Detailed Analytical Modelling of Inductances and Electromagnetic Torque in Fractional-Slot Concentrated-Wound Interior Permanent Magnet Machines Under Healthy and Open-Phase Fault Conditions

Abstract

This chapter builds upon the modelling of the stator and rotor magnetic characteristics performed in Chaps. 2, 4 and 5, and proposes detailed novel analytical models for the machine self- and mutual inductances, field-alignment torque, reluctance torque and torque ripple in FSCW IPM machines operating under healthy and open-phase fault conditions. The proposed analytical models are a function of the machine geometrical parameters which are then substituted by the machine electrical parameters to obtain equations that can be readily used for real-time implementation on the machine. At first healthy operation of the machine is considered and the proposed models for the electromagnetic torque is used to obtain the optimum current angle that results in maximum average torque at different operating conditions. The obtained results are validated through FEA simulation of a FSCW IPM machine. In the next step, under an open-phase condition a four-leg inverter is considered and injection of custom currents with adjustable phase angles is assumed. An analytical model is first proposed for the stator MMF generated by such currents. This model is then used to derive the average field-alignment torque, reluctance torque, and their torque ripple under the open-phase fault condition. The derived analytical models are used to propose a maximum torque per ampere (MTPA) algorithm under an open-phase fault condition.