TELKOM
NIKA
, Vol.12, No
.2, June 20
14
, pp. 297~3
0
4
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i2.2032
297
Re
cei
v
ed Fe
brua
ry 3, 201
4; Revi
se
d March 29, 201
4
;
Accepte
d
April 12, 201
4
Travelin
g-Wave-Based Fault Location in Electrical
Distribution Systems with Digital Simulations
Jinrui Tang*,
Xianggen Yin, Zhe Zhan
g
State Ke
y
L
a
b
o
rator
y
of Adva
nced El
ectrom
agn
etic
Eng
i
ne
erin
g and T
e
ch
nol
og
y (Hu
a
zh
ong U
n
ivers
i
t
y
of
Scienc
e an
d T
e
chn
o
lo
g
y
)
Luo
yu
Ro
ad 10
37, W
uhan
430
074, Hu
be
i Pro
v
ince, Ch
ina
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: tangji
n
rui
@
h
u
st.edu.cn
A
b
st
r
a
ct
Traveling-wav
e
-bas
ed fault location in
elec
trical distribution system
s is an
i
m
porta
nt sa
feguar
d
for the distrib
u
tion n
e
tw
ork rel
i
abi
lity. T
he effectiven
ess of
the
meth
ods is
verifie
d
directly
in pow
er gri
d
i
n
the early sta
g
e
s, w
h
ile differ
ent fault types
can'
t
appe
ar i
n
a short time
. And nor
ma
l dyna
mic physi
cal
simulati
on ca
n
not meet the t
each
i
ng
de
ma
nd eith
er bec
a
u
se of the li
mitation of trans
miss
ion
lin
e mode
l
and oth
e
r facto
r
s. So PSCAD/EMT
DC and M
A
T
L
AB are us
ed
to ill
ustrate the the fault lo
cation
meth
ods
in
this pap
er, which ca
n pro
m
ote th
e travelin
g-w
a
ve-b
as
ed fault-l
o
cati
on techn
o
l
ogy
. Meanw
hile,
th
e
traveli
ng-w
a
ve-
base
d
fault-l
o
c
a
tion
meth
od b
a
sed o
n
c
har
a
c
teristic freque
ncies is a
naly
z
ed in this p
a
p
e
r
.
Ke
y
w
ords
: characteristic frequency, fault locati
on, trans
mi
ssion li
ne
mo
d
e
l, traveli
ng w
a
ve
1. Introduc
tion
Fault lo
catio
n
in th
e ele
c
trical
dist
ribut
i
on
system
s
(EDSs) i
s
ve
ry impo
rtant
for the
se
cure and
st
able op
eratio
n [1]. In the past de
cad
e
, fault locatio
n
in EDSs h
a
s
been exten
s
i
v
ely
investigate
d
and several
appro
a
che
s
have been
propo
se
d, whi
c
h in
clud
es faulty feede
r
identificatio
n [2], fault se
ction lo
cation [
3
] and f
ault p
o
sition lo
catio
n
[1]. With the
developm
ent
of
sma
r
t distrib
u
t
ion grid
s, fault location be
comes m
o
re a
nd more impo
rtant.
The propo
se
d fault locatio
n
method
s can be
group
e
d
into two ca
tegorie
s: 1)
method
s
based on th
e
impeda
nce
measurement
[4]-[7]; 2)
method
s ba
se
d on the traveling waves [
8
]-
[12].
Travelin
g-wa
ve-ba
s
ed
fau
l
t-locatio
n
me
t
hods (T
WFL
M
s) have th
e
advanta
ges
of less
influen
ce
by saturation ch
ara
c
teri
stic
of
cu
rrent
transformer, fault res
i
s
t
anc
e
, fault type and the
operating mo
de of system,
so t
hey have been
su
cce
ssfully ap
plie
d into tran
sm
issi
on net
works
[13]. Ho
weve
r, they
can
h
a
rdly
be
appli
ed into
EDS
s
be
cau
s
e
the
feeders u
s
ual
ly inclu
d
e
ma
ny
laterals
.
