Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 30

While year‐to‐year variation in annual mean wind speeds remains hard to predict, wind speed variations during the year can be well characterised in terms of a probability distribution. The Weibull distribution has been found to give a good representation of the variation in hourly mean wind speed over a year at many typical sites. This distribution takes the form

(2.1)

where F(U) is the fraction of time for which the hourly mean wind speed exceeds U. It is characterised by two parameters, a ‘scale parameter’ c and a ‘shape parameter’ k, which describes the variability about the mean. The parameter c is related to the annual mean wind speed by the relationship

(2.2)

where Γ is the complete gamma function. This can be derived by consideration of the probability density function

(2.3)

because the mean wind speed is given by

(2.4)

A special case of the Weibull distribution is the Rayleigh distribution, with k = 2, which is actually a fairly typical value for many locations. In this case, the factor Γ(1 + 1/k) has the value . A higher value of k, such as 2.5 or 3, indicates a site where the variation of hourly mean wind speed about the annual mean is small, as is sometimes the case in the trade wind belts, for instance. A lower value of k, such as 1.5 or 1.2, indicates greater variability about the mean. A few examples are shown in Figure 2.2. The value of Γ(1 + 1/k) varies little, between about 1.0 and 0.885: see Figure 2.3.

Figure 2.2 Example Weibull distributions

Figure 2.3 The factor Γ(1 + 1/k)

The Weibull distribution of hourly mean wind speeds over the year is clearly the result of a considerable degree of random variation. However, there may also be a strong underlying seasonal component to these variations, driven by the changes in insolation during the year as a result of the tilt of the earth's axis of rotation. Thus, in temperate latitudes the winter months tend to be significantly windier than the summer months. There may also be a tendency for strong winds or gales to develop around the time of the spring and autumn equinoxes. Tropical regions also experience seasonal phenomena, such as monsoons and tropical storms, that affect the wind climate. Indeed, the extreme winds associated with tropical storms may significantly influence the design of wind turbines intended to survive in these locations.

Although a Weibull distribution gives a good representation of the wind regime at many sites, this is not always the case. For example, some sites showing distinctly different wind climates in summer and winter can be represented quite well by a double‐peaked ‘bi‐Weibull’ distribution, with different scale factors and shape factors in the two seasons, i.e.

(2.5)

Certain parts of California are good examples of this.