Transient Analysis of Track Circuit Based on Fractional Order Transmission Line Model

To accurately analyze the impact of transient signals on the ZPW-2000A track circuit，this paper considers the frequency-varying loss caused by the skin effect in transmission lines and establishes a fractional-order model of the Multi-conductor Transmission Line（MTL）in the track circuit. Aiming at the transient response analysis under high-frequency loss of the ZPW-2000A track circuit，a method for solving the voltage at the receiving end of the track circuit in the time domain is proposed. Based on transmission line theory，a model of the track circuit transmission line system is established， and a fractional-order transmission line equation is formulated and solved according to the obtained model. First，the partial differential equations of the fractional-order model of the track circuit transmission line are discretized into ordinary differential equations using the Compact Finite Difference Method （CFD） in the spatial domain. Then，the G-L fractional-order definition is utilized to transform these equations into integer-order ordinary differential equations. Finally，the voltage and current responses at each point on the transmission line are obtained by combining the precise integration method with recursive convolution. Under the excitation of double-exponential signals，the accuracy of this method is verified by comparison with the state variable method，with the error between the two solutions being within 7%，and the method presented in this paper requires less time. The variation of rail overvoltage under different transient signal inputs is analyzed，revealing that the higher the signal frequency，the smaller the amplitude of rail overvoltage；the greater the ballast resistance，the larger the amplitude of rail overvoltage and the longer it takes for the signal to decay to stability. © 2024 Hunan University. All rights reserved.