Global optimization of multilevel electricity market models including network design and graph partitioning |
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Affiliation: | 1. University of Illinois Urbana-Champaign, Department of Industrial and Enterprise Systems Engineering, United States;2. RWTH Aachen University, School of Business and Economics, Germany;3. University of Waterloo, Department of Combinatorics & Optimization, Canada;1. Mathematics Department, Milwaukee School of Engineering, Milwaukee, Wisconsin, USA;2. Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada |
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Abstract: | We consider the combination of a network design and graph partitioning model in a multilevel framework for determining the optimal network expansion and the optimal zonal configuration of zonal pricing electricity markets, which is an extension of the model discussed in Grimm et al. (2019) that does not include a network design problem. The two classical discrete optimization problems of network design and graph partitioning together with nonlinearities due to economic modeling yield extremely challenging mixed-integer nonlinear multilevel models for which we develop two problem-tailored solution techniques. The first approach relies on an equivalent bilevel formulation and a standard KKT transformation thereof including novel primal-dual bound tightening techniques, whereas the second is a tailored generalized Benders decomposition. For the latter, we strengthen the Benders cuts of Grimm et al. (2019) by using the structure of the newly introduced network design subproblem. We prove for both methods that they yield global optimal solutions. Afterward, we compare the approaches in a numerical study and show that the tailored Benders approach clearly outperforms the standard KKT transformation. Finally, we present a case study that illustrates the economic effects that are captured in our model. |
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Keywords: | Network design Graph partitioning Multilevel optimization Mixed-integer optimization Electricity market design |
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