2D and 3D Modeling of Magnet Eddy Currents in Inverter-Fed Permanent Magnet Machines

This paper presents new 2D and 3D methods for analytical modeling of magnet eddy currents in inverter-fed surface-mounted permanent magnet machines. The time harmonics of the inverter current cause the induced eddy currents and losses in the surface-mounted magnets. The modeling of eddy currents is performed with and without consideration of the reaction fields of eddy currents in arc-shaped magnets. Neglecting reaction fields is used to calculate a new end effect factor to consider the third dimension's effect on the eddy current losses in the 2D calculation. Closed-form equations for magnet losses are extracted using new 2D and 3D analytical methods for fast calculations of magnet eddy current losses. The Fourier series approach is utilized to solve differential equations in 3D modeling. The 2D magnet losses equation without the third-dimension effect is separated in the 3D magnet losses equation, which helps to clearly show the third-dimension effect. The analytical results are compared with 3D finite element calculations to evaluate the accuracy of analytically calculated eddy current losses. 2D and 3D magnet loss results are compared to evaluate the third-dimension effect on magnet losses. Two different surface-mounted permanent magnet machines are considered to validate analytical methods compared to finite element results.