Inverse Problem Solution and Regularization Parameter Selection for Current Distribution Reconstruction in Switching Arcs by Inverting Magnetic Fields

Jinlong Dong,Zhiqiang Zhang,Guogang Zhang,Jianhua Wang,Yingsan Geng

doi:10.1155/2018/7452863

Jinlong Dong, Zhiqiang Zhang + Show 3 more

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https://doi.org/10.1155/2018/7452863

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Abstract

Current density distribution in electric arcs inside low voltage circuit breakers is a crucial parameter for us to understand the complex physical behavior during the arcing process. In this paper, we investigate the inverse problem of reconstructing the current density distribution in arcs by inverting the magnetic fields. A simplified 2D arc chamber is considered. The aim of this paper is the computational side of the regularization method, regularization parameter selection strategies, and the estimation of systematic error. To address the ill-posedness of the inverse problem, Tikhonov regularization is analyzed, with the regularization parameter chosen by Morozov’s discrepancy principle, the L-curve, the generalized cross-validation, and the quasi-optimality criteria. The provided range of regularization parameter selection strategies is much wider than in the previous works. Effects of several features on the performance of these criteria have been investigated, including the signal-to-noise ratio, dimension of measurement space, and the measurement distance. The numerical simulations show that the generalized cross-validation and quasi-optimality criteria provide a more satisfactory performance on the robustness and accuracy. Moreover, an optimal measurement distance can be expected when using a planner sensor array to perform magnetic measurements.

Highlights

Low voltage circuit breakers (LVCBs) are widely used in power distribution systems to protect people and electrical equipment against a fault current
LVCBs are characterized by electric arcs, which are hot and conductive plasmas
This paper is focused on the reconstruction of current density distribution inside LVCBs by employing an inverse problem technique

Summary

Introduction

Low voltage circuit breakers (LVCBs) are widely used in power distribution systems to protect people and electrical equipment against a fault current. LVCBs are characterized by electric arcs, which are hot and conductive plasmas. A better knowledge of it helps to understand the complex physical behavior of electric arc plasmas. This paper is focused on the reconstruction of current density distribution inside LVCBs by employing an inverse problem technique. This technique is concerned with the solution of a linear magnetic inverse problem of reconstructing the internal current profiles from the measurements of magnetic fields [3]. A large wealth of applications can be addressed by this technique and has provided many interesting results in different fields [4,5,6,7]

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