基于ZoomFFT和多谱线插值算法的谐波分析方法*

doi:10.11985/2023.04.020

摘要/Abstract

摘要：

基于快速傅里叶变换(Fast Fourier transform，FFT)的各种检测算法，因其具备响应速度快以及便于工程实现等特点，现已成为电能质量分析常用方法，但易造成频谱泄漏，难以精确实现多个谐波的分离检测。因此提出一种基于Blackman-Harris窗函数四谱线插值算法和复调制频谱细化算法的复合型谐波检测方法。利用改进的加窗插值算法对谐波进行检测，对于发生主瓣干扰的频谱，采用复调制频谱细化算法，实现对谐波的精确分析。仿真试验结果表明，该方法能够分辨相近谐波分量，实时性较强，能够满足电力系统对电力参数检测的需求。

关键词: 谐波, Blackman-Harris窗, 四谱线插值, ZoomFFT, 主瓣干扰

Abstract:

Various detection algorithms based on fast Fourier transform have become a common method for power quality analysis due to their fast response speed and easy engineering implementation. It is easy to cause spectrum leakage, and difficult to accurately realize the separation and detection of multiple harmonics. A complex harmonic detection method based on the Blackman-Harris window function quadratic line interpolation algorithm and the complex modulation spectrum refinement algorithm is proposed. The improved windowed interpolation algorithm is used to detect harmonics. For the spectrum where main lobe interference occurs, the complex modulation spectrum refinement algorithm is used to analyze the harmonics accurately. The simulation results show that the method can distinguish similar harmonic components, has strong real-time performance, and can meet the needs of power system detection of power parameters.

Key words: Harmonic, Blackman-Harris window, four-spectral interpolation, ZoomFFT, main lobe interference

中图分类号:

TM711

朱坤, 陈乐柱, 许胜, 史琛筠. 基于ZoomFFT和多谱线插值算法的谐波分析方法^*[J]. 电气工程学报, 2023, 18(4): 179-187.

ZHU Kun, CHEN Lezhu, XU Sheng, SHI Chenjun. Harmonic Analysis Method Based on ZoomFFT and Multispectral Interpolation Algorithm[J]. Journal of Electrical Engineering, 2023, 18(4): 179-187.

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窗的类型	主瓣宽度	旁瓣电平/dB	旁瓣衰减速率/ (dB/oct)
Triangle	8π/N	-27	12
Rectangle	4π/N	-13	6
Hamming	8π/N	-43	6
Blackman	12π/N	-58	18
Blackman-Harris	16π/N	-92	6
Hanning	8π/N	-32	18
4项1阶Nuttall	16π/N	-93	18
4项3阶Nuttall	16π/N	-83	30

信号分量	频率f/Hz	幅值U/V	初相位φ/(°)
X₁	50	80	0
X₂	51	20	0
X₃	55	15	10
X₄	100	20	30
X₅	105	10	60
X₆	150	50	150
X₇	152	15	-20
X₈	200	14	30
X₉	250	20	-50

信号分量	频率f/Hz	幅值U/V	初相位φ/(°)
X₁	50.000 5	80.001 0	0.000 8
X₂	51.001 2	20.000 6	0.000 5
X₃	55.000 5	16.000 5	10.000 9
X₄	100.001 1	20.000 6	30.000 8
X₅	105.000 0	10.000 3	60.000 6
X₆	149.999 9	49.999 5	149.999 1
X₇	151.999 8	14.999 5	-19.999 2
X₈	200.000 0	15.000 6	30.000 9
X₉	250.000 0	20.000 6	-50.000 5

信号分量	频率f/Hz	幅值U/V	初相位φ/(°)
X₁	50.001 2	80.011 5	0.010 7
X₂	—	—	—
X₃	54.989 5	15.385 5	9.993 1
X₄	99.998 9	19.998 0	29.996 9
X₅	104.997 8	9.995 3	59.993 2
X₆	149.998 9	49.998 8	149.998 8
X₇	151.984 9	14.298 8	-19.002 3
X₈	199.998 5	14.978 2	29.991 2
X₉	249.999 2	19.998 9	-49.998 8

对比算法	采样点数目	计算时长/ms
ZFFT	10 240	29.00
Blackman-Harris窗	1 024	0.26
Hanning窗	1 024	0.21
Hamming窗	1 024	0.22
本文算法	1 024\|10 240	2.20