WIND ENERGY SYSTEMS - Cd3wd
WIND ENERGY SYSTEMS - Cd3wd WIND ENERGY SYSTEMS - Cd3wd
Chapter 2—Wind Characteristics 2–35 Figure 17: Weibull scale parameter c divided by mean wind speed u versus Weibull shape parameter k P (u ≥ u a )= ∫ ∞ u a [ ( ) ] k ua f(u)du =exp − c (41) The probability of the wind speed being within a 1 m/s interval centered on the wind speed u a is P (u a − 0.5 ≤ u ≤ u a +0.5) = ∫ ua+0.5 u a−0.5 f(u)du [ ( ) ] [ ua − 0.5 k ( ) ] ua +0.5 k = exp − − exp − c c Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001
Chapter 2—Wind Characteristics 2–36 ≃ f(u a )∆u = f(u a ) (42) Example The Weibull parameters atagivensitearec =6m/sandk = 1.8. Estimate the number of hours per year that the wind speed will be between 6.5 and 7.5 m/s. Estimate the number of hours per year that the wind speed is greater than or equal to 15 m/s. From Eq. 42, the probability that the wind is between 6.5 and 7.5 m/s is just f(7), which can be evaluated from Eq. 30 as f(7) = 1.8 6 ( ) [ 1.8−1 ( ) ] 1.8 7 7 exp − =0.0907 6 6 This means that the wind speed will be in this interval 9.07 % of the time, so the number of hours per year with wind speeds in this interval would be (0.0907)(8760) = 794 h/year From Eq. 41, the probability that the wind speed is greater than or equal to 15 m/s is which represents [ ( ) ] 1.8 15 P (u ≥ 15) = exp − =0.0055 6 (0.0055)(8760) = 48 h/year If a particular wind turbine had to be shut down in wind speeds above 15 m/s, about 2 days per year of operating time would be lost. We shall see in Chapter 4 that the power in the wind passing through an area A perpendicular to the wind is given by P w = 1 2 ρAu3 W (43) The average power in the wind is then ¯P w = 1 w 2 ρA ∑ p(u i )u 3 i W (44) i=1 Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001
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Chapter 2—Wind Characteristics 2–35<br />
Figure 17: Weibull scale parameter c divided by mean wind speed u versus Weibull shape<br />
parameter k<br />
P (u ≥ u a )=<br />
∫ ∞<br />
u a<br />
[ ( ) ] k ua<br />
f(u)du =exp −<br />
c<br />
(41)<br />
The probability of the wind speed being within a 1 m/s interval centered on the wind<br />
speed u a is<br />
P (u a − 0.5 ≤ u ≤ u a +0.5) =<br />
∫ ua+0.5<br />
u a−0.5<br />
f(u)du<br />
[ ( ) ] [<br />
ua − 0.5 k ( ) ]<br />
ua +0.5 k<br />
= exp −<br />
− exp −<br />
c<br />
c<br />
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001
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