Modeling of frequency-dependent impedance of the third rail used in traction power systems

This paper presents a numerical method based on the technique of subdivision of conductors to evaluate the frequency dependent impedance of the third rail used in the Taipei rapid transit systems. The influence of the skin effect upon variations of rail resistance and inductance is studied. Rail impedances calculated using a finite element method are taken as references to validate the results obtained from the proposed numerical method. An equivalent tubular conductor model has also been derived to approximate the variations of the third rail's resistance and inductance over a sufficiently wide range of frequency. With the proposed method, the distribution of current over the cross section of the third rail at different harmonic frequency can be clearly visualized.