Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 2
,
A
p
r
il
201
5, p
p
.
24
6
~
25
5
I
S
SN
: 208
8-8
7
0
8
2
21
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
Simplified Method for Single Line
to Grou
nd-Fault Location in
Electri
c
al Power Distribu
tion Sys
t
e
ms
M.
Z
a
hri
*
, Y.
Mench
a
fo
u **
,
H.
El M
a
rk
h
i
**,
M.
Habib
i
*
*
Labor
ator
y
of Telecommunication
and
Engin
e
ering Decision S
y
stems, Ibn To
f
a
il
Universit
y
,
Ken
itra
,
Moroc
c
o
** Labor
ator
y
of
Signals, S
y
stems a
nd componen
t
s, Sidi Mohamed
Ben A
bdellah U
n
iversity
, Fez,
Morocco
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 1, 2014
Rev
i
sed
Feb
12
, 20
15
Accepted
Feb 20, 2015
Power distribution s
y
stems play importa
nt rol
e
s
in m
odern s
o
ci
et
y. W
h
en
dis
t
ribution s
y
s
t
em
outages
occu
r, s
p
eed
y and pr
ecise fau
lt lo
cat
i
on is crucia
l
in acc
el
erat
ing
s
y
s
t
em
res
t
orat
i
on, re
ducing ou
tage time
and significantly
improving sy
stem reliability
, an
d then
improves the quality
of services and
custom
er satisfaction
.
In
this pap
e
r,
we propose
a reduced algori
t
h
m
utilizing
the sum of
sending-end curren
t
s of the three phases to calcu
late the fault
current
,
and th
er
efore,
avo
i
d th
e
iter
a
tiv
e as
pe
ct
of the
cl
as
s
i
c
al
gorithm
for
single lin
e to gr
ound fault
location and
redu
ce its computational
charge. Th
e
tes
t
res
u
l
t
s
are
obtain
e
d from
t
h
e num
er
ical simulation using the data of
a
distribution
lin
e
recognized
in
th
e liter
a
tur
e
.
Keyword:
C
o
m
put
at
i
onal
cha
r
ge
Fau
lt lo
cation
Po
wer Di
st
ri
bu
t
i
on
Sy
st
em
s
Si
ngl
e l
i
n
e
-
t
o
-
g
r
o
un
d
faul
t
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
:
M
u
st
ap
ha Za
hr
i
,
Lab
o
rat
o
ry
of
Tel
ecom
m
uni
cat
i
on a
n
d
E
ngi
neeri
n
g
Deci
si
on
Sy
st
em
s,
Ibn
Tofail Un
iv
ersity,
Ken
itra, Morocco
,
Em
a
il: m
u
stap
h
a
.zah
ri@g
m
a
i
l
.co
m
1.
INTRODUCTION
Distribution
ne
tworks a
r
e dis
p
erse
d in eac
h urba
n and rura
l region,
and a
r
e crossed
from each alle
y
and st
reet
. Eac
h
di
st
ri
b
u
t
i
o
n
feed
er
h
a
s m
a
n
y
laterals, su
b
-
laterals, lo
ad
tap
s
, balan
c
ed
an
d
u
n
b
a
lan
c
ed
load
and
di
f
f
ere
n
t
t
y
pes of c
o
nd
u
c
t
o
rs [
1
]
.
P
o
w
e
r di
st
ri
b
u
tion syste
m
s (PDSs) are su
bj
ected
to
fau
lt co
nd
itio
n
s
cause
d by
vari
ous s
o
urces s
u
ch as l
o
ad a
b
r
upt
cha
n
ges, a
dve
rse weat
her
con
d
i
t
i
ons
, eq
ui
pm
ent
s
fai
l
u
re an
d
external object
contacts. The
faults
statistics
can
o
r
ien
t
ate th
e strateg
i
c
choices of c
o
m
p
anies and researchers
to
gu
id
e th
eir
work toward
s th
e si
n
g
l
e
ph
ase to
g
r
ou
nd
fau
l
ts th
at cau
se the m
a
j
o
rity o
f
po
wer
d
i
sturb
a
nce.
Owi
ng
t
o
t
h
e
expa
nsi
on
o
f
d
i
st
ri
but
i
o
n
net
w
o
r
k
,
t
o
t
h
e
ra
di
al
t
o
p
o
l
o
gy
,
t
h
e exi
s
t
e
nce
of
sh
ort
a
n
d
het
e
r
oge
ne
ous
l
i
n
es and al
s
o
a l
o
wer
de
gree
of i
n
st
rum
e
nt
at
i
on i
t
i
s
very
di
ffi
c
u
l
t
and c
o
m
p
l
i
cat
ed t
o
locat
e
th
e fau
lt in
t
h
ese n
e
t
w
orks.
C
u
r
r
ent
l
y
t
h
e
onl
y
t
e
c
hni
que
use
d
f
o
r
l
o
cat
i
n
g
fa
ul
t
s
i
n
di
s
t
ri
but
i
o
n
sy
st
em
s of el
ect
ri
c
po
we
r i
s
t
h
e
vi
sual
i
n
spect
i
o
n
o
f
F
P
I
(Fa
u
l
t
Passage
I
n
di
cat
ors
)
whi
c
h i
m
poses an i
m
port
a
nt
t
i
m
e
of
r
e
st
orat
i
o
n
[2]
.
