WIND ENERGY SYSTEMS - Cd3wd

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