WIND ENERGY SYSTEMS - Cd3wd

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Chapter 3—Wind Measurements 3–37 [5] Marrs, R.W. and J. Marwitz: “Locating Areas of High Wind Energy Potential by Remote Observation of Eolian Geomorphology and Topography,” Third Wind Energy Workshop Proceedings, Washington, D.C., September, 1977, CONF 770921, pp. 307-320. [6] Middleton, W., E. Knowles, and A.F. Spilhaus: Meteorological Instruments, 3rd.ed., University of Toronto Press, Toronto, 1953. [7] Noll, K.E. and T.L. Miller: Air Monitoring Survey Design, Ann Arbor Science Publishers, Ann Arbor, 1977, pp. 215-237. [8] Putnam, P.C.: Power from the Wind, Van Nostrand, New York, 1948. Wind Energy Systems by Dr. Gary L. Johnson November 12, 2001
Chapter 4—Wind Turbine Power 4–1 <strong>WIND</strong> TURBINE POWER, <strong>ENERGY</strong>, AND TORQUE Who has gathered the wind in his fists? Proverbs 30:4 Gathering or harvesting the wind has been of concern to man for a long time. As mentioned earlier, wind turbines have been used for several centuries and literally millions of units have been put into service. For the most part, these machines performed their intended purpose well, and in many cases were still being used with minimum maintenance after half a century of service. Operational machines four centuries old are not unheard of, pointing out the fact that planned obsolescence does not have to be a part of engineering work. A major reason for their success was the lack of competition, of course. There was a choice of using the wind to perform some task or doing it by hand, and doing it by hand is last choice for most people. Today, wind turbines have to compete with many other energy sources. It is therefore important that they be cost effective. They need to meet any load requirements and produce energy at a minimum cost per dollar of investment. Performance characteristics such as power output versus wind speed or versus rotor angular velocity must be optimized in order to compete with other energy sources. Yearly energy production and its variation with annual wind statistics must be well known. The shaft torque must be known so the shaft can be built with adequate strength and the turbine load properly sized. We shall examine such performance characteristics in this chapter. 1 POWER OUTPUT FROM AN IDEAL TURBINE The kinetic energy in a parcel of air of mass m, flowing at speed u in the x direction is U = 1 2 mu2 = 1 2 (ρAx)u2 Joules (1) where A is the cross-sectional area in m 2 , ρ is the air density in kg/m 3 ,andx is the thickness of the parcel in m. If we visualize the parcel as in Fig. 1 with side x moving with speed u and the opposite side fixed at the origin, we see the kinetic energy increasing uniformly with x, because the mass is increasing uniformly. The power in the wind, P w , is the time derivative of the kinetic energy: P w = dU dt = 1 dx ρAu2 2 dt = 1 2 ρAu3 W (2) This can be viewed as the power being supplied at the origin to cause the energy of the parcel to increase according to Eq. 1. A wind turbine will extract power from side x, withEq.2 representing the total power available at this surface for possible extraction. Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
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