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

doi:10.19595/j.cnki.1000-6753.tces.231153

Abstract
Figure/Table
References
Related Citation (15)

Download: PDF (25243 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

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 i_s=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 u_o, series capacitance C_eq, 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 M_tr of the system and the eigenvalue of M_tr (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 E_m 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.

Key words： Ferroresonance nonlinear harmonic balance saddle-node bifurcation

Received: 18 July 2023

PACS:

TM71

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Wang Xian
	Wang Faqiang
	Yang Jiahang

Cite this article:

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[J]. Transactions of China Electrotechnical Society, 2024, 39(18): 5588-5598.

URL:

https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.231153 OR https://dgjsxb.ces-transaction.com/EN/Y2024/V39/I18/5588

[1] Tran-Quoc T, Pierrat L.An efficient non linear transformer model and its application to ferrore- sonance study[J]. IEEE Transactions on Magnetics, 1995, 31(3): 2060-2063.
[2] 韩国强, 刘相龙, 赵一龙, 等. 中性点不接地配电系统并联铁磁谐振状态频域解析方法[J]. 电气技术, 2020, 21(10): 88-92.
Han Guoqiang, Liu Xianglong, Zhao Yilong, et al.Frequency domain analytical method for parallel ferroresonance state of distribution system with neutral point ungrounded[J]. Electrical Engineering, 2020, 21(10): 88-92.
[3] 华超, 周岩, 胡震, 等. 基于移相调制的无线供电与信息协同传输技术[J]. 电工技术学报, 2023, 38(16): 4233-4245.
Hua Chao, Zhou Yan, Hu Zhen, et al.Simultaneous wireless power and information transmission method based on phase-shifted modulation[J]. Transactions of China Electrotechnical Society, 2023, 38(16): 4233-4245.
[4] Wei Jufang, Feng Junji, Yao Chuang, et al.Fault analysis of 10 kV voltage transformer using the “4PT” method[C]//2021 International Conference on Control Science and Electric Power Systems (CSEPS), Shanghai, China, 2021: 368-371.
[5] 周丽霞, 尹忠东, 郑立. 配网PT铁磁谐振机理与抑制的试验研究[J]. 电工技术学报, 2007, 22(5): 153-158.
Zhou Lixia, Yin Zhongdong, Zheng Li.Research on principle of PT resonance in distribution power system and its suppression[J]. Transactions of China Electrotechnical Society, 2007, 22(5): 153-158.
[6] 朱学成, 张德文, 董尔佳, 等. 发变组冲击跳闸铁磁谐振故障仿真分析[J]. 湖北电力, 2020, 44(6): 69-74.
Zhu Xuecheng, Zhang Dewen, Dong Erjia, et al.Simulation analysis on ferromagnetic resonance fault of generator-transformer unit impact trip[J]. Hubei Electric Power, 2020, 44(6): 69-74.
[7] 曹斌, 张鹏, 陈波, 等. 基于PSCAD的500kV自耦变压器铁磁谐振过电压仿真[J]. 高压电器, 2015, 51(12): 155-161.
Cao Bin, Zhang Peng, Chen Bo, et al.Simulation of ferroresonance overvoltage caused by commissioning 500kV auto-transformer based on the pscad[J]. High Voltage Apparatus, 2015, 51(12): 155-161.
[8] 王泽忠, 司远, 刘连光. 地磁暴对电力系统稳定性的影响[J]. 电工技术学报, 2022, 37(7): 1780-1788.
Wang Zezhong, Si Yuan, Liu Lianguang.Influence of geomagnetic storms on the stability of power system[J]. Transactions of China Electrotechnical Society, 2022, 37(7): 1780-1788.
[9] 许贵民, 姚帅, 尹红霞. 中性点非有效接地系统电磁式电压互感器铁磁谐振问题研究[J]. 电气应用, 2020, 39(5): 53-60.
Xu Guimin, Yao Shuai, Yin Hongxia.Comprehensive analysis on ferroresonance of electromagnetic potential transformer for power system with invalid neutral grounding modes[J]. Electrotechnical Appli- cation, 2020, 39(5): 53-60.
[10] 魏菊芳, 唐庆华, 王飞, 等. 小电流接地系统电压互感器铁磁谐振过电压与抑制措施仿真分析[J]. 电网与清洁能源, 2015, 31(12): 48-56.
Wei Jufang, Tang Qinghua, Wang Fei, et al.Simulation analysis for ferromagnetic resonance of potential transformer and restraining measures in small current neutral grounding system[J]. Power System and Clean Energy, 2015, 31(12): 48-56.
[11] 肖洪生. 图解法解工频铁磁谐振过电压[J]. 吉林电力技术, 1983, 11(2): 45-50, 24.
Xiao Hongsheng.Graphic solution of power frequency ferromagnetic resonance overvoltage[J]. Jilin Electric Power, 1983, 11(2): 45-50, 24.
[12] 陈昌鹏, 朱松. 配电系统铁磁谐振分析[J]. 东北电力技术, 2012, 33(7): 35-38.
Chen Changpeng, Zhu Song.Distribution system ferroresonance analysis[J]. Northeast Electric Power Technology, 2012, 33(7): 35-38.
[13] 刘宝稳, 曾祥君, 张慧芬, 等. 不平衡零序电压快速精准抑制与电压消弧全补偿优化控制方法[J]. 电工技术学报, 2022, 37(3): 645-654.
Liu Baowen, Zeng Xiangjun, Zhang Huifen, et al.Optimal control method for accurate and fast suppression of unbalanced zero-sequence voltage and voltage arc suppression full compensation[J]. Transa- ctions of China Electrotechnical Society, 2022, 37(3): 645-654.
[14] 亓志滨, 田君杨, 薛永端, 等. 不接地系统异名相两点接地故障工频电气量及其对选线的影响分析[J]. 电工技术学报, 2023, 38(13): 3539-3551.
Qi Zhibin, Tian Junyang, Xue Yongduan, et al.Analysis of power frequency electrical quantity and line selection applicability for two-point grounding faults occurring on different phases in isolated neutral system[J]. Transactions of China Electrotechnical Society, 2023, 38(13): 3539-3551.
[15] 李国庆, 彭石, 张少杰, 等. 变压器与并联电容器的铁磁谐振分析[J]. 电力系统保护与控制, 2014, 42(9): 26-32.
Li Guoqing, Peng Shi, Zhang Shaojie, et al.Analysis of ferromagnetic resonance between transformer and shunt capacitor[J]. Power System Protection and Control, 2014, 42(9): 26-32.
[16] 崔巨勇, 王帅, 赵子健, 等. 电磁式电压互感器铁磁谐振特性分析[J]. 电器与能效管理技术, 2023(1): 62-65, 77.
Cui Juyong, Wang Shuai, Zhao Zijian, et al.Analysis of electromagnetic voltage transformer ferroresonance characteristics[J]. Electrical & Energy Management Technology, 2023(1): 62-65, 77.
[17] 刘凡, 孙才新, 司马文霞, 等. 铁磁谐振过电压混沌振荡的理论研究[J]. 电工技术学报, 2006, 21(2): 103-107.
Liu Fan, Sun Caixin, Sima Wenxia, et al.Theoretical analysis of chaotic oscillation of ferroresonance overvoltage in power systems[J]. Transactions of China Electrotechnical Society, 2006, 21(2): 103-107.
[18] Radmanesh H, Nademi M, Nademi M.Circuit breaker shunt resistance effect on ferroresonancein voltage transformer including nonlinear core losses[J]. International Journal of Computer and Electrical Engineering, 2012: 743-747.
[19] 庞霞, 刘崇新. 含电磁式电压互感器的铁磁混沌电路的分析研究[J]. 物理学报, 2013, 62(15): 60-65.
Pang Xia, Liu Chongxin.Analysis of ferromagnetic chaotic circuit with nonlinear potential transformer[J]. Acta Physica Sinica, 2013, 62(15): 60-65.
