WIND ENERGY SYSTEMS - Cd3wd

Chapter 2—Wind Characteristics 2–57
Service stations will be mentioned briefly here. Its three-cup rotor drives a gear train which
momentarily closes a switch after a fixed number of revolutions. The cup speed is proportional
to the wind speed so contact is made with the passage of a fixed amount of air by or through
the anemometer. The anemometer can be calibrated so the switch makes contact once with
every mile of wind that passes it. If the wind is blowing at 60 mi/h, then a mile of wind will
pass the anemometer in one minute.
The contact anemometer is obviously an averaging device. It gives the average speed of
the fastest mile, which will be smaller than the average speed of the fastest 1/10th mile, or
any other fraction of a mile, because of the fluctuation of wind speed with time. But one has
to stop refining data at some point, and the fastest mile seems to have been that point for
structural studies.
The procedure is to fit a probability distribution function to the observed high wind speed
data. The Weibull distribution function of Eq. 30 could probably be used for this function,
except that it tends to zero somewhat too fast. It is convenient to define a new distribution
function F e (u) just for the extreme winds.
Weather related extreme events, such as floods or extreme winds[11], are usually described
in terms of one of two Fisher-Tippett distributions, the Type I or Type II. Thom[23, 24] used
the Type II to describe extreme winds in the United States. He prepared a series of maps
based on annual extremes, showing the fastest mile for recurrence intervals of 2, 50, and
100 years. Height corrections were made by applying the one-seventh power law. National
Weather Service data were used.
The ANSI Standard[1] is based on examination of a longer period of record by Simiu[21]
and uses the Type I distribution. Only a single map is given, for a recurrence interval of 50
years. Other recurrence intervals are obtained from this map by a multiplying factor. Tables
are given for the variation of wind speed with height.
Careful study of a large data set collected by Johnson and analyzed by Henry[12] showed
that the Type I distribution is superior to the Type II, so the mathematical description for
only the Type I will be discussed here. The Fisher-Tippett Type I distribution has the form
F e (u) =exp(− exp(−α(x − β))) (68)
where F e (u) is the probability of the annual fastest mile of wind speed being less than u. The
parameters α and β are characteristics of the site that must be estimated from the observed
data. If n period extremes are available, the maximum likelihood estimate of α may be
obtained by choosing an initial guess and iterating
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001