Can we operate a 60HZ Transformer on 50Hz Supply Source?

Suppose,  we have a 60 Hz Transformer

we want to test this 60Hz transformer on 60Hz supply source

V=5000V, Resistance R=6.1Ω, Inductance L=0.3 Henry, Frequency f=60Hz

Then X_L= 2πfL = 2 x 3.14 x 60 x 0.3 = 113.04 Ω , and

Z = √(R²+X_L²)  …. Impedence

Z = √(6.1²+113.04²) = 113.2 Ω

Z + V/I, Then   I + V/Z = 5000V/113.2 Ω = 44.16 A

But now we want to test this 60Hz transformer on 50Hz supply source.

V=5000V, Resistance R=6.1Ω, Inductance L=0.3 Henry, Frequency f=50Hz

Then X_L= 2πfL = 2 x 3.14 x 50 x 0.3 = 94.24 Ω , and

Z = √(R²+X_L²)  …. Impedence

Z = √(6.1²+94.24²) = 94.44 Ω

Z + V/I, Then   I + V/Z = 5000V/94.44 Ω = 52.94 A

We can see that when we decrease the frequency, the X_L decreases and current increases.

When we operated a 60Hz transformer on 60Hz supply, then current was 44.16A

But when we operated the same transformer on 50Hz supply, then current was 52.94A.

So this extra current may cause copper loss and produces heat which may leads to burn-out of the coil.

So if we install an additional current limiter in series with the winding by which we can increase the impedance to reduce this extra current. Then we can use a 60 Hz transformer on a 50 Hz supply without any difficulties.

The voltage and frequency are related in a reciprocal fashion if maximum flux in the transformer is to be kept constant. An increased magnetic flux than the rated maximum flux is unacceptable for the effective transformer action. So with constant voltage and reduced frequency, the flux will increase beyond the maximum. 

Thus if a 60Hz transformer to be used in 50Hz, its applied voltage must also be reduced considerably to keep the flux constant. This reduction in voltage with frequency is called Derating.  Similarly a 50Hz transformer may be operated at a 20% higher voltage on 60Hz if this action does not cause any insulation problem.