A Multi-Frequency Input-Admittance Model of Locomotive Rectifier Considering PWM Sideband Harmonic Coupling in Electrical Railways

Electrical railway harmonic instability issues are common in the high-frequency range. The effective frequency of the traditional converter’s small-signal averaging model is below 1/2 switching frequency since the pulse width modulation (PWM) sideband harmonic components are ignored. In this article, the dynamic propagations of perturbation frequency and the generated PWM sideband components are constructed first. Then the locomotive rectifier’s multi-frequency input-admittance model is derived appropriately. Afterward, an admittance conversion approach is used to convert the multi-frequency model into the single-input–single-output (SISO) model whereas retaining the sideband frequency couplings. The proposed SISO model is more accurate than the traditional small-signal averaging model in the frequency range higher than 1/2 switching frequency. It is found that PWM sideband harmonics dominate the locomotive rectifier’s input-admittance characteristic higher than 1/2 switching frequency. Finally, based on the proposed model, the influence of different switching frequencies, control bandwidths, and traction network impedance on system harmonic stability is revealed by the hardware-in-the-loop (HIL) results.