Category: Physics

Summary: Finding the minimum fast-support gain needed to restabilize an islanded microgrid after load stress has already pushed it past a small-signal instability.

Islanded microgrids rely on rapid support and reserve-sharing mechanisms to remain stable after disturbances. This experiment asks how much fast frequency support is needed once a modular islanded grid has already crossed into an unstable regime because of load stress.

The script constructs dense non-symmetric swing Jacobians for stressed islanded microgrids and uses GPU iterative deepening to bisect the gain threshold where stability returns. Rather than sweeping broadly, it carries forward a narrowing bracket across system sizes to estimate the rescue point directly from the leading eigenvalues.

That framing makes the result a quantitative rescue threshold, not just a general statement that support helps. It targets the minimum intervention needed to recover stability in finite modular grids, which is directly relevant to control design under tight response margins.

Method: GPU dense non-symmetric eigensolves with iterative deepening and bisection on fast-support gain in islanded microgrid swing Jacobians.

What is measured: Critical fast-support gain, leading-eigenvalue stability boundary, finite-size bracket width, and rescue behavior under fixed load stress.