Strengthening AC optimal power flow relaxation through offline bound tightening and linear approximations

Abstract

The alternating-current optimal power flow (ACOPF) problem is fundamental to power system operation and planning, but its nonconvexity makes globally optimal solutions of large-scale instances computationally challenging. Convex relaxations provide tractable lower bounds for assessing solution quality and supporting global optimization, although their effectiveness depends strongly on relaxation strength. This paper proposes an offline convexification and bound tightening framework for constructing strong linear programming (LP) relaxations for families of related ACOPF instances. Rather than repeating the tightening procedure for each instance, we compute variable bounds and second-order cone outer-approximation (SOC-OA) cuts offline using a demand-slack model and reuse them for subsequent instances with the same topology and admissible demand variations. Computational results on PGLib instances show that the fully offline approach achieves an average gap of $4.32\%$, compared with $3.80\%$ for the fully online approach, while achieving an average speedup of approximately $272\times$. The results demonstrate that offline convexification and bound tightening can recover most of the relaxation improvement of online tightening while significantly reducing the computational burden for repeated ACOPF evaluations.