Mathematical Modelling and Simulation of Synchronous Reluctance Motors

Sammanfattning

Synchronous Reluctance Motors (SynRMs) are gaining industrial attention as energyefficient, rare-earth-free alternatives to permanent magnet machines. Their operatingprinciple relies on magnetic saliency between the direct and quadrature axes,which produces reluctance torque without rotor windings or permanent magnets.The conventional circuit model does not resolve the spatial distribution of theelectromagnetic field within the machine cross-section, thereby limiting the accuracyof computed inductances and torque. A field-based approach derived from Maxwell’sequations and solved by the Finite Element Method (FEM) is required to overcomethese limitations.In this thesis, a complete two-dimensional magnetostatic FEM framework for SynRManalysis is developed from first principles. The governing partial differential equationis derived, formulated in weak form, and discretised using first-order Lagrangianelements, implemented in Julia 1.12 with the open-source Gridap.jl library. ThecomputedmagneticvectorpotentialfieldAz producesthefluxlinetopologyofthefourpole synchronous reluctance motor, including the flux loops through the stator androtor iron and the opposite circulation directions at the north and south poles. Theseresults constitutes an open-source FEM baseline for future nonlinear and barrierequipped SynRM models.