Energy and Power Engineering, 2013, 5, 780-784
doi:10.4236/epe.2013.54B150 Published Online July 2013 (http://www.scirp.org/journal/epe)
Research on Voltage Losses of AT Traction Power
Supply System
Yujie Xia, Guosong Lin, Liya Guo, Qiang Li
Southwest Jiaotong University, Chengdu, China
Email: xiayujie4028@126.com
Received April, 2013
ABSTRACT
Unilateral power supply system has been used because of the management status of the power grid system, while, bilat-
eral power supply system is adopted in the Soviet Union and France. The feasibility that whether bilateral system can be
put into applied in China is discussed[1]. Compared with unilateral power supply system, bilateral system has better
reliability and better capability of supply power system, which gives bilateral system more advantages over unilateral
system on both engineering investment and operating efficiency. In this paper, voltage losses under the two different
systems are calculated and also compared, the advantages of bilateral system is explored and then conclusion is drawn
by referring to the practical data of passenger transport lines.
Keywords: Unilateral AT Power System; Bilateral AT Power Supply System; Voltage Loss; Scheme of Power Supply
1. Introduction
With the development of the traction power supply sys-
tem, there are various power supply modes. In order to
meet the requirements of high-speed railway, the au-
to-passing phase separation system is installed in substa-
tion and section post. However, when electric locomotive
passes through the device, the over-voltage and
over-current frequently occur, as well as the electric
railway’s reliability and the speed of electric locomotive
is affected. If the bilateral power supply is improved, the
reliability and power supply capability could be im-
proved, as well as the auto-passing phase separation sys-
tem can be canceled. In this paper, the bilateral power
supply technology for passenger dedicated line is ana-
lyzed and researched.
2. The Models of Unilateral Power Supply
and Bilateral Power Supply System
The theoretical analysis of both unilateral[2 ] and b ilateral
AT supply systems is based on the assumptions below:
AT transformers are ideal, leakage reactance is ignored,
there is no excitation current, steel track s are insulated to
earth, there is no steel track current flowing to line re-
sidual current through leakage conductance to earth, and
mutual inductance between up and down lines. Deriva-
tion can be simplified because of the hypothesis above.
Meanwhile, the influences of AT leakage reactance and
leakage inductance of tracks to earth on electrical calcu-
lation can be counteracted to some degree and the result
will be identical to practical model.
2.1. Unilateral All-parallel AT Power Supply
System
Unilateral power system is shown in Figure 1, and the
substations are independent from the others. The electric
locomotive obtains power from one conjoint substation.
2.2. Bilateral All-parallel AT Power Supply
System
Under bilateral power supply system, electric locomotive
gets power from two adjacent substations, which is dif-
ferent from the situation un der unilateral system. Section
posts are built between the substations. Bilateral system
is gained through the closure of circuit breakers, which
are parallel with neutral section insulators. When one
feeding section is faulted, the other feeding section still
works. Under bilateral power supply system [5], 2×
Figure 1. Unilateral all-parallel AT pow er supply system.
27.5 kV AT supply system is adopted and the bilateral
Copyright © 2013 SciRes. EPE
Y. J. XIA ET AL. 781
system model is shown in Figure 2.
3. The Theoretical Analysis of Unilateral
Power Supply Voltage Loss
Electric traction network impedance is gained by the
equivalent circuit [3], the paper applies original network
circuit analysis and calculation of voltage loss needs
more complex equations. When many locomotives run
on the feeding section, the voltage drop of transmission
line is difficult to calculate. Using the conclusion of im-
pedance of traction network, primary circuit can be sim-
plified as shown in Figure 3. With the circuit and the
original network reaching the same conclusion, the anal-
ysis is more intuitive, convenient and simple to operate
[4].
When the feeding arm only has one locomotive k [4],
the train causes the voltage drop by itself:
•••
kk
AA BB
X
U=AZ I+XZ I1-D
()
(1)
Below the research of feeding arm within two loco mo-
tives for voltage drop interaction, it is assumed that the
AT section only has one locomotive, the voltage drop of
locomotive k caused by locomotive i is:
i
ik AA iik
ΔUZAIAA

(2)
Assume that the AT section only has one locomotive,
the voltage drop of locomotive k caused by locomotive j
is:
a
I
a
I
b
I
a
I
1
1
2
Z

23
23
2
ZZ
Z
Z
1
1
2
Z

23
23
2
ZZ
Z
Z
J
X
j
A
j
I
1
j
I
2j
I
K
I
2
2
Z
3
1
2
Z
U
U
1
Z
1
Z
K
X
D
k
A
Figure 2. Bilateral all-parallel AT power supply system.
K
I
Figure 3. The equivalent circuit diagram of the unilateral
all-parallel AT traction system.
••
j
jk AA kjk
U=ZAIA>A
(3)
When the AT sections have many locomotives, con-
sidering the mutual influence of the voltage drop be-
tween locomotives, the results of an equivalent circuit
and all-parallel AT equivalent circuit are similar. When
the AT section have two locomotives, the voltage drop of
locomotive k caused by locomotive j is:

