Ensemble-Based Peak Demand Probability Density Forecasting with Application to Risk-Aware Power System Scheduling

TL;DR

The paper tackles the challenge of forecasting the probability density of short-term peak power demand under nonstationary conditions. It introduces an ensemble-based framework that combines tree-structured partitioning with nonstationary generalized extreme value modeling to automatically modulate GEV parameters as covariates change. Through both a synthetic application and a real-world PJM case study, the method demonstrates superior tail calibration and substantial reductions in committed capacity (up to 38%) while maintaining reliability, compared with parametric and non-parametric benchmarks. The approach yields actionable risk metrics, such as daily EUE and VaR/CVaR-based capacity targets, enabling risk-aware capacity planning in high-renewable, volatile energy systems.

Abstract

Power systems face increasing challenges in maintaining resource adequacy due to lower operating margins, rising renewable energy uncertainty, and demand variability. Forecasting the probability distribution of peak demand on shorter timescales is a critical forward-facing issue under increasing volatility. This study introduces a novel ensemble-based machine learning method for peak demand probability density forecasting that extends classical extreme value theory to model time series peaks as nonstationary statistical distributions. The approach employs an ensemble of tree-based learners that recursively partition the covariate space and estimate local generalized extreme value distributions, allowing it to automatically capture complex covariate-dependent parameter variations. Unlike existing approaches, which often suffer from convergence issues or restrictive functional forms, this framework is both flexible and robust. Validation on a case study based on the PJM interconnection demonstrates that the method achieves a 38 percent reduction in committed capacity when generation is scheduled based on a reliability criterion. These improvements provide practical value for power system operation, enabling risk-aware capacity scheduling under peak demand uncertainty and supporting reliability-driven decision making in future energy systems.

Figures (18)

• Figure 1: Research workflow. DoE---Department of Energy.
• Figure 2: Sub-interval observations, interval maxima, and the predicted conditional probability density of the interval maximum.
• Figure 3: Example use case. The predictions are in the form of a conditional daily peak distribution $y \sim \text{GEV}(\hat{\boldsymbol{\theta}}|\boldsymbol{x})$ that is updated at every hour. The covariate elements and results in the artwork are examples intended to illustrate the mechanics of the proposed method and not to be taken as prescriptive implementation advice. GEV---generalized extreme value distribution.
• Figure 4: Ensemble fitting through bootstrapping, also known as resampling with replacement.
• Figure 5: Structure of one of the conditional estimators created during fitting. The artwork is intended to illustrate the fitting procedure. Deeper nodes are not shown to conserve ink.