Study of Resonances in 1 $\times$ 25 kV AC Traction Systems With External Balancing Equipment

AC traction systems are 1 × 25 or 2 × 25 kV/50 Hz single-phase, nonlinear, time-varying loads that can cause power-quality problems, such as unbalanced or distorted voltages. To reduce unbalance, external balancing equipment is usually connected to these systems, forming the Steinmetz circuit. Parallel resonances can occur in these types of circuits, exciting the harmonic emissions (below 2 kHz) of railway-adjustable speed drives. This paper studies these resonances at pantograph terminals and provides analytical expressions to determine their harmonic frequencies. The expressions are validated from several traction systems in the literature and PSCAD simulations.