Camp
ari
ng
with the wid
e
i
n
vestigatio
n
of
TWF
L
Ms,
test tech
nolo
g
y of travelin
g-wave
fault location
falls behi
nd o
b
viously. Earl
y verificati
on
of traveling-wave fault-lo
ca
tion techn
o
lo
gy
is difficult to
o
perate
di
re
ctly in po
we
r
gri
d
, whil
e diffe
rent fault type
s
can
'
t ap
pea
r in
a
sh
ort ti
me
[14]. At
the same time, normal dynami
c
physi
ca
l sim
u
lation ca
n't meet the test demand b
e
cau
s
e
of the limitati
on of t
r
an
smi
ssi
on
li
ne m
o
del a
nd
other
factors [1
5].
T
herefo
r
e, th
e
o
retical
re
sea
r
ch
and eq
uipm
ent develop
ment of traveling-wave
f
ault locatio
n
seri
ou
sly depen
d on di
gital
s
i
mulation [16].
To overcome
the problem
s, PSCAD/EMTDC,
whi
c
h
is widely used in electro
m
agneti
c
transi
ent si
m
u
lation
s [16]-[
17], and Matl
ab are u
s
ed t
o
study the T
W
FLM
s
. Me
a
n
whil
e, a nov
el
fault location
method b
a
sed on
cha
r
a
c
teri
stic fr
eq
uen
cie
s
of the re
corded t
r
ansi
ent wave
is
prop
osed.
2. Rev
i
e
w
o
f
Trav
eing-
w
a
v
e
-based Fa
ult-loca
t
ion
Metho
d
s
Gene
rally, T
W
FLM
s
ca
n
be g
r
ou
ped
i
n
to the follo
wing
main
categori
e
s:
1) method
s
based on wa
ve-front
i
dent
ification (si
n
g
l
e-en
ded
alg
o
rithm [1
8], two-end
ed
al
gorithm
[19]
and
netwo
rk-b
ase
d
algo
rithm
[20]); 2) alg
o
rithm
s
ba
sed on
cha
r
a
c
teri
stic fre
q
uen
cie
s
of the
recorded trav
eling wave [10]-[12].
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 2, June 20
14: 297 – 30
4
298
In this
pape
r,
take
the fault
-
location
met
hod
s b
a
se
d o
n
characte
ri
stic fre
que
nci
e
s a
s
an
example, PSCAD/EMT
DC and MATLA
B
are used to
sho
w
the effectivene
ss of the method
s.
Whe
n
the
en
d of th
e tra
n
s
missio
n lin
e
is set
a
s
th
e sta
r
ting
poi
nt of the
cal
c
ulatio
n
distan
ce
x
, the voltage ca
n
be rep
r
e
s
ent
ed in the time domain by [21]
0
0
2c
o
s
(
)
2c
o
s
(
)
x
x
uU
e
t
x
Ue
t
x
u
u
(1)
u
+
denote
s
the inci
dent
wave an
d u
-
represents t
he refle
c
ted
wave. Assu
ming the
impeda
nce o
f
the load equal
s Z
2
, the reflection
co
efficient at the end (
x
=0)
for the voltage
traveling wave is
02
2
0
c
c
UZ
Z
Z
Z
U
(2)
As sho
w
n in
Figure 1, Ref. [10] propo
se
d the
princi
pl
e of the characteri
stic freq
uen
cie
s
.
If the measu
r
i
ng poi
nt is pl
ace
d
at bu
s
A and the th
ree-p
h
a
s
e
sho
r
t-ci
rcuit fault occurs at mi
d
d
le
of line DF, the traveling
wave w
ill propagate back
an
d forth in the
paths A
-
B, A-B-D, A-B-C, A-B-
D-E and A-B-D-
f
(
f
is the fault point). S
o
t
he charact
e
risti
c
fr
equencies will
exis
t in the recorded
transi
ent sig
n
a
l at bus A an
d can b
e
cal
c
ulated by
,
i
pi
p
p
f
nL
(3)
Whe
r
e:
υ
i
d
enote
s
the
velocity of the
i
-mode
traveling
wav;
L
P
r
e
pr
es
en
ts
the
prop
agatio
n l
ength of th
e
path
P
a
nd n
p
depe
nds on
the reflectio
n
co
efficient
s at both
end
s of
the path. If t
he p
o
laritie
s
of the
reflecti
on coeffici
ent
s
at both end
s
a
r
e
th
e sa
me,
n
p
e
qual
s 2.
