Localized Reluctivity Stabilization of Hysteresis Model for Transient Finite Element Simulation of Ferromagnetic Materials

The hysteresis model can be used to accurately predict the magnetic hysteresis characteristics of ferromagnetic materials. Incorporating the hysteresis model into finite element calculations enables precise prediction of field distributions, voltage or current variations in circuits, and losses, which is essential for electromagnetic transient analysis involving remanent magnetization. When incorporating the hysteresis model into finite element analysis, prohibitively small time-steps are required to resolve hysteresis loops, leading to excessive simulation times compared to simplified BH curve approaches. Furthermore, numerical instabilities arise near zero-crossing points of magnetic flux density, where erroneous negative differential reluctivity values may lead to the divergence of the nonlinear solving process. A finer time resolution needs to be utilized to ensure the convergence of the nonlinear solver. This leads to more time-steps and longer computational time. This work proposes a localized stabilization strategy for regulating the differential reluctivity in instability-prone regions of the hysteresis loop, which can stabilize the nonlinear iteration while avoiding the local refinement of time resolution and thus reduce the overall computation time.