Abstract The combination of mirror image method and conformal transformation is used to calculate the air-gap relative permeance of slotted permanent magnet synchronous motor (PMSM). As a mirror, the surface of the ferromagnetic rotor is smooth. An image can be created from the air-gap of the slotted PMSM, and these two air-gap formed the analytical model. The air-gap relative permeance formula can be obtained by several conformal transformation. The analytical model could consider the slot effect on the radial and tangential components of the air gap magnetic field, and its analytical formula can be used to predict excitation magnetic field, armature magnetic field, electromagnetic force and cogging torque of the slotted PMSM. Based on the analytical model, air-gap relative permeance is solved on the specified path and in the region of a slotted PMSM. Compared with the finite element results, the accuracy of the analytical method is demonstrated.
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