If breakers B13 and B22 in Problem 11.13 open later than 3 cycles after the fault commences, determine the critical clearing time.

Problem 11.13

The generator in Figure 11.4 is initially operating in the steady-state condition given in Example 11.3 when a temporary three-phase-to-ground short circuit occurs at point F. Three cycles later, circuit breakers B13 and B22 permanently open to clear the fault. Use the equal-area criterion to determine the maximum value of the power angle \(\delta\).

Example 11.3

Figure 11.4 shows a single-line diagram of a three-phase, \(60-\mathrm{Hz}\) synchronous generator, connected through a transformer and parallel transmission lines to an infinite bus. All reactances are given in per-unit on a common system base. If the infinite bus receives 1.0 per unit real power at 0.95 p.f. lagging, determine

(a) the internal voltage of the generator and

(b) the equation for the electrical power delivered by the generator versus its power angle \(\delta\).

Figure 11.4

G XTA = 0.10 038 X = 0.30 B11 B12 F B13 X3 = 0.10 0.20 3 B21 X23 = 0.20 B22 2 XI Vous = 1.0