The generating unit in Problem 11.1 is initially operating at \(p_{m \text { p.u. }}=p_{\text {ep.u. }}=\) 0.7 per unit, \(\omega=\omega_{\text {syn }}\), and \(\delta=12^{\circ}\) when a fault reduces the generator electrical power output by \(60 \%\). Determine the power angle 3 five cycles after the fault commences. Assume that the accelerating power remains constant during the fault. Also assume that \(\omega_{\text {p.u. }}(t)=1.0\) in the swing equation.

Problem 11.1

A three-phase, \(60-\mathrm{Hz}, 500-\mathrm{MVA}, 11.8-\mathrm{kV}\), 4-pole steam turbine-generating unit has an \(\mathrm{H}\) constant of 5 p.u.-s. Determine:

(a) \(\omega_{\text {syn }}\) and \(\omega_{m \text { syn }}\);

(b) the kinetic energy in joules stored in the rotating masses at synchronous speed;

(c) the mechanical angular acceleration \(\alpha_{m}\) and electrical angular acceleration \(\alpha\) if the unit is operating at synchronous speed with an accelerating power of \(500 \mathrm{MW}\).