Reduced-Order Model Characterization of Nonlinear Sustained Oscillations
Abstract
Nonlinear sustained oscillations involving inverter-based resources can happen when device and network interactions produce an attracting limit cycle around an unstable equilibrium. A damping controller must then describe nonlinear dynamics over the region between the two invariant sets, where a local equilibrium linearization can be insufficient. In this paper, a controlled phase--isostable model is first developed on a two-dimensional invariant manifold connecting the equilibrium and the limit cycle. Dynamics on this surface are represented by phase and isostable coordinates, while physical states and control inputs are related to these coordinates through nonlinear reconstruction and response functions. The required functions are computed from connecting trajectories and periodic-orbit data. A control strategy is then designed to provide extra damping while limiting phase distortion. Case studies on a two-area system and an IEEE 39-bus system demonstrate more effective oscillation damping than the compared equilibrium-linearized designs under the same conditions.
Related
- Full-Order Safety for Nonlinear Reduced-Order MPC
- A Nonlinear Physics-based Reduced Order Model with Convolutional-based Operator Compression
- Isostable-Based Nonlinear Model Reduction for Power System Oscillations
- Weakly nonlinear dynamics of follower-force-induced oscillations in Cosserat rods
- Local Linearization and Exact Oscillations for the Nonlinear Stochastic Heat Equation with Spatially Rough Noise
BibTeX
@misc{huang2026reducedorder,
title = {{Reduced-Order Model Characterization of Nonlinear Sustained Oscillations}},
author = {Kaiyang Huang and Dan Wilson and Kai Sun},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37505},
eprint = {2609.37505},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37505},
}
RIS
TY - UNPB
TI - Reduced-Order Model Characterization of Nonlinear Sustained Oscillations
AU - Kaiyang Huang
AU - Dan Wilson
AU - Kai Sun
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.37505
UR - https://arxiv.org/abs/2609.37505
AB - Nonlinear sustained oscillations involving inverter-based resources can happen when device and network interactions produce an attracting limit cycle around an unstable equilibrium. A damping controller must then describe nonlinear dynamics over the region between the two invariant sets, where a local equilibrium linearization can be insufficient. In this paper, a controlled phase--isostable model is first developed on a two-dimensional invariant manifold connecting the equilibrium and the limit cycle. Dynamics on this surface are represented by phase and isostable coordinates, while physical states and control inputs are related to these coordinates through nonlinear reconstruction and response functions. The required functions are computed from connecting trajectories and periodic-orbit data. A control strategy is then designed to provide extra damping while limiting phase distortion. Case studies on a two-area system and an IEEE 39-bus system demonstrate more effective oscillation damping than the compared equilibrium-linearized designs under the same conditions.
ER -