Multilevel Mixed-Integer Nonlinear Optimization for Electricity Market Design: Motivation, Models, Solution Techniques, and Results

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. 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 Benders-like decomposition approach. 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 some case study that illustrates the economic effects that are captured in our model and discuss some recent results for the Germany electricity sector.

This talk is part of the enOptimal seminar series organized by Vladimir Dvorkin (MITEI & MIT LIDS), Stefanos Delikaraoglou (MIT LIDS) and Audun Botterud (MIT LIDS).