基于耦合混沌系统阵列的电力系统微弱谐波检测方法

doi:10.13229/j.cnki.jdxbgxb.20230626

Abstract

Abstract:

In view of the insufficient accuracy of classical time-frequency domain harmonic detection methods and the limited detection accuracy and noise immunity of weak harmonics in single chaotic systems， this paper first compares the Duffing system with the Van der pol system in terms of detection sensitivity， determines the critical driving force based on the bifurcation diagram， and judges the phase transition of the system by the phase diagram and Lyapunov index； Further utilizing the damping and restoring forces of the displacement coupling of the Duffing system and Van der pol system， a closed-loop feedback controlled coupling system is formed. By utilizing its high sensitivity to the amplitude of specific frequency periodic signals and noise resistance， the amplitude of each harmonic frequency component of the mixed harmonic signal is accurately detected； Based on the single coupling system， the phase response interval of the system is determined by analyzing the phase response relationship， and the coupling system array covering all phase response intervals is designed. Simulation experiments were conducted on harmonic signals with multiple integer harmonics and inter-harmonics mixed under harsh random noise backgrounds. The results show that the method proposed in this article can achieve accurate amplitude detection of various harmonic components in harsh noise environments， and eliminate the impact of phase on system detection performance.

Key words: Duffing system, Van der pol system, weak harmonic detection, bifurcation diagram, Lyapunov index

CLC Number:

TM764.1

Shu-qin SUN,Xin QI,Zheng-hai YUAN,Zai-hua LI,Xiao-jun TANG. Detection method of weak harmonics of power system based on coupled chaotic system array[J].Journal of Jilin University(Engineering and Technology Edition), 2025, 55(3): 1082-1092.

Figures/Tables 17

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Table 1

Comparison of the detection accuracy results of coupled system array and single duffing oscillator without initial phase difference"

谐波次数	信号幅值/p.u.
	理论值	耦合系统阵列精度	Duffing振子精度	SNR=-20 dB				SNR=-60d B
	理论值	耦合系统阵列精度	Duffing振子精度	耦合系统阵列检测值	耦合系统阵列误差/%	Duffing振子检测值	Duffing振子误差/%	耦合系统阵列检测值	耦合系统阵列误差/%	Duffing振子检测值	Duffing振子误差/%
基波	1.0	$10 - 8$	$10 - 6$	1.0	0	1.000 1	0.01	1.0	0	0.946 2	5.38
2.2	0.15	$10 - 8$	$10 - 6$	0.15	0	0.15	0	0.15	0	0.133 1	11.27
3	0.25	$10 - 8$	$10 - 6$	0.25	0	0.249 8	0.08	0.25	0	0.239 3	4.28
5	0.2	$10 - 8$	$10 - 6$	0.2	0	0.2	0	0.2	0	0.210 9	5.45
7	0.1	$10 - 8$	$10 - 6$	0.1	0	0.1	0	0.1	0	0.062 3	37.7

Table 1

Table 2

Comparison of the detection accuracy results of the coupling system array and the single duffing oscillator when there is an initial phase difference"

谐波次数	信号幅值/p.u.
	理论值	耦合系统阵列精度	Duffing振子精度	耦合系统阵列是否成功检出	Duffing振子是否成功检出	SNR=-20 dB				SNR=-60 dB
	理论值	耦合系统阵列精度	Duffing振子精度	耦合系统阵列是否成功检出	Duffing振子是否成功检出	耦合系统阵列检测值	耦合系统阵列误差/%	Duffing振子检测值	Duffing振子误差/%	耦合系统阵列检测值	耦合系统阵列误差/%	Duffing振子检测值	Duffing振子误差/%
基波	1.0	$10 - 8$	$10 - 6$	是	是	1.0	0	1.0	0	1.0	0	0.9491	5.09
2.2	0.15	$10 - 8$	$10 - 6$	是	否	0.15	0	Null	Null	0.15	0	Null	Null
3	0.25	$10 - 8$	$10 - 6$	是	否	0.25	0	Null	Null	0.25	0	Null	Null
5	0.2	$10 - 8$	$10 - 6$	是	否	0.2	0	Null	Null	0.2	0	Null	Null
7	0.1	$10 - 8$	$10 - 6$	是	否	0.1	0	Null	Null	0.1	0	Null	Null

