A Note on Branch Flow Models with Line Shunts

TL;DR

This paper extends branch flow models to include line shunts and proves that the equivalence to bus injection models and the exactness of second-order cone relaxations still hold under similar conditions as the zero-shunt case.

Contribution

It introduces a branch flow model with nonzero line shunts and proves the continued validity of model equivalence and relaxation exactness.

Findings

Model with line shunts maintains equivalence to bus injection models.

Second-order cone relaxation remains exact with line shunts.

Theoretical proof extends previous zero-shunt results.

Abstract

When the shunt elements in the Pi circuit line model are assumed zero, it has been proved that branch flow models are equivalent to bus injection models and that the second-order cone relaxation of optimal power flow problems on a radial network is exact under certain conditions. In this note we propose a branch flow model that includes nonzero line shunts and prove that the equivalence and the exactness of relaxation continue to hold under essentially the same conditions as for zero shunt elements.