Nonlinear Koopman Observability Measures on Subsets of Power System State Variables

Abstract

Recently, the perturbed Koopman mode analysis (PKMA) was proposed for analyzing oscillations arising from power system models under stressed operating conditions, using both linear and nonlinear Koopman eigenfunctions. A question of current interest is how one can use the information provided by these PKMA models to complement and enhance estimations obtained through data-driven Koopman operator-based approaches. Motivated by this question, in this paper we derive nonlinear Koopman measures of observability for a third-order PKMA model to assess the most dominant global dynamics underlying a selected set of observables. These nonlinear measures are generic by formulation; however, the focus is on a subset of the state variables of a power system. With the selected observables, we illustrate the usefulness of our approach in identifying a relatively small subset of dominant Koopman modes that closely mimic the global dynamical behavior. We validate our results on a test system, followed by a comparison with the extended dynamic mode decomposition (EDMD). The simulations demonstrate how the proposed model-based approach is complementary to these data-driven approaches. Utility of this method for model-order reduction, wide-area monitoring, and optimal sensor placement are also highlighted.