Methods to extrapolate wind resource to the turbine hub height based on power law: A 1-h wind speed vs. Weibull distribution extrapolation comparison

Abstract

Abstract An accurate wind shear model is crucial to extrapolate the observed wind resource from the available lower heights to the steadily increasing hub height of modern wind turbines. Among power law (PL) and logarithmic law (LogL), i.e., the two most commonly used analytical models, the former was found to give a better representation of wind speed profiles and thus set as the reference model addressed by the present study. As well as commonly used for vertical extrapolation of 1-h wind speed records, the PL wind profile was proved to be consistent with the Weibull wind speed distribution. As a matter of fact, Justus and Mikhail suggested being more useful to deal with the full range of wind speed, such as required to specify the wind speed probability distribution, rather than using the “instantaneous” records. Therefore, in this work a comparison is proposed between these two PL–based extrapolation approaches to the turbine hub height, not only in terms of wind resource and energy yield computation skill, but also of simplicity and usefulness: (i) extrapolation of 1-h wind speed records, and (ii) extrapolation of the Weibull distribution. In particular, the models of Smedman–Hogstrom and Hogstrom (SH) and Panofsky and Dutton (PD) were used to approach (i), while those from Justus and Mikhail (JM) and Spera and Richards (SR) to approach (ii). In addition, a comparison of models in estimating wind shear coefficient was carried out. PL extrapolation models have been tested over a coastal and complex–topography location in Tuscany, Italy, where thus the role played by atmospheric stability and surface roughness (z0), as well as their variability with time and wind characteristics, required to be deeply investigated. A 5-year (1997–2001) 1-h dataset, including wind measurements at 10 and 100 m, has been used. Starting from 10-m wind speed observations, the computation of 100–m extrapolated wind resource, Weibull distribution and energy yield has been made, where the latter was performed once a site most efficient 100–m hub height turbine was detected and then applied.