Low-frequency oscillations in AC railway traction power systems: Train input admittance calculation and stability analysis

Dynamic interactions among the AC railway power supply network and power electronic converters feeding the trains can result in low-frequency oscillation (LFO) of the catenary voltage, leading to a power outage of the substation and the shutdown of train traffic. To determine the low-frequency stability of the railway traction power systems, the impedance of the power supply network and the total differential admittance of the trains are required. This paper addresses the development of an analytical small-signal model of the train input admittance. For this purpose, small-signal models of each dynamic element involved are obtained. Specifically, the small-signal vector transformation from the actual $dq$-frame to the estimated $\widehat{dq}$-frame is presented to model the dynamics due to errors in the coordinate rotation of the single-phase four-quadrant converter (4QC) control system. Furthermore, the quadrature signal generator second-order generalized integrator (QSG-SOGI) model is calculated in the synchronous frame. The developed admittance model is intended to accurately predict various types of instabilities and serve as a powerful tool for conducting sensitivity analyses. The validation of the proposed models will be carried out through numerical simulations involving the power supply network and train systems.