Wind Power Probability Density Functions The probability density

Wind Power Probability Density Functions: The probability density function of the wind speed f (v) If we want to know the number of hours per year that the wind blows between any two wind speeds :

Wind speed probability density function (p. d. f). ``

The average wind speed can be found using the probability density function as:

Weibull and Rayleigh Statistics A very general expression that is often used as the starting point for characterizing the statistics of wind speeds is written as: Where : k is called the shape parameter, and c is called the scale parameter.

For k = 1, (not a good site for a wind turbine since most of the winds are at such low speeds). For k = 2, (the most realistic for a wind turbine site; since it has winds with low and high speeds. For k = 3, (not a good site for a wind turbine since the winds blow at almost constant speed).

Weibull probability density function with shape parameter k = 1, 2, and 3 (with scale parameter c = 8).

In fact, when little detail is known about the wind regime at a site, the usual starting point is to assume k = 2 , then the Rayleigh p. d. f. will be: The average speed will be determined as:

This is quite accurate for a range of shape factors k from about 1. 5 to 4. We can write the Rayleigh p. d. f. in terms of average wind speed v as :

The Rayleigh probability density function with varying scale parameter c