Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
4, N
o
. 2
,
A
p
r
il
201
4, p
p
.
20
0
~
20
6
I
S
SN
: 208
8-8
7
0
8
2
00
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Genetic Algorithm Based Reacti
ve Power Management by SVC
Md.
Imr
a
n
Az
im*,
Md
. F
a
yz
ur Rahm
an
**
* Departement o
f
Electr
i
cal
and
Electroni
c Engin
eering
,
R
a
jshahi University
of
En
gineer
ing and
Technolog
y
(RUET),
Rajshahi, Bang
ladesh
** Depart
em
ent
of El
ectr
i
c
a
l
and
El
ectron
i
c
Engi
neer
ing
,
Daffod
i
l International U
n
iversity
(DIU),
Dhaka, Bang
lad
e
sh
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 30, 2013
Rev
i
sed
Feb
27
, 20
14
Accepte
d
Mar 5, 2014
This paper con
t
ains an approach of
a genera
liz
ed optim
iza
tion
form
ulation
regarded
as genetic algor
ithm with
a vi
ew t
o
determ
ining t
h
e
optim
al
location of distr
i
buted gen
e
rators in
10-bus netw
ork offering r
e
activ
e power
capab
ili
t
y
. It
is
certa
inl
y
th
e cas
e
that th
e rea
c
t
i
ve
power m
a
nagem
e
nt pla
y
s
a
noteworth
y role
,
when it is required to
improve not just the voltage profile
but the
volt
a
ge
stabili
t
y
as we
ll.
In th
is pap
e
r, the requisite r
e
active power
planning has been precisely
solved b
y
the evo
l
utionar
y
gen
e
tic algorithm,
which is based on biological metaphor, in
which
best individuals are selected
among parents and offspring
gen
e
ration. In
addition,
gen
e
tic algo
rithm does
not need in
iti
al i
n
form
ation abou
t the
s
y
s
t
em to
begin the search
ing process
since it works onl
y
with th
e chro
m
o
som
e
s which
will be optim
ize
d
according
to the objective functions and the proper
constraints. As far as
this paper
goes, the injection of 228.5469553MVAR
rea
c
tiv
e power b
y
Static Var
Compensator (SVC) is enough to mainta
in voltage stability
thro
ughout th
e
sy
s
t
e
m
.
Keyword:
Slack bus
Gene
rato
r bu
s
Loa
d
bus
Lo
ad
ing
Parameter
Static Var C
o
m
p
ensator
(S
V
C
)
Reactive Powe
r Injection
Genetic Alg
o
ri
thm
(GA)
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M
d
. Im
ran
Azi
m
Depa
rtem
ent of Electrical a
n
d
El
ect
ro
ni
c E
n
gi
nee
r
i
n
g,
R
a
jsha
hi
Uni
v
ersi
t
y
of
En
gi
n
eeri
n
g a
n
d
Tec
h
n
o
l
o
gy
(R
UE
T)
R
a
jsha
hi
-
6
20
4,
B
a
n
g
l
a
des
h
Em
a
il: i
m
ran
.
azi
m
8
9
@
g
m
ai
l.co
m
1.
INTRODUCTION
M
ode
rn
p
o
we
r
sy
st
em
buses
are ge
ne
ral
l
y
cl
assi
fi
ed i
n
t
o
t
h
ree t
y
pe
s s
u
c
h
as sl
ac
k b
u
s
,
gene
rat
o
r
bus
an
d
lo
ad
bu
s [1
].
Th
e bu
s
at w
h
ich
t
h
e m
a
gnitude
a
n
d pha
s
e angle
of the
voltage a
r
e s
p
ecified is calle
d the
refe
rence
b
u
s
or
sl
ack
b
u
s.
I
t
i
s
co
nnect
e
d
t
o
t
h
e
ge
ne
rat
o
r
b
u
s a
n
d m
a
kes
u
p
t
h
e
di
f
f
ere
n
ce
bet
w
e
e
n t
h
e
sche
dul
e
d
l
o
a
d
an
d
gene
rat
e
d
p
o
we
r t
h
at
ar
e cause
d
by
t
h
e l
o
sses i
n
t
h
e
net
w
or
k.
Si
nce
,
i
n
t
h
i
s
b
u
s
t
h
e real
p
o
wer is no
t sp
ecified, it is also
called
th
e swing
bu
s.
