Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
4, N
o
. 4
,
A
ugu
st
2014
, pp
. 51
2
~
51
9
I
S
SN
: 208
8-8
7
0
8
5
12
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
Determination of Volume of
Capacitor Bank for Static VAR
Compen
sator
Md.
Ruhul
Amin, Rajib B
a
ran
Roy
Department o
f
Electrical and
Electroni
c Eng
i
neer
ing, Univ
ersity
o
f
Informa
tion
Technolog
y
and Sciences (UITS),
Dhaka-1212, Bangladesh
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Feb 15, 2014
Rev
i
sed
May 28
, 20
14
Accepted
Jun 15, 2014
In high voltage
AC sy
stem, th
e
s
y
stem
voltage
and frequen
c
y
ch
ange rap
i
d
l
y
with the var
i
at
io
n of load. Th
e re
act
ive
power also changes with the variatio
n
of load which af
fects
the s
y
s
t
em
voltage th
erefor
e it is
nec
e
s
s
a
r
y
to anal
yz
e
the power s
y
st
e
m
in order to de
term
in
e s
y
s
t
em
param
e
ters
and
its variation
under var
i
ous load conditions. The
cap
aci
tor
bank size is determined
b
y
cal
cula
ting
exis
t
i
ng re
act
ive pow
er and
requir
e
d r
eac
tive
power in
s
y
s
t
em
fo
r
Static VAR Compensator (SVC
) is focused
in this paper. Base c
a
s
e load flow
is
us
ed to
anal
ys
is
power s
y
s
t
em
. After
ident
i
f
y
ing low vo
lt
age bus
es
,
arbitr
ar
y
cac
ipto
r back
is
im
pos
ed in bu
es
es
and
res
u
lts
ar
e
check
ed wheth
e
r
it is
met or
not
in the s
y
stem demand
leve
l.
Her
e
MATLAB cod
i
ng is used
to
find th
e low
voltage
affected
bus
and au
tom
a
ted
c
a
lcu
l
at
ion of
cap
aci
tor ba
c
k
size is done b
y
MATLAB also.
The propos
ed method of id
entif
ication of low
voltag
e
bus
es
and determ
inat
ion of capac
itor ban
k
are fas
t
er and
eas
ier th
an
the conventional
method.
Keyword:
Bu
s
Cap
acito
r Bank
Fast D
e
C
o
up
led
MATLAB
Reactive Powe
r
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
:
Md
.
R
u
hu
l Amin
Depa
rtm
e
nt of
Electrical an
d Electronic
Engineering,
Un
i
v
ersity of
In
fo
rm
atio
n
Tech
no
log
y
an
d
Scien
ces
(UITS),
GA -
37
/1
, Prag
ati Sh
aran
i,
Gu
ls
ha
n-
2,
D
h
a
k
a-1
2
1
2
,
B
a
n
g
l
a
des
h
.
Em
a
il: ru
hu
l.amin
@u
its.edu
.b
d
1.
INTRODUCTION
In an electric p
o
we
r sy
stem
,
whic
h is AC (alternati
ng c
u
r
r
e
n
t
)
by
nat
u
re f
o
r t
h
e m
o
st
advant
a
g
es, t
h
e
equi
pm
ent
s
and ot
he
r i
n
dust
r
i
a
l
i
nduct
i
v
e
l
o
ads
dra
w
re
act
i
v
e po
wer
.
The i
n
c
r
easi
n
g
dem
a
nd of re
act
i
v
e
po
we
r
does
re
al
l
y
have i
t
s
o
w
n
m
a
jor i
m
pact
o
n
t
h
e
ge
ner
a
tin
g un
its, l
i
n
e
s, ci
r
c
u
it breakers
,
tra
n
s
f
orm
e
rs,
rel
a
y
s
an
d i
s
ol
at
ors.
M
o
re rea
c
t
i
v
e p
o
we
r
de
m
a
nd re
sul
t
s
i
n
i
n
c
r
easi
n
g
di
m
e
nsi
ons
an
d
cost
w
h
i
c
h
re
d
u
ce t
h
e
whole
power s
y
ste
m
efficiency [1].
In
d
i
stri
b
u
tion
system
s
,
th
e
v
o
ltag
e
at th
e lo
ad
en
d ten
d
s to
g
e
t lower due
to
th
e lack
of
reactiv
e power
[2
]. B
u
t if th
e t
o
tal reactiv
e load
is
feed
o
n
l
y
b
y
th
e g
e
n
e
rati
o
n
un
it, it
will lo
wer
th
e m
a
x
i
m
u
m
r
eal p
o
wer cap
acity o
f
g
e
n
e
rato
r. Moreov
er
th
e ad
d
ition
a
l cu
rren
t
flow asso
ciated
with
reactive
powe
r can cause increase
d
l
o
sses and e
x
ces
sive voltage
sa
gs.
In suc
h
ca
ses, local
VAR support is
offe
re
d
u
s
ing
shu
n
t
cap
acito
rs; t
h
is is called
reactiv
e po
we
r c
o
m
p
ensation.
