基于压缩感知的电能质量扰动数据稀疏分析与改进重构算法

doi:10.19595/j.cnki.1000-6753.tces.171096

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摘要基于压缩感知（CS）的电能质量扰动（PQD）信号多采用DFT基进行稀疏分析。但此方法存在频谱泄露问题,降低了原始数据的稀疏性,易造成后续重构算法稀疏度过度估计、执行效率下降。针对上述问题,在对PQD信号进行DFT稀疏分析的基础上,提出了一种对频谱泄露具有免疫能力的改进重构算法。首先对4种典型PQD信号进行了幅度谱推导,详细分析了信号相关参数与稀疏特性的关系。其次在此基础上对自适应匹配追踪（SAMP）算法进行改进,并提出频谱能量差的概念。频谱能量差可以反映出相邻迭代过程中重构信号频谱能量的变化,将该差值作为SAMP算法的迭代终止条件时,能有效地避免稀疏度过度估计并提高运算效率。最后,通过对比实验,验证了改进SAMP算法的优越性。

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关键词 ：压缩感知, 电能质量扰动, DFT, 稀疏性, 重构算法

Abstract：Power quality disturbance (PQD) data based on compressed sensing (CS) is subjected to sparse analysis mostly by using the DFT basis. However, this method incurs the problem of spectrum leakage, which reduces the sparseness of the original data, leads to overestimation of the sparseness in the subsequent reconstruction algorithm. In light of the above problem, based on the DFT sparse analysis of PQD signals, an improved reconstruction algorithm immune to spectrum leakage is proposed. Firstly, the amplitude spectra of four typical PQD models are theoretically deduced, and the relationship between the sparse characteristics of each model and the related parameters is analyzed in detail. Secondly, on the basis of this, the sparse adaptive march pursuit (SAMP) algorithm is improved and the concept of spectral energy difference is proposed. The spectral energy difference can effectively describe the change value of signal spectrum energy during adjacent reconstruction iteration. When the difference is used as the iterative termination condition of the SAMP algorithm, sparseness overestimation caused by spectrum leakage can be avoided and the operation efficiency of the algorithm can be improved. Finally, the contrast experiments have verified the superiority of the improved SAMP algorithm proposed in this paper.

Key words： Compressed sensing power quality disturbance DFT sparsity reconstruction algorithm

收稿日期: 2017-07-27 出版日期: 2018-08-14

PACS:	TH86
	TM935

基金资助:陕西省科技统筹创新工程计划项目（2016KTCQ01-35）、陕西省重点科技创新团队计划项目（2014KCT-15）和陕西省教育厅专项科研计划项目（14JK1083）资助

通讯作者: 刘嫣女,1982年生,博士研究生,讲师,研究方向为电能质量扰动监测及分析。E-mail：405586265@qq.com

作者简介: 汤伟男,1971年生,博士生导师,教授,研究方向为工业工程高级控制。E-mail：wtang906@163.com

引用本文:

刘嫣, 汤伟, 刘宝泉. 基于压缩感知的电能质量扰动数据稀疏分析与改进重构算法[J]. 电工技术学报, 2018, 33(15): 3461-3470. Liu Yan, Tang Wei, Liu Baoquan. Data Sparse Analysis and Improved Reconstruction Algorithm of Power Quality Disturbance Based on Compressed Sensing. Transactions of China Electrotechnical Society, 2018, 33(15): 3461-3470.

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