Transient Analysis of ZPW-2000A Rail Circuit Based on Fractional Order Transmission Line Theory

In practical circuit systems, inductance and capacitance have fractional-order characteristics, and attempting to describe them solely with integer-order models can introduce errors. Furthermore, existing methods for dealing with rail circuit termination to variable-frequency loads and addressing high-frequency losses induced by skin effects are fraught with challenges and time-consuming. Therefore, a method is proposed for solving the rail surface voltage at the receiving end of the ZPW-2000A rail circuit in the complex frequency domain. Firstly, a fractional-order transmission line model for the rail circuit is established. Subsequently, the node admittance method, in conjunction with the Quotient-difference(Q-D) algorithm, is employed to solve for the rail surface voltage. Finally, the correctness of this proposed method is validated through comparison with the time-domain finite-difference method, and the impact of overvoltage at the rail circuit’s power-receiving end under various transient signal excitations is analyzed. The results demonstrate that the fractional-order transmission line model for the rail circuit conforms to the propagation characteristics of rail surface voltage, providing a theoretical reference for the accurate modeling of rail circuits.