Question { 7018 }

Can a 50-Hz designed transformer be used at 60-Hz system?
Is the same remains true, when a 60-Hz designed transformer
be used at 50-Hz system? Consider only frequency variation.
The voltage remains as rated value in all cases.
Justify the answer.

Answer

For a transformer the voltage is proportional to the product of flux and frequency.
case-I
Voltage = constant
Frequency = increased from 50 to 60Hz i.e. change by 120%
For Transformer:
Voltage = flux * frequency * K; k is a constant
so when frequency increases by 120% flux decreases to 83.3% Now;
Hysteresis loss = flux^2 * frequency^2 * T; T is constant
At 50 Hz
Hy. Loss@50 = flux^2 * Frequency^2 * T
At 60 Hz
Hy. Loss@60 = (.833flux)^2 * (1.2Frequency)^2 * T
On evaluation:
Hysteresis loss@50Hz = Hysteresis loss@50Hz

Eddy Current Loss

Eddy C. L. = flux^1.6 * f * C; C is a constant
Eddy@50 HZ = flux^1.6 * f * C
Eddy@60 Hz = (.833flux)^1.6 * 1.2F * C
On evaluation;
Eddy@60Hz = 0.895 * Eddy@50HZ

So it is seen that a 50HZ transformer when operated at at 60Hz has same hysteresis loss eddy current decreases. As the core loss decreases the transformer can be safely operated.

But if a 60Hz transformer is operated at 50Hz, then just the reverse of above the core loss i.e. eddy current loss will increase and hence the core loss will go high; hence not advisable to operate.