A \(60 \mathrm{~Hz}\) generator is supplying \(400 \mathrm{MW}\) (and 0 Mvar) to an infinite bus (with 1.0 per unit voltage) through two parallel transmission lines. Each transmission line has a per unit impedance (100 MVA base) of \(0.09 j\). The per unit transient reactance for the generator is \(0.0375 j\), the per unit inertia constant for the generator \((\mathrm{H})\) is 20 seconds, and damping is 0.1 per unit (all with a 100 MVA base). At time \(=0\), one of the transmission lines experiences a balanced three-phase short to ground one third (1/3) of the way down the line from the generator to the infinite bus.

(a) Using the classical generator model, determine the prefault internal voltage magnitude and angle of the generator.

(b) Express the system dynamics during the fault as a set of first order differential equations.

(c) Using Euler's method, determine the generator internal angle at the end of the second timestep. Use an integration step size of one cycle.