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Home > > Wind turbine news > > Potential turbine power Potential turbine power The amount of power transferred to a wind turbine is directly proportional to the density of the air, the area swept out by the rotor, and the cube of the wind speed. The usable power P available in the wind is given by: P = \begin{matrix}\frac{1}{2}\end{matrix}\alpha\rho\pi r^2 v^3, where P = power in watts, ¦Á = an efficiency factor determined by the design of the turbine, ¦Ñ = mass density of air in kilograms per cubic meter, r = radius of the wind turbine in meters, and v = velocity of the air in meters per second.[7] As the wind turbine extracts energy from the air flow, the air is slowed down, which causes it to spread out. Albert Betz, a German physicist, determined in 1919 (see Betz¡¯ law) that a wind turbine can extract at most 59% of the energy that would otherwise flow through the turbine¡¯s cross section, that is ¦Á can never be higher than 0.59 in the above equation. The Betz limit applies regardless of the design of the turbine. This equation shows the effects of the mass rate of flow of air travelling through the turbine, and the energy of each unit mass of air flow due to its velocity. As an example, on a cool 15 ¡ãC (59 ¡ãF) day at sea level, air density is 1.225 kilograms per cubic metre. An 8 m/s (28.8 km/h or 18 mi/h) breeze blowing through a 100 meter diameter rotor would move almost 77,000 kilograms of air per second through the swept area. The total power of the example breeze through a 100 meter diameter rotor would be about 2.5 megawatts. Betz¡¯ law states that no more than 1.5 megawatts could be extracted. Distribution of wind speed Windiness varies, and an average value for a given location does not alone indicate the amount of energy a wind turbine could produce there. To assess the frequency of wind speeds at a particular location, a probability distribution function is often fit to the observed data. Different locations will have different wind speed distributions. The Rayleigh model closely mirrors the actual distribution of hourly wind speeds at many locations. Because so much power is generated by higher windspeed, much of the energy comes in short bursts. The 2002 Lee Ranch sample is telling; half of the energy available arrived in just 15% of the operating time. The consequence is that wind energy does not have as consistent an output as fuel-fired power plants; utilities that use wind power must provide backup generation for times that the wind is weak. Grid management Induction generators often used for wind power projects require reactive power for excitation, so substations used in wind-power collection systems include substantial capacitor banks for power factor correction. Different types of wind turbine generators behave differently during transmission grid disturbances, so extensive modelling of the dynamic electromechanical characteristics of a new wind farm is required by transmission system operators to ensure predictable stable behaviour during system faults. In particular, induction generators cannot support the system voltage during faults, unlike steam or hydro turbine-driven synchronous generators (however properly matched power factor correction capacitors along with electronic control of resonance can support induction generation without grid). Doubly-fed machines, or wind turbines with solid-state converters between the turbine generator and the collector system, have generally more desirable properties for grid interconnection. Transmission systems operators will supply a wind farm developer with a grid code to specify the requirements for interconnection to the transmission grid. This will include power factor, and dynamic behaviour of the wind farm turbines during a system fault. Related Questions: |
