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In this paper, 30-slot/24-pole five-phase PMSM with hybrid single/double layer (HL) fractional-slot concentrated winding (FSCW) is designed for wheel-driving application in electric vehicles (EVs). Third harmonic current injection in different operating stages of the machine is investigated, including normal operation and fault-tolerant operation. HL FSCW machine is validated to be suitable for injecting third harmonic current to enhance torque by both theoretical analysis and finite-element analysis (FEA), and compared with 20-slot/24-pole single-layer (SL) and double-layer (DL) FSCW machine under constant rms and peak harmonic injection. Besides, a novel flux weakening control method with third harmonic current injection is proposed, which improves torque and efficiency of HL FSCW machine. The influence of nonlinearity caused by stator core saturation and higher order harmonics contained in back electromotive force (EMF) is included in flux weakening operation with harmonic injection. Finally, fault-tolerant control of HL FSCW machine with one-phase open-circuit fault is investigated, and two compensatory strategies with and without third harmonic current injection are proposed. Torque ripple caused by one-phase opencircuit fault is suppressed effectively by the proposed strategies.INDEX TERMS Permanent-magnet synchronous machine (PMSM), five-phase, fractional-slot concentrated winding (FSCW), third harmonic injection, flux weakening, fault-tolerant control, open-circuit.