Energy and Power Engineering, 2013, 5, 1253-1258
doi:10.4236/epe.2013.54B238 Published Online July 2013 (http://www.scirp.org/journal/epe)
Study on Distribution Coefficient of Traction Return
Current in High-Speed Railway
Wen Huang, Zhengyou He, Haitao Hu, Qi Wang
School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China
Received March, 2013
ABSTRACT
The distribution coefficient of return current network is an important method to decrease the rail potential. In order to
resolve the problem of high rail potential in high-speed railway based on EN50122-1 and Pr EN50170 the distribution
coefficient of longitudinal traction return current conductors is calculated through changing the interval of transverse
connection. Based on field data and theoretical analysis, the parameters of longitudinal traction return current conduc-
tors are calculated. Results indicate that the best distance of the transverse connection is 400 m – 600 m.
Keywords: Traction Return Current; Rail Potential; Distribution Coefficient; Interval of Transverse Connection
1. Introduction
Traction return current system consists of the rail, the
protective wire (PW) and the integrated grounding line
(IGL). It plays an important role in traction power supply
system of high-speed railway. The design of the return
current network is critical to keep the safe and reliable
operation of the traction power supply system. With the
popularization of the ballast less track and increase of the
traction current, the vo ltage and th e current of the rail are
increased accordingly. As one of the traction return
channel, the rail is closely related to the safety of the
personnel and equipment. High rail potential will cause
many problems such as step voltage, touch voltage and
the electromagnetic interference with the track circuit [1].
Recently experts had studied on the method which can
reduce the rail potential thoroughly [2-6]. Distribution
co-efficient of the return current network can reflect the
rail potential well. Restrictions on the rail potential are
mainly divided into two kinds at present. One is to set up
IGL to share the rail potential which is widely used in
Germany, France and South Korea. The other uses the
rail voltage limiter in Japan who is the earliest developer
of high-speed railway [7]. The ideas and concrete tech-
nical measures to solve the problem are differed from
country to country. A distributed parameter model of rail
poten-tial under direct feeding system established with
the Matlab/Simulink studied in [8]. It brings in the lo-
como-tive coefficient to fix the peak of rail potential. But
it does not consider the share of rail current by longitu-
dinal traction return current conductors such as the return
line and the IGL in the actual situation. Computational
formula of the grounding resistance of the IGL is de-
duced in [9]. Furthermore, it studied on the distribution
relationship between rail and IGL. However, it didn’t
consider the distribution coefficient of the return line in
direct feeding system or the PW in the AT system. Cur-
rent distribution proportion of the rail, return line and
IGL is summarized in [10], in co mbination with the field
test data of the first b allastless track experimental section
in China. However, it doesn’t analyze appropriate inter-
val of transverse connection systematically.
In China, research on the distribution of longitudinal
return current conductors is differed a lot with the actual
situation because of without considering environment
when the parameters are calculated. Application of the
ballastless track in China is just starting out, and there is
no experience to design the appropriate transverse con-
nection. Therefore, based on the rail, PW and IGL, the
parameters of each wire should be calculated respectively
in this paper. Combining the field test data in China, re-
ferring the related standards in EN50122-1 and prEN-
50170, the optimal design of Chinese high-speed railway
traction return system is studied. The most appropriate
interval of transverse connection is concluded as well.
2. Traction Return Current System
Traction current is supplied to locomotive through the
catenaries by traction substation and returns to traction
substation through return current network, forming a
complete energy cycle system. In China, high-speed rail-
*This work is supported by High-Speed Railway Basic Research Fund
Key Project (U1234203, U1134104).

W. HUANG ET AL.
1254
way mainly adopts AT power supply mode, in order to
study the distribution of return current system, the interval
between each two AT transformers is taken as a study
subject as shown in Figure 1.
Traction return current network contains longitudinal
traction return current conducto rs and transverse connec-
tions. Among longitudinal traction return current con-
ductors, the most important wires are PW, rail, and IGL,
the sectional view of traction network as shown in Fig-
ure 2.
The laying way of PW is overhead and not insulated
with pillar, it not only saves the cost in in sulating aspect,
but also uses the pillar as a good earthling pole. Rail is
both running rail and return current conductor. It can be
considered that rail is a grounding conductor extending
infinitely to both ends. Rail is connected transversely to
PW and IGL through the neutral ground terminal of the
choke transformer. IGL is an equipotent connecting wire
of the integrated grounding system, which is mainly to
make the railway electrical and signal devices ground
intensively and unify the potential, and usually laid below
the ground on both sides of the double-track railway. The
environment of each line in return current network is
different, and the conductor structure and material have
its own characteristic, it must adopt different methods to
calculate the parameters for the PW impedance, rail
apparent impedance and IGL grounding impedance,
respectively. Transverse connections balance the current
distribution of return current system, and further to reduce
the rail potential, while it meets the design requirements
of the integrated grounding system, forming equipotent
Figure 1. Illustration of AT traction network.
Figure 2. Sectional view of traction network.
connecting network to facilitate th e unification of ground,
and traction return channel.
The study on longitudinal return current conductors’
shunt condition still exist a wide gap in actual condition,
which is caused largely by the error of the line parameters
calculation. Therefore, traction return current network
parameters must satisfy the service environment to
calculate.
3. Parameters Calculation of Longitudinal
Return Current Conductors
3.1. Impedance of PW
Short distance power line can be used as equivalent circuit
model of PW which is made up of steel-cored aluminum
strand as one of the longitudinal return current conductors.
Equivalent circuit model of PW is shown in Figure 3.
Steel-cored aluminum strand LGJ-120 can be considered
to be an example which is very common in high-speed
railway in china with equivalent radius and
resistance 7.22
e
rmm
K m0.255 /R

. Under power frequency,
stranded conductor can be equivalent to solid round wire
or tubular round wire by transformation formula. In order
to turn the PW into solid round wire, the radius of round
which have the same area as the stranded conductor with
the current-carrying part are define as equivalent radius
[11]. Because of the use of power frequency alternating
current in attractive power supply system, the skin effect
must be considered. In order to descript the size of the
skin effect quantificational, the concept of penetration
depth should be considered. Penetration depth can be
calculated as
2503.3
r
f





 (1)
where

is the angular frequency,

is the resistivity
of PW,

is permeability which Non ferromagnetic
materials can be deemed to that 7
410(/)
0
H
m 

   .
When return current passed by the PW, skin effect
should be taken into account. The internal impedance of
the PW can be described as
(2 )(2 )
2'( 2)'( 2)
jm berrjbeir
Zrber rjbei r






  (2)
where and are referred as Kelvin-function,
which is one of the Bessel-Function[1 2]
ber bei
Figure 3. Equivalent circuit model of PW.

W. HUANG ET AL. 1255
48
4282
26 10
262102
() 1...
2(2!) 2(4!)
() ...
22(3!)2(5!)
xx
ber x
xx x
bei x
  
 
This expression is too complicated to programmed, so
Semlyen and Deri gave a approximate formula to replace,
and the error is less than 6%[13], which can be described
as
2
PWdc 2
Z
RZ

 (3)
where the physical significance of
Z
 is the impedance
formula that the frequency tend to infinite, it can be de-
rived as (1)2 e
Z
jp r


 . The relationship between
PW impedance and leng th is shown as Figure 5.
Figure 4 shows the change law between impedance
and length of PW which can be approximate it at the
equivalent circuit model of short distance power line.
The impact of conductance and susceptance can be ig-
nored, so the relationship between PW impedance and
length is positive correlation.
3.2. Apparent Impedance of Rail
The monoblock track board of ballastless track which is
made up with armored concrete has been widely used in
high-speed railway. It leads to a serious defective insula-
tion between the rail and earth. Traction current leaks
into the earth continually when it pass by the rail, and it
forms the rail-earth potential when the current passed by
the rail leakage impedance. Rail apparent impedance can
not be determined by the series-parallel model of Soil
ground resistance and rail impedance. Computing method
of rail’s apparent impedance is concluded in 14, which
need to analysis the relationship between rail potential
and current. Figure 5 shows the model of rail distribu-
tion parameters.
The distribution of valid values of the rail current in
steady state is described as
02 4 6 810
0
1
2
3
4
5
resistance
react ance
Figure 4. Relationship between protective wire’s impedance
and length.
0
() 2
r
x
Ie
Ix
 
