Semi-Analytical Magnetic Field Predicting in Many Structures of Permanent-Magnet Synchronous Machines Considering the Iron Permeability

This paper deals with an adaptable semi-analytical model to calculate the open-circuit and armature reaction field distributions as well as the electromagnetic performances in many structures of permanent-magnet synchronous machines (PMSMs). It is based on the multi-layer models considering the iron permeability with the convolution theorem (i.e., Cauchy’s product theorem) using the harmonic modeling technique (or the Maxwell–Fourier method). The 2-D semi-analytical model can be used for surface-mounted–inset-mounted or spoke-type PMSMs with different permanent-magnet (PM) magnetization patterns, winding structures, internal/external rotors, and slotless or slotted stators without the need to adopt the model equations to a specific PM machine type. For example, this scientific contribution has been applied to three types of PMSM with different topologies, viz.: i) slotted surface-mounted external rotor PMSM; ii) slotted surface–inset internal rotor PMSM; and iii) slotless external rotor spoke-type tangential PMSM. Finally, the results of semi-analytical method are compared with those found by the finite-element method.