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Weibull Distribution

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The two-parameter Weibull distribution is often used to characterize wind regimes because it has been found to provide a good fit with measured wind data. The probability density function is given by the following equation:

equations_weibull-pdf

where:


 

 

v

= the wind speed [m/s]

 

k

= the Weibull shape factor [unitless]

 

c

= the Weibull scale parameter [m/s]

The cumulative distribution function is given by the following equation:

equations_weibull-cdf

The following equation relates the two Weibull parameters and the average wind speed:

equations_weibull-vbar

where:


 

 

Γ

= the gamma function

One can describe a Weibull distribution using an average wind speed and a Weibull k value. The graph below shows five Weibull distributions, all with the same average wind speed of 6 m/s, but each with a different Weibull k value. As the graph shows, lower k values correspond to broader distributions.

graphics_weibull-shape-factor

To fit a Weibull distribution to measured wind data, HOMER uses the maximum likelihood method given by Stevens and Smulders, 1979. The graph below shows a typical distribution of wind speeds and the best-fit Weibull distribution.

graphics_weibull-fitted-example

See also

Weibull k Value