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.

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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.Index Terms-Energy storage sizing, probability density function, short-term forecast error, state of charge, wind power.