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
7
~
21
1
I
S
SN
: 208
8-8
7
0
8
2
07
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
Improvement of Voltage Profile
through the Optimal Placement
of F
ACT
S Using L-Index Meth
od
1
K Ve
nk
ata
Ram
a
na Re
dd
y,
2
M Padma
L
a
litha
,
3
PB Ch
ennai
a
h
Department o
f
EEE, Annamachar
y
a
In
stitute
of Technolog
y
and
Scien
ces
Rajampet, Andh
rapradesh
(st), In
dia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 13, 2013
Rev
i
sed
Feb
27
, 20
14
Accepted
Mar 10, 2014
In this paper an IEEE stand
a
rd te
st sy
st
em
is considered and i
t
is tested usin
g
Newton-Raphson method with the help of
MATLAB. The voltag
e
magnitudes of each bus are
examined
and the
corresponding
weak bus is
incorpora
t
ed wit
h
F
A
CTS
s
u
ch as
S
V
C and TCSC. The op
tim
al p
l
ac
em
ent of
FACTS can be identified using
L-Index
method. The valu
e of L-
index which
approach un
ity
implies that
it r
each
es
to instab
ility
.
From
this instability
point the s
y
s
t
e
m
stabilit
y is im
proved during stead
y
st
at
e
and Fault
conditions
. Th
e
dis
t
urbanc
e is
c
r
eat
ed in
the s
y
s
t
em
b
y
changing
the
Load
Reac
tive
P
o
wer
at
a p
a
rti
c
ula
r
B
u
s
.
Keyword:
Fau
lt cond
itio
n
MATLAB
Stead
y State C
o
nd
itio
n
SVC
TCSC
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
Padm
a Lal
i
t
ha,
Pro
f
ess
o
r
a
n
d
HO
D,
De
parte
m
ent of
El
ectrical and Electronics E
ngi
neeri
n
g,
Ann
a
m
ach
arya In
stitu
te of Tech
no
log
y
an
d
Scien
ces, Raj
a
m
p
et, An
dhraprad
e
sh
(st), India
JNT
U
, Ananta
pur
Em
a
il: p
a
d
m
a
l
alith
a_
m
a
red
dy@yah
o
o
.
co
.i
n
1.
INTRODUCTION
As a res
u
l
t
o
f
eve
r-i
nc
reasi
ng
dem
a
nd o
f
el
ect
ri
c po
wer
,
t
h
e el
ect
ri
ci
t
y
suppl
y
i
n
d
u
st
ry
i
s
un
de
rg
oi
n
g
pr
of
o
u
n
d
t
r
a
n
sf
o
r
m
a
ti
on w
o
rl
d
w
i
d
e.
Thi
s
m
a
kes t
h
e e
x
i
s
t
i
n
g p
o
w
er t
r
a
n
s
m
i
ssi
on sy
st
em
hi
ghl
y
com
p
lex. T
o
meet the incre
a
sing
dem
a
n
d
o
f
electricity in
a power syste
m
it is esse
n
tial to
in
crease th
e
tran
sm
it
ted
power eith
er b
y
i
n
stallin
g
n
e
w t
r
an
sm
issio
n
lines or
b
y
im
p
r
ov
ing
th
e ex
istin
g tran
sm
issio
n
lin
es
by
addi
ng ne
w
devi
ces. I
n
st
a
l
l
a
t
i
on of ne
w t
r
ansm
i
ssi
on l
i
nes i
n
a po
wer
sy
st
em
l
eads to t
h
e t
echn
o
l
o
gi
cal
co
m
p
lex
ities su
ch as econ
o
m
ic and
en
v
i
ronmen
tal co
n
s
i
d
eratio
n
s
th
at i
n
clu
d
e
s co
st,
d
e
lay in
co
n
s
t
r
u
c
t
i
o
n
as
so o
n
. Fl
e
x
i
b
l
e
al
t
e
rnat
i
ng
cur
r
ent
t
r
a
n
sm
i
ssi
on sy
st
em
(FAC
T
S
) t
e
c
h
n
o
l
o
gy
ga
ve
up
new
way
s
fo
r
co
n
t
ro
lling
power
flows and
enh
a
n
c
ing
th
e u
s
ab
le
capacity o
f
tran
smissio
n
lin
es. FACTS are syste
m
com
p
ri
sed
of
st
at
i
c
equi
pm
ent
use
d
fo
r t
h
e AC
t
r
a
n
sm
is
sion
of electrical energy.
It is
m
ean
t to
enh
a
nce
co
n
t
ro
llab
ility an
d in
creasing
th
e power transfer
cap
ab
ility o
f
th
e
po
wer syste
m
n
e
two
r
k.
The c
once
p
t
o
f
F
A
C
T
S
was
fi
rst
de
fi
ne
d
by
N.
G.
Hi
ng
ora
n
i
i
n
1
9
8
8
.
It
us
ual
l
y
ref
e
rs t
o
t
h
e
appl
i
cat
i
o
n o
f
hi
g
h
po
wer
se
m
i
cond
uct
o
r
d
e
vi
ces t
o
c
o
nt
r
o
l
di
f
f
ere
n
t
par
a
m
e
t
e
rs and
el
ect
ri
cal
vari
abl
e
s suc
h
as voltage, im
p
e
dance
,
a
n
d phase angle, c
u
rrent, active
and
reactive
powe
r.
Thi
s
pape
r a
d
d
r
esses t
h
e st
at
i
c
m
odel
i
ng
of
St
at
i
c
Var C
o
m
p
ensat
o
r
(S
V
C
) an
d
Thy
r
i
s
t
o
r
C
o
nt
r
o
l
l
e
d
Series C
o
m
p
en
sato
r
(TCSC
)
,
an
d th
eir cap
abilit
ies to
im
p
r
ov
e th
e vo
ltag
e
p
r
o
f
ile
b
y
using
MATLAB
co
d
e
.
2.
L- IN
DE
X
In
orde
r
t
o
prevent
the occ
u
rrence
of vol
t
age
c
o
llap
s
e, it is essen
tial to
accu
r
ately pred
ict t
h
e
o
p
e
rating
co
nditio
n
of a
po
wer system
. Kessel et al. d
e
v
e
lop
e
d a
v
o
ltag
e
stab
ility in
d
e
x
based
o
n
th
e
so
l
u
tion
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
7 – 2
1
1
20
8
o
f
th
e
po
wer fl
o
w
equ
a
tio
n. Th
e L-i
n
d
e
x
is a q
u
a
n
titativ
e
measu
r
e
for th
e
esti
m
a
t
i
o
n
of th
e d
i
stance of
actu
a
l
state o
f
t
h
e syste
m
stab
ilit
y li
mit.
Th
e L- i
n
d
e
x
d
e
scri
b
e
s t
h
e stab
ility o
f
th
e
co
m
p
lete syste
m
. A lo
ad flow
resu
lt is
ob
tain
ed
fo
r
a
gi
ve
n sy
st
em
ope
rat
i
n
g c
o
n
d
i
t
i
on w
h
i
c
h
i
s
ot
he
rwi
s
e a
v
ai
l
a
bl
e fr
om
t
h
e out
put
of
an
o
n
l
i
n
e est
i
m
at
or. T
h
e
load
flow al
gorith
m
incorpora
t
es
load cha
r
ac
teristics and ge
ne
rat
o
r c
o
ntrol cha
r
acteristics.
For a
n
n-
bu
s p
o
we
r sy
st
em
, buses ca
n be se
parat
e
d i
n
t
o
t
w
o g
r
o
u
p
s:
B
r
i
n
g al
l
l
o
ad b
u
se
s t
o
t
h
e he
a
d
an
d d
e
no
te th
em
as
α
L an
d
p
u
t
t
h
e PV
bu
ses th
e tail and
term
th
e
m
as
α
G i.e.