•••
k
ii
ik AA iBBiik
X
U=ZAI+ZXI(1-)A<A
D
(4)
When the AT section have two locomotives, the volt-
age drop of locomotive k caused by locomotive j is:

j
j
j
jk AA kBBkk
X
ΔUZAIZXI1 AA
D

 () (5)
4. The Theoretical Analysis of Bilateral
Power Supply Voltage Loss
Electric traction network impedance is gained by the
equivalent circuit. The paper applies original network
circuit analysis and calculation of voltage loss needs
more complex equations. When many locomotives are
running, the voltage drop of transmission line is difficult
to calculate. By using the conclusion of impedance of
traction network, primary circuit can be simplified as
shown in Figure 4. With the circuit and the original
network reaching the same conclusion, the analysis is
more intuitive, convenient and simple to operate [4].
When the feeding arm between traction substation A
and B only has one locomotive k, the impedance of pow-
er traction system is [4]:
11
kk
kAAk
AX
BB
Z
AZX
LD
 
 
 
 
Z
(6)
So the voltage drop is caused by the locomotive itself:
••
kk
AA kkBBkk
Z
IAL-AZIX D-X
U= +
LD
()( )
(7)
Assume that the AT section only has one locomotive,
the voltage drop of locomotive k caused by locomotive i
is:
K
I
U
U
Figure 4. The equivalent circuit diagram of bilateral all-
parallel AT traction system.
Copyright © 2013 SciRes. EPE
Y. J. XIA ET AL.
782

i
AA k
ik ik
ZILA
ΔUA
L
<A
(8)
Assume that the AT section only has one locomotive,
the voltage drop of locomotive k caused by locomotive j
is:

k
j
AA kj
jk j
ZIALA
ΔUA
L

A
(9)
When the AT section has two locomotives, the voltag e
drop of locomotive k caus ed by locomotive i is:
 
••
ii
AA ikBBik
ik ik
ZAIL-A ZXID-X
U= +A<A
LD
(10)
When the AT section have two locomotives, the volt-
age drop of locomotive k caused by locomotive j is:
 
••
jj
kjBBkj
jk jk
AZ IL-AZXID-X
U= +A>A
LD
AA
(11)
When the up and down locomotives are in the same
AT section, the equivalent circuit diagram is needed, as
shown in Figure 5[4].
When studying locomotive j’s in fluence on the voltag e
drop of locomotive k. ,
j1
I
j2
I
, and
a
I
I
are ob-
tained as follows: [4]



j
jj
j1 a
3
2
23
ILXI
II
2L
()
2
j
j
jjj j
jb
DA LA
DL
IZ LXDAIA
II
LD ZZL




(12)
The voltage drop of locomotive k caused by locomo-
tive j is:
 

••
aa
1jj23j
jk
23
••
j1 j2
1k 2k
j
Z
IA-X ZZIA-X
U= +
22Z+Z
+ZX I+ZX I
(13)
a
I
a
I
b
I
a
I
1
1
2
Z

23
23
2
ZZ
Z
Z
1
1
2
Z

23
23
2
ZZ
Z
Z
J
X
j
A
j
I
1
j
I
2
j
I
K
I
2
Z
2
Z
3
1
2
Z
U
U
1
Z
1
Z
K
X
D
k
A
Figure 5. The equivalent circuit diagram of voltage loss.

jj jkjj
j
jk AA
LAAXXLX DA
UIZ LDL

 
 
(14)
Likewise, in the same AT section, the voltage drop of
locomotive j caused by locomotive k is:

jk k
kk k
k
kj AA
XLX DA
LAAX
UIZ LDL


 
(15)
When calculating the traction network voltage loss,
AA
Z
and should be replaced by
BB
Z'
AA
Z
and '
B
B
Z
,
that is:
'
AA AAAA
'
BB BBBB
Z
=r cos+xsin
Z
=r cos+xsin
(16)
where AA , AA are the real part and imaginary com-
ponent of the long loop of impedance; BB , BB are the
real part and imaginary component of the short loop of
impedance;
r xr x
is load power factor angle.
5. The Comparison between Voltage Loss in
Unilateral AT Traction System and in
Bilateral System
The impedance characteristics of unilateral and bilateral
all-parallel AT traction system are discussed in reference
[4], and their characteristic curves are saddle-shaped. The
peak voltage loss is not in the end of AT power supply
system, so we should calculate the voltage loss of loco-
motives according to the change of tracking interval, and
then, maximum voltage loss is gained by comparing and
analyzing the data.
5.1. The Voltage Loss Calculation of Unilateral
Power Supply System
The peak of voltage loss will occur in the last locomotive
when there are many locomotives on the feeding section.
So in this paper, we only calculate the last locomotive’s
voltage loss. Table 1 shows the position and peak volt-
age loss of the locomotive less than 3 minutes tracking
interval condition, and the position and peak voltage loss
of the locomotive under 4 minutes interval condition is
shown in Table 2.
From the data above, it can be deduced that the peak
voltage loss occurs in the end of the last locomotive.
When tracking and observing the locomotive in every
3 minutes; while, under 4-minute interval condition, the
peak voltage loss occurs at the last locomotive which is 1
km away from the end of the feeding section. So the peak
voltage mostly occurs at the section where there are the
most locomotives running under feeding section.
Copyright © 2013 SciRes. EPE
Y. J. XIA ET AL.
Copyright © 2013 SciRes. EPE
783
In the case of 3 minutes interval, there are 5 locomo-
tives at most and 4 at least in 60 km feeding arm. In the
case of 4 minutes interval, there are 4 locomotives at
most and 3 at least, and the location will change 1 km
every time from the left substation A, which is consid-
ered as the initial position. In Tables 3 and 4, voltage
loss of the locomotives (those locomotives’ maximum
voltage loss may occur) at corresponding position is cal-
culated.
From the Table above, it can be seen that the peak
voltage loss will occur in the end of the last locomotive
when the interval is 3 minutes, while, the peak loss will
occur 1 kilometer apart from the end of the last locomo-
tive when the interval is 4 minutes. Therefore, the loca-
tion where peak loss occurs is not fixed.
5.2. Comparison between Unilateral and
Bilateral Peak Voltage Loss
The comparison between unilateral and bilateral
all-parallel AT power supply systems under 3 and 4 min-
utes interval are shown in Table 5 . As is seen in Table 5 ,
the bilateral traction power supply network can save over
15% of the voltage loss of unilateral traction network.
Therefore, the length of feeding arms can be increased
when the voltage loss is the same under these two dif-
ferent systems.
Table 1. The locomotive position and voltage in the case of 3
minutes.
The locomotive 1 /km 0 1 2 4
The locomotive 2 /km 13.5 14.5 15.5 16.5
The locomotive 3 /km 27 29 29 30
The locomotive 4 /km 3.96 4.0944 4.2066 4.283
Table 2. The locomotive position and voltage loss in the case
of 4 minutes.
The locomotive 1 /km 0 1 2 3
The locomotive 2 /km 22.5 23.5 24.5 25.5
Peak voltage loss /kV 2.666 2 .8261 2.96063.0695
The locomotive 1 /km 4 5 6 7
The locomotive 2 /km 26.5 27.5 28.5 29.5
Peak voltage loss /kV 3.152 3 .2105 3.24263.249
Table 3. The locomotive position and voltage loss in the case of 3 minutes.
The distance from the initial position /km 0 1 2 3 4 5 6
The locomotive 2 voltage loss /kV 2.3022 2.2754 2.3943 2.6589 2.8898 3.0808 3.2317
The locomotive 3 voltage loss /kV 3.3794 3.2874 3.1617 2.9832 3.1617 3.2874 3.3794
The locomotive 4 voltage loss /kV 3.2317 3.0808 2.8898 2.6589 2.3943 2.2754 2.3022
Table 4. The locomitive position and voltage loss in the case of 4 minutes.
The distance from the initial position /km 0 1 2 3 4 5 6
The locomotive 2 voltage loss /kV 2.3288 2.5122.6582.76 692.83862.8732 2.8706
The locomotive 3 voltage loss /kV 2.8706 2.87322.83862.76692.6582.512 2.3288
Table 5. Traction network peak voltage loss of unilateral
and bilateral power supply.
The time interval 3min 4min
The peak voltage loss of unilateral
power supply /kV 4.2803 3.6381
The peak voltage loss of bilateral
power supply /kV 3.571 2.8732
The voltage loss reduced/The voltage
loss of unilateral power supply /% 16.57 21.02
The minimum voltage of unilateral
power supply /kV 21.5082 23.2209
The minimum voltage of bilateral
power supply /kV 22.6768 23.7743
6. Conclusions
After the models of unilateral and bilateral power supply
systems are analyzed and calculated, it can be concluded
that the voltage loss of b ilateral power supply syste m can
be decreased by 10% or more compared with that of uni-
lateral system. Besides, the lowest voltage of bilateral
system is higher than that of unilateral system, which
guarantees both the reliability and better capability of
power supply. Therefore, the application of bilateral
power supply system will be well worth exploring.
7. Acknowledgements
The authors acknowledg e the supports of the Ministry of
Y. J. XIA ET AL.
784
Railways Technology Research and Development Plan
of China (Grant No. 2011J017-B) and the Fundamental
Research Funds for the Central Universities (Grant No.
SWJTU12CX034).
REFERENCES
[1] Z. L. Li, W. Chen and P. Dang, “The Principle Analysis
of Auto-transformer in Electrified Railway,” Journal of
East China Jiaotong University, 1993, pp. 48-53.
[2] X. F. Zhang, “The Research on Co-phase at Traction
Power Supply in the Rapid Transit Railway,”Southwest
jiaotong university dissertation, 2006.
[3] C. S. Xin, “Equivalent Circuit Method of the AT Power
Supply System,” Electrified railway, 1995.
[4] Q. Li, “Study on Protective Schemes of Bilateral Traction
Power Supply Systems for High Speed Railways,” 2011,
pp. 21-24.
[5] Q. Z. Li and J. M. He, “The Analysis of Power Traction
System,” Southwest Jiaotong university press, 2007,
pp.10-13.
Copyright © 2013 SciRes. EPE