A Statistical Description of the Error on Wind Power Forecasts for Probabilistic Reserve Sizing

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 power system reliably. In most operational and economic models, the wind power forecast error (WPFE) is often assumed to follow a Gaussian or the so-called $\betab$ -distribution. However, these distributions might not be suited to fully describe the skewed and heavy-tailed character of WPFE data. In this paper, the Levy $\alphab$ -stable distribution is proposed as an improved description of the WPFE. The method presented allows us to quantify the probability of a certain error, given a certain wind power forecast. Based on recent historical wind power data, the feasibility of the Levy $\alphab$ -stable distribution as a WPFE description is demonstrated. The added value of this improved statistical model of the WPFE is illustrated in a state-of-the-art probabilistic reserve sizing method. Results show that this new statistical description of the WPFE can hold important information for short-term economic and operational (reliability) studies for power systems with a significant wind power penetration.