Optimal price zones of electricity markets: a mixed-integer multilevel model and global solution approaches

Abstract

Mathematical modelling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design yields welfare-optimal outcomes. This problem leads to a challenging multilevel model that contains a graph-partitioning problem with multi-commodity flow connectivity constraints and nonlinearities due to proper economic modelling. Furthermore, it has highly symmetric solutions. We develop different problem-tailored solution approaches. In particular, we present an extended Karush-Kuhn-Tucker (KKT) transformation approach as well as a generalized Benders approach that both yield globally optimal solutions. These methods, enhanced with techniques such as symmetry breaking and primal heuristics, are evaluated in detail on academic as well as on realistic instances. It turns out that our approaches lead to effective solution methods for the difficult optimization tasks presented here, where the problem-specific generalized Benders approach performs considerably better than the methods based on KKT transformation.

Keywords:

• multilevel optimization
• mixed-integer nonlinear optimization
• graph partitioning
• generalized Benders decomposition
• electricity market design

AMS Subject Classification:

• 90B10
• 90C11
• 90C35
• 90C90
• 91-08
• 91B26

Acknowledgments

We are very grateful to Lars Schewe for many insightful discussions on the topic of this paper. Finally, we thank Michael Müller and Fabian Hörmann for the help in preparing the data and their help on developing parts of our Python implementations.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The used parameters are Heuristics = 0, Cuts = 0, VarBranch = 1, MIPFocus = 2.

2 The used parameters for the master problems are Threads = 4, Symmetry = 0, and Cuts = 0. For the zonal spot-market QP we used Threads = 4, PreSolve = 1, and NumericFocus 2. The parameters used for the redispatch QP are Threads = 4 and PreSolve = 1.

Additional information

Funding

This research was performed as part of the Energie Campus Nürnberg and supported by funding through the ‘Aufbruch Bayern (Bavaria on the move)’ initiative of the state of Bavaria and the Emerging Field Initiative (EFI) of the Friedrich-Alexander-Universität Erlangen-Nürnberg through the project ‘Sustainable Business Models in Energy Markets’. We thank the DFG for their support within Project B06 and B08 in CRC TRR 154 and further acknowledge support of the ZISC.