Operational tracking loss in nonautonomous second-order oscillator networks
This work addresses operational stability in inverter-dominated energy systems, providing insights into tracking loss mechanisms in second-order oscillator networks.
The paper investigates when networks of coupled oscillators with inertia lose coherent tracking of time-dependent driving protocols, showing that frequency dynamics provide clearer diagnostic indicators than phase-based observables. They demonstrate that a tracking ratio based on frequency disagreement yields a robust protocol-dependent freeze-out time with decreasing dispersion as system size increases, and identify graph topology factors like Fiedler-mode localization that explain variations in this behavior.
We study when a network of coupled oscillators with inertia ceases to follow a time-dependent driving protocol coherently, using a simplified graph-based model motivated by inverter-dominated energy systems. We show that this loss of tracking is diagnosed most clearly in the frequency dynamics, rather than in phase-based observables. Concretely, a tracking ratio built from the frequency-disagreement observable $E_Ï(t)$ and normalized by the instantaneous second-order modal decay rate yields a robust protocol-dependent freeze-out time whose relative dispersion decreases with system size. Graph topology matters substantially: the resulting freeze-out time is only partly captured by the algebraic connectivity $λ_2$, while additional structural descriptors, particularly Fiedler-mode localization and low-spectrum structure, improve the explanation of graph-to-graph variation. By contrast, phase-sector observables develop strong non-monotonic and underdamped structure, so simple diagonal low-mode relaxation closures are not quantitatively reliable in the same regime. These results identify the frequency sector as the natural operational sector for nonautonomous tracking loss in second-order oscillator networks and clarify both the usefulness and the limits of reduced spectral descriptions in this setting.