The m
o
st common m
e
thod for t
h
is
co
m
p
en
satio
n
is to
ad
d
capacito
r
b
a
nk
s t
o
th
e system
[3]. Ca
pacitors are a
ttractive beca
use t
h
e
y
are
econ
o
m
i
cal
and easy
t
o
m
a
i
n
t
a
i
n
. N
o
t
o
n
l
y
t
h
at
, t
h
ey
ha
ve
no m
ovi
n
g
pa
rt
s, u
n
l
i
k
e s
o
m
e
ot
he
r de
vi
ces
use
d
for th
e sam
e
p
u
rpo
s
e. Usi
n
g
sh
un
t cap
acitors to
su
pp
ly th
e lead
in
g
currents req
u
i
red
b
y
th
e lo
ad
relieves th
e
g
e
n
e
rator fro
m
su
pp
lying
th
at p
a
rt of th
e i
n
du
ctiv
e cu
rren
t. Th
e system b
e
n
e
fits du
e to
th
e ap
p
licatio
n
o
f
shunt ca
pacitors include
[4
]
reactiv
e po
wer
su
ppo
rt, vo
ltage profile i
m
p
r
ov
em
en
ts, lin
e an
d tran
sfo
r
m
e
r lo
ss
reductions, rel
ease
of power syste
m
capacity
and savi
ng
s due
t
o
red
u
ce
d ener
gy
l
o
ss
.
T
h
ese be
nefi
t
s
a
p
pl
y
fo
r
bot
h di
st
ri
b
u
t
i
on a
n
d t
r
a
n
sm
i
ssi
on sy
st
em
s. M
a
i
n
t
a
i
n
i
n
g
a con
s
t
a
nt
st
a
nda
r
d
v
o
l
t
a
ge
i
s
very
i
m
port
a
nt
f
o
r
m
o
st
of t
h
e i
ndust
r
i
e
s an
d h
o
m
e
appl
i
a
nces. Lo
w v
o
l
t
a
ge
pr
ofi
l
e
m
a
y cause p
o
w
er l
o
s
s
es i
n
t
h
e sy
st
em
,
l
o
w
per
f
o
r
m
a
nce i
n
t
h
e
a
ppl
i
a
nc
es an
d
i
n
du
strial
m
ach
in
eries. So
m
e
ti
mes it
m
a
y cau
se sev
e
re d
a
m
a
g
e
to
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
51
2
–
51
9
51
3
appl
i
a
nc
es a
n
d
l
o
ss i
n
pr
od
uct
i
ons
. T
h
ese
pr
o
b
l
e
m
s
can be e
l
im
i
n
at
ed by
u
s
i
ng
SVC
wi
t
h
capaci
t
o
r
ba
n
k
s
[
5
]
.
To
attain
a cert
a
in
vo
ltag
e
level, d
e
term
in
ati
o
n
of t
h
e size
of these
capa
c
itor ba
nks is
nec
e
ssary.
A m
e
t
hod i
s
p
r
op
ose
d
t
o
det
e
rm
i
n
e capaci
t
o
r ba
nk si
ze i
n
t
h
i
s
wo
r
k
. T
h
e fast
deco
u
p
l
e
d
m
e
t
hod [
6
]
i
s
use
d
f
o
r
an
al
y
z
i
ng t
h
e
p
o
w
er
fl
o
w
of
4
2
buses
an
d l
a
t
e
r M
A
TL
AB
codi
ng
i
s
use
d
fo
r
det
e
rm
i
n
ing
t
h
e
bus
es
havi
ng
pr
o
b
l
e
m
i
n
ref
e
rence
sy
st
em
vol
t
a
ge
. T
h
e
p
r
o
p
o
sed
dec
o
u
p
l
e
d m
e
t
hod
o
f
i
s
fast
er a
n
d
easi
e
r
th
an
t
h
e co
nv
en
tio
n
a
l m
e
th
od also
.
2.
CONCEPT
OF DETERMINATION
OF CAPACITOR
VOL
U
ME
Prese
n
tly the s
i
ze of capacitor bank
nee
d
ed
for attain
ing
a
satisfacto
r
y
v
o
ltag
e
lev
e
l is
determin
ed
i
n
a tedious way
.
From
a base case load flow the voltage
sce
n
ario of the entire powe
r
system
is
obtaine
d.
Buses
suf
f
eri
ng
fr
om
l
o
w v
o
l
t
a
ge a
r
e m
a
rked
. First an arbitra
r
y
size of capaci
to
r ba
n
k
i
s
ass
u
m
e
d at
one o
f
t
h
e
can
d
i
d
a
te bu
ses. A lo
ad
-flow
is d
o
n
e
con
s
idering
th
at shu
n
t cap
acito
r to
ch
eck
t
h
e i
m
p
r
ov
em
en
t o
f
vo
ltag
e
of
th
at bu
s.
If it is no
t satisfactory, th
e cap
acit
o
r
b
a
n
k
si
ze i
s
cha
nge
d
(i
nc
r
eased
or
dec
r
e
a
sed)
co
rre
sp
o
ndi
ngl
y
and a
g
ai
n a
n
ot
her l
o
ad
fl
o
w
i
s
do
ne. T
o
fi
nd t
h
e act
ual
c
a
paci
t
o
r
ba
nk
si
ze, l
o
ad
-fl
ow
i
s
neede
d
t
o
be r
u
n
sev
e
ral tim
es u
n
til th
e
d
e
sired vo
ltag
e
lev
e
l (0
.9
5 p
e
r
un
it (p
.u
.)
o
r
1
.
