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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摘要

针对多频闪变信号在分辨率不足或快速傅里叶变换（FFT）出现频谱主瓣干扰的情况,提出一种基于自回归-线性调频Z变换-解析模态分解（AR-CZT-AMD）的算法。该算法可有效提升数据点不足（更短的时间内）或需超分辨率检测场景下的信号分析性能。首先,通过实验验证自回归（AR）模型对数据预测的有效性。该模型能够基于已知数据预测未知数据点,其预测后处理效果优于未采用数据预测的加窗插值FFT（WFFT）及线性调频Z变换（CZT）等方法。其次,利用CZT算法细化感兴趣频段,并选择相邻信号频率的二分点作为细化中心频率,以缓解平均频率引入的误差,且无需预知待分解信号的具体频率值。最后,应用解析模态分解（AMD）进行信号分解,该步骤要求信号时长至少为目标频率间隔时间的两倍。通过五组实验进行测试,该算法在无噪条件下,频率分辨率为$2 \Delta f$（$\Delta f$为目标频率间隔）,低噪条件下,频率分辨率为$\Delta f$及频率分辨率为$\Delta f / 2$的高分辨率场景下,均能实现高精度参数提取,相对方均根误差小于4%。对于多密频闪变信号,能够检测多频调幅波波动参数,短时闪变值误差小于5%,满足闪变检测标准要求。在频谱主瓣干扰不明显时（频谱分辨率为$\Delta f / 4$）,AMD与加窗插值FFT算法效果相当。在检测密频信号时,相同条件与其他算法对比,该算法所需的预测点数更少,可以减小AR长时间预测导致的误差。

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关键词 ：自回归（AR）模型预测, 线性调频Z变换（CZT）, 解析模态分解（AMD）, 密频参数检测, 加窗插值快速傅里叶变换（WFFT）

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)

收稿日期: 2025-08-27

PACS:

TM930.1

基金资助:

国家自然科学基金资助项目（52077089）

通讯作者: 李开成男,1962年生,教授,博士生导师,研究方向为电磁测量及仪器、电能质量分析等。E-mail：likaicheng@hust.edu.cn

作者简介: 徐奥傲男,2001年生,硕士研究生,研究方向为电能质量扰动装置研究、深度学习在电能质量扰动缺陷识别与定位等。E-mail：xaa@hust.edu.cn

引用本文:

徐奥傲, 李开成, 罗溢, 袁文涛, 陆梓浩. 基于AR-CZT-AMD的多密频闪变信号参数提取[J]. 电工技术学报, 2026, 41(18): 6287-6303. Xu Aoao, Li Kaicheng, Luo Yi, Yuan Wentao, Lu Zihao. A Method for Extracting Multi-Density Frequency Flicker Signal Parameters Based on AR-CZT-AMD. Transactions of China Electrotechnical Society, 2026, 41(18): 6287-6303.

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