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

Submission Status:under review
  • 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.
Author:Thomas Kleinert, Martin Schmidt
Document Type:Preprint
Date of Publication (online):2018/02/07
Date of first Publication:2018/02/07
Release Date:2018/02/07
Tag:Electricity market design; Graph partitioning; Mixed-integer optimization; Multilevel optimization; Network design
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg