An Analytical Model for an N-Flux Barrier per Pole Permanent Magnet-Assisted Synchronous Reluctance Motor

In this paper, a general analytical model for permanent magnet assisted synchronous reluctance machine with 'N' barrier, including space harmonics using winding function is being developed. Flux densities in the air gap, in the cutouts, and in the flux barriers are found. Back-EMF developed by the permanent magnets using winding function is derived. Equations for the d-axis and the q-axis inductances are also obtained. Electromagnetic torque is finally derived using the co-energy method. The developed analytical model results are supported by finite element analysis (FEA). Once the model is verified, then it is much faster to make changes to the geometrical dimensions and determine their effects on the torque, inductances, etc than FEA. The developed analytical model highlights the contributions of the reluctance variations and permanent magnets on the developed torque. An interactive software has been written in Matlab environment for 'N' flux barrier. Simulation results are obtained in the Ansoft/Maxwell environment for four flux barriers per pole. These results are supported by the experimental results obtained from a laboratory test bed.