Analytically determine whether there is a critical clearing time for Problem 11.15.

Problem 11.15

Building upon Problem 11.11, assume a \(60 \mathrm{~Hz}\) nominal system frequency, that the bus fault actually occurs on the line between buses five and two but at the bus two end, and that the fault is cleared by opening breakers B21 and B52. Again, neglecting the loads, assume that the generator at bus three is modeled with the classical generator model having a per unit value (on its 800 MVA base) of \(\mathrm{X}_{d}^{\prime}=0.24\), and \(\mathrm{H}=3\) p.u.-s. Before the fault occurs the generator is delivering \(300 \mathrm{MW}\) into the infinite bus at unity power factor. Further, assume the fault is cleared after 3 cycles.

Determine:

(a) the initial generator one power angle,

(b) the power angle when the fault is cleared, and

(c) the maximum value of the power angle using the equal area criteria.