Problem 97-4    Source:   Adapted Example 2-59 - page 191 - SAHDEV, S. K. -    Book: Electrical Machines - 1st edition - Cambridge University Press - 2018.

Consider a transformer "A" that has an open-circuit EMF of 6,600 V with a secondary-referenced impedance of 0.3 + j 3. This transformer is connected in parallel with a transformer "B" that has an open-circuit EMF of 6,400 V and a secondary-referenced impedance of 0.2 + j.

a) Find the current supplied by each transformer to a load 8 + j6  Ω.

b) What is the real and reactive power supplied to the load?

Solution of the Problem 97-4

Item a

Let's define the FEM's as follows:

And the respective impedances are:

Now, let us express the sum of the impedances, designated as Z_eq.

In polar form, Z_eq is given by:

Note that this problem deals with   Case 3 ,   studied in the theoretical part. The value of Z_L is:

With the data for Z_L and Z_eq, it is not possible to state that the value of Z_eq is much smaller than the value of Z_L. Therefore, we cannot use the simplified equations eq. 97-12 and eq. 97-13. Therefore, to calculate I₁, we will use eq. 97-10, shown below for a better understanding of the solution to the problem.

Item b

Note that, to determine the value of V_L, we used the data from transformer A. Naturally, when using the data from transformer B, the same result presented should be obtained. The reader is encouraged to verify this equivalence on his own.

Considering the two three-phase transformers, either in the Yy0 or Dd0 connection, and based on the data presented, it is possible to calculate the active and reactive power in the load using the following equations, as studied in Chapter 95 ( Three-Phase Transformers! ).

We know the value of φ_L, already calculated previously in eq. 97-4.1. Its value is φ_L = 36.87°. Then, substituting the numerical values ​​into the equations above, we find: