Wind speed distribution analysis.

Page first edition 02/10/2010, last updated 12/3/2012.

Although wind turbine prices tend to decline they still require a large investment, so before deciding to install one it makes sense to measure the wind speed at the proposed site to make sure it is suitable. Knowledge of the typical wind behaviour also helps with specifying the type of wind turbine to use and the support equipment needed, such as an inverter.

Wind speed is usually measured with an anemometer which records the average velocity experienced over regular intervals; a period of 10 minutes being a popular choice. Once sufficient data has been collected it needs to be analysed.

Turning a file of raw data from an anemometer into a wind speed distribution can be a challenge so I have prepared an example spreadsheet to help. The Open Office version is at;

www.copcutt.me.uk/WindSpeedStats.ods

This has been converted to Excel format at;

www.copcutt.me.uk/WindSpeedStats.xls.

Instructions to get you started are included on the first page (or sheet).

The spreadsheet calculates average wind speed, root mean cubed (RMC) wind speed and the Weibull speed parameter. If the shape parameter in cell I3 is set to 2 then the more general Weibull equation becomes the Rayleigh equation. This is a popular way for comparing wind turbine sites.

The second sheet demonstrates how to take the measured distribution and use it to predict the energy produced by some example turbines.

Details.

There is no shortage of reports of average wind speed but this can be a little misleading when considering wind turbines because they respond to the power in the wind which is proportional to the speed cubed.  To improve energy production forecasts a more detailed analysis of the wind speed distribution needs to be performed. There are a number of web pages that can do this for you behind the scenes. The spreadsheets I have written allow you to follow real examples and adapt the calculations to fit your particular needs. 

The first step is to paste the raw wind speed data into column B on the first sheet [Stats]. Column A can take the date and time data if you want to include that, but it is not required. The example already in the sheet comes from a site I was asked to assess recently. We did not recommend putting a turbine there! Hopefully you will have better data to paste in but the example is used because it is not atypical of sites actually chosen and it highlights why turbines on those sites perform so poorly. The large number of zero readings are due to friction in the anemometer bearings preventing it turning in very light winds.

Once the raw speed data is pasted in, the sheet automatically calculates the average speed, and also the root mean cube speed (RMC) which is another comparison figure sometimes used. However, a Weibull distribution is an even better system for assessing wind resources. The parameters for the equation could be calculated using a suitable minimization of errors method but with a modern computer it can be done well enough by trial and error. The wind changes every year so it is pointless trying to get high accuracy. Start with a shape parameter (cell I3) of 2 because most places are reasonably well modelled by this distribution (called Rayleigh). Adjust the speed parameter in cell I5 until the value in cell I1 is close to 100. This represents the value when the wind energy from the modelled distribution is the same as the energy from the raw data.

Watching the shape of the two curves on the graph helps with this trial and error process. The blue line is the raw data and the orange line is the modelled data. If the lines are not roughly the same shape then the shape parameter can be changed to correct for this. The speed parameter obviously needs resetting after each change of shape parameter.

Once the wind speed distribution has been modelled, the second sheet [Energy prediction] can be used to estimate the energy output from a particular turbine. In Cell C7 enter the height of the turbine's hub above sea level (in meters) and in D7 enter the average temperature at hub height (centigrade). These cells are used to calculate the density of the air passing the turbine. In Cell K4 enter the height of the anemometer above ground level and in Cell L4 do the same for the hub. Cell M4 is for the roughness factor (or Hellman exponent or friction coefficient) which is used to model the rate at which the wind speed increases with height above the ground. There are a number of examples given starting in cell P4.

Many of the cells requiring user input have a red dot in the top right corner. This means that by hovering the mouse over this cell a comment with more explanation appears.

Three turbine examples have been chosen ranging from a micro-turbine used for keeping batteries charged to one suitable for powering a very energy efficient dwelling to a large one capable of running a whole village or small town. The figures are not guaranteed to be accurate, but they illustrate how real turbines only achieve high power coefficients over a small range of wind speeds.

When describing particular turbines it is most common to see power curves published but if power coefficients are used instead it is possbile to correct for altitude and temperature. These are not normally large corrections, and things like wind turbulence and long-term seasonal variability have a bigger impact, but it does improve the accuracy of the energy prediction.

The last of the 4 columns devoted to each turbine example calculates the power generated at a selection of wind speeds. If you only have a power curve you can determine the power coefficient at each wind speed by adjusting them until the estimated power matches the measured power. Most power curves are reported for sea level at 15°C so adjust cells C7 and D7 to 0 and 15 first.

Suggestions about this page and the spreadsheets welcome on my contact page . If you want more help on a professional basis please again go to the contact page.

Links.

Once you have calculated an estimated annual energy yield using the spreadsheet above you can put the data into the economics calculator page of the Danish Wind Energy Association to estimate things like the rate of return and cost of energy.

Pages such as www.wind-works.org/articles/PowerCurves.html from respected wind energy author Paul Gipe explain wind energy prediction in more detail. Since it was written the rapid advancement of computer memory, and in particular flash memory, means data logging costs have dropped dramatically and there is now a good case for collecting more data than the old standards required.

Another page with a good discussion about choosing a wind turbine is at www.solacity.com/SmallWindTruth.htm

Since first writing this spreadsheet I have discovered there is a similar spreadsheet available at www.inl.gov/wind/software/, but only in .xls format. The page also has power generation data for a number of wind turbines. Another page, www.windustry.org, has a complex spreadsheet to help those interested in financing a large wind farm. There is also the Open Wind windfarm design program available at www.awsopenwind.org/ which has the advantage of running under Linux or Windows.