Undervoltage Relay for Low Voltage Motors

Absolutely. I have them on all motorized appliances. Refrigerators, A/C, freezers and washing machines.

Any guesses as to why I have done this?

You most certainly have a more reliable grid than I. You must determine the cost of the unit, the replacement cost including the labor of device(s) to be protected.

The only undervoltage relays I have ever seen applied on a motor circuit is a specialized relay designed to hold the motor contactor in, engaged, during an undervoltage event. These are typically applied on large motors, 500kW and up. These contactors have dc coils, so will not drop out until 20% voltage rather than the typical 60% dropout of ac contactors. The primary control circuit voltage is typically ac.

After a certain length of time the contactor will release.

The primary reason for these time delay undervoltage release relays is to avoid the situation where a large motor disconnects from the supply, and then reconnects before it has stopped turning. Out of step, or large magnetizing current can stress a power system, leading to a cascading power system failure. If not a momentary outage, the motor is disconnected and must be manually restarted.

Since electrical appliances now are typically rated to operate with-in a +/- voltage variation..

The decision to provide under voltage protection in my view would be dependent upon the importance or criticality of the connected electrical load and its application.. applications like for health sustenance and life support equipment are good examples.

Which would also be after giving due consideration on the reliability and voltage stability as supplied into the area or location..