Wind power

8.4.18 Outline the basic features of a wind generator.

Wind generator takes the kinetic energy of the wind and convert it to electrical energy.

The basic outline of the basic phases of a wind generator is the following:
Solar Energy ⇒ Kinetic Energy of Wind ⇒ Kinetic Energy of Turbine ⇒ Electric Energy. (Link)

At first, different parts of Earth's atmosphere is heated to different temperatures by a sun. The temperature differences in the atmosphere then causes pressure differences with hot air rising and cold air sinking. So the fluctuation of the different temperatures of the atmosphere causes the wind to occur.

As the wind is generated by the solar energy, the wind generator takes the kinetic energy of the wind to turn its turbines. As the turbine rotates, much of the wind's kinetic energy is converted into kinetic energy of turbine. This then is converted to electric energy.

Source: Tim Kirk page 73

8.4.19 Determine the power that may be delivered by a wind generator, assuming that the wind kinetic energy is completely converted into mechanical kinetic energy, and explain why this is impossible.

The wind power equation assumes that all of the wind kinetic energy has "completely" converted into mechanical kinetic energy which is impossible. There are three reasons to why it is impossible.
  1. Not all moving air contacts blades.
  2. Blades have air resistance.
  3. Air continues to move after contact with kinetic energy.

Source: Mr. Wagenaar

8.4.20 Solve problems involving wind power.

Question 1a: Calculate the maximum theoretical power, P, for a wind generator whose blades are 30 m long when a 20 m s-1 wind blows. The density of air is 1.3 kg m-3.

Answer 1a:

blades = r = 30 m, velocity of wind = v= 20 m s-1, density of air = p = 1.3 kg m-3, A = Area = πr2

Power = 1/2 Apv3 = 1/2 πr2pv3
Power = 1/2 (π)(30 m)2(1.3 kg m-3)(20 m s-1)3
= 14.7 x 106 W
= 14.7 MW

Question 1b: In practice, under these conditions, this generator only provides 3 MW of electrical power. Calculate the efficiency of this generator.

Answer 1b:

Efficiency = Pout / Pin
= 3MW / 14.7 MW
= .2041
= 20%

Question 2: A wind farm is to be built to supply electrical energy to a small town. The following data is available.

Energy consumption for the town for 1 year = 5.0 x 107kWh
Length of turbine blade = 20.0 m
Average wind speed = 8.0 m s-1
Density of air = 1.1 kg m-3

Deduce from this data that at a minimum, 16 wind turbines are required.


Power = 1/2 Apv3 = 1/2(πr2pv3)
= 1/2(π)(20.0m)2(1.1)(8.0)3
= 354 kW
354 kW x 1yr = 354 kW x 365 x 24 hours = 3.1 x 106 kWh
5.0 x 109 kWh / 3.1 x 106 kWh = 16

Therefore, 16 wind turbines are required minimum.