Energy and Power Engineering, 2013, 5, 546-551
doi:10.4236/epe.2013.54B104 Published Online July 2013 (http://www.scirp.org/journal/epe)
Analysis of the Electric Locomotives Neutral-section
Passing Harmonic Resonance
Xiaofeng Jiang, Zhengyou He, Haitao Hu, Yangfan Zhang
School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China
Received April, 2013
ABSTRACT
For the further analysis and suppression of the electric locomotives neutral-section passing overvoltage, on the basis of
theoretical analysis of the neutral-section passing harmonic resonance conditions, this paper establishes simplified har-
monic resonance simulation models of the electric locomotives neutral-section passing using MATLAB/Simulink, and
makes the overvoltage simulation analysis of the existing electric locomotives neutral-section passing system in the
event of a harmonic resonance. Results show that when the system harmonic resonance occurs, the operating overvolt-
age of the neutral-section passing is serious intensified by the overvoltage of the harmonic resonance, which will make
the voltage of the pantograph collector head exceeding 100 kV. This amplitude of the overvoltage will breakdown the
air gap, which will be a serious threat to the safety operation of the electric railway. However, this kind of neu-
tral-section passing overvoltage hasn’t cause the attention in the field and theoretical studies, which need more analysis
and verification in the further study.
Keywords: Neutral-section passing; Harmonic Resonance; Overvoltage; Equivalent Modeling; Simulation Analysis
1. Introduction
Recently, the electric railways develop rapidly in China.
With the high-speed, high-capacity and large-scale rail-
way, the electric sectioning device based on the overlap-
ping section with the advantages of hard-spot little and
enterclose-smoothly is widely used in heterogeneous
tractive power supply system. However, it exposes new
problems in electric field at the same time of the applica-
tion and popularization. While the locomotive passed by
the electrical sectioning device, it has strong transient
process such as overvoltage and overcurrent, and it
brings security issues in electric railway.
At present, in view of the electric locomotives neu-
tral-section passing overvoltage research has been com-
prehensive, and it conducts by two fields that the ex-
perimental research and simulation study. In the field of
experimental research, locomotive Department in Lan-
zhou Railway Bureau organizes relevant units which
sponsored Southwest Jiaotong University, China Railway
First Survey and Design Institute and Zhuzhou Electric
Locomotive Research Institute making field tests in the
Lan-Xin Railway Wuwei to Jiayuguan Segment. The
problem of over-voltage when the electric locomotive
passed by the electrical sectioning device based on the
overlapping section has been studied in [1]. In simulation
study, the traction-locomotive system was divided into
four transient processes by the physical process of the
electric locomotives neutral-section passing, to establish
equation of transient process, the voltage of the panto-
graph collector head and the renewed arc in a transient
process have been calculated respectively in [2]. Simula-
tion model of electric locomotive neutral-section passing
has been built with using Pspice in [3], which made si-
mulation analysis of the electric locomotives neutral-
section passing processes when the voltage working un-
der different degrees of saturation and the neutral-section
passing processes of the system which was added the
disincentives.
However, in present studies, few of them take the in-
fluence of harmonic resonance into account, except the
analysis of neutral-section passing overvoltage under the
condition of ferroresonance in [4]. Because of the appli-
cation of the electrical sectioning device based on the
overlapping section, the length of neutral section is about
150-300 m, which increases the likelihood of parameter
matching with resonance. In the case of parameter
matching, resonance and serious harmonic amplification
may occur when the system meets the condition of har-
monic resonance. Because of the voltage distortion
*This work is supported by High-Speed Railway Basic Research Fund
Key Project (U1134205); National Natural Science Foundation o
f
China (51177139); Science & Technology Research and Development
Key Project of Railway Ministry (2011J023-B).

X. F. JIANG ET AL. 547
which is caused by the resonance and the harmonic cur-
rent increased further, interanimation of the positive
feedback is formed, which results to a resonant over-
voltage and the burning loss of equipment in the process
of the neutral-section passing.
Based on this, according to the careful analysis of neu-
tral-section passing transient process in the condition of
harmonic resonance, the ‘traction network-locomotive’
equivalent model was built. Through the MATLAB/ Si-
mulink, the process of the electric locomotives neutral-
section passing harmonic resonance overvoltage is ana-
lyzed, and we can conclude that the harmonic resonance
has a strong impact on the neutral-section passing over-
voltage, which should be analyzed and considered in the
future research.
2. The Analysis of the Traction Network
Harmonic Transmission Characteristics
Due to the large number of actual traction network wire,
the multi-conductor transmission system was simplified
to an equivalent circuit of the harmonic transmission as
shown in Figure 1 to study the harmonic transmission.
Among which, L1 represents the distance of the section
post and harmonic source, L2 represents the distance of
the traction substation and harmonic source, Ih represents
equivalent current of the harmonic source, If represents
the component which the harmonic source current flows
to section post, Iq represents the component which the
harmonic source current flows to traction substation, Is
represents the traction network current where the dis-
tance from the traction substation is s, Zs represents the
equivalent impedance of traction substation.
Through the steady-state equation and the equivalent
circuit of the power transmission line, the equivalent cir-
cuit with distribution parameters on both sides of the
harmonic source can be shown in Figure 2.
Figure 1. Equivalent circuit of the traction power supply sys-
tem harmonic transmission.
Figure 2. Equivalent circuit of traction network.
It can be concluded from derivation that:
11
11
1
22
22
2
(1)
Z,
(1)
Z,
t
tt
t
t
tt
t
ZchL
s
hL
Y
sh LZ
ZchL
s
hL
Y
s
hL Z













(1)
In the equation, t
Z
represents the line characteristic
impedance, /
t
Z
ZY;
Z
, denote respectively the
equivalent impedance and admittance per unit length of
traction network;
Y

represents line propagation coeffi-
cient,
Z
Y  .
The magnification of the traction network harmonic
current can be gotten as[5]:
1
2121
()
=() ()
sst
mpx st
IZshsZchschL
A
2
I
ZshLLZchLL



 (2)
As seen in the equation (2) that Amax reaches its maxi-
mum when denominator is set approximately to 0, which
is seen as resonance. The resonance condition can be
deduced that:
12 12
() ()
st
Zsh LLZch LL0



 (3)
As 1L

, so th LL



, and
/( )
st
Z
ZL


 (4)
Consider that the equivalent impedances of traction
substation mainly consist by the traction transformer in-
ductance Ls , so
s
s
Z
L


(5)
And the resonance frequency can be deduced:
1/(2 )
s
LC   (6)
As is seen in the equations (5) and (6) that the farther
the harmonic wave source is away from the traction sub-
station, the larger the current magnification of harmonic
wave is. The transmission characteristics and resonant
frequency of harmonic current in the traction network are
mainly affected by the length of the traction network, the
equivalent impedance of traction substation, the distribu-
tion parameters of traction network, the position of lo-
comotive, and so on. When the harmonic frequency in-
jected from the harmonic source to traction network is
equal to or close to the resonant frequency of traction
network [6], the harmonic wave is enlarged significantly,
and the system resonates.
3. The Equivalent Modeling of
Neutral-section Passing Harmonic
Resonance Overvoltage
The process of electric locomotive’s passing section-
phase is relatively complex, during which the pantograph
has multiple instant contacts and separations with the

X. F. JIANG ET AL.
548
contact wire of catenaries and neutral line at different
positions. At these instant moments, the circuit topology
changes, causing the system’s electromagnetic transient
processes. During these processes [7], the system pa-
rameters may meet the resonance conditions, leading to
the harmonic resonance of neutral-section passing, which
exacerbates overvoltage of neutral-section passing.
As for the overvoltage above, it can be analyzed by the
use of the equivalent harmonic resonance overvoltage
model of neutral-section passing. Equivalent model con-
sists of four parts: catenaries, neutral section, locomo-
tives, and the harmonic source. To establish a simplified
equivalent model with coupling relationship makes a
great significance to the analysis of the neutral-section
passing transient process. The equivalent modeling of
catenaries and the neutral section is similar to the equiva-
lent circuit of the electric wire, which adopts

