Bivariate probability models for the description of average wind speed at two heights

Abstract

Two bivariate density functions, the Rayleigh-shifted Rayleigh and the Rayleigh-normal are developed for use in modeling wind speed at two different heights. Using data from the Millstone nuclear power plant in Waterford, Connecticut, it is then shown that the Rayleigh-normal is a more appropriate model. The problem of estimating annual energy from a wind energy conversion system at one height using wind speed data from a lower height is then discussed. It is shown that the use of the Rayleigh distribution with a one-seventh wind shear coefficient underestimates energy production when compared to the use of the Rayleigh-normal. It is also shown that the use of higher wind shear coefficients results in overestimates of energy. These results were derived for a typical range of wind shear coefficients employed in conjunction with a one-parameter Rayleigh distribution.