# Applied Koopman Operator Theory for Power Systems Technology

arXiv: https://arxiv.org/abs/1706.00159 · HTML: https://mlsanity.com/paper/1706.00159/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2017.

## Built on by (most cited first, 7 of 7)

- [CKNet: A Convolutional Neural Network Based on Koopman Operator for Modeling Latent Dynamics from Pixels](https://mlsanity.com/paper/2102.10205/) (2021)
- [On the lifting and reconstruction of nonlinear systems with multiple invariant sets](https://mlsanity.com/paper/2304.11860/) (2023)
- [Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approach](https://mlsanity.com/paper/2212.05259/) (2022)
- [Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations](https://mlsanity.com/paper/2110.01450/) (2021)
- [Supervised DKRC with Images for Offline System Identification](https://mlsanity.com/paper/2109.02241/) (2021)
- [KoopAGRU: A Koopman-based Anomaly Detection in Time-Series using Gated Recurrent Units](https://mlsanity.com/paper/2501.17976/) (2025)
- [A Unified Mamba--MoE Surrogate for Closed-Loop Simulation and Measurement-Window Forecasting of Inverter Transients](https://mlsanity.com/paper/2608.15051/) (2026)

## Abstract (arXiv)

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.