Using extreme value theory for the estimation of risk metrics for capacity adequacy assessment

TL;DR

This paper applies extreme value theory to model demand-net-of-wind for capacity adequacy, demonstrating its effectiveness in estimating risk metrics with less uncertainty compared to traditional methods.

Contribution

It introduces the use of the peaks over threshold approach of extreme value theory for demand-net-of-wind modeling without assuming dependence, validated on Great Britain data.

Findings

Extreme value theory yields similar risk estimates with less sampling uncertainty.

Assuming independence can lead to over- or under-estimation of risk metrics.

Method outperforms empirical distribution in uncertainty reduction.

Abstract

This paper investigates the use of extreme value theory for modelling the distribution of demand-net-of-wind for capacity adequacy assessment. Extreme value theory approaches are well-established and mathematically justified methods for estimating the tails of a distribution and so are ideally suited for problems in capacity adequacy, where normally only the tails of the relevant distributions are significant. The extreme value theory peaks over threshold approach is applied directly to observations of demand-net-of-wind, meaning that no assumption is needed about the nature of any dependence between demand and wind. The methodology is tested on data from Great Britain and compared to two alternative approaches: use of the empirical distribution of demand-net-of-wind and use of a model which assumes independence between demand and wind. Extreme value theory is shown to produce broadly similar estimates of risk metrics to the use of the above empirical distribution but with smaller sampling uncertainty. Estimates of risk metrics differ when the approach assuming independence is used, especially when data across different historical years are pooled, suggesting that assuming independence might result in the over- or under-estimation of risk metrics.