Analysis and Modelling of Fractional-Slot Concentrated-Wound Interior Permanent Magnet Machines

Abstract

This thesis focuses on the analytical modelling of fractional-slot concentrated-wound (FSCW) interior permanent magnet (IPM) machines and establishes a basis for their magnetic and electrical analysis. In the state of the art methods for analyzing such machines, the non-homogeneous magnetic saturation and the non-linear B-H curve of the rotor iron are not considered. Moreover, the effect of the FSCW stator on the machine magnetic characteristics is overlooked. Aiming at precise modelling of FSCW IPM machines’ magnetic and electrical characteristics, a comprehensive mathematical treatment of the stator magneto-motive force (MMF), the IPM rotor non-homogeneous magnetic saturation, and its airgap flux density are presented. The FSCW stator spatial MMF harmonics are analytically formulated, based on which, a novel heuristic algorithm is proposed for the design of optimal winding layouts for multiphase FSCW stators with different slot/pole combinations. The non-homogeneous magnetic saturation of the rotor iron due to its B-H curve and the residual flux of the embedded magnets is modelled and a saturation map is proposed for the rotor iron. Accordingly, a novel airgap function is proposed for FSCW IPM machines taking into account the effect of the FSCW stator and the non-homogeneously saturated rotor. A precise mathematical model is then proposed for calculation of the airgap PM flux density. The proposed mathematical models for the FSCW stator and the IPM rotor are combined to derive detailed mathematical expressions for its operational inductances, electromagnetic torque, torque ripple and their respective subcomponents, as a function of the machine geometry and design parameters. Both normal operation of the machine and open-phase fault condition are considered in the aforementioned formulations. A “maximum torque per ampere” algorithm is then proposed for the machine under an open-phase fault condition in which customized currents are injected such that maximum average torque with a low torque ripple is guaranteed. Lastly, the derived geometry-based models for the machine characteristics are used to propose an extended dq model for FSCW IPM machines which takes into account its non-sinusoidal parameters. The proposed theories and analytical models are validated using finite element analysis and experimental tests on a prototype FSCW IPM machine.