WIND ENERGY SYSTEMS - Cd3wd

Chapter 2—Wind Characteristics 2–66
u i 1 2 3 4 5 6 7 8 9 10
m i 82 5 69 81 137 199 240 274 157 291
u i 11 12 13 14 15 16 17 18 19 20
m i 134 186 167 140 159 110 124 141 38 67
u i 21 22 23 24 25 26 27 28 29 30
m i 16 21 21 17 12 7 5 5 0 7
u i 31 32 33 34 35 36 37 38 39 40
m i 0 3 1 1 3 0 0 0 0 0
12. At a given site, the mean wind speed for a month is 6 m/s with a standard deviation of
2.68 m/s. Estimate the Weibull parameters k and c using the Justus approximation of
Eq. 49.
13. Weibull parameters at a given site are c =7m/sandk = 2.6. About how many hours
per year will the wind speed be between 8.5 and 9.5 m/s? About how many hours per
year will the wind speed be greater than 10 m/s? About how many hours per year will
the wind speed be greater than 20 m/s?
14. The Dodge City anemometer was located 17.7 m above the ground for the 14 year period
1948-61. The location was at the Dodge City airport, on top of a gentle hill, and with
excellent exposure in all directions. The average Weibull parameters for this period were
c = 14.87 knots and k = 2.42. The mean speed was 12.91 knots.
(a) Plot both the Weibull and Rayleigh probability density functions f(u) onthesame
sheet of graph paper.
(b) Find the probability P (u ≥ u a ) of the wind speed being greater than or equal to
10, 15, and 20 knots for both distributions.
(c) How does the Rayleigh density function compare with the Weibull over the ranges
0-10, 11-20, and over 20 knots?
15. The monthly mean speeds for July in Dodge City for the years 1948 through 1973 are
12.82, 10.14, 10.49, 10.86, 14.30, 13.13, 12.13, 13.38, 11.29, 12.10, 12.56, 9.03, 12.20,
9.18, 9.29, 12.02, 12.01, 10.21, 11.64, 9.56, 10.10, 10.06, 11.38, 10.19, 10.14, and 10.50
knots.
(a) Find the mean ū m and the normalized standard deviation σ m /ū m .
(b) Find the 90% confidence interval for ū m , using the actual standard deviation. How
many months are outside this interval?
(c) Find the 90% confidence interval for the best and worst months, using the 90
percentile standard deviation for all U. S. sites. Do these intervals include the long
term monthly mean?
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001