 (4)
where 0
I
is the current which flow into the rail, and r

is attenuation constant of the rail current, which can be
described as ()(
rrrr )RjLGjC
  
r
According to the rail current distribution function, the
rail potential distribution function can be derived as
.
0
() ()2
r
x
rr
r
Ie
UxRj L




  (5)
According to the rule of rail potential distribution, the
apparent impedance between two points at rail is deduced
as
0
() (0)1
()
rl
rr gr
r
Ul Ue
ZRjLjM
I

 


 (6)
where
g
r
M
is the mutual reactance between rail and
IGL.
Figure 6 illustrates the relationship between rail ap-
parent impedance and length. The rail’s apparent imped-
ance becomes bigger and bigger with the increase of the
length of the rail, and the reactance value plays a main
role. But the impedance tends to steady when the length
increase to 2km. The apparent impedance of rail is only
0.2551 0.8653j

 when the length of rail increases to
10km, which shows that the rail impedance occupy a
little of proportion in traction network.
Figure 5. Equivalent circuit model of rail.
02 4 6 81
0
0
0.2
0.4
0.6
0.8
1
resistance
reacta nce
Figure 6. Relationship between rail’s apparent impedance
and length.

W. HUANG ET AL.
1256
3.3. Grounding Impedance of IGL
Because of the close relationship between IGL and earth,
the impact of soil parameters must be considered when
the impedance is calculated.
Figure 7 shows the distributed parameter model of
IGL. Based on article 9, mutual reactance is considered
in this paper now. It is shown in Figure 7 ,
g
R,
g
L,
g
C
and
g
G are the IGL inherent resistance, inductance,
capacitance and leakage conductance to earth per length,
respectively. The current of IGL can be described as
2
0
2
(,)2 sin
1
ggg
g
xlx
l
eee
ixtI t
e






 (7)
If we only consider the change of conductor’s current
effective value, the current distribution of finite length
earthing conductor is derived as
2
0
2
() 1
ggg
g
xlx
l
eee
I
xI
e





 (8)
where 0
I
is the current of point M, and the attenuation
coefficient of current is is described as
2
'
ln( )
2
gl
aha





(9)
where '

is the resistivity of IGL, and a is the cross
section area of conductor.

is the earth resistivity, and
is the burial depth.
hBecause of the close distance of IGL and rail, the mu-
tual reactance of IGL and rail must be considered. The
potential of IGL is described as
0
0
0
0
()()
()
(1) ()
(1 )
(1 )
(1 )
g
g
r
r
l
Mg g g
l
rgr
l
gg
l
g
lgr
N
N
lr
UIxRjLdx
Ix jMdxU
eRjL
I
e
ejM
I
U
e


























where the mutual reactance can be expressed as
02
=(ln 1
2
gr gr
ll
Md


) ,
Figure 7. Distributed parameter model of IGL.
g
r is the distance between IGL and rail. The grounding
resistance is deduced as
d
0
(1) ()
(1 )
ln( )
(1 )2
+
(1 )
g
g
r
r
M
l
gg
l
g
lgr
lr
U
ZI
eRjL
e
l
ejM ha
l e








 











(10)
Figure 8 gives the component of grounding resistance
decreases rapidly with the increase of the length of IGL.
It’s because of the leak conductance between IGL and
earth. The component of resistance keeps steady when
the length of IGL longer than 1 km. But the component
of reactance becomes bigger and bigger with the increase
of the length. The size of the grounding impedance de-
pends on the value of reactance when the length longer
than 1 km.
4. Distribution Coefficient and Interval of
Transverse Connection
In the longitudinal return current conductor, traction cur-
rent return to traction substation through three accesses
of PW, rail and IGL, the impedance of each conductor
determines the proportion of current in each line which is
distribution coefficient. Longitudinal return current con-
ductors are shown in Figure 9, where
P
W
Z
is the im-
pedance of PW, r
Z
is the impedance of rail and
g
Z
is
the impedance of IGL.
According to the circuit analysis theory, distribution
coefficients of each line are shown in Figure 10.
As seen from Figure 11, with length of PW increasing,
distribution coefficients of PW are decreasing, which is
due to the reason that PW can be seen as a short over-
head transmission line that the conductance and suscep-
tance are negligible, the resistance value increases as the
00.5 11.5 2
0
1
2
3
4
5resistance
reac t ance
Figure 8. Relationship betwe en integranted grounding line ’s
grounding impedance and length.

