Modeling Magnet Length In 2-D Finite-Element Analysis of Electric Machines

Two-dimensional finite-element-method (2-D FEM) calculations are widely used in electric machine modeling instead of three-dimensional calculations because of their faster calculation time and simplicity. However, the 2-D calculations ignore end effects, causing a large error in calculating eddy currents in permanent magnets of synchronous machines. In this paper, we develop three analytical models and one curve-fitting model based on numerical calculations. The models improve the eddy-current loss calculation accuracy in 2-D FEM. The method adjusts the resistivity of a magnet material according to magnet dimensions. The adjustment takes into account the resistivity, the temperature dependence, and anisotropy of the resistivity of rare-earth magnet materials. We compare the models against FEM calculations in two and three dimensions and show that all the models improve the eddy-current loss calculation accuracy significantly, especially when the time-harmonic caused eddy-current losses in permanent magnets are considered.