In this paper, a hybrid model in Cartesian coordinates combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series) is developed. This model coupling has been applied to a U-cored static electromagnetic device. The main objective is to compute the magnetic field behavior in massive conductive parts (e.g., aluminum, magnets, copper, iron) considering the skin effect (i.e., with the eddy-current reaction field) and to predict the eddy-current losses. The magnetic field distribution for various models is validated with 2-D and three-dimensional (3-D) finite-element analysis (FEA). The study is also focused on the discretization influence of 2-D generic MEC on the eddy-current loss calculation in conductive regions. Experimental tests and 3-D FEA have been compared with the proposed approach on massive conductive parts in aluminum. For an operating point, the computation time is divided by ~4.6 with respect to 3-D FEA.

This paper investigates the permanent-magnet (PM) eddy-current losses in multi-phase PM synchronous machines (PMSM) with concentric winding and surface-mounted PMs. A hybrid multi-layer model, combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series), performs the eddy-current loss calculations. First, the magnetic flux density was obtained from the 2-D generic MEC and then subjected to the Fast Fourier Transform (FFT). The semi-analytical model includes the automatic mesh of static/moving zones, the saturation effect and zones connection in accordance with rotor motion based on a new approach called “Air-gap sliding line technic”. The results of the hybrid multi-layer model were compared with those obtained by three-dimensional (3-D) nonlinear finite-element analysis (FEA). The PM eddy-current losses were estimated on different paths for different segmentations as follow: (i) one segment (no segmentation), (ii) five axial segments, and (iii) two circumferential segments, where the non-uniformity loss distribution is shown. The top of PMs presents a higher quantity of losses compared to the bottom.