A Multifrequency Model of Electric Locomotive for High-Frequency Instability Assessment

The high-frequency instability (HFI) issue results in serious harmonic overvoltage phenomena in the electrification railway system. This issue is rooted in the range that is not only below, but also above half the switching frequency. The commonly used small-signal averaging model is a single-frequency model in which the corresponding frequency component with perturbation frequency is considered merely. The inherent sampling nature has been neglected by the moving average operator. Therefore, it cannot reveal the effect of sideband components and may not be valid for predicting the high-frequency input admittance of a locomotive. To investigate the HFI issue, the sideband components generated by analog/data (A/D) sampling process and pulse width modulation (PWM) are taken into consideration. Then the multifrequency model of a locomotive is developed for evaluating the influences of sideband components. Meanwhile, the proposed model is validated by means of the frequency scan method, including the identification of PWM transfer functions and crossed-frequency transfer functions. Several HFI cases are summarized for comparing the accuracy between the traditional single-frequency model and the proposed multifrequency model. It denotes that the multifrequency model is more accurate to assess the high-frequency input admittance of a locomotive, especially the regions around the sampling frequency. Hardware-in-loop (HIL) results validate the theoretical analysis.