W. HUANG ET AL. 1257
Figure 9. Equivalent circuit of traction return current sys-
tem.
00.5 11.5 2
0
0.1
0.2
0.3
0.4
0.5
rail
protective wire
integ ra nted grounding line
Figure 10. Distribution coefficient of traction return current
system.
length increases, therefore, the longer the conductor is,
the smaller distribution coefficient the PW is. The distri-
bution coefficient of rail is increasing within 1 km. On
the contrary, the characteristic presents an opposite ten-
dency after 1 km, and the value of distribution coefficient
reaches the minimum around 1km. The distribution coef-
ficient of the IGL increases with the length of the IGL
increases and slightly decreases after the distribution
coefficient reaches the maximum around 1km.
In the practice, PW, rail and IGL in the longitudinal
return current conductor are connected by the transverse
connection in a certain interval which leads to realloca-
tion of the rail current when it reaches connection point
in order to lower rail potential. Rail potential is consid-
ered as standards to study the reasonable length between
transverse connections. A section of one railway in china
is the data source of the rail, ballastless track uses the
P60 gapless rail, the impedance of per unit is 4
1.63 10



6.38
r
, the reactance of per unit is ,the leak age
conductance of per unit is , depending on the
above data, the decay coefficient of rail is
4 5.53 10 
5
10 S

2.5



. The average burial depth of IGL is 0.7 m, the av-
erage resistivity of soil is
5
10
100 m

 [15]. The other pa-
rameters are referring to engineering design standard,
traction current is 0. Figure 11 sh ow s th e r ail
potential according to the distribution coefficient of rail.
10I00 A
It represents the product of distributive current with
different rail length and the impedance at this position.
According to the EN50122-1 railway applications-fixed
equipment-part one and communication system used in
the prEN50170, railway regulates that the rail potential is
no more than 120 V under the normal operating states
(t>300 s), and the rail potential is no more than 130 V
un- der the normal operating states (t < 300 s)[16]. Fig-
ure 11 shows that the rail potential is 129.5 V wh ich rail
trans- verse connection interval is 0.65 km, therefore the
trans- verse connections interval of rail-PW or rail-IGL
should be no more than 0.6 km. The data are shown in
Table 1.
Considering the actual situation that rail and IGL are
closely contacted with the earth and the current will in-
filtrate to the earth by the conductor, the values of distri-
bution coefficient of rail and IGL should be smaller than
the values in the practice, that is, the value of actual r
should be smaller than that in this table. On the premise
of keeping a margin, considering the current-carrying
capability and economical efficiency of the PW, rail and
IGL, the interval of transverse connection among these
three conductors should be designing 400 m - 600 m.
U
5. Conclusions
Based on the PW, rail, and IGL of the longitudinal return
current conductors in high-speed railway, the parameters
of the wires in different environments were calculated.
Combining with the field data and taking relevant require-
ments of rail potential in EN50122-1 and prEN50170 as
standards, the design which is suitable for traction return
current system is concluded, and the optimum transverse
connection interval of return current network is obtained.
00.5 11.5
2
0
50
100
150
200
250
300
Figure 11. Rail potential.
Table 1. Relationship among the interval of transverse con-
nection and shunting coefficient and ra il pote ntial.
Transverse interval (m)
Distribution
coefficient 350 400 450 500 550 600
PW 0.42650.41230.3985 0.3852 0.37280.3612
Rail 0.46900.46050.4519 0.4435 0.43560.4285
IGL 0.10450.12720.1496 0.1713 0.19160.2103
Ur 84.817093.7212101.9003 109.4542 116.4960123.1433

W. HUANG ET AL.
1258
In consideration of the current carrying cap ability of each
wire, economy and retaining a certain margin, the opti-
mum design of transverse interval is between 400 m and
600 m, and the distribution ratio of PW, rail, and IGL is
35%:45%:20%. Rail potential is less than 120 V, which
meets the rail potential standards.
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