Estimation of Weibull parameters in winds speed mixture using nonlinear optimization for wind energy applications

Abstract

Climate change and global warming are problems need to be tackled on a priority basis. The greenhouse gas (GHG) emissions and air pollution must be reduced by 25% and 40% compared to 1990 levels in 2020 and a reduction between 80% and 95% by 2050. To mitigate the GHG emissions, countries have adopted policies to use renewable energy sources. In the case of wind energy, the statistical analysis of wind data is a crucial stage for estimating the wind turbine energy output through the turbine performance. The Weibull distribution has been widely used in the recent years for describing the behavior of the wind speed and it can be treated as a probability density function. Herein, it is presented a new method for calculating the Weibull parameters of an infinity sum of Weibull distributions. This new method is based on a Hilbert space generated by scale and form factor as Fredholm integral. This new method is named Inversion of the Weibull Distribution in wind speed mixture (IWeD). The simulations results indicate that IWeD is adequate for estimating the Weibull parameters when the wind speed is composed of several Weibull distributions.