Using a Jiles-Atherton vector hysteresis model for isotropic magnetic materials with the finite element method, Newton-Raphson method, and relaxation procedure

This paper deals with the use of a Jiles-Atherton vector hysteresis model included in 2D finite element modeling. The hysteresis model is only valid for isotropic materials. It is implemented with the vector potential formulation in 2D along with electric circuit equations to account for a possible external circuit. The Newton-Raphson algorithm is used with a relaxation procedure, whereby at each iteration, the relaxation coefficient is sought so as to minimize the Euclidean norm of the residual of the finite element nonlinear system of equations. We have simulated several numerical examples with the proposed approach. First, simulations on a square domain were conducted so as to validate the model. We have further simulated a T-shaped magnetic circuit (exhibiting rotating flux) and a 3-phase 3-limb transformer model. For these 2 cases, the eddy current losses in the laminations are taken into account by a low-frequency model. We have finally performed simulations on the TEAM workshop problem 32, which consists of a 3-limb transformer with 2 windings, for which current and local magnetic flux density measurements are available. We obtained a good agreement between computed and measured results.