Analytical Model of Synchronous Reluctance Machines with Zhukovski Barriers

The interest in synchronous reluctance machines has grown in many applications due to their high torque density, robustness and low cost. A fast calculation of the air-gap flux density distribution and torque is necessary in order to evaluate a chosen geometry during the early design process. Therefore, an analytical model is used based on magnetic equivalent circuit technique consisting of air-gap and flux barrier reluctances. Theory of conformal mapping is employed to calculate the reluctance of "Zhukovski" shaped barriers, which are based on the flux line pattern in a solid rotor. In addition, the output torque is predicted by Lorentz force calculation. A comparison between the proposed analytical model and finite element analysis is carried out to confirm the accuracy of the analytical model.