CHEN Wanglong, LI Yaning, WANG Ye

(1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China；2. School of Environmental and Municipal Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China)

Abstract： In order to explore the influence of soil resistivity on stray current in power supply system of urban rail transit, we establish an equivalent circuit model of the rail-to-ground structure based on resistance network method first. After measuring the soil resistivity of a real subway system, a simulation model is established in Matlab to obtain the stray currents at different soil resistivities. Then the influence of soil resistivity on stray current is analyzed. Afterwards, to verify the rationality and reliability of the simulation model, we design a test circuit to measure the stray current and rail-to-ground voltage in a real subway system, and a comparison of the experimentally measured results and simulation results is presented. The results show that the stray current is the maximum when the soil resistivity is 211.57 Ω·m; when the soil resistivity is 768.47 Ω·m, the stray current is the minimum, that is, the smaller the soil resistivity, the greater the stray current. Therefore, the resistivity should be increased as much as possible when ramming the track foundation in urban rail transit system.

Key words： urban rail transit； power supply system； stray current； soil resistivity； four-electrode method

0 Introduction

The urban rail transit features fast speed, punctuality, large carrying capacity and low energy consumption so that it plays an increasingly important role in people’s daily lives. Accordingly, there exist currents leaking from the railway tracks into the ground, which is called stray currents caused by various elements[1-3]. At present, the research on stray currents mainly focuses on optimization of circuit model of rail-to-ground structure[4], design of current drainage net[5-8], electrochemic corrosion mechanism of metal pipelines[9], dynamic characteristics of stray current[10], layout of traction power supply structure[11-12], selection of grounding modes of traction substation[13], magnitude of resistivity[14]and voltage level of traction substation[15], etc. However, most of them focus on simulation analysis but lack of experimental data. Moreover, the theoretical analysis and experimental test on soil properties is uncomprehensive although soil resistivity is an important factor which affects the spatial and temporal distribution of stray current but is rarely reported. In our work, the influence of soil resistivity on stray current is studied by simulation and experimental tests on the soil of a real subway system.

1 Equivalent circuit of rail-to-ground structure

Taking a real subway system as the research object, considering the existence of stray current, we establish the equivalent circuit model of rail-to-ground structure with the distribution of stray current, as shown in Fig.1.

Fig.1 Equivalent circuit diagram of rail-to-ground structure of a subway system

The traction substation is regarded as the current source(I), each metal structure of the rail is regarded as a resistor(R), and the rail is regarded as being composed of series resistors. The transition resistance between the rail and the ground is represented asRg, and soil resistance is represented asRt. Based on this, letα2=R/Rg, we can derive the changing laws of stray current and rail-to-ground voltage as[17-19]

(1)

(2)

wherexis the distance from any point on the rail to the substation;Lis the distance between the locomotive and traction power substation;u(x) is the voltage at positionx; andis(x) is the stray current at positionx.

2 Measurement of soil resistivity

Soil resistivity is defined as the average value of soil resistance per unit length. It directly affects the grounding resistance of grounding device as well as the voltage distribution of ground network. Fig.2 shows the schematic diagram to measure the soil resistivity by means of four-electrode method.

Fig.2 Schematic diagram of measuring soil resistivity by four-electrode method

Soil resistivity can be got by

(3)

Table 1 Measurement results of soil resistivity

3 Simulation of stray current and rail-to-ground voltage

3.1 Simulation of stray current

According to the equivalent circuit model of the rail-to-ground structure in section 1, we can establish the simulation model of stray currents based on Matlab, as shown in Fig.3.

Fig.3 Simulation model of stray current and rail-to-ground voltage distribution

Fig.4 Simulation results of stray currents

The stray current distribution within a given rail section is shown in Fig.5.

Fig.5 Stray current distribution within a given rail section

It can be seen that in the direction parallel to the rail, the stray current increases first and then decreases, and its maximum value occurs in the middle of the rail section; in the direction perpendicular to the rail, the stray current decreases from the rail to both ends.

3.2 Simulation of rail-to-ground voltage

Fig.6 Simulation results of rail-to-ground voltage

The rail-to-ground voltage distribution within a given rail section is shown in Fig.7. It can be seen that in the direction parallel to the rail, the rail-to-ground voltage reaches the maximum at the track terminal and then linearly decreases to the minimum in the middle of the the track section; in the direction perpendicular to the rail, the rail-to-ground voltage decreases from the rail to both ends.

Fig.7 Rail-to-ground voltage distribution within a given rail section

4 Experimental verification

To verify the rationality and reliability of the simulation model, we design a test circuit[16]to measure the stray current and rail-to-ground voltage in a real subway system, as shown in Fig.8. A Fistech FT10010 DC power supply (output voltage: 0-100 V, output current: 0-10 A) is used to simulate the traction substation, and 11 cement resistors in series (R=1 Ω,P=10 W) are used to simulate the rails. Ten 7-cm probes are inserted into the soil at an interval of 4 cm between probes, and every probe is welded to the corresponding nodes between the two rail resistors. The negative pole of VICTOR 98A+ voltmeter is connected to the soil and its positive pole is connected to the nodes. In this way, the voltage between the node and the soil can be measured. The measured traction current values are displayed on ammeter A1, the measured stray current values are displayed on ammeter A2, and the measured rail-to-ground voltage values are displayed on voltmeter V. In our study, when the traction current is 0.5 A, 1.0 A, 1.5 A and 2 A, respectively, the average values of stray currents and rail-to-ground voltage are obtained through three times’ measurement.

Fig.8 Measuring principle diagram of stray current and rail-to-ground voltage

The simulation results and experimental results of stray currents and rail-to-ground voltages at different soil resistivities are compared and analyzed, as shown in Figs.9-10.

It can be seen from Fig.9 that with the increase of the traction current, the stray current flowing into the ground increases. If the the traction current is fixed, with the increase of soil resistivity, the stray current decreases. The maximum error between the simulation results and the measured results is about 1.5%, which is caused probably by the thermal effect of resistance, the error between the Matlab simulation calculation model and the experimental measurement.

Fig.9 Comparison of experimental and simulation results of stray current

It can be seen from Fig.10 that with the increase of the traction current, the amplitude of rail-to-ground voltage reaches the maximum at both ends of the track section and the minimum in the middle of the track section. The maximum error between the simulation results and the measured results is about 5%.

Fig.10 Comparison of simulation and experimental results of rail-to-ground voltage

5 Conclusions

Through the simulation analysis and experimental verification of stray current and rail-to-ground voltage at different soil resistivities, the conclusions are as follows:

2) With the increase ofthe traction current, the amplitude of rail-to-ground voltage reaches the maximum at both ends of traction section and reaches the minimum in the middle of traction section.

3) The error between the simulation results and the experimental results of the stray current is about 1.5%, and error of the rail-to-ground voltage is about 5%.