Non-monotonic increase of robustness with capacity tolerance in power grids

The robustness of different scale power grids is analyzed based on complex network theory in terms of electrical betweenness and weighted efficiency. The robustness of a power grid does not always increase monotonically with the capacity. This property is different from the results obtained in previous studies, which have indicated that the robustness increases monotonically with capacity. To understand the non-monotonic phenomenon, the cascading failure is divided into several sub-stages, and we analyze the number of overloaded nodes and the average remaining load in each sub-stage. The results indicate that the increasing capacity is barely able to reduce the number of overloaded nodes at the beginning of malfunction, which may lead to more nodes being removed subsequently, including certain nodes with many connections or large load. More loads remain in the power grid such that certain nodes cannot take the load. This eventually causes overloading of more nodes and a decline in the robustness of the power grid. The conclusion may be useful for power grid planners seeking to design grids with cost-effective capacity.