WIND ENERGY SYSTEMS - Cd3wd

Chapter 2—Wind Characteristics 2–45
Figure 20: Actual wind data, and Weibull and Rayleigh density functions for Tuttle Creek,
7:00–8:00 p.m., July 1980, 50 m.
wind power density as computed from Eq. 44 for standard conditions is ¯P w /A = 396 W/m 2 .
The power density computed from the Weibull model, Eq. 46, is 467 W/m 2 , while the power
density computed from the Rayleigh density function by a process similar to Eq. 44 is 565
W/m 2 . The Weibull is 18 % high while the Rayleigh is 43 % high.
If we examine just the wind speed range of 5-12 m/s, we get an entirely different picture.
The actual wind power density in this range is ¯P w /A = 362 W/m 2 , while the Weibull predicts
a density of 308 W/m 2 , 15 % low, and the Rayleigh predicts 262 W/m 2 , 28 % low. This
shows that neither model is perfect and that results from such models need to be used with
caution. However, the Weibull prediction is within 20 % of the actual value for either wind
speed range, which is not bad for a data set that is so difficult to mathematically describe.
Another example of the ability of the Weibull and Rayleigh density functions to fit actual
data is shown in Fig. 21. The mean speed is 4.66 m/s as compared with 7.75 m/s in Fig. 20
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001