X. Andy Sun

TL;DR: This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem that consistently outperforms previously proposed convex quadratic relaxations of the OPF problem and has numerous advantages over existing convex relaxations in the literature.

TL;DR: In this article, a new technique for reformulation of the rank constraints using both principal and non-principal 2-by-2 minors of the involved Hermitian matrix variable and characterize all such minors into three types.

TL;DR: In this paper, strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem were proposed, which can be directly used as a warm start in a local solver such as IPOPT.

TL;DR: A new technique for reformulation of the rank constraints using both principal and non-principal 2-by-2 minors of the involved Hermitian matrix variable is proposed and the equivalence of these minor constraints to the physical constraints of voltage angle differences summing to zero over three- and four-cycle power network is shown.

TL;DR: This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem based on a new bilinear extended formulation of the OPF problem, which have numerous advantages over existing convex relaxations in the literature.