I know the advantages of 3phase induction motor (IM) when compared with a single-phase IM one. However I need to justify using a single-phase IM (main and auxiliary windings) with a 3 legs inverter instead a 3phase IM with also a 3 legs inverter.
Are the single-phase IM cheaper the 3phase one (same power)?
Are the 3phase built for all ranges (power or voltage level) of the single phase one?
Thanks.

Comparatively, 3 phase motors are cheaper and economical with smaller in size as compared to single phase motors.

Single phase motors ratings are restricted max. Up to 10 hp. That too available at low voltage levels.

3phase motors are available right from 0.25 kw to any range with variance in voltage levels (415 volts, 3.3 kv, 6.6 kv, 11kv)