Efficient and Versatile Anhysteretic Magnetization Models for Soft Magnetic Materials in FEA and Circuit Simulations

For the efficient simulation and optimization of electrical machines, the soft magnetic behavior of core materials is typically represented by the magnetization curve rather than complex hysteresis models, and hysteresis losses are calculated and accounted for in post-processing instead. Currently, either interpolation methods or phenomenological magnetization models are used to describe the magnetization curve. However, the existing methods exhibit several disadvantages concerning identification, comparability, implementation, and the resulting behavior of the nonlinear solver. Based on these identified disadvantages, a set of criteria for magnetization models are developed. An analysis of the state of the art reveals that the existing methods do not meet these criteria. Therefore, three novel models are proposed to advance the state of the art: a simple algebraic model, a special arctangent model, and a special hyperbolic tangent model. To evaluate these models, the Langevin function, which describes anhysteretic behavior based on a physical approach in models, such as the Jiles-Atherton (JA) model, is used. The new methods are fitted to the anhysteretic Langevin functions of different materials and show excellent agreement in regression as well as improved computational efficiency compared to the Langevin function. The best models reach R-squared values exceeding 0.99 for the four reference materials. In particular, the algebraic and arctangent models exhibit excellent regression performance, and beyond, the algebraic model achieves outstanding computational efficiency, rendering them viable alternatives to the existing models for magnetization curves in technical simulations.