Statistical Tools - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 156

Table A.1 Statistical parameters characterizing the wind

Parameter Description

Mean wind speed Indicates the overall wind potential at a given site, expected wind

speed for a given time interval (first central moment)

Wind speed fluctuation Deviation of the momentary wind speed from the mean wind speed for

a given time interval

Wind speed increment Wind speed change for a given time span

Variance Indicates the mean amplitude of temporal or spatial wind fluctuations,

expected fluctuation in a given time interval (second central
moment)

Standard deviation Indicates the mean amplitude of temporal or spatial wind fluctuations

(square root of the variance)

Turbulence intensity Standard deviation normalized by the mean wind speed

Gust wind speed Maximum wind speed in a given time interval

Gust factor Gust wind speed divided by the mean wind speed in this time interval

Skewness Indicates the asymmetry of a wind speed distribution around the mean

value (third central moment)

Kurtosis (flatness) Indicates the width of the wind speed distribution around the mean

value (fourth central moment)

Excess kurtosis Kurtosis minus 3

Frequency spectrum Indicates the frequencies at which the fluctuations occur

Autocorrelation Indicates the gross spatial scale of the wind speed fluctuations, Fourier

transform of the spectrum

Structure function Indicates the amplitude of wind speed fluctuations, computed from

wind speed increments

Turbulent length scale Indicates the size of the large energy-containing eddies in a turbulent

flow

Turbulent time scale Indicates the time within which wind fluctuations at one point are

correlated

Probability density
function (pdf)

Indicates the probability with which the occurrence a certain wind
speed or wind speed fluctuation can be expected

The time series of the true wind speed u(t) at a given location can be
decomposed into a mean wind speed and a fluctuation around this mean (one-point
statistics):

u ð t Þ¼ u ð t ; T Þþ u 0 ð t ; T Þ ð A : 1 Þ

Here, the overbar denotes a temporal average over a time period, T and the
prime a deviation from this average. The most frequently used averaging period is
10 min. The mean over the fluctuations is zero by definition:

u 0 ð t ; T Þ¼ 0 ð A : 2 Þ

The variance of the time series u(t) is defined as:

r u ð t ; T Þ¼ u 0 2 ð t ; T Þ

ð A : 3 Þ

and the standard deviation is given by the square root of the variance: