A Dynamic Relaxation Framework for Global Solution of ACOPF

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.