Proving Global Optimality of ACOPF Solutions

TL;DR

This paper introduces new mathematical models and algorithms that successfully find globally optimal solutions for the ACOPF problem, closing the optimality gap on benchmark instances using advanced bound tightening and cut generation techniques.

Contribution

It presents novel methods combining valid cut generation with semidefinite programming for global ACOPF optimization, implemented in an open-source framework.

Findings

Closed optimality gaps on benchmark instances

Effective combination of cut generation and SDP-based bound tightening

Implementation in open-source platform Gravity

Abstract

We present our latest contributions in terms of mathematical modeling and algorithm development for the global optimization of the ACOPF problem. These contributions allow us to close the optimality gap on a number of open instances in the PGLIB and NESTA benchmark libraries. This is achieved by combining valid cut generation with semidefinite programming-based bound tightening. The mathematical formulations along with the solution algorithms are implemented in the modeling framework Gravity (www.gravityopt.com), an open-source platform for reproducible numerical experiments.