In rece
nt
y
ear
s, m
a
ny
t
echn
i
ques
have
be
en p
r
o
p
o
sed
f
o
r a
u
t
o
m
a
t
e
d
FL (Fa
u
l
t
Loc
a
t
i
on) i
n
t
h
e
di
st
ri
b
u
t
i
o
n
sy
s
t
em
s, t
h
ese m
e
t
h
o
d
s ca
n
be
di
vi
de
d i
n
t
o
t
h
ree
m
a
i
n
cat
eg
ori
e
s:
Travel
i
n
g
wa
v
e
-base
d
m
e
t
hods:
i
n
t
h
ese
m
e
t
h
o
d
s,
hi
gh
f
r
e
que
ncy
c
o
m
p
o
n
ent
s
o
f
v
o
l
t
a
g
e
an
d/
o
r
c
u
r
r
e
n
t
m
easured
at
s
ubst
a
t
i
o
n a
r
e
appl
i
e
d
[
3
]
,
[4
]
.
The
di
sa
dva
nt
age
o
f
t
h
e
s
e
m
e
t
hod
s i
s
t
h
e nee
d
of
hi
g
h
-
sam
p
l
i
ng fre
q
u
e
ncy
;
co
nse
que
nt
l
y
, ap
pl
y
i
ng
t
h
ese m
e
t
hods
i
s
ve
ry
ex
pe
nsi
v
e.
Artificial in
tellig
en
ce an
d
statistical An
alys
is o
r
h
y
b
r
i
d
meth
od
s can
h
e
l
p
op
erat
o
r
o
r
en
g
i
n
eers t
o
do
m
u
ch laborious work, to
re
duce
the tim
e factor and t
o
a
voi
d
the
hum
an m
i
s
t
akes [5]-[8].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
S
i
mp
lified
met
h
od
f
o
r si
n
g
l
e l
i
n
e
to
g
r
ou
nd
-Fau
lt lo
ca
tion
in
electrica
l power …
(Mu
s
taph
a Za
h
r
i)
22
2
Im
pedance-
bas
e
d m
e
t
hods
, i
n
whi
c
h t
h
e f
u
n
d
am
ent
a
l
fr
eque
ncy
c
o
m
pone
nt
of
v
o
l
t
a
ge a
n
d
c
u
r
r
en
t
m
easured at
s
ubst
a
t
i
o
n, a
r
e use
d
[9]
-
[
13]
.
These m
e
t
hods
gene
ral
l
y
can be easi
l
y
appl
i
e
d and t
h
ey
are
cheape
r
t
h
an the othe
rs.
Howev
e
r, in
d
i
v
i
du
ally th
ey
d
o
no
t fu
lly co
n
s
id
er th
e ch
aracteristics o
f
d
i
stribu
tio
n
system
s
(unbalance
d operation,
pres
en
ce
o
f
in
termed
iate lo
ad
s, laterals, an
d ti
m
e
-v
arying lo
ad
p
r
o
f
ile), wh
ich
significa
ntly affect their pe
rform
a
nce and
hi
nde
rs t
h
ei
r
pra
c
t
i
cal
im
pl
em
ent
a
t
i
on.
Fu
rt
h
e
rm
o
r
e,
fro
m
th
e fau
lt statistics, i
t
can
b
e
no
ted
th
at
th
e sin
g
l
e
p
h
a
se to
g
r
ou
nd
fau
lts are th
e
m
o
st frequent,
thus
, the
strate
gic ch
oices of com
p
anies
and
resea
r
che
r
s wo
r
k
s ca
n
be
ori
e
nt
at
ed t
o
wa
r
d
s t
h
e
si
ngl
e
p
h
ase t
o
gr
o
u
n
d
faul
t
l
o
cat
i
o
n [
1
4]
.
Thi
s
l
e
d
us t
o
wo
r
k
on
i
m
pr
o
v
i
n
g fa
ul
t
l
o
cat
i
o
n
al
g
o
ri
t
h
m
s
in
term
s of accuracy, sim
p
lic
ity and c
o
m
putational c
h
a
r
ge
, si
nce the
practical
use
of those
algorithm
s
requi
res
t
h
e i
m
pl
em
entat
i
on
on
p
r
og
ra
m
m
a
bl
e el
ect
r
oni
c
de
vi
ces.
The m
a
i
n
ob
je
ct
i
v
e of
t
h
e
pr
op
ose
d
m
e
t
hodol
ogy
i
s
t
o
us
e t
h
e sum
of s
e
ndi
ng
-e
nd c
u
r
r
ent
s
of t
h
e
three
phase
s to calculate the fault curre
nt
used t
o
de
termin
ate th
e fault lo
catio
n
,
in o
r
d
e
r t
o
reduce th
e
co
m
p
u
t
atio
n
a
l
ch
arg
e
o
f
th
e classic alg
o
rithm
fo
r sing
le lin
e to groun
d fau
lt lo
catio
n and
to avo
i
d its iterativ
e
aspect
. The
pr
op
ose
d
m
e
t
hod
was val
i
d
at
ed
usi
n
g real
u
nde
r-
gr
o
u
n
d
di
st
ri
but
i
o
n fee
d
er
d
a
t
a
and M
a
t
l
a
b as an
analysis tool.
