equation for power of wind turbin

The power output, P, from a wind turbine is given by the well-known equation



where
rho(greek symbol) is the density of air (1:225 kg/m3 )
Cp is the power coefficient,
A is the rotor
P swept area
U ist he wind speed.

The density of air is rather low, 800 times less than that of water which powers hydro plant, and this leads directly to the large size of a wind turbine. Depending on the design wind speed chosen, a 1.5 MW wind turbine may have a rotor that is more than 60 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 theoretical maximum value of 0.593 (the Betz limit) and rather lower peak values are achieved in practice

The power coefficient of a rotor varieswith the tip speed ratio (theratio of rotor tip speed to free wind speed) and is only a maximum for a unique tip speed ratio. 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 on sites with higher windspeeds.