Electronic – How to determine full-load RPM of an induction motor at any arbitrary frequency

Induction motors run on a design Volts per Hertz ratio. You didn't specify the rated voltage of the motor, but if it is 50Hz, I'll make the assumption that it is a 380VAC three phase motor. 380 VAC at 50Hz is a ratio of 7.6. Almost all 380VAC rated motors have an insulation system that can safely handle 460 VAC, which is another motor standard voltage. 460 at 60 Hz is a ratio of 7.666, so yes, the speed can be safely increased.

Now, you need to consider some other factors about induction motors. Almost all induction motors under 75KW or 100HP can be safely run up to twice rated speed, but in order to do that, you lose torque. When running over base speed, the stator voltage is kept at the maximum (380 or 460 for example), but the frequency increases. If you were to compare the operation of an induction motor from 0 RPM up to base speed, and then to the extended speed, it would be almost identical to running a DC motor from 0 to rated speed with full field, and then decreasing the field current to increase the motor speed. From 0 to base speed, both operate in the constant torque region. Past base speed, they operate in the constant power (KW or HP) region.

To answer what I think is your actual question, no, do not run a 50Hz motor at an increased voltage unless you increase the frequency to 60Hz to keep the same V/Hz ratio. Increasing the voltage without increasing the frequency leads too excessive winding heating and also reduced cooling capacity from the internal fan (or just the rotor turning).

Other considerations can come into play depending on the mode your VFD is running in, but the above are the basics.

In the last 25 years there has been an enormous amount of evolution and technology that has gone into controlling 3 phase Variable Frequency Drives. Discussing any details around how to do it in a new method or better exceeds the scope of a forum such as this, but would be a good basis for a PHD thesis.

A good starting point in your study is Vector mode control, which is typically one of 3 standards modes to run an off the shelf VFD drive in.

Constant Torque is a standard mode in most VFDs - BUT if you are talking a 50 or 60 hz motor - why would you choose to run at 100 hz UNLESS you had a reduction in torque requirement in your 60 hz - 100 hz range. In my experience every 3 phase motor rated at a base speed of 60 hz has a reduction in torque capability for speeds above 60 hz.

You will also want to do some reading and study the Pull up torque curve which has been a staple in motor theory and motor manuals for 75 years. If you get a good grasp for how Vector control modes manipulate this Torque curve at various speeds - you will have a foundation to start with.