The
rem
a
i
nder
of t
h
i
s
pa
pe
r
i
s
or
ga
ni
zed
as
follows: The
classical ite
rative and the re
duced
al
go
ri
t
h
m
s
are
prese
n
t
e
d i
n
se
ct
i
ons 2 a
nd
3 respect
i
v
el
y
,
the test resu
lts are sh
own
in
Sectio
n
4
,
wh
ereas th
e
co
n
c
l
u
sion
s
of
th
is wo
rk
are
presen
ted
in Sectio
n
5
.
2.
ITERATIVE FAULT
L
O
CA
TI
ON
A
L
GO
R
I
THM
After th
e
d
e
tectio
n
an
d th
e cl
assificatio
n
o
f
th
e fau
lts, th
e
FL pro
cess is i
n
itialized
. First
,
th
e syste
m
i
s
di
vi
de
d i
n
t
o
n
bra
n
c
h
es,
w
h
ere
n i
s
t
h
e n
u
m
b
er o
f
p
o
ssi
bl
e pat
h
s (e
n
d
no
des
)
. F
o
r ea
ch
bra
n
ch
, t
h
e
faul
t
di
st
ance i
s
e
s
t
i
m
at
ed, usi
n
g
a
n
i
m
pedance
-
b
a
sed m
e
t
hod
[
1
5]
-[
1
8
]
.
Fi
gu
re 1.
Si
n
g
l
e
-p
hase
-t
o-
g
r
o
u
n
d
fa
ul
t
m
odel
i
n
g
2.
1.
Ma
them
a
t
ical
devel
o
pme
n
t
The system
illustrated in
Figure
1,
co
nt
ai
n
s
a l
o
cal
bus
,
a ge
neri
c
faul
t
e
d
di
st
ri
b
u
t
i
o
n
l
i
n
e wi
t
h
con
s
t
a
nt
fa
ul
t
r
e
si
st
ance (R
F
)
,
an
d a
n
e
qui
val
e
nt
l
o
a
d
.
It is po
ssi
b
l
e to sho
w
th
at
for
a sing
le ph
ase-to
-g
ro
und
fau
l
t
in
p
h
a
se
m:
Smi
Smr
m
m
Fmr
Fmi
Fmr
m
Fmi
m
F
V
V
M
M
I
I
I
M
I
M
R
x
.
.
.
1
1
2
2
1
(1
)
Where t
h
e s
u
bscri
p
t indices
r a
nd i
repres
ent, re
sp
ectivel
y, the va
riable
s real and im
a
g
ina
r
y pa
rts,
the va
riables
are as follows:
V
sm
p
h
a
se
m s
e
ndi
ng
–e
n
d
v
o
l
t
ages (
i
n v
o
l
t
s
)
;
V
Fm
p
h
a
s
e
m f
a
u
lt-po
in
t
p
h
a
s
e vo
ltag
e
s (in vo
lts)
;
x
fau
lt po
i
n
t to
lo
ca
l
b
u
s
d
i
sta
n
c
e (in
kilometers)
;
I
Fm
fau
lt cu
rren
t (in
a
m
p
e
res)
.
Also,
M
1m
an
d
M
2m
are
defi
ne
d i
n
(
2
)
an
d
(
3
)
k
Ski
mki
Skr
mkr
m
I
Z
I
Z
M
)
(
1
(2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
22
1 – 2
3
0
22
3
k
Skr
mki
Ski
mkr
m
I
Z
I
Z
M
)
(
2
(3
)
Whe
r
e
k
pha
ses
a,b
an
d c;
Z
mk
i
m
pe
d
a
n
ce bet
w
een
p
h
a
se
m
an
d
k [
Ω
/km
]
;
I
Sk
p
hase
k s
e
ndi
ng
-e
nd
cur
r
ent
(
i
n
am
per
e
s)
.
The fault distance
is
estim
ate
d
by
(4):
Fmr
m
Fmi
m
Smi
Fmr
Smr
Fmi
I
M
I
M
V
I
V
I
x
.
.
.
.
2
1
(4
)
Fro
m
(4
) it is p
o
ssi
b
l
e to
ob
tain
th
e fau
lt d
i
stan
ce fro
m
th
e p
a
ram
e
ter
s
o
f
th
e system:
th
e fau
lt
cur
r
ent
a
n
d t
h
e sen
d
i
n
g-e
n
d
vol
t
a
ge
s.
Si
nce
v
o
l
t
a
ges a
r
e
alr
ead
y k
now
n, an
iter
a
tiv
e procedure
that update
s
th
e fau
lt current is u
s
ed
to
estimate the fault
distance.
2.
2.
Fault Current Estimation P
r
ocedure
I
n
equ
a
tion
(
4
)
th
e on
ly unkn
own
p
a
r
a
m
e
t
e
r
is th
e f
a
u
lt cur
r
e
n
t
IFm
r
, i. A
ll
o
t
h
e
r
var
i
ab
les ar
e
sy
st
em
param
e
t
e
rs o
r
m
easure
d
vari
a
b
l
e
s.
Referri
n
g
to
Fig
u
re
1
,
th
e
fau
l
t cu
rren
t can be ob
tain
ed b
y
(5
):
La
Sa
Ra
Sa
Fa
I
I
I
I
I
(5
)
Whe
r
e
I
La
is the phase
a
l
o
ad
current.
Nev
e
rth
e
less, th
e lo
ad
curren
t
d
u
ring
th
e
fault p
e
riod
is d
i
fferen
t
fro
m
th
e
p
r
e-fau
lt lo
ad
cu
rren
t,
du
e
t
o
vol
t
a
ge dr
o
p
s an
d sy
st
em
s dy
nam
i
cs duri
n
g t
h
e fa
ul
t
.
