Power from the wind

The extraction of power from the wind with modern turbines and energy conversion systems is an established industry. Machines are manufactured with a capacity from tens of watts to several megawatts, and diameters of about 1m to more than 100m. Traditional mechanical-only machines have been further developed for water pumping, but the overriding commerce today is for electricity generation. Such ‘wind turbine generators’ have become accepted as ‘mainstream generation’ for utility grid networks in many countries with wind power potential, e.g. in Europe, the USA and parts of India and China; other countries are steadily increasing their wind power capacity. Smaller wind turbine generators are common for isolated and autonomous power production. The rapid growth of world wind turbine electricity generation capacity is shown in Figure 9.1. Since about 2002, much additional generation capacity is being installed at sea in offshore wind farms where the depth is moderate. Later sections will show that in a wind of speed u0 and density , a

turbine intercepting a cross-section A of wind front will produce power to its rated maximum according to

PT = 1 2 CPAu0

3 (9.1)

Here Cp is an efficiency factor called ‘the power coefficient’. Note that the power PT is proportional to A and to the cube of wind speed u0. Thus whereas doubling A may produce twice the power, a doubling of wind speed produces eight times the power potential. The power coefficient Cp also varies with wind speed for individual machines. Since wind speed distribution is skewed, at any one time speeds less than average are more likely than speeds greater than average. Therefore the optimum design size of rotor and generator at a particular site depends on the power requirement, either to maximise generated energy per year or to provide frequent power. Often the average annual power from a wind turbine approximates to the

product of Cp, air density and the mean wind speed cubed: P¯T ∼CPAu¯03, see (9.74). The structure comprising the rotor, its matched electricity generator and

other equipment is sometimes called a wind energy conversion system – WECS, however it is increasingly common to use name wind turbine for the whole assembly, as in this edition. The maximum rated power capacity of a wind turbine is given for a specified ‘rated’ wind speed, commonly about 12ms−1. At this speed, power production of about 03kWm−2 of cross-section would be expected with power coefficients Cp between 35 and 45%. The optimum rotation rate depends on the ratio of the blade tip speed to the wind speed, so small machines rotate rapidly and large machines slowly. Tables 9.1 and 9.2 give outline details of wind speeds and machine size. Machines would be expected to last for at least 20-25 years and cost about E 700-1000 ($US 850-1200) per kW rated capacity, ex-factory. When installed in windy locations and given some credit for not polluting, power production is competitive with the cheapest forms of other generation. Wind power for mechanical purposes, milling and water pumping has

been established for many hundreds of years. Wind electricity generators date from around 1890, with most early development from about 1930 to about 1955. At this time development almost ceased due to the availability of cheap oil, but interest reawakened and increased rapidly from about 1973. A few of the older machines kept operating for several tens of years, e.g. the Gedser 100 kW, 24-m diameter machine in Denmark, built in 1957.