A three-phase, 50-Hz synchronous generator having inertia constant of H 10 MJ/MVA and a direct axis transient reactance of X₁' = 0.3 per unit, connected through transformer and parallel transmission lines to an infinite bus is shown in Figure Q3B. All reactances are given in per-unit on a common system base. 1 X₁-0.2 X-0.3 HO V-10 O+38 X=0.3 Xa=0.15X3=0.15 トロ 5 +རོt3=015 Figure Q3B 180 d -P-P Useful Formulae: EV P- sind x cost -8)+cos P 2H-8) cos- P-8)P cos-Pcos, P P-P Z ZZZZZZZ ZZZZZ ZZZZZ.ZZ.ZZ z (a) If the infinite bus receives 1.0 per-unit real power at 0.95 p.f. lagging at a voltage of 1.0 per unit, determine the internal voltage of the generator and the machine power angle. with respect to infinite bus. (4 marks) (b) Determine the equation for the electrical power delivered by the generator versus its power angle, and the maximum power that can be delivered. Write the swing equation for the machine. Determine the initial angular position of generator rotor. marks) (4 (c) A temporary three-phase fault occurs at the sending end of the line 1-3 at point F. When the fault is cleared, all lines are intact. Determine the critical clearing angle and the critical fault clearing time. (6 marks) (d) The synchronous generator is initially operating in in steady-state condition. A permanent three-phase to ground bolted fault occurs at bus 3, and the fault is cleared by opening the circuit breakers at the ends of line 1-3 and 2-3. These circuit breakers then remain open. Write the power angle equations and swing equations during the fault and for post. fault. Determine the critical (6 marks) angle. clearing