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This paper presents an impedance-based method to systematically investigate the interaction between multiple trains and a traction network, focusing on evaluating the harmonic instability problem. First, the interaction mechanism of the multitrain and the traction network is represented as a feedback interconnection of the two subsystems, i.e., an equivalent output impedance of the traction network and an equivalent input admittance of the multitrain. Then, the harmonic instability is evaluated through a series of pole-zero diagrams drawn from the closed-loop transfer matrix of the multitrain and network system. The interaction system is unstable, and the harmonic instability will happen if there are some high-frequency poles of the closed-loop system locating in the right-half plane. This method is used for analyzing the harmonic instability phenomena, the characteristics, influential factors, and potential mitigation schemes. The theoretical results are further validated by the simulations and experiments.
Tao et al. (Mon,) studied this question.