Extreme value distributions of peak loads for non-residential customer segments

Abstract

Electrical grid congestion is a growing challenge in Europe, driving the need for accurate prediction of load, particularly of peak load. Non-time-resolved models of peak load offer the advantages of simplicity and compactness, and among them, Velander's formula (VF) is a traditional method that has been used for decades. Moreover, VF can be adapted into a quantile VF, which learns a truncated cumulative distribution function of peak load based on electricity consumption. This paper proposes a mathematical model based on extreme value theory to characterize the probability distribution of peak load for large non-residential customers. The model underpins the quantile VF as demonstrated through multiple quantile regression and reduces its representation to just four parameters without sacrificing predictive performance. Moreover, using maximum likelihood estimation and the likelihood ratio test, we validate that the probability distribution of peak load of analysed groups belongs to the heavy-tailed Fr\'echet class.