A Multivariate and Multimodal Wind Distribution model

Abstract

This paper presents a new methodology to accurately characterize and predict the annual variation of wind conditions. The estimate of the distribution of wind conditions is necessary to quantify the available energy (power density) at a site, and to design optimal wind farm configurations. A smooth multivariate wind distribution model is developed to capture the coupled variation of wind speed, wind direction, and air density. The wind distribution model developed in this paper avoids the limiting assumption of unimodality of the distribution. This method, which we call the Multivariate and Multimodal Wind Distribution (MMWD) model, is an evolution from existing wind distribution modeling techniques. Multivariate kernel density estimation, a standard non-parametric approach to estimate the probability density function of random variables, is adopted for this purpose. The MMWD technique is successfully applied to model (i) the distribution of wind speed (univariate); (ii) the joint distribution of wind speed and wind direction (bivariate); and (iii) the joint distribution of wind speed, wind direction, and air density (multivariate). The latter is a novel contribution of this paper, while the former offers opportunities for validation. Both onshore and offshore wind distributions are estimated using the MMWD model. Recorded wind data, obtained from the North Dakota Agricultural Weather Network (NDAWN) and the National Data Buoy Center (NDBC), is used in this paper. The coupled distribution was found to be multimodal. A strong correlation among the wind condition parameters was also observed.