Generalized Fixed-Point Iteration Technique for Solving Magnetic Hysteresis Problems

Accurate simulation of the electromagnetic field in iron cores requires accounting for the hysteresis behavior of magnetic materials, which imposes higher requirements on the robustness and efficiency of nonlinear solvers. This paper first discusses the deficiencies of existing fixed-point (FP) methods in magnetic field computation involving hysteresis media. Then, a generalized FP iteration technique for multi-valued nonlinear problems is proposed, featuring a modified formula for conditioning FP coefficient and a numerical approach for estimating the differential reluctivity. Time-stepping finite element analysis (FEA) of a synchronous motor is performed where the ferromagnetic material is characterized by three representative hysteresis models. The proposed solution technique demonstrates remarkable performance on adaptability and convergence rate compared with Newton-Raphson (NR) methods and traditional FP methods. Additionally, experimental results from a motor prototype validate the effectiveness of the numerical simulation.