Fig. 4: Network isolators can contain cascading failures in power grids.

a Line loading (colour code) on the Scandinavian grid in units relative to maximal loading before the initial failure of a single line (coloured red). b The initial failure results in a cascade of overloads (red coloured lines) until the grid disconnects into several parts. c Magnification of the grid structure in Eastern Norway (grey box, a). A small modification of the grid enables the construction of a network isolator: adopting the recipe presented in Fig. 3a, we select two nodes (left) that are further split up into two separate nodes each which are mutually connected via a network isolator by adding four edges (right, green). Note that the removal of these two nodes would disconnect the network into two separate parts, i.e. they form a vertex cut of size two. d Introducing the network isolator completely suppresses the spreading of failures from Western Norway to the rest of the grid thus inhibiting the cascade observed in (b). The first two steps of this cascade are shown in Supplementary Fig. 12.