,
α
L
=
{
1,
2,…
,
n
L} a
n
d
α
G
={ nL+
1
,
nL+
2
,…
…n
-
1
,
n}
Whe
r
e,
n
L
is th
e
nu
mb
er of lo
ad
bu
ses.
The
fol
l
o
wi
n
g
hy
b
r
i
d
sy
st
em
equat
i
o
n i
s
t
h
e
n
obt
ai
ne
d:
G
L
GG
LG
GL
LL
G
L
V
I
Y
F
K
Z
I
V
(1
)
Whe
r
e,
ZLL, FLG, KGL,
and YGG
are s
u
b-bloc
k
of m
a
trix
H;
VG, I
G
,
VL,
I
L
are
voltage a
n
d
curre
nt
vect
or of PV
buses
and loa
d
buses
.
Vo
ltag
e
stab
ility in
d
e
x
Lj
for
any
l
o
a
d
bu
s c
a
n
be
defi
ned
a
s
gi
ven
bel
o
w
.
g
i
Vj
Vi
Fji
Lj
1
1
(2
)
3.
STA
T
IC VAR C
O
M
P
EN
SATOR
SVC can
be define
d as a shunt connecte
d
static var
gene
ra
t
o
r o
r
abs
o
r
b
e
r
wh
ose o
u
t
p
ut
i
s
adj
u
st
e
d
to
ex
ch
an
g
e
cap
acitiv
e or indu
ctiv
e cu
rren
t
so
as t
o
m
a
in
t
a
in
or co
n
t
ro
l
sp
ecific
p
a
ram
e
ters of th
e electrical
p
o
wer system
(typ
ically b
u
s
vo
ltag
e
).
SVCs are
primarily u
s
ed
in
po
wer system
s f
o
r
v
o
ltag
e
con
t
ro
l or for im
p
r
o
v
i
n
g
system
s
t
ab
ility. Th
e
adva
nce
d
m
odel
s
depa
rt
fr
o
m
t
h
e con
v
ent
i
onal
ge
ne
rat
o
r-t
y
pe
rep
r
ese
n
t
a
t
i
on
of t
h
e
SVC
an
d ar
e
based
in
stead
on
th
e v
a
riab
le sh
un
t su
scep
tance concept.
In the la
tter case, the SVC state
variables are combi
n
e
d
wi
t
h
t
h
e
no
dal
v
o
l
t
a
ge m
a
gn
i
t
udes a
n
d a
n
g
l
es of
t
h
e
n
e
twork in a si
ng
le fram
e o
f
referen
ce
for
un
ified,
i
t
e
rat
i
v
e sol
u
t
i
ons
u
s
i
n
g t
h
e
Newt
on
–R
a
p
h
s
on
m
e
t
hod.
In
practice the SVC can
be seen as
an
ad
ju
stab
le reactan
ce with
ei
th
er firi
n
g
-an
g
le li
mits o
r
reactance lim
its.
Th
e eq
u
i
v
a
lent circu
it is u
s
ed
to
d
e
ri
v
e
t
h
e SVC non
lin
ear
po
wer equ
a
tio
ns and
the lin
earised
equat
i
o
ns
re
qui
red
by
Ne
wt
o
n
’
s m
e
t
hod.
Fi
gu
re
1.
Va
ri
abl
e
s
h
u
n
t
s
u
sce
p
t
a
nce m
odel
The l
i
n
ea
ri
sed
equat
i
o
n i
s
gi
v
e
n
by
,
SVC
SVC
k
k
k
B
B
Q
Q
P
k
0
0
0
(3
)
At th
e end
o
f
iteratio
n (i), th
e
v
a
riab
le shun
t
su
scep
tan
ce B
SV
C
is u
p
d
a
ted as fo
llo
ws,
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Imp
r
o
vemen
t
of Vo
ltag
e
Pro
file th
roug
h th
e
Op
tima
l
Pl
a
c
emen
t
o
f
FAC
TS
… (M Pa
dma
La
lith
a
)
20
9
1
)
(
1
i
SVC
i
SV
C
SVC
i
SV
C
i
SVC
B
B
B
B
B
(4
)
4.
