Problem 92-1    Source:  Problem developed by the site author.

A 10 kVA transformer with a rated voltage of 2,300/230 V and that was subjected to a short circuit test showing, in this condition, V_cc = 80 V (already referred to the secondary) and the power measured by the wattmeter was 400 W. Calculate:

a) The transformation relation a.

b) The resistances and leakage reactances of the primary and secondary of the transformer.

c) The power factor of the transformer in short circuit.

Solution of the Problem 92-1

Item a

As the nominal voltages of the primary and secondary of the transformer were provided, we easily calculate the transformation relation. Like this:

Item b

Initially we must determine the short-circuit current, that is, the nominal current at the secondary of the transformer. As the apparent power of the transformer and the nominal voltage of the secondary were supplied, then:

Having the values of V_cc and I_cc, then by eq. 92-09:

Note that we are using secondary values and we indicate this using Z"_eq. On the other hand, using eq. 92-06 let's calculate the value of R_eq using the other data provided, namely the power W_cc consumed by the transformer when short-circuited. Soon:

With the values of Z"_eq and R"_eq already calculated, we can calculate the value of X"_eq using the eq. 92-08.

Therefore, the value of X"_eq will be:

With these values, we can calculate R₂ and X₂ using the equations 92-09 and 92-10, or:

And finally, using the equations 92-11 e 92-12, we have:

Item c

To calculate the power factor we use the equation below:

And so, solving step by step, we can calculate the main parameters of a transformer.