Statistical description of the error on wind power forecasts via a Lévy α-stable distribution

As the share of wind power in the electricity system rises, the limited predictability of wind power generation becomes increasingly critical for operating a reliable electricity system. In most operational & economic models, the wind power forecast error (WPFE) is often assumed to have a Gaussian or so-called -distribution. However, these distributions are not suited to fully describe the skewed and heavy-tailed character of WPFE data. In this paper, the Lévy -stable distribution is proposed as an improved description of the WPFE. Based on 6 years of historical wind power data, three forecast scenarios with forecast horizons ranging from 1 to 24 hours are simulated via a persistence approach. The Lévy -stable distribution models the WPFE better than the Gaussian or so-called -distribution, especially for short term forecasts. In a case study, an analysis of historical WPFE data showed improvements over the Gaussian and -distribution between 137 and 567% in terms of cumulative squared residuals. The method presented allows to quantify the probability of a certain error, given a certain wind power forecast. This new statistical description of the WPFE can hold important information for short term economic & operational (reliability) studies in the field of wind power.