Simulation of Energy Systems
Modeling and simulation of fluids in large networks is a challenging problem, especially if the simulation is used to provide solutions to optimal control problems or other optimization questions. Our first goal is to be able to simulate this systems in a stable and efficient manner as truely transient systems, considering in particular the underlying network stucture.
Simulation of gas networks is a complex problem, however absolutely necessary in view of the political, technical and environmental changes that happened over the last 20 years and will happen even more so in the next 20 years. Our goals are
- fast simulation
- good coupling of reduced components
- hierachical understanding of the system
- control theory
Analysis of the DAE structure for gas and water networks
- Index Calculations
- Decoupling Methods
- Discretization schemes in view of the index
Reduction of Network Systems
Multi-agent systems appear in a wide range of applications, such as transport networks, robot swarms, and opinion networks. They consist of many small simple systems (agents) connected in a huge complex network. To be able to simulate or control such a huge system, a reduced model is necessary. Since the interesting dynamics originates from the network structure, it is preferable to preserve it in the reduced model. This motivates the research into clustering-based model reduction methods, where clusters become agents in the reduced model, thus preserving network structure.
Sara Grundel and Lennart Jansen, "A joint IMEX-MOR approach for Water Networks", in IFAC-PapersOnLine, (2015), Vol. 48, pp. 260-261.
Sara Grundel, Lennart Jansen, Nils Hornung, Tanja Clees, Caren Tischendorf, and Peter Benner, "Model Order Reduction of Differential Algebraic Equations Arising from the Simulation of Gas Transport Networks", in Progress in Differential-Algebraic Equations, Deskriptor 2013, edited by Sebastian Schöps, Andreas Bartel, Michael Günther, E. Jan W. ter Maten, and Peter C. Müller (Springer, Berlin, 2014), pp. 183-205.
Sara Grundel, Nils Hornung, Bernhard Klaassen, Peter Benner, and Tanja Clees, "Computing Surrogates for Gas Network Simulation Using Model Order Reduction", in Surrogate-Based Modeling and Optimization, edited by S. Koziel and L. Leifsson (Springer, New York, 2013), pp. 189-212.