The paper provides a description of the analysis of a subway system (track-in-tunnel) by using FEM analysis and comparing to classical analytical approaches by Carson, Pollaczek, Bickford and Tylavsky.
Reviews of methods to determine self and mutual impedance for electrified railroads are provided. These methods include frequency response and are directly applicable to a three-rail track DC track system.
The analytic impedance models are built on Carson-Pollaczek–Bickford equations, adjusted by Tylavsky, for two situations: when the ground is perfectly insulated and when considering the earth return current. For the latter, the authors assume a return current path only through the tunnel concrete structure below the railway track support structure. The model is extended by considering the effects of the soil beneath under tunnel as a conductor.
The solution of finite element method (FEM) applied for the determination of impedance for the three-rail track subway train configuration, modeled and examined, consists of computational analysis based upon minimizing the energy of electromagnetic field.
The paper continues by examining the frequency effects on the track and system. The track/trolley model developed by Tylavsky was modified such that the trolley feeder is provided by the power rail and used to calculate the return current through the traction rails. The subway train, supplied with a rectified DC power, is subjected to a significant harmonic content, which may affect the signal and control circuits.
Both experimental data and preliminary analytical and numerical calculations are presented, showing the variation of resistances and inductances of the running track with the current magnitude and frequency response. In the study, a large frequency range was considered (15Hz to 5000Hz) in order to cover all of the significant frequencies used for control and signal systems in common tracks configurations, and for which measurements have been carried. It is then shown that the power and signaling characteristics of the modeled system can predict the magnitude of the perturbation current for different values of frequency. The current density profile is illustrated for the case of a concrete tunnel structure in a subway application.
The last section consists of a discussion regarding future developments and further work.