Problem 97-7    Source:   Adapted from example 2-60 - page 192 - SAHDEV, S. K. -    Book: Electrical Machines - 1st edition - Cambridge University Press - 2018.

A 500 kVA transformer "A" is connected in parallel with a 150 kVA transformer "B". In this configuration, a 750 kVA load is connected with PF = 0.8 lagging. Their open-circuit voltages are 405 V and 415 V, respectively. Transformer "A" has 1% resistance and 5% reactance, and transformer "B" has 1.5% resistance and 4% reactance. Find:

a) The current circulating through the transformer secondaries when they operate without load.

b) The apparent power that each transformer supplies to the load.

Solution of the Problem 97-7

In this type of problem, it is more advantageous to work with the impedances in their ohmic values. The problem statement does not provide the value of the voltage across the load. Therefore, we will adopt a value of V_L = 400 V. This will not imply an appreciable error. So, initially, we will calculate the values ​​of R_A and X_A, values ​​of the transformer "A". First, we must calculate the value of I_A. Applying the basic concepts of power, we have:

The value of R_A is defined as:

Replacing the variables with their respective numerical values ​​and performing the calculation, we obtain:

Using the same reasoning, we can calculate the value of X_A.

Replacing the variables with their respective numerical values ​​and performing the calculation, we obtain:

Now, let's apply the same procedure to transformer "B". Thus, we will calculate the value of I_B :

Following the procedure, we have:

Replacing the variables with their respective numerical values ​​and performing the calculation, we obtain:

Using the same reasoning, we can calculate the value ofX_B.

Replacing the variables with their respective numerical values ​​and performing the calculation, we obtain:

At this point, it is possible to write the impedances of the two transformers.

And the phasor sum of the two impedances is:

Item a

Item b