For t
h
i
s
rea
s
on
, an i
t
e
rat
i
v
e t
echni
q
u
e us
ed t
o
esti
m
a
te th
e lo
ad
cu
rren
t
du
ri
n
g
th
e
fau
lt, is
d
e
scri
b
e
d as
follo
w:
Fig
u
re
2
.
Con
v
en
tio
n
a
l iterati
v
e
Algo
rith
m
1)
Lo
ad
cu
rren
t
du
ri
n
g
th
e
fau
lt
I
La
is ass
u
m
e
d to be
the
sam
e
as the
pre
-fa
ult
load curre
nt.
2)
Th
e
fau
lt cu
rren
t is calcu
lated u
s
i
n
g (5
)
I
L
= I
S
I
F
= I
Sf
– I
L
= I
Sf
– I
S
Deter
m
ina
t
ion of
x
Co
m
p
utation of
V
F
Update I
L
Convergence of
x
I
F
= I
Sf
- I
L
Deter
m
ina
t
ion of
x
The distance
is x
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Simplified met
h
od f
o
r si
ngle l
i
ne to
grou
nd-Fault location
in
electrical power …
(Mu
s
taph
a Za
h
r
i)
22
4
3)
Fau
lt d
i
stan
ce i
s
esti
m
a
ted
u
s
i
n
g (1
),
(2), and (3
).
4)
Fault-poi
nt vol
t
ages are
estimated using (6)
Fc
Fb
Fa
cc
cb
ca
bc
bb
ba
ac
ab
aa
Sc
Sb
Sa
Fc
Fb
Fa
I
I
I
Z
Z
Z
Z
Z
Z
Z
Z
Z
x
V
V
V
V
V
V
.
(6
)
5)
L
o
ad
cu
rr
e
n
t
I
L
a
is up
d
a
ted
u
s
i
n
g th
e
fau
lt-poin
t
vo
ltag
e
s i
n
(7) an
d (8
):
T
Fc
Fb
Fa
ac
ab
aa
La
V
V
V
Y
Y
Y
I
.
(7
)
1
)
(
Lpq
pq
pq
Z
Z
x
l
Y
(8
)
Whe
r
e
Z
pq
is the line
impe
d
ance
(
m
utual
or
self)
betw
een
ph
ase
p
a
n
d
q
;
Z
Lpq
is th
e load imp
e
da
n
c
e (mu
t
ua
l or self)
b
e
tween
pha
se
p an
d q;
l is the tot
a
l line lengt
h.
6)
Check if
x
h
a
s
conv
erg
e
d, usin
g
(9
)
)
1
(
)
(
x
x
(9
)
Whe
r
e
δ
i
s
a
p
r
evi
o
usl
y
de
fi
ne
d t
h
res
hol
d
val
u
e a
n
d
α
is th
e
iteratio
n
n
u
m
b
e
r.
7)
If
x
ha
s c
o
n
v
er
ged
,
st
op
t
h
e
p
r
oce
d
ure;
ot
he
r
w
i
s
e,
g
o
back
t
o
st
e
p
2).
3.
PROP
OSE
D
ALGO
RITH
M
In th
e case
o
f
a b
a
lanced symme
trical o
p
e
ratio
n
,
an
alysis
o
f
th
ree-p
h
a
se
syste
m
s is si
m
i
lar to
t
h
at of
an e
qui
val
e
nt
si
ngl
e-
p
h
ase s
y
st
em
,
characterized by
voltages, phase
c
u
rre
nt
s an
d
p
h
a
s
e im
pedan
ces
of
t
h
e
powe
r system
.
Once
a signific
ant asy
mmetry appears
in t
h
e
conf
igu
r
ation
or op
eratio
n of t
h
e
p
o
wer system
, i
t
i
s
no l
o
n
g
e
r
p
o
ssi
bl
e t
o
est
a
bl
i
s
h el
ect
ri
cal
equat
i
o
ns
usi
ng
cy
cl
i
c
im
pedances. Thi
s
i
s
t
h
e
case o
f
di
st
ri
b
u
t
i
o
n
net
w
or
ks
w
h
er
e t
h
e l
o
ad
i
s
fu
ndam
e
nt
al
l
y
unbal
a
nced
due
t
o
t
h
e
l
a
r
g
e
nu
m
b
er of
u
n
e
q
u
a
l
si
ngl
e
p
h
ase
l
o
a
d
s
.
An
add
itio
n
a
l
asy
m
m
e
try is
in
trodu
ced
b
y
th
e un
ev
en
s
p
acing
of the c
o
nductors
of three
-
phase lines and
un
de
rg
ro
u
nd c
a
bl
es.
Neut
r
a
l
of
ge
nerat
o
rs
and
p
o
we
r t
r
ansf
o
r
m
e
rs can be
g
r
o
u
nde
d i
n
di
ff
ere
n
t
way
s
depe
n
d
i
n
g o
n
t
h
e p
r
ot
ect
i
o
n
n
eeds,
po
we
r su
ppl
y
sy
st
em
an
d t
h
e c
h
aract
er
i
s
t
i
c
s of l
o
a
d
s
sup
p
l
i
e
d
.
Ge
ne
ral
l
y
,
an im
pedance
is placed bet
w
een the
ne
utral
of the tra
n
s
f
ormer and the ea
rt
h to e
n
able
relay to detect single
lin
e
to
g
r
ou
nd
fau
lts [19
]
.
