(Solved): Consider a balanced three-phase power system with the one-line diagram shown in the figure below. ...

Consider a balanced three-phase power system with the one-line diagram shown in the figure below. The corresponding rated parameter values are given in the following table, with all per unit quantities defined on the component bases. The load impedance \( Z_{L} \) is connected in Wye with an impedance of \( 100+j 50 \Omega \) between the line voltage and the the neutral. Table 1: Parameter Values for Each Component The generator is modeled with an internal voltage source \( V_{\text {int }} \) in series with the reactance \( j X_{G} \), as shown below. Complete the tasks described in parts (a) and (b). (a) Draw the single-phase equivalent circuit for this system including labels showing the per unit values for all the impedances and the internal voltage of the voltage source. Define all per unit quantities according to the system base quantities. Use a line-to-line base voltage of \( 14.4 \mathrm{kV} \) in the portion of the system with the generator \( \mathrm{G} \) and a three-phase base power of 10 MVA. [15 points] (b) The generator operates with an internal voltage \( V_{\text {int }} \) at a line-to-line voltage magnitude equal to \( 13.5 \mathrm{kV} \) and a \( 0^{\circ} \) phase angle. Compute the total (three-phase) active and reactive power produced by the generator, \( \mathbf{P}_{\mathrm{G}}+\mathrm{j} \mathbf{Q}_{\mathrm{G}} \), both in per unit and actual quantities (MW, MVAr). [10 points]