Hi Ayush;

The Weibull or Rayleigh distribution is used to represent a probabilistic based model to estimate the wind power in a given region;

This model is also introduced in the energy conversion chain to optimize energy harvesting.

Dear Ayush,

The usual method for estimation of (average) power output from wind turbines is using the turbine power curve (e.g., as provided by the manufacturer) and a wind speed frequency distribution. The wind speed frequency distributions typically used in the literature are the Weibull or the Rayleigh probability density functions, which in this case give the probability of occurrence of a given wind speed. That is, if you have a wind speed data series measured in situ or obtained by other means, you can obtain for example the Weibull distribution that fits best your collection of observations, and then you use that probability density function to compute the average power output with the expression in the attached figure, where Vci is the cut-in wind speed, Vco is the cut-out wind speed, Pturb(V) is the curve power  vs. wind speed and f(V) is the Weibull function.

I recommend you to check this paper:

Walker, S.L., Building mounted wind turbines and their suitability for the urban scale — A review of methods of estimating urban wind resource, Energy & Buildings 43(8) (2011) 1852-1862

Hope this is useful,

jose

In the practical application for wind turbines it is important to take into account several factors:

1) A Rayleigh distribution is often observed when the overall magnitude of a vector is related to its directional components. One example where the Rayleigh distribution naturally arises is when wind velocity is analyzed into its orthogonal 2-dimensional vector components.

2) In real life the spectrum of wind speed depends on geographical location. The average wind direction is usually not zero, and wind turbine has certain fixed orientation, typically along the most frequent wind. Wind rose represent an important practical distribution, however not analytical; see for example the graph

http://help.autodesk.com/cloudhelp/2015/ENU/Revit-Analyze/images/GUID-95716CE9-C9DC-43C3-8B31-D3D0046B8605.png .

Using it, one can get wind histogram along each direction. Then for the chosen direction of wind turbine orientation it is possible to get distribution of projections of wind speed on this orientation.

3) The generated energy is a non-linear function of wind speed.

Hi Ayush,

Both Rayleigh and Weibull probability density function (pdf) are used to know wind condition at the selected site. In an easier explaination, what is the wind speed that mostly exist at your site. Thus you can do wind turbine selection accordingly. The objective is to optimize the available wind at the selected site, know when it will start (start up wind speed) and design protection system when it reach cut off wind speed.

You can further read at my favourite reference:

Renewable and Efficient Electric Power System, Gilbert M. Masters.

See one application  of Weibull and Rayleigh distribution for wind data analysis,   in the attached file.

You can as well visit the link below;

http://www.mathworks.com/help/stats/rayleigh-distribution.html

The long term wind data shows definite pattern. In order to analyze that pattern distribution is used. Weibull is generalized distribution to analyse wind data.estimating its parameters helps in estimating the power production of wind turbine. 

The Weibull distribution is a two parameter

function commonly used to fit the wind speed frequency distribution.

For anyone else reading this question, the reason why a Weibull distribution is used is because it is the distribution that most closely represents the actual distribution of wind speeds. A Weibull distribution is a type of Rayleigh distribution, one with a shape value of 2. It is a positively-skewed distribution with most of the density in the slow to moderate wind speed range, as these speeds are more commonplace than gales or hurricanes, which would be considered extreme events.

From the cut-in speed of the turbine to the top of the power curve, the maximum power the turbine can deliver is directly proportional to the cube of the wind speed, so a small change in the speed can result in a significant change in output. Being able to accurately predict in advance what the speed profile will be allows operators to determine how much power they will generate.

Contrary to what Yuri suggested, wind turbines do not have a fixed orientation, but instead employ a yaw motor, installed between the tower and the nacelle, to ensure the blades face into the wind and can extract the maximum power from it.

Simply it provides a statistical model for finding wind speed.