Advanced mathematical model for surface mounted permanent magnet machines with equivalent virtual salient rotor

This paper proposes a mathematical model for surface mounted permanent magnet machines (SPM) considering saturation effect due to armature reaction. Saturation in nonlinear ferromagnetic stator core brings a quasi-sinusoidal reluctance distribution in the circumferential direction. An equivalent virtual salient rotor (EVSR) is placed in the physical rotor position to represent the variation of reluctance. Shape and direction of EVSR are determined by the resultant spatial flux linkage vector produced by permanent magnets and armature current. EVSR causes the second and higher order winding inductance harmonics, which is similar to interior permanent magnet machines (IPM). Misalignment of EVSR and machine magnet poles causes a phase shift in permanent magnet flux linkage vector. A simulation algorithm is built with the concept of EVSR. Finite element analysis (FEA) is utilized to verify the feasible and precision of the proposed mathematical model. This model provides a fast simulation method for nonlinear machine simulation and parameter analysis. The saliency discussed in this paper can also give an idea on sensorless control of SPM.