Reconsider Problem 3.64 with the change that now (T_{b}) includes both a transformer of the same turns

Question:

Reconsider Problem 3.64 with the change that now \(T_{b}\) includes both a transformer of the same turns ratio as \(T_{a}\) and a regulating transformer with a \(4^{\circ}\) phase shift. On the base of \(T_{a}\), the impedance of the two components of \(T_{b}\) is \(j 0.1\) per unit. Determine the complex power in per unit transmitted to the load through each transformer. Comment on how the transformers share the real and reactive powers.

Problem 3.64

The per-unit equivalent circuit of two transformers \(T_{a}\) and \(T_{b}\) connected in parallel, with the same nominal voltage ratio and the same reactance of 0.1 per unit on the same base, is shown in Figure 3.43. Transformer \(T_{b}\) has a voltage-magnitude step-up toward the load of 1.05 times that of \(T_{a}\) (that is, the tap on the secondary winding of \(T_{b}\) is set to 1.05). The load is represented by \(0.8+j 0.6\) per unit at a voltage \(V_{2}=1.0 / 0^{\circ}\) per unit. Determine the complex power in per unit transmitted to the load through each transformer. Comment on how the transformers share the real and reactive powers.

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