Solutions Manual

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Solutions Manual

Professor of Electrical Engineering Milwaukee School of Engineering Milwaukee, Wisconsin

McGraw-Hill, Inc.

CONTENTS

1 THE POWER SYSTEM: AN OVERVIEW 2 BASIC PRINCIPLES 3 GENERATOR AND TRANSFORMER MODELS; THE PER-UNIT SYSTEM 4 TRANSMISSION LINE PARAMETERS 5 LINE MODEL AND PERFORMANCE

1 5 25 52 68 107 147 170 181 208 244 263

6 POWER FLOW ANALYSIS 7 OPTIMAL DISPATCH OF GENERATION 8 SYNCHRONOUS MACHINE TRANSIENT ANALYSIS 9 BALANCED FAULT 10 SYMMETRICAL COMPONENTS AND UNBALANCED FAULT 11 STABILITY 12 POWER SYSTEM CONTROL

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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 numerous 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 . . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . . . ... . . . . ....