Output torque of variable speed drive running above 50Hz

Generally, electric motors are designed according to 50Hz power supply, its rated torque also in this frequency. Therefore, the speed adjustment under rated frequency called constant torque speed adjustment. (T = Te, P <= Pe).

If the variable speed drive outputs frequency exceeds 50Hz, the motor torque is inversely proportional to the frequency in linear relationship decrease.
When the motor running in above 50Hz frequency, we should consider the motor loads to avoid motor lacks of torque.

For example, the motor torque is about a half in 100Hz running against 50Hz. Therefore, the speed adjustment in above rated frequency called constant power speed adjustment. (P = Ue * Ie).

As we know, for a specified motor, the rated voltage and rated current is constant.

For example, the variable speed drive and motor rated values are: 15kW/380V/30A, motors can operate at 50Hz or above.
When the frequency is 50Hz, the variable speed drive output voltage is 380V, current is 30A. Then if we increase the output frequency to 60Hz, the variable speed drive maximum voltage and current also is 380V/30A, it is obviously that the output power is fixed, so it called constant power speed adjustment, what's the torque status now?

Since P = wT (w: angular speed, T: torque), as P keeps same, w increases, so the torque will decrease accordingly.

From another point: motor stator voltage U = E + I * R (I is the current, R is the electrical resistance, E is the EMF)
Then we can see, U and I are constant, E is constant.
And E = k * f * X, (k: constant, f: frequency, X: flux), when f changes from 50 to 60Hz, X will decrease accordingly.

For the motor, T = K * I * X, (K: constant, I: current, X: flux), so the torque T will decrease along with the flux X.

And, if the frequency is less than 50Hz, as I * R is very small, so if the U/f = E/f is constant, the magnetic flux (X) is constant, the torque is proportional to the current, which is why use the variable speed drive overcurrent capability to describe its overload (torque) capability, and known as constant torque speed adjustment (rated current is constant -> Maximum torque is constant).

Conclusion: When the variable speed drive outputs frequency increases from 50Hz, the motor outputs torque will decrease.