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Wind Power

Power generated from the wind

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windmill

Theoretically power in moving air - or wind - can be calculated

P = 1/2 ρ A v3  

   =  1/8 ρ π d2 v3                                               (1)

where

P = power (W)

ρ = density of air (kg/m3)

A = wind mill area perpendicular to the wind (m2)

v = wind speed (m/s)

π = 3.14....

d = wind mill diameter (m)

Be aware that the density of air decreases with temperature and altitude and that the major factor in wind power generation is wind speed.

  • 20% increase in wind velocity will increase the power generation with 73%

The theoretical and rated wind power generation from a typical windmill is indicated in the "wind speed-power curve" below. Cut-in wind speed, rated wind speed, shut-down wind speed and rated power for windmills with 20% and 40% efficiency.

wind speed power curve

Actual Available Power

Actual available wind power can be calculated

Pa = 1/2 ξ ρ A v3  

     1/8 ξ ρ π d2 v3                                                (2)

where

ξ = efficiency of the windmill (in general less than 0.4 - or 40%)

Example - Wind Power

The actual available power from a wind mill with diameter 1 m, efficiency 0.2 (20%) - with wind velocity 10 m/s - can be calculated as

Pa = 1/8 (0.2) (1.2 kg/m3) π (1 m)2 (10 m/s)3

    = 94.2 W

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Online Wind Power Calculator

The calculator below can be used to calculate the available power from a windmill:

ρ - density of air (kg/m3)

ξ - efficiency of windmill 

v - wind speed (m/s)

d - windmill diameter (m)

Generated Wind Energy

The energy generated over time depends on the wind mill potential power generation (as indicated above) - and how often, or how many hours the wind blows - or more scientifically - the "wind speed frequency distribution" at the actual location.

The total energy generated over a year can be calculated by summarizing the power generation for all velocities (ranging from the actual windmill cut-in speed to the shut-down speed) multiplied with the no. of hours the wind blows at the actual speeds.

A typical wind speed frequency distribution diagram with energy produced at the different velocities is indicated below.

wind speed frequency distribution diagram

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  • Engineering ToolBox, (2009). Wind Power. [online] Available at: https://www.engineeringtoolbox.com/wind-power-d_1214.html [Accessed Day Mo. Year].

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