Research on Arc Inversion Based on Fractional Tikhonov Regularization Method
Zhao Hongchen1, Liu Xiaoming1,2, Yang Yingxuan3, Chen Hai2, Yang Luyu3
1.School of Electrical Engineering Shenyang University of Technology Shenyang 110870 China; 2.Tianjin Key Laboratory of Advanced Electrical Engineering and Energy Technology Tianjin Polytechnic University Tianjin 300387 China; 3.State Grid Liaoning Electric Power Research Institute Shenyang 110006 China
Abstract：The switching apparatus with contact will inevitably produce arc when breaking the circuit. In this paper, a three-dimensional arc model of a straight contact system is constructed, that the arc is assumed to be a cluster of broken lines. Based on the Biot-Savart law, the magnetic distribution is measured in-plane around the arc through the forward analysis, thus the arc current density distribution is inversed according to the magnetic field. In order to improve the accuracy of current reconstruction, the Tikhonov regularization method is used to solve the ill-posed equations based on the electromagnetic inverse problem. Considering the approximate solution of the standard Tikhonov regularization method is too smooth because of the loss of the details of the reconstructed data due to the function of the filter operator, the fractional Tikhonov regularization method is adopted to improve the accuracy of the solution, and the Morozov discrepancy criterion is used to obtain the regularization parameter. The inversion result shows that by reducing the order of α can slow down the convergence speed of the filtering operator, which will increase the norm of the solution vector to approximate to the exact solution. Under the magnetic interference with a standard deviation of 0.001, the maximum relative error of arc inversion is 21.26% and the mean relative error is 8.99% compared with the preset values, which shows more accuracy than the standard Tikhonov method and truncated singular value decomposition, thus the inversion results can indicate the trend of arc distribution.
赵宏晨, 刘晓明, 杨滢璇, 陈海, 杨璐羽. 基于分数阶Tikhonov正则化方法的电弧反演研究[J]. 电工技术学报, 2019, 34(1): 84-91.
Zhao Hongchen, Liu Xiaoming, Yang Yingxuan, Chen Hai, Yang Luyu. Research on Arc Inversion Based on Fractional Tikhonov Regularization Method. Transactions of China Electrotechnical Society, 2019, 34(1): 84-91.
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2019, Vol. 34 