0 p.u.) is ach
i
ev
ed.
Th
en
th
is pro
c
ess
of
rep
eated
lo
ad-flo
w is app
lied
t
o
find
th
e req
u
i
red cap
aci
t
o
r
b
a
nk
si
ze at
ot
h
e
r ca
ndi
dat
e
b
u
s
es o
n
e
by
one
.
3.
LOAD FLOW TECHNIQUES
Loa
d
fl
o
w
s ca
n be
pe
rf
orm
e
d u
s
i
n
g di
f
f
er
e
n
t
t
ech
ni
q
u
es.
Th
ose are
Ga
u
ss-Sei
d
el
m
e
t
hod
, Ne
wt
o
n
-
Rap
h
s
on
m
e
th
o
d
and
Fast Deco
up
led
m
e
th
o
d
. Th
e last on
e is th
e m
o
st
p
opu
lar m
e
th
o
d
. To
calibrate th
e
pr
o
pose
d
m
e
t
h
od
, he
re Fast
Deco
u
p
l
e
d m
e
t
h
o
d
has
been
cho
s
en as i
t
i
s
t
h
e fast
est
of al
l
t
h
e conve
nt
i
onal
m
e
t
hods
.
Al
g
o
r
i
t
h
m
for
pe
rf
orm
i
ng l
o
a
d
fl
ow
i
n
fast
dec
o
u
p
l
e
d
m
e
t
hod i
s
e
x
pl
ai
ned
he
re.
Pri
o
r t
o
t
h
at
,
al
go
ri
t
h
m
for c
onst
r
uct
i
n
g t
h
e
Y
bus
m
a
trix
is b
r
iefly ex
p
l
ai
ned
as it is
a pre-req
u
i
site for an
y lo
ad
-flow.
3.
1.
Fi
ndi
n
g
B
u
s A
d
mi
tt
an
ce M
a
tri
x
(
Y
bu
s
Ma
trix
)
St
eps i
n
c
onst
r
uct
i
n
g
t
h
e
Y
bus
b
y
in
sp
ection
[7
]
The Y
bus
is symme
tric.
Y
ij
=Y
ji
Y
ii,
th
e self-admit
tan
ce (d
iago
n
a
l elem
en
t), is eq
u
a
l to
t
h
e
su
m
o
f
th
e pri
m
it
iv
e ad
m
i
t
t
a
n
ces
o
f
all th
e
com
pone
nt
s c
o
nnect
e
d
t
o
t
h
e
i
t
h
n
o
d
e.
Y
ij
, th
e ij
th
el
e
m
en
t o
f
th
e
Y
bus
(o
ff d
i
agon
al ele
m
en
t), is eq
u
a
l to
th
e n
e
g
a
tiv
e
o
f
t
h
e primitiv
e
adm
i
t
t
a
nce of al
l
co
m
pone
nt
s con
n
ect
ed b
e
t
w
een n
o
d
es i
and j. It
i
s
t
o
be n
o
t
e
d t
h
at
i
f
m
o
re t
h
an o
n
e
com
pone
nt
i
s
con
n
ect
ed i
n
pa
ral
l
e
l
bet
w
een
t
w
o n
o
d
es, eq
u
i
val
e
nt
pri
m
i
tive adm
i
tt
ance of t
h
e com
p
o
n
e
nt
s i
s
first o
b
t
ain
e
d
before d
e
term
in
i
n
g
th
e
en
try
i
n
th
e
Y
bus
.
3.
2.
F
a
st
Dec
o
upl
ed
Me
th
o
d
The al
go
ri
t
h
m
fo
r Fast
Dec
o
u
p
l
e
d M
e
t
h
o
d
[
6
]
-
[
1
0]
i
s
desc
r
i
bed
bel
o
w.
Step 1.
Form
ulate and
Assem
b
le Y
bus
in
Per Un
it.
Step 2.
Mak
e
n
ecessary in
i
tia
l assu
mp
tio
n
s
fo
r
v
o
ltag
e
m
a
g
n
i
t
ude and p
h
ase angl
es, for l
o
ad (P
Q
)
buses t
a
ke
1
0
o
and f
o
r
gener
a
t
o
r (PV
)
b
u
s t
a
ke 1.
02
0
o
Step 3.
Calculate
real powe
rs of all
the buses with
a
ssum
e
d dat
a
fr
om
t
h
e fol
l
o
wi
ng
eq
uat
i
o
n.
N
2
i
i
ii
i
n
in
in
n
i
n=1
,
n
i
P=
V
G
+
V
V
Y
c
o
s
(
θ
+
δ
-
δ
)
Calcula
t
e initial real power
mis
m
a
t
ch vector
Δ
P
V
from
t
h
e gi
ven dat
a
(real
po
wer) a
nd c
a
l
c
ul
at
ed real
powe
r
.
Step 4.
Gen
e
rate
th
e
‘
B
’ m
a
trix
tak
i
n
g
n
e
g
a
tiv
e
o
f
th
e su
scep
tances o
f
Y
bus
. It
will b
e
u
s
ed
as con
s
tan
t
Jacob
i
an
Matri
x
for th
e rest
of th
e calcu
lation
s
.
Step 5.
Com
pute the correction
vector of
pha
se angles
b
y
m
u
lt
ip
lyin
g
th
e inv
e
rse o
f
th
e ‘B
’ matrix
by
real powe
r mis
m
a
t
ch
vect
or
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I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Determi
n
a
tion
o
f
Vo
lume
o
f
Ca
pa
cito
r Ban
k
fo
r
S
t
a
tic VAR
Co
mp
en
sa
t
o
r (
M
d
.
Ruhu
l Amin
)
51
4
-1
Δ
P
as
,
B
.
Δδ
=
V
Δ
P
Δδ
=B
.
V
Step 6.
Update the pha
s
e angles.
(1
)
(
0
)
(
0
)
δ
=
δ
+
Δδ
Step 7.
Calculate reactive powers
of
o
n
l
y th
e lo
ad
bu
ses.
N
2
i
i
ii
i
n
in
i
n
n
i
n=1,
n
i
Q=
-
V
B
-
V
V
Y
s
i
n
(
θ
+
δ
-
δ
)
Calculate initial reactive
powe
r m
i
s
m
atch vec
t
or
Δ
Q
V
Step 8.
Co
m
pute the correction
vector of phase angles
Δ
V
b
y
m
u
ltip
l
y
in
g
th
e in
v
e
rse o
f
th
e ‘B’ m
a
trix
by real powe
r
mis
m
a
t
ch vector.
*
-1
*
Δ
P
as
,
B
.
Δ
V=
V
Δ
P
Δ
V=
B
.
V
Step 9.
Updat
e
t
h
e v
o
l
t
a
ge m
a
gni
t
udes.
(1
)
(
0
)
(0
)
V=
V+
Δ
V
.Thi
s i
s
d
o
n
e
onl
y
for
t
h
e l
o
ad
buses.
Step 10.
Retu
rn
to
step
3
,
rep
eat
th
e pro
cedures u
n
til a
ll
m
i
s
m
atch
es are
with
in th
e
sp
ecified to
leran
ce.
3
.
3
.
Traditio
na
l Metho
d
fo
r
Co
mputing Ca
pa
cito
r Bank Size
The al
g
o
ri
t
h
m
for
det
e
rm
i
n
ing t
h
e si
ze o
f
capaci
t
o
r
ban
k
by
t
r
adi
t
i
onal
m
e
t
hod i
s
des
c
ri
be
d bel
o
w
[1
1]
-[
1
2
]
.
1.
Form
Y
bus
m
a
tri
x
of
t
h
e net
w
or
k.
2.
Per
f
or
m
b
a
se case lo
ad
f
l
o
w
by th
e g
i
v
e
n netw
or
k data.
3.
M
a
rk t
h
e
bu
ses
su
ffe
ri
n
g
fr
om
l
o
w
v
o
l
t
a
ges
h
a
vi
n
g
vol
t
a
ges
un
de
r
0.
95
p
.
u
.
4.
Select a candidate bus
K a
n
d
choose
a si
ze
for shunt capaci
tor
ba
n
k
fo
r the bu
s.
5.
Perf
o
r
m
anot
h
e
r l
o
a
d
fl
o
w
a
n
d
obs
er
ve t
h
e
b
u
s
vol
t
a
ge
V
K
.
6.
Calculate absolute error from
the target volt
a
ge, |V
K
-V
desired
| and chec
k whet
her the e
r
ror is less than a
fi
xe
d t
o
l
e
r
a
nce
l
e
vel
(s
uc
h as
0.
00
1
)
.
7.
If the e
r
ror is
greater t
h
an t
h
e tole
rance
,
check whethe
r the attained vo
l
t
a
ge i
s
bel
o
w
o
r
o
v
er t
h
e desi
re
d
vol
t
a
ge
.
8.
If t
h
e
v
o
ltag
e
is still b
e
lo
w t
h
e
d
e
sired
v
o
l
tag
e
, th
en
m
o
re VAR is need
ed. So
i
n
crease th
e
v
a
lu
e
of
capacitor ba
nk
and
GO
TO
step
5
.
9.
If t
h
e
vol
t
a
g
e
i
s
ab
o
v
e t
h
e
des
i
red
v
o
l
t
a
ge, t
h
en
decrease
t
h
e
val
u
e
o
f
ca
pac
i
t
o
r
ban
k
a
n
d
GO
TO
st
ep
5
.
10
.
In step
6
,
if t
h
e bu
s
v
o
ltag
e
abso
lu
te erro
r is l
e
ss th
an
th
e to
l
e
ran
c
e, sav
e
t
h
e cap
acitor
b
a
nk
size.
11
.
Check whethe
r the sizes
of
ca
paci
t
o
r
ba
n
k
s f
o
r al
l
t
h
e
ca
ndi
dat
e
b
u
ses
are
det
e
rm
i
n
ed
o
r
not
.
I
f
not
,
t
h
e
n
GO
TO
step 4.
12
.
End.
4.
