Input Impedance Modeling of Three-Level Multi-Stage NPC Topology

This paper presents a simple and vivid method to model the small signal input impedance of a single-phase three-level multi-stage neutral point clamped (NPC) converter system based on an electric locomotive (Re460) as used for e.g. passenger trains and operated by Swiss Federal Railways (SBB - “Schweizerische Bundesbahnen”). In general, these trains consist of several phase-shifted and paralleled NPC sub-stages in order to handle more than 6MW maximum output power. Each NPC branch is typically operated at 200 Hz switching frequency which results in a rather low and limited maximum bandwidth for every appropriate current control circuit. Therefore an input impedance resonant peak at very low frequency values can be expected. Without proper damping of all occurring critical input impedance frequency areas of the electric train, the stability of the total system-grid/locomotive(s)-can not be guaranteed especially if two or more trains are operated simultaneously and the capacitive share in such a railway network is fairly high (e.g. high amount of cabling). Therefore, a simple analytically derived averaged mathematical model of such locomotive becomes beneficial if an optimization of locomotive design parameters and a rough evaluation of the stability (electric vehicle-grid output impedance) of the system at different locations within the railway network is of interest. The proposed solution is, furthermore, supported by and compared to simulation results (performed with the simulation software PLECs) of an actual switched three-level NPC implementation (including low-frequency transformer and all 8 sub-stages) of the train.