Hybrid Modeling of Joukowsky-Barrier Synchronous Reluctance Machines

This article presents the hybrid modeling of synchronous reluctance (SynRe) machines equipped with any number of Joukowsky flux barriers (JFBs). The rotor, which includes the JFBs, the flux guides (FGs), and tangential ribs, is modeled using the magnetic equivalent circuit (MEC) method, considering the iron nonlinearity. The reluctance of the JFBs and FGs is calculated through the conformal mapping (CM) and the Joukowsky function, and the reluctance network is used for other regions, e.g., tangential rib regions that are in deep saturation under normal operating conditions. The stator slots, slot openings, and the air gap are modeled using the Fourier-based (FB) method, i.e., sub-domain technique. The stator has double-layer distributed windings, and the stator iron is assumed to be infinitely permeable. The MEC and the FB models are directly coupled by applying the coupling boundary conditions (BCs) on the rotor’s outer surface. Then, the total system of equations is solved through an iterative process. As the proposed hybrid model (HM) can be applied to SynRe machines with any number of JFBs, the results, e.g., components of the magnetic flux density, electromagnetic torque, and back electromotive force (back EMF), are presented for two, four, and six JFBs per rotor pole. The finite-element method (FEM) validates the proposed hybrid analytical method.