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Electrical resonance instability (ERI) phenomenon has frequently occurred near the resonance frequency of the traction network in the heavy-duty railways system. Since the effective range of the small-signal average model is lower than the 1/2 switching frequency, to analyze ERI, this paper first analyzes the sampling and PWM process in detail. Then, a multi-frequency model of the locomotive rectifier that considers sampling sideband harmonics is derived. The passive criterion is used to analyze the stability of the system. Finally, the influence of the control delay on the input-admittance is revealed. The simulation and experiments verify the correctness of the theoretical analysis.