Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality

Kevin-Martin Aigner (), Robert Burlacu (), Frauke Liers () and Alexander Martin ()
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Kevin-Martin Aigner: Discrete Optimization, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
Robert Burlacu: Discrete Optimization, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany; Energie Campus Nürnberg, 90429 Nürnberg, Germany; Fraunhofer Institute for Integrated Circuits, 90411 Nürnberg, Germany
Frauke Liers: Discrete Optimization, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany; Energie Campus Nürnberg, 90429 Nürnberg, Germany
Alexander Martin: Discrete Optimization, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany; Energie Campus Nürnberg, 90429 Nürnberg, Germany; Fraunhofer Institute for Integrated Circuits, 90411 Nürnberg, Germany

INFORMS Journal on Computing, 2023, vol. 35, issue 2, 458-474

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.

Keywords: AC optimal power flow; mixed-integer nonlinear programming; discrete decisions; second order cone programming; piecewise linear relaxation; generator switching; transmission line switching; curtailment of renewables (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:35:y:2023:i:2:p:458-474

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