李冬,刘子源,曾非同,胡浩亮,周峰.基于非参数估计与滑动窗口改进的主成分分析方法研究[J].电测与仪表,2024,61(11):107-115. Li Dong,Liu Ziyuan,Zeng Feitong,Hu Haoliang,Zhou Feng.Research on principal component analysis method based on nonparametric estimation and sliding window improvement[J].Electrical Measurement & Instrumentation,2024,61(11):107-115.
基于非参数估计与滑动窗口改进的主成分分析方法研究
Research on principal component analysis method based on nonparametric estimation and sliding window improvement
The measurement accuracy of capacitive voltage transformer (CVT) is related to the accurate measurement of electric energy. The monitoring difficulty is that the error change is small and not easy to detect. Aiming at the characteristics that CVT data does not strictly meet the Gaussian distribution, an improved principal component analysis (PCA) method based on nonparametric estimation and sliding window is proposed. Firstly, the Johnson transform is performed on the phase difference and amplitude of each CVT at the same voltage level to enhance the Gaussianity, and then the principal component and the residual component are decomposed by PCA. On this basis, the Hotelling statistic (T2) and the square prediction error (Q) are established respectively. Finally, T2 and Q to be monitored are first processed by sliding window, and then compared with the control limits to determine whether the angle difference and the ratio difference are out of tolerance. The control limits are obtained by nonparametric estimation of T2 and Q during CVT normal operation. Based on the CVT data of a substation site, this method can effectively identify the angle difference out-of-tolerance in the range of ±10 ′ and the ratio difference out-of-tolerance in the range of ±0.2 % by artificially applying fixed/ gradual deviation.