Otherwise n
p
equal
s 4.
r
Loa
d
AB
C
D
E
F
L1=3km
L2=2km
L5
=
2
k
m
L4=1km
L3=3km
Lo
ad
Loa
d
f
Figure 1. One
typical distrib
u
tion system
Once the fre
quen
cie
s
of the re
co
rded
transi
ent sig
n
a
l are ide
n
tified, the fault positio
n
can b
e
locate
d based on e
quation (3).
3. Transm
iss
i
on Line Model in PSCAD/EMTD
C
The follo
wing
transmi
ssion
line model
s have been
provide
d
in simulation
softwares:
multiple
Π
o
r
T line model,
Berge
r
on lin
e
model and freque
ncy-dep
ende
nt line model.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Tra
v
elin
g-Wa
ve-B
ased Fa
ult Locatio
n in Electri
c
al Di
stributio
n System
..... (Jinru
i Tang)
299
3.1. Multiple
Π
or T Line Model
The pri
n
ci
ple
of distribute
d
para
m
eter
circ
uit should
be use
d
to analyze the travelin
g
wave
propag
ation in
tra
n
smissi
on
line.
As
sho
w
n
in
Figure 2,
mul
t
iple
Π
o
r
T
li
ne m
odel
is u
s
e
d
and a short ci
rcuit fault hap
pend
s at the end.
Figure 2. Multiple
Π
o
r
T lin
e model
Assu
me
equi
valent indu
ct
ance of the
system is
zero
, from the
an
alysis in [15],
multiple
Π
line
mod
e
l
and m
u
ltiple
T line mo
del
have the
sam
e
differe
nce e
quation, the v
o
ltage at the
p
th
chai
n of the line is a
s
follo
ws:
=1
1
(t
)=U(
1
-
-
c
ot
si
n
c
o
s
)
2
n
pk
k
pk
k
p
ut
nn
n
n
(4)
whe
r
e:
2
=s
i
n
2
k
k
n
LC
.
The e
quatio
n
(4
)
sho
w
s th
at: 1) o
s
cillati
on
would
ha
p
pend
in the
chain
network; 2) th
ere
exists
n
o
sci
llating angul
ar freq
uen
cie
s
whi
c
h eq
u
a
ls the num
ber of the chain
s
.
In digital
simulatio
n
or dynamic p
h
ysical sim
u
lation, numb
e
r
o
f
the chain
s
can't b
e
infini
te. Then it ca
n't
simulate th
e traveling
wav
e
front accu
rately and c
a
n
'
t meet the test dema
nd of
the fault loca
tion
alogrith
m
ba
sed on wave-front ident
ificati
on as
sho
w
n i
n
Figure 3.
Whe
n
n
a
p
p
r
oa
che
s
to i
n
finity, equation (5)
can
be de
rived
a
nd it is th
e
basi
s
of
cha
r
a
c
teri
stic-freq
uen
cy fault-location al
ogrithm.
0
2
=[
l
i
m
(
si
n
)]/
2
=
2
2*
*
n
kk
f
n
LC
l
L
C
(5)
Thus sim
u
lati
on result
s of
multiple
Π
o
r
T line
mod
e
l ca
n’t de
scribe the
a
c
tu
al wave
-
front cha
r
a
c
t
e
risti
cs a
nd
cha
r
a
c
teri
stic frequen
cy
o
f
traveling wave becau
se
of the limited
numbe
r of the chai
ns.
(a) T
r
avelin
g wave in Jm
arti line model
[16]
(b)
"Tra
veling wave" i
n
multiple T line model
Figure 3. Co
mpari
s
io
n of simulatio
n
re
sults b
e
twe
e
n
Jmarti an
d m
u
ltiple T line model
0.
1
0
1
0
.
10
15
0.
1
0
2
0
.
10
25
0.
1
0
3
0.
1
035
-60
0
-40
0
-20
0
0
T
i
m
e
t/s
V
o
l
t
ag
e U
/
k
V
0.
1
0
1
0
.
10
15
0.
1
0
2
0
.
10
25
0.
1
0
3
0.
