Can a 3-phase 480V 60Hz motor run on a 380V 50Hz power supply?

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.
50Hz 60Hz Motor
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.

Also, motor developed torque is proportional to the square of the voltage – AT ALL POINTS ON THE TORQUE CURVE. So a machine rated 480v 60Hz but operated at 380v 50Hz is going to produce (380/480)*(380/480) * (rated torque) . . . roughly 62 percent of the expected value. In most cases, that is going to result in a stall condition, since the motor will not be able to move the load at some in the acceleration profile.

Bottom line – I expect you either damaged the winding with thermal overload (continuous run), OR damaged the winding because of the resulting stall condition.

To run a 480v 60Hz motor on 380v 50Hz power supply, or vice, it’s better to buy a GoHz frequency converter which can convert both Voltage and Frequency.

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