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Mathematical modelling, simulation and optimization using the example of gas networks.
The “turnaround in energy policy” is currently in the main focus of public opinion. It concerns social, political and scientific aspects as the dependence on a reliable, efficient and affordable energy supply becomes increasingly dominant. On the other side, the desire for a clean, environmentally consistent and climate-friendly energy production is stronger than ever.
To balance these tendencies while making a transition to nuclear-free energy supply, gas becomes more and more important in the decades to come. Hydrogen is an energy carrier and can deliver or store a remendous amount of energy. Gaseous hydrogen can be transported through pipelines much the way natural gas is today.
On the other side focusing on an efficient handling of gas transportation induces a number of technical and regulatory problems, also in the context of coupling to other energy carriers. As an example, energy transporters are required by law to provide evidence that within the given capacities all contracts defining the market are physically and technically feasible.
Given the amount of data and the potential of stochastic effects, this is a formidable task all by itself, regardless from the actual process of distributing the proper amount of gas with the required quality to the customer. It is the goal of the Transregio-CRC to provide certified novel answers to these grand challenges, based on mathematical modeling, simulation and optimization. In order to achieve this goal new paradigms in the integration of these disciplines and in particular in the interplay between integer and nonlinear programming in the context of stochastic data have to be established and brought to bear.
Clearly, without a specified underlying structure of the problems to face, such a breakthrough is rather unlikely. Thus, the particular network structure, the given hierarchical hybrid modeling in terms of switching algebraic, ordinary and partial differential-algebraic equations of hyperbolic type that is present in gas network transportation systems gives rise to the confidence that the challenges can be met by the team of the proposed Transregio-CRC.
Moreover, the fundamental research conducted here will also be applicable in the context of other energy networks such as fresh- and waste water networks. In this respect the proposed research goes beyond the exemplary problem chosen and will provide, besides a cutting edge in enabling technologies, new mathematics in the emerging area of discrete, respectively, integer and continuous problems.
The mathematical insights to be gained are, on one hand, motivated by the example of gas networks, but on the other hand, they are inherently generalizable and thus applicable to other contexts. This pertains, for example, to other physical transport networks, such as water networks, as well as, more broadly, to the development of solution methods for mixed-integer nonlinear optimization problems.
All of these presented questions will be addressed in the proposed TRR 154, with the dual aim of developing mathematical foundations to tackle issues arising in practice and advancing the development of mathematical theory and methods.
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