Frequency-Constrained UC via Second-Order ODEs with ML Surrogates

Abstract

This paper proposes a fast and interpretable framework for frequency-constrained unit commitment (FCUC) using machine-learning (ML) surrogates. Unlike prior studies that rely on proprietary system-frequency-response tools, we use an open-source second-order differential equation (SODE) model to simulate generator outages, generating a 117000 -scenario dataset. Three linear classifiers -Logistic Regression (LR), Linear Discriminant Analysis (LDA), and a log-loss Stochastic-Gradient-Descent model (SGD-Log)-are trained on this dataset and inserted as linear constraints in a mixed-integer UC model to enforce frequency adequacy. The surrogates detect ≥98.8 % of unsafe operating points (≤32 false negatives) while training in only 0.1 s to 2.3 s. Applied to a spring-week case study on the La Palma island system, they uphold a strict -3 Hz nadir limit, achieve average nadirs of -1.23 Hz to -1.31 Hz, compared with -1.41 Hz in the unconstrained base case, and raise weekly cost by no more than 1.3 % above that baseline. Also, in comparison with a first-order differential equation (FODE) model, the SODE-ML formulations solve 40−390× faster (12.2s to 101.4s vs. 4767s) without linearisation assumptions. These results demonstrate that reproducible, SODE-labelled surrogates enable secure and computationally efficient FCUC for low-inertia grids.

This paper proposes a fast and interpretable framework for frequency-constrained unit commitment (FCUC) using machine-learning (ML) surrogates. Unlike prior studies that rely on proprietary system-frequency-response tools, we use an open-source second-order differential equation (SODE) model to simulate generator outages, generating a 117000 -scenario dataset. Three linear classifiers -Logistic Regression (LR), Linear Discriminant Analysis (LDA), and a log-loss Stochastic-Gradient-Descent model (SGD-Log)-are trained on this dataset and inserted as linear constraints in a mixed-integer UC model to enforce frequency adequacy. The surrogates detect ≥98.8 % of unsafe operating points (≤32 false negatives) while training in only 0.1 s to 2.3 s. Applied to a spring-week case study on the La Palma island system, they uphold a strict -3 Hz nadir limit, achieve average nadirs of -1.23 Hz to -1.31 Hz, compared with -1.41 Hz in the unconstrained base case, and raise weekly cost by no more than 1.3 % above that baseline. Also, in comparison with a first-order differential equation (FODE) model, the SODE-ML formulations solve 40−390× faster (12.2s to 101.4s vs. 4767s) without linearisation assumptions. These results demonstrate that reproducible, SODE-labelled surrogates enable secure and computationally efficient FCUC for low-inertia grids.