基于AR-CZT-AMD的多密频闪变信号参数提取

doi:10.19595/j.cnki.1000-6753.tces.251510

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Abstract

Modern power systems face power quality issues such as voltage fluctuations and flicker due to high penetration of renewable energy. Conventional IEC flicker meters, which perform well for stable single-frequency amplitude-modulated waves, may introduce errors when analyzing time-varying or multi-component flicker signals and are constrained by fixed sampling rates. To overcome these drawbacks, this paper proposed an algorithm based on autoregressive-chirp Z-transform-analytical mode decomposition (AR-CZT-AMD). The method enables accurate flicker parameter detection without being constrained by fixed sampling rates.
The procedure included five steps. First, data were acquired and a preliminary spectrum was estimated using FFT or CZT. Second, whether the data length met the AMD requirement was checked. Third, if data were insufficient, AR modeling was applied for forward and backward prediction to extend the sequence. Model order was carefully selected to avoid noise-induced drift. Fourth, when data were sufficient, CZT refined the frequency band of interest. Bisection points between adjacent frequencies were used as refinement centers to avoid errors from averaging. This step did not require prior knowledge of exact frequencies. Finally, Hilbert transform resolved instantaneous parameters. Median values were used for ideal signals, while sliding-window filtering was applied in noisy cases.
The algorithm was validated through simulations tests. Tests showed that at a resolution of $\Delta f$ conditions($\Delta f$ representing dense frequency intervals), both WFFT and AMD perform similarly, while the proposed method maintains high accuracy. Under the three specified resolution scenarios—$2 \Delta f$, in noise-free conditions, $\Delta f$ in low-noise conditions, and $\Delta f / 2$ for high-resolution requirements—the method consistently achieved high-precision parameter extraction. In all these cases, the relative root-mean-square error remained below 4%. Furthermore, simulations and practical measurements on multi-component dense flicker signals confirmed that the algorithm effectively detects parameters of multi-frequency amplitude-modulated waves. The short-term flicker error was less than 5%, meeting IEC standards.
The following conclusions are drawn: (1) The proposed algorithm requires fewer data points (in a shorter period of time) than other methods, reducing error accumulation from prolonged AR prediction. (2) AR-based data extension outperforms non-predictive approaches such as WFFT, AMD, and CZT. (3) CZT accurately locates bisection frequencies, avoiding mainlobe interference and enabling robust AMD decomposition. (4) The method is also applicable to multi-component harmonic and flicker signal analysis.

Key words： Autoregressive (AR) model prediction chirp Z-transform (CZT algorithm) analytical mode decomposition (AMD) frequency parameter detection windowed interpolation fast Fourier transform (WFFT)

Received: 27 August 2025

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TM930.1

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	Xu Aoao
	Li Kaicheng
	Luo Yi
	Yuan Wentao
	Lu Zihao

Cite this article:

Xu Aoao,Li Kaicheng,Luo Yi等. A Method for Extracting Multi-Density Frequency Flicker Signal Parameters Based on AR-CZT-AMD[J]. Transactions of China Electrotechnical Society, 2026, 41(18): 6287-6303.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.251510 OR https://dgjsxb.ces-transaction.com/EN/Y2026/V41/I18/6287

