Guys, here's the issue from a VFD mfr's perspective.
When you UL list a VFD, you are allowed to list it for TWO motor power ratings, based on the fact that a VFD is a power CONVERSION device, not simply a motor controller. So back in the day (it's changed a little now*), we could UL list the EXACT SAME drive as a 30HP Variable Torque drive, or a 25HP Constant Torque drive. It was EXACTLY the same drive, but the NAMEPLATE had to state the worst case scenario, the Constant Torque rating.
The difference is in the LOAD APPLICATION, because the VFD has a different Overload Capacity based on what you want to do with it. In a Variable Torque application, such as a CENTRIFUGAL pump or fan, the load does not couple with the machine at the same rate throughout the speed range, so you do NOT need the same overload capacity in the VFD components. It's essentially an acknowledgement that there is nothing about the machine (pump or fan) that will cause the VFD to need to pump out more current that what it is safely able to handle. If the machine was a Constant Torque application, it might need that extra "umph" to get started, so the VFD might need to pump out 150% of it's rated continuous current for upward of 60 seconds. That meant the transistors needed to be de-rated to handle that potential.
The difference INSIDE of the drive was (is) in the overload settings. If you are using the VFD on a Variable Torque load, there is a programming parameter or a switch inside that changes the V/Hz output from being linear, to being a curve, V/Hz2. When using that feature, it ONLY works on a VT load, so then they use that info to allow you to program a HIGHER motor FLA into the drive, based on the VT motor HP rating. If you disable that, then the VFD will LOWER the maximum motor FLA that you can set it at commensurate with the CT motor HP rating.
Example: VFD says it is 75HP CT, but can be used as 100HP VT. If you enable the VT settings, you can program the motor FLA to be 124A, what it would need for a 100HP motor. If you do NOT enable the VT settings, you can only set the motor FLA to 104A, the FLC of a 75HP motor. All of this is ONLY possible with a VFD because it is controlling ALL aspects of the power going to the motor. Did this stop people from hooking up a 100HP motor on a machine that was Constant Torque and trying to run it from a VFD that was only rated for 100HP as a VT drive? No, it did not. But the VFD would simply co into current limit and NOT ALLOW the motor to develop more than 75HP, which means it would not allow it to go to more than 3/4 speed, or trip off line.
So can you use a 25HP "rated" drive on a 30HP motor? Maybe. If it is on a centrifugal fan or pump, the VFD may indeed be rated for 30HP VT, but will say that you cannot overload it for more than 105% for 30 seconds (which is essentially saying that you CANNOT overload it). Because of some more archaic rules, the controller nameplate was only able to list the CT rating, the WORST CASE scenario for the drive, but if you look up the listing information, the VFD mfr was allowed to state that it is appropriate for use on 30HP motor if it is enabled as a Variable Torque application.
* Much of this has changed now, we no longer use the terms VT and CT for drives, it was something that a lot of people had a hard time understanding. So now we say "Normal Duty" and "Heavy Duty", and state the specific motor power ratings at both of the two levels. Plus the DEFAULT settings of the drive now are for "Normal Duty", so if you ACTIVELY SELECT the HD feature, THEN it lowers the FLA setting range you can program it for.