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 nonparametricestimation and sliding window improvement

作　　者：李冬[1] 刘子源 曾非同 胡浩亮 周峰 LI Dong;LIU Ziyuan;ZENG Feitong;HU Haoliang;ZHOU Feng(School of Electrical and Electronic Engineering,Huazhong University of Science and Technology,Wuhan 430074,China;China Electric Power Research Institute Co.,Ltd.,Wuhan 430074,China)

机构地区：[1]华中科技大学电气与电子工程学院,武汉430074 [2]中国电力科学研究院有限公司,武汉430074

出　　处：《电测与仪表》2024年第11期107-115,共9页Electrical Measurement & Instrumentation

基　　金：国家电网公司总部科技项目(5400-202116474A-0-5-ZN)。

摘　　要：电容式电压互感器(CVT)测量准确性关乎电能的准确计量,监测难点是误差变化微小不易察觉。针对CVT数据非严格满足高斯分布的特点,提出了基于非参数估计与滑动窗口改进的主成分分析(PCA)方法。对同一电压等级下的各CVT相位差与幅值进行Johnson变换增强高斯性,由PCA分解为主成分与残差成分;在此基础上分别建立霍特林统计量(T^(2))和平方预测误差(Q);对待监测的T^(2)和Q先进行滑动窗口处理,再与控制限相比较,以判断角差和比差是否超差。控制限由CVT正常运行时的T^(2)和Q进行非参数估计得到。基于某变电站现场的CVT数据,通过人为施加固定/渐变偏差,该方法可有效识别±10′范围的角差超差与±0.2%范围的比差超差。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 do not strictly meet the Gaussian distribution,an improved principal component analysis(PCA)method based on nonparametric estimation and sliding window is proposed.The Johnson transform is performed on the phase difference and amplitude of each CVT at the same voltage level to enhance the Gaussianity.The principal component and the residual component are decomposed by PCA.On this basis,the Hotelling statistic(T^(2))and the square prediction error(Q)are established respectively.T^(2) 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 T^(2) 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.

关 键 词：非参数估计 滑动窗口 Johnson变换 主成分分析 电容式电压互感器 在线监测 

分 类 号：TM45[电气工程—电器]