基于增量谐波平衡与自适应弧长法的铁路电力系统铁磁谐振分岔分析

doi:10.19595/j.cnki.1000-6753.tces.260624

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摘要

非线性参数匹配激发的铁磁谐振在铁路电力系统中频繁发生,严重时会导致铁路行车通信、信号等一级负荷供电中断。该文以铁路10 kV电力系统为研究对象,提出一种基于增量谐波平衡与自适应弧长法的铁磁谐振分岔分析方法。首先,考虑电压互感器铁芯饱和的非线性,建立了铁磁谐振零序等效模型。其次,利用增量谐波平衡法构造解析切线刚度矩阵,并设计具备奇异值监测功能的步长自适应弧长法,实现了多值非线性响应曲线的连续追踪。然后,利用Floquet理论识别启振与消振对应的分岔类型,揭示了铁磁谐振鞍结分岔的机理。与传统方法的仿真对比表明,所提方法在非线性响应的完整追踪方面更具优势。最后,定量揭示了系统等效参数与非线性系数对分岔边界的影响规律,并通过ATPDraw平台验证了所提方法及分析结果的正确性。

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	王嘉伟
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	吴命利

关键词 ：铁路电力系统, 铁磁谐振, 增量谐波平衡法, 自适应弧长法, Floquet理论, 鞍结分岔

Abstract：

Ferroresonance in railway power systems, driven by potential transformer (PT) core saturation coupled with rising cable-induced ground capacitance, can interrupt power supply to critical traffic communication and signaling loads. To overcome these limitations, this paper proposes a nonlinear bifurcation analysis method for 10 kV railway power systems based on the incremental harmonic balance and adaptive arc-length method (IHB-AALM).
A zero-sequence equivalent ferroresonance model incorporating PT core saturation is established, with the nonlinear magnetization curve approximated by an odd-order polynomial. The incremental harmonic balance procedure is then formulated by expanding both excitation and response in truncated Fourier series and applying Galerkin projection to the residual, yielding an analytical tangent stiffness matrix around the reference solution that eliminates the error accumulation inherent in numerical differentiation. To traverse bifurcation singularities where the stiffness matrix becomes ill-conditioned, an arc-length continuation scheme augmented by a singular-value monitor is constructed: a normalized arc-length constraint replaces load-controlled stepping so that the predictor advances along the solution manifold, while the minimum singular value of the tangent matrix is tracked at each step. Three coordinated mechanisms govern step evolution—convergence-rate-based step adjustment that enlarges or contracts the arc increment according to Newton iteration counts; an emergency compression trigger that abruptly shrinks the step when the singular-value ratio between adjacent steps drops below 0.1, signaling proximity to a turning point; and a divergence-recovery strategy that reduces harmonic truncation order to restore solvability when iteration fails. This combination enables continuous tracking of response curves across saddle-node points and complete acquisition of unstable branches. Floquet theory is finally embedded to identify saddle-node bifurcation boundaries from the monodromy spectrum, with the unit-circle crossing of the dominant multiplier serving as the stability criterion.
Compared with the Runge-Kutta, conventional harmonic balance, and harmonic balance arc-length methods, the proposed method continuously tracks global response branches and accurately locates saddle-node bifurcation points. At rated frequency, excitation amplitudes of 1 935.51 V and 12 041.12 V partition the excitation axis into a non-resonant monostable region, a multi-stable coexistence region, and a ferroresonant monostable region; once ferroresonance occurs, the PT peak voltage reaches two to three times the normal value with severe waveform distortion. Parametric analysis reveals that the equivalent capacitance C_e and core nonlinear coefficient b dominate bifurcation boundaries: reducing b raises the ignition threshold and lowers the extinction threshold, whereas enlarging C_e improves both in amplitude and frequency. Accordingly, C_e is recommended to be no less than twice the baseline and b no larger than 0.6 times the baseline. PT waveforms at eight verification points reproduced on ATPDraw agree with the bifurcation predictions.
Three conclusions are drawn. (1) Through the analytical tangent stiffness matrix and adaptive step-adjustment strategy, the IHB-AALM overcomes convergence failure at bifurcation singularities and completes tracking of multi-valued response curves including unstable branches. (2) Ferroresonance state jumps manifest dynamically as saddle-node bifurcations, and the rated operating point falling within the multi-stable coexistence region explains why transient disturbances trigger resonance. (3) Reducing b, or enlarging C_e or core-loss resistance R_e, expands the non-ferroresonant stable region, offering practical guidance for resonance suppression without hardware modification.

Key words： Railway power system ferroresonance incremental harmonic balance method adaptive arc-length method Floquet theory saddle-node bifurcation

收稿日期: 2026-04-26

PACS:

TM922.0

基金资助:

先进轨道交通自主运行全国重点实验室(北京交通大学)自主研究课题(RAO2025ZD002)和中央高校基本科研业务费专项资金资助项目(2025YJS078)

通讯作者: 杨少兵男,1972年生,博士,教授,博士生导师,研究方向为电力系统、铁道电气化、负荷建模、牵引供电智能化。E-mail：shbyang@bjtu.edu.cn

作者简介: 王嘉伟男,2001年生,硕士研究生,研究方向为铁道电气化、牵引回流系统建模、新能源储能技术。E-mail：24121339@bjtu.edu.cn

引用本文:

王嘉伟, 王迎晨, 杨少兵, 吴命利. 基于增量谐波平衡与自适应弧长法的铁路电力系统铁磁谐振分岔分析[J]. 电工技术学报, 0, (): 624-. Wang Jiawei, Wang Yingchen, Yang Shaobing, Wu Mingli. Analysis of Ferroresonance Bifurcation Behavior in Railway Power Systems Based on Incremental Harmonic Balance and Adaptive Arc-Length Method. Transactions of China Electrotechnical Society, 0, (): 624-.

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https://dgjsxb.ces-transaction.com/CN/10.19595/j.cnki.1000-6753.tces.260624 https://dgjsxb.ces-transaction.com/CN/Y0/V/I/624

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