EURO 2024 Copenhagen
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169. Addressing Non-Convexities in Sector Coupling Problems via the Difference of Convex Functions Algorithm

Invited abstract in session MB-21: Energy sector coupling, optimization and equilibrium, stream OR in Energy.

Monday, 10:30-12:00
Room: 49 (building: 116)

Authors (first author is the speaker)

1. Dominic Flocco
Department of Mathematics, University of Maryland
2. Steven Gabriel
Mech. Engin./ Applied Math and Scientific Computation Program, University of Maryland
3. Trine Krogh Boomsma
Department of Mathematical Sciences, University of Copenhagen
4. Martin Schmidt
Department of Mathematics, Trier University
5. Miguel Lejeune
George Washington University

Abstract

We present the difference of convex functions algorithm (DCA) applied to a variety of non-convex optimization problems arising in energy sector coupling and equilibrium problems. Non-convexities emerge frequently in many energy models, such as though bilinear terms, integer constrained variables and non-convex quadratic constraints. Recently, DCA has proven effective in solving such problems by linearizing non-convex terms and converging to an optimal solution iteratively by solving convex subproblems. In our work, we use DCA to solve a wide range of non-convex problems, such as linear complementarity problems, mixed integer linear programs and quadratic programs with non-convex quadratic constraints. We demonstrate the effectiveness and versatility of DCA by applying it to a variety of energy models, such as the unit commitment problem, district heating networks and energy market equilibrium problems.

Keywords

Status: accepted

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