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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.
Title: Optimal Control for ODEs and PDEs: The Turnpike Phenomenon, by Michael Schuster
Title: Probabilistic Constrained Optimization with Differential Equations: An Application to Gas Transport, by Michael Schuster
Martin Gugat and Martin Lazar are leading an invited session at MTNS 2022 (12-16 September 2022, Bayreuth, Germany) with title "Recent developments…
From differential calculus to differential equations, 14.07.22, Michael Schuster
This special issue is guest edited by Miguel F. Anjos, Falk M. Hante and Frauke Liers