Po
wer
Di
st
ri
b
u
t
i
on sy
st
em
can t
h
us
be m
o
d
e
l
e
d by
t
h
ree
v
o
l
t
a
ge
gene
rat
o
rs
wi
t
h
a
com
m
on poi
nt
N
su
pp
lying
b
a
lan
ced three si
nu
so
i
d
al
v
o
ltages V1
, V2
a
nd V3.
They a
r
e
connected to
th
ree lo
ad
im
p
e
d
a
n
c
es,
vi
a t
h
ree l
i
n
es
num
bere
d 1,
2,
and
3.
A si
m
p
l
i
f
i
e
d m
odel
i
ng o
f
an el
ect
ri
c
a
l
di
st
ri
but
i
o
n
net
w
or
k i
s
sh
o
w
n i
n
Fi
gu
re 3.
Fig
u
re
3
.
Sim
p
lified
m
o
d
e
lin
g of an
electrical d
i
stribu
tion
network
I
1
,
I
2
and
I
3
, t
h
e
cu
rre
nt
s t
h
ro
u
g
h
t
h
ree l
o
a
d
i
m
pedan
ces, t
h
us, t
h
e
ne
utral
current is
zero.
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
. 2, A
p
ri
l
20
15
:
22
1 – 2
3
0
22
5
0
3
2
1
3
2
1
Z
V
Z
V
Z
V
I
I
I
I
N
(1
0)
Ho
we
ver
,
i
f
a
faul
t
occu
rs
o
n
one
phase
(
S
i
ngl
e
p
h
ase to
g
r
ou
nd
fau
lt), t
h
e
fau
lt cou
r
an
t is, th
en,
tran
sm
it
ted
to
t
h
e
n
e
u
t
ral v
i
a t
h
e ea
rt
h,
an
d
t
h
e rel
a
t
i
on (
1
0
)
becom
e
s:
0
1
1
3
2
1
3
2
1
Z
V
Z
V
R
Z
V
I
I
I
I
f
N
0
1
3
2
1
3
2
1
f
N
R
V
Z
V
Z
V
Z
V
I
I
I
I
0
1
3
2
1
f
f
N
I
R
V
I
I
I
I
0
3
2
1
I
I
I
I
I
f
N
(1
1)
Usi
n
g (
1
1)
, we
can cal
cul
a
t
e
t
h
e fa
ul
t
di
st
an
ce wi
t
h
out
hav
i
ng t
o
g
o
t
h
ro
u
gh t
h
e i
t
e
rat
i
v
e
m
e
t
hod
o
f
th
e classical alg
o
rith
m
;
th
e red
u
c
ed
al
g
o
rithm
is th
en
illu
st
rated
i
n
Fi
g
u
re
4
:
1)
Acqu
isitio
n of
th
e sen
d
i
n
g
-end
cu
rren
ts and
v
o
ltag
e
s
o
f
each
p
h
a
se;
2)
Faul
t
cu
rre
nt
c
a
n
be cal
c
u
l
a
t
e
d
usi
n
g
(1
1
)
;
3)
Fau
lt d
i
stan
ce i
s
so ob
tain
ed
usin
g th
e equ
a
tio
n
s
(1
),
(2) and
(3).
Fi
gu
re
4.
Fa
ul
t
Locat
i
o
n
re
du
ced al
g
o
r
i
t
h
m
.
4.
TESTS AND
RESULTS
4.
1.
Tests
To ve
ri
fy
per
f
o
rm
ances of t
h
i
s
al
gori
t
h
m
,
we have
co
nd
uct
e
d seve
ral
sim
u
l
a
t
i
ons u
s
i
n
g dat
a
fr
om
a
d
i
stribu
tio
n syste
m
reco
gn
ized in
literature [20
]
.
The sy
st
em
t
h
at
we ha
ve
st
u
d
i
e
d i
s
a
pa
rt
o
f
t
h
e
u
nde
rg
r
o
un
d
di
st
ri
b
u
t
i
o
n
net
w
or
k, i
t
i
s
a l
i
n
e f
r
o
m
20
K
V
di
st
ri
bu
t
i
on net
w
o
r
k o
f
t
o
t
a
l
l
e
ngt
h 2
2
.
5
Km
, com
pose
d
o
f
6
sect
i
ons
o
f
di
ffe
ren
t
l
e
ngt
hs
, si
m
u
l
a
t
e
d
usi
n
g
di
st
ri
b
u
t
e
d
param
e
t
e
r l
i
n
e m
odel
as s
h
ow
n i
n
Ta
bl
e
1
.
Usi
n
g M
a
t
l
a
b
[2
1]
as
si
m
u
l
a
ti
on t
o
ol
,
26
fa
ul
t
cases a
r
e si
m
u
l
a
t
e
d at
di
ff
erent
FL
bet
w
een
0-
1
0
0
%
,
fo
r
fault re
sistance Rf
=1
0
Ω
and
f
o
r
di
ffe
re
nt
l
o
a
d
di
st
ri
b
u
t
i
ons as
ex
pl
ai
ned
i
n
Tabl
e
2.
Balanced l
o
ads
;
L
o
ad
a
t
th
e le
f
t
e
n
d
;
L
o
ad
a
t
th
e r
i
gh
t e
n
d
.
