AC traction systems can be 25 kV/50 Hz single-phase, non-linear, time-varying loads of random naturecausing unbalance and distortion of the supply voltages. To reduce voltage unbalance, thyristor controlledreactances are usually delta-connected with traction systems. This setup, called Steinmetz circuit, canadapt reactance values to traction load fluctuations in order to balance consumed currents. To avoidvoltage distortion problems due to harmonic currents injected by traction loads, resonances betweenthe Steinmetz and supply system reactances “observed” from the traction system must be analyzed. Thispaper characterizes stochastic behavior of these resonances, which is caused by random variations intraction power consumption. The study used simulations of an AC traction system with intercity servicesand measurements of a French railway traction substation.