中文摘要：

压缩感知（compressed sensing,CS）技术在采样中完成对数据的压缩,相比传统Nyquist采样方法有效降低采样信号数据量,克服采样端压缩复杂度高,对硬件需求大的缺点。该文通过理论证明指出电网信号基波–谐波稀疏度特性,并基于此特性提出一种新型基波滤除谱投影梯度算法（SPGFF）。通过西门子Benchmark 0.4 k V电网通用模型实验,结果表明SPG-FF算法比现有方法有效提升了谐波检测精度和信号重构精度,对谐波和间谐波的检测误差分别小于6.8×10^-5和6.2×10^-3,重构信号的信噪比高于89 d B。

英文摘要：

Compressed sensing technique can accomplish data compression during the process of sampling. As a result, it can avoid common problems like large data storage capacity, waste of storage space and high complexity of compression in sampling side when collecting harmonic-information under the Nyquist sampling framework. This paper revealed the sparsity of harmonic components in power electrical systems, and presented the mathematical proof. Based on these findings, this paper proposed a novel reconstruction algorithm, which was named the spectral projected gradient with fundamental filter（SPG-FF） algorithm. Results of experiments from Siemens Benchmark 0.4 k V grid model had shown that the SPG-FF algorithm was able to enhance the accuracy of harmonic detection and precision of signal reconstruction. Specifically, the detection accuracy of harmonics and inter-harmonics is within 6.8×10^-5 and 6.2×10^-3, and the SNR of reconstructed signals are above 89 d B.