Problem 94-1    Source:  Problem created by the site's author.

Consider a conventional single-phase two-winding transformer of 110 kVA and nominal voltage of 2,200 / 220 volts. It is connected as an autotransformer as shown in Figure 94-01.1, that is, a voltage step-up. Consider N₁ the common winding of the autotransformer. Find:

a) the currents in the windings.

b) the power transformed by induction and conduction.

c) the total power that the autotransformer can deliver to the load.

Solution of Problem 94-1

Item a

Since we know the nominal power value (S_n) of the conventional transformer and the voltage values ​​V₁ and V₂, it is possible to calculate the values ​​of I₁ and I₂.

The currents calculated above are the currents when the transformer operates conventionally, that is, with two independent windings. When the transformer operates as an autotransformer at full power, the terminal currents I_L and I_H are:

Item b

The transformed power can be calculated by the equation given below.

Thus, we have:

Item c

And the power supplied by the autotransformer is equal to the input (or output) power, shown below.

Performing the calculation, we obtain:

It would also be possible to calculate the input power by adding the transformed power and the conduction power, that is: