The paper assesses the steady-state performance of a five-phase induction machine fed by a modified open loop constant volt/hertz (V/f) control method, which imposes a trapezoidal induction waveform in the air gap under varying load conditions. The trapezoidal air gap induction is achieved through the imposition of an appropriate combination of the third harmonic and fundamental stator voltages. This harmonic combination is determined from the steady-state model using a mathematical optimization procedure, which allows to obtain the optimal weighting factors for each harmonic component. The optimized reference voltages lead to a trapezoidal air gap induction, which allows a better iron utilization and higher output torque for the same rms stator current when compared to sinusoidal air gap induction. The resulting air gap induction is obtained from the induced voltage of a full pitch search coil placed in the air gap. The proposed control scheme was successfully simulated and implemented on a five-phase prototype machine running under different load conditions. Experimental and simulations results show an increase in the torque/ampere relationship for loads above 50% when compared to the conventional V/f method using only the fundamental current and air gap induction. A comparison between the simulation and experimental curves presents a very good agreement that confirms and validates the parameters and model used.