Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 1
,
Febr
u
a
r
y
201
5,
pp
. 1
~
1
2
I
S
SN
: 208
8-8
7
0
8
1
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
Fault Location Effect on Short-C
ircuit Calculations of a TCVR
Compen
sat
e
d Li
ne in Al
geri
a
M
o
hamed
Z
e
lla
g
u
i
*
, Heba
A
h
med
Ha
ssan**
, A
b
dela
ziz
C
h
ag
hi*
* LSTE Laborator
y
,
Dep
a
rtment
of El
ectr
i
c
a
l
Eng
i
neer
ing,
F
acul
t
y
of T
echno
log
y
,
Univers
i
t
y
of
Ba
tna,
Alger
i
a
** Departmen
t
o
f
Electr
i
cal
and
Computer Engin
eering
,
Co
lleg
e
of Engin
eerin
g,
Dhofar Univers
i
t
y
,
S
u
lt
anat
e of
O
m
an
& E
l
ec
tri
cal
P
o
wer and
M
achin
es
Departm
e
n
t
,
F
acult
y
of
Engin
eering
,
C
a
iro Un
ivers
i
t
y
,
Eg
yp
t
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 8, 2014
R
e
vi
sed Dec 2,
2
0
1
4
Accepted Dec 26, 2014
This
res
earch w
o
rk inves
tiga
t
ed
the e
ffect of fault location on short-cir
c
uit
cal
cula
tions
for
a high vo
lt
age
trans
m
ission line equipp
ed with a nov
el
FACTS device, namely
Th
y
r
is
tor Cont
rolled
Voltage Regulator (TCVR).
This m
a
in fun
c
ti
on of th
is devi
ce
was
to
control the voltage and
activ
e power
of
the line. The paper considered
a
st
ud
y
case for
a 220 kV tr
ansmission line,
in the Alger
i
an transmission power netw
ork, which was subjected to a phas
e
to earth fau
lt in
the pres
enc
e
of a fixed faul
t res
i
s
t
ance
. The pap
e
r pres
ented
theore
tic
al an
al
ys
is
of the s
hort-circu
it c
a
lcu
l
a
tio
ns which was confirm
e
d
b
y
the il
lustra
ted si
m
u
lation resul
t
s.
Sim
u
lation resu
lts showed the i
m
p
act of the
fault lo
cation on
the s
y
mmetrical current
and vo
ltage components
of the lin
e,
and trans
m
is
s
i
on line ph
as
e curr
e
n
ts
and
voltages; before using TC
VR and in
the presen
ce of
TCVR for both cas
es of positive and n
e
ga
tive TCVR
controlled vo
ltag
e
.
Keyword:
Fau
lt Lo
catio
n
Ph
ase to
Earth
Fau
lt
Power System
s
Sho
r
t-Circu
it Calcu
l
atio
n
s
T
C
V
R
FA
CT
S D
e
v
i
ce
Copyright ©
201
5 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
:
Dr.
M
o
ham
e
d Zel
l
a
gui
,
D
e
p
a
r
t
m
e
n
t
o
f
Electr
i
cal En
g
i
n
eer
i
n
g, Facu
lty o
f
Techno
logy, Un
iv
er
sity of
Batn
a,
C
a
m
pus C
U
B
,
St
reet
M
e
d
El
Hadi
B
o
uk
hl
o
u
f
,
0
5
0
0
0
, B
a
t
n
a, Al
geri
a.
Em
a
il: m
.
ze
lla
g
u
i
@un
i
v-b
a
t
n
a.d
z
1.
INTRODUCTION
Sho
r
t-ci
rcu
it calcu
latio
n
s
in
po
wer syste
m
s ar
e im
p
o
rta
n
t. These
calculations
enable
powe
r
engi
neers t
o
determine the ra
tings
of electrical equipm
ent whic
h can
w
ithstand the
r
m
a
l and electrom
a
gnetic
effects of the s
h
ort-circ
uit
cu
rren
t. Th
ey sign
ifican
tly h
e
lp to
d
e
term
in
e t
h
e settin
g
s
and co
ord
i
n
a
tion
o
f
t
h
e
protection equi
pm
ent in the s
y
ste
m
acco
rding to well esta
blished
national an
d inte
rnational standards
s
u
ch as
IEC a
n
d ANS
I
/IEEE
[1].
The sel
ect
i
o
n
of a ci
rcui
t
bre
a
ker
f
o
r a
p
o
w
e
r sy
st
em
depends
,
not
onl
y
u
p
o
n
t
h
e cu
rre
nt
t
i
e
brea
ker
i
s
t
o
carry
u
n
d
er
no
rm
al
operat
i
ng c
o
ndi
t
i
ons
, b
u
t
al
so
up
o
n
t
h
e m
a
xi
m
u
m
curre
nt
i
t
m
a
y
have t
o
carr
y
m
o
men
t
arily an
d th
e cu
rren
t it
m
a
y h
a
v
e
t
o
in
terru
p
t
at
t
h
e
v
o
ltag
e
of
th
e lin
e in which
it is p
l
aced
.