Table 2

References 24

1	商立群, 许海洋, 臧鹏, 等. 基于DFT和群组谐波能量回收理论的谐波与间谐波检测算法[J]. 电力系统保护与控制, 2022, 50(15): 91-98.
	Shang Li-qun, Xu Hai-yang, Zang Peng, et al. A harmonic and interharmonic detection algorithm based on DFT and group harmonic energy recovery theory[J].Power System Protection and Control, 2022, 50(15): 91-98.
2	郑晓娇, 王斌, 李卜娟, 等. 基于参数优化变分模态分解的间谐波检测[J]. 电力系统保护与控制, 2022, 50(11): 71-80.
	Zheng Xiao-jiao, Wang Bin, Li Bu-juan, et al. Inter-harmonic detection based on parameter optimization variational mode decomposition[J].Power System Protection and Control, 2022, 50(11): 71-80.
3	陶顺, 郭傲, 刘云博, 等. 基于矩阵束和奇异值分解的间谐波检测算法[J]. 电力系统保护与控制, 2021, 49(2): 57-64.
	Tao Shun, Guo Ao, Liu Yun-bo, et al. Interharmonic detection algorithm based on a matrix pencil and singular value decomposition[J]. Power System Protection and Control, 2021, 49(2): 57-64.
4	王进花, 胡佳伟, 曹洁, 等.基于自适应变分模态分解和集成极限学习机的滚动轴承多故障诊断[J]. 吉林大学学报:工学版,2022, 52(2): 318-328.
	Wang Jin-hua, Hu Jia-wei, Cao Jie,et al. Multi⁃fault diagnosis of rolling bearing based on adaptive variational modal decomposition and integrated extreme learning machine[J].Journal of Jilin University(Engineering Science),2022, 52(2): 318-328.
5	童涛, 张新燕, 刘博文, 等.基于傅里叶同步挤压变换和希尔伯特变换的谐波间谐波检测分析[J].电网技术, 2019, 43(11): 4200-4208.
	Tong Tao, Zhang Xin-yan, Liu Bo-wen, et al. Analysis of harmonic detection based on fourier-based synchrosqueezing transform and hilbert transform[J]. Power System Technology, 2019, 43(11): 4200-4208.
6	陈至豪, 王立德, 王冲, 等. 基于组合余弦优化窗四谱线插值FFT的电力谐波分析方法[J]. 电网技术, 2020, 44(3): 1105-1113.
	Chen Zhi-hao, Wang Li-de, Wang Chong, et al. Power harmonic an approach for electrical harmonic analysis based on optimized composite cosine window four-spectrum-line interpolation FFT[J].Power System Technology, 2020, 44(3): 1105-1113.
7	段晨, 杨洪耕. 邻近基波/谐波的间谐波检测算法[J]. 电网技术, 2019, 43(5): 1818-1825.
	Duan Chen, Yang Hong-geng. An algorithm for detecting interharmonics adjacent to fundamental/harmonic components[J].Power System Technology,2019, 43(5): 1818-1825.
8	窦嘉炜, 杨小煜, 杨晓忠. 基于分数阶小波变换的电力系统谐波检测方法[J].中国电机工程学报, 2024,44(3): 872-880.
	Dou Jia-wei, Yang Xiao-yu, Yang Xiao-zhong. A power system harmonic detection method based on fractional wavelet transform[J].Proceedings of the CSEE, 2024,44(3): 872-880.
9	聂春燕. 混沌理论及基于特定混沌系统的微弱信号检测方法研究[D]. 长春: 吉林大学通信工程学院, 2006.
	Nie Chun-yan. Research on the weak signal detection method based on the chaos theory and specific chaotic system[D]. Changchun: College of Communicayion Engineering, Jilin University, 2006.
10	Kumar P, Narayanan S, Gupta S. Bifurcation analysis of a stochastically excited vibro-impact Duffing-Van der Pol oscillator with bilateral rigid barriers[J]. International Journal of Mechanical Sciences, 2017,127: 103-117.
11	冀常鹏, 许素娜, 冀雯靖. 基于Duffing振子的微弱信号参数估计[J]. 重庆邮电大学学报: 自然科学版,2020, 32(2): 263-270.
	Ji Chang-peng, Xu Su-na, Ji Wen-jing. Estimation of weak signal parameters based on Duffing oscillators[J].Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition), 2020,32(2): 263-270.
12	孙文军, 芮国胜, 张驰, 等. 混沌检测系统对噪声的免疫性分析及稳健建模[J]. 电子科技大学学报, 2017, 46(3): 492-497.
	Sun Wen-jun, Rui Guo-sheng, Zhang Chi, et al. Analysis on noise immunity of chaotic detection system and robustness modeling approach[J]. Journal of University of Electronic Science and Technology of China, 2017, 46(3): 492-497.
