# Managing the Uncertainty in System Dynamics Through Distributionally Robust Stability-Constrained Optimization

arXiv: https://arxiv.org/abs/2309.03798 · HTML: https://mlsanity.com/paper/2309.03798/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2023.

## Built on by (most cited first, 2 of 2)

- [Learning-Augmented Power System Operations: A Unified Optimization View](https://mlsanity.com/paper/2505.05203/) (2025)
- [Certified Safety Radii in Forecast-Error Space for Wasserstein Distributionally Robust Small Signal Stability-Constrained AC Optimal Power Flow via Lifted Spectrahedral Containment](https://mlsanity.com/paper/2608.30201/) (2026)

## Abstract (arXiv)

With the increasing penetration of Inverter-Based Resources (IBRs) and their impact on power system stability and operation, the concept of stability-constrained optimization has drawn significant attention from researchers. In order to manage the parametric uncertainty due to inaccurate modeling that influences the system dynamics, this work proposes a distributionally robust stability constraint formulation. However, the uncertainty of system dynamic parameters influences the stability constraints indirectly through a nonlinear and implicit relationship. To address this issue, a propagation mechanism from the uncertainty of the system dynamic parameters to the stability constraint coefficients is established. Since these coefficients are connected to the uncertain parameters through highly nonlinear and implicit functions, an approximation approach utilizing Taylor expansion and the Delta method is developed to estimate the statistical moments of the stability constraint coefficients based on the first and second-order derivatives, with which an ambiguity set for the distributionally robust optimization can be formulated. The accuracy of the uncertainty propagation as well as the effectiveness of the distributionally robust stability constraints are demonstrated through detailed case studies in the modified IEEE 39-bus system.