Ensuring Network Connectedness in Optimal Transmission Switching Problems

TL;DR

This paper introduces linear connectedness constraints for optimal transmission switching problems, ensuring network connectivity efficiently and effectively, with a reduction method to improve computational performance.

Contribution

It proposes a novel set of linear constraints based on electrical flow feasibility to guarantee network connectedness in OTS models, including a reduced version for better efficiency.

Findings

Constraints are compatible with existing OTS models.

Numerical studies show the importance of considering connectedness.

Reduced constraints significantly improve computational efficiency.

Abstract

Network connectedness is indispensable for the normal operation of transmission networks. However, there still remains a lack of efficient constraints that can be directly added to the problem formulation of optimal transmission switching (OTS) to ensure network connectedness strictly. To fill this gap, this paper proposes a set of linear connectedness constraints by leveraging the equivalence between network connectedness and feasibility of the vertex potential equation of an electrical flow network. The proposed constraints are compatible with any existing OTS models to ensure topology connectedness. Furthermore, we develop a reduction version for the proposed connectedness constraints, seeking for improvement of computational efficiency. Finally, numerical studies with a DC OTS model show the deficiency of OTS formulations without full consideration of network connectedness and demonstrate the effectiveness of the proposed constraints. The computational burden caused by the connectedness constraints is moderate and can be remarkably relieved by using the reduced version.