Repeat Example 11.1 except assume the number of poles is changed from 32 to \(16, \mathrm{H}\) is changed from 2.0 p.u.-s to 1.5 p.u.-s, and the unit is initially operating with an electrical and mechanical power of 0.5 p.u.

Example 11.1

A three-phase, \(60-\mathrm{Hz}, 500-\mathrm{MVA}, 15-\mathrm{kV}\), 32-pole hydroelectric generating unit has an \(\mathrm{H}\) constant of 2.0 p.u.-s and \(\mathrm{D}=0\).

(a) Determine \(\omega_{\text {syn }}\) and \(\omega_{\text {msyn. }}\).

(b) Give the per-unit swing equation for this unit.

(c) The unit is initially operating at \(p_{m \text { p.u. }}=\) \(p_{\text {ep.u. }}=1.0, \omega=\omega_{\text {syn }}\), and \(\delta=10^{\circ}\) when a three-phase-to-ground bolted short circuit at the generator terminals causes \(p_{\text {ep.u. }}\) to drop to zero for \(t \geqslant 0\). Determine the power angle 3 cycles after the short circuit commences. Assume \(p_{\text {mp.u. }}\) remains constant at 1.0 per unit. Also assume \(\omega_{\text {p.u. }}(t)=1.0\) in the swing equation.