A semi-parametric trivariate model of wind speed, wind direction, and air density for directional wind energy potential assessment

Given that wind speed, wind direction, and air density, which determine the magnitudes of energy factors, are dependent, modelling the joint distribution of the three variables is essential for directional wind energy potential assessment. In this study, a semi-parametric trivariate model was proposed based on the vine copula theory. Under this framework, the mixture distributions were utilized to fit the marginal distributions of wind speed, wind direction, and air density, the Johnson-Wehrly model was employed to model the bivariate distributions of circular-linear variables, and the non-parametric copula was used to describe the complex relationship between wind speed and air density. Additionally, two effective procedures for bivariate and trivariate random number generation were designed. To verify the proposed model, thirty-year of hourly wind data at eight positions along the Chinese coastline were adopted. Results demonstrate that the trivariate distribution characteristics of both total and seasonal data can be accurately captured by the proposed model. Especially, the cyclicity of wind direction is guaranteed in the constructed models. Furthermore, based on the trivariate models, the directional wind energy potential assessment was performed and the influence of directional air density on the estimation of energy factors was quantified.