奇异值与特征值分解在谐波源定阶中的等价性

The Rank-decision Equality of Singular Value and Eigen Value Decomposition for Harmonics Analysis

现代谱估计理论较好的解决了随机白噪声下平稳的电力系统谐波和间谐波模型的求解问题,算法的关键在于准确的确定谐波和间谐波源的个数,称为"定阶",定阶的方法有奇异值分解和特征值分解两种。本文通过理论推导论证两种定阶方法本质上是等价的,并对实测的电弧炉电流波形,采用Esprit进行仿真验证。

Harmonics and inter-harmonics in power system are often considered as a stationary signal with white noise. Advanced Spectrum Estimation, used for stationary signal analysis, are efficient methods for their measurement. Estimating the numbers of the harmonics and inter-harmonics is the main point of these methods, named Rank-Decision. The normal way of Rank-Decision is singular value decomposition decomposition （EVD）. The Rank-Decision equality of SVD and EVD is proved in the paper. also used to prove this equality for a field current signal of an arc furnace.