TURBINE OPERATION/ENERGY OUTPUT
Turbine annual energy output
Now it is time to calculate the relationship between average wind speeds and annual energy output from a wind turbine.
To draw the graph, the Turbine Power Calculator on the previous page has been used and the power curve from the default example 600 kW wind turbine. A standard atmosphere with an air density of 1.225 kg/m3 has been used.
Output varies almost with the cube of the wind speed
Look at the red curve with k=2, which is the curve normally shown by manufacturers: with an average wind speed of 4.5 m/s at hub height the machine will generate about 0.5 GWh per year. With an average wind speed of 9 m/s it will generate 2.4 GWh/year. Thus, doubling the average wind speed has increased energy output 4.8 times.
If we had compared 5 and 10 m/s instead, we would have obtained almost exactly 4 times as much energy output. The reason why we do not obtain exactly the same results in the two cases, is that the efficiency of the wind turbine varies with the wind speeds, as described by the power curve. Note, that the uncertainty that applies to the power curve also applies to the result above.
You may refine your calculations by accounting for the fact that e.g. in temperate climates the wind tends to be stronger in winter than in summer and stronger during the daytime than at night.
The capacity factor
Another way of stating the annual energy output from a wind turbine is to look at the capacity factor for the turbine in its particular location. Capacity factor is the actual annual energy output divided by the theoretical maximum output, if the machine were running at its rated (maximum) power during all of the 8766 hours of the year.
Example: If a 600 kW turbine produces 1.5 million kWh in a year, its capacity factor is = 1500000 : ( 365.25 * 24 * 600 ) = 0.285 = 28.5%.
Capacity factors may theoretically vary from 0-100%, but in practice they will usually range from 20-70%, and mostly be around 25-30%.
The capacity factor paradox
Although one would generally prefer to have a large capacity factor, it may not always be an economic advantage. This is often confusing to people used to conventional or nuclear technology. For instance, in a very windy location it may be an advantage to use a larger generator with the same rotor diameter, or a smaller rotor diameter for a given generator size. This would tend to lower the capacity factor (using less of the capacity of a relatively larger generator), but it may mean a substantially larger annual production, as can be verified using the Turbine Power Calculator.
Whether it is worthwhile to go for a lower capacity factor with a relatively larger generator, depends both on wind conditions and on the price of the different turbine models of course. Another way of looking at the capacity factor paradox is to say, that to a certain extent you may have a choice between a relatively stable power output, close to the design limit of the generator, with a high capacity factor or a high energy output (which will fluctuate) with a low capacity factor.
- Energy conversion definitions: definitions and usage
- Wind speed PDF distribution (A): probability density, graph
- Wind speed PDF distribution (B): energy density, P(V) curve
- Energy pattern factor: graph, Weibull k for design
- Energy conversion efficiency (A): graph, general theoretical efficiency
- Energy conversion efficiency (B): graph, control implication to production
- Productive wind speeds: graph
- Calculation of energy yield: graphs, calculation of energy