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Global Optimization of Multilevel Electricity Market Models Including Network Design and Graph Partitioning

Thomas Kleinert (thomas.kleinert***at***fau.de)
Martin Schmidt (martin.schmidt***at***uni-trier.de)

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 [25] 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 [25] 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.

Keywords: Network design, Graph partitioning, Multilevel optimization, Mixed-integer optimization, Electricity market design

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Global Optimization

Category 3: Applications -- OR and Management Sciences


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Entry Submitted: 02/07/2018
Entry Accepted: 02/07/2018
Entry Last Modified: 10/29/2018

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