The
bus at
whi
c
h t
h
e m
a
gni
t
ude
of t
h
e v
o
l
t
a
ge
and
real
p
o
wer is sp
ecified
and
th
e phase ang
l
e of the vo
ltag
e
a
n
d
reactiv
e po
wer
h
a
v
e
to
b
e
d
e
term
in
ed
is called
th
e
gene
rat
o
r b
u
s
or P
-
V b
u
s
or
vol
t
a
ge c
o
nt
r
o
l
l
e
d b
u
s. T
h
e
b
u
s at
w
h
i
c
h t
h
e real
p
o
we
r a
nd t
h
e react
i
v
e
po
we
r
are s
p
ecified a
nd t
h
e m
a
gnitude a
nd
phas
e an
g
l
e
o
f
th
e
v
o
l
t
a
g
e
are to
b
e
determin
ed
is called
th
e lo
ad
bu
s.
At
th
is bu
s
vo
ltage and
freq
u
e
n
c
y rem
a
in
co
n
s
t
a
n
t
and
it is also
called
i
n
fi
n
ity b
u
s
.
It
is
certain
l
y
th
e
case
th
at v
o
ltag
e
i
n
stab
ility in
p
o
wer system
is
g
e
n
e
rally cau
sed
b
y
th
e lo
ad
ch
ange
scen
ari
o
s. Th
is p
h
e
n
o
m
en
on
easily
may cau
s
e
an
u
n
s
tab
l
e eq
u
ilibriu
m
an
d
co
n
s
eq
uen
tly th
e syste
m
wo
uld
b
e
una
bl
e t
o
ope
r
a
t
e
so
un
dl
y
an
y
l
o
n
g
er
. F
o
r
pr
o
p
er c
o
m
p
ensat
i
o
n, t
h
e
be
st
way
i
s
t
o
m
a
i
n
t
a
i
n
an a
d
eq
uat
e
react
i
v
e
po
we
r
m
a
nagem
e
nt
i
n
t
h
e
net
w
o
r
k
and
a
pr
o
p
er
v
o
l
t
a
ge l
e
vel
[
2
-
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 2, A
p
ri
l
20
14
:
20
0 – 2
0
6
2
01
Fi
gu
re 1.
1
0
-B
us di
st
ri
b
u
t
i
o
n net
w
or
k
In o
r
der t
o
m
e
et
t
h
e change
s pr
o
v
i
d
e
d
by
gr
i
d
sy
st
em
s, a new pe
rspect
i
v
e
on net
w
o
r
k
op
erat
i
on c
a
n
b
e
app
lied
,
in wh
ich
th
e in
t
e
llig
en
ce
m
u
st b
e
sp
read
over Flex
ib
le AC Tran
sm
issio
n
Syste
m
s (FACTS)
devi
ces
, su
ch
as St
at
i
c
VAR
C
o
m
p
ensat
o
r
(SVC
) a
nd t
h
u
s
, di
st
ri
but
i
o
n
po
we
r net
w
o
r
k bec
o
m
e
s fl
exi
b
l
e
.
Mo
re im
p
o
r
tan
tly, FACTS
d
e
v
i
ces
h
a
v
e
sto
o
d
o
u
t
as
a feasib
le
o
p
t
i
o
n
t
o
im
p
r
o
v
e
v
o
ltag
e
stab
ility b
y
i
n
fl
ue
nci
n
g p
o
w
er
fl
o
w
s an
d vol
t
a
ge
p
r
ofi
l
e
s
[
4
]
.
The
im
ple
m
entation of
an efficient reactive po
wer
p
l
an
n
i
n
g
is allowed b
y
th
e activ
e power
net
w
or
ks, i
n
w
h
i
c
h t
h
e
o
p
t
i
m
u
m
VAR
so
ur
ces l
o
cat
i
on i
s
chos
en
du
ri
n
g
t
h
e pl
an
ni
n
g
s
t
age an
d act
i
n
g t
h
i
s
way
,
an e
ffi
ci
e
n
t
react
i
v
e p
o
w
er
di
spat
c
h
c
oul
d be al
s
o
ac
hi
eve
d
by
sc
he
dul
i
n
g a
n
o
p
t
i
m
u
m
regul
at
i
o
n o
f
t
h
e
v
o
ltag
e
set poin
t
at th
e g
e
nerato
rs con
n
e
ctio
n
po
in
t and at th
e VAR settin
g
s
du
ri
n
g
th
e reactiv
e p
o
wer
d
i
sp
atch
[5
].
