Quote by stevenb
....... if you observe a system in which a small change in voltage results in an inverse change in current, you likely have a nearly constant power situation. Mechanical power is torque times rotational speed, so the motor may slow down and have more torque capability at lower voltage. The details matter and the situation is not always simple.

If you have a quasisynchronous induction motor running at 60 Hz, and you reduce the voltage and not the frequency, the RPM change is very small, you have a constant load power situation. I have made measurements on induction motors under load at reduced voltage and observed the current increase.
[added] When the voltage is reduced slightly, say 10%, the power factor usually increases.
Bob S