PROP
OSE
D
METHO
D
Let a si
m
p
le
ci
rcu
it [8
] with
an
AC v
o
ltag
e
so
urce, a resistor, an
ind
u
c
t
o
r
an
d
lo
ad
b
e
con
s
id
ered
i
n
fi
g
u
re
1.
T
h
e c
o
r
r
es
po
n
d
i
n
g
p
h
as
or
di
ag
ram
of
v
o
l
t
a
ge
& c
u
r
r
ent
o
f
t
h
e
ci
rcui
t
i
s
s
h
ow
n i
n
fi
g
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
JECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
51
2
–
51
9
51
5
Fi
gu
re
1.
A
si
m
p
l
e
AC
seri
es ci
rcui
t
Fi
gu
re
2.
P
h
as
or
di
a
g
ram
of t
h
e si
m
p
l
e
AC
s
e
ri
es ci
rc
ui
t
Fro
m
th
e fi
g
u
re 2, it can be
written
,
2
22
'
s
VV
V
V
(1
)
Whe
r
e t
h
e
∆
V= I
R
co
s
+ IX
sin
=
RP
X
Q
+
VV
An
d
Δ
V’=
I
X
co
s
- IX
sin
=
XP
R
Q
-
VV
Practically,
'
VV
V
so
ne
gl
ect
i
n
g
Δ
V',
eq
u
a
tion
(1) can
b
e
written
as
s
VV
V
V
RP
X
Q
+
VV
Hence
t
h
e
reac
t
i
v
e p
o
we
r i
s
g
i
ven
by
2
s
VV
-
V
-
P
R
Q =
X
(2
)
Differen
tiatin
g equ
a
tio
n no
(2)
wit
h
re
spect
t
o
V, we get
S
V-
2
V
δ
Q
=
δ
VX
(3
)
For a t
h
ree
pha
s
e short
circu
it
at the recei
ving e
n
d (V=
0
)
S
SC
V
δ
Q
=
= I
δ
VX
(4
)
Th
e
rate of chan
g
e
of reactive po
wer
with
resp
ect to
vo
ltag
e
at a
n
o
d
e
is equ
a
l to
th
e sh
ort circu
it cu
rren
t.
Howev
e
r in
a
syste
m
with
man
y
bu
ses th
e
sh
ort circu
it cu
rr
en
t
[5
] at an
y bu
s
K
i
s
o
b
t
ai
ned
negl
ect
i
n
g
p
r
e-
fau
lt cu
rren
t
(i.e. no
l
o
ad) as fo
llo
ws
f,K
sc
,K
KK
V
I =
Z
(5
)
Whe
r
e V
f,
K
= Pre-
fa
ul
t
v
o
l
t
a
ge
t
bu
s K whi
c
h
i
s
us
ual
l
y
consi
d
ere
d
a
s
1 p.
u.
Z
KK
= Di
ag
o
n
a
l
el
em
ent
cor
r
e
s
po
n
d
i
n
g t
o
bu
s K i
n
t
h
e sy
st
e
m
bus i
m
pedan
ce m
a
t
r
i
x
Z
bus
.
So
equ
a
tio
n (2
an
d 4) can
b
e
ex
tend
ed to
an
y
b
u
s
K in
larg
e
syste
m
as fo
llows.
δ
φ
φ
φ
IX
I
R
Δ
V
V
I
Δ
V´
V
S
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I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Determi
n
a
tion
o
f
Vo
lume
o
f
Ca
pa
cito
r Ban
k
fo
r
S
t
a
tic VAR
Co
mp
en
sa
t
o
r (
M
d
.
Ruhu
l Amin
)
51
6
Star
t
Form Y
bu
s
Identify
lo
w
voltage
buse
s
,
K
Perfo
r
m a
test
Load-flo
w
Print the value
of
c
a
pac
i
tor bank
+
NO
YES
I
s
ever
y b
u
s
Compensated?
End
Do base
c
a
se
Load-flow
Z
bus
= Y
bus
-1
Determin
e
cap
a
citor
b
a
n
k
s
i
z
e
K
KK
1
Δ
Q=
Z
K
V
sc
KK
δ
Q1
= I
=
δ
VZ
(6
)
So
VAR re
quired at a
bus i
n
resp
ect to th
e ch
ang
e
i
n
its
v
o
l
tag
e
Δ
V
can alway
s
be
obtaine
d
a
s
KK
KK
1
Q =
V
Z
(7
)
i.e.
K,r
e
q
d
.
K
,exi
s
t
in
g
K
,r
eq
d.
exi
s
ti
n
g
KK
1
Q-
Q
=
(
V
-
V
)
Z
(8
)
4.
1.
Al
g
o
ri
t
h
m an
d Fl
ow
C
h
ar
t
of
Pro
p
o
s
ed
Meth
od
o
f
C
o
mpu
t
ati
o
n
1.
Form
Y
bus
m
a
tri
x
of
t
h
e net
w
or
k.
2.
Find
Z
bus
m
a
tri
x
o
f
th
e
n
e
two
r
k
inv
e
rtin
g th
e
Y
bus
m
a
trix
.
Z
bus
= Y
bus
-1
.
3.
Per
f
or
m
b
a
se case lo
ad
f
l
o
w
by th
e g
i
v
e
n netw
or
k data.
4.
