Analytical Modeling of Equivalent Air-Gap Length and Inductance Calculation of Interior Permanent Magnet Motors

Stator and rotor cores of interior permanent magnet (IPM) motors are usually saturated, and the saturation distribution and saturation depth vary with the stator current. Also, their rotor structures are complex; hence, the saturation cannot be accurately reflected by a saturation factor. These considerations lead to the existing equivalent air-gap length models of induction motors and inset permanent magnet (PM) motors no longer suitable for IPM motors. Therefore, based on the consideration of stator and rotor saturation, this article proposes the equivalent air-gap length model of IPM motors expressed by magnetic potentials on the stator inner surface and the rotor outer surface. The proposed equivalent air-gap length model can accurately reflect the influences of complex structure and severe saturation of IPM motors. Compared with the existing models, the proposed one is no longer uniquely determined by motor structure parameters; it is also a function of stator current and rotor position. Furthermore, the obtained equivalent air-gap length model is combined with the winding function and the modified winding function to solve the inductances under different stator currents and different rotor eccentricity states. Finally, the proposed method is verified by both finite element analysis (FEA) and experiments.