# Calculation Of Rail Impedance Of Track Circuit Considering Earth Stratification

Bin Zhao This email address is being protected from spambots. You need JavaScript enabled to view it.1, Jingning Ou1, and Dong Wang1

1School of Automation Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

Accepted: March 28, 2022
Publication Date: April 29, 2022

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

## ABSTRACT

Rail impedance directly affects the transmission performance of track circuit. Considering the condition of earth stratification, it is difficult to calculate the rail impedance due to the semi-infinite integration interval and the oscillation of the integrand by the Carson formula. Then proposing a truncation method which is applied to divide the impedance formula into definite integral and tail integral revised: a truncation method is proposed,which is applied to divide the impedance formula into definite integral and tail integral. The definite integral is approximated by the spline function which can obtain by using moments method, and the tail integral is calculated by the exponential integral and Euler formula. The rail impedance calculation formula of track circuit is obtained. The electromagnetic field model of track circuit with earth stratification is simulated by finite element method. Comparing the results of proposed method with finite element method, the relative error is within 5%, so the validity of proposed mothed is proved. The influence of current frequency and soil depth on rail impedance is studied . The results show that the formula can correctly reflects the law of rail impedance variation with current frequency and soil depth. A reliable reference is provided for the theoretical calculation of rail impedance of track circuit.

Keywords: Rail impedance, Earth stratification, Carson formula, Truncation method, Finite element method

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0.9
2021CiteScore

42nd percentile