Category: Physics

Summary: Finding how strongly a fixed total inertia deficit can be concentrated into one island before an islanded microgrid develops a localized oscillatory instability.

Islanded microgrids and inverter-dominated power systems often run with little mechanical inertia, which makes the placement of that missing support matter as much as the total amount available. This experiment asks when clustering the same overall inertia deficit into one island stops being just an uneven design choice and starts creating a distinct unstable oscillatory mode concentrated in that region.

The model builds dense swing-equation Jacobians for modular islanded microgrids and then carries a threshold bracket across increasing system sizes. By repeatedly bisecting the clustering parameter and solving the full eigenvalue problem, it estimates the point where the dominant mode becomes both unstable and spatially localized.

That is useful because many studies analyze average inertia levels or optimal support placement, but fewer map the finite-size boundary where concentrated weakness creates a localized failure mode. The output is meant to show how unevenly inertia can be distributed before modular structure itself becomes a liability.

Method: Dense real eigensolves on 2N x 2N swing Jacobians with iterative deepening and bisection on low-inertia clustering.

What is measured: Critical clustering threshold, instability onset, localization of the dominant oscillatory mode, system size reached, and bracket width.