Transients computation in electrical circuits in the presence of ferromagnetic hysteresis

This article is a contribution to the evaluation of transients in nonlinear inductive circuits containing a soft ferromagnetic sample in the magnetic circuit where hysteresis and eddy currents are taken into account. A hybrid finite element method (FEM)/boundary method is used to evaluate the instantaneous magnetic field. The FEM formulation is adequate to describe the field inside the ferromagnetic sample and, on the other hand, the boundary method is used to impose the adequate relation between the field and its normal derivative values on the boundary. This relationship is obtained from the exterior circuit equation. The dynamic field is evaluated in the time domain for which an implicit integration approach is used based on a second order trapezoidal (Crank–Nicolson) method. A classical Preisach model is used to simulate the magnetic hysteresis.