Figure 4
Single-node phase space of a consumer in the Scandinavian grid.
(a) We plot the initial frequency deviation ωn vs. the phase difference to the fixed point at node n, visualising the definition of the following areas using the simulation results from (b). The central green area resembles the infinite-time basin of survival, while the yellow and red areas contain finite-time surviving states. The union of the blue, yellow and green regions resembles the synchronous state’s basin of attraction, while trajectories starting in the white or red regions approach different attractors. The frequency threshold is chosen as ωcrit. = ±5 and initial conditions correspond to perturbations at a single consumer node of the network. (b) Simulated maximum frequency deviations ωmax along all dimensions, measured over the time evolution of the system for initial conditions that correspond to perturbations at node n of the network. For comparison with (a), we give the numerically estimated basin of attraction’s boundaries in red. (c) Corresponding analytic upper bound for the maximum frequency deviation (cf. Eq. 16) for the linear approximation.