model
equivalent circuit. The locomotive’s equivalent model is
divided into two parts of normal operation and cutting
the main circuit breaker off the locomotives. When run-
ning normally, locomotive’s equivalent model is replaced
by impedance; otherwise, the locomotive left only inter-
related circuit on the high-pressure side, and thus uses
resistors, inductors and capacitors to represent that on the
high-pressure side.
Based on the field measurement, more serious over-
voltage in neutral-section passing occurred in the tran-
sient process after the main breaker was cut. Thus, the
harmonic source considered in this paper is not provided
by the locomotive itself but by other locomotives through
the traction network, which here equivalent with an ideal
current source. On the basis of the four parts of equiva-
lent circuit above [8], we considered the equivalent
source and equivalent impendence of the traction substa-
tion and the capacitance between catenaries and neutral
section to build the equivalent model of the neu-
tral-section passing harmonic resonance overvoltage as
shown in Figure 3.
Among this, the left and right powered arm in the trac-
tion network are series-connected by traction substation’s
equivalent power (ua, ub) and equivalent impedance (Zsl,
Zsr); the locomotive model is replaced by the locomotive
equivalent impedance (Zm); the harmonic source is
equivalent to an ideal current source(Ih); the traction
network and neutral section line equivalent circuit of left
and right powered arm are formed by two parts of equiv-
alent impedance (Ztl,Zn,Ztr) and capacitance (Ctl,Ctl1,
Cnl,Cnr,Ctr,Ctr1) to ground, taking the capacitance
(Ccnl,Ccnr) between left, right arms and neutral segment of
traction network into consideration at the same time, to
accomplish the equivalent modeling for simulation model
of harmonic resonance overvoltage of section-phase
passing.
4. Simulation Analysis of the Neutral-section
Passing Harmonic Resonance Overvoltage
This paper selects the automatic on-board neutral-section
passing system based on the overlapping section as the
research object, and the neutral-section passing transient
process is divided into five transient processes, based on
the different operating position of the locomotives in the
electrical sectioning device.
4.1. The First Transient Process
The first transient process is the contact of the closure
and the dead section transient process when the electric
locomotives enter the dead section. On the basis of the
previous analysis, after the appropriate circuit simplifica-
tion and equivalent, the establishment of the transient
process simulation model is shown in Figure 4.
The simulation model is built in MATLAB / Simulink
as shown in Figure 4, by controlling the closure of the
circuit breaker and setting the current value of the har-
monic source analog the harmonic resonance overvoltage
analysis, as the contact of the closure and the dead sec-
tion transient process when the electric locomotives enter
the dead section.
4.2. The Second Transient Process
The second transient process is the separate of the clo-
sure and the dead section transient process when the
electric locomotives enter the dead section. On the basis
of the previous analysis, after the appropriate circuit
simplification and equivalent, the establishment of the
transient process simulation model is shown in Figure 5.
Figure 3. The equivalent schematic of the electric locomo-
tives neutral-section passing harmonic resonance overvolt-
age.
Figure 4. Simulation analysis schematic diagram of the first
transient process.

