Comparison of calculation methods for wind shear exponent in complex terrain at altitude above 1000 meters

Abstract: Among all uncertainty factors affecting the wind power assessment at a site, wind speed extrapolation is probably one of the most critical, particularly if considering the increasing of the size of modern multi-Megawatt wind turbines, and therefore of their hub height. Wind measurements are generally performed below wind turbine hub heights due to avoiding higher measurement and tower costs. In order to obtain the wind speed at the hub height of the turbine, the measurements are extrapolated, assuming that the wind shear exponent is constant. So it is important to calculate the wind shear exponent accurately. The wind shear exponents of different areas are different because of the influence of roughness. What's more, the wind shear exponent may change in the same area at different time. Therefore, to obtain an accurate value of the wind shear exponent in a certain area at a certain time, only the local wind speed data can be used to calculate it. Here, the situation is set as some complex terrain above 1000 meters. There are many different methods to calculate the wind shear exponent, and in this paper, four different methods are chosen, which are: the Panofsky and Dutton (PD) method, annual average wind speed method, wind profile method and all of the data method. The PD method is based on Monin-Obukhov similarity theory, and Panofsky and Dutton proposed the semiempirical formulation to estimate the wind shear exponent as a function of stability and roughness. First of all, according to the classification method of Pasquill, the stability can be calculated. Then, choose the right formulation based on the value of stability to calculate the wind shear exponent. Method 2 and 4 use the wind speed and the exponential formula to calculate wind shear exponent. Method 3 uses wind profile fitting to calculate the wind shear exponent. Choose the example of actual wind speed data within a complete year on three wind measurement heights at an anemometer tower of some complex terrain above 1000 meters in Hunan Province. Four different results of the wind shear exponent can be calculated. Thus, the wind speed at the known height can be extrapolated through the power law, then by comparing the extrapolated value and actual value, the methods which produce smaller errors can be chosen. The results show that due to the impact of ground roughness and the topography, wind shear exponents are different not only in different areas, but also when calculated by different methods even in the same area at the same time. And the results calculated by the PD method and the annual average wind speed method are more accurate than the all of the data method and wind profile method. The PD method is more accurate than the annual average wind speed method, and the results are very close. The result calculated by using all of the data is better than using the wind profile, while the wind profile method is the most accurate in flat topography. Therefore, these methods should be comprehensively used to choose the most accurate wind shear exponent.