Welfare optimal nominations in gas networks and associated equilibria

Third Party Funds Group - Sub project

Overall project details

Overall project: SFB TRR 154 “Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzen”

Project Details

Project leader:
Prof. Dr. Veronika Grimm
PD Dr. Lars Schewe
Prof. Dr. Martin Schmidt
Prof. Dr. Karl Gregor Zöttl

Project members:
Julia Grübel

Contributing FAU Organisations:
Economics - Discrete Optimization - Mathematics (EDOM)
Juniorprofessur für Optimierung von Energiesystemen
Lehrstuhl für Volkswirtschaftslehre, insbesondere Wirtschaftstheorie
Professur für Volkswirtschaftslehre

Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
Start date: 01/10/2016
End date: 30/06/2018

Abstract (technical / expert description):

The goal of this project is the analysis of the relation between (i) the equilibria of simple models of competitive natural gas markets, using complementarity problems for modeling the behavior of different players, and (ii) the solution of corresponding single-level welfare maximization problems. The understanding of this fundamental relation is a prerequisite for an analysis of the current entry-exit gas market design in Europe. Similar questions have been studied in detail in the context of electricity market modeling in the past. For natural gas markets, however, the addressed questions are much more complex and not yet well understood for adequate models of gas physics. The reasons for the high level of complexity is twofold: First, gas flow through pipeline systems is inherently nonconvex due to gas physics. This renders classical first-order optimality conditions possibly insufficient. Second, the operation of gas transport networks comprises the control of active network devices like (control) valves or compressors. These devices introduce binary aspects and thus a further type of non-convexity to the models of the underlying equilibrium problems. As a result of the project we will obtain a first reference model that combines gas physics and a market analysis in a well-understood way. This will lay the ground for multilevel models of entry-exit natural gas markets that account for network characteristics. Beyond that, our results will enhance the understanding of binary equilibrium problems.

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Kleinert, T., & Schmidt, M. (2019). Global Optimization of Multilevel Electricity Market Models Including Network Design and Graph Partitioning. Discrete Optimization. https://dx.doi.org/10.1016/j.disopt.2019.02.002
Grimm, V., Kleinert, T., Liers, F., Schmidt, M., & Zöttl, G. (2019). Optimal price zones in electricity markets: a mixed-integer multilevel model and global solution approaches. Optimization Methods & Software, 34(2), 406-436. https://dx.doi.org/10.1080/10556788.2017.1401069
Robinius, M., Schewe, L., Schmidt, M., Stolten, D., Thürauf, J., & Welder, L. (2019). Robust optimal discrete arc sizing for tree-shaped potential networks. Computational Optimization and Applications. https://dx.doi.org/10.1007/s10589-019-00085-x
Schmidt, M., Sirvent, M., & Wollner, W. (2018). A Decomposition Method for MINLPs with Lipschitz Continuous Nonlinearities. Mathematical Programming. https://dx.doi.org/10.1007/s10107-018-1309-x
Groß, M., Pfetsch, M.E., Schewe, L., Schmidt, M., & Skutella, M. (2018). Algorithmic Results for Potential-Based Flows: Easy and Hard Cases. Networks. https://dx.doi.org/10.1002/net.21865
Schewe, L., & Schmidt, M. (2018). Computing Feasible Points for Binary MINLPs with MPECs. Mathematical Programming Computation. https://dx.doi.org/10.1007/s12532-018-0141-x
Gugat, M., Leugering, G., Martin, A., Schmidt, M., Sirvent, M., & Wintergerst, D. (2018). MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems. Computational Optimization and Applications, 70(1), 267-294. https://dx.doi.org/10.1007/s10589-017-9970-1
Mehrmann, V., Schmidt, M., & Stolwijk, J. (2018). Model and Discretization Error Adaptivity within Stationary Gas Transport Optimization. Vietnam Journal of Mathematics. https://dx.doi.org/10.1007/s10013-018-0303-1
Grimm, V., Grübel, J., Schewe, L., Schmidt, M., & Zöttl, G. (2018). Nonconvex Equilibrium Models for Gas Market Analysis: Failure of Standard Techniques and Alternative Modeling Approaches. European Journal of Operational Research. https://dx.doi.org/10.1016/j.ejor.2018.09.016
Geißler, B., Morsi, A., Schewe, L., & Schmidt, M. (2018). Solving Highly Detailed Gas Transport MINLPs: Block Separability and Penalty Alternating Direction Methods. Informs Journal on Computing, 20(2). https://dx.doi.org/10.1287/ijoc.2017.0780

Last updated on 2018-03-12 at 11:03