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

TL;DR

This paper introduces a mathematical model based on extreme value theory to accurately predict peak loads for large non-residential electricity consumers, simplifying existing methods while validating their heavy-tailed nature.

Contribution

It develops a new extreme value theory-based model for peak load distribution, reducing complexity and validating the heavy-tailed characteristics of the data.

Findings

Peak load distribution belongs to the heavy-tailed Fréchet class.

The model reduces to four parameters without losing predictive accuracy.

Quantile VF effectively captures peak load distribution.

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.