Pratishtha Shukla | Search arXiv

arXiv2026

Dynamic Operational Reserve Margin Assessment from Risk-Constrained Unit Commitment States

We propose Dynamic Reserve Margin (DRM) as a time-varying operational adequacy metric derived from risk-constrained unit commitment (RCUC) states. DRM quantifies reserve adequacy using the additional generation capacity that committed generators can provide within a 5-minute response window relative to uncertainty and contingency reserve requirements. We introduce a complementary Reserve Risk Envelope (RRE) metric to quantify operational reserve headroom in directly interpretable MW terms. A low-margin duration metric is further developed to quantify the persistence of reserve stress over an operating horizon. We use an IEEE 14-bus example to illustrate these concepts, followed by large-scale RCUC case studies under multiple operating scenarios. Results demonstrate that reserve requirements and ramp-accessible reserve capability can vary substantially across operating conditions, and that commitment decisions adapt to maintain reserve adequacy under changing system conditions. The proposed DRM and RRE metrics provide an interpretable operational characterization of reserve adequacy, reveal reserve accessibility and stress persistence that are not captured by conventional reserve margin metrics.

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arXiv2026

Finite-Sample Limits of Entropy-Based Structure Identification in Discretized Nonlinear Systems

Discretization fundamentally limits structure identification in stochastic systems. When system stochasticity exceeds the discretization resolution, entropy-based methods lose their ability to distinguish which input drives the output. We study this in Fuzzy Inductive Reasoning (FIR), a nonparametric framework for learning dynamical systems from discretized measurements, where the choice of input variables determines both predictive accuracy and the interpretability of the learned input--output relationships. Entropy-based selection targets explainability, i.e., identifying which variables causally drive the output, while mean-squared-error-based selection targets prediction. We introduce a resolution-stochasticity ratio that governs when entropy-based selection is reliable. Three results follow. First, entropy-based selection is consistent below this threshold but loses discriminative power above it, regardless of sample size. Second, using the entropy-selected variables for prediction instead of the MSE-selected ones incurs a closed-form excess prediction risk that grows with input complexity and shrinks with sample size. Third, reliable identification of the causally relevant inputs requires data that scales with the number of input combinations and inversely with the strength of the entropy signal. The theory is validated on a two-state Markov model and demonstrated on a distribution grid reliability dataset analyzing the impact of infrastructure investment, where the goal is to explain which investments drive reliability improvements rather than merely predict outcomes.

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