Comparison of bivariate distribution construction approaches for analysing wind speed and direction data

Abstract

Statistical distribution models for estimating wind energy potential spurred a great interest among researchers and practitioners recently. Bivariate statistical models for representing both wind direction and speed are helpful for the design and implementation of more effi cient systems for harnessing wind energy. In this study, we construct seven different bivariate joint distributions based on three construction approaches, namely, angular-linear (AL), Farlie-Gumbel-Morgenstern (FGM) and anisotropic lognormal approaches, and then compare them using the adjusted R 2 and root mean square error (RMSE) as measures of goodness of fi t. For both AL and FGM approaches, the distributions of wind speed and direction need to be obtained separately before the construction of joint distribution. While using the mixture of von Mises distribution for representing the wind direction, we utilize two different mixtures of distributions for representing the wind speed, with one being the mixture of singly truncated below Normal and Weibull distribution, and the other being the mixture of three-parameter inverse Gaussian and lognormal distributions. A case study is conducted for this purpose on multiple sites in North Dakota, USA. It indicates that the two mixtures of distributions for wind speed have comparable performances. Meanwhile, there is little difference in terms of adjusted R 2 and RMSE values in modelling wind direction with AL and FGM approaches. Although the anisotropic approach signifi cantly lags behind AL and FGM approaches, the adjusted R 2 and RMSE values provided by the latter two approaches are comparable.share of wind energy is relatively higher compared with the USA. Germany, Spain and Denmark take a leading role in generation of electricity from wind-powered turbines. 4 In Spain, the electricity from wind power supplies 4% of the total demand. 5 In order to estimate the wind power resource for a site, statistical models have been proposed and utilized for analysing the wind characteristics. A major focus on statistical analysis of wind characteristics is the identifi cation of the probability density function governing the wind attributes. Research is directed at fi nding out the most appropriate distribution for the characterization of wind speed and parameters. The statistical distributions based on twoparameter Rayleigh and Weibull models are by far the RESEARCH ARTICLE Wind Energ. 2011; 14:27-41

ARMA based approaches for forecasting the tuple of wind speed and direction

“…The first approach uses the component model where the prevailing wind direction is obtained and the wind speed is decomposed into lateral and longitudinal components based on the prevailing wind direction. Decomposing the wind speed into the lateral and longitudinal components has been used for characterization of the joint distribution of wind speed and direction by the researchers [27,28]. The second approach employs two independent ARMA models, namely, a traditional ARMA model for forecasting the wind speed, and a linked ARMA model for wind direction.…”

Modelling Wind for Wind Farm Layout Optimization Using Joint Distribution of Wind Speed and Wind Direction

“…Carta et al [14] proposed to construct a joint distribution from two marginal distributions, i.e., truncated Normal-Weibull mixture distribution for wind speed and a finite mixture of von Mises distributions for wind direction. Erdem and Shi [15] constructed seven different bivariate joint distributions using three construction approaches, namely, angular-linear, Farlie-Gumbel-Morgenstern and anisotropic lognormal approaches. Zhang et al [16] presented a multivariate distribution of wind speed, wind direction and air density by using a non-parametric approach, multivariate kernel density estimation.…”

Market Suitability and Performance Tradeoffs Offered by Commercial Wind Turbines across Differing Wind Regimes

“…Appreciable work has been done (and is ongoing) (i) to account for the variation of wind conditions at a particular site (e.g., wind distribution modeling [1,2]) and (ii) to address the intermittency of wind resources in the context of grid integration (e.g., energy storage technologies [3,4]). In contrast, there has been a limited amount of work that investigates the complex demands on wind turbine performance (when In this paper, we are particularly concerned with the role of the third factor in wind farm performance.…”