Fig. 5: Data-driven fault recovery in the New England power-grid network.
Panel (a) depicts the 39-node New England power-grid network (see ref. 70, Appendix A). The black nodes {1, …, 29} represent load nodes, while the red nodes {30, …, 39} are power generators. The generators are labeled according to the numbers in the red brackets. The red cross denotes the location of the fault. Panel (b) plots the behavior of the phases and frequencies of generators {2, …, 10} after the occurrence of the fault. The onset time of the fault is t = 2 s and the fault duration is 0.5 s (red area in the plots). At time t = 2.5 s the fault is cleared. The phase and frequency of generator 1 (not shown) are fixed to a constant (see “Methods”). The left plots of the panel (c) show the behavior of the phases and frequencies of generators {2, …, 10} after the application of the data-driven control input (4). The duration of the control action is 0.1 s (green area in the plots) which corresponds to a control horizon T = 400 for the discretized network dynamics with sampling period Ts = 2.5 × 10−4 s. For the computation of the control input, we employ N = 4000 experimental data collected offline by perturbing the state of the generators locally around its steady-state value (see “Methods”). We use weighting matrices R = I and Q = εI, with ε = 0.01. The insets illustrate the behavior of the phases and frequencies during the application of the control. The right plots of the panel (c) show the asymptotic behavior of the phases and frequencies of generators {2, …, 10} after the application of the data-driven control (4).
