Data-driven transient stability analysis using the Koopman operator

We present data-driven methods for power system transient stability analysis using a unit eigenfunction of the Koopman operator. We show that the Koopman eigenfunction with unit eigenvalue can identify the region of attraction of the post-fault stable equilibrium. We then leverage this property to estimate the critical clearing time of a fault. We provide two data-driven methods to estimate said eigenfunction; the first method utilizes time averages over long trajectories, and the second method leverages nonparametric learning of system dynamics over reproducing kernel Hilbert spaces with short bursts of state propagation. Our methods do not require explicit knowledge of the power system model, but require a simulator that can propagate states through the power system dynamics. Numerical experiments on three power system examples demonstrate the efficacy of our method.