Analytical Calculation of the Air-gap Flux Density and Magnetizing Inductance of Synchronous Reluctance Machines

摘要

This paper proposes an analytical method to calculate the air-gap flux density and magnetizing inductance of the direct and quadrature ( d and q) axes of synchronous reluctance machines (SynRMs). Both magnetizing inductances are obtained through precise calculation of the air-gap flux density profile, which is achieved by taking advantage of conformal mapping and Maxwell's equations. A nonlinear magnetic equivalent circuit (MEC) model is built to take the saturation effect into consideration by solving iteratively, and finally yields magnetic potentials on the rotor. Such magnetic potentials are then used as boundary conditions to solve the potential equations and calculate the air-gap flux density, from which the d and q axes magnetizing inductance can be computed. The computation results are verified by finite element analysis (FEA), and are showing perfect match with FEA simulation.