A mixture kernel density model for wind speed probability distribution estimation

Wind speed probability distributions estimated at relevant wind installation sites are widely used in electric power systems to evaluate appropriate wind energy indices in system performance and cost evaluation. An accurate estimation of wind speed probability distribution is essential to the increase of computational accuracy of these indices. To achieve this goal, a new analytical approach designated as the mixture kernel density model is developed. This model can produce highly accurate estimation of wind speed probability distributions. The mixture kernel density function consists of a selected number of kernel densities with weight coefficients. An analytic relation between the weight coefficients and the asymptotic integrated mean squared error is derived and used in the Lagrangian multiplier method to obtain the optimal weight coefficients that minimize the asymptotic integrated mean squared error. As a result, the requirement of choosing an optimal bandwidth in the conventional kernel density models is eliminated. The goodness-of-fit of the proposed mixture kernel density model and six conventional models is assessed on collected wind speed samples using the Chi-square and the Kolmogorov-Smirnov tests. Applicability of the proposed model is demonstrated using six types of wind turbine generators and three major wind energy assessment indices on eight actual wind sites. The results show that the mixture kernel density model is more accurate than other models for wind speed probability distribution estimation. Moreover, the most preferable wind turbine generator and the wind site containing the richest wind resources can be identified using the proposed model.