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CONTENTS
1 THE POWER SYSTEM: AN OVERVIEW 1
2 BASIC PRINCIPLES 5
3 GENERATOR AND TRANSFORMER MODELS;
THE PER-UNIT SYSTEM 25
4 TRANSMISSION LINE PARAMETERS 52
5 LINE MODEL AND PERFORMANCE 68
6 POWER FLOW ANALYSIS 107
7 OPTIMAL DISPATCH OF GENERATION 147
8 SYNCHRONOUS MACHINE TRANSIENT ANALYSIS 170
9 BALANCED FAULT 181
10 SYMMETRICAL COMPONENTS AND UNBALANCED FAULT 208
11 STABILITY 244
12 POWER SYSTEM CONTROL 263
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CHAPTER 1 PROBLEMS
1.1 The demand estimation is the starting point for planning the future electric
power supply. The consistency of demand growth over the years has led to numer-
ous attempts to fit mathematical curves to this trend. One of the simplest curves
is
P = P0 ea(t−t0 )
where a is the average per unit growth rate, P is the demand in year t, and P0 is
the given demand at year t0 .
Assume the peak power demand in the United States in 1984 is 480 GW with
an average growth rate of 3.4 percent. Using MATLAB, plot the predicated peak
demand in GW from 1984 to 1999. Estimate the peak power demand for the year
1999.
We use the following commands to plot the demand growth
t0 = 84; P0 = 480;
a =.034;
t =(84:1:99)’;
P =P0*exp(a*(t-t0));
disp(’Predicted Peak Demand - GW’)
disp([t, P])
plot(t, P), grid
xlabel(’Year’), ylabel(’Peak power demand GW’)
P99 =P0*exp(a*(99 - t0))
The result is
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2 CONTENTS
Predicted Peak Demand - GW
84.0000 480.0000
85.0000 496.6006
86.0000 513.7753
87.0000 531.5441
88.0000 549.9273
89.0000 568.9463
90.0000 588.6231
91.0000 608.9804
92.0000 630.0418
93.0000 651.8315
94.0000 674.3740
95.0000 697.6978
96.0000 721.8274
97.0000 746.7916
98.0000 772.6190
99.0000 799.3398
P99 =
799.3398
The plot of the predicated demand is shown n Figure 1.
800 . . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ..
. . . . . . ..... .
. . . . . . ...... . .
......
750 . . . . . . . .. . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... ............................ . . ... . . . . . . ..
. . . . . ....... . .
......
. . . . . ...... . . .
......
. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . .............. . . .. .
700 .
.
.
.
.
.
.
.
. ......
. .......
. .
.
. . . . . ..
.
.
. . . . . ..
.
.
.......
. . . . ........ . . .
Peak . . .
. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . ............... . . .. . . . . . . .. .
. .
...
........ . . . .
Power 650 . . . ..........
...
...
. .
. . . . . ..
.
. . . . . ..
.
......
.
. . . ....... . . . . .
. . . ....... . . . . .
Demand 600 .
...
.........
. . . . . . . . . . . . . . .. . . . . . . .. ........ . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . ..
. . .....
.. . . . . .
..
...
..
GW . . ...... . . . . . .
.......
. . .............. . . . . . .
.
...
...
550 . . . . . . . .. . . . . . .............. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. .
.
.
........
...
..... . . . . .
. . . . . ..
.
. . . . . ..
.
. ........ . . . . . . .
. ....... . . . . . . .
.
...
...........
. . . . . . . .
..
. . . .................. . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. .
500 ....
.........
.
...
...
. . . . . .
. . . . . ..
.
. . . . . ..
.
. . . . . . . .
. . . . . . . .
450 . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . ..
