Controlled islanding via weak submodularity

Cascading failures typically occur following a large disturbance in power systems, such as tripping of a generating unit or a transmission line. Such failures can propagate and destabilize the entire power system, potentially leading to widespread outages. One approach to mitigate impending cascading failures is through controlled islanding, in which a set of transmission lines is deliberately tripped to partition the unstable system into several disjoint, internally stable islands. Selecting such a set of transmission lines is inherently a combinatorial optimization problem. Current approaches address this problem in two steps: first, classify coherent generators into groups and then separate generator groups into different islands with minimal load-generation imbalance. These methods, however, are based on computationally expensive heuristics that do not provide optimality guarantees. This paper proposes a novel approach to controlled islanding based on weak submodularity. The new formulation jointly captures the minimal generator non-coherency and minimal load-generation imbalance in one objective function. The islanding problem is then relaxed to a formulation with bounded submodularity ratio and a matroid constraint. An approximation algorithm is proposed which achieves a provable optimality bound on non-coherency and load-generation imbalance. The proposed framework is tested on IEEE 39-bus and 118-bus power systems.