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Given a power grid and a transmission (coupling) strength, basin stability isa measure of synchronization stability for individual nodes. Earlier studieshave focused on the basin stability's dependence of the position of the nodesin the network for single values of transmission strength. Basin stabilitygrows from zero to one as transmission strength increases, but often in acomplex, nonmonotonous way. In this study, we investigate the entire functionalform of the basin stability's dependence on transmission strength. To be ableto perform a systematic analysis, we restrict ourselves to small networks. Wescan all isomorphically distinct networks with an equal number of powerproducers and consumers of six nodes or less. We find that the shapes of thebasin stability fall into a few, rather well-defined classes, that could becharacterized by the number of edges and the betweenness of the nodes, whereasother network positional quantities matter less.

Building blocks of the basin stability of power grids