A Hybrid Submodular Optimization Approach to Controlled Islanding with Heterogeneous Loads

Cascade failures, in which the failure of generators or transmission lines causes neighboring generators or lines to trip offline, threaten power system stability. Controlled islanding mitigates cascade failures by deliberately removing a subset of transmission lines in order to partition the system into disjoint, internally stable islands. In this paper, we investigate algorithms for controlled islanding to ensure stability while minimizing power flow disruption and load-generator imbalance. We consider a scenario where there are heterogeneous loads with varying costs of load shedding and formulate a hybrid optimization problem of jointly selecting a set of transmission lines to remove (discrete variables) and how much load to shed at each bus (continuous variables). In order to solve this optimization problem with provable optimality bounds, we propose a new notion of hybrid submodularity. We develop a polynomial-time islanding algorithm that achieves a provable 1/2-optimality bound. We use IEEE 118-bus and ACTIVsg 500-bus case studies to demonstrate that our approach provides better islanding solutions compared to a Mixed-Integer Linear Program (MILP)-based approach.