Hi,
about 2.2kW is about the practical maximum for single phase VFD's. Above that level all the manufacturers design and build them for three phase.
Having said that the larger drives will work with single phase supply despite being designed for three phase. They need to be derated, I'm not sure what the formula
is but its something like 1/3.
Thus if you have a 3.7Kw spindle you'd probably need a 5kW inverter if using single phase supply.
Craig