Method to include lumped devices in multi-conductor transmission line system models

Transient analysis and crosstalk in multiconductor transmission line (MTL) systems with internal and external losses has been widely studied by solving telegrapher´s equation using the finite difference time domain (FDTD) method. Most of those studies are carried out with lumped loads/devices connected at the line terminations (at source and load ends). However, in practical systems such as typical railway and power systems, lumped devices, like, transformers, rotary converter stations, line interconnections and insulators, substation and switchgear equipments (grounding systems, insulators, surge protectors, circuit breakers, etc.) and signaling equipments exist either in series or in shunt with the MTL systems, but not necessarily at the ends. Detailed/complex circuit models (linear or nonlinear) for all those devices either exist in the literature or can be developed from experiments. In this paper a more general method based on Kirchoff´s current law (nodal analysis) is proposed to interface the FDTD code with Alternative Transients Program/Electromagnetic Transients Program (ATP/EMTP) circuit simulation software for transient analysis with any complex circuit model along the MTL system. The method is efficient and simple and it could be beneficial for accurate and realistic transient protection, mitigation and insulation coordination studies in large distributed electrical systems. A case study is made for an electrified railway with booster transformer traction system.