Problem 1 (Computing Critical Clearing Time (CCT) using EAC):

A three-phase 50 Hz synchronous generator is supplying power through pure reactive parallel transmission lines to an infinite bus. The machine is delivering 1.0 per unit power ( ) before a three phase short circuit fault occurs in the system.

The mechanical power is Pm=1.1pu, Eq'=1.1pu and the per unit inertia constant H=10 MJ/MVA. Figure 1 shows the power angle characteristics before, during and after the fault with all values in pu:

Compute:

a) The steady-state power angle δ₀.

b) The maximum power angle δ_max.

c) The critical clearing angle δ_cr.

d) Compute the critical clearing time t_cr(in sec).

e) If the clearance time can be reduced to 120msec, what is the maximum power that this machine can deliver while remaining stable?

f) If the generator is required to supply 1.1 pu load with the critical fault clearance time as calculated in section (d), propose possible options to ensure the generator remains stabile.

Figure 1. The power angle characteristics before, during and after the fault for Question 1 with all values in pu.

Problem 2:

Find the equation for the Synchronizing Torque Coefficient of the following system around the operating point δ = δ₀

Problem 3:

Derive the state equation of the following system in form:

Δx^· = A Δx+B Δu   Δy = C Vx + DΔu

Problem 4:

What is the maximum transfer capability of the following system to supply a constant PQ load at 0.8 lag power factor? How much can this transfer capability be increased by installing capacitor banks?

The System voltage at normal operational condition is within a range of 0.9pu-1.1pu.