Current identification in vacuum circuit breakers as a least squares problem

Abstract

In this work, a magnetostatic inverse problem is solved, in order to reconstruct the electric current distribution inside high voltage, vacuum circuit breakers from measurements of the outside magnetic field. The (rectangular) final algebraic linear system is solved in the least square sense, by involving a regularized singular value decomposition of the system matrix. An approximated distribution of the electric current is thus returned, without the theoretical problem which is encountered with optical methods of matching light to temperature and finally to current density. The feasibility is justified from the computational point of view as the (industrial) goal is to evaluate whether, or to what extent in terms of accuracy, a given experimental set-up (number and noise level of sensors) is adequate to work as a “magnetic camera” for a given circuit breaker.