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The high-frequency negative damping characteristics of the electric train and the traction network interaction system may excite harmonic instability issues. This paper proposes a detailed impedance model and a simplified method in the αβ-frame for investigating the high-frequency impedance characteristic of the electric train. Meanwhile, the impedance model is validated by means of the frequency sweeping method. Based on the αβ-frame impedance model of the train, the negative damping range is mathematically expressed. It is helpful for analyzing the impacts of controller bandwidths and network impedances on the harmonic instability. In addition, a voltage feedforward filter combining its transfer function is proposed to enhance the system stability. Taking advantages of the proposed voltage feedforward filter, the output impedance of the train can maintain passive characteristics well in a specific high-frequency range, effectively avoiding harmonic instability issues. Simulation and experimental results validate the effectiveness of the proposed harmonic instability analysis and suppression methods.
Tao et al. (Thu,) studied this question.