Th
e
current
whic
h
a brea
ker m
u
st interrupt
is
us
ually asymmetrical since it sti
ll contains s
o
me of t
h
e decayi
ng
DC
com
pone
nt
s [
2
]
.
Thi
s
cu
rre
nt
i
s
pr
ope
rl
y
cal
l
e
d t
h
e rat
e
d
sym
m
et
ri
cal
sho
r
t
-
ci
rc
ui
t
cu
rre
nt
o
r
t
h
e
re
qui
red
symm
e
t
rical interrupting capa
b
ility. It is necessary to de
te
rmine the likely
fault curre
n
ts in a syste
m
unde
r
v
a
ri
o
u
s
fau
lt co
nd
itio
ns
b
e
fore selectin
g pro
p
e
r
p
r
o
t
ec
tion
d
e
v
i
ces. Dep
e
nd
ing
up
on
th
e co
m
p
lex
ity o
f
th
e
syste
m
, the calculations
could also
be t
o
o m
u
ch involve
d
.
Accu
rat
e
fa
ul
t
cur
r
ent
cal
cul
a
t
i
ons are
n
o
r
m
al
ly
carri
ed
out
usi
n
g sy
m
m
e
t
r
i
cal
co
m
pone
nt
s as a
n
anal
y
t
i
cal
t
echni
q
u
e
used
by
desi
g
n
e
n
gi
ne
ers a
nd
p
r
act
i
c
i
ng
pr
ot
ect
i
o
n e
ngi
neers
[
3
]
.
It
i
s
base
d
on
t
h
e
p
r
i
n
cip
l
e th
at an
y un
b
a
lan
c
ed set o
f
v
ectors
can
b
e
re
p
r
esen
ted
b
y
a set of th
ree
b
a
lan
c
ed
qu
an
tities, na
m
e
l
y
direct, i
nve
rse
and zero se
que
n
ce.
In
literatu
re, man
y
researchers h
a
v
e
focu
sed
on
th
e i
m
p
act o
f
fau
lt con
d
ition
s
on
power system
s
su
ch
as t
h
e erro
r i
n
estim
ated
fau
lt
d
i
stan
ce
in
case
o
f
gro
u
n
d
fau
lts [4
], fau
lt lo
cation
in d
i
stribu
tion
sy
ste
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 1, Feb
r
uar
y
20
1
5
:
1 – 12
2
[5]
,
fa
ul
t
l
o
cat
i
on f
o
r t
r
a
n
sm
i
ssi
on sy
st
em
usi
n
g spa
r
se
m
easurem
ent
m
e
t
hod [
6
]
,
fa
ul
t
l
o
cat
i
on f
o
r hy
b
r
i
d
t
r
ansm
i
ssi
on l
i
n
es [
7
]
,
di
st
an
ce pr
ot
ect
i
on
per
f
o
r
m
a
nce [8]
,
ada
p
t
i
v
e di
gi
t
a
l
di
st
ance
rel
a
y
i
ng sc
he
m
e
for
d
oub
le tran
smissio
n
lin
e [9], ad
ap
tiv
e d
i
g
ital relayin
g
sch
e
m
e
to
t
ack
le fu
se
re-clo
sure and
lack
of
co
ord
i
n
a
tion
i
n
case o
f
Dist
ribu
ted
Gen
e
ratio
n
(DG)
[1
0
]
, ad
ap
tiv
e reach
setting
s
o
f
d
i
stan
ce relay o
n
a
t
r
ansm
i
ssi
on l
i
n
e i
n
p
r
ese
n
ce
of
UP
FC
[
1
1]
,
and
b
u
s
-
ba
r
pr
ot
ect
i
on
[
12]
.
I
n
[1
3
]
, a
study o
f
t
h
e im
p
act
o
f
DG
o
n
ov
er
cur
r
e
n
t
pro
t
ectio
n
h
a
s
b
een
i
n
v
e
stig
ated
u
s
i
n
g a typ
i
cal
UK
ru
ral
di
st
ri
but
i
o
n
net
w
or
k
whi
l
e
co
nsi
d
e
r
i
n
g rel
e
va
nt
factors for fa
ult current in
cluding
arc fault. A
fa
ult
l
o
cat
i
on ap
pr
o
ach has bee
n
p
r
o
p
o
sed
f
o
r
t
h
e
di
st
ri
b
u
t
i
o
n ne
t
w
o
r
k
i
n
c
o
r
p
o
r
at
i
ng DG
s
[
1
4]
.
The im
pact of fault resistance
on the m
easured
im
peda
nce by distance rel
a
y in the prese
n
ce TCSC
has bee
n
i
n
ve
st
i
g
at
ed [
15]
,
t
h
e im
pact
of faul
t
re
sistanc
e
on zero-sequence c
u
rren
t an
d
fau
lt co
m
p
on
en
t
reactance rela
ys
has bee
n
st
udie
d
[16]
, a
n
d the
effect of fa
ult condition
on pe
rform
a
nce
of distanc
e
relay
protection in t
h
e presence
seri
es FACT
S
de
vice
on
t
r
a
n
sm
i
s
si
on
l
i
n
e
has
b
een a
d
d
r
esse
d
[1
7]
.
In
t
h
e l
i
g
ht
of
t
h
e
rapi
d
dev
e
l
opm
ent
of
F
l
exi
b
l
e
AC
Tr
ansm
i
ssi
on Sy
st
em
s (FAC
T
S
)
devi
ces
as
wel
l
as t
h
ei
r num
ero
u
s ad
v
a
nt
ages i
n
p
o
w
er sy
st
em
s cont
rol
,
faul
t
c
a
l
c
ul
at
i
ons s
h
oul
d be c
o
nsi
d
ere
d
t
o
include t
h
e presence
of thes
e devices in t
h
e system
. In a
m
e
shed power netw
or
k
and
und
er
steady state
co
nd
itio
ns, FACTS d
e
v
i
ces allo
w tran
sm
issi
o
n
lin
es to
op
er
ate clo
s
e to
their th
erm
a
l li
mits an
d
to
reduce th
e
l
o
o
p
fl
o
w
s by
pro
v
i
d
i
ng
or
abs
o
r
b
i
n
g reac
t
i
v
e po
wer, i
n
creasi
n
g or r
e
duci
ng
vol
t
a
ge
and co
nt
r
o
l
seri
es
im
pedance
o
r
pha
se-a
ngl
e.
One
of t
h
e rec
e
nt
FAC
T
S de
vi
ces i
s
t
h
e Th
y
r
i
s
t
o
r C
o
nt
r
o
l
l
ed V
o
l
t
a
ge R
e
gul
at
o
r
(
T
C
V
R
)
w
h
i
c
h i
s
depl
oyed i
n
thi
s
resea
r
ch work. T
h
e
r
efore
,
t
h
is res
earc
h
wo
rk
con
t
ribu
tes to
th
e inv
e
stigatio
n
o
f
th
e
phase to
earth
fau
lt calcu
latio
n
s
wh
ile
u
s
ing
TC
VR
dev
i
ce wh
ich
aim
s
to
con
t
ro
l th
e
v
o
ltag
e
and active power
of t
h
e
lin
e th
ro
ugh
a
TCVR con
t
ro
ller vo
ltag
e
,
d
e
no
ted
b
y
V
TCVR
. This pa
pe
r ana
l
yses the effect
of t
h
e fa
ult loc
a
tion,
for either
10 kV inc
r
em
en
t
or -
10
k
V
de
cre
m
ent
of
V
TCVR
v
o
ltag
e
,
o
n
t
h
e sy
mm
e
t
rical c
u
rren
t an
d vo
ltage
com
pone
nt
s a
s
wel
l
as t
h
e
l
i
n
e ph
ase cu
r
r
ent
s
a
n
d
v
o
l
t
a
ges, i
n
case
of a
p
h
ase
A
to
earth
fau
lt for a
t
r
ansm
i
ssi
on l
i
n
e com
p
ensat
e
d by
TC
VR
i
n
22
0
kV
Al
ge
ri
an net
w
o
r
k
.
T
C
VR
de
vi
ce i
s
l
o
cat
ed at
t
h
e m
i
d of
th
e lin
e,
b
e
tween
Batn
a and
Bisk
ra
22
0
/
6
0
kV su
bstatio
ns in the
prese
n
ce of a
fixe
d fault resistance
. The
p
a
p
e
r
p
r
esen
ts
th
e th
eo
retical
an
alysis wh
ich is d
e
riv
e
d
an
d v
e
ri
fied
b
y
si
m
u
la
tio
n
resu
lt
s in
th
e absen
c
e and
prese
n
ce
of TC
VR.
2.
TCVR CONT
ROLLED
VOLTAGE
The
rapi
d s
p
e
e
d o
f
F
A
C
T
S
devi
ces
o
ffe
r
s
seve
ral
be
ne
fi
t
s
t
o
sy
st
em
ope
rat
i
o
n a
n
d co
nt
r
o
l
i
n
d
y
n
a
m
i
c stab
ility stu
d
i
es.
In
ad
d
ition
,
FACTS
d
e
v
i
ces h
a
v
e
b
e
n
e
fits
in case
of sho
r
t
-
circu
its b
y
limit
in
g
th
e
sho
r
t
-
ci
rc
ui
t
cur
r
ent
[
18]
. A
not
her ad
va
nt
a
g
e of F
A
C
T
S
devi
ces i
s
gi
vi
n
g
t
h
e o
p
p
o
r
t
u
ni
t
y
t
o
ext
e
nd t
h
e
cu
rren
t t
r
an
sm
issio
n
lin
e limits in
a step-by-step
m
a
n
n
e
r with
an
i
n
cremen
tal in
v
e
st
men
t
wh
en
req
u
i
red.
Fu
rt
h
e
rm
o
r
e,
FACTS con
t
rollers o
f
fer th
e
p
o
s
sib
ility to
m
o
v
e
an
in
stallatio
n
wh
en
it
b
eco
m
e
s n
o
t
u
s
eful
any
m
ore. Di
f
f
e
rent
t
y
pes
of
devi
ces
ha
ve
been
de
vel
o
pe
d an
d t
h
ere a
r
e vari
ous
way
s
t
o
cl
assi
fy
t
h
em
i
n
term
s o
f
th
e tech
no
log
y
of the u
s
ed
sem
i
co
n
d
u
c
tor, th
e
po
ssib
l
e
b
e
n
e
fits o
f
th
e con
t
rollers, and
th
e typ
e
of
co
m
p
en
satio
n an
d
conn
ection.
Fi
gu
re 1 s
h
o
w
s
t
h
e act
i
v
e pow
er fl
o
w
eq
uat
i
o
n bet
w
ee
n t
w
o bus
es 1 an
d 2
and t
h
e
vari
a
b
l
e
s t
h
at
can
be m
odified by
each
FACT
S
device
[19].
Fi
gu
re
1.
Ef
fec
t
s of
F
A
C
T
S
d
e
vi
ces
on
act
i
v
e p
o
we
r e
q
uat
i
o
n
V
1
and
V
2
a
r
e
t
h
e v
o
l
t
a
ge
m
a
gni
t
u
des
o
f
bu
ses 1
an
d
2,
X
12
is the tra
n
s
m
ission line
re
actance a
n
d
(
δ
1
-
δ
2
=
δ
)
i
s
t
h
e
di
ffe
re
nce i
n
pha
se a
ngl
e
bet
w
ee
n t
h
e
t
w
o
pha
so
r
vol
t
a
ges
of
V
1
an
d
V
2
.
Th
e FACTS dev
i
ce em
p
l
o
y
e
d
in
th
is p
a
p
e
r is th
e TCVR wh
ich
op
erates b
y
in
serting
an
in
-ph
a
se
v
o
ltag
e
to
t
h
e
main
b
u
s vo
ltag
e
to ch
ang
e
its m
a
g
n
itu
d
e
. To
m
o
d
e
l TCVR, an
i
d
eal tap ch
an
g
e
r tran
sfo
r
m
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Fau
lt Lo
ca
tion Effect o
n
Sho
rt-Circu
it Ca
lcula
tio
n
s
o
f
a
TCVR Comp
en
sa
t
e
d
Li
n
e
in Alg
e
ria
(M. Zellagui
)
3
can be
use
d
wi
t
h
o
u
t
seri
es i
m
peda
nce as i
n
Fi
gu
re
2. T
h
e
val
u
e
of t
h
e t
u
rn
’s rat
i
o
i
s
gi
ven
by
t
h
e
rat
i
o
o
f
t
h
e
ad
d
ition
a
l transform
a
tio
n
rel
a
tiv
e to
t
h
e
n
o
min
a
l tran
sf
ormatio
n
and
its v
a
lu
es
rang
e
b
e
tween
0
.
9
an
d 1.1
;
wh
ere
un
ity v
a
lu
e correspon
ds to
no
ad
d
ition
a
l tran
sfo
r
m
a
tio
n
[1
8
]
.
Fi
gu
re
2.
M
o
d
e
l
of
TC
VR
There
f
ore,
TC
VR
ca
n
be m
odel
e
d as
an
i
d
eal
t
a
p
cha
n
g
e
r t
r
a
n
sf
o
r
m
e
r wi
t
h
out
seri
e
s
i
m
pedance
[1
8]
, [1
9]
.
T
h
e TC
VR c
o
efficient
K
TCVR
tak
e
s th
e
fo
llowing
rang
es, as
p
r
esen
ted
b
y
th
e follo
wing
eq
u
a
ti
o
n
s
:
V
TCVR
= K
TCVR
. V
bus
(1
)
-0
.1
5
K
TCVR
+
0
.
15
(
2
)
-0
.1
5 x
V
bus
V
TCVR
+ 0.
15
x
V
bus
(3
)
3.
PHA
S
E TO E
ARTH
F
AUL
T CAL
C
U
LA
TIONS IN PRESENCE
OF
TCVR
Sym
m
et
ri
cal
com
pone
nt
s m
e
t
h
o
d
has al
wa
y
s
been use
d
i
n
t
h
e anal
y
s
i
s
of u
n
b
al
ance
d t
h
ree-
p
h
ase
syste
m
s, unsy
mme
trical faul
t currents
, and ro
tating
electro
d
y
n
a
m
i
cs
m
a
ch
in
ery. It
was o
r
i
g
in
ally presen
ted
by
C
.
L. Fo
rt
escue
i
n
1
9
1
8
and has bee
n
po
p
u
l
a
r
e
v
er s
i
nce [
20]
,
[2
1]
. The
ba
sic theory
of symmetrical
com
pone
nt
s c
a
n b
e
st
at
ed a
s
a m
a
t
h
em
at
ical
conce
p
t
.
