Wind Velocity Vertical Extrapolation by Extended Power Law

Wind energy gains more attention day by day as one of the clean renewable energy resources. We predicted wind speed vertical extrapolation by using extended power law. In this study, an extended vertical wind velocity extrapolation formulation is derived on the basis of perturbation theory by considering power law and Weibull wind speed probability distribution function. In the proposed methodology not only the mean values of the wind speeds at different elevations but also their standard deviations and the cross-correlation coefficient between different elevations are taken into consideration. The application of the presented methodology is performed for wind speed measurements at Karaburun/Istanbul, Turkey. At this location, hourly wind speed measurements are available for three different heights above the earth surface. 1. Introduction Wind energy, as one of the main renewable energy sources in the world, attracts attention in many countries as the efficient turbine technology develops. Wind speed extrapolation might be regarded as one of the most critical uncertainty factor affecting the wind power assessment, when considering the increasing size of modern multi-MW wind turbines. If the wind speed measurements at heights relevant to wind energy exploitation lacks, it is often necessary to extrapolate observed wind speeds from the available heights to turbine hub height [1], which causes some critical errors between estimated and actual energy output, if the wind shear coefficient, , cannot be determined correctly. The difference between the predicted and observed wind energy production might be up to 40%, due to turbulence effects, time interval of wind data measurement, and the extrapolation of the data from reference height to hub heights [2]. In the literature, the wind shear coefficient is generally approximated between 0.14 and 0.2. However, in real situations, a wind shear coefficient is not constant and depends on numerous factors, including atmospheric conditions, temperature, pressure, humidity, time of day, seasons of the year, the mean wind speed, direction, and nature of terrain [3–6]. Table 1 demonstrates the various wind shear coefficients for different types of topography and geography [3]. Table 1: Wind shear coefficient of various terrains [ 3]. According to the calculations of wind resource analysis program (WRAP) report, in 39 different regions, out of 7082 different wind shear coefficients, 7.3% are distributed between 0 and 0.14 and 91.9% above 0.14, while 0.8% are calculated as negative [7], due to the measurements error.