A VFD in and of itself couldn't care less what the frequency is, all it does is rectify it. So the only other issue is voltage; it cannot create voltage that isn't there, so using a VFD at a lower voltage limits the maximum output voltage to the input voltage (for the most part). So you cannot put 380V into a VFD and get 480V out of it. But again, that has nothing to do with the current rating of the VFD.
Now that said, sure, the maximum HP/kW capacity of the MOTOR you can connect to that VFD will change because of that, but that is the answer to a question not asked.
And just for the record, 99% of all low voltage VFDs come in 3 voltage classes: 240V class, 400V class and 600V class:
240V class VFD cover 200-240V inputs,
400V class VFDs cover 380-480V inputs,
600V class VFDs cover 550-690V inputs (although 690V is more rare)
So rarely is there a difference between a 380V and a 480V VFD, and even if there were, a 480V VFD would almost certainly accept a lower input voltage. There are always exceptions, these are generalities.
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