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Consider a power system with a single machine connected to an infinite bus as shown in Figure 1. The synchronous generator is initially operating at a steady-state condition (8 = 81) when a permanent three-phase-to-ground bolted short occurs on line 1-3 at bus 3. The fault is cleared at (t = te) by opening the circuit breakers at the ends of line 1-3 and line 2-3. These circuit breakers then remain open. IT 1 2 xa 21 W اللللا 31 EZO V 20° 3 Figure 1. a. Calculate the electrical power output Pep of the generator with the given parameters in Figure 1, and write the second-order swing equation of the pre-fault system (the inertia is M, the mechanical input power is Pm and neglect the damping term (D = 0); b. Draw Pe-d curves of the pre-fault (Pep), fault-on (Pef) and post-fault systems (Pe); C. Based on the Pe-d curves drawn in part (b), briefly discuss how to use the Equal Area Criterion to test the transient stability property of the system; d. Proof that the Equal Area Criterion is equivalent to the energy function method by selecting a proper energy function.