Resonance effect of insulated negative current rail in a subway network

A modeling technique of a subway network is performed in order to quantify the effect of insulated negative current rail on resonance frequencies. A DC track circuit is modeled by means of transmission line modeling (TLM) approach to perform line current and voltage calculation. Impedance and admittance required by TLM equations are first derived. System impedance is expressed in terms of internal and external impedance. The former is calculated using exact expression of a cylindrical conductor whereas the external impedance is taken as the sum of conductor's reactance considering a perfect conducting plane and the ground impedance. The well-known Carson's formulas for ground impedance are compared to Sunde's one to investigate frequency range applicability of the former. Simulations reveal that Carson's expressions are valid for frequencies up to 50 kHz. It appears, however, that using Cason's formulas for higher frequencies lead to underrating ground impedance. To investigate the accuracy impact of internal impedance, ground impedance and inductance on resonance frequencies, a sensitivity analysis is performed. A noticeable resonance effect is observed at 8 kHz for a 10 km length rail. Simulation results show the network impedance effect on track current and voltage.