ELEC7310, MODULE I: POWER SYSTEM STABILITY AND DYNAMICS
(SECURITY)
Assignment #2: Transient Stability
Questions:
Fig. 1. Single-machine infinite bus system (Simple system-I).
1. The synchronous generator in Fig.1 delivers 0.8 p.u. real power at 0.85 power factor leading at voltage at infinite bus (1.0 p.u. voltage). Determine
a) The real and reactive power output of the generator.
b) The generator internal voltage.
c) An equation for the electrical power delivered by the generator as a function of δ .
d) For a three-phase-to ground bolted short circuit at F, determine the power delivered by the generator as a function of δ .
e) The fault is cleared by the opening of circuit breakers B13 and B22 simultaneously, find the power delivered by the generator as a function of δ .
f) Draw the power angle curves for post-fault, during the fault and pre-fault conditions and determine the critical clearing angle.
2. The power system shown in Fig.2 consists of four 555 MVA, 20 kV, 60 Hz units supplying power to infinite bus through two transmission circuits. The network reactances shown in the figure are in p.u. on 2220 MVA, 20 kV base. Resistances are assumed to be negligible.
Fig. 2. Single-machine infinite bus system (Simple System –II).
The initial operating condition, with quantities expressed in p.u. on 2220 MVA and 20 kV base, is as follows:
Synchronous generator generates P=0.7, Q=0.536 at a lagging power factor measured at the generator end. Et=1.0 and 23.34o .
The generators are modeled as single equivalent generator represented by the classical model with the following parameters expressed in p.u. on the same bases as above.
Xd’=0.3, H=3.5 MW. s/MVA and KD= 10 (Damping coefficient).
System experienced a solid three-phase fault at point F. The fault is cleared by isolating the faulted circuit.
(a) Calculate the critical clearing angle and critical fault clearing time using equal area criterion.
(b) Verify the critical fault clearing time and critical clearing angle by computing the time response of the rotor angle, using numerical integration (you also can use the ode23, or ode45 functions in MATLAB to check your program).
3. Briefly explain another method, other than “Equal Area Criterion” and “Time Domain Simulation” for studying transient stability in power system (list out references that you have read to answer this question).
Total mark: 8 marks