基于PCA-Copula理论的电磁式电流互感器性能评估

Performance Evaluation of Electromagnetic Current Transformer Based on PCA-Copula Theory

  • 摘要: 电流互感器有不同负载级别、不同电流百分比和不同误差表现等多个维度的评价标准,这为通过分析误差数据实现电流互感器的性能评估带来了极大困难。为避免因孤立分析导致缺乏统一标准带来的困扰,提出一种基于主成分分析和Copula函数相结合的分析方法。首先,通过试验测得各品牌电流互感器在不同电流百分比下的比值误差和相角误差数据,并将可以反映数据整体水平的不同电流百分比误差数据作为评价指标;其次,基于主成分分析方法对评价指标进行降维,求出比值误差和相角误差对应的综合评价值;然后,基于核密度估计将得到的比值误差和相角误差综合评价值作为Copula函数的边缘分布函数,并依靠极大似然估计求出Copula函数的参数值;最后,通过最优模型选择准则确定拟合效果最好的Copula函数,并将基于Copula函数求得的数学期望作为最终的评价标准。试验结果表明,此分析方法充分利用数据信息,计算简单,有效实现对各品牌电流互感器的性能评估。

     

    Abstract: Current transformers have evaluation criteria of different load levels, different current percentages and different error performance, which brings great difficulties to evaluate the performance of current transformers by analyzing error data. To avoid the trouble caused by the lack of unified standard caused by isolated analysis, a new analysis method based on the combination of principal component analysis and Copula function is proposed. First of all, the ratio error and phase Angle error of each brand of current transformer are measured under different current percentages through experiments, and the different current percentages that can reflect the overall level of the data are taken as evaluation indicators. Secondly, based on the principal component analysis method, the evaluation index is reduced, and the comprehensive evaluation value corresponding to the ratio error and phase Angle error is obtained. Then, based on kernel density estimation, the comprehensive evaluation value of ratio error and phase Angle error is obtained as the edge distribution function of Copula function, and the parameter values of common Copula function are obtained by means of maximum order estimation. Finally, the Copula function with the best fitting effect is determined by the optimal model selection criterion, and the mathematical expectation based on the Copula function is taken as the final evaluation standard. The experimental results show that the proposed evaluation method makes full use of the data information, the calculation is simple, and the performance evaluation of each brand current transformer is effectively realized.

     

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