Category: Science

Summary: Finding how heterogeneous support allocation can be before an islanded microgrid loses stability despite adequate mean support.

Mean support levels can look sufficient on paper while real grids remain vulnerable because support is spread unevenly across islands. This experiment asks how much dispersion in fast-support allocation an islanded microgrid can tolerate before small-signal stability is lost.

The model fixes mean support and load stress, then bisects a dispersion parameter that increases heterogeneity in support distribution. Dense non-symmetric Jacobians are solved at increasing sizes to locate the instability threshold and to track whether localized island modes and power-sharing imbalance intensify near the transition.

The resulting threshold is useful as a design margin: it quantifies not only how much support is needed, but how evenly it must be delivered for the rescue mechanism to remain effective.

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

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