Building blocks of the basin stability of power grids

Given a power grid and a transmission (coupling) strength, basin stability is a measure of synchronization stability for individual nodes. Earlier studies have focused on the basin stability's dependence of the position of the nodes in the network for single values of transmission strength. Basin stability grows from zero to one as transmission strength increases, but often in a complex, nonmonotonous way. In this study, we investigate the entire functional form of the basin stability's dependence on transmission strength. To be able to perform a systematic analysis, we restrict ourselves to small networks. We scan all isomorphically distinct networks with an equal number of power producers and consumers of six nodes or less. We find that the shapes of the basin stability fall into a few, rather well-defined classes, that could be characterized by the number of edges and the betweenness of the nodes, whereas other network positional quantities matter less.