a
t
i
on
of t
h
e wi
nd i
s
do
ne
by
t
h
e P
S
O
al
g
o
r
i
t
hm,
al
ways
pr
o
g
r
a
mme
d
u
n
d
e
r
MATLAB
a
n
d
te
sted on
the
IEEE33-
bus
di
stribution net
w
ork syste
m
c
ontainin
g
33 buse
s
a
n
d
32 bra
n
c
h
es
as
sh
own
i
n
Figu
re
3
.
Th
e bu
s
a
n
d li
n
e
d
a
ta
a
r
e t
a
k
e
n fr
om [2
3-2
4
]
.
Th
e
r
e
a
l
an
d r
e
ac
tiv
e
po
w
e
r
l
o
a
d
s a
nd
v
o
lta
g
e
o
f
ra
dia
l
d
i
str
i
bu
ti
on sy
st
em ar
e 3.72
, 2.
3
a
n
d
12
.6
6
K
V
re
sp
ect
i
v
el
y.
Thi
s
p
r
og
ra
m
sea
r
ch
es
for
the
b
e
st w
i
nd
t
u
rb
in
e
lo
ca
tion
on
th
e n
e
t
w
ork
to
min
i
mi
ze
t
o
t
a
l a
c
tiv
e
l
o
sse
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Opt
i
m
a
l
plac
e
m
ent
of
wi
n
d
t
u
rbi
n
e i
n
a r
a
d
i
al
dist
rib
u
t
i
o
n
net
w
ork
u
s
i
n
g
PS
O
m
e
t
h
od
(
Y
a
h
i
a
oui
Merz
ou
g
)
1
079
F
i
gu
r
e
3.
S
i
ngl
e l
i
ne
di
a
g
r
a
m of
3
3
B
u
s el
ec
t
r
i
c
di
st
ri
buti
o
n
syst
em
s.
Vol
t
a
g
e
se
nsit
i
v
i
t
y i
nde
x wa
s ca
l
c
ul
at
ed at
a
l
l
no
des
.
Bu
s
18
was
fo
u
n
d
t
o
ha
ve t
h
e
l
e
a
s
t
VS
I
.
Hen
c
e
Win
d
Tu
rbi
n
e
was pl
ac
e
d
at
t
h
i
s
b
u
s.
T
h
e
a
c
t
i
v
e po
wer l
o
sse
s
be
fore
t
h
e p
l
ac
ement
(
b
asi
c
cal
c
u
la
ti
on)
of t
h
e
di
st
ri
b
u
t
e
d
gen
e
rat
o
r
(wi
n
d
)
is
20
8,
4
9
2
KW
a
n
d
t
h
e
mi
ni
mum
vol
t
a
ge
i
s
0.
9
1
0
7
5
pu
a
t
no
de
l
e
v
e
l
n
u
m
be
r
1
8
.
Th
e
firs
t st
ep
i
n
d
e
t
e
r
m
i
n
i
n
g
t
h
e
w
i
nd
p
o
wer
i
n
jec
t
e
d
i
n
t
o
th
e
gr
id
u
s
ing
th
e
(1
1),
w
i
th
a
n
a
v
erag
e
a
n
n
u
a
l
wi
n
d
spe
e
d
c
o
nside
r
ed
to
be
6.
02
m/
s t
o
de
te
rmine
t
h
e
o
p
ti
mal
l
o
ca
t
i
o
n
.
[
2
5
]
.
F
i
gu
r
e
4.
Lo
ss S
e
nsi
t
i
v
i
t
y
at
a
l
l no
des
F
i
gu
r
e
5.
B
u
s
Vol
t
a
ge
s Be
f
o
r
e
an
d
Aft
e
r
O
p
t
i
m
a
l
D
G
In
s
t
al
la
tio
n
in th
e
33
-
B
u
s
S
y
stem
Af
t
e
r
ins
e
r
t
ion
of
t
h
e wi
nd,
it
i
s
no
ted t
h
at t
h
er
e is
an improv
ement in all the vol
tages
and an
act
i
v
e
los
s
r
e
d
u
cti
on of
th
e 33
.3
55%
as sh
o
w
n in
t
h
e
f
o
llo
win
g
tabl
e
1.