The
fault
distance is calc
u
lated for eac
h cas
e using t
h
e cu
rren
ts and
v
o
ltag
e
s at th
e inp
u
t o
f
t
h
e lin
e,
an
d using
th
e two algo
rith
m
s
(classical and
red
u
c
ed).
Tab
l
e
1
.
Stud
ied
Section
s
of lin
es Param
e
ters
I
nput voltages [K
V]
Vs=11.
547,
U=20
Rf [Oh
m
s]
10
L
i
ne im
pedance [
O
h
m
s/K
m
]
Z
1
=0.
56+j0.
831,
Z
0
=0.
845+j2.
7
42
L
i
ne section length[Km
]
l1=2.
4
;
l2=4; l3=4; l4=4;
l5=4.1; l6=4 ;
V
,
I
I
f
=
I
1
+
I
2
+
I
3
Determination of
x
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Simplified met
h
od f
o
r si
ngle l
i
ne to
grou
nd-Fault location
in
electrical power …
(Mu
s
taph
a Za
h
r
i)
22
6
Tab
l
e 2
.
Differen
t
lo
ad
d
i
stribu
tio
ns
balanced loads
Bus
Load
(KVA) Bus
Load
(KVA)
1
15
4 15
2
15
5 15
3
15
6 15
load at the lef
t
end
Bus
Load
(KVA) Bus
Load
(KVA)
1 89,
5
4
0,
1
2
0,
1 5 0,
1
3
0,
1 6 0,
1
load at the right en
d
Bus
Load
(KVA) Bus
Load
(KVA)
1
0,
1 4 0,
1
2
0,
1 5 0,
1
3 0,
1
6
89,
5
4.
2.
Results
4.
2.
1.
Perfor
mances
Comparison
The
pr
op
ose
d
al
go
ri
t
h
m
i
s
ext
e
nsi
v
el
y
t
e
st
ed
in
co
mp
ariso
n
with
th
e conv
en
tion
a
l iterativ
e
alg
o
rith
m
to
verify th
e effect
o
f
th
e fau
lt lo
catio
n
(n
ear
o
r
far fro
m
th
e e
n
tran
ce sectio
n), th
e fau
lt resistan
ce
and
l
o
a
d
di
st
ri
but
i
o
n
o
n
t
h
e
p
e
rf
orm
a
nce o
f
t
h
i
s
m
e
t
hod.
The pe
rf
orm
a
nces of
fa
ul
t
l
o
ca
tion algori
thm
are us
ually
m
easur
ed by the errors
on the
fa
ult
distance:
l
estimated
x
actual
x
err
)
(
)
(
(%)
(1
2)
W
h
er
e
x(estimated)
:
estimated fault distance (in
me
ters)
;
x(
actual)
:
real
fault dist
ance
(
i
n meters)
;
l : tot
a
l line lengt
h (in
meters)
.
Fig
u
res
5
,
6
an
d 7
illu
st
rate
so
m
e
o
b
t
ain
e
d test resu
lts,
fo
r
Sing
le Lin
e
to
Gro
und
fau
ltswith
R
f
=
10
Ω
. T
h
e
obt
a
i
ned
res
u
l
t
s
sh
ow
a c
o
m
p
ari
s
on
bet
w
een
t
w
o
c
u
rves, the
first presents
t
h
e errors
on the
fault
distance usi
ng
the classical iterative algorithm
.
The seco
nd tracks the errors on fa
ul
t
di
st
ance usi
n
g t
h
e new
redu
ced
algo
rit
h
m
(with
ou
t iteratio
n
s
).
Fr
om
Fi
gure
5, i
t
can be
o
b
ser
v
e
d
t
h
at
f
o
r t
h
e l
o
ad
di
stribution at the left end, the curves are
,
ap
pro
x
i
m
a
tel
y
, th
e sam
e
, wh
ich
m
ean
s bo
th
algorithm
s
have the sam
e
perform
ances.
As seen
on Fi
gu
re 6 an
d 7
,
t
h
e erro
rs o
b
t
ai
ned by
t
h
e pr
o
pose
d
al
g
o
r
i
t
h
m
are bet
t
er t
h
ant
hose
obt
ai
ne
d usi
n
g
t
h
e
co
n
v
ent
i
on
al
one
.
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
. 2, A
p
ri
l
20
15
:
22
1 – 2
3
0
22
7
Fi
gu
re
5.
Er
ro
r
o
n
faul
t
di
st
an
ce f
o
r a
l
o
a
d
di
st
ri
but
i
o
n at
t
h
e l
e
ft
en
d
Fi
gu
re
6.
Er
ro
r
o
n
faul
t
di
st
an
ce f
o
r a
l
o
a
d
di
st
ri
but
i
o
n at
t
h
e ri
g
h
t
e
n
d
Fi
gu
re
7.
