richerdick, let's start over here and think this thru with the data you have. First, rather than simply replace your old drive/motor system with an AC equivalent and possibly duplicate errors in that system, it would be better to understand your load's torque and speed requirements and go with that.
Since you have an existing DC motor, you can find load torque quite easily since motor current is directly proportional to load torque. Notice that I did not mention motor kw or hp. Sizing a drive/motor system can best be done with torque and speed, leaving hp to come out wherever if finally does.
Since I am more familiar with hp and ft-lbs, I coverted your 2kw to 2.68hp, multiplied it by 5250 and divided the result by 3000rpm to get 4.7ft-lbs of torque. This is the motor's continuous torque rating from 3000rpm down to whatever slower speed it can cool itself. If it has a shaft fan, that point would be about 20% speed or 600rpm. If it has an auxiliary blower, it will cool all the way to zero speed. But, the more important question is "how slow does my load have to run at full torque" That will determine the type of motor cooling required.
Next, observe the DC motor amps carefully for enough time to capture all of the operating conditions in the load. Watch particularly for overcurrent when starting, accelerating, and for any sudden overload conditions in the load. That will tell you how much torque overload capacity you will need in the new system.
Once you know the load's torque requirements and speed range, take the highest continuous torque level and the highest speed and size your AC motor to cover that both. Select the cooling method that will cover for the slowest continuous torque condition.
Using the highest shortterm overload torque level, figure the motor amps required. Size your AC drive using, first, the continuous current rating of the motor and, second, the highest shortterm overload amps to cover for the overload torques. For example, you may need a four amp drive continuous but 5.2 amps shortterm. That would require a drive with a larger overload capacity than the common 10% variable torque or normal duty rating. You would have to select the nest larger size to cover the overload amps.
One other thing. You need to understand what the speed stability requirements of the load are. For example, when the load torque changes from a small torque to a large torque, does the speed have to remain absolutely stable or can it sag a little. Selecting a V/Hz drive will get you about 1% speed droop from no load to full load. A sensor-less vector drive will get you about .5% droop, and a full flux vector drive (requires an encoder on the motor shaft) will get you essentially no droop.
That's the process I use. Hope it helps you make your selection. Just one last comment. Don't be taken in by the notion that "just oversize everthing and you'll be ok" is a good way to go. You have to understand your load's speed and torque requirements and, once you meet them, any oversizing is just waste.
