# Applied Koopman Operator Theory for Power Systems Technology

## TL;DR

This paper reviews Koopman operator theory for nonlinear systems and demonstrates its application to power systems for stability analysis, diagnostics, and data-driven insights without relying on explicit models.

## Contribution

It introduces a data-centric approach using Koopman spectral analysis for power system stability and diagnostics, expanding the application of this theory beyond traditional nonlinear analysis.

## Key findings

- Koopman spectral analysis enables stability assessment without explicit models.
- Application of Koopman theory improves detection of system instabilities.
- Data-driven methods facilitate power system diagnostics and coherency identification.

## Abstract

Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman operator itself is linear but infinite-dimensional (evolves on a function space). This linear operator captures the full information of the dynamics described by the original nonlinear system. In particular, spectral properties of the Koopman operator play a crucial role in analyzing the original system. In the first part of this paper, we review the so-called Koopman operator theory for nonlinear dynamical systems, with emphasis on modal decomposition and computation that are direct to wide applications. Then, in the second part, we present a series of applications of the Koopman operator theory to power systems technology. The applications are established as data-centric methods, namely, how to use massive quantities of data obtained numerically and experimentally, through spectral analysis of the Koopman operator: coherency identification of swings in coupled synchronous generators, precursor diagnostic of instabilities in the coupled swing dynamics, and stability assessment of power systems without any use of mathematical models. Future problems of this research direction are identified in the last concluding part of this paper.