84 86 88 90 92 94 96 98 100
Year
FIGURE 1
Peak Power Demand for Problem 1.1
1.2 In a certain country, the energy consumption is expected to double in 10 years.
Elitestudyvault
1
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CONTENTS
1 THE POWER SYSTEM: AN OVERVIEW 1
2 BASIC PRINCIPLES 5
3 GENERATOR AND TRANSFORMER MODELS;
THE PER-UNIT SYSTEM 25
4 TRANSMISSION LINE PARAMETERS 52
5 LINE MODEL AND PERFORMANCE 68
6 POWER FLOW ANALYSIS 107
7 OPTIMAL DISPATCH OF GENERATION 147
8 SYNCHRONOUS MACHINE TRANSIENT ANALYSIS 170
9 BALANCED FAULT 181
10 SYMMETRICAL COMPONENTS AND UNBALANCED FAULT 208
11 STABILITY 244
12 POWER SYSTEM CONTROL 263
i
Elitestudyvault
,3
CHAPTER 1 PROBLEMS
1.1 The demand estimation is the starting point for planning the future electric
power supply. The consistency of demand growth over the years has led to numer-
ous attempts to fit mathematical curves to this trend. One of the simplest curves
is
P = P0 ea(t−t0 )
where a is the average per unit growth rate, P is the demand in year t, and P0 is
the given demand at year t0 .
Assume the peak power demand in the United States in 1984 is 480 GW with
an average growth rate of 3.4 percent. Using MATLAB, plot the predicated peak
demand in GW from 1984 to 1999. Estimate the peak power demand for the year
1999.
We use the following commands to plot the demand growth
t0 = 84; P0 = 480;
a =.034;
t =(84:1:99)’;
P =P0*exp(a*(t-t0));
disp(’Predicted Peak Demand - GW’)
disp([t, P])
plot(t, P), grid
xlabel(’Year’), ylabel(’Peak power demand GW’)
P99 =P0*exp(a*(99 - t0))
The result is
1
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2 CONTENTS
Predicted Peak Demand - GW
84.0000 480.0000
85.0000 496.6006
86.0000 513.7753
87.0000 531.5441
88.0000 549.9273
89.0000 568.9463
90.0000 588.6231
91.0000 608.9804
92.0000 630.0418
93.0000 651.8315
94.0000 674.3740
95.0000 697.6978
96.0000 721.8274
97.0000 746.7916
98.0000 772.6190
99.0000 799.3398
P99 =
799.3398
The plot of the predicated demand is shown n Figure 1.
800 . . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ..
. . . . . . ..... .
. . . . . . ...... . .
......
750 . . . . . . . .. . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... ............................ . . ... . . . . . . ..
. . . . . ....... . .
......
. . . . . ...... . . .
......
. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . .............. . . .. .
700 .
.
.
.
.
.
.
.
. ......
. .......
. .
.
. . . . . ..
.
.
. . . . . ..
.
.
.......
. . . . ........ . . .
Peak . . .
. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . ............... . . .. . . . . . . .. .
. .
...
........ . . . .
Power 650 . . . ..........
...
...
. .
. . . . . ..
.
. . . . . ..
.
......
.
. . . ....... . . . . .
. . . ....... . . . . .
Demand 600 .
...
.........
. . . . . . . . . . . . . . .. . . . . . . .. ........ . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . ..
. . .....
.. . . . . .
..
...
..
GW . . ...... . . . . . .
.......
. . .............. . . . . . .
.
...
...
550 . . . . . . . .. . . . . . .............. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. .
.
.
........
...
..... . . . . .
. . . . . ..
.
. . . . . ..
.
. ........ . . . . . . .
. ....... . . . . . . .
.
...
...........
. . . . . . . .
..
. . . .................. . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. .
500 ....
.........
.
...
...
. . . . . .
. . . . . ..
.
. . . . . ..
.
. . . . . . . .
. . . . . . . .
450 . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . ..
84 86 88 90 92 94 96 98 100
Year
FIGURE 1
Peak Power Demand for Problem 1.1
1.2 In a certain country, the energy consumption is expected to double in 10 years.
Elitestudyvault
