Frequency-Constrained Unit Commitment Using SODE-Labelled Affine Surrogates

Abstract

Frequency nadir is one of the most informative indicators of post-contingency frequency security, but embedding it in frequency-constrained unit commitment (FCUC) remains challenging because nadir relations are nonlinear, non-convex, and are often introduced through computationally burdensome analytical approximations. This paper develops a scalable, opensource workflow for FCUC in which nadir security is enforced through calibrated affine surrogates learned from a secondorder differential equation (SODE) model while preserving unitcommitment mixed-integer linear programming (MILP) structure. The study employs Adaptive Latin Hypercube Sampling (A-LHS) to generate UC-relevant operating points, thereby avoiding exhaustive grid search, and are labelled using the opensource SODE model that captures dynamic effects neglected by simplified first-order formulations. Probability-calibrated linear surrogates are then embedded directly into UC through a common affine inequality, with conservatism controlled by an operator-selected probability threshold. The study focuses on the IEEE RTS-96 system under the largest contigency event of 400MW and positions this benchmark as an extension of our earlier smaller-system study to a materially larger test system. Results show that the analytical first-order formulation remains systematically optimistic against the SODE model. Also the SODE-trained surrogates show a much stronger security performance with modest cost impact and substantially lower computational burden.