What makes a motor to run in its rated power?
A low voltage forces a motor to draw extra current to deliver the power expected of it thus overheating the motor windings.


The quoted statement applies to AC induction or synchronous motors, It does not apply to universal motors or DC motors. It does not mention "rated power." It says "the power expected." The power expected is really the power required to drive the load at the speed at which the motor is trying to run. The speed of an AC induction or synchronous motor is mostly determine by the frequency. If the voltage is reduced without reducing the frequency, the motor still tries to run at about the same speed. That requires about the same torque and the same power.

There is a big exception to that rule. Fans and most centrifugal pumps require much less power when the speed is reduced. With many induction motors, the speed at which the motor is trying to run drops sufficiently with reduced voltage to allow the motor to run at reduced power when the voltage is reduced.