[1] 王田戈, 田铭兴, 尹路, 等. 磁饱和式可控电抗器非线性动态电磁网络模型研究[J]. 电工技术学报, 2025, 40(12): 4004-4016.
Wang Tiange, Tian Mingxing, Yin Lu, et al.Research on nonlinear dynamic electromagnetic network model of magnetically-saturated controllable reactor[J]. Transactions of China Electrotechnical Society, 2025, 40(12): 4004-4016.
[2] 申刘飞, 翟雨佳, 吴星徵, 等. 海上超导风电制氢一体化研究进展与发展趋势[J]. 电工技术学报, 2025, 40(11): 3362-3380.
Shen Liufei, Zhai Yujia, Wu Xingzheng, et al.Progress and development trend of integrated research on hydrogen production from offshore superconducting wind power[J]. Transactions of China Electrotechnical Society, 2025, 40(11): 3362-3380.
[3] 黄杰, 李建闽, 朱冰凡, 等. 基于条件网络和知识注入的多标签学习电能质量扰动识别与分类方法[J]. 电工技术学报, 2025, 40(23): 7652-7663.
Huang Jie, Li Jianmin, Zhu Bingfan, et al.A multi-label learning method based on conditional networks and knowledge injection for power quality disturbance identification and classification[J]. Transactions of China Electrotechnical Society, 2025, 40(23): 7652-7663.
[4] 任祖华, 王柏林. 精确提取闪变波动分量的新方法[J]. 电力系统及其自动化学报, 2014, 26(4): 56-60.
Ren Zuhua, Wang Bolin.Novel method on accurate extraction of flicker components in voltage[J]. Proceedings of the CSU-EPSA, 2014, 26(4): 56-60.
[5] 张民谣, 高云鹏, 吴聪, 等. 基于改进平方检测和新型K-N互卷积窗的闪变参数检测[J]. 仪器仪表学报, 2019, 40(8): 222-229.
Zhang Minyao, Gao Yunpeng, Wu Cong, et al.Flicker parameters detection based on the improved square demodulation method and new K-N mutual convolution window[J]. Chinese Journal of Scientific Instrument, 2019, 40(8): 222-229.
[6] 蔡星月. IEC闪变仪不适用性分析和动态闪变参数检测技术研究[D]. 长沙: 湖南大学, 2022.
Cai Xingyue.Inapplicability analysis of IEC flicker meter and research on dynamic flicker parameters detection technology[D]. Changsha: Hunan University, 2022.
[7] 奚鑫泽, 邢超, 覃日升, 等. 基于改进平方检测与自适应TLS-ESPRIT的电压闪变参数检测方法[J]. 南方电网技术, 2023, 17(7): 37-44.
Xi Xinze, Xing Chao, Qin Risheng, et al.Voltage flicker parameter detection method based on improved square detection and adaptive TLS-ESPRIT[J]. Southern Power System Technology, 2023, 17(7): 37-44.
[8] 安海清, 李振动, 岳娜, 等. 基于稀疏复原算法的风电并网电压闪变包络线提取[J]. 电力系统自动化, 2020, 44(7): 139-144.
An Haiqing, Li Zhendong, Yue Na, et al.Envelope tracking of voltage flicker caused by wind power integration based on sparse recovery algorithm[J]. Automation of Electric Power Systems, 2020, 44(7): 139-144.
[9] 高云鹏, 李峰, 陈婧, 等. 基于Teager-Kaiser能量算子Rife-Vincent窗频谱校正的电压闪变测量[J]. 电工技术学报, 2014, 29(6): 248-256.
Gao Yunpeng, Li Feng, Chen Jing, et al.Voltage flicker measurement using the Teager-Kaiser energy operator based on Rife-Vincent window spectral correction[J]. Transactions of China Electrotechnical Society, 2014, 29(6): 248-256.
[10] 彭佳伟, 潘树国, 高旺, 等. 基于加窗插值和ZoomFFT的电网宽频信号自适应测量方法[J]. 电力系统自动化, 2022, 46(8): 172-180.
Peng Jiawei, Pan Shuguo, Gao Wang, et al.Adaptive measurement method for wide-band signal in power grid based on windowed interpolation and ZoomFFT[J]. Automation of Electric Power Systems, 2022, 46(8): 172-180.
