I use VFD on one of the inverters used for salt water RO on an off shore island... 240v in 240v out.
I agree with pete on most of it, but I find there are more motors in star 415v here than delta which is good for me as I run rotary a inverter here for the mill and brake press etc in the work shop. ( 10 hp motor with 700uf start and 50 uf on the phases for run ( I think..)... been 12 years since I looked at it, but use it near every day..... and I have stolen some of them and not replaced em later on so it was 1500uf originally).... uses the third phase winding to sense voltage to control the start switching relay.
So it will run any vfd you choose..... and you can always wind a small 10A 415v winding on the torroid as well for 415v operation...
.... well you have done near everything else with it... why not that??
Easiest to just look for star 415v motor and rewire to delta.... and run 240:240 vfd, they are so cheap now.
The voltage is not terribly important 380-415 no biggie as speed is a hertz problem, not a voltage problem, you will only loose a bit of torque
... which you can dial away anyhow.
380v or 415v inputs use less current not more, for the same power than 240v, so better chance for single phase to run it.... but rally it is only the bridge input that will make any difference at all.. 4 diodes or 6 carrying the load ( single or 3ph inputs).. after the rectifier there is no difference.
I run up to 4kw in single 240v for water pumps on farms here, usually 3ph 415 for 5kw and over.
A vfd with 5-10 second ramp will do very nicely for the inverter.
............oztules