Power in the Wind

The purpose of a wind turbine is to capture the energy of the wind and convert it into useful energy, usually in the form of electrical energy. Consider the kinetic energy of a wind of velocity Vqo as it passes through a disk of area A in the atmosphere. If the disk is normal to the wind vector, then the mass flow rate through the disk will be m = pAVoo and so the kinetic energy per unit time contained in the wind that flows through this disk is

This is equivalent to the power that could be extracted from the wind assuming the energy conversion process was 100% efficient. A modem turbine may extract only half of this potential energy because of aerodynamic and mechanical losses (see Section 13.4). Notice from Eq. 13.1 that the potential power output from the turbine is proportional to the square of its size (diameter) and cube of the wind speed.

For example, consider a wind turbine of 5 m (16.4 ft) in diameter with a net efficiency of 50% that operates with its disk properly pointed perpendicular to a wind of speed of 10 m/s (32.8 ft/s) at standard sea level conditions. The potential power output will be

P = (0.5) x A і Tool3 = 0.25 x 1.225 х(7г2.52)х(і0)3 «okWorBhp. (13.2)

This example shows why wind turbines have to be very large in size (diameter) and have to be located where the wind blows on average at relatively high speeds. Wind turbines are often situated in groups or farms with many tens or hundreds of turbines to produce a sufficiently useful and economically attractive net power output.

Notice that if the turbine is not pointed into the wind then it will be apparent that the velocity normal to the disk will be reduced by a factor cos у, where у is the yaw angle. In

such a case, according to Eq. 13.2 the power output drops by cos3 */ and so the importance of accurately controlling the orientation of the turbine relative to the wind direction becomes immediately clear. This must be done by design or by some sort of mechanical control device that senses wind direction and automatically points the turbine accurately into the wind.