PowerWorld Simulator case Problem 11_26 duplicates Example 11.10, except with the synchronous generator initially supplying \(75 \mathrm{MW}\) at unity power factor to the infinite bus.

(a) Derive the initial values for \(\delta, \mathrm{E}_{q}^{\prime}, \mathrm{E}_{d}^{\prime}\) and \(\mathrm{E}_{f d}\).

(b) Determine the critical clearing time for the Example 11.10 fault.

Example 11.10

With the synchronous generator modeled using a two-axis model, determine

(a) the initial conditions, and then

(b) use PowerWorld Simulator to determine the critical clearing time for fault (three phase fault at bus 3, cleared by opening lines 1-3 and 2-3). Assume \(\mathrm{H}=3.0\) per unit-seconds, \(\mathrm{R}_{a}=0, \mathrm{X}_{d}=2.1, \mathrm{X}_{q}=2.0, \mathrm{X}_{d}=0.3, \mathrm{X}_{q}=0.5\), all per unit using the 100 MVA system base.