电能质量检测中的压缩感知理论基础研究

项目名称： 电能质量检测中的压缩感知理论基础研究

项目编号： No.51307144

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 电工技术

项目作者： 朱云芳

作者单位： 西南交通大学

项目金额： 24万元

中文摘要： 现有电能质量监测系统，都基于Nyquist采样定理，大量数据给采样、传输、存储和分析等带来很大困难。压缩感知理论突破了传统采样定理，有望少量采样就能恢复信号。但是，该理论的应用必须满足信号稀疏性和观测矩阵非相干性两个前提，目前在电能质量领域还未见相关报道。本项目拟对此开展研究，为电能质量扰动信号的压缩信号处理和压缩信息采样提供理论基础。首先，研究典型电能质量扰动信号的稀疏性，构造超完备稀疏字典，提出选取稀疏原子的优化方法，求解电能质量扰动信号稀疏度，建立稀疏模型；然后，在此基础上估计最佳观测数，构造非相干观测矩阵，研究其约束等距特性及与稀疏矩阵的非相干性，建立稳定的观测模型；最后，将信号重构转化为一个约束优化问题，并基于智能优化算法，提出L0-范数下的信号重构算法。本项目将系统论证压缩感知理论应用于电能质量扰动信号的可行性，并提出相应的理论依据和实现方法，具有一定的理论意义和实际价值。

中文关键词： 电能质量；压缩感知理论；稀疏模型；观测模型；信号重构算法

英文摘要： Because the existing power quality monitoring system is based on the Nyquist sampling theorem, a large number of power quality disturbance data has caused great difficulties for sampling, transmission, storage and analysis. Recently, a novel theory, compressed sensing, has been proposed, which breaks through the Nyquist sampling theorem. Based on this theory, it is only the expected small amount of sample that can be used to reconstruct the original signal. However, the compressed sensing theory can be applied only when the two premises can be met, namely, the sparsity of the signal and the non-correlation of the measurement matrix. However, now no systematic research in the field of power quality is conducted on these two premises. Hence, the project intends to carry out in-depth study these two premises, and establish the theoretical basis for power quality disturbance signal compressive sampling and compressive signal processing. First, an in-depth study will be made on the sparsity of the power quality disturbance signals in order to construct overcomplete sparse dictionary, present the optimization algorithm for the sparse basis selection, obtain the sparse matrix with the least rank, then establish the sparse model. Secondly, the non-coherent measurement matrix will be constructed, and the stable measureme

英文关键词： power quality；compressive sensing theory；sparse model；measurement model；signal reconstruction algorithm