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580 12 POWER SYSTEM CONTROL
The frequency deviation step response is shown in Figure 12.50. The transient re
sponse settles to a steady-state value
of
ss
-0.0007 per unit in about 0.6
second.
b) A S MUL NK model named sim12xx1.mdl is constructed
as
shown in Figure
12.51. The state-space description dialog box is opened, and the
A B C
and
D
constants are entered in the appropriate box in
M Tl B
matrix notation. Also,
the LQR description dialog box is opened, and weighting matrix
Q
and weighting
coefficient
R
are set to the given values. The simulation parameters are set to the
Step
FIGURE 12.51
State-space
Feedback gain
using LQR design
K
Simulation block diagram for Example 12.11.
Demux
t w
Scope
appropriate values. The file
is
opened and is run in the S MUL NK window. The
simulation results in the same response
as
shown in Figure 12.50.
PROBLEMS
12.1. A 250-MW, 60-Hz turbine generator set has a speed regulation of 5 percent
based on its own rating. The generator frequency decreases from 60 Hz to
a steady state value
of
59.7Hz. Determine the increase in the turbine power
output.
12.2. Two generating units rated for 250 MW and 400 MW have governor speed
regulation
of
6.0 and 6.4 percent, respectively, from no-load to full-load,
respectively. They are operating in parallel and share a load of 500
MW
Assuming free governor action, determine the load shared by each unit.
12.3. A single area consists
of
two generating units, rated at 400 and 800 MVA,
with speed regulation
of
4 percent and 5 percent on their respective ratings.
The units are operating in parallel, sharing 700 MW. Unit 1 supplies 200
MW and unit 2 supplies 500 MW at 1.0 per unit 60 Hz) frequency. The load
is
increased by 130
MW
a) Assume there is no frequency-dependent load, i.e.,
O
Find the
steady-state frequency deviation and the new generation on each unit.
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12 8 INTRODUCTORY MODERN CONTRO L APPLICATION 581
b) The load varies 0.804 percent for every 1 percent change in frequency,
i.e.,
D
0.804. Find the steady-state frequency deviation and the new gen
eration on each unit.
12.4.
An isolated power station has the LFC system as shown in Figure 12.9 with
the following parameters
Turbine time constant
T 0.5 sec
Governor time constant
7
g
0.25 sec
Generator inertia constant 8 sec
Governor speed regulation =R per unit
The load varies by 1.6 percent for a 1 percent change in frequency, i.e.,
D
=
1.6.
a) Use the Routh-Hurwitz array Appendix B.2.1) to find the range of
R
for
control system stability.
b) Use
MATLAB rlocus
function to obtain the root-locus plot.
12.5. The governor speed regulation of Problem 12.4 is set to
R
0.04 per unit.
The turbine rated output is 200 MW at nominal frequency of 60 Hz. A sud
den load change of 50 MW b.PL 0.25 per unit) occurs.
a) Find the steady-state frequency deviation in Hz.
b) Obtain the closed-loop transfer function and use MATLAB to obtain the
frequency deviation step response.
c) Construct the
SIMULINKblock
diagram and obtain the frequency devia
tion response.
12.6. The LF system in Problem 12.5 is equipped with the secondary integral
control loop for automatic generation control as shown in Figure 12.16.
a) Use the MATLAB step function to obtain the frequency deviation step
response for a sudden load change of b.PL 0.25
per
unit. Set the integral
controller gain to KJ 9
b) Construct the
SIMULINKblock
diagram and obtain the frequency devia
tion response for the condition in part a).
12.7.
The load changes of 200 MW and 150 MW occur simultaneously in areas 1
and 2 ofthe two-area system of Example 12.4. Modify the SIMULINKblock
diagram simI2ex4.mdl), and obtain the frequency deviation and the power
responses.
12.S. Modify the
SIMULINKmodel
for the two-area system of Example 12.5 with
the tie-line bias control simI2ex5.mdl) to include the load changes specified
in Problem 12.7. Obtain the frequency and power response deviation for each
area.
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