## Weibull Distribution

Posted on: December 3rd, 2011
The General Pattern of Wind Speed Variations
It is very important for the wind industry to be able to describe the variation of wind speeds. Turbine designers need the information to optimise the design of their turbines, so as to minimise generating costs. Turbine investors need the information to estimate their income from electricity generation. If you measure wind speeds throughout a year, you will notice that in most areas strong gale force winds are rare, while moderate and fresh winds are quite common. The wind variation for a typical site is usually described using the so-called Weibull distribution.
Statistical Description of Wind Speeds
People who are familiar with statistics will realise that the graph shows a probability density distribution. The area under the curve is always exactly 1, since the probability that the wind will be blowing at some wind speed including zero must be 100 per cent.
Half of the blue area is to the left of the vertical black line at 6.6 metres per second. The 6.6 m/s is called the median of the distribution. This means that half the time it will be blowing less than 6.6 metres per second, the other half it will be blowing faster than 6.6 metres per second.
You may wonder then, why we say that the mean wind speed is 7 metres per second. The mean wind speed is actually the average of the wind speed observations we will get at this site.
As you can see, the distribution of wind speeds is skewed, i.e. it is not symmetrical. Sometimes you will have very high wind speeds, but they are very rare. Wind speeds of 5.5 metres per second, on the other hand, are the most common ones. 5.5 metres is called the modal value of the distribution. If we multiply each tiny wind speed interval by the probability of getting that particular wind speed, and add it all up, we get the mean wind speed.
The statistical distribution of wind speeds varies from place to place around the globe, depending upon local climate conditions, the landscape, and its surface. The Weibull distribution may thus vary, both in its shape, and in its mean value.
If the shape parameter is exactly 2, as in the graph on this page, the distribution is known as a Rayleigh distribution. Wind turbine manufacturers often give standard performance figures for their machines using the Rayleigh distribution.
Balancing the Weibull Distribution
Another way of finding the mean wind speed is to balance the pile of blue bricks to the right, which shows exactly the same as the graph above. Each brick represents the probability that the wind will be blowing at that speed during 1 per cent of the time during the year. 1 m/s wind speeds are in the pile to the far left, 17 m/s is to the far right.
The point at which the whole pile will balance exactly will be at the 7th pile, i.e. the mean wind speed is 7 m/s.