Power Density Function
Power of the Wind
From the page on the energy in the wind , we know that the energy potential per second (the power ) varies in proportion to the cube (the third power) of the wind speed, and in proportion to the density of the air. (Its weight per unit of volume).
Power density curve
We may now combine everything we have learned so far: If we multiply the power of each wind speed with the probability of each wind speed from the Weibull graph, we have calculated the distribution of wind energy at different wind speeds = the power density.Notice, that the previous Weibull curve changes shape, because the high wind speeds have most of the power of the wind.
From Power Density to Power Output
This graph was drawn using the wind turbine power calculator on this web site. The area under the grey curve (all the way to the axis at the bottom) gives us the amount of wind power per square metre wind flow we may expect at this particular site. In this case we have a mean wind speed of 7 m/s and a Weibull k=2, so we get 402 W/m 2 . You should note that this is almost twice as much power as the wind has when it is blowing constantly at the average wind speed.
The graph consists of a number of narrow vertical columns, one for each 0.1 m/s wind speed interval. The height of each column is the power (number of watts per square metre), which that particular wind speed contributes to the total amount of power available per square metre.
The area under the blue curve tells us how much of the wind power we can theoretically convert to mechanical power. (According to Betz' law , this is 16/27 of the total power in the wind).
The total area under the red curve tells us how much electrical power a certain wind turbine will produce at this site. We will learn how to figure that out in a moment when we get to the page on power curves.
The Important Messages in the Graph
The most important thing to notice is that the bulk of wind energy will be found at wind speeds above the mean (average) wind speed at the site.
This is not as surprising as it sounds, because we know that high wind speeds have much higher energy content than low wind speeds.
The Cut In Wind Speed
Usually, wind turbines are designed to start running at wind speeds somewhere around 3 to 5 metres per second. This is called the cut in wind speed. The blue area to the left shows the small amount of power we lose due to the fact the turbine only cuts in after, say 5 m/s.
The Cut Out Wind Speed
The wind turbine will be programmed to stop at high wind speeds above, say 25 metres per second, in order to avoid damaging the turbine or its surroundings. The stop wind speed is called the cut out wind speed. The tiny blue area to the right represents that loss of power.
© Copyright 1997-2003 Danish Wind Industry Association
Updated 19 September 2003
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