11.2
11.3
11.4
11.5
The moment ofinertia ofa 250-MVA generator is 75000 kgm2 • Ifthe operating
frequency is 50 Hz and the generator has two poles, compute (i) kinetic energy
of the rotating parts, (ii) H, and (iii) M.
A two-pole, three-phase, 50-MVA, 11-kV generator is supplying rated power
at 0.8 lagging power factor to an 11-kV bus. Due to a fault the generator output
is reduced to 40%. Compute (i) accelerating power and (ii) acceleration at the
time of fault. Assume that the kinetic energy stored in the moving parts of the
generator is 175 MJ.
In Problem 11.3, if the generated voltage is 11 kV and the synchronous
reactance of the generator is 2 Q/phase, calculate the rotor angle just before
loss of generation. If the acceleration due to loss of generation continues for
5 cycles, determine (i) rotor angle and (ii) rotor speed in rpm at the end of the
acceleration period.
Two synchronous machines are connected as shown in Fig. 11.20. All values in
the diagram are in per unit on a common system base. Ifthe inputs and outputs
to the two machines are represented by P Ii, P 1 11, P2;, and P211 respectively, derive
expressions for input and output power for the equivalent machine. IfH1 = 4.5
MJ/MVA and H2 = 6.0 MJ/MVA, calculate the inertia constant, input power,
and the maximum power of the equivalent machine. Assume P li = 1.25 pu,
P2; = 1.1 pu. Write the swing equation of the equivalent machine.
J0.40
V= 1.05 pu
Fig. 11.20
11.6
x; =jO.lS
V= 1.0pu
Two machine system for Problem 11.5
A synchronous generator is supplying power to an infinite bus via two parallel
lines as shown in Fig. 11.21. All values in the circuit diagram are in per unit
on a common system base. If the power frequency is 50 Hz and the inertia
constant of the generator is 4 MJ/MVA, calculate the voltage behind transient
reactance and write the swing equation. Assume that the machine is delivering
a power of 0.8 at a power factor of0.85 lagging.
A three-phase fault occurs at the generator end through a reactance of0.05 per
unit. Determine the accelerating power and the acceleration at the time offault.
X =J0.3
Line I
E©-ti
X,l =JO.to X,= )0.15
Fig. 11.21
11.7
E{ = 1.l5Lo2
V= 1L0°
Infinite bus
X =J0.3
Line2
All values in pu
Schematic diagram of a system for Problem 11.6
In problem 11.6, a three-phase fault occurs at the sending of one of the lines,
which is cleared after 10 cycles with the faulted line remaining intact. Establish
11.8
11.9
whether the system is stable or not. If the system is stable, determine the
maximum rotor angle following the three-phase fault.
The generator in Problem 11. 7 is delivering 1.2 pu power at unity power factor
when a three-phase fault occurs in the middle of one of the parallel lines. The
fault is cleared by opening the faulted line. Determine the critical clearing
angle. Use MATLAB graphics to plot the power output versus power angle
for the pre-fault, during fault, and post-fault conditions.
A synchronous generator is supplying a real power of 1.0 pu to an infinite bus
as shown in Fig. 11.22. A temporary three-phase fault occurs in line 2, at one­
tenth the distance from the infinite bus end. (i) What is the rotor angle when
the generator is operating synchronously? (ii) What is the generator output,
accelerating power, and acceleration when the fault occurs? (iii) If the fault
is cleared after 15 cycles, by opening of the faulted line, compute the rotor
angle, decelerating power, and deceleration immediately after the faulted line
X=j0.4
E= 1.25Lo
©-ti
Fig. 11.22
Line I
Infinite bm
X =j0.6
Lme2
All values in pu
Schematic diagram of a system for Problem 11.9
is opened. Why is the generator decelerating? Assume the power frequency
to be 50 Hz and the inertia constant of the generator to be 3.5 MJ/MVA. All
values in the circuit diagram are in per unit on a common system base.
11.10 Write a program to use the MATLAB ODE solver to solve and plot the following
differential equation:
dy
=t3 -y2
dt
for O � t � 1.0. Assume that at t0 = 0, Yo= 0.5.
11.11 The following equation represents the swinging of a synchronous generator,
connected to the infinite bus, during a fault.
d2 8
-2-=Pa
dt
Write (a) the swing equation as two first-order differential equations, and
(b) a MATLAB function to compute the state derivatives, that is,
and ciJ.
Use ode 23 or ode 45 to solve the second-order differential equation. Plot rotor
angle versus time. Assume that the power angle prior to the disturbance is 30°
and the fault is cleared in 0.25 s. Take Pa = 0.75 + 0.3sin8pu during the fault,
and Pa = 0.75 + 1.5 sin8during the post-fault period.
11.12 A 50-Hz synchronous generator is connected to an infinite bus of voltage
l .OL'.'. 0° via two parallel lines each having a reactance of 0.4 pu. If the generator
delivers 0.75 pu real power at 0.85 lagging power factor to the infinite bus,
compute (i) the damping factor and (ii) the natural frequency of oscillations
when a disturbance of A8 = 12.5° occurs due to a temporary opening and
immediate closing of one of the circuit breakers. Assume the following data
8
500 Power System Analysis
for the generator: transient reactance = 0.4pu, inertia constant H = 8 MJ/MVA,
and coefficient of power damping = 0.15. Write a MATLAB function to plot
rotor angle and frequency versus time.