THYRISTOR CONTROLL
ED
SE
RIES COMPENSATOR
A TCSC can
be d
e
fin
e
d
as a
cap
acitiv
e reactan
ce co
m
p
en
sato
r
wh
ich
consists o
f
a series cap
acitor
b
a
nk
shu
n
t
ed
b
y
a th
yristor-co
n
t
ro
lled
reacto
r in ord
e
r t
o
p
r
o
v
i
d
e
a sm
o
o
t
h
l
y v
a
riab
le series capacitiv
e
reactance. T
h
e basic c
once
p
tual TC
SC module com
p
ris
e
s a series capacitor,
C
, in
p
a
rallel with
a th
yristo
r-
co
n
t
ro
lled reacto
r, L
S
, as show
n in
Figu
r
e
2.
Fig
u
re 2
.
Th
y
r
isto
r-con
t
ro
lled
series
co
m
p
en
sato
r
The TC
SC
p
o
w
er fl
ow m
o
d
e
l
present
e
d i
n
t
h
i
s
sect
i
on i
s
based
on t
h
e s
i
m
p
l
e
concept
of a va
ri
abl
e
series reactanc
e
, the value
of
whic
h is
adjust
ed autom
a
tically to constrain
t
h
e powe
r flow
acros
s the bra
n
ch to
a specifie
d
value.
The
am
ount of
reactance
is determ
ined e
fficiently usi
n
g
Newt
on’s m
e
thod.
The
cha
ngi
ng
reactance X
TCSC
repre
s
ent
s
t
h
e equi
val
e
nt
re
act
ance o
f
al
l
t
h
e seri
es
-co
n
n
ect
ed m
odul
es
m
a
ki
ng
up
t
h
e
TC
SC
,
wh
en
op
erating
in eith
er th
e i
n
du
ctiv
e
or th
e cap
acitiv
e
reg
i
o
n
s
.
The tra
n
s
f
er admittance m
a
trix
of the
varia
b
l
e
seri
es c
o
m
p
ensat
o
r i
s
gi
ve
n
by
m
k
mm
km
mk
kk
m
k
V
V
jB
jB
jB
jB
I
I
(5
)
Fo
r th
e
p
o
wer
eq
u
a
tion
s
at
bu
s m
,
th
e sub
s
crip
ts k
and m are exc
h
a
n
ge
d and t
h
e active and reactive
powe
r
equat
i
o
ns
at
b
u
s
k
are
)
cos(
)
sin(
2
m
k
km
m
k
kk
k
k
m
k
km
m
k
k
B
V
V
B
V
Q
B
V
V
P
(6
)
5.
RESULTS
A
N
D
DI
SC
US
S
I
ON
Fig
u
r
e
3
.
IEEE 5 – bu
s test syste
m
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
7 – 2
1
1
21
0
A M
A
TL
AB
code
fo
r b
o
t
h
t
echni
que
s was
devel
o
pe
d f
o
r
t
h
e val
i
d
at
i
o
n
of t
h
e p
r
o
p
o
s
e
d FAC
T
S
,
and it is tested on IEEE
5-Bus test system
and the
foll
owi
ng
observa
tions were m
a
de by
using Newton-
Rap
h
s
on
m
e
th
o
d
und
er no
rm
al an
d tran
sien
t
con
d
ition
s
.
5.
1.
Ste
a
d
y
S
t
ate
C
o
ndi
ti
on
After
r
u
nni
ng the
powe
r fl
ow
by
using Ne
w
t
on-
Raphs
o
n m
e
thod on
a
n
IEEE standar
d
test
system
(5
-bu
s
), a
weak
bu
s is id
en
tified
.
