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Inverter dead-time effects have been investigated in detail in the past for three-phase drives supplied from a three-phase voltage source inverter (VSI). A similar study has never been conducted in conjunction with multi-phase (more than three phases) drives, supplied from multi-phase VSIs. Regardless of the type of ac machine and its number of phases, the power supply of the drive is typically a two-level VSI, which requires a method of PWM for its operation. If a multi-phase machine is with sinusoidal field distribution, the PWM technique must generate sinusoidal harmonic-free output voltages in order to avoid appearance of low-order stator current harmonics. Recently a great deal of research has concentrated on PWM methods suitable for multi-phase VSIs. All of these PWM methods theoretically produce sinusoidal output voltages with no low order harmonics. As a consequence, rotor flux oriented control of multi-phase ac machines with sinusoidal MMF distribution can be theoretically realised by using only two current controllers in the synchronous reference frame. The paper shows that despite using a PWM method that does not produce low-order harmonics, in practice they do appear in the output voltage, and consequently currents, of the multi-phase VSI. Simulation studies show that low-order harmonics are generated as a result of inverter dead-time and that the effect of such harmonics on a five-phase ac machine can be significant due to the low machine impedance presented to these harmonics. Experimental results collected from a five-phase induction motor drive laboratory prototype are presented which reinforce this hypothesis. The paper further suggests a modified current control scheme that is able to fully compensate inverter dead-time effect and thus provide practically perfect sinusoidal currents. The proposed current control scheme is validated via simulation and experimentally.