Mitigating impact of spatial variance of turbulence in wind energy applications

Abstract

Abstract. For the first time an analytical solution for the quantification of the spatial variance of the second-order moment of correlated wind speeds was developed in this work. The spatial variance is defined as random differences in the sample variance of wind speed between different points in space. The approach is successfully verified using simulation and field data. The impact of the spatial variance on three selected applications relevant to the wind energy sector is then investigated including mitigation measures. First, the difference of the second-order moment between front-row wind turbines of Lillgrund wind farm is investigated. The variance of the difference ranges between 25 % and 48 % for turbulence intensities ranging from 7 % to 10 % and a sampling period of 10 min. It is thus suggested to use the second-order moment measured at each individual turbine as input to flow models of wind farm controllers in order to mitigate random error. Second, the impact of the spatial variance of the measured second-order moment on the verification of wind turbine performance is investigated. Misalignment between the mean wind direction and the line connecting the meteorological mast and wind turbine is observed to result in an additional random error in the observed second-order moment of wind speed. In the investigated conditions the random error was up to 34 %. Such a random error adds uncertainty to the turbulence intensity-based classification of the fatigue loads and power output of a wind turbine. To mitigate the random error, it is suggested to either filter the measured data for low angles of misalignment or quantify wind turbine performance using the ensemble-averaged measurements of the same wind conditions. Third, the verification of sensors in wind farms was investigated with respect to the impact of distant reference measurements. In the case of a misalignment between the wind direction and the line connecting sensor and reference, an increased random error will hamper the comparison of the measured second-order moments. The suggested mitigation measures are equivalent to those for the verification of turbine performance.