Ta
b
l
e
1.
Po
we
r
loss r
e
duct
i
o
n.
Without w
i
nd
Wit
h
w
i
nd
P
o
we
r
loss (
K
W)
208.
45
92
138.
9275
P
o
we
r
loss re
duct
i
on
-
33.
355
%
Mi
nim
u
m volta
g
e 0.
9107
5
Th
e
co
mp
a
r
ison
fo
r
th
e
r
e
a
l
po
w
e
r
l
o
sse
s i
n
th
e
b
r
a
n
ch
es
is
sho
w
n
i
n
F
i
gur
e
6 fo
r
th
e
in
itia
l n
e
tw
or
k
(w
i
t
h
o
u
t
win
d
)
a
n
d
wi
th w
i
nd
(c
as
e
1
a
n
d ca
se 2
)
,
r
e
s
p
ec
ti
v
e
ly
, Th
e powe
r
lo
sse
s
in a
l
m
o
st
e
v
e
r
y
b
r
an
ch
in
c
a
se 2
re
duce
d
,
e
x
ce
pt
at
18
, 1
9
,
2
0
,
21, 3
3
, 3
4
a
n
d
3
5
,
whe
r
e the
r
e
was
a smal
l
i
n
crea
se
i
n
l
o
sses.
0
5
10
15
20
25
30
35
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
SEN
SI
T
I
VI
T
Y
B
u
s
N
u
m
ber
SE
N
S
I
T
I
V
I
T
Y F
A
C
T
O
R
PL
O
T
0
5
10
15
20
25
30
35
0.
91
0.
92
0.
93
0.
94
0.
95
0.
96
0.
97
0.
98
0.
99
1
V
o
l
t
ag
e (
p
.
u
)
N
ode
V
o
lt
ag
e p
r
o
fi
l
e
w
i
th
o
u
t w
i
n
d
W
i
th
w
i
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 10
74
–
1
0
81
1
080
F
i
gu
re 6.
R
e
a
l
po
we
r l
o
sse
s
i
n
33
-bus
sy
st
em
6.
CO
NCL
U
S
I
O
N
The
o
p
t
i
m
a
l
i
n
serti
o
n
of w
i
nd t
u
rbine
s
i
n
t
o
t
h
e
di
stribut
i
o
n ne
tw
o
r
k, t
h
e te
ch
ni
q
u
e
use
d
to
cont
ri
b
u
te
t
o
t
h
e
ma
na
ge
me
nt
of
di
strib
u
t
i
on
ne
t
w
orks
wit
h
t
h
e a
i
m
of mi
n
i
mi
zi
ng
tot
a
l
po
we
r l
o
sses
b
y
ens
u
ri
n
g
a
g
ood
v
o
lt
age
p
r
o
f
i
l
e
, are c
a
rrie
d
out
i
n
the
proc
e
ss o
f
ba
se
d
o
n
o
p
t
i
mi
za
ti
on
by
a
met
a
he
uri
s
t
i
c
me
th
od
c
a
l
l
ed
p
s
o
a
l
go
r
ithm
.
M
a
n
y
p
e
rsp
e
c
t
i
v
es
op
en up
on
th
e su
b
j
ec
t of
t
h
e
op
tim
al
i
n
s
e
rtio
n
of
dec
e
nt
ral
i
zed
pro
duct
i
o
n
i
n
t
h
e
di
stri
b
u
t
i
on
net
w
ork, i
n
p
a
rti
c
ul
ar
wi
t
h
re
gard t
o
t
h
e
ty
pe
s
of
D
G
s
i
n
st
al
l
e
d
(p
h
o
t
o
volt
a
i
c
,
wi
n
d
, e
t
c
.
) a
n
d the
i
r ma
xim
u
m
n
u
mbe
r
s
to
be
inst
al
l
e
d
,
t
hus
re
c
o
nfi
g
uri
ng t
h
e
dist
ri
but
io
n
net
w
ork t
a
ki
n
g
i
n
t
o
acc
o
u
n
t
o
t
her c
o
nst
r
a
i
nt
s su
c
h
as tra
n
si
t
l
i
mi
t
s
a
n
d
t
h
e
a
s
su
ra
nce
of
c
onti
n
ui
ty
o
f
se
rvic
e
in
th
e
ev
en
t o
f
f
a
u
l
ts.
RE
FERE
NC
E
S
[1]
El-F
ergany
, A
t
ti
a, "
O
p
t
i
m
al
cap
aci
to
r a
l
lo
c
a
tion
s u
s
ing
evolutio
nary
alg
o
r
ith
m
s
,
"
Gener
a
tion, Tr
ansmiss
ion &
Distribution I
E
T,
vo
l.
7, n
o
.
6
,
pp.
59
3-6
01,
20
13.
[2]
Se
y
e
d Mo
hse
n
Mo
usa
v
i Kh
orm
a
nd
ic
ha
li
1,
Me
hrda
d
Ah
ma
di
K
a
marpos
hti, "O
ptimal
pl
ace
men
t
o
f
win
d
gen
e
rat
i
o
n
u
n
i
t
s
in ord
e
r to
i
n
c
r
ea
se re
ve
nu
es
a
n
d
re
d
u
c
e
t
h
e
i
m
po
se
d
c
o
st
s
in the di
st
rib
u
ti
on
sy
st
e
m
c
o
n
s
i
d
e
r
in
g un
ce
rta
i
n
t
y,
”
In
te
rn
at
io
na
l J
ourna
l
o
f
E
l
ec
t
r
ica
l
a
n
d
Co
mpu
t
e
r
En
gi
n
e
e
r
i
ng (IJECE
)
, vo
l.
9
,
no. 6, pp
.
4
5
2
4
-
45
3
9
,
Dec
2
0
1
9
.
[3]
Katherin
e C
a
ba
na, J
o
h
n
C
a
nd
e
l
o
,
Rafael
Casti
l
lo, E
m
ir
o
D
e
-la-Ho
z-F
r
anco
,
“V
oltag
e
s
e
ns
it
iv
ity
ana
l
ysis
to
det
e
r
m
i
n
e
th
e
o
p
t
i
ma
l
in
teg
r
at
i
o
n of
d
i
st
ri
b
u
ted
ge
ne
ra
tio
n in d
i
st
rib
u
t
i
o
n
syste
m
s,
”
In
te
rn
atio
na
l J
o
urna
l
o
f
E
l
ec
t
r
ic
al a
nd
Compu
t
e
r
En
gi
nee
r
i
n
g
(IJECE
)
,
v
o
l.
9
,
no.
1
,
pp.
55
-65
,
Fe
b 20
19
.
[4]
T
e
ng
,
Je
n-Ha
o
,
"A
d
i
re
c
t
a
p
p
r
oac
h
for distri
bu
ti
on sy
st
e
m
lo
a
d
flo
w
sol
u
t
i
o
n
s,
"
P
o
wer Deliver
y,
I
E
EE T
r
a
n
sa
ction
s
on
,
vo
l. 1
8
,
no.
3,
pp. 8
8
2
-
88
7, 200
3.
[5]
H.
Abde
llatif, Z. Khal
ed, “Eff
i
c
i
e
nt
load
f
l
o
w
me
th
od
fo
r ra
dia
l
d
i
stri
bu
ti
on fee
d
e
r
s,”
J
o
u
r
n
a
l
of Ap
pl
ie
d S
c
ie
nc
e
,
vo
l.
13
,
pp
. 7
4
1
–
8
,
20
06
.
[6]
Kittay
a S
o
msai,
“Con
tro
l
l
e
r d
e
s
i
g
n
of
U
P
QC fo
r en
h
a
ncing
po
wer qua
lity
in
d
i
strib
u
tion
s
y
s
t
e
m
,”
Inte
rn
a
t
i
onal
Jou
r
na
l
of
Po
wer
Ele
c
tr
on
ics
an
d D
r
ive S
y
s
t
em
(
I
JPED
S)
,
v
o
l
.
