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

吉林大学学报(工学版) ›› 2025, Vol. 55 ›› Issue (3): 1082-1092.doi: 10.13229/j.cnki.jdxbgxb.20230626

• 通信与控制工程 • 上一篇

基于耦合混沌系统阵列的电力系统微弱谐波检测方法

孙淑琴^1,²(),祁鑫^1,²,袁正海^1,²,李再华^3,⁴(),唐晓骏^3,⁴

^1.吉林大学仪器科学与电气工程学院，长春 130026
^2.吉林大学地球信息探测仪器教育部重点实验室，长春 130026
^3.中国电力科学研究院有限公司，北京 100192
^4.中国电力科学研究院电网安全全国重点实验室，北京 100192

收稿日期:2023-06-19 出版日期:2025-03-01 发布日期:2025-05-20
通讯作者: 李再华 E-mail:sunsq@jlu.edu.cn;lizaihua@epri.sgcc.com.cn
作者简介:孙淑琴（1969-），女，教授，博士.研究方向：电力系统建模及仿真计算技术.E-mail：sunsq@jlu.edu.cn
基金资助:
国家自然科学基金项目(U22B20109);国家电网公司科技项目(5100-202124011A-0-0-00)

Detection method of weak harmonics of power system based on coupled chaotic system array

Shu-qin SUN^1,²(),Xin QI^1,²,Zheng-hai YUAN^1,²,Zai-hua LI^3,⁴(),Xiao-jun TANG^3,⁴

^1.College of Instrumentation and Electrical Engineering，Jilin University，Changchun 130026，China
^2.Key Laboratory of Geophysical Exploration Equlpment，Ministry of Education of China，Jilin University，Changchun 130026，China
^3.China Electric Power Research Institute Co. ，Ltd. ，Beijing 100192，China
^4.National Key Laboratory of Grid Security，China Electric Power Research Institute，Beijing 100192，China

Received:2023-06-19 Online:2025-03-01 Published:2025-05-20
Contact: Zai-hua LI E-mail:sunsq@jlu.edu.cn;lizaihua@epri.sgcc.com.cn

摘要/Abstract

摘要：

针对经典时频域谐波检测方法精度不足以及单混沌系统对微弱谐波检测精度和抗噪能力有限的缺陷，首先在检测灵敏度方面将Duffing系统与Van der pol系统进行对比，以分岔图为依据确定临界驱动力，以相图和李雅普诺夫指数判断系统相变；进一步利用Duffing系统与Van der pol系统的位移耦合二者的阻尼力和恢复力，形成闭环反馈控制的耦合系统，利用其对特定频率周期信号幅值的极高敏感性和抗噪性对混合谐波信号的各谐波频率分量进行幅值精准检测。在单耦合系统基础上，通过分析相位响应关系，确定系统的相位响应区间，设计覆盖全相位响应区间的耦合系统阵列。对恶劣随机噪声背景下的多整次谐波与间谐波混叠的谐波信号进行仿真实验。结果表明，本文方法能在恶劣的噪声环境中实现各谐波分量的无差幅值检测，并消除了相位对系统检测性能的影响。

关键词: Duffing系统, Van der pol系统, 微弱谐波检测, 分岔图, 李雅普诺夫指数

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

中图分类号:

TM764.1

孙淑琴,祁鑫,袁正海,李再华,唐晓骏. 基于耦合混沌系统阵列的电力系统微弱谐波检测方法[J]. 吉林大学学报(工学版), 2025, 55(3): 1082-1092.

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.

图/表 17

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表1

无初相位差时耦合系统阵列与单Duffing振子检测精度结果对比"

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

表1

表2

存在初相位差时耦合系统阵列与单Duffing振子检测精度结果对比"

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

表2

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基于耦合混沌系统阵列的电力系统微弱谐波检测方法

Detection method of weak harmonics of power system based on coupled chaotic system array

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