Suppressing cascades of load in interdependent networks

TLDR

Understanding how interdependence among systems affects cascading behaviors is increasingly important across many fields of science and engineering. The study investigates the Bak–Tang–Wiesenfeld sandpile model on modular random graphs and real interdependent power grids, aiming to develop a multitype branching process framework for improved prediction of cascading processes. The authors employ a multitype branching process and simulations on modular random graphs and real interdependent power grid networks to analyze load cascades and estimate optimal interconnectivity. The analysis shows that moderate interconnectivity between networks suppresses the largest cascades, whereas excessive interconnectivity opens pathways for large cascades and increases capacity, leading to larger cascades; the authors estimate an optimal interconnectivity level that balances these effects, which could help grid owners minimize cascade size and highlights that asymmetric capacities may drive an arms race for greater capacity.

Abstract

Understanding how interdependence among systems affects cascading behaviors is increasingly important across many fields of science and engineering. Inspired by cascades of load shedding in coupled electric grids and other infrastructure, we study the Bak–Tang–Wiesenfeld sandpile model on modular random graphs and on graphs based on actual, interdependent power grids. Starting from two isolated networks, adding some connectivity between them is beneficial, for it suppresses the largest cascades in each system. Too much interconnectivity, however, becomes detrimental for two reasons. First, interconnections open pathways for neighboring networks to inflict large cascades. Second, as in real infrastructure, new interconnections increase capacity and total possible load, which fuels even larger cascades. Using a multitype branching process and simulations we show these effects and estimate the optimal level of interconnectivity that balances their trade-offs. Such equilibria could allow, for example, power grid owners to minimize the largest cascades in their grid. We also show that asymmetric capacity among interdependent networks affects the optimal connectivity that each prefers and may lead to an arms race for greater capacity. Our multitype branching process framework provides building blocks for better prediction of cascading processes on modular random graphs and on multitype networks in general.