Traditionally, reactive powe
r
planning
has
been form
ulated as an op
timiza
tion problem
in whic
h
the
d
e
term
in
atio
n
o
f
th
e i
n
stan
tan
e
ou
s op
tim
a
l
stead
y state of
an electric power system
is
solve
d
by a
n
Optim
al
Power
Flow
p
r
ob
lem
(OPF) [6
].
In tho
s
e situ
atio
n
s
,
Gen
e
tic
Algo
rith
m
(GA), a typ
e
of evo
l
u
tio
n
a
ry
opt
i
m
i
zati
on al
go
ri
t
h
m
i
s
defi
ned a
s
a si
n
g
l
e
ob
ject
i
v
e
fu
nc
t
i
on ex
p
r
esse
d
as a m
a
t
h
em
at
ical
fu
nct
i
on
ba
sed
on som
e
criteria [7].
An
SVC is a con
t
ro
lled shu
n
t
su
scep
tan
c
e (B)
wh
ich
i
n
j
ects
reactiv
e po
wer in
t
o
th
e system
.
Th
erefo
r
e, t
h
e b
u
s
vo
ltag
e
is in
creased
to
th
e d
e
sire
d
level. If
b
u
s
vo
ltag
e
in
creases,
SVC will in
j
e
ct less
reactive powe
r or TCR will abso
rb m
o
re reactive power. The dynam
i
c nature
of the SVC lies in th
e use
of
t
h
y
r
i
s
t
o
r
d
e
vi
ces s
u
ch
as
GTO
,
I
G
B
T
[
8
]
.
T
h
y
r
i
s
t
o
r
b
a
sed
SVC
i
s
sh
ow
n i
n
Fi
gu
re
2,
Figure
2. Static VAR com
p
ensator
diagram
As is ob
ser
v
e
d
,
V
SVC
is th
e v
o
ltag
e
at SVC
co
nn
ection
po
i
n
t th
at is b
e
in
g co
n
t
ro
lled
.
X
L
is th
e to
tal
inductance
and
X
C
is th
e cap
a
citan
ce. If
α
SVC
i
s
t
h
e
fi
ri
ng
a
ngl
e
o
f
S
V
C
t
h
en reactive power
injected by SVC
[9]
ca
n
be e
x
p
r
essed a
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Genet
i
c
Al
go
ri
t
h
m Base
d Rea
c
t
i
ve
Pow
e
r
M
a
n
a
g
eme
n
t
by SVC
(
M
d
.
Imr
a
n
Azi
m
)
20
2
]
2
sin
2
1
[
2
X
X
V
Q
L
SVC
SVC
C
SVC
SVC
(1
)
2.
R
E
SEARC
H M
ETHOD
Gen
e
tic Algorith
m (GA) was
first in
trodu
ced
b
y
Ho
llan
d
i
n
19
75
and
it b
e
lon
g
s to
th
e ev
o
l
u
tio
n
a
ry
opt
i
m
i
zati
on al
go
ri
t
h
m
s
. It
i
s
a m
e
t
a
-heu
ri
st
i
c
opt
i
m
i
zati
on
m
e
t
hod,
t
h
at
i
s
, i
t
i
t
e
rat
i
v
el
y
sol
v
es a
p
r
o
b
l
e
m
by
im
pro
v
i
n
g t
h
e
candi
dat
e
s
o
l
u
t
i
on
base
d
o
n
c
e
rt
ai
n cri
t
e
ri
a
[
10]
.
The
m
a
jor
st
eps i
n
v
o
l
v
e
d
i
n
a t
y
pi
cal
G
A
a
r
e
in
itializin
g
th
e po
pu
latio
n, cro
s
so
v
e
r, m
u
tatio
n
,
selectio
n
an
d term
in
atio
n
b
a
sed on
t
h
e term
in
atio
n
criterio
n
[11
]
illu
strated b
e
low:
1.
Pop
u
l
ation
In
i
tializat
io
n
:
Gen
e
tic alg
o
rithm is star
ted
with
a set o
f
so
lu
tion
s
called
pop
u
l
ation
.
