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A design methodology dedicated to multi-phase permanent magnet synchronous machines (PMSMs) supplied by pulse width modulation voltage source inverters (PWM VSIs) is presented. First, opportunities for increasing torque density using the harmonics are considered. The specific constraints caused by the PWM supply of multi-phase machines are also taken into account during the design phase. All the defined constraints are expressed in a simple manner by using a multi-machine modelling of the multi-phase machines. This multi-machine design is then applied to meet the specifications of a marine propeller: verifying simultaneously four design constraints, an initial 60-pole three-phase machine is converted into a 58-pole five-phase machine without changing the geometry and the active volume (iron, copper and magnet). First, a specific fractional-slot winding, which yields to good characteristics for PWM supply and winding factors, is chosen. Then, using this winding, the magnet layer is designed to improve the flux focussing. According to analytical and numerical calculations, the five-phase machine provides a higher torque (about 15%) and less pulsating torque (71% lower) than the initial three-phase machine with the same copper losses.