1
035
-80
0
-60
0
-40
0
-20
0
0
20
0
T
i
m
e
t/s
Vo
l
t
a
g
e
U/
k
V
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 2, June 20
14: 297 – 30
4
300
3.2. Berger
o
n
Line Model
Assu
me p
a
ra
meters of th
e co
ndu
cto
r
are
i
nde
pend
ent of fre
que
ncy, Bergero
n
mod
e
l
can b
e
used for tran
sie
n
t cal
c
ulatio
n for loss
le
ss tra
n
smi
ssi
on lin
e as sho
w
n in Figure 4. When
line loss is t
a
ke
n into a
c
cou
n
t, the total system resi
stan
ce ca
n be eq
uivalent to lumpe
d
para
m
eter
( 1
/
2 in the middle of the line and 1/4 at ea
ch en
d).
Actually para
m
eters are a
ffected by freque
nc
y due
to skin effect and it is the mai
n
reason
of traveling-wave
dispersion. T
he disp
ersion will be more obvious
i
n
zero-mode wave
.
For a th
re
e-p
hase tran
smi
ssi
on lin
e, co
mpari
s
io
n
of
the sim
u
latio
n
re
sult
s bet
wee
n
Bergeron
model a
nd
Jmarti mod
e
l i
n
whi
c
h di
sp
ersi
on i
s
con
s
ide
r
ed i
s
sh
own i
n
Figu
re 5 when a
single
pha
se-to
-
g
r
o
und fault hap
pend
s.
From
the
ana
lysis
mention
ed a
bove, Be
rge
r
on
line
m
odel
ca
n't me
et the te
st d
e
mand
of
the fault lo
ca
tion alo
g
rithm
ba
sed
on
wave-fro
nt ide
n
tification
be
cau
s
e
it ign
o
res the
travel
ing-
wave di
sp
ersion. But trave
ling-wave p
r
o
pagatio
n wou
l
d be
simulat
ed a
c
curately
whe
n
the
ski
n
effect can be
omitted. Because the freq
uen
cy
of the
comp
omn
ent
used in fault
location alo
g
r
i-
thm base
d
o
n
cha
r
a
c
teri
st
ic frequ
en
cy is usua
lly low and the alogrithm do
esn
'
t
need to recog-
nize
wave fronts [10]-[13]
, the
dispersi
on ha
s little
affection on t
h
is algo
rithm.
Thus Bergeron
can
be u
s
e
d
to test the f
ault location
algorith
m
ba
sed
on
cha
r
acteri
stic fre
quen
cy to so
me
extent.
Figure 4. Bergero
n
line mo
del
(a) T
r
avelin
g wave in Jm
arti line model
(b) Tra
v
eling wave i
n
Berge
r
on li
ne model
Figure 5. Co
mpari
s
io
n of simulatio
n
re
sults b
e
twe
e
n
Jmarti an
d Berge
r
o
n
line
model
3.3. Frequen
c
y
-
depende
nt Line Mod
e
l
Whe
n
p
a
ra
m
e
ters of th
e
condu
ctor vary
wi
th f
r
eq
uen
cy, the traveli
ng
wave
prop
agation
must be
cal
c
ulated in fre
q
uen
cy domai
n while the
el
ectro
m
ag
neti
c
tran
sie
n
t ca
lculatio
n is e
a
sy
to ca
rry out i
n
time dom
ai
n. To solve this p
r
obl
em,
one meth
od i
s
to utilize F
ourie
r tra
n
sfo
r
m,
anothe
r met
hod i
s
to treat the
cha
r
acteri
stic
im
peda
nce an
d
pro
pagatio
n
coeffici
ent
with
approximatio
n by rational functio
n
ba
se
d on Bode di
agra
m
[22] and etc.
The cu
rrent o
n
both sid
e
s
of transmi
ssi
on line
k
-
m
is
as
follows
:
0
.
099
0.
0995
0.
1
0.
1005
0.
1
0
1
0
.
101
5
0.
10
2
0.
1025
-4
0
0
-3
0
0
-2
0
0
-1
0
0
0
10
0
Ti
m
e
t
/
s
Z
e
r
o
-
m
o
d
e v
o
l
t
ag
e U/
k
V
0.
09
9
0.
09
95
0.
1
0.
10
05
0.
10
1
0
.
10
15
0.
10
2
0.
10
25
-30
0
-20
0
-10
0
0
10
0
20
0
T
i
m
e
t/s
Z
e
r
o
-m
od
e
vol
t
a
g
e
U
/
kV
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Tra
v
elin
g-Wa
ve-B
ased Fa
ult Locatio
n in Electri
c
al Di
stributio
n System
..... (Jinru
i Tang)
301
2
1
()
2
1
()
k
kk
h
c
m
mm
h
c
m
kh
m
c
m
cc
k
mh
k
c
k
cc
U
II
Z
U
II
Z
F
I
UZ
I
A
A
ZZ
F
I
UZ
I
A
A
ZZ
(6)
Whe
r
e:
I
k
,
U
k
–
cu
rrent an
d voltage on
the
k
side;
I
m
,
U
m
–
curre
n
t and voltage o
n
the
m
side;
Z
c
–
cha
r
acte
ri
stic im
peda
nce
;
A
–
pro
pag
ation coeffici
ent
,
Z
Yl
Ae
,
l
–
le
ngth of the line
k
-
m
.
The line mo
del pro
p
o
s
ed
in [22] is the kn
o
w
n
Jm
arti line mod
e
l. In the paper two
rational fun
c
ti
ons a
r
e utilized to simulat
e
Z
c
(
ω
) an
d
A
(
ω
). The p
r
i
n
cipl
e of this method is to
use
analo
g
filterin
g technol
ogy to ide
n
tify freque
nc
y-dep
ende
nt pa
ra
meters in
fact. Based
on t
h
i
s
method, Jm
arti line model is the co
mmo
n model
u
s
ed
in traveling-wave fault location.
4. Analy
ses
of the
Char
a
c
teris
t
ic Fre
quencie
s
Whe
n
the EDS ope
rates normally an
d an impul
se signal i
s
injecte
d
at bus A, the
cha
r
a
c
teri
stic frequ
en
cie
s
of
the
re
corded tran
sient
sign
al at
bu
s A a
r
e
call
ed the i
nhe
rent
cha
r
a
c
teri
stic frequen
cie
s
of the system
.
Table 1. Inhe
rent ch
aracte
ristic frequ
en
cie
s
of the EDS sho
w
e
d
in Figure 1
Propaga
tio
n
pa
t
h
Leng
th of the pr
opag
a
ti
on
lengt
h (
k
m)
inhere
nt c
h
arac
teristic
freq
uen
c
ies
(kHz
)
A-B 4*3
25.00
A-B-C
2*4
37.50
A-B-D
4*5
15.00
A-B-D-
F
2*8
18.75
A-B-D-E
2*7
21.43
Take
the
di
stribution
sy
ste
m
sho
w
n i
n
Fi
gure 1
a
s
an exa
m
ple,
and th
en th
e
inhe
rent
cha
r
a
c
teri
stic frequen
cie
s
can b
e
cal
c
ul
ated and
sho
w
n in Tabl
e 1
.
Whe
n
a fault
occurs i
n
the
electri
c
al
dist
ri
bution
syste
m
, the freq
ue
ncie
s of the
reco
rde
d
signal at bus A will be diff
enrent from
the inher
ent characteristi
c
f
r
equen
cies.
Take the faul
t a
t
the middle
of
line DF
shown in Fig
u
re
1
as a
n
ex
am
ple, the re
co
rd
ed tra
n
sie
n
t signal at b
u
s A
is
s
h
ow
n
in
F
i
gu
r
e
6
.
The
whol
e
wind
ow
of d
a
ta, whi
c
h i
s
an
al
yze
d
by Fast F
o
u
r
ier t
r
an
sform (FFT
),
contai
ned 1m
s of pre-fa
ult and 1m
s of post-fault dat
a,
and the resu
lts corre
s
po
n
d
ing to the fault
at middle of li
ne DF
are
sh
own in
Figu
re
7. T
hen the
chara
c
te
risti
c
frequ
en
cie
s
of
10.74 kHz a
nd
24.41
kHz ca
n be foun
ded
. But in theory, the char
acteristic f
r
eq
ue
ncie
s
can b
e
cal
c
ulated
a
s
follows: 25.0
0
kHz, 1
5
.00
kHz, 37.5
0
kHz, 2
1
.43
kH
z an
d 11.
5
4
kH
z.
S
o
t
he
big erro
r exists in
the extraction
of frequen
cie
s
, as same
a
s
the re
sult
s mentione
d in [10]-[12].
