If a VFD doesn't have nameplate or installation manual ratings for single phase service you have to treat it as a three phase rated unit. If you want to run it from single phase you have to crank in some fudge factors so your VFD to be happy with the motor it serves.
I have several three phase only rated VFD's I run from single phase power. You gotta remember that most machine tools are low duty cycle not like a pump or blower where the load is constant. A minute or so of full HP heavy roughing then a minute of cranking back and dialing in with maybe a size check equals 50% duty cycle. the other 90% of the time it's in service the machine loafs along taking lighter cuts and fine finishes. The motor demand will be correspondily lower and the demand from the line will be lower yet depending on the Hz setpoint. If the motor is run at 40 Hz or below (varies with motor service factor and VFD max current ratings) you don't need to de-rate a three phase rated VFD at all.
If you wish to run a motor from a three phase rated VFD to full ratings from single phase power you have to work the math. Start with the full load motor amps @ 3 Phase Vs the VFD ratings. The input diodes of the VFD are rated for the nameplate load rating. The filter capacitors are sized for the three phase bridge ripple current. The VFD's output transistors are rated for the VFD's three phase full load. All this is complicated by environmental factors, demand , duty cycle etc so a flat statement of X de-rating may not hold up to technical scrutiny.
The best we can do is generalize on some rules of thumb. Here's mine:Generally, a VFD serving a motor expected to be loaded to 60% FLA can equal the motor HP. A VFD feeding a motor loaded to about 80% needs to be rated at 2/3 the motor HP. A heavy duty motor running a 100% duty cycle for extended periods of time needs to be double the HP rating of the motor is serves. Students of the topic can quibble these figures but I believe them to be reliable enough for first estimates. IOW YMMV.
A 20 HP VD may be overkill for a 7 1/2 HP motor. Its current detecting circuitry may not function properly at too small an operating current. You'd almost have to try it and see.
As for accel surges, if you insist on dynamite accels a VFD will do them at a much smaller line current surge than across the line starts. For one thing the VFD will go into current limit if the accel is set too short. For another a VFD will "motor" the armature at best torque slip to setpoint RPM quicker and more efficiently. Compare that to an across-the-line start where the motor's magnetic field windnills accellerating the armature far less efficiently.
Much depends on the connected inertia. I have my lathe VFD set for 3.5 seconds accel and decel and seldom exceed full load line current even when accellerating the spindle to 2000 RPM with my biggest 3 jaw on it.
I have a 10 HP VFD feeding a 10 HP motor. I set the motor current limit to 35 Amps to save the input diodes from embarassment. The VFD is rated for 150% overload for some seconds (can't remember how many) so my dialed-in limits are safe for the rectifier stage and maybe the filters. There's been no smoke, smells, or loud noises for 5 years now. (knocking on wood)