(Solved): Figure 3 shows a single-line diagram of a three-phase, 60- \( \mathrm{Hz} \) synchronous generator, ...

Figure 3 shows a single-line diagram of a three-phase, 60- \( \mathrm{Hz} \) synchronous generator, connected through a transformer and parallel transmission lines to an infinite bus. In Figure 3, all reactances are given in per-unit on a common system base. CB indicates circuit breaker. Figure 3: Single-line diagram of a 3-bus three-phase system with a \( 60-\mathrm{Hz} \) synchronous generator (a) If the infinite bus receives \( 1.0 \) per unit real power at \( 0.95 \) p.f. lagging, determine (i) The internal voltage of the generator. [04] (ii) The equation for the electrical power delivered by the generator versus its power [02] (b) The synchronous generator shown in Figure 3 is initially operating in the steady-state condition given in (a) above, when a temporary threephase to-ground short circuit occurs on line 1-3 at bus 1 , shown as point \( F \) in Figure 3. The inertia constant of the generating unit is \( 3.0 \) per unit-seconds on the system base. Assume pm remains constant throughout the disturbance. We also assume the temporary short circuit lasts longer than 3 cycles, (i) Determine the initial operating power angle \( \delta_{0} \); [02] (ii) Show the fault electrical power equation; [03] (iii) Show the post-fault electrical power equation; [03] (iv) Calculate the critical angle. [06]