Th
e
so
lu
tion
to
a
p
r
o
b
l
em
is called
a ch
ro
m
o
so
me. A ch
ro
m
o
some is
m
a
d
e
u
p
o
f
a co
llectio
n o
f
g
e
nes wh
ich
are sim
p
ly th
e p
a
ram
e
ters to
b
e
o
p
tim
ized
[1
2
]
.
2.
Fitness Evalua
tion a
n
d Select
ion: Th
e
fitness function is a
represe
n
tati
on
of the
quality of each soluti
on
(chro
m
o
s
o
m
e). Acco
rd
ing
t
o
th
e fitn
ess
v
a
l
u
e, t
h
e
f
ittest ch
ro
m
o
so
m
e
s are selected and th
en cro
s
sov
e
r
and m
u
tation are perform
ed on these chrom
o
som
e
s
to
gene
rate the new chrom
o
somes. One of the
techniques is t
h
e roulette wheel selection in which,
pa
rents are selected according to t
h
eir fitne
ss. T
h
e
better the
chrom
o
so
m
e
s, the
m
o
re chances
t
h
ey
ha
ve t
o
be
sel
ect
ed [
13]
.
3.
C
r
oss
o
ver a
n
d
M
u
t
a
t
i
on:
C
r
o
sso
ver a
n
d m
u
t
a
t
i
on are t
h
e
m
a
i
n
fu
nct
i
o
n
s
of a
n
y
genet
i
c al
go
ri
t
h
m
after
sel
ect
i
on. T
h
e
y
are t
h
e fu
nct
i
ons r
e
sp
o
n
si
bl
e fo
r t
h
e creat
i
on
of
new c
h
r
o
m
o
som
e
s out
of t
h
e e
x
i
s
t
i
n
g
c
h
r
o
mo
s
o
me
s
.
In
t
h
e cro
s
sover ph
ase, all of th
e
selected
ch
ro
m
o
so
m
e
s are
p
a
ired up
, and
with
a
p
r
o
b
a
b
ility called
crossover
probability, they are
m
i
xed t
oget
h
er so that a certain part of one of the
pare
nt
s is replaced
by a
part of
the same
lengt
h from
the
othe
r
pare
nt chrom
o
som
e
. The c
r
o
ssove
r is
accom
p
lished by
ra
ndom
ly
cho
o
si
ng a si
t
e
al
ong t
h
e l
e
ng
t
h
of t
h
e c
h
r
o
m
o
so
m
e
, and excha
n
gi
n
g
t
h
e
gene
s of t
h
e t
w
o c
h
r
o
m
o
so
m
e
s
fo
r eac
h
gene
p
a
st
t
h
i
s
cr
oss
o
v
e
r si
t
e
.
After t
h
e cro
s
so
v
e
r, each
of th
e g
e
n
e
s
o
f
th
e ch
ro
m
o
so
m
e
s
(ex
c
ep
t fo
r th
e elite ch
ro
m
o
so
m
e
) is
m
u
ta
ted
to
an
y
on
e
o
f
th
e co
d
e
s
with
a prob
ab
ility d
e
fin
e
d
as t
h
e m
u
tatio
n
prob
ab
ility.
W
i
t
h
t
h
e cr
oss
ove
r an
d m
u
t
a
t
i
ons com
p
l
e
t
e
d, t
h
e c
h
r
o
m
o
som
e
s are onc
e agai
n e
v
al
ua
t
e
d fo
r an
ot
he
r
roun
d
of selectio
n
and
reprod
u
c
tion
.
Setting
th
e p
a
ra
m
e
ters con
cern
e
d
with
crossov
e
r an
d
m
u
tatio
n
is
m
a
i
n
l
y
depe
nd
ent
o
n
t
h
e a
p
pl
i
cat
i
on at
ha
nd
an
d th
e chr
o
m
o
so
m
e
struct
ure [13-14].
In
th
is p
a
p
e
r,
th
e research
m
e
th
od
invo
lv
es Gen
e
tic Algo
ri
th
m
(GA)
du
e to
th
e
fact
t
h
at th
e
unk
nwn
am
ount
of
reac
t
i
v
e po
we
r has
t
o
be i
n
ject
e
d
i
n
t
h
e sy
st
em
wi
t
h
t
h
e
un
k
n
o
w
n
fl
uct
u
at
i
o
n
of t
h
e b
u
s
vol
t
a
ges
owi
ng t
o
t
h
e c
h
an
gi
n
g
o
f
l
o
a
d
fact
o
r
, w
h
i
c
h
i
s
t
h
e rat
i
o
of avera
g
e l
o
a
d
and m
a
xim
u
m
dem
a
nd.
W
i
t
h
a vi
e
w
to
app
l
yin
g
GA
, Tab
l
e 1, is co
nsid
er
ed
f
o
r
en
cod
i
ng
pur
po
se
w
h
er
e
λ
and
Q
a
r
e loading pa
ram
e
ter and
reactive powe
r respectively.
The m
a
xim
u
m
rat
i
ng
of t
h
e
i
n
ject
ed
reactiv
e po
wer is assu
m
e
d
to
b
e
2
50
M
VAR.
Tab
l
e 1
.
In
itial
Valu
es
Q
MVAR
239
.
48
233
.
82
221
.
81
209
.
82
202
.
75
187
.
46
164
.
98
149
.
54
Q
P.U
0.
9579
0.
9353
0.
8873
0.
8393
0.
8110
0.
7498
0.
6599
0.
5982
λ
P.U
0.
1020
0.
1320
0.
1830
0.
2450
0.
3570
0.
4860
0.
6990
0.
7500
Now, fro
m
Tab
l
e 1, th
e obj
ectiv
e fu
n
c
tion
relatin
g
λ
an
d
Q
is
Q
Q
f
5104
.
0
9933
.
0
)
,
(
(2
)
3.
R
E
SU
LTS AN
D ANA
LY
SIS
In
orde
r to
run Genetic algori
thm
using MATLA
B optim
iz
ation
toolbox, in
jecte
d
reacti
v
e power,
Q
in
itially
h
a
s b
een
d
e
fi
n
e
d
as
1
Per Un
it wh
i
l
e 0
.
1
Per Un
it
v
a
lu
e h
a
s b
e
en
cho
s
en
for lo
ad
i
n
g
p
a
ram
e
ter,
λ
.
No
w,
Pr
o
g
ram
has
bee
n
st
art
e
d a
n
d
t
h
e
fol
l
owi
n
g
dat
a
de
m
onst
r
at
ed i
n
Tabl
e-
II
ha
ve
been
f
o
u
n
d
.
Al
l
t
h
ese
are si
m
u
l
a
t
e
d as wel
l
s
h
o
w
n i
n
Fi
gu
re
3,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 2, A
p
ri
l
20
14
:
20
0 – 2
0
6
2
03
Tabl
e 2. Sol
u
t
i
ons
o
f
Ge
net
i
c
Al
g
o
ri
t
h
m
(G
A)
Gener
a
tions
Fitness Function,
f
(
λ
,
Q
)
Best Fitness Function
Mean Fitness Func
tion
1
-
0
.
3378,
-
0
.
3378,
-
0
.
3273,
-
0
.
3378,
0.
457
0,
0.
2109,
-
0
.
2458,
-
0
.
1228,
-
0
.
1940,
-
0
.
1345,
-
0
.
2699,
0
.
2904,
0.
3055,
0.
34
50,
0.
4245,
-
0
.
3378,
0.
291
4,
0.
0311,
-
0
.
3378,
-
0
.
3378
-
0
.
3378
-
0
.
02682
2
-
0
.
3378,
-
0
.
3378,
-
0
.
1228,
-
0
.
3378,
-
0
.
3378,
-
0
.
2458,
-
0
.
3378,
0.
280
8,
0.
3055,
0.
3546,
-
0
.
183
9,
0.
3055,
-
0
.
3378,
0.
280
8,
0.
2808,
0.
4347,
-
0
.
337
8,
-
0
.
3378,
0.
2914,
0.
30
55
-
0
.
3378
-
0
.
04826
3
-
0
.
3378,
-
0
.
3378,
0
.
2808,
-
0
.
3378,
0.
280
8,
-
0
.
3378,
-
0
.
3378,
-
0
.
1839,
-
0
.
3273,
-
0
.
3378,
-
0
.
3378,
-
0
.
2458,
-
0
.
3378,
0.
280
8,
-
0
.
3378,
-
0
.
3378,
-
0
.
0469,
0
.
0074,
0.
3055,
-
0
.
337
8
-
0
.
3378
-
0
.
02075
4
-
0
.
3378,
-
0
.
3378,
-
0
.
1839,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
0.
2808,
-
0
.
337
8,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
0.
3055,
-
0
.
337
8,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
0
.
2808,
0.
2808,
-
0
.
337
8
-
0
.
3378
-
0
.
1682
5
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
0
.
2808,
0.
2808,
-
0
.
337
8,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
0
.
2808,
-
0
.
3378,
0.
280
8,
0.
2808,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
0.
3055,
-
0
.
337
8
-
0
.
3378
-
0
.
2052
6
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
0
.
2808,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
0
.
2808,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3918,
-
0
.
3378
-
0
.
3378
-
0
.
151
7
-
0
.
3918,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
0.
2808,
-
0
.
337
8,
0.
2808,
-
0
.
3378,
-
0
.
3378
-
0
.
3918
-
0
.
2786
8
-
0
.
3918,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
0.
226
8,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3918,
-
0
.
3378,
-
0
.
3378,
0.
5225,
-
0
.
3378,
-
0
.
3378
-
0
.
3918
-
0
.
2786
9
-
0
.
3918,
-
0
.
3918,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3918,
-
0
.
3378,
-
0
.
3918,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3378,
-
0
.
3918,
-
0
.
3378
-
0
.
3918
-
0
.
272
10
-
0
.
39182
635
773
19
361
-
0
.
39182
6
-
0
.
35131
5
Fin
a
l So
lu
tion
s
prov
id
i
n
g op
tim
u
m
v
a
lu
es:
Lo
ad
ing
Parameter,
λ
=0.922
68
522
039
216
79
Reactive Powe
r,
Q
=0.9141
878
212
437
735
*2
50
MVA
R
=22
8
.546
955
3 M
V
A
R
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Genet
i
c
Al
go
ri
t
h
m Base
d Rea
c
t
i
ve
Pow
e
r
M
a
n
a
g
eme
n
t
by SVC
(
M
d
.
Imr
a
n
Azi
m
)
20
4
Fi
gu
re 3.
S
o
l
u
t
i
on o
f
genet
i
c
al
go
ri
t
h
m
Th
e l
o
cal
g
e
neratio
n of
reactiv
e power red
u
c
es its imp
o
rt
fro
m
th
e feed
er, thu
s
redu
ces th
e
asso
ciated
l
o
sses, and
im
p
r
oves th
e vo
ltag
e
p
r
o
f
ile.
As a
resu
lt, th
e
v
o
ltag
e
secu
rity is also
im
p
r
o
v
e
d
[15
]
.
W
i
t
h
o
u
t
a
hi
nt
of
d
o
u
b
t
t
h
e
am
ount
of
rea
c
t
i
v
e po
we
r i
n
ject
i
o
n
l
a
rgel
y
depe
n
d
o
n
t
h
e avai
l
a
bl
e l
o
a
d
b
u
s
vol
t
a
ge
val
u
e.
No
rm
al
ly
, whe
n
t
h
e
b
u
s
vol
t
a
ges
fl
uct
u
at
e
fr
om
expect
ed
uni
t
y
pe
r
uni
t
val
u
e
o
w
i
n
g t
o
t
h
e
v
a
riation
s
in
load
ing
p
a
ram
e
t
e
r as shown
in “Fig
.4
”,
certai
n
reactive
powers are
n
ecessary to
b
e
su
pp
lied
for
th
e so
le pu
rpo
s
e of co
m
p
en
satio
n
so as to ensu
re th
e stab
le
op
eration
o
f
th
e
syste
m
.
It is co
nsid
ered
th
at to
tal ind
u
c
tan
ce,
X
L
=
5
, ca
pacitance
X
c
=0.
6
5 an
d
fi
ri
n
g
an
gl
e
of
SVC
,
α
SVC
=5
0
.
No
w,
fro
m
“(1
)
”, th
e requ
irem
en
t o
f
reactiv
e
p
o
wer d
e
p
e
n
d
i
n
g
up
on
th
e av
ailabilit
y o
f
bu
s
v
o
l
tag
e
s can
b
e
adj
u
sted
as illu
strated
i
n
Tab
l
e
3
,
Table
3. Reacti
v
e Power Managem
e
nt
Bus L
o
cations
L
o
ading Factor
s,
λ
(P
.
U
)
Available Bus Voltages,
V
(P
.U)
Voltage Varia
tions
Fro
m
Unity
∆
V
=1-
V
(P
.
U
)
Requir
e
d Reactive
Po
wer In
jec
tio
n
,
Q
(M
V
A
R
)
3 0.
102
0.
9240
0.
076
239.
48
4 0.
132
0.
9130
0.
087
233.
82
5 0.
183
0.
8890
0.
111
221.
81
6 0.
245
0.
8650
0.
135
209.
82
7 0.
357
0.
8500
0.
150
202.
75
8 0.
486
0.
8170
0.
183
187.
46
9 0.
699
0.
7699
0.
233
164.
98
10
0.
750
0.
7310
0.
269
149.
54
Fu
rt
h
e
rm
o
r
e,
fro
m
fin
a
l so
lu
tion
of gen
e
tic alg
o
rith
m
,
if th
e o
p
tim
u
m
v
a
l
u
e of
λ
is
0.92268522039216
79 Per Unit and
reactive power is
228.5469
553 MVAR, t
h
en t
h
e bus
voltage
m
u
st be
0.90265395 Pe
r Unit
whic
h is
stabilized
by the
proper
react
ive power pla
n
ning.
Vo
ltag
e
Stab
ili
ty
m
a
rg
in
(VSM) after co
m
p
letio
n
o
f
GA,
%
100
Optimum
Base
Optimum
VSM
=8
9.161
740
73%
0
1
2
3
4
5
6
7
8
9
10
-0
.
4
-0
.
2
0
0.
2
0.
4
G
ener
at
i
o
n
F
i
tn
e
ss va
l
u
e
B
e
s
t
:
-
0
.
391826 M
ean
:
-
0
.
351315
1
2
0
0.
5
1
N
u
m
ber
of
v
a
r
i
a
b
l
e
s
(
2
)
C
u
r
r
e
nt
bes
t
i
n
di
v
i
dual
C
u
r
r
ent
B
e
s
t
I
n
d
i
v
i
dual
B
e
s
t
f
i
tnes
s
M
ean f
i
tnes
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 2, A
p
ri
l
20
14
:
20
0 – 2
0
6
2
05
Fig
u
re
4
.
Av
ailab
l
e lo
ad
b
u
s
vo
ltag
e
s
requ
ired
to b
e
con
t
ro
lled
to reach
t
h
e
tx
p
ected limit
It
has be
en
fo
u
nd
fr
om
t
h
e anal
y
s
i
s
of ge
net
i
c
al
gori
t
h
m
t
h
at
t
h
e opt
i
m
al
am
ount
of
reac
t
i
v
e po
wer
th
at is requ
ired to
b
e
i
n
j
ected
in
fou
r
bu
s
syste
m
is 2
8
2
.
9
5
MVAR
[2
], wh
ereas th
e inj
e
ctio
n
o
f
228
.54
695
53
MVAR optim
al reactive power is ascer
taine
d
in this pa
per notifying th
e reduce
d am
ount of reactive powe
r
in
j
ection
.
4.
CO
NCL
USI
O
N
Th
e propo
sed
strateg
y
d
eals with
op
ti
m
a
l r
eactiv
e p
o
wer in
j
ection
so
as to
i
m
p
r
o
v
e
t
h
e vo
ltage
stab
ility o
f
th
e 1
0
-b
u
s
p
o
wer syste
m
. A step
b
y
step
d
e
scrip
tio
n
o
f
t
h
e evo
l
u
tion
a
ry op
ti
mizatio
n
p
r
ocess h
a
s
b
een d
e
tailed in
th
is p
a
p
e
r
fo
r und
er
stan
d
i
n
g
th
e wo
rk
ing
p
r
o
c
ed
ur
e
o
f
g
e
n
e
tic algo
r
i
th
m
.
I
t
g
o
e
s
beyond
di
sp
ut
at
i
o
n
t
h
at
genet
i
c
al
g
o
ri
t
h
m
has
be
en
pr
o
v
ed
t
o
be a
ve
ry
us
e
f
ul
m
e
t
hod
t
o
sol
v
e l
a
r
g
e s
cal
e,
co
m
b
in
ato
r
ial
o
p
tim
izat
io
n
prob
lem
lik
e reactiv
e po
wer
p
l
an
n
i
n
g
fo
r th
e
sak
e
o
f
vo
ltag
e
stab
ility. It is
su
ffice
to
say th
at th
is fo
rm
u
l
atio
n
op
ens up
sev
e
ral p
o
ssib
ilities in
th
e field
o
f
p
o
wer syste
m
n
e
two
r
k
con
t
ain
i
ng
Distribu
ted
Gen
e
rat
o
rs
(DG)
th
at co
u
l
d
p
l
ay an
an
ch
or
ing
p
a
rt fo
r th
e
u
tility p
l
an
n
e
rs an
d
o
p
erators in
th
e
rel
e
va
nt
fi
el
d.
