Mathematics for Sustainable Energies

The last years have brought a fundamental political change towards energy management in Germany: As soon as possible regenerative energies on all scales are to replace nuclear as well as fossil fuel energies. Electromobility is changing traffic profiles, in particular urban traffic. Decentralized compact power stations that save one portion of the inevitable thermodynamic degree of efficiency by consuming the heat at the generation site will have to be established and optimally linked. Apart from these individual topics, the overall topic of energy efficiency has gained a dominant importance. All of these topics induce numerous new quantitative problems of high complexity, which are the source of new mathematical challenges.

Photovoltaics is one of the fastest growing regenerative energy sectors. In the focus of present interest are demands of higher efficiency with lower material usage and production costs.

In the Action Plan for Electromobility 2020, Berlin sets the goal of becoming Europe's leading location for electromobility. As for the technological basis, the key words are fuel cells, novel batteries or plug-in hybrids. Of course, urban traffic will be the topic of main interest for Berlin.

Decentralized power station networks. In the years to come, an increasing number of buildings will produce energy in a regenerative way, e.g., via solar cell roofs and walls. Whenever the produced electrical energy is not needed at the homes, the locally available electrical power will have to be fed into the communal electrical network systems. This gives rise to multiple problems of energy distribution and optimal network management, problems of utmost mathematical and computational complexity.

Projects

Project heads

Staff

SE1

Reduced order modeling for data assimilation

Project heads Prof. Dr. Volker Mehrmann
Dr. Christian Schröder

Staff Dr. Matthias Voigt

Duration: - Status: completed Located at: Technische Universität Berlin (TU Berlin)

Description

One of the bottlenecks of current procedures for the generation and distribution of green (wind or solar) energy is the accurate and timely simulation of processes in the ocean and atmosphere that can be used in short term planning and real time control of energy systems. A particular difficulty is the real time construction of physically plausible model initializations and 'controls/inputs' to bring simulations into coherence with available observations when observation locations and observations are coming in at variable times and locations.

The currently best approach for fixed observation times and locations are variational data assimilation techniques. These methods use a four dimensional model that is adapted to the incoming observations using a combination of different filtering techniques and numerical integration of the dynamical system. In order to make these methods efficient in real time data assimilation they have to be combined with appropriate model order reduction methods. A major difficulty in these techniques is the combination of approximate transfer functions and approximate initial and boundary conditions as well as the construction of guaranteed error estimates and the capturing of essential features of the original model. The so-called representer approach formulates the data assimilation problem as the numerical solution of a large-scale nonlinear optimal control problem and incorporates the assimilation of the model to the observations, via an extended ensemble Kalman filter, and the adaptation of the initial data in one approach. Adding further assumptions and linearization this optimization problem usually reduces to a linear quadratic optimal control problem which is solved via the solution of a boundary value problem with Hamiltonian structure.