Estimating Transient Stability Regions of Large-Scale Power Systems Part I: Koopman Operator and Reduced-Order Model

Abstract

This paper presents an estimation of transient stability regions for large-scale power systems. In Part I, a Koopman operator based model reduction (KOMR) method is proposed to derive a low-order dynamical model with reasonable accuracy for transient stability analysis of large-scale power systems. Unlike traditional reduction methods based on linearized models, the proposed method does not require linearization, but captures dominant modes of the original nonlinear dynamics by employing a Koopman operator defined in an infinite-dimensional observable space. Combined with the Galerkin projection, the obtained dominant Koopman eigenvalues and modes produce a reduced-order nonlinear model. To approximate the Koopman operator with sufficient accuracy, we introduce a Polynomial-based Multi-trajectory Kernel Dynamic Mode Decomposition (PMK-DMD) algorithm, which outperforms traditional DMD in various scenarios. In the end, the proposed method is applied to the IEEE 10-machine-39-bus power system and IEEE 16-machine-68-bus power system, which demonstrates that our method is significantly superior to the modal analysis method in both qualitative and quantitative aspects.