Energy and Power Engineering, 2013, 5, 1026-1031
doi:10.4236/epe.2013.54B196 Published Online July 2013 (http://www.scirp.org/journal/epe)
Comparison of Three Modes of AT-fed Traction Power
Networks
Qingan Ma, Qunzhan Li, Zehui Mi
Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, China
Received April, 2013
ABSTRACT
The features of three modes of AT-fed traction power networks (TPNs) have been briefly described in the existing lit-
erature, which is not adequate yet. In this paper, these three modes of TPNs are compared mainly on TPN capacity,
transformer capacity, rail potential and voltage level, etc., and conclusions are drawn.
Keywords: AT-fed Traction Power Network; Comparison; Capacity; Rail Potential; Voltage Level
1. Introduction
There are two existing modes of AT-fed traction power
networks (TPNs), i.e., Japanese-mode (J-mode) and
French-mode (F-mode), as shown in Figures 1(a) and
(b). Here, only single-line railway is shown for simplic-
ity, and T, R and F are abbreviated for trolley wire, rail
track and power feeder respectively. A Novel-mode
(N-mode) TPN was proposed by Ref [1] recently, as
shown in Figure 1(c). The features of the three modes of
TPNs have been briefly described in Ref [1], current dis-
tribution and equivalent impedance have been studied in
Ref [2, 3]. However, their features have not been totally
compared and should be studied further.
In this paper, these three modes of AT-fed TPNs are
compared on TPN capacity, transformer capacity, and
rail potential, voltage level, etc., and conclusions are
drawn at last.
2. TPN Capacity
2.1. Current Distribution Analysis
As all-parallel connection is always adopted in China,
terminal-parallel connection is not taken into considera-
tion in this paper.
Only the first AT-section is needed to be compared as
it is identical in other AT-sections of these three modes
of TPNs.
As current distributions are the same in J-mode and
F-mode TPNs except in transformer, only J-mode and
N-mode TPNs are compared here.
1) J-mode
Generalized method of symmetrical components can
be used to the first AT-section of J-mode TPN[4]. If AT
leakage impedance is neglected, it is easily to derive the
composite sequence network as shown in Figure 2(a).
The total current at any point is the sum of its sequence
components. So currents flowing in T and F in the fist
AT-section of the up TPN are
(a) J-mode
AT1 AT2
n1
T
R
F
Transformer
n1
n2n2
(b) F-mode
(c) N-mode
Figure 1. Three modes of AT-fed TPNs.

Q. A. MA ET AL. 1027
0123
3
14
TU L
x
I
IIII I
D




 
(1)
0123 4
F
U
xL
I
IIII I
D

 
(2)
the sign “-” in Equ.(2) indicates that the current re-
verse the defined direction. Currents flowing in conduc-
tor T and F in the fist AT-section of the down TPN are
D 0123
4
T
xL
I
IIIII
D

 
(3)
FD0 1 234
L
x
I
IIII I
D

 
(4)
2) N-mode
Using the method as before, the composite sequence
network for the N-mode TPN is shown in Figrue 2(b).
From Figrue 2(b), the following equations can be de-
rived
0123
3
42
TU L
x
I
IIII I
D

 


 
(5)
01 23
1
4
F
UL
I
IIII I
 
(6)
D 0123
1
24
T
xL
I
IIII I
D

 


 
(7)
FD0 1 23
1
4
L
I
IIII I
 
(8)
E


z1
z0
4
L
I

+
z2
z3
4zL
0
I

1
I

2
I

3
I

zs
(a) J-mode TPN
E


4
L
I

0
I

1
I

2
I

3
I

(b) N-mode TPN
Figure 2. Composite sequence network of the first AT-sec-
tion of an double-line railway TPN.
It is easily induced from traction power system theory
that currents in TPN reach its maximum value at the ini-
tiating-terminal in the feeding section. The cross-section
area of every conductor doesn’t vary along the line for
convenience, and mainly depends on the current of its
initiating-terminal.
2.2. TPN Capacity
The RMS current at the initiating-terminal of every con-
ductor as the load passing through the first AT-section
can be defined as
 
11
22
00
1
1T
ss
I
ItdtItdt
T
 


(9)
where, Is(t) is the current flowing in the initiating-termi-
nal of the conductor, T1 is the time consumed by the load
to pass through the first AT-section, t* is per-unit time
taking T1 as base value.
Assuming that the velocity of the load is constant, t*
can be replaced by load location, thus the following equ-
ation is derived