I
d
en
tif
y K bu
ses suf
f
e
r
i
ng
f
r
om
lo
w
v
o
ltages h
a
v
i
ng
v
o
ltages und
er
0
.
95
p.u
.
5.
Sel
ect
a can
di
d
a
t
e
bu
s
K a
n
d
f
i
nd t
h
e
desi
re
d
vol
t
a
ge
rai
s
e
,
K
V
.
K
V
=
K
,
r
e
qd.
K
V-
V
6.
Fi
nd
t
h
e re
qui
r
e
d VAR
si
ze.
KK
KK
1
Q =
V
Z
Whe
r
e,
KK
Z
= Corresponding
diagonal elem
ent of Z
bus
f
o
r t
h
e
ca
ndi
dat
e
b
u
s
K
.
K
Q
=
K
,
req
d
.
K
,exi
st
i
n
g
Q-
Q
7.
Ru
n a test lo
ad-
f
l
ow
u
s
i
n
g a cap
acito
r b
a
nk
,
K
Q
M
VAR
at
t
h
e
bus
K
an
d
fi
n
d
ne
w
K
V
.
8.
R
e
peat
st
eps
5
,
6 a
n
d
7
fo
r
ot
h
e
r
buse
s
m
e
nt
ione
d i
n
st
e
p
4.
Fi
gu
re
3.
Fl
o
w
cha
r
t
o
f
pr
o
p
o
s
ed m
e
t
hod
o
f
com
put
at
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
51
2
–
51
9
51
7
5.
RESULTS
A
N
D
DI
SC
US
S
I
ON
In the pre
v
ious chapter,
a
m
e
t
h
o
d
has bee
n
pro
p
o
se
d fo
r react
i
v
e p
o
we
r
com
p
ensat
i
o
n
t
o
im
prove
th
e vo
ltag
e
pro
f
ile
o
f
a power system
. In
t
h
is ch
ap
ter, to v
e
rify th
e
v
a
l
i
d
ity o
f
t
h
e meth
od
, it is app
lied
o
n
vari
ous
p
r
act
i
cal
po
we
r sy
st
e
m
net
w
or
ks.
5.
1. Sys
t
em
N
e
tw
ork
The
net
w
or
k
u
s
ed
here i
s
a
ve
ry
si
m
p
l
e
four
bus
net
w
o
r
k co
nsi
s
t
i
n
g
t
w
o ge
nerat
o
r
-
b
u
s a
n
d t
w
o l
o
a
d
-
bus
with no transform
e
r connected to
an
y
o
f
th
e bu
ses. H
e
r
e
bu
s no
1 n
a
m
e
d
B
i
r
c
h
is th
e slack
-
bus. The
capaci
t
y
of
ge
nerat
o
r c
o
nnec
t
ed at
b
u
s
4 i
s
31
8M
W.
Al
l
t
h
e f
o
u
r
buse
s
su
ppl
i
e
s s
o
m
e
l
o
ads
o
f
di
ff
erent
lev
e
ls.
Fi
gu
re
4.
F
o
u
r
bus
sy
st
em
net
w
o
r
k
.
5.
2. Resul
t
s
U
s
ing
Fast
D
e
co
up
led Meth
od
lo
ad
-f
low
analysis f
o
r
t
h
e fo
ur
b
u
s
n
e
t
w
ork
dep
i
cted
abov
e,
vo
ltag
e
level and a
n
gle of all buses
are found from
the network
data given i
n
Ta
ble 1. Fo
r each load-bus (bus
2 and
3)
, desi
red
v
o
l
t
a
ge rai
s
e
,
Δ
V
i
s
cal
cul
a
t
e
d f
r
om
subt
ract
i
ng t
h
e
base case
v
o
l
t
a
ge f
r
om
t
h
e t
a
r
g
et
v
o
l
t
a
ge
1.
0
p.
u. C
a
paci
t
o
r ban
k
si
ze i
s
t
h
en det
e
rm
i
n
ed by
t
h
e pr
op
ose
d
m
e
t
hod
. A t
e
st
l
o
ad-fl
ow i
s
ru
n t
o
fi
n
d
t
h
e
new
v
o
ltag
e
lev
e
l after in
stalling
th
e calcu
lated cap
acito
r
b
a
n
k
.
Th
en
in
trad
itio
n
a
l
way,
lo
ad-flow an
alysis is run
several tim
es
to find the actual capacitor ba
nk size.
T
h
e bar chart s
h
ows
the details graphical com
p
arison
bet
w
ee
n t
w
o m
e
t
h
o
d
s i
n
fi
gu
r
e
5 a
n
d
fi
g
u
re
6.
Tabl
e
1. Li
ne
Dat
a
o
f
t
h
e
4-
B
u
s Sy
st
em
Net
w
o
r
k
Lin
e
Bus to Bus
Series Im
pedance Z
Shunt
Ad
m
ittance
Y
Resistance/R in p.u.
Reactance/X in
p.
u.
Y/2 in p.u.
1-
2 0.
0100
8
0.
0504
0.
0512
5
1-
3 0.
0074
4
0.
0372
0.
0387
5
2-
4 0.
0074
4
0.
0372
0.
0387
5
3-
4 0.
0127
2
0.
0636
0.
