A Modification of Sufficient Conditions to Ensure the Exact Conic Relaxation

TL;DR

This paper refines the conditions under which convex conic relaxations of the AC optimal power flow problem are guaranteed to be exact, by adding a new criterion related to line reactance.

Contribution

It introduces a new sufficient condition involving line reactance to improve the guarantee of exactness in conic relaxations.

Findings

Adding a no-negative-reactance line condition ensures exactness.

The modified conditions better predict when the relaxation is exact.

The approach enhances the reliability of convex approximations in power flow problems.

Abstract

To solve the AC optimal power flow problem, it is proposed in [1,2] that a convex conic approximation to branch flow model (BFM) can be obtained if we first eliminate phase angles of voltages and currents and then relax a set of equality constraints to second order conic ones. In particular, provided a set of sufficient conditions are satisfied, the conic relaxation is exact. We note, however, that those conditions do not always guarantee the exactness. In this letter, we analyze the argument of exactness and include a new condition that there is no line with negative reactance to ensure the conic formulation's exactness.