WIND ENERGY SYSTEMS - Cd3wd

Chapter 2—Wind Characteristics 2–41
Table 2.3. 1970 Wind Data
Kansas City
Dodge City
u i x i m i p(u i ) F (u) y i m i p(u i ) F (u) y i
1 0 300 0.103 0.103 -2.22 47 0.016 0.016 -4.12
2 0.69 161 0.055 0.158 -1.765 0.002 0.018 -4.02
3 1.10 127 0.044 0.202 -1.49 82 0.028 0.046 -3.05
4 1.39 261 0.090 0.292 -1.06 65 0.022 0.068 -2.65
5 1.61 188 0.065 0.356 -0.82 140 0.048 0.116 -2.09
6 1.79 294 0.101 0.457 -0.49 219 0.075 0.92 -1.55
7 1.95 151 0.052 0.509 -0.34 266 0.091 0.283 -1.10
8 2.08 347 0.119 0.628 -0.01 276 0.095 0.378 -0.75
9 2.20 125 0.043 0.671 0.11 198 0.068 0.446 -0.53
10 2.30 376 0.129 0.800 0.48 314 0.108 0.554 -0.22
11 2.40 67 0.023 0.823 0.55 155 0.053 0.607 -0.07
12 2.48 207 0.071 0.894 0.81 177 0.061 0.668 0.10
13 2.56 67 0.023 0.917 0.91 141 0.048 0.716 0.23
14 2.64 91 0.031 0.948 1.09 142 0.049 0.765 0.37
15 2.71 29 0.010 0.958 1.16 133 0.046 0.810 0.51
16 2.77 51 0.017 0.976 1.32 96 0.033 0.843 0.62
17 2.83 19 0.006 0.982 1.40 102 0.035 0.878 0.75
18 2.89 39 0.013 0.996 1.70 101 0.035 0.913 0.89
19 2.94 1 0 0.996 1.72 48 0.016 0.930 0.98
20 3.00 7 0.002 0.999 1.89 78 0.027 0.956 1.14
21 3.05 0 0 0.999 1.89 28 0.010 0.966 1.22
22 3.09 2 0.001 0.999 1.97 21 0.007 0.973 1.29
23 3.13 0 0 0.999 1.97 23 0.008 0.981 1.38
24 3.18 1 0 1.000 2.08 12 0.004 0.985 1.44
25 3.22 1 0 1.000 - 19 0.006 0.992 1.57
26 3.26 0 0 8 0.003 0.995 1.65
27 3.30 0 0 2 0.001 0.995 1.67
28 3.33 0 0 9 0.003 0.998 1.85
>28 0 0 5
2912 2912
We first use Eq. 22 to compute F (u i )foreachu i and Eqs 55 to compute y i for each F (u i ). These
are listed in Table 2.3 as well as the original data.
We are now ready to use Eqs. 58 and 56 to find a and b. First, however, we plot the point pairs
(x i ,y i )foreachu i as shown in Fig. 18 for both sites. The readings for calm (0 and 1 knot) are assumed
to be at 1 knot so that x i =lnu i is zero rather than negative infinity.
Placing a straight edge along the sets of points shows the points to be in reasonable alignment
except for calm and 2 knots for Kansas City, and calm for Dodge City. As mentioned earlier, the goal
is to describe the data mathematically over the most common wind speeds. The Weibull function is
zero for wind speed u equal to zero (if k>1) so the Weibull cannot describe calms. Therefore, it
is desirable to ignore calms and perhaps 2 knots in order to get the best fit over the wind speeds of
greater interest.
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001