[11] 胡殿刚, 马喜平, 赵凤展, 等. 一种基于短时傅里叶变换的电压闪变信号的检测[J]. 电网与清洁能源, 2020, 36(3): 27-33, 41.
Hu Diangang, Ma Xiping, Zhao Fengzhan, et al.A new method of voltage flicker detection based on short time Fourier transform[J]. Power System and Clean Energy, 2020, 36(3): 27-33, 41.
[12] 堵俊, 邵振国, 郭晓丽, 等. 用小波分析提取电压闪变的幅值调制信号[J]. 电力系统及其自动化学报, 2006, 18(3): 34-37.
Du Jun, Shao Zhenguo, Guo Xiaoli, et al.Tracking the envelope of voltage flicker using wavelet analysis[J]. Proceedings of the CSU-EPSA, 2006, 18(3): 34-37.
[13] 张宇辉, 陈晓东, 刘思革. 采用小波包分析和拟同步检波的电压闪变信号检测新方法[J]. 继电器, 2004, 32(3): 6-9.
Zhang Yuhui, Chen Xiaodong, Liu Sige.Detection of voltage flicker using wavelet package analysis and simulating synchronous detection[J]. Relay, 2004, 32(3): 6-9.
[14] 刘阳, 杨洪耕. 盲信号分离在电压闪变分析中的应用[J]. 电工技术学报, 2007, 22(3): 138-142.
Liu Yang, Yang Honggeng.Application of blind signal separation method in analysis of voltage flicker[J]. Transactions of China Electrotechnical Society, 2007, 22(3): 138-142.
[15] 倪良华, 肖李俊, 吕干云, 等. 基于改进HHT的电压闪变检测[J]. 电测与仪表, 2017, 54(18): 72-78.
Ni Lianghua, Xiao Lijun, Lü Ganyun, et al.Voltage flicker parameters detection based on modified HHT[J]. Electrical Measurement & Instrumentation, 2017, 54(18): 72-78.
[16] Eghtedarpour N, Farjah E, Khayatian A.Effective voltage flicker calculation based on multiresolution S-transform[J]. IEEE Transactions on Power Delivery, 2012, 27(2): 521-530.
[17] 杜文龙, 杨洪耕, 马晓阳. 基于快速独立分量分析的谐波间谐波频谱分离算法[J]. 电力系统自动化, 2020, 44(13): 115-122.
Du Wenlong, Yang Honggeng, Ma Xiaoyang.Harmonic/interharmonic spectrum separation algorithm based on fast independent component analysis[J]. Automation of Electric Power Systems, 2020, 44(13): 115-122.
[18] 李林, 高云鹏, 张韵琦, 等. 基于改进k值能量算子改进Chirp-Z变换的闪变包络参数提取[J]. 电工技术学报, 2018, 33(11): 2636-2646.
Li Lin, Gao Yunpeng, Zhang Yunqi, et al.Voltage flicker envelope tracking based on improved k-value energy operator and improved Chirp-Z transform[J]. Transactions of China Electrotechnical Society, 2018, 33(11): 2636-2646.
[19] 王梦昊. 基于DSP+ARM的三相电能质量分析系统的设计与分析[D]. 武汉: 华中科技大学, 2021.
Wang Menghao.Design and analysis of three-phase power quality analysis system based on DSP+ARM[D]. Wuhan: Huazhong University of Science and Technology, 2021.
[20] Tripathy P, Srivastava S C, Singh S N.A modified TLS-ESPRIT-based method for low-frequency mode identification in power systems utilizing synchrophasor measurements[J]. IEEE Transactions on Power Systems, 2011, 26(2): 719-727.
[21] Sun Zhongmin, He Zhengyou, Zang Tianlei, et al.Multi-interharmonic spectrum separation and measurement under asynchronous sampling condition[J]. IEEE Transactions on Instrumentation and Measurement, 2016, 65(8): 1902-1912.
[22] Chen Genda, Wang Zuocai.A signal decomposition theorem with Hilbert transform and its application to narrowband time series with closely spaced frequency components[J]. Mechanical Systems and Signal Processing, 2012, 28: 258-279.
[23] 邹培源, 黄纯, 江辉, 等. 基于全相位谱细化与校正的谐波和间谐波测量方法[J]. 电网技术, 2016, 40(8): 2496-2502.
