Data-driven Koopman Theory for Transient Stability and Safety Analysis of Power Systems with Renewable Penetration

Abstract

This dissertation presents a novel approach to analyzing and controlling nonlinear systems using the Koopman operator framework and data-driven methods. Nonlinear power systems, characterized by complex behaviors and sensitivity to initial conditions, pose significant challenges for stability and safety assessment, especially during transient events. The first part of this work focuses on reachability analysis using the spectral properties of the Koopman operator. By leveraging eigenfunctions extracted from sampled trajectory data, the approach computes forward and backward reachable sets efficiently, even in high-dimensional nonlinear systems, without requiring dense state-space sampling. This method is validated through numerical examples, demonstrating its ability to recover nonconvex reachable sets in both stable and unstable regimes. Building on this, the dissertation develops a Koopman spectrum-based method for identifying stability boundaries in nonlinear systems. This method, applied to power system models, enables accurate computation of critical clearing times and transient stability analysis by constructing unstable eigenfunctions through a path integral formulation. Finally, the dissertation addresses voltage safety under renewable generation uncertainty. A data-driven Koopman-based model is constructed using Extended Dynamic Mode Decomposition (EDMD), and a control barrier function is synthesized to enforce voltage safety. The resulting formulation is posed as a constrained optimization program, through which the minimum rated power capacity is computed to ensure safe operation across all disturbance scenarios. The proposed methodologies provide scalable, data-driven tools for stability analysis and safe control in nonlinear systems, with practical applications in power system analysis and control