Mechanism Analysis of Ferroresonance in 10 kV Power Supply System for High-Speed Railway Based on Harmonic Balance Method and Floquet Theory
Wang Xian1,2,3, Wang Faqiang1,2, Yang Jiahang1,2
1. School of Electrical Engineering Xi’an Jiaotong University Xi’an 710049 China; 2. State Key Laboratory of Electrical Insulation and Power Equipment Xi’an 710049 China; 3. China Railway Xi’an Group Co. Ltd Xi’an 710054 China
Abstract：10 kV power supply system of high-speed railway is a neutral ungrounded system. Ferromagnetic saturation in the phase of electromagnetic voltage transformers (VT) can cause overvoltage due to the neutral offset when the system is disturbed by open circuit, short circuit, and reclosing. With the increase of excitation or magnetic field intensity of the VT, the excitation inductance exhibits significant nonlinear characteristics with magnetic saturation. In this scenario, the secondary winding can be ignored, and the primary side’s magnetic saturation and hysteresis loss characteristics are considered. Therefore, this system is a typical nonlinear, non-autonomous system with time-varying excitation, rich in complex nonlinear phenomena like ferroresonance. In the paper, VT is represented by the parallel connection of nonlinear inductance L and iron loss conductance G. The principal saturation flux-current curve of the nonlinear inductance can be expressed by the polynomial is=aφ+bφ n, where n is taken as 5 based on the actual engineering, a is 8.6×10-5, and b is 7.3×10-11 from the measured volt-ampere characteristic data of the voltage transformer. This paper forms a simplified circuit model containing excitation source uo, series capacitance Ceq, excitation conductance G, and nonlinear inductance L. The state equation of the system is established with the nonlinear inductance flux φ and voltage u as the state variables using Thevenin's theorem. Then, based on the orthogonality of the trigonometric function, the harmonic balance method solves the periodic approximate solutions of the system under different parameters, and the periodic Jacobian matrix J(t) of the system under the parameters is derived. On this basis, J(t) is piecewise integrated, and its average value in the m-th section ${{\bar{J}}_{m}}$ is obtained. The transfer matrix Mtr of the system and the eigenvalue of Mtr (i.e., the Floquet multiplier) can be obtained conveniently. There are three kinds of relations between Floquet multiplier and bifurcation behavior of the nonlinear system, according to which the stability of periodic solution can be identified. The calculation shows that with the gradual increase of the excitation, the Floquet multiplier is changed from a conjugate complex number to independent real numbers with a pair of real numbers gradually increasing and imaginary numbers decreasing. Herein, one real Floquet multiplier gradually increases in the positive direction and moves out of the unit circle, the other remains in the unit circle and gradually decreases, and the saddle junction bifurcation occurs, leading to ferroresonance. With the change of series and parallel capacitance of the saturated phase, the critical excitation amplitude Em for maintaining stable operation of the system changes. Furthermore, the stability region of spatial parameters under different conditions can be obtained. The paper also gives the critical parameters related to the stability of the system through sensitivity analysis and mathematical calculating for this system’s parameter design. Finally, the circuit simulation results in ATPDraw align with the theoretical calculation. Therefore, the ferroresonance phenomenon in the 10 kV power supply system of the high-speed railway can be effectively analyzed using the harmonic balance method and Floquet theory. In conclusion, this study has practical value in the prevention and elimination of ferroresonance in neutral ungrounded systems containing electromagnetic voltage transformers.
王显, 王发强, 杨佳航. 基于谐波平衡法及Floquet理论的高速铁路10 kV供电系统铁磁谐振机理分析[J]. 电工技术学报, 2024, 39(18): 5588-5598.
Wang Xian, Wang Faqiang, Yang Jiahang. Mechanism Analysis of Ferroresonance in 10 kV Power Supply System for High-Speed Railway Based on Harmonic Balance Method and Floquet Theory. Transactions of China Electrotechnical Society, 2024, 39(18): 5588-5598.
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2024, Vol. 39 
