In the modern power systems, where integration of converter-based renewable energy sources (like wind and solar) is rapidly increasing and the load demands have become highly dynamic, maintaining stability has become a crucial concern.

Traditional Optimal Power Flow (OPF) algorithms focus primarily on steady state objectives, requiring additional post small-signal stability analysis. This is not only computationally extensive, but also, in case of instability detection, requires mitigation actions with cost implications. The paper proposes a unified, single step framework that integrates small signal stability constraints directly into Optimal Power Flow (OPF) formulation utilizing regression-based machine learning (ML) approach. Use of an appropriate machine learning technique minimizes the computational complexity associated with conventional analytical methods, especially in high dimensional grid configurations, which makes this approach potentially more scalable.

The paper will present a comprehensive methodology required offline (before using in the operation) and results from validation on the IEEE 9-bus AC system. To construct a robust training dataset, Latin Hypercube Sampling (LHS) technique is leveraged to generate several samples of operating conditions across the entire operating space. This is essential to ensure the regression model is trained across a wide range of system conditions. Conventional AC OPF is run on the samples using a specific objective function to obtain the operationally feasible points. Small signal stability of the samples is investigated using a MATLAB based tool which yields the eigenvalues of the system considering these operating points and the dynamic parameters of the synchronous generators and inverter-based resources (IBRs). The output is a numeric damping-ratio based stability index.

Feature selection is performed based on operating conditions and stability indices using several ML algorithms to identify the most significant input features. Multiple non-linear regression models like polynomial regression and symbolic regression are evaluated quantitatively and qualitatively. The performances of the models are compared based on the root mean squared errors (RMSE) and the number of false stabilities and instabilities obtained. Polynomial regression with Lasso (L1) regularisation is found to offer the best trade-off between the prediction accuracy and the complexity of the analytical function obtained. Incorporating sample weights during model training further improves the prediction accuracy, especially near the stability boundaries.

The paper will present the methodology, validation process, and performance parameters of the proposed model on unseen test data. The approach intends to obtain small signal stable and optimal solutions under varied operating scenarios for the tested grid configuration.