WIND ENERGY SYSTEMS - Cd3wd

Chapter 2—Wind Characteristics 2–59
a few years of data, then we might want to find the distribution of monthly extremes. The
procedure is the same, but we now have 12 values for each year instead of one. If we have
only a few months to a year of wind data, then we can find the distribution of daily extremes.
When modeling is conducted using one period length and it is desired to express the results
in terms of a larger period, the parameters of the distribution must be altered. If there are n
of the smaller periods within each larger unit, the distribution function for the larger period
is
F L =[F s ] n (73)
where F s is the distribution function for the smaller period. The relationship between parameters
is then
α L = α s and β L = β s + ln n
α s
(74)
For example, the relationship between monthly and yearly extremes is
α a = α m , β a = β m + 2.485
α m
(75)
An example of values of α and β for daily extremes is shown in Table 2.7. These are
calculated from a large data set collected by Kansas State University for the period October,
1983 through September, 1984 at 7 Kansas locations, using the daily fastest minute.
Table 2.7 α and β for seven Kansas sites, daily fastest minute in mi/h
50 m 30 m 10 m
α β α β α β
Tuttle Creek Lake 0.1305 23.47 0.1298 22.25 0.1414 20.76
Plainville 0.1410 26.04 0.1474 23.63 0.1660 19.57
Beaumont 0.1441 26.14 0.1522 24.71 0.1620 21.74
Lyndon 0.1582 23.00 0.1547 21.24 0.1648 18.21
Dodge City 0.1448 25.86 0.1483 23.92 0.1552 20.83
Lyons 0.1537 23.55 0.1594 21.75 0.1689 19.49
Oakley 0.1435 26.89 0.1457 24.51 0.1556 20.72
mean 0.1451 24.24 0.1482 23.14 0.1591 20.19
std. dev. 0.0089 2.16 0.0094 1.39 0.0094 1.17
Differences among sites are relatively small, as seen by the standard deviations. There is
a tendency for α to get smaller and β to get larger with height.
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001