Und
e
r
no
rmal co
n
d
itio
n
with
SVC it is foun
d
t
h
at
th
e v
o
ltag
e
profile
at
b
u
s
5 where SVC i
s
connecte
d
is im
proved. Initially unde
r
norm
al condition
without S
V
C the voltage m
a
gnitude
i
n
pe
r u
n
i
t
(
p
u
)
at
bus
5 i
s
0.
9
7
7
6
, a
n
d t
h
e L
-
i
n
dex
of
co
rre
spo
n
d
i
n
g
bus
5
i
s
0.
03
2
8
,
but
aft
e
r
pl
aci
ng
SVC
,
vol
t
a
ge m
a
gni
t
ude i
m
pro
v
ed
t
o
1.
0
00
pu a
n
d t
h
e L-i
nde
x
of c
o
r
r
es
po
n
d
i
ng
bu
s 5 i
s
0.
00
9
9
. Si
m
i
l
a
rly
aft
e
r
pl
aci
ng TC
SC
,
t
h
e vol
t
a
ge
pr
ofi
l
e
at
bus
5 i
s
al
so im
pro
v
e
d
t
o
0
.
9
7
89
p
u
as sho
w
n i
n
t
a
bl
e-
1. The L
-
i
nde
x
val
u
e
o
f
eac
h l
o
ad
b
u
s
i
s
pe
rf
orm
e
d as s
h
ow
n i
n
t
a
bl
e
2.
Tab
l
e 1
.
Steady
State
Co
nd
itio
n
Bus
no
Volt
age
m
agnit
ude
w
i
tho
u
t
SVC (
O
R
)
TCSC
Volt
age
m
agnit
ude
w
i
th S
V
C
Volt
age
m
agnit
ude
wi
t
h
TC
S
C
1
1.
0600
1.
0600
1.
0600
2
1.
0000
1.
0000
1.
0000
3
0.
9925
0.
9956
0.
9966
4
0.
9894
0.
9934
0.
9924
5
0.
9776
1.
0000
0.
9789
6
0.
9784
Tabl
e 2.
L
-
I
n
di
ces
Bus
no
L-index
Witho
u
t
SVC (or
)
TCSC
L-index
With
SVC
L-index
With
TCSC
3
0.
0299
0.
0262
0.
0296
4
0.
0304
0.
0267
0.
0324
5
0.
0328
0.
0099
0.
0234
6
-
-
-
-
-
-
-
-
-
-
-
--
0.
0536
5.
2. Fa
ul
t Co
n
d
i
t
i
o
n
Tabl
e 3. U
nde
r
Faul
t
c
o
n
d
i
t
i
o
n
Bus
no
Volt
age
m
agnit
ude
w
i
tho
u
t SVC
(
O
R
)
TCSC
Volt
age
m
agnit
ude
w
i
th S
V
C
Volt
age
m
agnit
ude w
i
t
h
TCSC
1
1.
0600
1.
0600
1.
0600
2
1.
0000
1.
0000
1.
0000
3
0.
9899
0.
9967
0.
9900
4
0.
9860
0.
9948
0.
9856
5
0.
9639
1.
0000
0.
9641
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0.
9631
The
n
by
cha
n
gi
n
g
r
eact
i
v
e
po
we
r at
b
u
s
5, i
.
e
.
f
r
o
m
Q= 0.
0
5
t
o
Q
=
0
.
2
M
V
AR
,
a
wea
k
bus
i
s
id
en
tified
as bu
s
5
and
it is in
corp
orated
b
y
SVC an
d TC
SC in
or
d
e
r
to im
p
r
o
v
e
th
e vo
l
t
ag
e pr
of
ile as
sh
own
in
tab
l
e
3
.