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ISSN: 16
93-6
930
TELKOM
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Vol. 12, No. 2, June 20
14: 297 – 30
4
302
Figure 6. The
reco
rd
ed tra
n
sie
n
t sign
al at bus A sh
o
w
n in Figu
re
1
Figure 7. Fre
quen
cie
s
of the re
co
rde
d
signal at
bu
s A associ
ated to the fault at
middle of BC
5. A Nov
e
l F
a
ult Loca
t
io
n Method
Ba
sed on Ch
ar
acte
r
istic Fr
equen
c
ies
A novel fault-location met
hod ba
se
d o
n
cha
r
a
c
teri
stic frequ
en
ci
es can b
e
propo
sed.
Firstly, FFT
i
s
u
s
e
d
to
extract th
e fre
q
uen
cie
s
of th
e re
co
rd
ed
signal. Se
con
d
ly, the whol
e
freque
ncy is
divied to several sub
-
freq
uen
cy band
s,
and ea
ch su
b-fre
que
ncy
band
contain
one
of the inhere
n
t characeri
s
tics freq
uen
cies. Thir
dly,
the energy value
s
of the sub-f
r
equ
en
cy
band
s
can
b
e
cal
c
ul
ated
and n
o
rm
alized. Fou
r
thly
, the en
ergy
values
co
rre
s
po
ndin
g
to
the
typical fault
positio
ns can
be
obtain
e
d
in a
d
van
c
e.
Finally, on
e
a fault
occu
rs, th
e follo
wing
equatio
n ca
n use
d
to identi
f
y the fault po
sition.
2
1
mi
n
(
)
,
n
if
ij
j
i
EE
j
V
(7)
Whe
r
e: V
d
enote
s
the
set of th
e t
y
pical
fa
ult
positio
ns in
the p
r
iori
da
tabase;
j
rep
r
e
s
ent
s the
j
th
typical fault position;
E
if
repre
s
e
n
ts the energy v
a
lue of the
i
th
frequen
cy sub-
freque
ncy ba
nd for the re
al fault; E
ij
repre
s
e
n
ts th
e energy value of the
i
th
frequen
cy sub-
freque
ncy
ba
nd for the j
th
typical
fault p
o
sition
an
d
n
rep
r
e
s
e
n
ts t
he n
u
mbe
r
o
f
the fre
quen
cy
sub
-
fre
que
ncy bands
corre
s
po
ndin
g
to the distri
butio
n system.
0.5
1
1.5
2
2.
5
3
3.5
4
x 1
0
4
0
0.
5
1
1.
5
2
x 1
0
4
F
r
eq
u
e
n
c
y
f
/
(
H
z)
FFT
re
s
u
lts
X
:
1
.
074
e
+
00
4
Y:
1
.
997
e
+
00
4
X
:
2.
44
1e
+
0
0
4
Y:
7
81.
9
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TELKOM
NIKA
ISSN:
1693-6
930
Tra
v
elin
g-Wa
ve-B
ased Fa
ult Locatio
n in Electri
c
al Di
stributio
n System
..... (Jinru
i Tang)
303
6. Conclusio
n
s
Digital
simul
a
tions
are
imp
o
rtant fo
r the
study
of T
W
FLMs in E
D
Ss. Using
th
e Jm
arti
line m
odel
an
d the
alg
o
rith
ms
of digital
sign
al p
r
o
c
e
s
sing
p
r
ovided
in M
a
tlab, th
e T
W
FLM
s
can
be dee
ply discu
s
sed.
Becau
s
e the
fault-gene
ra
ted transi
ent
traveling wave must be
transfe
rre
d throug
h
transmissio
n line,
mutual
i
ndu
ctor and se
con
dary
circuit befo
r
e it i
s
u
s
ed, th
e
modelin
g met
hod
of mutual ind
u
ctor, in
clu
d
i
ng TA mod
e
l, TV
model a
n
d
CVT mo
del
, need to be
discu
s
sed in
the
future paper.
.
Ackn
o
w
l
e
dg
ement
This work wa
s su
ppo
rted b
y
the National
Natural S
c
ie
nce Fo
und
ation of Chin
a (Grant
No. 511
770
5
8
).
Referen
ces
[1]
Jinrui
T
,
Xia
n
g
gen
Y, Z
he Z
,
and
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l
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x
tracti
on
of detecte
d z
e
r
o
-mod
e
w
a
ve
velocit
y
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d
its app
lic
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i
n
sin
g
l
e
p
hase
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ul
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ault Locatio
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ault Originate
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