Category: Science

Summary: Finding how uneven fast-support allocation can become before a stabilized islanded microgrid loses stability again.

Adding fast support to an islanded microgrid can restore stability, but that support may be distributed unevenly across islands. This experiment asks how much imbalance can be tolerated before the rescue fails and the dominant mode again becomes unstable.

The script fixes the average support gain at a stabilizing level, applies modular load stress, and bisects an imbalance parameter that redistributes support across islands. Dense Jacobian eigensolves determine when the leading mode crosses back into instability, and iterative deepening repeats the search for larger networks.

This turns a practical engineering concern into a clear threshold question: not just whether support exists, but whether it is allocated fairly enough to work. It provides a finite-size stability margin for uneven support policies.

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

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