Analytical Prediction of Magnetic Field in Parallel Double Excitation and Spoke-Type Permanent-Magnet Machines Accounting for Tooth-Tips and Shape of Polar Pieces

This paper presents an analytical method based on subdomain method for the computation of open circuit, armature reaction, and on-load magnetic field distribution in integer slot winding parallel double excitation and spoke-type tangential permanent-magnet machines. The proposed model takes into account for stator and rotor slots tooth tips and shape of polar piece. A 2-D exact analytical solution of magnetic field distribution is established. It involves solution of Laplace's and Poisson's equations in semi-closed stator and rotor slots, air-gap, buried permanent magnets into rotor semi-closed slots, and nonmagnetic region under magnets. Obtained exact analytical results of open circuit, armature reaction, and on-load magnetic field distribution are verified with those issued from the finite element method.