(a) Consider complex power transmission via the three-phase short line for which the per-phase circuit is shown in Figure 5.19. Express \(S_{12}\), the complex power sent by bus 1 (or \(V_{1}\) ), and \(\left(-S_{21}ight.\) ), the complex power received by bus 2 (or \(V_{2}\) ), in terms of \(\mathrm{V}_{1}, \mathrm{~V}_{2}, \mathrm{Z}, \angle Z\), and \(\theta_{12}=\) \(\theta_{1}-\theta_{2}\), which is the power angle.

(b) For a balanced three-phase transmission line in per-unit notation with \(Z=1 \angle 85^{\circ}, \theta_{12}=10^{\circ}\), determine \(S_{12}\) and \(\left(-S_{21}ight)\) for (i) \(\mathrm{V}_{1}=\mathrm{V}_{2}=1.0\)
(ii) \(\mathrm{V}_{1}=1.1\) and \(\mathrm{V}_{2}=0.9\)
Comment on the changes of real and reactive powers from parts (i) to (ii).

Transcribed Image Text:

V= Vej, a CT3 + 171 S2 R Z=Z/Z S21 a' + C n' V= Ve0