A continuous bivariate model for wind power density and wind turbine energy output estimations

The wind power probability density function is useful in both the design process of a wind turbine and in the evaluation process of the wind resource available at a potential site. The continuous probability models used in the scientific literature to estimate the wind power density distribution function and wind turbine energy output assume that air density is independent of the wind speed. A constant annual value for air density of 1.225 kg m-3, corresponding to standard conditions (sea level, 15 oC), is generally used. A bivariate probability model (BPM) is presented in this paper for wind power density and wind turbine energy output estimations. This model takes into account the time variability of air density and wind speed, as well as the correlation existing between both variables. Contingency type bivariate distributions with specified marginal distributions have been used for this purpose. The proposed model is applied in this paper to meteorological data (temperature, pressure, relative humidity, wind speed) recorded over a one year period at a weather station located at the facilities of the Technological Institute of the Canary Islands (Spain). The conclusion reached is that the BPM presented in this paper is more realistic than the univariate probability models (UPMs) normally used in the scientific literature. In the particular case under study, and for all the situations analysed, the BPM has provided values for the annual mean wind power density and annual energy output of a wind turbine that fit the sample data better than the UPMs. However, as a result of the climatological characteristics of the area where the analysis was performed, the results do not differ notably from those obtained through the use of a UPM and the mean air density of the area