Input Convex Neural Network as a Surrogate in Stability-Constrained Optimization for IBR-dominated Power Systems
For researchers and practitioners in power system optimization, this work clarifies critical pitfalls in embedding ICNN-based stability constraints, enabling correct and efficient optimization formulations.
The paper identifies and corrects two formulation errors in using input convex neural networks as surrogates for stability constraints in power system optimization, providing exact LP-based and outer-approximation schemes that preserve convexity and global convergence guarantees. Simulations on IEEE 14- and 118-bus systems demonstrate the effectiveness of the proposed corrections.
Input convex neural networks (ICNNs) are increasingly used as surrogates for stability indices and embedded as constraints in power-system optimization. This letter clarifies two recurring formulation limitations that can negate ICNN convexity benefits: (i) applying generic Big-$M$ mixed-integer reformulations introduces auxiliary binaries that are unnecessary for enforcing ICNN sublevel constraints; and (ii) reversing the stability inequality transforms a convex sublevel set into a generally nonconvex superlevel set, invalidating global-convergence guarantees of cut-based methods. After clarifying the limitations, we provide (i) an exact LP-based epigraph reformulation for ReLU-ICNNs, (ii) an outer-approximation scheme with global guarantees under the sublevel convention, and (iii) a feasibility-preserving inner-approximation scheme for the superlevel convention, with simulations on IEEE 14- and 118-bus unit commitment instances.