Investigation of Volumic Permanent-Magnet Eddy-Current Losses in Multi-Phase Synchronous Machines from Hybrid Multi-Layer Model

Abstract

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.

Mathematical Models for the Design of Electrical Machines

“…The analytical solution was applied to regions with homogeneous material properties, while the linear MEC approach was used for the regions containing non-homogeneous material properties. The resulting thrust and normal forces showed excellent agreement with respect to FEA and the measurement data; Benmessaoud et al [11,12]. In [11], the authors developed a 2-D hybrid model in Cartesian coordinates, combining an MEC with the Maxwell-Fourier method for eddy current loss calculation.…”

“…Experimental tests and 3-D FEA were compared with the proposed approach on massive conductive parts in aluminum. In [12], the developed hybrid model was extended in polar coordinates to multi-phase synchronous machines for the volumic PM eddy current losses. A global revision on the calculation and analysis of PM eddy current losses can be found in [13].…”

A Review of Axial-Flux Permanent-Magnet Motors: Topological Structures, Design, Optimization and Control Techniques

“…In order to implement the electromagnetic modeling and electromagnetic performance analysis of AFPM motors more quickly and accurately, some studies comprehensively use FEA and MEC methods. In addition, some studies combine FEA and MEC methods to implement electromagnetic modeling and the electromagnetic performance analysis of AFPM motors more quickly and accurately [77][78][79], which is the trend of modeling and analysis for AFPM motors in the future as well. The core concept of magnetic equivalent circuit is to simplify and assume the complex magnetic field to be equivalent to a simple circuit.…”

Improved Semi-Analytical Magnetic Field Solution for High-Speed Permanent-Magnet Machines With Permeable Retaining Sleeve Including Diffusion Effect

“…However, MEC is less flexible than MF method, as it requires meshing, and does not consider eddy-current reaction fields properly [11,19] The MF methods (e.g., multi-layer models, eigenvalue model and subdomain technique) provide satisfactory accuracy for complex structures with less computation time than FEM. The adoption of a hybrid method, with the combination of MEC and MF methods, is proposed to accommodate the advantages of each technique [22,23]. These (semi-)analytical models are suitable for optimization in design early stages, where analytical calculations can be done in order to constrain the machine dimensions [1,24,25].…”