[20] 代姚, 司马文霞, 孙才新, 等. 应用T-S模糊方法对铁磁谐振过电压的混沌抑制[J]. 高电压技术, 2010, 36(4): 878-883.
Dai Yao, Sima Wenxia, Sun Caixin, et al.Chaos controlling in ferroresonance overvoltage with T-S fuzzy method[J]. High Voltage Engineering, 2010, 36(4): 878-883.
[21] Hui Meng, Liu Chongxin.Effect of power frequency excitation character on ferroresonance in neutral- grounded system[J]. Chinese Physics B, 2010, 19(12): 120509.
[22] Milicevic K, Emin Z.Initiation of characteristic ferroresonance states based on flux reflection model[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2013, 60(1): 51-55.
[23] Mork B A, Stuehm D L.Application of nonlinear dynamics and chaos to ferroresonance in distribution systems[J]. IEEE Transactions on Power Delivery, 1994, 9(2): 1009-1017.
[24] 李其莹. 中性点不接地系统铁磁谐振的并联电路计算模型与诊断方法[J]. 变压器, 2019, 56(2): 34-38.
Li Qiying.Parallel circuit calculation model and diagnostic method of ferroresonance for neutral ungrounded system[J]. Transformer, 2019, 56(2): 34-38.
[25] 王宾, 张超, 丁心志. 中性点直接接地系统单相串联铁磁谐振时域解析分析[J]. 中国电机工程学报, 2022, 42(6): 2124-2133.
Wang Bin, Zhang Chao, Ding Xinzhi.Time domain analytical analysis of single-phase series ferro- magnetic resonance in neutral point solid grounding power system[J]. Proceedings of the CSEE, 2022, 42(6): 2124-2133.
[26] 张超, 王宾, 张海, 等. 中性点直接接地电网单相串联铁磁谐振检测与类型辨识[J]. 电力系统自动化, 2022, 46(19): 172-179.
Zhang Chao, Wang Bin, Zhang Hai, et al.Detection and type identification of single-phase series ferro- resonance in neutral point solid grounding power grid[J]. Automation of Electric Power Systems, 2022, 46(19): 172-179.
[27] 冯慈璋, 马西奎. 工程电磁场导论[M]. 北京: 高等教育出版社, 2000.
[28] 沈泽亮, 汪金刚, 王谦, 等. 一种基于低频窄带扫描的电磁式电压互感器杂散电容测量与精确建模方法[J]. 电工技术学报, 2023, 38(8): 2211-2221.
Shen Zeliang, Wang Jingang, Wang Qian, et al.A method for stray capacitance measuring and refined modeling of potential transformer based on low frequency and narrow band scanning[J]. Transactions of China Electrotechnical Society, 2023, 38(8): 2211-2221.
[29] Rezaei-Zare A, Iravani R, Sanaye-Pasand M.Impacts of transformer core hysteresis formation on stability domain of ferroresonance modes[J]. IEEE Transa- ctions on Power Delivery, 2009, 24(1): 177-186.
[30] 丛伟, 孙允, 路庆东, 等. 电压互感器励磁特性曲线拟合的复合解法[J]. 电力系统保护与控制, 2013, 41(12): 60-64.
Cong Wei, Sun Yun, Lu Qingdong, et al.Comprehensive solving method for the fitting of electromagnetic PT excitation characteristic[J]. Power System Protection and Control, 2013, 41(12): 60-64.
[31] Wang Faqiang, Zhang Hao, Ma Xikui.Analysis of slow-scale instability in Boost PFC converter using the method of harmonic balance and Floquet theory[J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2010, 57(2): 405-414.
[32] Zhang Hao, Dong Shuai, Zhang Yuan, et al.Intermediate-frequency oscillation behavior of one- cycle controlled SEPIC power factor correction converter via Floquet multiplier sensitivity analysis[J]. International Journal of Bifurcation and Chaos, 2016, 26(10): 1650163.