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
Let's define the FEM's as follows:
And the respective impedances are:
Now, let us express the sum of the impedances, designated as Zeq.
In polar form, Zeq is given by:
Note that this problem deals with Case 3 , studied in the theoretical part.
The value of ZL is:
With the data for ZL and Zeq, it is not possible to state that the value of Zeq
is much smaller than the value of ZL. 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.
Note that, to determine the value of VL, 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 φL, already calculated previously in eq. 97-4.1.
Its value is φL = 36.87°. Then, substituting the numerical values into the equations above, we find: