Energy Output from a Wind Turbine
We are now ready to calculate the relationship between average
wind speeds and annual energy output from a wind turbine.
To draw the graph to the right,
we have used the power calculator
on the previous page, and the power curve
from the default example 600 kW wind turbine. We have used a
standard atmosphere with an air density of 1.225 kg/m3.
For each of the Weibull
parameters 1.5, 2.0, and 2.5 we have calculated the annual energy
output for different average wind speeds at turbine hub height.
As you can see, output may vary up to 50
per cent depending on the shape parameter
at a low average wind speed of 4.5 m/s, while it may vary some
30 per cent at a very high average wind speed of 10 m/s at hub
varies almost with the cube of the wind speed
Now, let us 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,
i.e. 500,000 kWh per year. With an average wind speed of 9 metres
per second it will generate 2.4 GWh/year = 2,400,000 kWh per
year. Thus, doubling the average wind speed has increased energy
output 4.8 times.
If we had compared 5 and 10 metres per second
instead, we would have obtained almost exactly 4 times as much
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.
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. By capacity factor we mean its 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 ) = 1500000 : 5259600 = 0.285 = 28.5 per cent.
Capacity factors may theoretically vary from
0 to 100 per cent, but in practice they will usually range from
20 to 70 per cent, and mostly be around 25-30 per cent.
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.
In a very windy location, for instance, 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 you can verify using
the Power calculator on this web
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.