Michael Graham - Wind Energy Handbook

Apart from these long‐term trends, there may be considerable changes in windiness at a given location from one year to the next. These changes have many causes. They may be coupled to global climate phenomena such as el niño , changes in atmospheric particulates resulting from volcanic eruptions, and sunspot activity, to name a few.

These changes add significantly to the uncertainty in predicting the energy output of a wind farm at a particular location during its projected lifetime.

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.

On shorter timescales than the seasonal changes described in Section 2.4, wind speed variations are somewhat more random and less predictable. Nevertheless, these variations contain definite patterns. The frequency content of these variations typically peaks at around four days or so. These are the ‘synoptic’ variations, which are associated with large‐scale weather patterns, such as areas of high and low pressure and associated weather fronts as they move across the earth's surface. Coriolis forces induce a circular motion of the air as it tries to move from high‐ to low‐pressure regions. These coherent large‐scale atmospheric circulation patterns may typically take a few days to pass over a given point, although they may occasionally ‘stick’ in one place for longer before finally moving on or dissipating.

Following the frequency spectrum to still higher frequencies, many locations will show a distinct diurnal peak, at a frequency of 24 hours. This is usually driven by local thermal effects. Intense heating in the daytime may cause large convection cells in the atmosphere, which die down at night. This process is described in more detail in Section 2.6because it also contributes significantly to turbulence, on timescales representative of the size of the convection cells. Land and sea breezes, caused by differential heating and cooling between land and sea, also contribute significantly to the diurnal peak. The daily direction reversal of these winds would be seen as a 12‐hour peak in the spectrum of wind speed magnitude.

Turbulence refers to fluctuations in wind speed on a relatively fast timescale, typically less than about 10 minutes. In other words, it corresponds to the highest frequency spectral peak in Figure 2.1. It is useful to think of the wind as consisting of a mean wind speed determined by the seasonal, synoptic, and diurnal effects described previously, which varies on a timescale of one to several hours, with turbulent fluctuations superimposed. These turbulent fluctuations then have a zero mean when averaged over about 10 minutes. This description is a useful one as long as the ‘spectral gap’ as illustrated in Figure 2.1is reasonably distinct.

Turbulence is generated mainly from two causes: ‘friction’ with the earth's surface, which can be thought of as extending as far as flow disturbances caused by such topographical features as hills and mountains, and thermal effects, which can cause air masses to move vertically as a result of variations of temperature and hence in the density of the air. Often these two effects are interconnected, such as when a mass of air flows over a mountain range and is forced up into cooler regions where it is no longer in thermal equilibrium with its surroundings.