Nonlinear Power System Analysis Using Koopman Mode Decomposition and Perturbation Theory

A new model-based framework for studying nonlinear dynamic behavior of stressed power systems that combines Koopman mode analysis and perturbation theory is proposed. First, a systematic approach to deriving high-dimensional representations of nonlinear dynamical systems based on perturbation theory is presented. Nonlinear behavior is interpreted as a projection of the Koopman operator eigenfunctions of an extended coordinate system onto the physical variables of the system. Analytical formulations are then obtained for the construction of the extended coordinate system based on perturbation theory. The analysis methodology is demonstrated on three test systems: A single-machine, infinite-bus system, a three-machine test system, and the IEEE 50-machine test system.