Abstract:
South Africa has great potential for considering wind energy as an alternative resource.
The climatology allows for significant wind energy production. An accurate joint description of
the wind speed (linear) and wind direction (circular) characteristics is important for wind farm
development. In this paper, a bivariate class of flexible joint probability density functions of wind
speed and wind direction for the use in wind energy analysis is presented. This joint model accounts
for bimodality, skewness, and a dependency structure between the wind speed and wind direction.
For the joint probabilistic description of the wind speed and wind direction, special cases of this
bivariate class are evaluated, namely the semi-parametric Möbius model on the disc, the Möbius
distribution on the disc, and the Beta type III Möbius distribution on the disc. These three special
cases are applied to wind speed and wind direction data recorded every ten minutes at two locations
in South Africa. Evaluation of the models is based on three different information criteria and
normalized deviation. Overall, the semi-parametric model is superior to the parametric models based
on the performance measures. The wind energy potential at the two locations is evaluated using the
semi-parametric model.
