In modern power systems, the increasing integration of converter-based renewable energy sources and dynamic load behaviors necessitates real-time assessment of small-signal stability. Traditional stability analysis could be computationally intensive for real-time applications. This paper proposes a methodology to evaluate small-signal stability based on operating conditions using a regression model that correlates a damping-ratio-based stability index to system parameters via polynomial regression. The resulting polynomial function is designed to serve as an additional constraint in a unified single-step small-signal stability-constrained optimal power flow (S3C-OPF) formulation, enabling stable and optimal solutions. To ensure compatibility with optimal power flow (OPF) solvers, the model is constructed to be convex, continuous, and twice-differentiable. A multi-stage regression approach is employed: the first stage fits a polynomial model, and the second enforces convexity through eigenvalue clipping and linear regression. The training dataset is generated using Latin Hypercube Sampling, followed by OPF computations to ensure operational feasibility. The methodology is validated on a modified IEEE-9 bus AC system. Results show high prediction accuracy, with root mean squared error (RMSE) of 0.04 and misclassification rates below 1%. Convexification preserves model accuracy, while ensuring convergence when integrated into an OPF framework. The proposed approach could be utilized for real-time operations and replace computationally intensive simulations during real-time operations.
Agrawal et al. (Sun,) studied this question.