13	Zhao H T, Lin Y P, Dai Y X. Hidden attractors and dynamics of a general autonomous van der pol-duffing oscillator[J].International Journal of Bifurcation and Chaos,2014,24(6): No.14450080.
14	蔡思航, 丁国斌, 李彬. 电力系统故障状态下微弱信号检测方法研究[J]. 能源与环保, 2021, 43(5): 239-245.
	Cai Si-hang, Ding Guo-bin, Li Bin. Research on weak signal detection method based on power system fault state [J].Energy and Environmental Protection,2021, 43(5): 239-245.
15	唐登平, 汪应春, 余鹤. 基于Duffing振子的电网电力线宽带载波检测[J]. 电子设计工程, 2020, 28(18): 144-147, 152.
	Tang Deng-ping, Wang Ying-chun, Yu He. Broadband carrier detection of power line based on Duffing oscillator[J]. Electronic Design Engineering, 2020, 28(18): 144-147, 152.
16	邓生文.随机噪声激励下Van der pol-Duffing振子模型的稳定性及分岔分析[D]. 兰州: 兰州交通大学数理学院, 2021.
	Deng Sheng-wen. Stability and bifurcation analysis of Van der pol-Duffing oscillator model excited by stochastic noise[D]. Lanzhou: School of Mathematica and Physics,Lanzhou Jiaotong University, 2021.
17	姜敏敏, 罗文茂, 崔应留. 基于耦合Duffing振子的局部放电信号去噪方法研究[J]. 电子器件, 2022, 45(2): 346-351.
	Jiang Min-min, Luo Wen-mao, Cui Ying-liu. Research on partial discharge signal denoising method based on coupled Duffing oscillator[J].Electronic Devices, 2022, 45(2): 346-351.
18	王晓东, 杨绍普, 赵志宏.Duffing振子和Van der Pol振子耦合的动力学行为分析[J].石家庄铁道大学学报: 自然科学版,2015, 28(4): 53-57, 80.
	Wang Xiao-dong, Yang Shao-pu, Zhao Zhi-hong. Analysis of dynamical behavior of a Van der pol oscillator coupled to a duffing oscillator[J]. Journal of Shijiazhuang Tiedao University (Natural Science Edition),2015,28(4):53-57, 80.
19	孙淑琴, 祁鑫, 袁正海, 等.基于混沌理论的电力系统微弱谐波检测方法研究[J]. 电力系统保护与控制, 2023, 51(15): 76-86.
	Sun Shu-qin, Qi Xin, Yuan Zheng-hai,et al. A weak harmonic detection method for a power system based on chaos theory[J]. Power System Protection and Control, 2023, 51(15): 76-86.
20	张宇辉, 李哲, 李天云, 等. 次同步谐振的变尺度全方位扫描Duffing振子检测方法[J]. 电力系统保护与控制, 2014, 42(14): 122-127.
	Zhang Yu-hui, Li Zhe, Li Tian-yun, et al. Subsynchronous resonance variable scale and comprehensive scanning Duffing oscillator detection method[J]. Power System Protection and Control, 2014,42(14): 122-127.
21	张丹瑾. 周期激励下Duffing-Van der pol系统的簇发振荡及其分岔机理[D]. 金华: 浙江师范大学数学与计算机科学学院, 2021.
	Zhang Dan-jin.Bursting oscillation and its bifurcation mechanism of Duffing-Van der pol system with periodic excitation[D].Jinhua: College of Mathematics and Computer Science, Zhejiang Normal University, 2021.
22	El-Dib Y O. An efficient approach to solving fractional Van der pol-Duffing jerk oscillator[J].Communications in Theoretical Physics, 2022, 74(10): 54-63.
23	石兆羽.基于Van der pol-Duffing振子的微弱信号检测研究[D].石家庄: 石家庄铁道大学机械工程学院, 2018.
	Shi Zhao-yu. Research on weak signal detection based on Van der pol-Duffing oscillator[D].Shijiazhuang: School of Mechanical Engineering,Shijiazhuang Tiedao University, 2018.
24	吴建章, 梅飞, 陈畅, 等.基于经验小波变换的电力系统谐波检测方法[J]. 电力系统保护与控制, 2020,48(6): 136-143.
	Wu Jian-zhang, Mei Fei, Chen Chang, et al. Harmonic detection method in power system based on empirical wavelet transform[J]. Power System Protection and Control, 2020, 48(6): 136-143.

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