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Working paper / Energy

Statistical Description of the Error on Wind Power Forecasts via a Lévy α-stable Distribution

Author(s): BRUNINX Kenneth, DELARUE Erik, D'HAESELEER William

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ABSTRACT

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 β-distribution. However, these distributions are not suited to fully describe the skewed and heavy-tailed character of WPFE data. In this paper, the L´evy α-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 L´evy α-stable distribution models the WPFE better than the Gaussian or so-called β-distribution, especially for short term forecasts. In a case study, an analysis of historical WPFE data showed improvements over the Gaussian and β-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.