New method computes power system stability in sub-second time

A team of researchers (Damola Ajeyemi, Antonin Colot, Sairaj Dhople, Emiliano Dall'Anese, Saber Jafarpour) has introduced a computationally efficient framework for reachability analysis of power systems with heterogeneous resources. Their method addresses the challenge of analyzing stability and dynamic behavior in transmission-level grids that include synchronous generators, grid-forming and grid-following inverters, and uncertain power injections/withdrawals. Starting from reduced-order device models and a frequency-divider representation, they derive a linear ordinary-differential-equation (ODE) model that enables efficient reachable-set computation under bounded disturbances across network buses.

The core innovation is the application of real Jordan transformation to separate non-oscillatory modes (handled via a linear embedding system) from oscillatory modes (enclosed using contraction-based ball bounds). This approach combines interval reachability with contraction-based bounds to construct certified over-approximations for the linear ODE model. Numerical experiments on a modified IEEE 39-bus system demonstrate that the reachable tubes closely match high-fidelity electromagnetic-transient (EMT) simulations, while achieving multi-second reachable sets in sub-second computation time. This represents a significant speedup for real-time stability assessment in increasingly complex power grids.