Magnetic Equivalent Circuit Model for Electromagnetic Analysis of Synchronous Reluctance Motors

This paper proposes an accurate magnetic equivalent circuit (MEC) model for synchronous reluctance motors (SynRM) which is including the limited number of permeances in air-gap, and iron parts of stator and rotor. In proposed approach, the complex geometry of SynRM is divided into some parts, and the conformal maps are then used to calculate the permeance of relevant part in different paths. The conformal maps such as Schwartz-Christoffel ($\mathrm{S}-\mathrm{C}$) mapping is used to transform the complex geometry of different parts of SynRM into the canonical geometry in rectangle form. The permeance in relavant direction is then easily calculated in canonical geometry. It should be noted that the permeance is maintained while mapping the geometry from the physical domain into the canonical domain. After calculating the linear and non-linear permeances, the non-linear system of equations is created through writing the magnetic equation in different nodes of motor geometry. The newton-Raphson method is then used to solve the system of non-linear equations, to determine the scalar magnetic potential in all magnetic nodes, and to calculate the motor performance. In final, the accuracy of proposed MEC model is verified through comparing with corresponding results obtained from finite element method (FEM).