Er
ro
r
o
n
faul
t
di
st
an
ce f
o
r a
B
a
l
a
nc
ed l
o
a
d
s
0
0.001
0.002
0.003
0.004
0.005
0
0.5
1.5
2
2.4
3.4
4.4
5.4
6.4
7.4
8.4
9.4
10.4
11.4
12.4
13.4
14.4
15.4
16.4
17.4
18.5
19.5
20.5
21.5
22.5
error
(%)
fault
distance(km)
err
o
r(%)
on
fa
u
l
t
dis
t
ance,
load
dis
t
ribution
at
the
le
ft
end
Proposed
Algorithm
Iterative
Algorithm
0
0.01
0.02
0.03
0.04
0
0.5
1.5
2
2.4
3.4
4.4
5.4
6.4
7.4
8.4
9.4
10.4
11.4
12.4
13.4
14.4
15.4
16.4
17.4
18.5
19.5
20.5
21.5
22.5
error
(%)
fault
distance
(km)
err
o
r(%)
on
fa
u
l
t
dis
t
ance,
load
dis
t
ribution
at
the
righ
t
end
Proposed
Algorithm
Iterative
Algorithm
0
0.005
0.01
0.015
0
0.5
1.5
2
2.4
3.4
4.4
5.4
6.4
7.4
8.4
9.4
10.4
11.4
12.4
13.4
14.4
15.4
16.4
17.4
18.5
19.5
20.5
21.5
22.5
error
(%)
Fault
distance(km)
err
o
r
(%)
on
fa
u
l
t
dis
t
ance,
Balanced
loads
Proposed
Algorithm
Iterative
Algorithm
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Simplified met
h
od f
o
r si
ngle l
i
ne to
grou
nd-Fault location
in
electrical power …
(Mu
s
taph
a Za
h
r
i)
22
8
4.
2.
2.
Com
p
u
t
a
t
i
o
n
a
l
C
h
ar
ge
C
o
mpari
s
on
In
com
put
er
s
c
i
e
nce, t
h
e
a
n
a
l
y
s
i
s
of al
g
o
r
i
t
h
m
s
i
s
t
h
e de
t
e
rm
i
n
at
i
on
of
t
h
e am
ount
o
f
res
o
urce
s
(suc
h a
s
tim
e a
n
d storage
)
ne
cessary to
exec
ute them
.
Both cha
r
acteristics can be
eval
uated
by e
x
am
ining t
h
e
structure
of the
algorithm
.
A give
n com
puter will take a
discrete am
ount of ti
m
e
to
execute each
of th
e instructions i
n
volve
d
wi
t
h
ca
rry
i
n
g
out
t
h
i
s
al
g
o
ri
t
h
m
.
The spec
i
f
i
c
am
ount
o
f
t
i
m
e
t
o
carry
o
u
t
a
gi
ve
n i
n
st
r
u
ct
i
o
n
wi
l
l
va
ry
depe
n
d
i
n
g o
n
whi
c
h i
n
st
r
u
ct
i
on i
s
bei
n
g e
x
ecut
e
d a
n
d w
h
i
c
h com
put
er i
s
execut
i
ng i
t
,
b
u
t
o
n
a c
o
n
v
e
n
t
i
onal
com
puter, this
am
ount will be
determ
in
istic.
Say that the
actions carried
out in step
1 are c
onsi
d
ered t
o
consum
e tim
e
T
1
, step 2 use
s
tim
e
T
2
, an
d so fo
r
t
h.
In the classica
l iterative algorithm
above, s
t
eps
1
will onl
y be run once
and its m
a
y cons
um
e T
1
ti
m
e
.
Th
e
l
o
op
i
n
step
s
2
,
3
,
4
,
5
,
6
an
d
7
is trick
i
er to ev
al
u
a
te. Th
e inn
e
r i
n
stru
ction
s
o
f
t
h
e loop
will
execut
e
n t
i
m
e
s for eac
h i
n
st
ruct
i
o
n (
w
i
t
h
n
i
s
t
h
e num
ber of i
t
e
rat
i
ons
),
whe
r
e n
vari
es
bet
w
een
1 an
d i
>
1
depe
n
d
i
n
g
on
t
h
e c
o
n
v
e
r
ge
nc
e o
f
x, t
h
e t
i
m
e co
ns
um
ed i
n
t
h
e l
o
o
p
i
s
t
h
en:
7
6
5
4
3
2
.
T
T
T
T
T
T
n
(1
3)
The test in
step
8 c
o
ns
um
es T
8
tim
e
, and t
h
e s
t
ep 9 exec
utes
T
9
ti
m
e
.
Altoget
h
er, the total ti
m
e
requ
ired t
o
run the
algorithm
is:
9
8
7
6
5
4
3
2
1
.
T
T
T
T
T
T
T
T
n
T
T
classical
(1
4)
In t
h
e
othe
r
ha
nd
, the
sim
p
lif
ied alg
o
rithm
con
s
um
es 3 st
eps
with T
1
, T
2
and T
3
tim
es
without any
loops
or tests, t
h
e total tim
es
of this al
gorithm
is then:
3
2
1
T
T
T
T
simplified
(1
5)
Table 3.
T
o
tal excusion
tim
e
com
p
arison
T
o
tal tim
e
iter
a
tif algor
ith
m
Pr
oposed algor
ith
m
Best scenario (n=1
)
9 unit
of tim
e
3 unit of tim
e
Wo
rst scen
a
r
io
(n
=
i
>1
)
(3
+6
. i)
unit of tim
e
3 unit of tim
e
In analyzing the com
p
lexity conpari
so
n i
n
table3,
It ca
n
be see
n
t
h
at,
with a t
h
ird
c
o
m
putational
com
p
lexity, the proposed al
go
rithm
allows not
only to
o
b
t
ain th
e perf
or
m
a
n
ces
of the classical iterative
algorithm
of fault location
but
also t
o
im
prov
e them
for
som
e
load
distri
b
u
tions
.
5.
