Interior-Point vs. Spatial Branching Approaches for Solving the AC Optimal Power Flow Problem
Ignacio Repiso, Salvador Pineda, Juan Miguel Morales
TL;DR
This paper compares interior-point and spatial-branching strategies for solving the nonconvex AC-OPF, introducing data-boosted variants that leverage historical data to guide initialization for IP and to tighten search bounds for SP. Through a large-scale empirical benchmark across networks from 14 to 118 buses and conditions designed to induce local optima, the study shows that modern interior-point solvers are remarkably robust and frequently reach the global optimum, especially when combined with history-informed initialization or polar formulations. While data-driven variants can significantly reduce computation time for both IP and SP, spatial branching remains computationally demanding and, in some cases, infeasible due to overly tight bounds; overall, SP methods do not yet contend with IP in efficiency or reliability. The results advocate for continued use of interior-point approaches in practice, with future SP research targeting scalability, bound safety, and stronger global guarantees.
Abstract
The AC Optimal Power Flow (AC-OPF) problem is a non-convex, NP-hard optimization task essential for secure and economic power system operation. Two prominent solution strategies are interior-point methods, valued for computational efficiency, and spatial branching techniques, which provide global optimality guarantees at higher computational cost. In this work, we also explore data-boosted variants that leverage historical operating data to enhance performance by guiding initialization in interior-point methods or constraining the search region in spatial branching. We conduct a comprehensive empirical comparison across networks of varying sizes and under both standard benchmark conditions and modified configurations designed to induce local optima. Our results show that data-boosted strategies can improve convergence and reduce computation times for both approaches. Spatial branching, however, remains computationally demanding, requiring further development for practical application. In contrast, modern interior-point solvers exhibit remarkable robustness, often converging to the global optimum even in challenging instances with multiple local solutions.