A Submodular Optimization Approach to Controlled Islanding under Cascading Failure

Cascading failures occur when the power system is subject to a significant disturbance, such as tripping one or more transmission lines. Such failures can severely impact power system stability, potentially leading to widespread outages. One proposed approach for mitigating cascading failures is to partition the system into internally stable islands (a process known as controlled islanding). Selecting a subset of transmission lines to trip to form desired islands is inherently a combinatorial optimization problem. Current approaches for selecting such subsets, however, rely on computationally expensive heuristics that do not provide optimality guarantees. In this paper, we propose a submodular optimization approach for controlled islanding. Our approach has two stages. In the first stage, generators are assigned to each island based on existing methods such as slow coherency theory in order to ensure that each island is dynamically stable. In the second stage, we determine which edges to cut in order to minimize the generator-load imbalance within each island to ensure that a stable steady-state operating point exists. We relax the problem of minimizing imbalance to a supermodular minimization problem with a matroid constraint, implying that a greedy algorithm gives a provable optimality bound of 1/2. Our results are demonstrated using the IEEE 39-bus New England Test System.