Efficient bounds tightening based on SOCP relaxations for AC optimal power flow

Abstract

A new bounds tightening algorithm for globally solving AC optimal power flow (ACOPF) problems is presented. Practical ACOPF instances are too large to be solved by conventional global optimization algorithms based on extensive search-space partitioning. However, tailored optimization-based bounds tightening (OBBT) algorithms using advanced relaxation techniques have been shown to achieve tight optimality gaps for many test cases with no partitioning at all. Unfortunately, OBBT is still costly because it requires solving two convex subproblems per decision variable in each iteration. We present a new OBBT algorithm, using a new SOCP based relaxation, that achieves tight optimality gaps while only solving subproblems for a small subset of variables. For PGLIB benchmarks up to 300 buses, the algorithm achieves the best gap on more test problems and is significantly faster on average than two existing OBBT algorithms chosen for comparison.