Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Polynomial approximations of the Normal toWeibull Distribution transformation

Departamento de Enxeñería Eléctrica, Universidade de Vigo, 36310 Vigo, Spain

Special Issues: Wind Power Implementation Challenges

Some of the tools that are generally employed in power system analysis need to use approaches based on statistical distributions for simulating the cumulative behavior of the different system devices. For example, the probabilistic load flow. The presence of wind farms in power systems has increased the use of Weibull and Rayleigh distributions among them. Not only the distributions themselves, but also satisfying certain constraints such as correlation between series of data or even autocorrelation can be of importance in the simulation. Correlated Weibull or Rayleigh distributions can be obtained by transforming correlated Normal distributions, and it can be observed that certain statistical values such as the means and the standard deviations tend to be retained when operating such transformations, although why this happens is not evident. The objective of this paper is to analyse the consequences of using such transformations. The methodology consists of comparing the results obtained by means of a direct transformation and those obtained by means of approximations based on the use of first and second degree polynomials. Simulations have been carried out with series of data which can be interpreted as wind speeds. The use of polynomial approximations gives accurate results in comparison with direct transformations and provides an approach that helps explain why the statistical values are retained during the transformations.
  Article Metrics

Keywords Normal; Weibull; Rayleigh distributions; correlation; autocorrelation; polynomial approximation

Citation: Andrés Feijóo, Daniel Villanueva. Polynomial approximations of the Normal toWeibull Distribution transformation. AIMS Energy, 2014, 2(4): 342-358. doi: 10.3934/energy.2014.4.342


  • [1] Freris, L. L. (1990) Wind energy conversion systems. Prentice Hall.
  • [2] Kavasseri, R. J. (2004) Evidence of crossover phenomena in wind-speed data. IEEE Transac- tions on Circuits and Systems I: Fundamental Theory and Applications, Volume 51, 2255-2262.
  • [3] Damousis, I. G., Alexiadis, M. C., Theocharis, J. B., Dokopoulos, P. S. (2004) A fuzzy model for wind speed prediction and power generation in wind parks using spatial correlation. IEEE Transactions on Energy Conversion, Volume 19, 352-361.
  • [4] Brown, B. G., Katz, R. W., Murphy, A. H. (1984) Time series models to simulate and forecast wind speed and wind power. Journal of Climate and Applied Meteorology, Volume 23, 1184-1195.
  • [5] Song, W. T., Hsiao, L. C. (1993) Generation of autocorrelated random variables with a speci ed marginal distribution. Proceedings of the Winter Simulation Conference, 374-377.
  • [6] Feijóo, A., Villanueva, D., Pazos, J. L., Sobolewski, R. (2011) Simulation of correlated wind speeds. A review. Renewable and Sustainable Energy Reviews, Volume 15, 2826-2832.
  • [7] Correia, P. F., Ferreira de Jesus, J. M. (2010) Simulation of correlated wind speeds and power variates in wind parks. Electric Power Systems Research, Volume 80, 592-598.
  • [8] Segura-Heras, I., Escrivá-Escrivá, G., Alcázar-Ortega, M. (2011) Wind farm electrical power production model for load flow analysis. Renewable Energy, Volume 36, 1008-1013.
  • [9] Karaki, S. H., Salim, B. A., Chedid, R. B. (2002) Probabilistic model of a two site wind energy conversion system. IEEE Transactions on Energy Conversion Volume 17, 530-536.
  • [10] Young, D. J., Beaulieu, N. C. (2000) The generation of correlated Rayleigh random variates by inverse discrete Fourier transform. IEEE Transactions on Communications, Volume 48, 1114- 1127.
  • [11] Huang, Z., Chalabi, Z. S. (1995) Use of time-series analysis to model and forecast wind speed. Journal of Wind Engineering and Industrial Aerodynamics Volume 56, 311-322.
  • [12] Shamshad, A., Bawadi, M. A., Wan Hussin, W. M. A., et al. (2005) First and second order Markov chain models for synthetic generation of wind speed time series. Energy Volume 30, 693-708.
  • [13] Villanueva, D., Feijóo, A., Pazos, J. L. (2012) Simulation of correlated wind speed data for Economic Dispatch Evaluation. IEEE Transactions on Sustainable Energy, Volume 3, 142-149.
  • [14] Feijóo, A., Cidrás, J., Dornelas, J. L. G. (1999) Wind speed simulation in wind farms for steady-state security assessment of electrical power systems. IEEE Transactions on Energy Con- version, Volume 3, 1582-1588.
  • [15] Feijóo, A., Sobolewski, R. (2009) Simulation of correlated wind speeds. International Journal of Electrical Energy Systems, Volume 1, 99-106.
  • [16] Carta, J. A., Ramírez, P., Velázquez, S. (2009) A review of wind speed probability distribu- tions used in wind energy analysis. Case studies in the Canary Islands. Renewable and Sustainable Energy Reviews Volume 13, 933-955.
  • [17] Dialynas, E. N., Machias, A. V. (1989) Reliability modelling interactive techniques of power systems including wind generating units. Archive fur Elektrotechnik, Volume 72, 33-41.


This article has been cited by

  • 1. Andrés Feijóo, Daniel Villanueva, Assessing wind speed simulation methods, Renewable and Sustainable Energy Reviews, 2016, 56, 473, 10.1016/j.rser.2015.11.094
  • 2. Elio Chiodo, Pasquale De Falco, Luigi Pio Di Noia, Fabio Mottola, Inverse Log-logistic distribution for Extreme Wind Speed modeling: Genesis, identification and Bayes estimation, AIMS Energy, 2018, 6, 6, 926, 10.3934/energy.2018.6.926

Reader Comments

your name: *   your email: *  

Copyright Info: 2014, Andrés Feijóo, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved