An Analytical Method for Predicting 3-D Eddy Current Loss in Permanent Magnet Machines Based on Generalized Image Theory

This paper proposes an analytical method, based on the generalized image theory, for accurate prediction of 3-D eddy current distributions in the rotor magnets of permanent magnet (PM) machines and the resultant eddy current loss. The analytical framework is established in a 3-D rectangular coordinate system, and the boundary conditions that govern the eddy current flows on the surfaces of magnets are represented by equivalent image sources in a homogenous 3-D space extending into infinity. By introducing a current vector potential, the 3-D eddy current distributions in magnets are derived analytically by employing the method of variable separation, and the total eddy current loss in the magnets is subsequently established. The proposed method has been validated by a 3-D time-stepped transient finite-element analysis (FEA). It is shown that the proposed method is extremely computationally efficient. When combined with the 2-D FEA of magnetic field distributions, the proposed method provides an accurate and computationally efficient means for predicting 3-D eddy current loss in a variety of PM machines with due account of complex machine geometry, various winding configurations, and magnetic saturation.