Koopman mode analysis of very large datasets: Numerical experience

The increase in both, the volume (dimensionality), and the complexity and variety of measured data, requires advances in methodology to systematically extract the important dynamical motions from the observed dynamic trajectories. In this paper, methods for analysis or large volumes of data based on Koopman mode analysis (KMA) are investigated. Three specific methods are compared and tested: Koopman mode decomposition (KMD), Dynamic Mode Decomposition (DMD), and multi-channel Prony analysis. The methods are implemented and compared in terms of their ability to accurately estimate power system electromechanical modes. Numerical aspects associated with application of these approaches are investigated and recommendations for improving the analysis tools are provided. Case studies arising from the analysis of transient stability swings are presented. The efficiency and accuracy of the methods is demonstrated by comparison to other multivariate techniques.