A Dynamic Relaxation Framework for Global Solution of ACOPF

TL;DR

This paper introduces a unified dynamic relaxation framework for solving the ACOPF problem to global optimality by combining static relaxations with on-the-fly cut generation, improving accuracy and scalability.

Contribution

It proposes novel static and dynamic relaxation formulations (PR, QPR, DPR, DQPR) with a cut-generation mechanism for tighter relaxations and better scalability in ACOPF solutions.

Findings

Effective elimination of conic violations in benchmarks

Flexible trade-offs between accuracy and runtime achieved

Guidelines for selecting relaxation variants based on network size

Abstract

Solving the Alternating Current Optimal Power Flow (AC OPF) problem to global optimality remains challenging due to its nonconvex quadratic constraints. In this paper, we present a unified framework that combines static piecewise relaxations with dynamic cut-generation mechanism to systematically tighten the classic Second-Order Cone Programming (SOCP) relaxation to arbitrarily small conic violation, thus enabling the recovery of globally optimal solutions. Two static formulations, Pyramidal Relaxation (PR) and Quasi-Pyramidal Relaxation (QPR), are introduced to tighten each branch-flow second-order cone via a finite union of wedges, providing controllable accuracy. Their dynamic counterparts, Dynamic PR (DPR) and Dynamic QPR (DQPR), embed on-the-fly cut generation within a branch-and-cut solver to improve scalability. Convergence is further accelerated through warm starts and a lightweight local-search post-processing. Extensive experiments on benchmarks demonstrate effective elimination of conic violations and flexible trade-offs between solution accuracy and runtime. Practical guidelines are derived for selecting appropriate variants based on network size and accuracy requirements.