Schewe L, Schmidt M, Thürauf J (2020)

**Publication Language:** English

**Publication Type:** Journal article, Original article

**Publication year:** 2020

**URI:** http://www.optimization-online.org/DB_HTML/2020/01/7576.html

**DOI:** 10.1007/s10479-020-03725-2

As a result of its liberalization, the European gas market is organized as an entry-exit system in order to decouple the trading and transport of natural gas. Roughly summarized, the gas market organization consists of four subsequent stages. First, the transmission system operator (TSO) is obliged to allocate so-called maximal technical capacities for the nodes of the network. Second, the TSO and the gas traders sign mid- to long-term capacity-right contracts, where the capacity is bounded above by the allocated technical capacities. These contracts are called bookings. Third, on a day-ahead basis, gas traders can nominate the amount of gas that they inject or withdraw from the network at entry and exit nodes, where the nominated amount is bounded above by the respective booking. Fourth and finally, the TSO has to operate the network such that the nominated amounts of gas can be transported. By signing the booking contract, the TSO guarantees that all possibly resulting nominations can indeed be transported. Consequently, maximal technical capacities have to satisfy that all nominations that comply with these technical capacities can be transported through the network. This leads to a highly challenging mathematical optimization problem. We consider the specific instantiations of this problem in which we assume capacitated linear as well as potential-based flow models. In this contribution, we formally introduce the problem of Computing Technical Capacities (CTC) and prove that it is NP-complete. To this end, we first reduce the Subset Sum problem to CTC for the case of capacitated linear flows in trees. Afterward, we extend this result to CTC with potential-based flows and show that this problem is also NP-complete on trees by reducing it to the case of capacitated linear flow. Since the hardness results are obtained for the easiest case, i.e., on tree-shaped networks with capacitated linear as well as potential-based flows, this implies the hardness of CTC for more general graph classes.

Decomposition methods for mixed-integer optimal control (A05) (2018 - 2022)
TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154)
July 1, 2018 - June 30, 2022
Multilevel mixed-integer nonlinear optimization for gas markets (B08) (2018 - 2022)
TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154)
July 1, 2018 - June 30, 2022
MIP techniques for equilibrium models with integer constraints (B07) (2018 - 2022)
TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154)
July 1, 2018 - June 30, 2022
Energiemarktdesign (EMD)
Energie Campus Nürnberg (EnCN2)
Jan. 1, 2017 - Dec. 31, 2021

**APA:**

Schewe, L., Schmidt, M., & Thürauf, J. (2020). Computing Technical Capacities in the European Entry-Exit Gas Market is NP-Hard. *Annals of Operations Research*. https://doi.org/10.1007/s10479-020-03725-2

**MLA:**

Schewe, Lars, Martin Schmidt, and Johannes Thürauf. "Computing Technical Capacities in the European Entry-Exit Gas Market is NP-Hard." *Annals of Operations Research* (2020).

**BibTeX:** Download