Project
AA4-12
Advanced Modeling, Simulation, and Optimization of Large Scale Multi-Energy Systems
Project Heads
Volker Mehrmann
Project Members
Andrea Brugnoli (formerly), Riccardo Morandin
Project Duration
01.01.2023 − 31.12.2024
Located at
TU Berlin
Description
The transition of the energy system by including renewable sources and the coupling of different energy sectors make the dynamical models large and highly volatile. To prevent system failures and to reduce costs, the operation of systems needs to change to real-time. To achieve this we will use the energy-based framework of constrained port-Hamiltonian PDEs to construct model hierarchies for every network node, ranging from PDEs to data-based models, in combination with structure preserving model order reduction and space-time-model-adaptive methods.
At the top of the hierarchy of models are the generators. These electrical machines are complex technological devices, as they intrinsically couple electromagnetism and mechanics during their operation. A model problem for this coupling is represented by the equations of magnetohydrodynamics (MHD), that describes the physics of ionized fluids such as plasma. Structure-preserving numerical schemes for MHD are currently under investigation. These algorithms can then be extended to electrical machines by replacing the material behaviour of the fluid to that of a solid. Once an high-fidelity description of electrical machines is available, simplifications can be introduced to obtain coarser models for other components of the electrical grid.
Related Publications
[1] F. Achleitner, A. Arnold, and V. Mehrmann: Hypocoercivity and hypocontractivity concepts for linear dynamical systems. Electronic Journal of Linear Algebra Vol. 38, 883-911, 2023.
[2] F. Achleitner, A. Arnold, and V. Mehrmann: Hypocoercivity in algebraically constrained partial differential equations with application to Oseen equations. Journal of Dynamics and Differential Equations, 2023.
[3] F. Achleitner, A. Arnold, V. Mehrmann, and E. Nigsch: Hypocoercivity in Hilbert spaces. Submitted to J. Func. Amnal. Preprint http://arxiv.org/2307.08280.
[4] N. Behera, A. Bist, and V. Mehrmann: Fiedler Linearizations of Rectangular Rational Matrix Functions. Bull. Iranian Math. Society, 2023.
[5] A. Brugnoli, and V. Mehrmann: On the discrete equivalence of Lagrangian, Hamiltonian and mixed finite element formulations for linear wave phenomena. Preprint http://arxiv.org/abs/2401.09348.
[6] K. Cherifi, H. Gernandt, D. Hinsen, and V. Mehrmann: On dissipative and port-Hamitlonian discrete-time descriptor systems. Mathematics of Control Signals and Systems, 2023.
[7] K. Cherifi, V. Mehrmann, and P. Schulze: Simulations in a Digital Twin of an Electrical Machine. Preprint http://arxiv.org/abs/2207.02171.
[8] D. Chu, and V. Mehrmann: Stabilization of linear Port-Hamiltonian Descriptor Systems via Output Feedback. Preprint http://arxiv.org/abs/2403.18967.
[9] T. Faulwasser, J. Kirchhoff, V. Mehrmann, F. Philipp, M. Schaller, and K. Worthmann: Hidden regularity in singular optimal control of port-Hamiltonian systems. Preprint https://arxiv.org/abs/2305.03790.
[10] H. Gernandt, B. Severino, X. Zhang, V. Mehrmann, and K. Strunz: Port-Hamiltonian modeling of electric vehicle charging stations. In revision to IEEE Transactions on Transportation Electrification, 2024.
[11] P. Kunkel, and V. Mehrmann: Discretization of an inherent ODE and the geometric integration of DAEs with symmetries. BIT, Numerical Mathematics, 63:29, 2023.
[12] P. Kunkel, and V. Mehrmann: Local and global canonical forms for differential-algebraic equations with symmetries. Vietnam Journal of Mathematics, Vol. 51, 177-198, 2023.
[13] P. Kunkel, and V. Mehrmann: Differential-Algebraic Equations – Analysis and Numerical Solution. EMS Publishing House, Zürich, Switzerland, 1. ed. 2006. EMS Press, Berlin, Germany, 2. ed. 2024.
[14] J. Liesen, and V. Mehrmann: Lineare Algebra. Ein Lehrbuch über die Theorie mit Blick auf die Praxis. 4. Ed. Springer Nature Studium, Wiesbaden, 2024.
[15] C. Mehl, V. Mehrmann, and M. Wojtylak: Spectral theory of infinite dimensional dissipative Hamiltonian systems. Preprint https://arxiv.org/2405.11634.
[16] V. Mehrmann, and B. Unger: Control of port-Hamiltonian differential-algebraic systems and applications. Acta Numerica, 395-515, 2023.
[17] V. Mehrmann, and A.J. van der Schaft: Differential-algebraic systems with dissipative Hamiltonian structure. Math. Control Signals Systems, 1-44, 2023.
[18] V. Mehrmann, and H. Xu: Eigenstructure perturbations for a class of Hamiltonian matrices and solutions of related Riccati inequalities. To appear in SIAM J. Matrix Analysis and its Applications, 2024.
[19] V. Mehrmann, and H. Zwart: Abstract dissipative Hamiltonian differential-algebraic equations are everywhere. https://arxiv.org/5223640, 2023.
[20] R. Morandin: Modeling and Numerical Treatment of Port-Hamiltonian Descriptor Systems. PhD thesis, Technische Universität Berlin, 2024.
[21] R. Morandin, J. Nicodemus, and B. Unger: Port-Hamiltonian Dynamic Mode Decomposition. SIAM Journal on Scientific Computing, Vol. 45 (4), A1690-A1710, 2023.
[22] A.J. van der Schaft, and V. Mehrmann: Linear port-Hamiltonian DAE systems revisited. System and Control Letters, Vol. 177, 105564, 2023.
[23] P. Schwerdtner, T. Moser, V. Mehrmann, and M. Voigt: Optimization-based model order reduction of port-Hamiltonian descriptor systems. Systems & Control Letters, 2023.