Category: Science

Summary: Finding the fast frequency-support gain needed to restabilize stressed islanded microgrids.

Islanded microgrids can lose small-signal stability when load stress rises and normal support pathways are weakened. This experiment asks how much fast support must be added before a modular islanded grid regains stability after crossing into an unstable regime.

The script constructs dense swing-equation Jacobians for stressed islanded grids and bisects a fast-support gain parameter until the dominant eigenvalue returns to the stable side. Iterative deepening carries that threshold bracket through progressively larger bus counts, producing a finite-size rescue curve.

The resulting map connects controlled islanding, reserve sharing, and eigenvalue-based stability analysis in a single quantitative workflow. Rather than testing a few hand-picked settings, it estimates the minimum support required for recovery across a broad size range.

Method: Dense non-symmetric Jacobian eigensolve with iterative deepening and bisection on fast-support gain.

What is measured: Critical fast-support threshold, leading eigenvalue real part, island localization score, fixed load stress, and bracket width.