TY - JOUR A1 - Gugat, Martin A1 - Schuster, Michael A1 - Steffensen, Sonja T1 - A Dynamic Multilevel Model of the European Gas Market N2 - The European gas market is governed by rules that are agreed on by the European Union. We present a mathematical market model that takes into account this structure, where the technical system operator (TSO) offers certain transportation capacities that can be booked and later nominated within the previously chosen bookings. The TSO also fixes booking fees and defines an operational control of the gas pipeline system in order to deliver the gas according to the nominations. Since the gas flow is governed by a system of partial differential equations, to realize this control structure partial differential equations (PDEs) should be involved in the model. While the four level gas market model has been discussed previously, in this paper we take into account the flow model by PDEs in the discussion of the model and in the reduction to a single level problem, where we also state the corresponding necessary optimality conditions. KW - Gas Dynamics KW - Gas Market KW - Nodal Control KW - Isothermal Euler Equations Y1 - 2022 UR - http://cot.mathres.org/archives/1488 IS - Volume 2023 SP - 1 EP - 26 PB - Communications in Optimization Theory ER - TY - CHAP A1 - Gugat, Martin A1 - Schuster, Michael T1 - Max-p optimal boundary control of gas flow N2 - In the transition to renewable energy sources, hydrogen will potentially play an important role for energy storage. The efficient transport of this gas is possible via pipelines. An understanding of the possibilities to control the gas flow in pipelines is one of the main building blocks towards the optimal use of gas. For the operation of gas transport networks it is important to take into account the randomness of the consumers’ demand, where often information on the probability distribution is available. Hence in an efficient optimal control model the corresponding probability should be included and the optimal control should be such that the state that is generated by the optimal control satisfies given state constraints with large probability. We comment on the modelling of gas pipeline flow and the problems of optimal nodal control with random demand, where the aim of the optimization is to determine controls that generate states that satisfy given pressure bounds with large probability. We include the H2 norm of the control as control cost, since this avoids large pressure fluctuations which are harmful in the transport of hydrogen since they can cause embrittlement of the pipeline metal. KW - gas pipeline flow KW - nodal control KW - hyperbolic differential equation KW - random demand KW - state constraints Y1 - 2022 U6 - https://doi.org/https://doi.org/10.15495/EPub_UBT_00006809 VL - Extended Abstracts of the 25th International Symposium on Mathematical Theory of Networks and Systems Bayreuth, Germany, 12-16 September 2022 ER -