# Tight Piecewise Convex Relaxations for Global Optimization of Optimal Power Flow

## TL;DR

This paper introduces a novel adaptive piecewise convex relaxation method with bound tightening for solving the ACOPF problem, improving solution accuracy and reducing optimality gaps in benchmark tests.

## Contribution

It develops tight piecewise convex relaxations with convex-hull representations and an adaptive partitioning algorithm that converges to the global optimum.

## Key findings

- Reduces optimality gaps in challenging ACOPF cases.
- Demonstrates effectiveness on benchmark test cases.
- Improves solution quality over existing methods.

## Abstract

Since the alternating current optimal power flow (ACOPF) problem was introduced in 1962, developing efficient solution algorithms for the problem has been an active field of research. In recent years, there has been increasing interest in convex relaxations-based solution approaches that are often tight in practice. Based on these approaches, we develop tight piecewise convex relaxations with convex-hull representations, an adaptive, multivariate partitioning algorithm with bound tightening that progressively improves these relaxations and, given sufficient time, converges to the globally optimal solution. We illustrate the strengths of our algorithm using benchmark ACOPF test cases from the literature. Computational results show that our novel algorithm reduces the best-known optimality gaps for some hard ACOPF cases.