On the Tightness of the Second-Order Cone Relaxation of the Optimal Power Flow with Angles Recovery in Meshed Networks

TL;DR

This paper examines the tightness and angle recovery of second-order cone relaxations in the optimal power flow problem for meshed networks, supported by theoretical analysis and numerical tests on IEEE cases.

Contribution

It provides new insights into the conditions under which the second-order cone relaxation is tight and feasible for meshed power networks.

Findings

Second-order cone relaxation can be tight under certain conditions.

Nodal voltage angles can be recovered successfully in meshed networks.

Numerical experiments validate the theoretical properties on IEEE test cases.

Abstract

This letter investigates properties of the second-order cone relaxation of the optimal power flow (OPF) problem, with emphasis on relaxation tightness, nodal voltage angles recovery, and alternating-current-OPF feasibility in meshed networks. The theoretical discussion is supported by numerical experiments on standard IEEE test cases. Implications for power system planning are briefly outlined.