If I run a 3-phase motor rated 480V 60Hz on a 380V 50Hz power supply what will happen in terms of permanent damage?

There are a couple of relationships to remember about voltage, frequency, speed, and current.

For 3-phase designs, speed is proportional to frequency (and inversely to pole count). The governing equation to determine “synchronous” speed is:

120 * (poles) / (hertz) = (revolutions per minute). For squirrel cage induction, the actual speed will be slightly lower, due to the effects of slip.

When attached to a given load, the motor will try to produce power (defined as the product of volt and ampere, or more commonly “watt”) according to the process logic. This means that for a machine nominally rated 480v 60Hz, operating at a lower voltage like 380v 50Hz may well mean it attempts to draw (480/380)* it “normal” rated current. This is guaranteed to result in severe thermal damage, if left this way for any appreciable time.

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