High voltage square wave drives induction motor
Electronic variable frequency drives (VFDs) have been supplied for three phase motors for about 55 years. I can name about a dozen large manufacturers that sell VFDs over a wide part of the world. There must be a dozen more that I am not as familiar with. The early designs did not have very good waveforms, but there was not a lot of difficulty with the motors. The most significant problem was with high torque at low speeds. That is something that a centrifugal pump does not require. Newer designs have better waveforms except that they use fast-switching IGBTs that generate high voltage switching transients causing motor insulation stress failures. There are several remedies for that including improved insulation in VFD rated motors.

There is much less history of using VFDs for single-phase motors. There may be only one manufacturer making VFDs for single-phase motors. Capacitor-start motors do not work with VFDs at all. Permanent-split-capacitor (PSC) and shaded pole motors will work with a single-phase VFD for centrifugal pumps and fans. It may be difficult to find information about waveform quality requirements. Centrifugal pump motors are likely be quite tolerant of extra heating due to harmonics. Since the power required to drive the pump drops drastically as the speed is reduced, the average load on a variable-speed pump is significantly less than what the motor is designed for. Therefore the extra heating can be tolerated well. Using the VFD to operate the motor at full-speed all the time would probably be the highest risk operating condition.

The VFD design must include a ramp-up circuit to avoid high starting current. A ramp-down circuit is required to prevent regeneration. Other protection circuits will also be needed.