Wind power forecast error usually has been assumed to have a near Gaussian distribution. With a simple statistical analysis, it can be shown that this is not valid. To obtain a more appropriate probability density function (pdf) of the wind power forecast error, an indirect algorithm based on the Beta pdf is proposed. Measured one-year time series from two different wind farms are used to generate the forecast data. Three different forecast scenarios are simulated based on the persistence approach. This makes the results comparable to other forecast methods. It is found that the forecast error pdf has a variable kurtosis ranging from 3 (like the Gaussian) to over 10, and therefore it can be categorized as fat-tailed. A new approximation function for the parameters of the Beta pdf is proposed because results from former publications could not be confirmed. Besides, a linear approximation is developed to describe the relationship between the persistence forecast and the related mean measured power. An energy storage system (ESS), which reduces the forecast error and smooths the wind power output, is considered. Results for this case show the usefulness of the proposed forecast error pdf for finding the optimum rated ESS power.

A novel method is proposed for designing an energy storage system (ESS) which is dedicated to the reduction of the uncertainty of short-term wind power forecasts up to 48 h. The investigation focuses on the statistical behavior of the forecast error and the state of charge (SOC) of the ESS. This approach gives an insight into the influence of the forecast conditions (horizon, quality) on the distribution of SOC. With this knowledge, an optimized sizing of the ESS can be done with a well-defined uncertainty limit. For this study, one-year time series of power output measurements and forecasts were available for two wind farms. As a reference, different forecast quality degrees are simulated based on a persistence approach. With the forecast data, empirical probability density functions (pdfs) are generated which are the basis of the proposed method. This approach can lead to a considerable reduction of the ESS and provides important information about the unserved energy. This unserved energy represents the remaining forecast uncertainty. As a consequence, the proposed probabilistic method permits the sizing of energy storage systems as a function of the desired remaining forecast uncertainty, reducing simultaneously power and energy capacity.

This paper presents, for the first time, an application of two well-know multiobjective optimization techniques, namely, nondominated sorting genetic algorithm (NSGA) and strength Pareto evolutionary algorithm (SPEA), to the multiobjective design of power distribution systems. These algorithms have been applied to a multiobjective optimization problem with some technical constraints, minimizing the total costs while maximizing the reliability of the power distribution system. The NSGA uses a fitness sharing scheme to achieve diversity among the obtained solutions. In SPEA, it is necessary to apply a reduction procedure because of the number of solutions. For this purpose, a fuzzy c-means (FCM) clustering algorithm has been applied, with this being the first time that an FCM algorithm in the SPEA has been used. The obtained results from both techniques have been compared, concluding that both offer similar efficiency in order to solve the stated multiobjective optimization problem. The developed methodology is applicable to practical cases of design, allowing for additional requirements that the designer imposes