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arXiv · 2607.05599

Reachability Analysis for Power Systems with Heterogeneous Resources via Jordan Transformation

Damola Ajeyemi·Antonin Colot·Sairaj Dhople·Emiliano Dall'Anese·Saber Jafarpour
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Abstract

This paper develops a computationally efficient framework for reachability analysis of transmission-level power system dynamics with synchronous generators, grid-forming and grid-following inverters, and uncertain power injections/withdrawals. Starting from reduced-order device models and a frequency-divider representation, we derive a linear ordinary-differential-equation model suitable for efficient reachable-set computation under bounded disturbances across network buses. The proposed reachability method combines interval reachability and contraction-based bounds to construct certified over-approximations for the linear ordinary-differential-equation model. A real Jordan transformation separates non-oscillatory modes, handled through a linear embedding system, from oscillatory modes, enclosed using contraction-based ball bounds. Numerical experiments on a modified IEEE 39-bus system validate the reachable tubes against high-fidelity electromagnetic-transient (EMT) simulations, and demonstrate multi-second reachable sets computed in sub-second time.

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Damola Ajeyemi, Antonin Colot, Sairaj Dhople, Emiliano Dall'Anese, Saber Jafarpour. 2026-07-06. Reachability Analysis for Power Systems with Heterogeneous Resources via Jordan Transformation. https://arxiv.org/abs/2607.05599

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