A
sy
st
em
of t
h
r
ee co
pl
anar
v
ect
ors i
s
c
o
m
p
l
e
t
e
l
y
defi
ned
by
si
x
param
e
t
e
rs, an
d t
h
e sy
st
em
can be sai
d
t
o
p
o
ssess si
x de
g
r
ees of free
d
om
. A poi
nt
i
n
a st
rai
ght
l
i
n
e, bei
n
g co
n
s
t
r
ai
ned t
o
l
i
e
on t
h
e l
i
n
e
,
p
o
ssesses o
n
e de
gree
of f
r
ee
do
m
,
and by
t
h
e
sam
e
anal
ogy
,
a poi
nt
in space
has t
h
ree de
grees of
free
dom
. A c
o
plana
r
vect
or
i
s
defi
ned by its terminal and length; t
h
ere
f
ore it
pos
sesses t
w
o
de
grees
o
f
f
r
eedom
. Fi
g
u
re
3 s
h
ows t
h
e
equi
val
e
nt
ci
rc
ui
t
of
a t
r
a
n
s
m
i
ssi
on l
i
n
e
m
odel
,
com
p
ensated
by TCVR a
n
d s
u
bjected to a
phase
A t
o
eart
h
fa
ult, in t
h
e
presence
of fa
ult
resistance
(
R
F
).
Fi
gu
re
3.
Eq
ui
val
e
nt
ci
rc
ui
t
m
odel
of a
p
h
a
s
e t
o
ea
rt
h
fa
ul
t
whi
l
e
usi
n
g T
C
VR
[
22]
Line
V
bus
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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088
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08
IJEC
E V
o
l
.
5, No
. 1, Feb
r
uar
y
20
1
5
:
1 – 12
4
The
basi
c e
q
u
a
t
i
ons
fo
r t
h
i
s
t
y
pe
of
fa
u
lt tak
e
th
e
fo
llowing
form
[1
], [23
]
:
I
B
=
I
C
=
0
(4
)
V
A
=
V
1
+
V
2
+
V
0
=
R
F
x
I
A
0
(
5
)
The sy
m
m
et
ri
cal
com
pone
nt
s
of
t
h
e c
u
r
r
e
n
t
s
are [
2
3]
, [
2
4]
:
0
2
1
2
2
11
1
1
1
3
1
A
B
C
I
I
Ia
a
I
aa
II
(6
)
From
eq
uat
i
o
n
(4
) a
n
d
m
a
t
r
i
x
(6
), t
h
e sy
m
m
et
ri
cal
com
pone
nt
s
of t
h
e c
u
r
r
e
n
t
s
t
a
ke
t
h
e
f
o
l
l
o
wi
n
g
f
o
rm
:
12
0
3
A
I
II
I
(7
)
The sy
m
m
et
ri
cal
com
pone
nt
s
of
t
h
e
v
o
l
t
a
ges
are:
0
2
1
2
2
11
1
1
1
3
1
A
B
C
V
V
Va
a
V
aa
VV
(8
)
From
eq
uat
i
o
n
s
(
5
)
an
d
(8
),
t
h
e
di
rect
c
o
m
pone
nt
of
t
h
e
v
o
l
t
a
ges bec
o
m
e
s:
V
1
= - (
V
0
+
V
2
) +
(
R
F
x
I
A
) (
9
)
x
(1
0)
whe
r
e,
.
x
.
x
.
x
(1
1)
3
.
x
(1
2)
From
eq
uat
i
o
n
s
(
1
2
)
, t
h
e
faul
t
cu
rre
nt
o
f
p
h
a
s
e A i
n
t
h
e
pre
s
ence
of
a TC
VR
i
s
gi
ve
n
by
:
3x
x
3x
(1
3)
From
equations (7)
and
(13),
the curre
nt sy
mme
trical
co
mp
on
en
ts in th
e
p
r
esen
ce
of
TC
V
R
ar
e g
i
v
e
n by:
x
3x
(1
4)
The
di
rect
sy
m
m
e
t
r
i
cal
co
m
pone
nt
of
t
h
e
v
o
l
t
a
ges i
s
de
fi
ne
d
by
:
V
1
=
V
S
V
TCVR
–
M
1
(1
5)
20
1
1
12
0
23
3
ST
C
V
R
L
L
L
F
FL
L
L
F
VV
Z
Z
Z
R
V
nZ
Z
Z
R
(1
6)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Fau
lt Lo
ca
tion Effect o
n
Sho
rt-Circu
it Ca
lcula
tio
n
s
o
f
a
TCVR Comp
en
sa
t
e
d
Li
n
e
in Alg
e
ria
(M. Zellagui
)
5
Th
e i
n
v
e
rse sy
mme
trical co
mp
on
en
t of t
h
e
vo
ltag
e
s is
d
e
fined
b
y
:
V
2
= –
M
2
(1
7)
2
2
12
0
3
ST
C
V
R
L
F
LL
L
F
VV
Z
V
nZ
Z
Z
R
(1
8)
The ze
ro
sy
m
m
e
t
r
i
cal
co
m
pone
nt
of
t
h
e
v
o
l
t
a
ges i
s
gi
ve
n
by
:
V
0
= –
M
0
– (
R
F
x
I
0
) (
1
9
)
0
0
12
0
()
3
ST
C
V
R
L
F
F
LL
L
F
VV
Z
R
V
nZ
Z
Z
R
(2
0)
The c
o
efficient
s
A
a
to A
f
are define
d
as follows:
(2
1)
1
(2
2)
3
x
1
(2
3)
(2
4)
1
(2
5)
3
x
1
(2
6)
Fr
o
m
eq
u
a
tions (
16)
,
(
1
8
)
, (2
0)
an
d m
a
tr
i
x
(8
), th
e th
ree ph
ase
v
o
ltages o
f
th
e transmissio
n
lin
e
in
the
prese
n
ce
o
f
TC
VR
t
a
ke
t
h
e
fol
l
owi
n
g
f
o
rm
:
12
0
3
3
FS
T
C
V
R
A
F
LL
L
F
RV
V
V
nZ
Z
Z
R
(2
7)
20
12
0
.)
