# The Missing Link Between Air Density And Wind Power Production

The power produced by a wind turbine is given by a simple formula:

P=1/2 x the density of air x the area swept out by the turbines x (the windspeed)^3

Clearly the most important variable is windspeed. The area swept out by of the turbine is a constant and the density of air is generally taken as 1.225 kg/m^3, its value at sea level at 15 degrees C.

Today, Zénó Farkas from Eotvos University in Hungary, points out that the density of air is not constant. And that taking it into account is a relatively straightforward and valuable exercise when calculating the power that a turbine can produce.

To prove the point, he took standard air temperature, pressure and relative humidity measurements to calculate the air density at a wind farm in Hungary over a period from 2004 to 2006. His calculations show that, in that time, the pressure varied by more than 20 per cent.

He then used a neural network to fit the data from the wind speed and air density to the curve of the actual power produced at the windfarm. In fact, he used data from 2005 and 2005 to train the net and the data from 2006 to test it.

The result was a significantly improved estimate of the power production. Compared to the estimate using a constant air density, Farkas says his results are 16 per cent more accurate.

So that’s an easy way to improve power estimates from wind farms. It’s the kind of simple but effective science that can sometimes make a difference .

Ref: arxiv.org/abs/1103.2198: Considering Air Density in Wind Power Production

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