12
0s
I
Ixdx
 
 (10)
Here, x* is per-unit distance between substation and
the load choosing AT-section length D as base value.
RMS current can also be represented by its per-unit value
2
12
0
ss
1
0
I
IIIIdx Idx




 



(11)
Here, ss
I
II
 is per-unit current flowing in the in-
itiating-terminal of the conductor.
It is assumed that the feeding section considered here
has three AT-sections and currents of all loads are equal
to I. Sometimes there may be 2 loads on the up and down
rail tracks of the first AT-section. As these 2 loads in the
first AT-section are different, it is assumed here that
x
xD


 (12)
When there are 4 and 6 loads in the feeding section
respectively, and 2 of them are located in the first
AT-section, the RMS currents are calculated and shown
in Table 1. If the currents flowing in initiating-terminal
of conductor T and F are summed, it can be seen that the
summations are equal for these two modes of TPN, i.e.,
more load current is transferred from conductor T to
conductor F in the N-mode TPN, however the total cur-
rent flowing in TPN nearly does not change, as can be
seen in Table 2.
3. Transformer Capacity
As current distribution is the same in the transformer for
J-mode and F-mode, only J-mode and N-mode trans-
former capacities are compared here.

Q. A. MA ET AL.
1028
Table 1. RMS current of conductor T and F (pu).
J-mode N-mode
Load number T F T F
4 1.283 0.764 1.041 1.0
6 1.774 1.258 1.528 1.5
Table 2. Conductors summary current in TPN.
Load number J-mode N-mode
4 2.033 2.041
6 3.024 3.028
In the F-mode transformer, currents flowing in the two
segments of the secondary winding are unequal. How-
ever, the cross-section areas of these two sections of
winding are identical in manufacturing for convenience,
and they depend on the bigger one, that produced by the
up load is shown as below via generalized method of
symmetrical components
12
S
xL
I
I
D





(13)
In the same manner, the current produced by the down
load is
12
S
xL
I
I
D






(14)
Here,
x
—distance between substation and the down
load, the total current is derived by summing Equ.13 and
14
11
22
SL
xx
L
I
I
DD



 



I

(15)
Taking into account Equ.12, Equ.15 becomes
3
2
SL
I
I


(16)
If there are 4 loads in feeding section, the total current
flowing in the secondary winding of traction transformer
is
4
5
2
SL
I
I


(17)
If there are 6 loads, the current is
6
7
2
TL
I
I


(18)
As only positive sequence current flows in the second
winding of the J-mode transformer, the total current
flowing in the secondary winding is 2
L
I
 and 3
L
I
 for 4
or 6 loads, respectively. Let, the per-unit current
flowing in the secondary winding is derived and shown
in Table 3. Thus the capacity of the F-mode transformer
is bigger than that of the J-mode transformer.
1
L
I

4. Other Aspects
In this section, three modes of TPNs are compared on rail
potential, voltage level and earthling-current, etc., based
on its chain circuit model [5].
Here the load is represented by constant admittance of
0.02S. It is specified in Ref [6] that the resistance of the
earthling electrode in the traction substation should not
exceed 0.5Ω. In high soil resistivity area, the value
should not exceed 5Ω. Both 0.5Ω and 5Ω are applied in
the simulation for comparison.
TPN parameters are listed in Tables 4-7. Here, PW
(protection wire) and GW (grounding wire) are reduced
to conductor H. “U” and “D” is used for up and down
TPNS respectively.
4.1. Rail Potential
As current distribution is identical for J- mode and
F-mode of TPNs [5], it can be induced that rail potentials
are also the same. It is only needed to compare J-mode
and N-mode TPNs.
Table 3. Transformer capacity comparison.
Load number J-mode F-mode
4 2 2.5
6 3 3.5
Table 4. Admittances of current return circuit (S/km).
H
U R U H D R D
HU 1.655 0 -0.646 0
RU 0 0.01 0 0
Table 5. Impedances of current return circuit (Ω/km).
H
U R U H D R D
HU 0.163+0.584i0.050+0.372i 0.049+0.317i 0.049+0.317i
RU 0.050+0.372i0.117+0.801i 0.049+0.339i 0.049+0.339i
Table 6. Impedances of T and F (Ω/km).
T
U F U T D F D
TU0.135+0.646i 0.052+0.381i 0.050+0.381i 0.050+0.340i
FU0.052+0.381i 0.190+0.777i 0.050+0.340i 0.050+0.317i
Table 7. Mutual impedances between T, F and H, R(Ω/km).
T
U F U T D F D
HU0.048+0.374i 0.046+0.416i 0.049+0.338i 0.049+0.315i
RU0.048+0.375i 0.047+0.353i 0.049+0.358i 0.048+0.331i

Q. A. MA ET AL. 1029
Rail potential distributions are shown in Figure 3. It
can be seen that rail potential are nearly identical for both
modes of TPNs and the resistance of earthling electrode
have neglectable effect on rail potential.
4.2. Voltage Level
Voltage levels are shown in Figure 4 for J-mode and
N-mode of TPNs. As can be seen, the resistance of 0.5 Ω
or 5 Ω does not have obvious effect on voltage level.
Besides, the minimum appears about at 2/3 in the first
AT- section of J-mode AT-section; however, in the
N-mode TPN, it appears at the initiating-terminal, as can
be illustrated from the TPN’s equivalent impedance.
It can be seen from Figure 4 that, the minimum volt-
age is about 200 V lower in N-mode TPN than that in the
J-mode TPN. As the load is located in the first
AT-section, the minimum voltage hardly exceeds its
corresponding limit in engineering. Thus the voltage lev-
els are almost identical.
4.3. Earting-current and Electro-magnetic
Interference to Nearby Conductors
From the fact that the J-mode, F-mode TPNs have the
same equivalent circuit [5], it can be induced that both
modes of TPNs have the same earthling-current distribu-
tion. Thus only N-mode, J-mode TPNs are needed to be
compared.
Earthling-current distributions are shown in Figure
6(a) at several load locations in the first AT-section of
the J-mode TPN, and the maximum earthling-current on
the left- and right- side of the load is shown in Figure
6(b). The maximum earthling-current is nearly 60 A,
about 1/9
(a) Earthing resistance 0.5 Ω
(b) Earthing resistance 5Ω
Figure 3. Rail potential distribution.
of the load current. To evaluate the electro-magnetic in-
terference to other adjacent conductors, the relationship
between A·km index caused by the whole length of the
first AT-section and load location is calculated also and
given in Figure 7. A·km index reaches its maximum in
the middle of the AT-section, about 1.1 times the load
current.
(a) J-mode
(b) N-mode
Figure 4. Voltage level at the load location.
Figure 5. TPN impedance in relation with load location.
(a) Earthing-current distribution at several load locations

Q. A. MA ET AL.
1030
(b) Left- and right-side maximum earthing current
Figure 6. Earting current distribution in the first AT-sec-
tion of J-mode TPN with earthing resistance 0.5Ω.
Figure 7. A·km index of the first AT-section in J-mode
TPN.
(a) Earthing-current distribution at several load locations
(b) Left- and right-side maximum earthing current
Figure 8. Earting-current distribution in the first AT-sec-
tion of N-mode TPN with earthing resistance 0.5Ω.
For the first AT-section of the N-mode TPN, the
curves are shown in Figure 8. As the distance between
the load and adjacent ATP(AT post) exceeds 5km,
earthing-current reaches its maximum of about 90 A,
A·km index
Figure 9. A·km index of the first AT-section in N-mode
TPN.
nearly 1/6 of the load current. As can be seen from Fi-
grue 9, A·km index is nearly linear with the load loca-
tion, and the maximum is about 1330 A·km, about 2.4
times the load current.
It is found that earthling resistance has neglectable ef-
fect on the earthling current and electro-magnetic inter-
ference.
4.4. Fault Location
As substation AT is omitted in the N-mode TPN, the
fault location method—AT neutral current ratios, which
is widely utilized in engineering, does not work any more.
As the mutual impedance between T and R is nearly
equal to that between F and R, and the mutual effect of T
and F to R cancel each other out, the positive current has
neglectable effect to R. Thus earthling current and elec-
tro-magnetic interference mainly depend on the zero se-
quence current.
5. Conclusions
Three modes of AT-fed TPN are compared, mainly on
transformer capacity, TPN capacity, rail potential, etc. It
can be concluded that these three modes of TPN are
nearly identical on rail potential, TPN capacity, and vol-
tage level. In N-mode TPN, AT or transformer tapping is
not necessary in the substation, earthling-current is big-
ger than that of other modes of TPN, and the “AT neutral
current ratios” fault location method become invalid.
F-mode TPN needs transformer tapping and bigger
transformer capacity, however substation AT is omitted.
J-mode TPN doesn’t necessitate transformer tapping,
however substation AT is needed in instead.
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Q. A. MA ET AL.
1031
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