3
ST
C
V
R
a
L
b
L
c
F
B
FL
L
L
F
VV
A
Z
A
Z
A
R
V
nZ
Z
Z
R
(2
8)
20
12
0
)
3
ST
C
V
R
d
L
e
L
f
F
C
FL
L
L
F
VV
A
Z
A
Z
A
R
V
nZ
Z
Z
R
(2
9)
From
what is
above, it is clear
th
at th
e sh
ort-circu
it calcu
latio
n
s
d
e
p
e
n
d
o
n
t
h
e fo
llowin
g
:
TCVR
cont
rol
l
e
d vol
t
a
ge
(
V
TCVR
) and
op
eration
m
o
d
e
, and
th
e fault co
n
d
itio
ns rep
r
esen
ted
in
fau
lt lo
catio
n
(
n
F
) and
fault resistan
ce
(
R
F
).
Wh
ile
u
s
in
g
a
fix
e
d
fau
lt resistan
ce, the effect of fau
l
t lo
catio
n
is stud
ied
,
i
n
th
e ab
sen
c
e
o
f
TCVR an
d in
its presen
ce for
p
o
s
itiv
e
an
d n
e
g
a
tiv
e
TCVR con
t
ro
l
l
ed
vo
ltag
e
, as sho
w
n
in th
e n
e
x
t
sect
i
on.
4.
R
E
SU
LTS AN
D ANA
LY
SIS
The electrical
network st
udied in t
h
is pa
per is
for t
h
e
Eastern Al
ge
rian tra
n
sm
ission net
w
ork,
So
nel
g
az g
r
ou
p w
h
i
c
h i
s
t
h
e Nat
i
onal
S
o
ci
et
y
for El
ect
ri
ci
ty
and Gas i
n
A
l
geri
a, as sh
ow
n i
n
Fi
g
u
re 4 [
25]
.
I
t
is a state-owned
u
tility in
c
h
arg
e
o
f
elect
ricity an
d
n
a
tu
ral
g
a
s tran
smissio
n
and
distrib
u
tion
in
Alg
e
ria,
estab
lish
e
d
in 1
969
.
The case study of this research
work
is for a 2
2
0
kV tran
sm
issio
n
lin
e wh
ich
co
nn
ects Batn
a and
B
i
skra
2
20/
60
kV
su
bst
a
t
i
o
ns
i
n
t
h
e
m
e
nt
i
oned
net
w
o
r
k.
The l
i
n
e
i
s
e
q
u
i
ppe
d
wi
t
h
a
T
C
VR
de
vi
ce i
n
st
al
l
e
d
at
i
t
s
m
i
dpoi
nt
. The
vol
t
a
g
e
cont
rol
l
e
d
by
t
h
e i
n
st
al
l
e
d T
C
VR
sy
st
em
(
V
TCVR
) vari
es
bet
w
ee
n m
i
nim
u
m
of
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 1, Feb
r
uar
y
20
1
5
:
1 – 12
6
-1
0
kV
, an
d a
m
a
xim
u
m
of +
10
kV
. Th
e fau
lt
lo
catio
n
n
F
vari
es
bet
w
ee
n
50
% (at
t
h
e
m
i
d of t
h
e l
i
n
e
)
t
o
1
0
0
% (at th
e end
of th
e lin
e at
b
u
s-b
a
r
B
).
A
fa
u
lt resistance
R
F
is
u
s
ed
who
s
e mag
n
itu
d
e
is main
tain
ed
at 2
0
Ω
.
Fi
gu
re
4.
East
e
r
n
re
gi
o
n
of
Al
geri
a
n
t
r
a
n
sm
i
s
si
on
net
w
o
r
k
Fi
gu
res
5.a,
b
,
c rep
r
ese
n
t
t
h
e va
ri
at
i
on
o
f
t
h
e c
u
r
r
ent
sym
m
et
ri
cal
com
pone
nt
s (
I
1
,
I
2
and
I
0
),
respectively and Figures
6.a
,
b, c re
pres
en
t th
e v
a
riatio
n
o
f
th
e lin
e cu
rren
ts (
I
A
,
I
B
a
nd
I
C
), re
spectivel
y as a
fun
c
tion
of th
e fau
lt lo
cation
n
F
withou
t and with
TC
VR.
