Analytical Modeling of Armature Reaction Air-Gap Flux Density Considering the Non-Homogeneously Saturated Rotor in a Fractional-Slot Concentrated-Wound IPM Machine

The flux of the embedded magnets in the rotor of an interior permanent magnet (IPM) synchronous machine causes a nonhomogeneously saturated rotor iron. This alters the reluctance of the stator flux path due to the nonlinear B-H curve of the rotor iron and should be considered in the analytical field calculations; however, it is often neglected in the prior-art methods leading to inaccurate results. Moreover, the effect of a fractional-slot concentrated-wound (FSCW) stator on the analytical field calculations is not addressed in the existing literature. The magnetic field characteristics of IPM synchronous machines are commonly formulated using an equivalent air-gap function. In order to account for the aforementioned shortcomings in the existing methods for the analytical field calculations, an equivalent air-gap function is proposed in this paper that considers the particular properties of an IPM rotor and an FSCW stator. To this aim, based on the rotor geometry and the nonlinear B-H curve of the iron core, a method is first proposed to model the saturation level and the relative permeability at different regions of the rotor iron. This model is then used in the proposed equivalent air-gap function to compute the armature reaction air-gap flux density. The proposed theory is validated through finite element analysis and experimental results on a prototype FSCW IPM machine in the laboratory.