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An optimization procedure is proposed to determine the shapes and orientations of permanent magnets in interior permanent magnet synchronous motors with concentrated armature windings. In the proposed procedure, 2D finite element analysis coupled with the armature voltage equation is used to take into account the leakage flux at the end windings. The end leakage inductance in the equation is determined by 3D finite element analysis in advance. By using this procedure, the rotor shape of the motor can be optimized within a practical computational time. First, the validity of the analysis is confirmed by comparing measured and calculated characteristics of the motor. Then, the optimal shape and orientation of the permanent magnets in the motor are discussed using the results of the proposed optimization procedure. It is revealed that the consideration of the end-leakage flux is indispensable to estimate the characteristics of the motors with concentrated windings whose core length is relatively short as compared to the diameter, particularly under flux weakening control. An optimized rotor that reduces the iron loss at high speeds without considerable deterioration of the other important characteristics is also obtained by the proposed optimization procedure.

Procedure for Optimization of Interior Permanent Magnet Synchronous Motors with Concentrated Windings by Considering End-Leakage Flux