Wind Energy Handbook. Michael Barton Graham
spectra are deficient at the high frequency end (Veldkamp 2006). Mann (1998) suggests that this may be realistic, because it represents averaging of the turbulence over finite volumes of space, which is appropriate for practical engineering applications. However, a practical simulation tool will perform all necessary spatial averaging in any case, and so the high frequency variations are really lost. Mann (1998) does suggest a remedy for this, but in practice it is extremely intensive computationally.
2.7 Gust wind speeds
It is often useful to know the maximum gust speed that can be expected to occur in any given time interval. This is usually represented by a gust factor G, which is the ratio of the gust wind speed to the hourly mean wind speed. G is obviously a function of the turbulence intensity, and it also clearly depends on the duration of the gust – thus the gust factor for a one‐second gust will be larger than for a three‐second gust, because every three‐second gust has within it a higher one‐second gust.
Figure 2.8 Gust factors calculated from Eq. (2.46)
While it is possible to derive expressions for gust factors starting from the turbulence spectrum (Greenway 1979; ESDU 1983), an empirical expression due to Weiringa (1973) is often used because it is much simpler and agrees well with theoretical results. Accordingly, the t‐second gust factor is given by
where Iu 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 that 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 exceedance of 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 distribution is required, and this will not be very reliable because almost all of the data that 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 that is useful in this context. If a measured variable (such as hourly mean wind speed
(2.47)
as the observation period increases. U′ is the most likely extreme value, or the mode of the distribution, while 1/a represents the width or spread of the distribution and is termed the dispersion.
This makes it possible to estimate the distribution of extreme values based on a fairly limited set of measured peak values, for example, a set of measurements of the highest hourly mean wind speeds
(2.48)
where m(
An illustration of the Gumbel method is provided in Figure 2.9, using some sample extreme wind data for a particular 29‐year period. The upper plot shows the sample of extreme values. The middle plot shows the estimated cumulative distribution obtained by ordering these values, with the dashed line showing the fitted distribution