Chapter 3, Problem 3.47P

Consider the oneline diagram shown in Figure 3.40. The three-phase transformer bank is made up of three identical single-phase transformers, each specified by $X_1=0.24\Omega$ (on the low-voltage side), negligible resistance and magnetizing current, and turns ratio $\eta =N_2/N_1=10$. The transformer bank is delivering 100 MW at 0.8 p.f. lagging to a substation bus whose voltage is 230 kV.

(a) Determine the primary current magnitude, primary voltage (line-to-line) magnitude, and the three-phase complex power supplied by the generator. Choose the line-to-neutral voltage at the bus, $V_{a\text{'}\eta \text{'}}$ as the reference Account for the phase shift, and assume positive-sequence operation.

(b) Find the phase shift between the primary and secondary voltages.