For
i
n
st
ance
, i
n
f
u
t
u
re, t
h
e p
r
o
p
o
sed m
e
t
h
o
dol
ogy
ca
n
be
appl
i
e
d t
o
a
di
st
ri
b
u
t
i
o
n
ne
t
w
o
r
k
co
m
p
o
s
ed b
y
1
0
0
bu
ses, in
wh
ich
no
t on
l
y
th
e
o
p
tim
u
m
v
a
l
u
e
o
f
th
e in
j
ected
reactive po
wer bu
t al
so
t
h
e
lo
catio
n
o
f
(DG)
u
n
its cou
l
d b
e
d
e
term
in
ed so
th
at b
o
t
h
th
e syste
m
v
o
ltag
e
stab
ility a
n
d
th
e
DG p
e
netratio
n
lev
e
l co
u
l
d
b
e
i
m
p
r
ov
ed. Mo
reo
v
e
r,
Gen
e
tic alg
o
r
it
h
m
s
ma
y b
e
u
tilized
in so
lv
ing
a
wide rang
e of prob
lem
s
acro
s
s m
u
ltip
l
e
field
s
su
ch
as scien
ce,
b
u
s
i
n
ess, eng
i
n
e
erin
g, and
m
e
d
i
ci
n
e
lik
e produ
ctio
n
sch
e
du
ling
,
call
rou
ting
for call cen
ters, rou
t
i
n
g
for tran
sportatio
n
,
d
e
te
rm
i
n
i
ng el
ect
ri
cal
ci
rcui
t
l
a
y
out
s, desi
g
n
i
n
g n
e
ural
n
e
two
r
k
s
, d
e
sig
n
i
n
g
and
contro
llin
g ro
bo
ts, fi
n
a
n
c
ial trad
ing
,
cred
it ev
alu
a
tion
,
budg
et allo
cation
,
fraud
det
ect
i
o
n
an
d
m
a
ny
m
o
re.
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l
t
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t
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Bu
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Bu
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s
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t
i
m
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l
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i
n
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8.
BIOGRAP
HI
ES OF
AUTH
ORS
Md. Imran Azim has completed h
i
s B.Sc. in
Electr
i
cal and
Electron
ic Eng
i
neer
ing fr
om Rajshahi
University
of Engineer
ing and
Techno
log
y
(R
U
ET), B
a
nglad
e
s
h. His
m
a
in re
s
earch
area
of
concern
e
d is Po
wer s
y
stem and
Renewable En
er
g
y
.
He h
a
s wor
k
ed in
severa
l
t
opics re
lat
e
d to
this field
,
such as FACTS devi
ces, gen
e
tic alg
o
rithm, pulse width modul
ated inverters,
solar
energ
y
and s
o
on
.
Prof. Dr. Md. Fay
z
ur Rahman is a renowned pr
of
essor and head of Elec
t
r
ic
al
and E
l
ec
t
r
onic
Engineering dep
a
rtment of Daffo
dil Intern
ation
a
l
University
(DIU), Banglad
esh.
He is engaged
in te
aching
in th
e are
a
of E
l
ec
tr
onics
and m
achi
n
e contro
l. His
res
earch
int
e
res
t
includ
es
high
voltag
e
disch
a
r
g
e app
lic
ation
with speci
al
iza
t
ion in Ozon
e
genera
tion s
y
st
em
and im
age
processing. He is a
life long
member of B
a
nglad
es
h El
ect
ronic S
o
ci
et
y,
F
e
llow of IEB
,
Banglad
esh. He has more than 60 publications in
different field
s
of
Electri
cal &andEl
e
c
t
ronic
Enigineering
. H
e
has supervised
man
y
B.Sc., M
.
Sc
. and PhD the
s
ises. He is curr
e
n
tl
y working as
a reviewer of several journ
a
ls in
cluding
, JEER
, I
J
CSI, IJCA, IJATER, ACTA PRESS and many
more
.
Evaluation Warning : The document was created with Spire.PDF for Python.