Current Distribution Reconstruction in Low-Voltage Circuit Breakers Based on Magnetic Inverse Problem Solution Considering Ferromagnetic Splitters

Current density distribution in electric arcs inside low-voltage circuit breakers (LVCBs) 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 field. This paper is focused on the modeling and computational phase for the magnetic inverse problem when linear ferromagnetic regions are considered in the model. To address the ill-posedness of the inverse problem, the standard method of least-squares approximation by Tikhonov regularization is studied, complemented with the generalized cross-validation criterion for regularization parameter selection. Considering the inclusion of a ferromagnetic region, two regularization approaches have been analyzed for the formulation of the currents in splitters and their corresponding magnetic field contribution. Effects of several features on the performance of the regularized solution have been investigated, including the signal-to-noise ratio, the value of permeability of the splitters, and the measurement distance. The numerical tests show the direct accessibility for the 3-D current density distribution with the proposed scheme, providing the accuracy and robustness for the applicability to study the arc behavior in LVCBs.