Statistical Tools - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 167

A.4 Extreme Gusts

Extreme wind gusts lead to short-term loads on wind turbines. The gust wind
speed, u gust can be coupled to the mean wind speed via a gust factor G. This factor
usually depends on the averaging time for the gust t, the related averaging time for
the mean wind speed T (t T ), the height above ground z, the surface roughness
z 0 and the mean wind speed u (Wieringa 1973 ; Schroers et al. 1990 ):
G ð t ; T ; z ; z 0 ; u Þ¼ u gust ð t ; z Þ
u ð T ; z ; z 0 Þ

ð A : 33 Þ

Trends have to be removed before calculating G (Wieringa 1973 ). Vertical
profiles of G are discussed in Chap. 3 . Frequency distributions of G can be
described by a Weibull distribution (Jensen and Kristensen 1989 ). Assuming a
normal distribution of the momentary wind speeds in an averaging interval (which
probably is a good assumption for higher wind speeds), i.e., stipulating:

u gust ð t ; z Þ¼ u ð T ; z ; z 0 Þþ kr u ð T ; t ; z ; z 0 ; u Þ ð A : 34 Þ

allows for a description of the gust factor G from the standard deviation and the
mean wind speed (Mitsuta and Tsukamoto 1989 ):

G ð t ; T ; z ; z 0 ; u Þ¼ 1 þ kr u ð T ; t ; z ; z 0 ; u Þ
u ð T ; z ; z 0 Þ

¼ 1 þ kI u ð t ; T Þ ð A : 35 Þ

where k is a so-called peak factor. Equation ( A.35 ) shows, that the gust factor is
closely related to the turbulence intensity [see ( A.6 )]. Wieringa ( 1973 ) gives for k:

k ð D = t Þ¼ 1 : 42 þ 0 : 3013 ln ð D = t 4 Þ ð A : 36 Þ

while Mitsuta and Tsukamoto (1989) cite a more simple relation:

Þ 0 : 5 k ð D = t Þ¼ 2 ln ð D = t Þ ð ð A : 37 Þ

where D is the length of the observation period. Typical values for G are in the
order of 1.3-1.4. Wieringa ( 1973 ) showed that gust factors for hourly mean wind
speeds are about 10 % higher than for 10 min mean wind speeds. Over land
G usually decreases with increasing wind speed due to the similar behaviour of r u
and I u (Davis and Newstein 1968 ).
The Gumbel method presented in Sect. A.3 can be used to estimate a 50 year
extreme 1 s gust as well. An evaluation from the FINO1 dataset from September
2003-August 2007 gives 52.1 m/s (Türk 2008 ).