Energy-barrier characterization of secured basins in coupled oscillators with inertia
Abstract
The second-order Kuramoto model captures rotor dynamics relevant to synchronization in power grids. In actual power grids, violation of angle-stability limits can trigger protective actions that are not included in the model, restricting its validity to trajectories that remain within these limits. We therefore define the secured basin as the region of disturbance space comprising disturbances whose trajectories remain within the angle-stability limits throughout the transient. We then characterize the secured basin through energy barriers, quantifying their characteristic energy scale and heterogeneity across perturbation directions. Across seven power-grid models, this characterization revealed angle-stability vulnerabilities overlooked when stability is assessed solely by the final synchronization state. It also showed that the two energy-barrier measures characterizing the secured basin exhibit distinct associations with structural connectivity and dynamical parameters. This characterization further offers practical advantages, as energy thresholds derived from state-space perturbations remain effective in distinguishing secured and unsecured outcomes under short-duration power disturbances and can be estimated efficiently by concentrating simulations near the secured-basin boundary. Overall, the secured-basin framework provides a useful basis for distinguishing node-level structural and dynamical influences on transient stability in oscillator networks with synchronization constraints.
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BibTeX
@misc{lee2026energybarrier,
title = {{Energy-barrier characterization of secured basins in coupled oscillators with inertia}},
author = {Jaiyong Lee and Daekyung Lee and Seung-Woo Son and Sang Hoon Lee and Mi Jin Lee and Heetae Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11147},
eprint = {2610.11147},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11147},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Energy-barrier characterization of secured basins in coupled oscillators with inertia
AU - Jaiyong Lee
AU - Daekyung Lee
AU - Seung-Woo Son
AU - Sang Hoon Lee
AU - Mi Jin Lee
AU - Heetae Kim
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11147
UR - https://arxiv.org/abs/2610.11147
AB - The second-order Kuramoto model captures rotor dynamics relevant to synchronization in power grids. In actual power grids, violation of angle-stability limits can trigger protective actions that are not included in the model, restricting its validity to trajectories that remain within these limits. We therefore define the secured basin as the region of disturbance space comprising disturbances whose trajectories remain within the angle-stability limits throughout the transient. We then characterize the secured basin through energy barriers, quantifying their characteristic energy scale and heterogeneity across perturbation directions. Across seven power-grid models, this characterization revealed angle-stability vulnerabilities overlooked when stability is assessed solely by the final synchronization state. It also showed that the two energy-barrier measures characterizing the secured basin exhibit distinct associations with structural connectivity and dynamical parameters. This characterization further offers practical advantages, as energy thresholds derived from state-space perturbations remain effective in distinguishing secured and unsecured outcomes under short-duration power disturbances and can be estimated efficiently by concentrating simulations near the secured-basin boundary. Overall, the secured-basin framework provides a useful basis for distinguishing node-level structural and dynamical influences on transient stability in oscillator networks with synchronization constraints.
ER -