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Multivariate Weibull Distribution for Wind Speed and Wind Power Behavior Assessment

Author

Listed:
  • Daniel Villanueva

    (Departamento de Enxeñería Eléctrica, Universidade de Vigo, Maxwell s/n, Vigo 36301, Spain)

  • Andrés Feijóo

    (Departamento de Enxeñería Eléctrica, Universidade de Vigo, Maxwell s/n, Vigo 36301, Spain)

  • José L. Pazos

    (Departamento de Enxeñería Eléctrica, Universidade de Vigo, Maxwell s/n, Vigo 36301, Spain)

Abstract

The goal of this paper is to show how to derive the multivariate Weibull probability density function from the multivariate Standard Normal one and to show its applications. Having Weibull distribution parameters and a correlation matrix as input data, the proposal is to obtain a precise multivariate Weibull distribution that can be applied in the analysis and simulation of wind speeds and wind powers at different locations. The main advantage of the distribution obtained, over those generally used, is that it is defined by the classical parameters of the univariate Weibull distributions and the correlation coefficients and all of them can be easily estimated. As a special case, attention has been paid to the bivariate Weibull distribution, where the hypothesis test of the correlation coefficient is defined.

Suggested Citation

  • Daniel Villanueva & Andrés Feijóo & José L. Pazos, 2013. "Multivariate Weibull Distribution for Wind Speed and Wind Power Behavior Assessment," Resources, MDPI, vol. 2(3), pages 1-15, September.
    • Handle: RePEc:gam:jresou:v:2:y:2013:i:3:p:370-384:d:28500
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    References listed on IDEAS

    as
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    2. Jye Lu & Gouri Bhattacharyya, 1990. "Some new constructions of bivariate Weibull models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 543-559, September.
    3. Patra, Kaushik & Dey, Dipak K., 1999. "A multivariate mixture of Weibull distributions in reliability modeling," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 225-235, November.
    4. Segura-Heras, Isidoro & Escrivá-Escrivá, Guillermo & Alcázar-Ortega, Manuel, 2011. "Wind farm electrical power production model for load flow analysis," Renewable Energy, Elsevier, vol. 36(3), pages 1008-1013.
    5. Lee, Larry, 1979. "Multivariate distributions having Weibull properties," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 267-277, June.
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