9
,
no
. 4, pp
.
1
5
9
1
-
16
06
,
Dec
20
1
8
.
[7]
Y. Xi
a,
et a
l
, "Wi
n
d tu
rbi
n
e
po
we
r coe
ffi
ci
ent
a
n
al
ysis
of a
new
ma
xi
mu
m po
w
e
r poi
nt
t
r
ac
ki
n
g
t
echni
q
u
e,"
IE
EE
Tr
a
n
sact
i
o
ns
on
I
ndust
r
i
a
l
Ele
c
t
r
onic
s
,
vo
l. 6
0
,
n
o
.
3
,
pp
. 11
22-
113
2,
M
a
r. 2
013
.
[8]
Div
y
a
KC,
Ra
o PSN.
,
“
M
od
e
l
s
f
o
r wi
nd
tu
rbi
n
e
g
e
ne
ra
t
i
n
g
syste
m
s a
n
d
the
i
r
ap
pl
ica
t
io
n
i
n
lo
ad
fl
ow st
ud
ie
s,
”
El
e
c
tri
P
o
w
e
r S
y
st
R
e
s
,
v
o
l
.
7
6
,
p
p
.
84
4–
56
,
20
06
.
[9]
S
u
resh
ku
mar S
u
d
a
bat
t
ula
,
K
o
w
s
alya M
,
“Optim
al a
l
loc
a
tio
n
o
f
wind
bas
e
d d
i
s
t
r
i
bu
ted
g
e
n
e
rator
s
in
d
i
s
t
rib
u
t
i
o
n
sy
stem
us
in
g
Cu
ck
oo S
e
arch
Alg
o
rith
m
,
”
2n
d
Int
e
rn
ation
a
l
Co
nf
é
r
ence
on
In
tel
l
igent Computing, Communicati
on
& Convergence
(ICCC-2016),
pp.
29
8-3
0
4
, 2
0
1
6
.
[10]
Gh
ofrani M
.,
"A
F
r
amewo
r
k
f
o
r Op
tim
a
l
P
l
a
cemen
t o
f
En
erg
y
S
t
o
r
ag
e U
n
i
t
s
with
in
a P
o
w
e
r
S
y
s
t
em
w
i
th
H
i
g
h
Wi
nd
P
e
n
e
tr
a
t
io
n,"
I
E
EE
T
R
AN
S
A
C
T
I
O
N
S
ON
SUS
T
AI
N
A
BL
E
E
N
ER
GY
,
v
o
l
.
4
,
no
.
2,
Ap
r
20
13
[11]
B
a
kh
tvar
M
., "
O
pt
imal
Al
lo
c
a
t
i
o
n
of
W
i
nd Gen
e
r
a
t
i
o
n
S
u
b
j
e
c
t to
V
o
l
t
ag
e S
t
ab
il
it
y Co
ns
tr
ai
nts
,
"
IEEE
PES
Inn
o
vative
Sma
r
t Gr
id
T
echn
o
l
o
g
ies
,
vo
l.
4
,
2
0
1
4
.
[12]
Sa
t
i
sh
Ka
n
s
a
l
,
et al
,
“Opt
ima
l
p
l
ace
ment
of d
i
str
i
bu
ted
g
e
ne
ratio
n
in d
i
strib
u
t
i
on
netw
ork
s
,”
Inter
n
ation
a
l
Jo
ur
na
l
o
f
E
ngin
e
e
r
in
g
,
Sc
i
e
nc
e a
n
d
Te
ch
no
lo
gy
, v
o
l. 3,
n
o
.
3, p
p
.
47
-5
5
,
20
11
.
[13]
Ach
a
rya N
.
, M
a
h
a
t P
.
, M
i
thu
l
an
anth
an
N.,
“
A
n
analyt
ica
l
a
p
p
r
o
ach
for D
G
allo
cation
in
p
r
imary d
i
s
t
ribut
io
n
network
,
”
E
l
ec
tric
Po
wer
&
En
erg
y
Sys
t
em
s
,
vol
.
2
8, n
o
.
10,
pp
.66
9
-6
78,
De
c 2
0
0
6
.
