Category: Physics

Summary: Finding the load-stress level where reserve-coupled islanded microgrid Jacobians lose small-signal stability.

Controlled islanding can make power networks more resilient, but the stability of the resulting microgrids still depends on how much stress the system is carrying. This experiment asks when modular swing-dynamics Jacobians with reserve coupling cross from stable to unstable as load increases.

The script builds dense non-symmetric Jacobians for reserve-coupled islanded microgrids with fixed intra-island coherency and inter-island ties. It then bisects the load-stress parameter while increasing system size to estimate the finite-size stability threshold.

That produces a direct spectral map of islanding limits rather than a single operating-point analysis. It is aimed at the point where reserve sharing stops compensating for growing stress.

Method: Dense non-symmetric Jacobian eigensolve with iterative deepening and bisection on load stress in reserve-coupled microgrid swing operators.

What is measured: Critical load-stress threshold, leading-eigenvalue stability boundary, small-signal stability status, and bracket width.