The internal impedance of rail exhibits non-linear freuqnecy-dependent charcateristics. If it is treated as a constant value in the transient modeling of the DC short circuit in the subway traction power supply system

it will inevitably lead to an increase in transient calculation errors

adversely affecting the subsequent fault distance measurement. To determine the frequency-dependent internal impedance of rail

the rail is modeled as long straight cylindrical conductor

and the analytical formula of internal impedance expressed by Bessel function is derived. As for the unreliable calculation result of inetrnal impedance formula due to the limitation of Bessel series expression

a Prony method with expotential approximation is proposed to approximate Bessel function. An internal impedance calculation correction formula with ease of programming and high accuracy is obtained. At the same time

the finite-element method is used to simulate the eddy current field of rail and the radii of model suitable for calculating rail internal impedance in different frequency bands is given. The results of research show that the modified internal impedance calculation formula can not only avoid the numerical calculation problem of large parameters

but also correctly reflect the non-linear variations of rail resistance and internal inductance with current frequency (0-500 Hz) and amplitude (300-10 000 A). When the current amplitude varies from 300 A to 10 000 A

the Pearson correlation coefficients between the calculated results and simulated results of rail resiatance and internal inductace under different frequencies are all above 0.999 8

and the relative errors are all within ±5%

which verify the accuracy and effectiveness of the proposed method

providing reliable data for rail impedance modeling in DC short-circuit transient calculation of metro traction power supply system.