*GC*: *n*

CT: Wind statistics and the Weibull distribution.

It is a matter of common observation that the wind is not steady and in order to calculate the mean power delivered by a wind turbine from its power curve, it is necessary to know the probability density distribution of the wind speed. For those unfamiliar with statistics, this is simply the distribution of the proportion of time spent by the wind within narrow bands of wind speed.

As an example, the figure below shows a histogram of the frequency of different hourly wind speeds at 1 knot intervals (0.52 metres/second) from a weather station in Plymouth, UK. The data consists of three years of observations.

The overall mean wind speed is 10.2 knots (5.26 metres/second) and, because the histogram is skewed, it should be noted that this is not the most commonly occuring wind speed which is somewhat less than this at around 5 knots (2.58 metres/second) .

The basic measure of the unsteadiness of the wind is the standard deviation (or root mean square) of the speed variations. For the above data, the standard deviation is 6.28 knots (3.24 metres/second) so that the ratio of the standard deviation to the mean speed is 0.62 – and this almost certainly representative of the unsteadiness of the wind everywhere in the UK. However, the value used in the calculation of mean power is normally set at 52% which corresponds to a particular form of the wind distribution known as the Rayleigh distribution – see below.

In order to calculate the mean power from a wind turbine over a range of mean wind speeds, a generalised expression is needed for the probability density distribution. An expression which gives a good fit to wind data is known as the Weibull distribution.

S: http://www.wind-power-program.com/wind_statistics.htm (last access: 26 December 2014)

N: 1. Named for its inventor, Waloddi Weibull, this distribution is widely used in reliability engineering and elsewhere due to its versatility and relative simplicity.

2. A statistical distribution function used for describing precipitation, wind velocity and streamflow data.

3. A distribution used for random variables which are constrained to be greater or equal to 0.

4. It is characterized by two parameters: shape and scale. Source 1, fiche 1, Anglais, Observation 1 – Weibull%20distribution

5. The Weibull distribution is one of the few distributions which can be used to model data which is negatively skewed.

S: 1. http://www.weibull.com/hotwire/issue14/relbasics14.htm (last access: 26 December 2014). 2. GDT. 3, 4 & 5. TERMIUMPLUS.

SYN: Weibull probability distribution

S: TERMIUMPLUS

CR: wind energy