Controlled Islanding via Weak Submodularity

TL;DR

This paper introduces a novel optimization approach for controlled islanding in power systems using weak submodularity, providing provable guarantees for partitioning to prevent cascading failures.

Contribution

It formulates the controlled islanding problem as a weak submodular optimization with a matroid constraint, offering an approximation algorithm with theoretical optimality bounds.

Findings

Effective partitioning of power systems demonstrated on IEEE test cases.

The proposed method outperforms heuristic approaches in minimizing non-coherency.

Provable guarantees on solution quality are established.

Abstract

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. In this paper, we propose a novel approach to controlled islanding based on weak submodularity. Our formulation jointly captures the minimal generator non-coherency and minimal load-generation imbalance in one objective function. We relax the problem to a formulation with bounded submodularity ratio and a matroid constraint, and propose an approximation algorithm 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.