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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (1): 178-188    DOI: 10.3785/j.issn.1008-973X.2020.01.021
Electrical Engineering     
Dense frequency harmonic/interharmonic detection based on apFFT-AMD
Shu-guang SUN1(),Peng TIAN1,Tai-hang DU1,Jing-qin WANG2
1. School of Artificial Intelligence, Hebei University of Technology, Tianjin 300130, China
2. State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China
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Abstract  

A combining detection method of all-phase fast Fourier transform (apFFT) and analytical mode decomposition was proposed aiming at the harmonic/interharmonic problem with dense frequency in power harmonic signals. Since AMD needs to determine the frequency components in the signal before decomposing, apFFT was used to perform spectrum analysis on the analyzed signals to obtain the values of the frequencies in the spectrum. The flat characteristics of the apFFT phase spectrum were used to determine whether the signal contains dense spectrum frequency component, and the approximate position of dense spectrum harmonic/interharmonic frequency was obtained. If there were dense spectral components, the dense spectrum segment of the signal was optimized by using quantum particle swarm to find the best binary frequency. The power harmonic signal was decomposed into a series of single-frequency signal components through the binary frequency between each frequency component by using AMD method in order to complete the measurement of harmonics with dense frequency. The method is better for the decomposition of harmonic/interharmonic signals with dense frequency compared with Hilbert-Huang transform (HHT) method. The simulation and experimental results showed the effectiveness and accuracy of the proposed method.

Key words： harmonics      interharmonics      dense spectrum      all-phase fast Fourier transform (apFFT)      quantum particle swarm      analytical mode decomposition (AMD)     
Received: 24 November 2018      Published: 05 January 2020
CLC:  TM 935  
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Shu-guang SUN
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Jing-qin WANG
Cite this article:

Shu-guang SUN,Peng TIAN,Tai-hang DU,Jing-qin WANG. Dense frequency harmonic/interharmonic detection based on apFFT-AMD. Journal of ZheJiang University (Engineering Science), 2020, 54(1): 178-188.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.01.021     OR     http://www.zjujournals.com/eng/Y2020/V54/I1/178


基于apFFT-AMD的密集频率谐波/间谐波检测

针对电力谐波信号中含有密集频率的谐波/间谐波问题，提出全相位快速傅里叶变换（apFFT）与解析模态分解法（AMD）相结合的检测方法. 由于AMD在分解前需要确定信号中各个频率成分，应用apFFT对待分析信号进行频谱分析，得到频谱中各个频率的值；通过apFFT相位谱的平坦特性来判断信号中是否含有密集谱频率成分，获得密集频谱谐波/间谐波频率的大概位置，若含有密集频谱成分，对信号中的密集频段使用量子粒子群进行优化，寻找最佳的二分频率；通过各个频率成分之间的二分频率，利用AMD方法将电力谐波信号分解为一系列的单频信号分量，以完成含有密集频率的谐波测量. 与希尔伯特-黄变换法（HHT）相比，该方法对于含有密集频率的谐波/间谐波信号分解效果更好. 仿真和实验结果都表明了该方法的有效性和准确性.


关键词： 谐波,  间谐波,  密集频谱,  全相位快速傅里叶变换（apFFT）,  量子粒子群,  解析模态分解法（AMD） 
Fig.1 Flow diagram of apFFT spectrum analysis
Fig.2 All-phase fast Fourier transform amplitude and phase spectrum of single-frequency signals and dense-spectrum signals
Fig.3 Diagram of binary frequency
Fig.4 ApFFT-AMD flow chart of algorithm
成分 f/Hz I/A θ/（°）
间谐波 20.0 1 10
基波 50.2 15 30
谐波 100.4 8 200
间谐波 228.0 4 100
间谐波 520.0 2 250
Tab.1 Signal parameters of example 1
Fig.5 Amplitude spectrum of signal
Fig.6 Phase spectrum of signal
Fig.7 Original signal and decomposition results of this paper
Fig.8 Decomposition results of EMD
分量 本文方法 EMD
fe/Hz ξf/% Ie/A ξI/% fe/Hz ξf/% Ie/A ξI/%
1 20.07 0.35 1.04 4.00 19.92 0.40 0.86 14.00
2 50.08 0.24 14.96 0.27 49.92 0.56 14.28 4.80
3 99.95 0.45 7.99 0.13 99.92 0.48 8.00 0.00
4 228.00 0.00 4.00 0.00 227.93 0.03 3.96 1.00
5 519.98 0.01 2.00 0.00 519.91 0.02 2.00 0.00
Tab.2 Parameter detection results of each component with proposed method and EMD
成分 f/Hz I/A θ/（°）
间谐波 20 1 10
基波 50 15 30
间谐波 160 1 200
间谐波 162 2 100
谐波 250 6 250
Tab.3 Signal parameters of example 2
Fig.9 Amplitude spectrum of signal
Fig.10 Phase spectrum of signal
Fig.11 Trend graph of fitness value and particle position
Fig.12 Original signal and decomposition results of this paper
Fig.13 Decomposition results of EMD
Fig.14 Instantaneous amplitude and frequency of single-frequency signal components
Fig.15 Semi-physical overall scheme of experiment
Fig.16 Semi-physical experimental equipment
成分 f/Hz I/A θ/（°）
间谐波 25 2 20
基波 50 20 80
谐波 150 10 200
间谐波 152 3 90
谐波 250 8 250
Tab.4 Specific parameters of signal model
Fig.17 Amplitude spectrum of measured current signal
Fig.18 Phase spectrum of measured current signal
Fig.19 Measured current signal and decomposition results of this paper
Fig.20 Instantaneous amplitude and frequency of single frequency component of measured current signal
分量 fe/Hz ξf/% Ie/A ξI/%
$x_1$ 24.99 0.04 1.98 1.00
$x_2$ 50.00 0.00 19.84 0.80
$x_3$ 150.00 0.00 9.91 0.90
$x_4$ 151.98 0.01 2.98 0.67
$x_5$ 250.00 0.00 7.93 0.88
Tab.5 AMD parameter detection results of each component
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