Improving Optimal Power Flow Relaxations Using 3-Cycle Second-Order Cone Constraints

TL;DR

This paper introduces a new second order cone relaxation method for optimal power flow that improves upon existing relaxations by leveraging 3-cycle constraints, enhancing solution accuracy for meshed networks.

Contribution

It extends second order cone relaxations to 3x3 matrices for better power flow solutions, without relying on angle relaxation, advancing the state-of-the-art in power system optimization.

Findings

Enhanced relaxation accuracy for meshed networks

Numerical results demonstrate improved solution bounds

Novel 3-cycle second-order cone constraints

Abstract

This paper develops a novel second order cone relaxation of the semidefinite programming formulation of optimal power flow, that does not imply the `angle relaxation'. We build on a technique developed by Kim et al., extend it for complex matrices, and apply it to 3x3 positive semidefinite matrices to generate novel second-order cone constraints that augment upon the well-known 2x2 principal-minor based second-order cone constraints. Finally, we apply it to optimal power flow in meshed networks and provide numerical illustrations.