On the analytical determination of the complex relative permeance function for slotted electrical machines

The complex relative permeance function is a suitable tool to predict the air gap magnetic field in slotted stator electrical machines. In the literature, the complex permeance function is usually identified by means of numerical techniques based on complex approaches such as conformal mapping or subdomain method. In this paper, an alternative approach is proposed. This method is based on solving the magnetostatic Laplace equation over a portion of the slotted air gap by imposing appropriate boundary conditions in the slot opening region. Such boundary condition tries to represent the theoretical trend of the magnetic field divergence near the corner-shaped ferromagnetic regions. The Carter theory for the slot fringing effect is also used. A fully analytical formulation for the complex relative permeance function is obtained, and its accuracy is assessed by comparison with Finite Element Analysis (FEA).