Prediction of the Conditional Probability Densities of Time Interval Extrema with Application to Risk-Sensitive Scheduling

Abstract

Planning and scheduling activities in the electrical power system, such as the commitment of reserve generation, often involve the statistical characterization of peak demand. Due to the stationarity assumption of classical extreme value analysis (EVA), existing approaches in the industry apply EVA on simulated annual peaks created by weather-dependent surrogate models using Monte-Carlo simulations on a per-scenario basis. In day-ahead scheduling, the daily peak demand changes upon various factors besides temperature, Monte-Carlo experiments become intractable, and state-of-the-art generalized additive model for location, scale and shape (GAMLSS)-based nonstationary EVA is often impractical due to convergence issues on high-dimensional covariates. This article explores uncharted territories and proposes a novel nonstationary EVA estimator that predicts the probable peaks of high-resolution time intervals and their corresponding conditional probability densities based on calendar information and weather conditions where historical peaks are observed. Compared to GAMLSS, our method automatically discovers and robustly models complex relationships between the covariate and the peak demand density. We present a case study on the determination of day-ahead scheduling capacity and demonstrate that compared to the industry approach, our approach results in a 38% reduction in the yearly total committed capacity while maintaining the given risk requirement.

Tasks

Reproductions