A Gradient-Based Capacity Accreditation Framework in Resource Adequacy: Formulation, Computation, and Practical Implications

TL;DR

This paper introduces a gradient-based framework for capacity accreditation in resource adequacy, unifying ELCC and MRI methods, and demonstrates significant computational speedups and robustness improvements through advanced analysis and algorithms.

Contribution

It formulates capacity accreditation as a gradient-based approach, unifies ELCC and MRI, and develops efficient algorithms with large-scale validation for power system applications.

Findings

Gradient-based accreditation unifies ELCC and MRI.

Infinitesimal perturbation analysis speeds up gradient estimation by up to 1000x.

MRI offers faster and more robust capacity assessment than ELCC.

Abstract

Probabilistic resource adequacy assessment is a cornerstone of modern capacity accreditation. This paper develops a gradient-based framework, in which capacity accreditation is interpreted as the directional derivative of a probabilistic resource adequacy metric with respect to resource capacity, that unifies two widely used accreditation approaches: Effective Load Carrying Capability (ELCC) and Marginal Reliability Impact (MRI). Under mild regularity conditions, we show that marginal ELCC and MRI yield equivalent accreditation factors, while their numerical implementations exhibit markedly different computational characteristics. Building on this framework, we demonstrate how infinitesimal perturbation analysis enables up to a $1000\times$ speedup in gradient estimation for capacity accreditation, and we implement gradient-informed search algorithms that significantly accelerate ELCC computations relative to standard bisection methods. Large-scale Monte Carlo experiments show that MRI achieves substantial runtime reductions compared to ELCC and exhibits greater robustness to perturbation step-size selection. These results provide practical guidance for implementing efficient and scalable capacity accreditation in large-scale power systems.