A Submodular Optimization Approach to Stable and Minimally Disruptive Controlled Islanding in Power Systems

Power systems must maintain dynamical stability while meeting user demand in the presence of major disturbances including failures of multiple generators and transmission lines. One approach to mitigating disturbances is controlled islanding, in which a subset of edges is deliberately removed in order to partition the network into disjoint, internally stable and self-sufficient islands. In this paper, we present a submodular optimization approach to controlled islanding. We prove that computing optimal islands under three standard metrics, namely, generator coherence, load-generation imbalance, and power flow disruption, is equivalent to minimizing a supermodular function with a matroid basis constraint. Based on this result, we present the first polynomial-time islanding algorithms with constant-factor optimality bounds with respect to the three aforementioned metrics. We test the proposed approach on IEEE 30-bus, 57-bus, and 118-bus power systems. We demonstrate that our proposed algorithm converges and present the islanding strategies when different combinations of the metrics are considered.