wind turbine power caculation

1. Wind electricity generation

The first wind powered electricity was produced by a machine built by Charles F. Brush in Cleveland, Ohio in 1888. It had a rated power of 12 kW (direct current - dc). Direct current electricity production continued in the form of small-scale, stand-alone (not connected to a grid) systems until the 1930's when the first large scale AC turbine was constructed in the USA. There was then a general lull in interest until the 1970's when the fuel crises sparked a revival in research and development work in North America (USA and Canada) and Europe (Denmark, Germany, The Netherlands, Spain, Sweden and the UK). Modern wind turbine generators are highly sophisticated machines, taking full advantage of state-ofthe-art technology, led by improvements in aerodynamic and structural design, materials technology and mechanical, electrical and control engineering and capable of producing several megawatts of electricity. During the 1980's installed capacity costs dropped considerably and windpower has become an economically attractive option for commercial electricity generation. Large wind farms or wind power stations have become a common sight in many western countries.

2. The power in the wind

Significant areas of the world have mean annual windspeeds of above 4-5 m/s (metres per second) which makes small-scale wind powered electricity generation an attractive option. It is important to obtain accurate windspeed data for the site in mind before any decision can be made as to its suitability

The power in the wind is proportional to:

  • the area of windmill being swept by the wind

  • the cube of the wind speed

  • the air density - which varies with altitude

The formula used for calculating the power in the wind is shown below:

P = 0.5 x rho x A x V3


  • P: is power in watts (W)

  • rho: is the air density in kilograms per cubic metre (kg/m3), (about 1.225 kg/m3 at sea level, less higher up)

  • A: is the swept rotor area in square metres (m2)

  • V: is the windspeed in metres per second (m/s).

The fact that the power is proportional to the cube of the windspeed is very significant. This can be demonstrated by pointing out that if the wind speed doubles then the power in the wind increases by a factor of eight. It is therefore worthwhile finding a site which has a relatively high mean windspeed.

3. Wind into Watts

Although the power equation above gives us the power in the wind, the actual power that we can extract from the wind is significantly less than this figure suggests. The actual power will depend on several factors, such as the type of machine and rotor used, the sophistication of blade design, friction losses, and the losses in the pump or other equipment connected to the wind machine. There are also physical limits to the amount of power that can be extracted realistically from the wind. It can been shown theoretically that any windmill can only possibly extract a maximum of 59.3% of the power from the wind (this is known as the Betz limit). In reality, this figure is usually around 45% (maximum) for a large electricity producing turbine and around 30% to 40% for a windpump.

So, modifying the formula for ‘Power in the wind’ we can say that the power which is produced by the wind machine can be given by:

Pm = 0.5 x Cp x rho x A x V3


  • Pm: is power (in watts) available from the machine

  • Cp: is the coefficient of performance of the wind machine (power efficiency)

  • rho: is the air density in kilograms per cubic metre (kg/m3), (about 1.225 kg/m3 at sea level, less higher up)

  • A: is the swept rotor area in square metres (m2)

  • V: is the windspeed in metres per second (m/s).

4. Wind Speeds

There are various important wind speeds to consider:

  • Start-up wind speed - the wind speed that will turn an unloaded rotor

  • Cut-in wind speed – the wind speed at which the rotor can be loaded

  • Rated wind speed – the windspeed at which the machine is designed to run (this is at optimum tip-speed ratio)

  • Furling wind speed – the windspeed at which the machine will be turned out of the wind to prevent damage

  • Maximum design wind speed – the windspeed above which damage could occur to the machine


  • Paul Gipe: Wind Energy Basics, a guide to small and micro wind systems. Chelsea Green Publishing Company, 1999,

  • Wind for Electricity Generation, ITDG Technical Brief, Intermediate Technology Development Group

  • S. Dunnett: Small Wind Energy Systems for Battery Charging. ITDG Technical Information Leaflet, KIS Unit

  • Hugh Piggott: It’s A Breeze, A Guide to Choosing Windpower. Centre for Alternative Technology, 1998

  • E. H. Lysen: Introduction to Wind Energy, basic and advanced introduction to wind energy with emphasis on water pumping windmills. SWD, Netherlands, 1982

  • Jack Park: The Wind Power Book.Cheshire Books, USA, 1981

  • Hugh Piggot: Windpower Workshop, building your own wind turbine. Centre for Alternative Technology, 1997

  • E. W. Golding: The Generation of Electricity by Wind Power. Redwood Burn Limited, Trowbridge, 1976

  • David, A. Spera: Wind Turbine Technology, fundamental concepts of wind turbine engineering. ASME Press, 1994

  • T. Anderson, A. Doig, D. Rees and S. Khennas: Rural Energy Services - A handbook for sustainable energy development. ITDG Publishing, 1999.

  • L.A. Kristoferson, and V. Bokalders: Renewable Energy Technologies - their application in developing countries. ITDG Publishing, 1991.

  • S. Lancashire, J. Kenna and P. Fraenkel: Windpumping Handbook. I T Publications, London, 1987

  • Windpumping. ITDG Technical Brief, KIS Unit

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