2-D Analytical Magnetic Field Prediction for Consequent-Pole Permanent Magnet Synchronous Machines

Consequent-pole permanent magnet (PM) synchronous machines (PMSMs) provide especial features by the use of alternate PM and ferromagnetic poles. The design of these types of electric machines requires an accurate model due to the asymmetrical flux distribution in the air gap under adjacent poles. The equivalent magnetic circuit technique can hardly offer an accurate model for consequent-pole PMSMs. To this end, a 2-D analytical model is presented for consequent-pole slotted stator PMSMs to accurately compute the magnetic field distribution due to PMs and armature reaction. The slotting effects and the tooth-tip effects are taken into consideration by using the subdomain technique. The proposed model is used to calculate the magnetic flux density distributions of three consequent-pole PMSMs: an 8-pole, 9-slot machine with a non-overlapping winding; a 4-pole, 15-slot machine with an overlapping winding; and a 10-pole, 12-slot machine with a non-overlapping winding, each with three different magnetization patterns, i.e., radial, parallel, and Halbach. Based on the magnetic flux distribution, the electromagnetic torque, the self-and mutual-inductances, and the unbalanced magnetic forces have been analytically calculated. The analytical results are compared with those obtained from the finite-element method to show the accuracy and efficacy of the proposed 2-D analytical model.