[14]
Ac
ke
rm
a
nn
T.
,
An
de
rsso
n G.,
an
d So
ld
e
r
L
.
,
“
D
ist
r
ib
ut
e
d
g
e
n
e
rat
i
o
n
:
a
d
e
fi
n
i
t
i
o
n
,
”
Electric
Powe
r
sys
t
em
Res
e
ar
c
h
,
v
o
l
.
57
, n
o
.
3
,
p
p
.
1
9
5
-
20
4,
Ap
20
01.
[15]
X.
Wang
, Y
.
Wang
,
H.
Zen
g
,
H
.
Zho
u
,
“P
a
r
ticle
sw
arm
o
p
t
imi
z
at
io
n
with
es
cap
e
ve
locit
y
,”
In
t
.
Conf
.
on
Com
putatio
na
l I
n
tellig
e
nt
an
d
Se
cur
i
ty
, vo
l.
1
,
pp
. 45
7–
46
0
,
200
6
.
[16]
S. He, Q.
H
.
Wu, J. Y.
W
e
n, J
.
R.
Saund
e
rs
, R.
C.
Paton, “A
par
t
i
c
l
e
s
w
arm optimizer
with pa
ssiv
e
c
o
ng
re
g
a
ti
on”,
Jou
r
na
l of
Bios
ys
tem
s
,
v
o
l.
7
8
,
pp.
13
5
–
1
47,
2
004
.
0
5
10
15
20
25
30
35
40
0
10
20
30
40
50
60
P
o
w
e
r
L
o
s
se
s(
K
W
)
br
anc
h
e
s
P
o
w
e
r L
o
s
s
e
s
(K
W
)
w
i
th
o
u
t
w
i
n
d
wi
t
h
wi
nd
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Opt
i
m
a
l
plac
e
m
ent
of
wi
n
d
t
u
rbi
n
e i
n
a r
a
d
i
al
dist
rib
u
t
i
o
n
net
w
ork
u
s
i
n
g
PS
O
m
e
t
h
od
(
Y
a
h
i
a
oui
Merz
ou
g
)
1
081
[17]
K
e
nn
edy J
., Eb
e
r
h
a
rt R
.
, “P
ar
ticle S
w
arm
Op
timi
zer
,”
IE
EE
In
ter
n
a
t
iona
l C
o
n
f
er
enc
e
on
N
e
u
r
al N
e
twor
ks
,
Perth(Au
stra
lia)
,IEEE
S
e
r
v
ic
e C
e
ntre
Pis
c
atawa
y
,
N
J
,
IV
,
pp.
1942
-19
4
8
,
19
95.
[18]
Ch
io
u, J
i
-P
yn
g,
et
a
l
,
"Va
r
ia
b
l
e
sc
al
in
g
hy
brid
di
ffe
re
nt
ia
l
ev
ol
ut
io
n
for
so
lv
ing
netwo
r
k r
econ
f
ig
ur
ation
of
di
st
r
i
b
u
t
i
on sy
st
e
m
s"
,
I
E
EE T
r
ans
actio
n
s
on
Po
wer S
y
stems
,
vo
l.
20
, no
. 2
,
p
p
.
6
6
8
-
67
4,
20
05
[19]
A
.
Wa
zir
and
N. A
r
bab
,
"
A
na
ly
s
i
s
and
optim
iza
t
ion
of I
EEE
33 bu
s ra
d
i
a
l
d
i
stribu
te
d
sy
ste
m
u
s
i
n
g
op
ti
mi
za
ti
on
al
go
r
ith
m,"
J
o
urna
l o
f
E
m
e
r
gi
ng
Tre
n
d
s
i
n
Ap
p
l
i
e
d E
n
g
i
ne
e
r
i
n
g
,
v
o
l.
1
,
no.
2
,
pp.
17
-21
,
2
0
1
6
.
[20]
U
.
S
u
ltan
a, A
.
B.
Kh
airu
ddin
,
M
.
M
.
A
m
an,
A.S
.
Mo
kh
tar,
N
.
