arXiv subjects

Gord Stephen

Publications and source records attributed to Gord Stephen.

3 recordsLinked to original sources

arXiv2026

On the Convexity of Common Resource Adequacy and Capacity Accreditation Metrics

Many emerging capacity expansion optimization formulations implicitly presume the convexity (or concavity) of power system adequacy risk (or capacity accreditation) metrics. These assumptions have yet to be formally justified. We present concise mathematical proofs validating the claim for certain metrics (expected unserved energy and effective load carrying capability), but also provide simple invalidating counterexamples for others (loss-of-load expectation and equivalent firm capacity). Formulations built on non-convex (non-concave) metrics structurally undervalue candidate portfolio adequacy, and so cannot claim to produce least-cost expansion plans.

eess.SY↗

arXiv2026

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

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.

eess.SY↗

arXiv2024

Generation Expansion Equilibria with Predictive Dispatch Model

This paper proposes a methodology to solve generation expansion equilibrium problems by using a predictive model to represent the equilibrium in a simplified network constrained electricity market. The investment problem for each generation company (Genco) is a bi-level problem with the investment decision made in the upper level and market clearing condition in the lower level, which traditionally is represented as a Mathematical Program with Equilibrium Constraint (MPEC). The predictive model is trained for estimating the system-wide revenues for each technology type across energy, ancillary services and capacity markets given the amount of technology-specific installed capacity on the grid. The profit maximization investment problem for each Genco is solved using a global search algorithm, which uses the predictive model to evaluate the objective function. To solve for the strategic equilibrium, each Genco's problem is plugged into a diagonalization algorithm that is generally used in multi-leader, single-follower bi-level problems. The methodology presented here enables significant computational improvements while still capturing the desired market characteristics and dynamics of traditional equilibrium modeling approaches

eess.SY↗