= =
SOLUTION MANUAL
=
, 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
, CHAPTER 1 PROBLEMS = =
1.1 The=demand=estimation=is=the=starting=point=for=planning=the=future=electric=p
ower=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= ==P0ea(t−t0)
where=a=is=the=average=per=unit=growth=rate,=P= is=the=demand=in=year=t,=and=P0=is=t
he=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’)=P
99= =P0*exp(a*(99= -= t0))
The=result=is
1
, 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=.= .= .= .= .= .= .= .= .= .= .= .= ..= .= ..= .= .= .=. .= .= .= ..= .=. .= .= .= .= .=...= .= .= .= .=..= .=..= .= .= ..= .= .= .=..= .=. .= .= .= .= .=...= .= .= .= .= .= ..
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Demand . . . .= .
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550 .
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500 .
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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.