Linear constraints with critical region refinement for frequency stability-constrained optimisation

The growing adoption of renewables in modern power grids has made security-constrained generator dispatch more important than ever. However, introducing non-linear stability constraints significantly increases its complexity, often making it much harder to solve while meeting essential efficiency requirements for practical applications. To address this, linear models are typically used to approximate nonlinear stability constraints. Among these, deep neural networks have shown promise due to their adaptability and ability to be linearised. However, such linear approximations involve a trade-off in accuracy and convergence, especially where the stability boundary is highly nonlinear. While this limitation is commonplace among all linearised constraints, in this paper, we present a technique to refine and enhance the performance of these constraints, especially in the critical region, that is, near the stability boundary, without significant loss of generality across the entire stability space. Using multiple scenarios on the modified IEEE 39 Bus network, we demonstrate that the proposed approach outperforms standard linear regression-based constraints, including those trained specifically on critical region data. Ultimately, our method reduces the risk of stability violations resulting from false indications seen by the solver.