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Energies 2016, 9(2), 91; doi:10.3390/en9020091

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

1
Renewable Energy Research Institute and DIEEAC/EDII-AB, Universidad de Castilla-La Mancha, Albacete 02071, Spain
2
Department of Applied Mathematics and Statistics, Universidad Politécnica de Cartagena, Cartagena 30202, Spain
3
Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, TX 75080, USA
4
National Renewable Energy Laboratory, Golden, CO 80401, USA
5
Department of Electrical Engineering, Universidad Politécnica de Cartagena, Cartagena 30202, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Frede Blaabjerg
Received: 8 November 2015 / Revised: 22 December 2015 / Accepted: 22 January 2016 / Published: 2 February 2016
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Abstract

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. View Full-Text
Keywords: wind power generation; Weibull distributions; Weibull mixtures; Akaike information criterion (AIC); Bayesian information criterion (BIC) wind power generation; Weibull distributions; Weibull mixtures; Akaike information criterion (AIC); Bayesian information criterion (BIC)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Gómez-Lázaro, E.; Bueso, M.C.; Kessler, M.; Martín-Martínez, S.; Zhang, J.; Hodge, B.-M.; Molina-García, A. Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures. Energies 2016, 9, 91.

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