In order to deal with the difficulty in calculation of rail internal impedance caused by skin effect and irregular sections of the rail

the rail is taken as a cylindrical conductor at first.Based on that

the formula of internal impedance under the current at both low and high frequency are derived.According to the derived formulae and Rolle’s average value theorem as well as Maclaurian approximate formula

the formula adapted to the whole frequency range is obtained.Finite element method is used on the rail model to simulate and calculate the impedance.The result shows that the formula can correctly reflect the change rules of rail alternating current resistance and internal inductance with current amplitude and frequency.The error between the calculation result and the simulation result is less than 6 %

which verifies the formula.The research can be a theoretical basis for the calculation of rail internal impedance under the establishment of a traction power supply system model.