Zou Peiyuan, Huang Chun, Jiang Hui, et al.Method of harmonics and interharmonics measurement based on all-phase spectrum zoom and correction[J]. Power System Technology, 2016, 40(8): 2496-2502.
[24] 舒泓, 王毅. 基于数学形态滤波和Hilbert变换的电压闪变测量[J]. 中国电机工程学报, 2008, 28(1): 111-114.
Shu Hong, Wang Yi.Voltage flicker detection method based on mathematical morphology filter and Hilbert transform[J]. Proceedings of the CSEE, 2008, 28(1): 111-114.
[25] 张民谣, 高云鹏, 吴聪, 等. 基于自适应变分模式分解的非稳态电压闪变包络参数检测[J]. 电工技术学报, 2021, 36(3): 599-608.
Zhang Minyao, Gao Yunpeng, Wu Cong, et al.Non-stationary voltage flicker envelope parameters detection based on adaptive variational mode decomposition[J]. Transactions of China Electrotechnical Society, 2021, 36(3): 599-608.
[26] 许伯强, 王彪, 孙丽玲, 等. 基于改进集合经验模态分解和强化视觉Transformer模型的风电机组故障预警[J]. 电工技术学报, 2025, 40(20): 6537-6551.
Xu Boqiang, Wang Biao, Sun Liling, et al.Fault warning of wind turbine based on improved ensemble empirical mode decomposition and enhanced visual Transformer model[J]. Transactions of China Electro-technical Society, 2025, 40(20): 6537-6551.
[27] 钱龙, 吴先红, 宋俊材, 等. 基于杂散磁场信号螺旋曲线投影变换与ResNeXt-18的永磁直线电机偏心故障诊断[J]. 电工技术学报, 2024, 39(18): 5705-5718.
Qian Long, Wu Xianhong, Song Juncai, et al.Eccentricity fault diagnosis of permanent magnet linear motor based on spiral curve transformation of stray magnetic field signal and ResNeXt-18[J]. Transactions of China Electrotechnical Society, 2024, 39(18): 5705-5718.
[28] 李和明, 康伟, 颜湘武, 等. 一种基于Chirp-Z变换的闪变测量方法[J]. 电工技术学报, 2009, 24(3): 209-215.
Li Heming, Kang Wei, Yan Xiangwu, et al.Voltage flicker measurement based on Chirp-Z transform[J]. Transactions of China Electrotechnical Society, 2009, 24(3): 209-215.
[29] 宋知用. MATLAB数字信号处理85个实用案例精讲: 入门到进阶[M]. 北京: 北京航空航天大学出版社, 2016.
[30] 卢建昌, 王柳. 基于时序分析的神经网络短期负荷预测模型研究[J]. 中国电力, 2005, 38(7): 11-14.
Lu Jianchang, Wang Liu.Study of short-term load forecasting based on ANN and time series[J]. Electric Power, 2005, 38(7): 11-14.
[31] 熊少锋, 王可东, 姜锐, 等. 自回归滑动平均建模中观测噪声方差估计的新方法[J]. 控制理论与应用, 2013, 30(2): 178-185.
Xiong Shaofeng, Wang Kedong, Jiang Rui, et al.A new measurement noise estimation method for autoregressive and moving average modeling[J]. Control Theory & Applications, 2013, 30(2): 178-185.
[32] 李燕青, 袁燕舞, 郭通. 基于AMD-ICSA-SVM的超短期风电功率组合预测[J]. 电力系统保护与控制, 2017, 45(14): 113-120.
Li Yanqing, Yuan Yanwu, Guo Tong.Combination ultra-short-term prediction of wind power based on AMD-ICSA-SVM[J]. Power System Protection and Control, 2017, 45(14): 113-120.
[33] 徐方维, 周全, 王川, 等. 基于频谱泄漏干扰多层消除的密集谐波/间谐波参数估计方法[J]. 电力自动化设备, 2024, 44(11): 178-186.
Xu Fangwei, Zhou Quan, Wang Chuan, et al.Dense harmonics/interharmonics parameter estimation method based on multilayer elimination of spectrum leakage interference[J]. Electric Power Automation Equipment, 2024, 44(11): 178-186.
[34] 国家质量监督检验检疫总局, 中国国家标准化管理委员会. 电磁兼容试验和测量技术闪烁仪功能和设计规范: GB/T 17626.15—2011[S]. 北京: 中国标准出版社, 2012.