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Chapter 9—Wind Power Plants 9–37 APPENDIX B ANSWERS TO SELECTED PROBLEMS 2.1 (a) ρ = 1.146 kg/m 3 ;(b)ρ = 1.423 kg/m 3 2.3 (a) p = 92.5 kPa; (b) p = 83.5 kPa; (c) p = 59.3 kPa 2.5 T g =15 o C 2.7 ū = 8.773 m/s, σ 2 = 1.012, σ = 1.006 2.10 (a) Γ(1.8333) = 0.94066; (b) Γ(1.3571) = 0.89046 2.13 711 hours/year between 8.5 and 9.5 m/s, 699 hours/year greater than 10 m/s, 0.0019 hours/year greater than 20 m/s. 2.15 (a) ū = 11.18 knots, σ = 0.1262; (b) 8.86 to 13.50 knots, one month outside; (c) from best month 10.89 to 17.71 knots, from worst month 6.88 to 11.18 knots; both intervals include the long-term monthly mean. 2.17 u W = 0.369u DC +8.51 knots, r = 0.476 2.18 (a) u = 41.66 m/s once every 20 years; (b) u = 78.67 m/s once every 500 years. 3.1 0–1.109, 1.109–1.328, 1.328–1.547, 56.672–57.000 3.2 1.28 s 3.4 6.44 m/s 4.1 1943 kW 4.2 15 m/s 4.4 4876 m 2 , 78.79 m 4.6 (a) 9.82; (b) 22.44; (c) 0.273 4.8 (a) 0.264, 19,010 kWh; (b) 0.413, 29,770 kWh; (c) 0.576, 41,500 kWh 4.9 The 25-kW machine produces 48,180 kWh per year while the 60-kW machine produces 32,540 kWh per year. 4.11 3.5 inches 4.13 (a) θ =1.921 cos 0.262t rad; (b) 5.296 s; (c) Yes! Large currents flow during the out of phase condition. 5.3 I = 83.33/ − 60 o , Q =+17.32 kvar 5.4 S = 113.14/ +45 o kVA, pf = 0.707 lag 5.5 (a) I 1 =25/ − 53.13 o A, P = 3750 W, Q = 5000 var, pf = 0.60 lag; (b) E = 325.96/4.40 o ; Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
Chapter 9—Wind Power Plants 9–38 (c) P = 625 W; (d) I c =20/90 o A, I 1 =15/0 o A, pf = 1; (e) E = 268.79/9.64 o , P = 225 W; (e) reduces reactive power requirement and reduces power line loss. 5.7 I = 231.3/ − 25.84 o A, E = 4009.0/31.10 o , δ =31.10 o , P = 962.9 kW/phase, ohmic losses = 17.65 kW. 5.11 X s,pu,new =6.01 5.18 R a = 0.00479 days/year or about 1 day in 209 years. 6.2 (a) I a = 12.83 A; (b) k e = 0.383; (c) X s = 4.91 Ω; (d) 16 percent decrease. 7.2 The 14-ft-diameter propeller and 2.5-in.-diameter cylinder clearly meet the requirements. The 12-ft-diameter propeller and 2-in.-diameter cylinder will probably be quite satisfactory at a lower cost. 7.4 (a) n s = 350; (b) P m = 19,260 W = 25.83 hp. 7.5 h 2 = 416 ft, Q 2 = 113 gal/min, P m2 = 12.66 kW 8.1 $862 8.3 13 units 8.5 P v = $44.88. You should buy the cover. 8.7 P v,X = $12,275.92, P v,Y = $12,551.84. You should buy machine X. Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
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