The L
-
index
of each loa
d
bus
was pe
rform
e
d with
and wit
h
out SVC as we
ll as TCSC under tra
n
sie
n
t
co
nd
itio
n as sho
w
n
i
n
tab
l
e
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Imp
r
o
vemen
t
of Vo
ltag
e
Pro
file th
roug
h th
e
Op
tima
l
Pl
a
c
emen
t
o
f
FAC
TS
… (M Pa
dma
La
lith
a
)
21
1
Tabl
e 4.
L
-
I
n
di
ces
Bus
no
L-index
Witho
u
t
SVC (or
)
TCSC
L-index
With
SVC
L-index
With
TCSC
3
0.
0326
0.
0255
0.
0365
4
0.
0338
0.
0247
0.
0396
5
0.
0475
0.
0099
0.
0391
6
-
-
-
-
-
-
-
--
0.
0702
6.
CO
NCL
USI
O
N
Thi
s
pa
per
de
pi
ct
s t
h
at
t
h
e im
prove
d
vo
l
t
a
ge pr
ofi
l
e
of t
h
e
p
o
we
r
sy
st
em
under
No
rm
al
and
Transien
t co
nd
itio
n
s
with t
h
e inco
r
por
atio
n of
Static VA
R co
m
p
en
sa
to
r (
S
V
C
) an
d Th
yr
isto
r Con
t
ro
lled
Series Co
m
p
ensato
r
(TCSC).
SVC an
d
TCSC were ab
le to regu
late th
e
bu
s
v
o
ltag
e
m
a
g
n
itud
e
at
wh
i
c
h
it is
connected ove
r
its full
range
of
ope
ra
tio
n when
th
ere is a need
.
Th
e op
tim
a
l
lo
catio
n is iden
tified
b
y
u
s
in
g L-
in
d
e
x
m
e
th
o
d
.
Th
is can also
b
e
p
e
rfo
rm
ed
b
y
using
Fast
d
ecoup
led m
e
t
h
od
t
o
an
alyse
th
e Tran
sien
t stab
ilit
y
due
t
o
c
h
a
nge
i
n
real
p
o
w
er.
REFERE
NC
ES
[1]
Kiran Kumar Kuthadi. “Enhancement of Voltage Stabilit
y
thr
ough Optimal Placement of Facts Controllers
in
Powe
r S
y
ste
m
s”.
American
Journal of Susta
inable Cities and
Society
. 2012
; 1(1)
.
[2]
NG Hingorani.
“
Power ele
c
tron
ics in
ele
c
tri
c
al
util
iti
es: role
of power electr
onics in
future
power systems
”.
Proceedings of
t
h
e IE
EE
. 1988;
76(4): 481-482
.
[3]
GW
Stagg, and
AH El-Abiad
. “
C
om
puter Meth
ods in Power S
y
stem
Anal
y
s
is”.
McGraw-Hill.
1
968
[4]
I Kuma
rs
wa
my
a
nd P Ra
ma
na
re
ddy
.
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ly
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ge
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b
ility
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thod”
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2011.
ECO Se
rvic
e
s
Interna
tiona
l.
[5]
Enrique Acha. “
F
ACTS modeling a
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University
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[6]
SB Bhaladhare, P.P. Bedeka
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l Journal of Electron
i
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eer
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cation of
SVC. 2277-1956: I
SSN-2277-1956/
V2N2-671-677.
[7]
SB Bhaladhare,
PP Bedekar, B.
Bhalad
h
a
re et al. “Enhancement
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Stability
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SVC”
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IJECS
E
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ISSN: 2277-1956/V2N2671-677. Volume2, Number 2S.
[8]
Mohammed Osman Hassan,
SJ Cheng, Zakari
a Anwar Zakaria.
“
Steady-Sta
te
Modeling of S
V
C and TCSC for
Power Flow Analysis
”. Proce
e
d
i
ngs of the Internation
a
l Multi
Confer
enc
e
of Engineers and Com
puter Scientist
s
2009, Hong Kon
g
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S 2009, Mar
c
h 1
8
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Evaluation Warning : The document was created with Spire.PDF for Python.