A Submodular Energy Function Approach to Controlled Islanding with Provable Stability

Shiyu Cheng, Luyao Niu, Andrew Clark, Radha Poovendran

Abstract: Cascading failures occur when failures of one or more nodes in a network lead to failures in neighboring nodes that propagate through the remainder of the network. One approach to mitigate cascading failures is through controlled islanding, in which a subset of edges is deliberately removed in order to partition the network into disjoint and stable islands. In this paper, we propose a submodular optimization algorithm for selecting edges to remove in order to create islands with provable stability. In contrast to existing approaches that optimize over stability-related metrics such as network coherence, our approach maps standard Lyapunov stability conditions to the objective function of an optimization problem. We prove that this optimization problem is equivalent to minimizing a supermodular function subject to a matroid basis constraint. We propose a local search algorithm for selecting the islands with provable optimality bounds, and discuss special cases including signed linear consensus and nonlinear synchronization dynamics. We simulate our approach using linear consensus dynamics with negative edges and find that our proposed algorithms partition the network into a stable island and an unstable island.