Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality

Abstract

We present a solution framework for general alternating current optimal power flow (AC OPF) problems that include discrete decisions. The latter occur, for instance, in the context of the curtailment of renewables or the switching of power-generation units and transmission lines. Our approach delivers globally optimal solutions and is provably convergent. We model AC OPF problems with discrete decisions as mixed-integer nonlinear programs (MINLPs). The solution method starts from a known framework that uses piecewise linear relaxations. These relaxations are modeled as mixed-integer linear programs and adaptively refined until some termination criterion is fulfilled. In this work, we extend and complement this approach by problem-specific as well as very general algorithmic enhancements. In particular, these are mixed-integer second order cone programs as well as primal and dual cutting planes. For example, objective and no-good cuts help to compute good feasible solutions in which outer approximation constraints tighten the relaxations. We present extensive numerical results for various AC OPF problems in which discrete decisions play a major role. Even for hard instances with a large proportion of discrete decisions, the method is able to generate high-quality solutions efficiently. Furthermore, we compare our approach with state-of-the-art MINLP solvers. Our method outperforms all other algorithms. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This research has been funded by the Federal Ministry of Education and Research of Germany [Grant 05M18WEB]. This research has been performed as part of the Energie Campus Nürnberg and is supported by funding of the Bavarian State Government. The authors thank the Deutsche Forschungsgemeinschaft for support within projects A05, B06, B07, and B10 of the Sonderforschungsbereich/Transregio 154 “Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks.” This work has been supported by the Federal Ministry for Economic Affairs and Energy, Germany [Grant 03El1036A]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.1270 .