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Extra info for Large Scale Renewable Power Generation: Advances in Technologies for Generation, Transmission and Storage
Instead, the two-parameter Weibull distribution, which Probabilistic Modeling and Statistical Characteristics (a) 25 (b) Fig. 3 Histograms of wind speed from two locations with fit Weibull probability density functions. a wind speed distribution for location 1, b wind speed distribution for location 2 is a special case of the Generalized Gamma distribution, is commonly used. The Weibull probability density function  is ﬃ ^fv ð~vÞ ¼ k À~vÁkÀ10 Àð~v=kÞk ~v\0 ð2Þ ~v ! 0 e k k where k and k are the shape and scale parameters, respectively.
10. The parameters of the Beta pdf can be estimated using the method of moments according to ^ð1 À l ^Þ l ^a ¼ l ^ À 1 ð24Þ ^2 r ^ ð1 À l ^Þ l ^ ^Þ b ¼ ð1 À l À1 ð25Þ ^2 r ^ and r ^2 are the sampled mean and variance of the wind power data. There where l ^ but numerical methods can be used to compute is no closed-form MLE of ^a and b, them . Traces of the Beta pdf with parameters fit using MLE to aggregate wind power data from four large systems in different years are found in Figs.
5 Influence of Variation Period An important factor influencing the pdf of wind power variation is the variation period. As discussed in Sect. 4, the variation in wind power from wind plants exhibits greater correlation as the variation period increases. Additionally, there is also more time for the wind power to change, so there is greater potential for extreme variation. Figure 17 shows histograms and fit Laplace pdfs for hourly and 4-hourly variation periods. It is clear that a longer variation period results in a broader distribution, and hence, more variability that must be managed.