Fast and accurate Neural-Network-based Ferromagnetic Laminated Stack Model for Electrical Machine Simulations in Periodic Regime

peer reviewedElectromagnetic fields and eddy currents in thin electrical steel laminations are governed by the laws of magnetodynamics with hysteresis. Conventional homogenization techniques are however complex and very time-consuming. In consequence, hysteresis and eddy currents in ferromagnetic laminated cores are usually outright disregarded in finite element simulations, considering only saturation, and magnetic losses are only evaluated a posteriori, by means of a Steinmetz-Bertotti like empirical formula. This model simplification yields however potentially inaccurate results in the presence of non-sinusoidal B-fields, common in modern electrical devices. Assuming a time-periodic excitation of the system, a more accurate and fast approach, based on homogenization and neural networks (NN), is presented. A parametric homogenized material law is used in the macroscopic model, whose parameters are given element-wise by a NN according to the actual local waveform of the magnetic field. It is shown that, with an appropriately trained NN, this NN-based material law allows computing fields and losses inside ferromagnetic laminated stacks efficiently and accurately

Neural network-based simulation of fields and losses in electrical machines with ferromagnetic laminated cores

peer reviewedDue to the distribution of eddy currents inside ferromagnetic laminations, the accurate modeling of magnetic fields and losses in the laminated cores of electrical machines requires resolving individual laminations with a fine 3D discretization. This yields finite element models so huge and costly that they are unusable in daily industrial R&D. In consequence, hysteresis and eddy currents in laminations are often simply disregarded in the modeling: the laminated core is assumed to be made of a reversible (non lossy) saturable material, and magnetic losses are evaluated a posteriori, by means of Steinmetz-Bertotti like empirical formulas. However, in a context where industry is struggling to minutely assess the impact of magnetic losses on their devices, this simplified approach is more and more regarded as inaccurate and unsatisfactory. This paper proposes a solution to this issue, based on homogenization and on detailed mesoscopic simulations of eddy currents and hysteresis inside the laminations. The proposed approach results in a close-to-conventional 2D magnetic vector potential finite element model, but equipped with an irreversible parametric material law to represent the ferromagnetic stack. In each finite element, the parameters of the law are obtained from a neural network trained to best fit the detailed mesoscopic simulations of the laminations subjected to the same local magnetic field. This way, all aspects of the irreversible ferromagnetic response are appropriately accounted for in the finite element simulation, but at a computational cost drastically reduced with regard to a brute force 3D calculation, and comparable to that of conventional 2D finite element simulations

A Material Law Based on Neural Networks and Homogenization for the Accurate Finite Element Simulation of Laminated Ferromagnetic Cores in the Periodic Regime

peer reviewedElectromagnetic fields and eddy currents in thin electrical steel laminations are governed by the laws of magnetodynamics with hysteresis. If the lamination is large with respect to its thickness, field and current distributions are accurately resolved by solving a one-dimensional finite element magnetodynamic problem with hysteresis across half the lamination thickness. This 1D model is able to deliver mesoscocpic information to be used, after appropriate homogenization, in the macroscopic modelling of an electrical machine or transformer. As each evaluation of such a homogenised model implies a finite element simulation at the mesoscale, a monolithic coupling might be very time-consuming. This paper proposes an alternative approach, assuming a periodic excitation of the system, where the parameters of a parametric homogenized material law are determined in each finite element with a neural network. The local material law can then be used as a conventional constitutive relationship in a 2D or 3D modelling, with a massive speed-up with respect to the monolithic coupling