Zar
een, "
A
revi
ew
of o
p
timu
m DG
plac
emen
t bas
e
d
on mi
ni
mi
zati
o
n
of power l
o
sses
and vol
t
age stabi
lity
enh
a
ncement of di
st
r
i
buti
o
n system,
"
Renewabl
e
an
d
Susta
i
n
a
bl
e Ene
r
gy
Re
vie
w
s,
no
.
6
3
,
p
p
.
36
3-3
78, 20
16
.
[21]
A
.
M
.
El-
Z
o
nko
ly
., "
O
pt
ima
l
pla
cem
en
t of
mul
t
i-
distribu
ted
ge
ne
ra
t
i
o
n
u
n
it
s inc
l
udi
ng
d
i
ffe
r
e
n
t
loa
d
m
ode
ls u
s
i
ng
pa
rt
ic
le swa
r
m
opt
im
iz
a
t
i
o
n
,
"
Sw
a
r
m
an
d Evolu
tio
nar
y Com
p
u
t
a
t
i
o
n
,
vo
l.
1
,
pp
.
50
-59
,
2
011
.
[22]
Kh
oa
T.
Q.
D.,
Bi
nh
P.T
.
T.
,
Tra
n
H.
B., “
O
p
t
im
i
z
in
g
loc
a
ti
o
n
a
nd siz
i
ng o
f
d
i
strib
u
t
e
d
ge
n
e
ra
ti
o
n
i
n
di
st
ri
buti
o
n
sy
st
e
m
s
,
”
P
r
o
c
ee
d
i
n
g
s of
IEE
E
P
E
S
P
o
we
r Sy
ste
m
s Con
f
e
r
e
n
ce
an
d Ex
po
siti
on
-P
SCE
20
06
, pp
. 72
5-7
3
2
,
2
006
.
[23]
U
n
iversity
of
Wash
in
gton
, “
Power Systems
Test Cas
e
A
r
chive
,”
Av
ail
a
bl
e o
n
l
ine:
http
s://w
w
w
.
ee.was
h
ing
t
on
.
ed
u/re
s
e
arch
/pstca/ (acces
sed
on
12
J
une 20
17)
.
[24]
K
a
shem,
M
.
A.
G
a
nap
a
th
y
,
V
.
Jas
m
on,
G.B
.
a
nd Bu
har
i
,
M
.
I
.
,
“A
no
vel
me
tho
d
fo
r
lo
ss
min
i
m
i
za
tio
n
in
di
st
rib
u
t
i
on network
s
,
”
In
Pro
ceed
in
gs
of
I
n
terna
t
ion
a
l
Co
nferen
c
e
on
Electri
c Utility
D
e
reg
u
la
tion
a
n
d
Re
stru
c
t
u
r
i
ng and P
o
we
r Tec
h
n
o
lo
gi
e
s
, pp
. 25
1-255
,
20
00.
[25]
h
t
tp://w
w
w
.
sy
nerg
yenv
iro
n
.
c
o
m
/too
l
s
/
wind
_d
ata.
as
p
BIO
G
RA
PHIES OF
AU
THOR
S
Ya
hi
a
o
ui
M
e
rz
o
u
g i
s
bo
rn
i
n
Sai
d
a
(Alge
r
ia
) i
n
1
9
6
6
.
He o
b
t
a
ine
d
a di
plo
m
a of e
n
g
i
n
e
e
r
in
Ele
c
trot
echn
i
cs
in
1
9
9
2
. He
r
e
c
e
ived
his m
a
ster
Dep
a
rtment
o
f
Ele
c
tri
cal Eng
i
n
eering
at
th
e
EN
SET, in
O
r
a
n
,
Alg
e
ria.
H
e
rece
ived
“Do
c
to
r
a
t Es-S
ci
enc
e” i
n
Ele
c
trica
l
Con
t
rol fro
m
th
e
Un
ivers
i
ty of S
c
ienc
es
an
d Tech
n
o
log
y
of Oran
(
A
lgeria) in 201
4
.
He is
an
as
so
ciate pro
f
ess
o
r
a
t
un
ive
r
sit
y
o
f
Sa
i
d
a
.
