Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 21

The power output from a wind turbine is given by the well‐known expression:

 ρ is the density of air (1.25 kg/m3)

 Cp is the power coefficient

 A is the rotor swept area

 U is the free wind speed

The density of air is rather low, 800 times less than water, which powers hydro turbines, and this leads inevitably to the large size of a wind turbine. Depending on the design wind speed that is chosen, a 3.5 MW wind turbine may have a rotor that is 100 m in diameter. The power coefficient describes that fraction of the power in the wind that may be converted by the turbine into mechanical work. It has a maximum value of 16/27 or 0.593, and rather lower peak values are achieved in practice (see Chapter 3). Incremental improvements in the power coefficient are continually being sought by detailed design changes of the rotor, and by operating at variable speed it is possible to maintain the maximum power coefficient over a range of wind speeds. However, these measures will give only a modest increase in the power output. Major increases in the output power can only be achieved by increasing the swept area of the rotor or by locating the wind turbines in higher wind speeds.

Figure 1.6 Largest commercially available wind turbines.

Hence, over the last 25 years there has been a continuous increase in the rotor diameter of commercially available wind turbines from around 40 m to several manufacturers offering turbines of more than 170 m (Figure 1.6). A tripling of the rotor diameter leads to a nine times increase in power output. The influence of the wind speed is even more pronounced, with a doubling of wind speed leading to an eightfold increase in power. Thus, there have been considerable efforts to ensure that wind farms are developed in areas of the highest wind speeds and the turbines optimally located within wind farms. In certain countries, with modest wind speeds, very high towers are being used to take advantage of the increase of wind speed with height.

In the past a number of studies were undertaken to determine the optimum size of a wind turbine by balancing the complete costs of manufacture, installation, and operation of various sizes of wind turbines against the revenue generated (Molly et al. 1993). However, these early estimates would now appear to be too low, and more recent studies indicate that the lowest cost of energy is obtained with rotors approaching 150 m diameter, although smaller turbines may be preferred on some sites for reasons of environmental impact and difficulty of transporting very large components to the site. Even larger turbines give the lowest cost of energy offshore, where the foundation and cabling costs of individual turbine are high and the very large blades can be transported by ship directly from the factory to the site.

All modern electricity generating wind turbines use the lift force derived from the blades to drive the rotor. A high rotational speed of the rotor is desirable to reduce the gearbox ratio required, and this leads to a low solidity rotor (the ratio of blade area to rotor swept area). The low solidity rotor acts as an effective energy concentrator, and as a result the energy generated over a wind turbine's life is much greater than that used for its manufacture and installation. An energy balance analysis of a 3 MW wind turbine showed that the expected average time to generate a similar quantity of energy to that used for its manufacture, operation, transport, dismantling, and disposal was six to seven months (European Wind Energy Association 2009). A similar time was calculated for offshore wind turbines. Offshore the higher mean wind speeds, and hence greater energy output, compensate for the higher wind farm costs and energy expended in construction and operation.

Until around the year 2000, the installed wind turbine generating capacity was so low that its output was viewed by electricity Transmission System Operators simply as negative load that supplied energy but played no part in the operation of the power system and maintaining its stability. Since then, with the greatly increased capacity of wind generation, turbines are required to contribute to the operation of the power system. The requirements for their performance are defined through the Grid Codes, issued by the Transmission System Operators (Roberts 2018). Compliance is mandatory and must be demonstrated before connection to the network is allowed. Compliance with the Grid Code requirements is difficult to achieve with simple fixed speed induction generators using the Danish concept, and these regulations have been a major driver for the use of variable‐speed generators.