A Method for Interfacing Lumped-Circuit Models and Transmission-Line System Models With Application to Railways

Transient analysis of lossy multiconductor transmission lines (MTLs) has been studied using the finite-difference time-domain (FDTD) method with lumped loads/devices connected at line terminations. In electrified railway networks, series and shunt devices (whose circuit models are derived either from experiments/borrowed off the shelf), e.g., transformers, converters, switchgear, signal equipments, etc., are found distributed along the MTL system. To simulate such railway systems involving both transmission lines (TLs) and lumped circuits, an interface technique between TL systems, which is solved using FDTD, and all the lumped circuits, which are solved using alternative transients program/electromagnetic transients program software (circuit solver), is proposed. This sufficiently accurate method is simple to apply as only instantaneous voltages and currents are transmitted between the stand-alone FDTD routine and circuit solver. Moreover, the user avoids coding complex circuit models within the FDTD, while at the same time, efficiently uses the potential of accurate frequency-dependent loss models (nonexistent in circuit software) coded in FDTD. The technique is applied on typical electrified railway systems to demonstrate how traction transformers, track circuits, and line interconnections affect the propagating voltages and currents. The method could be beneficial for transient protection and insulation coordination studies in electrified railway systems.