Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures

Brian Hodge, Emilio Gomez-Lazaro, Maria Bueso, Mathieu Kessler, Sergio Martin-Martinez, Jie Zhang, Angel Molina-Garcia

Research output: Contribution to journalArticlepeer-review

24 Scopus Citations


The Weibull probability distribution has been widely applied to characterize wind speeds for wind energy resources. Wind power generation modeling is different, however, due in particular to power curve limitations, wind turbine control methods, and transmission system operation requirements. These differences are even greater for aggregated wind power generation in power systems with high wind penetration. Consequently, models based on one-Weibull component can provide poor characterizations for aggregated wind power generation. With this aim, the present paper focuses on discussing Weibull mixtures to characterize the probability density function (PDF) for aggregated wind power generation. PDFs of wind power data are firstly classified attending to hourly and seasonal patterns. The selection of the number of components in the mixture is analyzed through two well-known different criteria: the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Finally, the optimal number of Weibull components for maximum likelihood is explored for the defined patterns, including the estimated weight, scale, and shape parameters. Results show that multi-Weibull models are more suitable to characterize aggregated wind power data due to the impact of distributed generation, variety of wind speed values and wind power curtailment.

Original languageAmerican English
Article number91
Number of pages15
Issue number2
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016 by the authors.

NREL Publication Number

  • NREL/JA-5D00-65841


  • Akaike information criterion (AIC)
  • Bayesian information criterion (BIC)
  • Weibull distributions
  • Weibull mixtures
  • Wind power generation


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