As earlier m
e
ntio
n
e
d wh
ile usin
g
TC
VR, cases are
st
udi
e
d
f
o
r
V
TC
VR
decrem
ent and inc
r
em
ent such that
V
TCVR
is eith
er equ
a
l t
o
-10
k
V
or
+
1
0
kV
, r
e
sp
ectiv
ely.
Fi
gu
res
5.a
,
b
,
c
,
al
so
sh
o
w
s t
h
at
t
h
e t
h
re
e sym
m
et
ri
cal cur
r
e
n
t
com
pone
nt
s a
r
e e
q
ual
,
i
n
e
ach
i
ndi
vi
dual
ca
se
of
usi
n
g
TC
V
R
and
wi
t
h
o
u
t
i
t
,
whi
c
h m
a
t
c
hes e
quation
(7). It is als
o
clear that inc
r
eas
ing t
h
e
val
u
e of
n
F
l
eads t
o
a
decrem
ent
i
n
t
h
e m
a
gni
t
ude
o
f
t
h
e c
u
r
r
ent
sy
m
m
etri
cal
com
pone
nt
s, i
n
t
h
e abse
nce a
n
d
prese
n
ce
of T
C
VR. This is e
xpecte
d
due to increasing th
e sh
ort-circu
it im
p
e
d
a
n
ce as a resu
lt o
f
add
i
ng
m
o
re
l
i
n
e im
peda
nce
w
h
en
n
F
incre
a
ses.
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I
J
ECE
I
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208
8-8
7
0
8
Fau
lt Lo
ca
tion Effect o
n
Sho
rt-Circu
it Ca
lcula
tio
n
s
o
f
a
TCVR Comp
en
sa
t
e
d
Li
n
e
in Alg
e
ria
(M. Zellagui
)
7
(a)
(b
)
(c)
Fi
gu
re
5.
Im
pact
of
n
F
on
t
h
e cur
r
ent
sy
m
m
e
t
r
i
cal
com
pone
nt
s
In Figures 6.a
,
b, c, it is noticeable
that the line currents of pha
ses
B
and
C
are always z
e
ro which i
s
con
f
i
r
m
e
d
by
equat
i
o
n (4
).
Ho
we
ver
,
i
n
c
r
easi
ng
t
h
e val
u
e of
n
F
shows a red
u
c
tion
i
n
th
e lin
e cu
rren
t of th
e
faul
t
y
pha
se
A
i
n
al
l
st
udi
ed c
a
ses;
bef
o
re a
n
d aft
e
r
usi
n
g T
C
VR
. Th
is is also
attrib
u
t
ed
to
th
e in
crease
o
f
th
e
short-circ
uit i
m
pedance wit
h
the inc
r
ease
of
n
F
.
Fi
gu
res
7.a
,
b
,
c re
prese
n
t
t
h
e
vari
at
i
o
n o
f
t
h
e
v
o
l
t
a
ge
sym
m
et
ri
cal
com
pone
nt
s (
V
1
,
V
2
and
V
0
)
respectively a
n
d Figures
8.a, b, c
re
pres
en
t th
e
v
a
riatio
n of t
h
e lin
e ph
ase
vo
ltages (
V
A
,
V
B
and
V
C
),
resp
ectiv
ely as a fun
c
tio
n of t
h
e
fau
lt lo
cation
n
F
wit
h
ou
t an
d with TCVR
, wh
ere
V
TCVR
is -1
0 kV
o
r
+
10
k
V
.
In
Fig
u
re
s
7.a,
b,
c, the i
n
crease of
n
F
val
u
e lea
d
s to a
decrease
in
the direct
voltage com
p
onent
,
wh
ile th
e inv
e
rse and
zero voltag
e
co
m
p
on
en
ts are sh
own
to
in
crease. This is v
a
lid
for e
ach
indivi
dual case,
whet
her
TC
VR
i
s
i
n
st
al
l
e
d
or
not
,
w
h
i
c
h
i
s
c
o
n
f
i
r
m
e
d by
e
q
uat
i
o
n
s
(
1
6)
, (
1
8)
an
d
(2
0
)
.
In Fi
g
u
r
es 8.a
,
b, c
,
it is observe
d that the increase of
n
F
value leads to
a decr
ease in the value
of
pha
se
A
and
B
v
o
ltag
e
s, wh
ile
th
e v
o
ltage o
f
p
h
a
se
C
s
h
ows
an i
n
crem
ent w
ith
th
e in
crease of
n
F
for all
cases.
