Page 56 - Wind Energy Handbook

30 THE WIND RESOURCE

turbulence spectrum (Greenway, 1979; ESDU, 1983), an empirical expression due to
Weiringa (1973) is often used as it is much simpler, and agrees well with theoretical
results. Accordingly the t s gust factor is given by
3600
G(t) ¼ 1 þ 0:42I u ln (2:40)
t

where I u is the longitudinal turbulence intensity. Figure 2.8 shows the gust factors
for several different turbulence intensities and gust durations calculated according
to this expression.

2.8 Extreme Wind Speeds

In addition to the foregoing descriptions of the average statistical properties of the
wind, it is clearly of interest to be able to estimate the long-term extreme wind
speeds which might occur at a particular site.
A probability distribution of hourly mean wind speeds such as the Weibull
distribution will yield estimates of the probability of exceeding any particular level
of hourly mean wind speed. However, when used to estimate the probability of
extreme winds, an accurate knowledge of the high wind speed tail of the distribu-
tion is required, and this will not be very reliable since almost all of the data which
was used to fit the parameters of the distribution will have been recorded at lower
wind speeds. Extrapolating the distribution to higher wind speeds cannot be relied
upon to give an accurate result.
Fisher and Tippett (1928) and Gumbel (1958) have developed a theory of extreme
values which is useful in this context. If a measured variable (such as hourly mean
wind speed U) conforms to a particular cumulative probability distribution F(U),
i.e., F(U) ! 1as U increases, then the peak values of hourly mean wind speed in a
given period (a year, for example) will have a cumulative probability distribution of
N
F , where N is the number of independent peaks in the period. In the UK, for
example, Davenport (1964) has estimated that there are about 160 independent
wind speed peaks per year, corresponding to the passage of individual weather
systems. Thus if
!
k
U
F(U) ¼ 1 exp
c
as for a Weibull distribution, the wind speed peaks in 1 year will have a cumulative
probability distribution given approximately by
" !#
k 160
U
1 exp
c
However, as indicated above, this is unlikely to give accurate estimates for extreme