Two-Dimensional Analytical Permanent-Magnet Eddy-Current Loss Calculations in Slotless PMSM Equipped With Surface-Inset Magnets

Two-dimensional (2-D) analytical permanent-magnet (PM) eddy-current loss calculations are presented for slotless PM synchronous machines (PMSMs) with surface-inset PMs considering the current penetration effect. In this paper, the term slotless implies that either the stator is originally slotted but the slotting effects are neglected or the stator is originally slotless. The analytical magnetic field distribution is computed in polar coordinates from the 2-D subdomain method (i.e., based on formal resolution of Maxwell's equation applied in subdomain). Based on the predicted magnetic field distribution, the eddy-currents induced in the PMs are analytically obtained and the PM eddy-current losses considering eddy-current reaction field are calculated. The analytical expressions can be used for slotless PMSMs with any number of phases and any form of current and overlapping winding distribution. The effects of stator slotting are neglected and the current density distribution is modeled by equivalent current sheets located on the slot opening. To evaluate the efficacy of the proposed technique, the 2-D PM eddy-current losses for two slotless PMSMs are analytically calculated and compared with those obtained by 2-D finite-element analysis (FEA). The effects of the rotor rotational speed and the initial rotor mechanical angular position are investigated. The analytical results are in good agreement with those obtained by the 2-D FEA.