Effective Material Transformation for Laminated Iron Cores With T, Φ–Φ Formulation and Vector Hysteresis

Abstract

Accurate simulation of eddy currents in laminated iron cores is essential for analysing electromagnetic behavior and predicting iron losses in electrical machines and transformers. However, resolving the fine-scale structure of laminations in fully three-dimensional simulations is computationally expensive. This work presents an efficient modelling approach based on effective material (EM) transformation using the T ,Φ-Φ formulation and a non-linear magnetic material model incorporating vector hysteresis via the vector Preisach model. A cell problem is solved to derive the EM, which captures both alternating and rotational magnetic effects. The method enables separation of eddy current and hysteresis losses, including their alternating and rotational components, while significantly reducing the number of degrees of freedom and simulation time. Validation is performed through comparison with high-resolution reference solutions and multiscale finite element method simulations in both transformer and electric machine scenarios. The results confirm that the EM approach offers accurate predictions of iron losses and reactive power with a fraction of the computational cost, making it highly suitable for practical machine design and optimisation workflows.