His fie
l
ds o
f
in
te
re
st
inc
l
ude
: FACTS
po
we
r fl
ow i
n
ra
d
i
al d
i
stri
bu
ti
on
sy
ste
m
and
Ren
e
wab
l
e
En
erg
i
es
.
I am
a me
mbe
r
in
ele
c
tro
tech
nical e
n
g
i
ne
erin
g Labo
r
a
to
ry
(L
.G
.E)).
P
o
s
t
ad
dres
s:Yahiaou
i
M
e
r
z
o
u
g
,
le
ctur
er, Un
iv
ers
i
ty of S
a
ida
,
B
P
1
3
8
En-Nas
r, (2
00
00
S
a
ida)
, A
L
GERIA
E
m
ail: myahiaoui
2001@yahoo.
f
r
Bo
ua
na
n
e
Ab
de
lkri
m
is
bo
rn i
n
S
A
IDA,
Al
ge
ri
a
in
1
9
7
0
I
o
b
t
a
in
ed
a
dip
l
o
m
a
of en
gi
n
e
e
r
in
El
e
c
trot
echn
i
cs
i
n
19
95
.I
rec
e
iv
e
d
my
M
a
st
er
in
20
06
at th
e EN
S
E
T Oran
an
d
PH
D
at the
EN
PO
o
r
an in
2
0
1
3
.
I
am
a
te
at
c
h
er in
th
e D
e
p
a
rt
me
n
t
of
Ele
c
tri
c
al
Eng
i
n
e
ering
,
F
acu
lty
o
f
Tech
no
log
y
a
t
th
e D
r
.
M
o
u
l
ay
Ta
h
e
r Un
iv
e
r
s
ity
of
SAID
A. My
res
e
a
r
ch interest
s
incl
ude
in
tel
l
igen
t
con
t
r
o
l o
f
p
o
we
r s
y
s
t
em
an
d F
A
CTS
,
Ele
c
trical
M
ach
in
es an
d
Ren
e
wa
b
l
e
Energi
es.I
am a memb
er in ele
c
tro
t
echn
i
ca
l eng
i
n
e
ering
La
b
o
ratory
(
L
.G
.E))
E
m
ail: bouanan
e
abd@yahoo.fr
B
o
u
m
ed
ien
e
L
a
r
b
i
is bo
r
n
i
n
S
a
i
d
a
(
A
lg
er
ia)
in
19
64.
H
e
ob
ta
i
n
ed
a
di
pl
o
m
a
o
f
en
g
i
n
e
er
in
Ele
c
trot
echn
i
cs
in
1
9
9
0
. He
r
e
c
e
ived
his m
a
ster
Dep
a
rtment
o
f
Ele
c
tri
cal Eng
i
n
eering
at
th
e
EN
SET, in
O
r
a
n
,
Alg
e
ria.
H
e
rece
ived
“Do
c
to
r
a
t Es-S
ci
enc
e” i
n
Ele
c
trica
l
Con
t
rol fro
m
th
e
Un
ivers
i
ty of S
c
ienc
es
an
d Tech
n
o
log
y
of Oran
(
A
lgeria) in 201
0
.
He is
an
as
so
ciate pro
f
ess
o
r
a
t
univ
e
rsity
of Sa
i
d
a. Hi
s fie
l
d
s
o
f
i
n
te
re
st
inc
l
ud
e: ha
rm
on
ic
p
o
we
r flo
w
in d
i
stri
buti
on
sy
ste
m
, qu
ali
t
y
o
f
en
ergy
.
I a
m
d
i
rector
o
f
elect
ro
tec
h
n
i
ca
l en
gine
erin
g
Labo
r
a
to
ry
(L.G
.
E
))
.
P
o
s
t
ad
dres
s:
La
rb
i Bou
m
edien
e
, lecturer, Univers
i
ty
of
Saida, BP 138 En
-Nas
r, (20000 Saida)
, A
L
GERIA
E
m
a
i
l
:
l
b
o
u
m
e
di
e
n
e
2
00
5@
y
a
ho
o
.
fr
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