I
n
t
h
e ab
ov
e st
u
d
i
ed
cases
wh
en u
s
i
n
g TC
V
R
, it is ob
serv
ed th
at th
e
g
r
ap
hs cor
r
e
spond
ing
to
V
TCVR
equal
s
t
o
+
1
0
kV
sh
o
w
hi
g
h
e
r m
a
gni
t
udes
t
h
an t
h
o
s
e
co
r
r
esp
o
ndi
ng
t
o
V
TCVR
of -
1
0
k
V
whi
c
h i
s
no
rm
all
y
expecte
d
.
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I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 1, Feb
r
uar
y
20
1
5
:
1 – 12
8
(a)
(b
)
(c)
Fi
gu
re
6.
Im
pact
of
n
F
on the t
r
ansm
ission line curre
nts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Fau
lt Lo
ca
tion Effect o
n
Sho
rt-Circu
it Ca
lcula
tio
n
s
o
f
a
TCVR Comp
en
sa
t
e
d
Li
n
e
in Alg
e
ria
(M. Zellagui
)
9
(a)
(b
)
(c)
Fi
gu
re
7.
Im
pact
of
n
F
on
t
h
e
vol
t
a
ge
sy
m
m
e
t
r
i
cal
com
pone
nt
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 1, Feb
r
uar
y
20
1
5
:
1 – 12
10
(a)
(b
)
(c)
Fi
gu
re
8.
Im
pact
of
n
F
on the t
r
ansm
ission line phase
voltages
5.
CO
NCL
USI
O
N
In t
h
is re
searc
h
work, s
h
ort-circuit analysis
of
a p
h
a
se
to
earth
fau
lt
is deriv
e
d
using
sy
mmetrical
com
pone
nt
s
m
e
t
h
o
d
fo
r a pr
act
i
cal
hi
gh vo
l
t
a
ge t
r
ansm
i
s
si
on l
i
n
e i
n
t
h
e 22
0 kV
Al
ger
i
an po
wer
net
w
o
r
k
.
Th
e lin
e is equ
i
pp
ed
with
on
e of
th
e
recen
t
FACTS d
e
vices; n
a
m
e
ly
TCVR wh
ich
works to
regu
l
a
te th
e
v
o
ltag
e
of th
e l
i
n
e
.
Wh
ile usin
g
TCVR, th
e
effect
o
f
fa
u
lt l
o
catio
n on
short-circu
it calculatio
n
p
a
ram
e
t
e
rs, i
n
case o
f
po
sitiv
e and
n
e
gativ
e TCVR contro
lled
vo
ltag
e
s, is in
v
e
stig
ated
wh
ile
m
a
in
tain
in
g
a fix
e
d
fau
l
t
resistance. T
h
e
theoretical analysis
usi
ng sy
m
m
e
t
r
i
cal
co
m
p
o
n
e
n
t
s
and si
m
u
l
a
t
i
ons of t
h
e pr
o
p
o
s
ed m
odel
,
before
and a
f
te
r
using TC
VR, showe
d
excell
e
nt agreem
ent.
Fro
m
th
is p
a
per, it is co
nfirmed
th
at th
e use o
f
TCVR lead
s to
a si
g
n
i
fican
t redu
ction in
th
e fau
lt
current. In t
h
e
meanwh
ile, it i
s
clear th
at i
n
creasing
th
e v
a
l
u
e
o
f
t
h
e
fau
lt
lo
catio
n
lead
s t
o
a
redu
ction
i
n
th
e
cur
r
ent
sy
m
m
e
t
r
i
cal
co
m
pone
nt
s, i
n
t
h
e abse
nce an
d prese
n
ce of TC
VR
,
wi
t
h
a not
i
cea
bl
e decl
i
n
at
i
o
n
i
n
t
h
e
m
a
gni
t
ude
of
t
h
e faul
t
c
u
r
r
ent
.
Fu
rt
he
r resea
r
ch st
udi
es
w
h
i
l
e
usi
n
g T
C
VR
are cu
r
r
ent
l
y
u
nde
r
i
nvest
i
g
at
i
o
n
fo
r o
n
goi
ng
publications
. T
h
ese include various s
h
ort-ci
rcuit cases
su
c
h
as t
h
ree
phas
e fault a
n
d pha
s
e to
pha
se fa
ult, as
well as stud
ying
th
e effect
o
f
fau
lt re
sistance
on s
h
ort-circ
ui
t calculations.
REFERE
NC
ES
[1]
.
J. Schlabb
ach
,
"Short-Circuit
Currents", se
co
nd edi
ti
on,
pub
lished b
y
The
Institut
i
on of
Engin
eering
a
nd
Techno
log
y
(I
ET),
London, UK, June 2008
.
[2]
.
A. Beriz
z
i
,
S. M
a
ssucco, A. Si
lv
estri,
and D.
Zan
i
nell
i,
"Short-Cir
c
uit Curr
ent C
a
l
c
ula
tion: A Com
p
arison Betwe
e
n
Methods of IEC
and ANSI Standards usi
ng D
y
n
a
mic Simulation
as Refer
e
nce",
IEEE Transacti
ons on Industry
Applica
tions
, Vol. 30
, No
. 4
,
pp.
1099-1106, 199
4.
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