基于投影近似子空间跟踪算法的谐波检测方法

Projection Approximation Subspace Tracking Algorithm for Harmonics Detection

子空间分解类算法在理论上具有任意的高分辨率,非常适合于电力系统各类谐波的分析,但需要对高维矩阵进行特征值分解,这不仅费时而且不易于工程实现。本文将投影近似子空间跟踪算法引入电力系统谐波分析领域,详细分析评估了PASTd算法的性能。仿真结果表明,紧缩投影近似子空间跟踪算法即PASTd算法不仅保留了子空间分解类算法的超分辨率特性,而且收敛速度较快,稳定性好,可推广用于电力系统谐波检测领域。

The subspace decomposition method based on modem spectrum estimation theory can achieve very high frequency resolution, and it is very suitable to harmonics analysis of power systems. But this kind of algorithms require eigenvalue decomposition of the sample correlation matrix or singular value decomposition of the data matrix, which is a very time-consuming task. To overcome this difficulty, a new approach for tracking signal subspace recursively which is referred to as the projection approximation subspace tracking deflation algorithm, is introduced to harmonics analysis in this paper. The performance of this algorithm has been evaluated by simulation tests. The simulation results show that the PASTd algorithm has not only super-resolution ability, but also fast convergence and high stability for tracking both the signal subspace and its rank. The PASTd algorithm can be used in the actual harmonics measurement in power systems.