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Abstract

Dynamical stability of the synchronous regime remains a challenging problem for secure functioning of power grids. Based on the symmetric circular model [Hellmann et al., Nat. Commun. 11, 592 (2020)], we demonstrate that the grid stability can be destroyed by elementary violations (motifs) of the network architecture, such as cutting a connection between any two nodes or removing a generator or a consumer. We describe the mechanism for the cascading failure in each of the damaging case and show that the desynchronization starts with the frequency deviation of the neighboring grid elements followed by the cascading splitting of the others, distant elements, and ending eventually in the bi-modal or a partially desynchronized state. Our findings reveal that symmetric topology underlines stability of the power grids, while local damaging can cause a fatal blackout.
A particular complexity of the power grid stability is caused by the fact that the desired synchronous state is only locally stable, not globally. In the system phase state, it repeatedly co-exists with many other desynchronized states. In such a case, the desired grid synchrony can be secured only against small perturbations but not against large impacts, even applied to a single grid element or to a single connection. If so, the system’s dynamics can switch to another, desynchronized attractor as soon as a large perturbation is applied. The essential difficulties of the power grid studies are also induced by intricate, highly asymmetric architectures of the realistic grids, often caused by geographical and historical reasons. What is the role of asymmetry for the stability? Which grids with symmetric or asymmetric topology are more reliable? We attack this problem by examining a symmetric circular power grid model and compare its stability with the situation when the symmetry is broken by elementary violations of the network structure.