0617
5
G4
50 M
W
30.
99
MVAR
SWI
N
G
Bir
c
h 1
Pine 3
200 M
W
123.
94 M
VAR
El
m
2
M
a
ple 4
318 M
W
80 M
W
49.
58
MVAR
170 M
W
105.
35
MVAR
G1
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Determi
n
a
tion
o
f
Vo
lume
o
f
Ca
pa
cito
r Ban
k
fo
r
S
t
a
tic VAR
Co
mp
en
sa
t
o
r (
M
d
.
Ruhu
l Amin
)
51
8
Fi
gu
re
5.
R
e
l
a
t
i
v
e com
p
ari
s
on
bet
w
ee
n t
r
adi
t
i
onal
a
n
d
p
r
op
ose
d
m
e
t
hod
f
o
r
det
e
rm
i
n
i
n
g
t
h
e ca
paci
t
o
r
b
a
nk
Fi
gu
re
6.
C
o
m
p
ari
s
on
bet
w
ee
n
desi
re
d
(1
.0
p.
u.
) a
n
d
achi
e
ved
v
o
l
t
a
ge l
e
v
e
l
by
p
r
op
ose
d
m
e
t
hod i
n
7-
b
u
s
net
w
or
k
So it has been
obs
erved that
our proposed
m
e
thod wo
rks
quite succes
sfully fo
r the four-bus system
.
The m
e
t
hod w
o
r
k
s pe
rfect
l
y
for t
h
e si
m
p
l
i
c
ity
of t
h
e net
w
or
k w
h
i
c
h co
nsi
s
t
s
of t
w
o ge
ne
r
a
t
o
r-
b
u
ses an
d onl
y
tw
o
lo
ad
-b
us
es
.
Th
e
g
e
n
e
r
a
to
r bu
s
e
s a
r
e ab
le
to me
e
t
the reactive
power dem
a
nd
of th
e lo
ad
bu
ses. So
v
o
ltag
e
lev
e
l
deterio
r
ates a little. As
v
o
ltag
e
lev
e
l d
e
teri
o
r
at
es a little fo
r t
h
e four
b
u
s
syste
m
, a m
o
re com
p
le
x
net
w
or
k
nee
d
s
t
o
be
anal
y
z
e
d
t
o
ve
ri
fy
t
h
e
va
l
i
d
i
t
y
of
ou
r
pr
op
ose
d
m
e
t
hod
o
f
c
o
m
put
at
i
on.
6.
CO
NCL
USI
O
N
To m
a
intain the syste
m
reliabilit
y it
is necessary to com
p
ensate
the reacti
v
e power a
nd t
h
ere
b
y the
selection o
f
rea
c
tor (ca
p
acito
r
or in
d
u
cto
r)
ba
nk is
req
u
ir
e
d
.
Thi
s
w
o
r
k
i
s
s
o
l
e
l
y
dev
o
t
e
d t
o
de
vel
o
p a fa
s
t
and
sim
p
l
e
al
gori
t
hm
for t
h
e c
o
m
put
at
i
on o
f
c
a
paci
t
o
r
an
d i
n
d
u
ct
o
r
ba
nk
s
i
ze fo
r st
at
i
c
VAR
c
o
m
p
ens
a
t
o
r.
I
n
traditional m
e
thod se
veral tri
a
ls and e
r
rors
are to
be
done
each
of
whic
h com
p
rise
s several iterations
whic
h
m
a
ke t
h
i
s
m
e
tho
d
c
o
m
p
l
i
cated an
d t
i
m
e cons
um
i
ng,
wh
ereas t
h
e
pr
o
p
o
se
d m
e
t
hod o
f
com
put
at
i
on
need
s
a
triv
ial co
m
p
u
t
atio
n
wh
ich
is less ti
m
e
con
s
u
m
in
g
and
si
m
p
le. It is
v
e
ry t
o
ugh
to i
m
p
l
e
m
en
t th
e ti
m
e
con
s
um
i
ng an
d
com
p
l
i
cat
ed t
r
adi
t
i
onal
m
e
t
h
od
fo
r o
n
l
i
n
e c
a
paci
t
o
r
or i
n
d
u
ct
o
r
ba
nk c
o
m
put
i
ng p
u
r
p
o
s
e.
O
n
the othe
r
hand, being ext
r
em
ely fast, the propos
ed m
e
t
hod
of c
o
m
putation has
high opportunities to be
us
e
d
fo
r
onl
i
n
e
cap
aci
t
o
r o
r
i
n
d
u
c
t
o
r
ban
k
c
o
m
put
at
i
on p
u
r
pos
e.
In ca
se
of a
d
di
t
i
on
o
f
ne
w b
u
ses
o
r
s
o
m
e
m
odi
fi
cat
i
on o
f
t
h
e sy
st
em
, the Z
bus
can be
m
odified easily using certain proce
d
ures
. In case of rea
c
tive
po
we
r c
o
m
p
ensat
i
on
of
t
w
o
o
r
m
o
re b
u
ses
a
t
a t
i
m
e
wi
t
h
t
h
e
pr
o
pose
d
m
e
t
h
o
d
of
com
put
ai
on
, t
h
e m
e
tho
d
i
s
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
Elm
Pine
Required Capacitor
Siz
e
in
p.u
Low
Voltage
Buses
Requir
e
d
Capacitor Bank
Size in
Pr
oposed
M
e
thod
Requir
e
d
Capacitor Bank
Size in
Traditional
M
e
thod
0.