X. F. JIANG ET AL. 549
Figure 5. Simulation analysis schematic diagram of the
second transient process.
The simulation model is built in MATLAB / Simulink
as shown in Figure 5, by controlling the closure of the
circuit breaker and setting the current value of the har-
monic source analog the harmonic resonance overvoltage
analysis, as the separate of the closure and the dead sec-
tion transient process when the electric locomotives enter
the dead section.
4.3. The Third Transient Process
The third transient process is the contact of the closure
and the dead section transient process when the electric
locomotives exit the dead section [9]. On the basis of the
previous analysis, after the appropriate circuit simplifica-
tion and equivalent, the establishment of the transient
process simulation model is shown in Figure 6.
The simulation model is built in MATLAB / Simulink
as shown in Figure 6, by controlling the closure of the
circuit breaker and setting the current value of the har-
monic source analog the harmonic resonance overvoltage
analysis, as the contact of the closure and the dead sec-
tion transient process when the electric locomotives exit
the dead section.
4.4. The Fourth Transient Process
The fourth transient process is the separate of the closure
and the dead section transient process when the electric
locomotives exit the dead section. On the basis of the
previous analysis, after the appropriate circuit simplifica-
tion and equivalent, the establishment of the transient
process simulation model is shown in Figure 7.
The simulation model is built in MATLAB / Simulink
as shown in Figure 7, by controlling the closure of the
circuit breaker and setting the current value of the har-
monic source analog the harmonic resonance overvoltage
analysis, as the separate of the closure and the dead sec-
tion transient process when the electric locomotives exit
the dead section.
4.5. The Fifth Transient Process
The fifth transient process is the closure of the main cir-
cuit breaker transient process when the electric locomo-
tives exit the dead section [10]. On the basis of the pre-
vious analysis, after the appropriate circuit simplification
and equivalent, the establishment of the transient process
simulation model is shown in Figure 8.
The simulation model is built in MATLAB / Simulink
as shown in Figure 8, by controlling the closure of the
circuit breaker and setting the current value of the har-
monic source analog the harmonic resonance overvoltage
analysis [11], as the closure of the main circuit breaker
transient process when the electric locomotives exit the
dead section.
5. Simulation Analysis
Calculating and setting the parameters in the above mod-
els [12], the value of Cm is 1 uF, the value of Lm is 5H,
the value of Rm is 100 MΩ, the value of Ln is 0.001H, the
value of Rn is 0.039 Ω, the values of Cnl and Cnr are 71 nF,
the values of Rsl and Rsr are 0.02 Ω, the values of Lsl and
Lsr are 1.19 mH, the values of Ctl、Ctl1、Ctr、Ctr1 are 40.26
nF, the values of Rtl and Rtr are 2.34 Ω, the values of Ltl
and Ltr are 0.06 H ,the values of Ccnl and Ccnr are 5 uF.
Figure 6. Simulation analysis schematic diagram of the
third transient process.
Figure 7. Simulation analysis schematic diagram of the
fourth transient process.
Figure 8. Simulation analysis schematic diagram of the fifth
transient process.

X. F. JIANG ET AL.
550
(a) The voltage oscillogram of the first transient process
(b) The voltage oscillogram of the second transient process
(c) The voltage oscillogram of the third transient process
(d) The voltage oscillogram of the fourth transient process
(e) The voltage oscillogram of the fifth transient process
Figure 9. The voltage oscillograms of the pantograph col-
lector head.
By setting the circuit breaker operation time is 0.20428
s, and the frequency of the ideal current source was taken
to the resonant frequency of the transient process [13].
When the value of is 0 A to simulate that the system does
not occur harmonic resonance overvoltage, and when the
value of is 5A to simulate that the system occurs har-
monic resonance overvoltage. Simulation analysis of the
all five transient processes, Figure 9 shows the wave-
form summary of the voltage of the pantograph collector
head.
The simulation analysis shows that the operating
overvoltage of the neutral-section passing is serious in-
tensified by the overvoltage of harmonic resonance [14],
when the system harmonic resonance occurs, which
made the amplitude of the overvoltage exceed 100kV.
Over time, the overvoltage of the neutral-section passing
tends to smooth. In the first four transient processes, the
harmonic resonance occurred before and after the circuit
breaker operation. This is because that the system pa-
rameters don’t before and after the breaker action, so the
resonant frequency doesn’t change significantly. How-
ever, in the fifth transient process, the system didn’t oc-
cur the harmonic resonance before circuit breaker opera-
tion [15]. This is because that the system parameters
change significantly after the breaker action. The fre-
quency of the harmonic source applied to the system is
the resonance frequency after the circuit breaker opera-
tion.
6. Conclusions
Through modeling the simplified traction power supply
system and electric locomotive, and dividing, modeling,
analyzing and simulating for the electric locomotives
neutral-section passing process, one can know that over-
voltage caused by the harmonic resonance when the sys-
tem meet a condition that harmonic resonance could
taken place can lead to the voltage during
phase-separation process operating seriously intensifica-

X. F. JIANG ET AL.
551
tion [16], which will make the voltage of the pantograph
collector head exceeding 100 kV and penetrating the air
gap and causing serious threats to the electric railway
safety operation. However, this kind of neutral-section
passing overvoltage hasn’t cause the attention in the field
and theoretical studies, which need more analysis and
verification in the further study.
7. Acknowledgements
The authors would like to thank the High-Speed Railway
Basic Research Fund Key Project (U1134205); National
Natural Science Foundation of China (51177139); Sci-
ence & Technology Research and Development Key
Project of Railway Ministry (2011J023-B) for financial
support.
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