电能质量检测中的压缩感知理论基础研究

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 measurement model will be developed by using the learning algorithm. Finally, based on intelligent optimization algorithms, the signal reconstruction algorithm will be proposed under l0-norm. In a word, this project will present a systematic proof for the feasibility of power quality disturbance signal compressed sensing theory, and provide the appropriate theoretical foundation, which has important theoretical and practical value. If the power quality compressed sensing theory could be established, a profound impact will be thrown on both the power quality and the entire power system.

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。

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。本项目对此开展研究，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。.本项目的研究内容包括：1、研究超完备稀疏字典的构建方法和最佳匹配稀疏基的选取算法。2、基于电能质量扰动信号的稀疏模型，估计最佳观测数，研究观测矩阵的设计方法。3、研究信号重构优化算法，分析算法的收敛性、稳定性和复杂性。.取得的成果1)采用差分进化算法实现了基于Gabor和衰减正弦量原子的匹配追踪过程，解决了传统电能质量扰动信号原子分解的计算量大和全局优化问题。取得的成果有：给出了算法流程；仿真结果表明，本文方法大大减少了计算耗时、且不受信号长度的影响，进一步提高了原子的全局匹配能力、且具有很好的抗噪声能力；2)提出了基于正交匹配追踪(OMP)的压缩感知谐波检测方法。取得的成果：给出了检测方法流程；仿真结果表明，该方法能精确检测奇偶次、非整次及其混合谐波信号的频率和幅值检测；3)提出了两个用于电能质量扰动信号压缩采样的改进测量矩阵：其一，基于仅含正负1的2×2正交矩阵和1×N的随机矢量，利用结构化矩阵原理构造测量矩阵；其二，在其一的基础上，构造稀疏循环结构化矩阵，得到稀疏的测量矩阵。取得的成果：给出了测量矩阵构造流程；仿真结果表明，重建性能优于（或相当于）传统测量矩阵；4）提出了基于离散平稳小波变换的电能质量扰动信号压缩采样方法。取得的成果：给出了压缩采样方法流程；仿真实验表明，重构性能提升，且更具普适性；5）提出了一种电能质量扰动信号压缩感知识别新方法，该方法提取稀疏向量特征，利用神经网络实现电能质量扰动信号的分类识别。取得的成果：给出了方法流程；仿真结果表明，本文方法的平均准确率高达98.71%。