9997
0.
9998
0.
9999
1
1.
0001
1.
0002
1.
0003
1.
0004
1.
0005
1.
0006
Elm
P
in
e
Voltage
Level in p.u.
Low
Voltage
Buses
Achieved
Voltage
Level in
Pr
oposed
M
e
thod
Desired
Voltage
Lev
e
l (1
.0
p.
u)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
51
2
–
51
9
51
9
t
o
be ap
pl
i
e
d o
n
t
h
e b
u
ses
on
e by
one
. A
f
t
e
r
appl
y
i
n
g
t
h
e m
e
t
hod
once i
n
o
n
e o
f
t
h
e b
u
s
es, a t
e
st
l
o
ad
-fl
o
w
i
s
to
b
e
run
to observ
e
th
e effect o
n
th
e vo
ltages. Th
ese
ne
w
vol
t
a
ge
s a
r
e t
o
be t
a
ke
n i
n
ac
cou
n
t
whi
l
e
a
p
pl
y
i
ng
t
h
e m
e
t
hod
o
n
t
h
e
ne
xt
b
u
s.
The Z
bus
o
f
a net
w
or
k d
u
ri
n
g
faul
t
s
di
f
f
ers
fr
om
t
h
e
Z
bus
in steady
state as s
ub
transient react
ance of ge
nerators
is
i
n
cluded.
For sim
p
licity, it is avoi
ded duri
ng the
de
velopm
ent of t
h
e
pr
o
pose
d
m
e
tho
d
o
f
com
put
i
o
n
.
Fu
rt
he
r
wor
k
nee
d
s
t
o
be d
one t
o
m
odi
fy
t
h
e pro
p
o
se
d m
e
t
h
o
d
of
com
putaiton by analyzing the syste
m
taking tra
n
sient
and s
u
b-tra
n
si
ent reactance
in
account.
While
d
e
v
e
l
o
p
i
n
g
th
e th
eory, th
e load
cu
rren
t
o
f
th
e circu
it is ign
o
red
,
th
is
can cau
se so
m
e
effect
o
n
th
e
d
e
sired
resul
t
.
T
h
e pr
o
pos
ed m
e
t
hod
of com
put
ai
t
o
n
i
s
a sim
p
l
e
and u
n
com
p
l
i
cat
ed m
e
t
hod
fo
r anal
y
z
i
ng t
h
e
po
we
r
flow a
n
d reacti
v
e
powe
r c
o
mpensation of c
o
m
p
licated
power system
network
ha
ving m
a
ny buses
.
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ur Ra
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BIOGRAP
HI
ES OF
AUTH
ORS
Md. Ruhul Amin has been work
ing as a
Lecturer
at th
e Dep
a
rtment of El
ectrical and
Electronic
Engineering
in
the Univ
ersity
of
Informat
ion Technolog
y & Sciences (
U
ITS), Dhaka,
Banglad
esh since Januar
y
2013
. He ho
lds a B
achel
or of Science d
e
gree in
Electrical and
Electronic Engineering with
sp
ecialization on
Power Sy
stem
s
Engineering fro
m UITS’2012,
Dhaka. He h
a
s
a number of
pap
e
rs in n
a
tion
a
l a
nd
international journals and con
f
erence in
his
area of
expert
is
e
.
His
res
earch
ar
ea addr
es
s
e
s
the
is
s
u
es
related
t
o
Elec
tri
cal P
o
w
e
r S
y
s
t
em
and
Engineering; F
A
CTS, Distribut
ed Gener
a
tion
and Control; HV
DC; Renewable Energ
y
; Smart
Grid; Power
Ele
c
troni
cs.
Rajib Bar
a
n Roy is curren
t
l
y
working as an Assistant Professor in the Ele
c
tri
c
a
l
and Elec
tronic
Engineering dep
a
rtment of the
University
of
Information Technolog
y
and Sciences (UITS),
Dhaka, B
a
ngl
ad
es
h. He h
a
s
com
p
let
e
d Ba
chelor
of S
c
ien
ce
in E
l
ectr
i
ca
l E
l
e
c
tron
ic Eng
i
ne
ering
from
Chittagong Universit
y
of Engineering and
Technolog
y
(C
UET), Chitt
ago
ng, Banglad
esh
and Master’s of
Science
in Sustain
a
ble Energ
y
S
y
stem and
Management
from Uni
v
e
r
si
ty
of
Flensburg, Ger
m
an
y
.
So far h
e
has fiv
e
pub
lica
tions in
int
e
r
n
ation
a
l jou
r
nal
s
. His resear
ch
inter
e
s
t
s
are e
l
e
c
tri
cal power s
y
s
t
em
an
al
y
s
is, reactive power
compensation, h
y
brid power
s
y
stem, and ren
e
wable en
erg
y
based distributed
power sy
stem
and applicatio
n of industrial
ele
c
troni
cs
in
po
wer s
y
s
t
em
.
Evaluation Warning : The document was created with Spire.PDF for Python.