Reachability Analysis for Power Systems with Heterogeneous Resources via Jordan Transformation
For power system operators, it enables fast and certified reachability analysis of dynamics with mixed resources and uncertainties, addressing a key computational bottleneck.
This paper develops a reachability analysis framework for power systems with heterogeneous resources, achieving sub-second computation of multi-second reachable sets validated against high-fidelity EMT simulations on a modified IEEE 39-bus system.
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.