Magnetic Field Analysis of SynRel and PMASynRel Machines with Hyperbolic Flux Barriers using Conformal Mapping

Synchronous reluctance (SynRel) and permanent magnet (PM)-assisted SynRel (PMASynRel) machines with hyperbolic-shaped flux barriers are gaining more interest in commercialized products of known companies, because of their high saliency ratio. This article presents a faster approach for calculation of the air-gap flux density distribution and the electromagnetic torque of these machines than the finite-element method (FEM). The method is based on the conformal mapping (CM) techniques and magnetic equivalent circuit (MEC) solutions. A suitable CM is introduced to compute the magnetic reluctance of hyperbolic-shaped rotor flux barriers. The analytical method is then implemented on both SynRel and PMASynRel machines with the same stator structure as the Prius interior PM motor and five hyperbolic flux barriers per pole in their rotors. The accuracy of analytical results is assessed by the finite-element analysis (FEA).