CO
NCL
USI
O
N
This pa
per
pr
o
pos
es an
d disc
usses a sim
p
lif
ied
m
e
t
hod f
o
r
single line to gr
o
u
n
d
fa
ult location,
usin
g
the se
ndi
ng
-en
d
c
u
r
r
ents
an
d
voltage
s, a
n
d
n
e
two
r
k
pa
ram
e
ters.
Furt
herm
ore, t
h
e p
r
o
p
o
se
d algo
rith
m
allows, with a low com
putati
onal charge (with a
non-iterative
procedure), the fault location not onl
y with the sam
e
perform
ances of
the conventional iterative algorithm
,
but als
o
better
fo
r s
o
m
e
distributio
n l
o
ad
s.
The
perform
a
nces of t
h
is algorith
m
are veri
fied
by seve
ral tests sim
u
latin
g 26 cases
of s
i
ngle phas
e
to g
r
o
u
nd
fault
s
fo
r di
ffe
rent
load
distrib
u
tions
, u
s
in
g real
un
de
r-
gr
o
u
n
d
distrib
u
tion fe
eder data
an
d M
a
tlab
as an analysis t
ool.
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5, pp
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.
BIOGRAP
HI
ES OF
AUTH
ORS
Za
hr
i
M
u
st
a
p
h
a
was born in
Agadir, Morocco on August 1,
1969; He r
e
ceiv
ed th
e electrical
engineering d
e
g
r
ee
in 1993
fr
om Superior Na
tion
a
l Schoo
l
of electr
i
city
and mechanics
(ENS
EM
), Cas
a
blan
ca
, M
o
rocco.He is
curr
e
n
tl
y
purs
u
ing t
h
e P
h
.D. degre
e
in el
ectr
i
c
a
l
engine
eringa
t th
e Universit
y
lbn
Totail
, Facul
t
y
des Sciences, D
e
partment
of Physics
,
Kénitra
,
M
o
rocco; and
h
e
is
at
the s
a
m
e
tim
e the h
ead o
f
the e
l
e
c
tri
c
it
y
d
e
partm
e
nt
in th
e
ele
c
tri
c
i
t
y
and
water d
i
stribut
io
n com
p
an
y
in K
e
nitr
a (RAK).
His
res
earch int
e
res
t
s
includ
e the dete
ction an
d fault loca
tion
,
rem
o
te contro
l sy
st
em
s and
protection of
electrical
distribu
tion networks
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Simplified met
h
od f
o
r si
ngle l
i
ne to
grou
nd-Fault location
in
electrical power …
(Mu
s
taph
a Za
h
r
i)
23
0
Men
ch
afou
You
s
s
e
f
was born in Skoura, Bou
l
emane, Moro
cco, on April 6
,
199
0. He r
e
ceived
the el
ec
tronics
a
nd Tel
ecom
m
unica
tion eng
i
neer
i
ng degree
in 201
3, from
the fa
cul
t
y
of S
c
ien
ces
and Technics (FST), Sidi M
ohamed Ibn Abdullah Univ
ersity, Fez, Morocco
, where h
e
is
currently
pursuing the Ph.D. deg
r
ee in electr
ical engineering.
His resear
ch in
te
rests inc
l
ude
fau
lt d
e
te
ctio
n
and
location, and d
i
stributed
generatio
n
Hassane
El mar
khi
was born
in Morrocco on 1971. He received th
e Engin
eer degr
ee in
electri
cal
engin
e
ering from
HassanIIUniversit
y
,
Casablan
ca in 1
995. He receiv
e
d
his Habilit
at
ion
degree
in signal processing fo
r
wireless communications from
Sidi Mohamed Ben Abdellah
University
, Fez in 2007. He is currently
a profes
s
o
r in the Department of Electr
i
cal Engin
eering
with S
c
ienc
e an
d Techni
ca
l F
a
c
u
lt
y, F
ez (M
oro
cco). His
m
a
in r
e
s
earch
inter
e
s
t
s
include s
m
art
grid, f
a
ul
t lo
ca
ti
on, and
ren
e
wab
l
e
energ
y
s
y
s
t
em
s
.
M
o
hame
d Habibi
was born in 1957 in Khémisset in Moro
cco. He r
e
ceiv
ed his Thesis
d’Univers
ité
de
3° C
y
cl
e (E
le
ctr
onics
) from
the
Université
of Sc
ienc
es
and Tech
niques, Lille
Flandres Artois, France,
in 1985
and the State d
o
ctoral thesis (Electronics) from the Univers
ity
Mohammed V,
Ecole Mohammadia d’lng
é
nieur
s
,
Rabat, Morocco, in 1993. He
was member of
the Labor
atoir
e
d’Electronique et Communicati
ons since 198
9 at the
‘E
cole
Mohamm
adia
d’lngénieurs’, R
a
bat. He was
responsible of the Laborato
i
re
d’
Automatique et
de Micro-ondes
(LAM
O) and pres
entl
y he
is
m
e
m
b
er of the Lab
o
ratoir
e des
S
y
s
t
èm
es
de Tél
éco
m
m
unications
et
Ingénier
ie de la
Décision (LASTID) since 2005. He
is Professor
of Electrical En
gineer
ing at the
Univers
ité lbn T
o
tail
, F
acul
t
é de
s
S
c
iences
, Dép
a
rtem
ent de P
h
ys
ique, Kénitr
a,
M
o
rocco s
i
nce
1985. He is wor
k
ing on
applications of microwav
es.
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