Basic version:
A VFD (Variable Frequency Drive) consists of 3 parts: A Converter, which converts the AC incoming power to DC and filters the ripple, a Controller that decides what needs to happen and how to get there, and an Inverter, which takes the DC and fires high speed transistors to re-convert (invert) it back into something that motors use the same as AC (pseudo AC).
In the Converter section, AC line power is nothing more than the "raw material" to make DC, from which the new pseudo AC is going to be created. So the incoming AC power can be 3 phase OR single phase. The only difference is that if you use single phase, the number of sine waves going through the rectifier and making DC is lower, so the DC will have more ripple in it. Therefore, the filtering part of the Converter needs to be capable of handling and smoothing that higher ripple, i.e. more capacitance. In addition, the power that the 3 phase motor will draw remains the same, but now it has to come from a 1 phase source instead of a 3 phase source. So the incoming current will go up by the 1 to 3 phase ratio, the square root of 3. So the 1 phase current will increase to 1.732 time what the 3 phase current would have been. This means that the Converter section, when combined with the extra capacitance needed, must be twice the size of the 3 phase motor it is going to control.
In small 230V VFDs (3HP and under), most manufacturers go ahead and make the Converter components big enough to do this since they are relatively small currents anyway. A couple of mfrs go up to 5HP without derating, but the general rule is, above 3 HP you should plan on doubling the size of the VFD. So if you have a 10HP motor, you buy a 20HP VFD if you want a 1 phase input.