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] P. Kunkel and V. Mehrmann. Differential-Algebraic Equations. EMS Press, 2 edition, 2024.
[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, 37(2):1747–1786, 2023. doi:10.1007/s10884-023-10327-6.
[3] F. Achleitner, A. Arnold, V. Mehrmann, and E. A. Nigsch. Hypocoercivity in Hilbert spaces. Journal of Functional Analysis, 288(2):110691, 2025. doi:10.1016/j.jfa.2024.110691.
[4] K. Cherifi, H. Gernandt, D. Hinsen, and V. Mehrmann. On discrete-time dissipative port-Hamiltonian (descriptor) systems. Mathematics of Control, Signals, and Systems, 36(3):561–599, 2024. doi:10.1007/s00498-023-00376-z.
[5] H. Dänschel, L. Lentz, and U. von Wagner. Error measures and solution artifacts of the harmonic balance method on the example of the softening Duffing oscillator. Journal of Theoretical and Applied Mechanics, 62(2):435–455, 2024-04. doi:10.15632/jtam-pl/186718.
[6] H. Gernandt, B. Severino, X. Zhang, V. Mehrmann, and K. Strunz. Port-Hamiltonian modeling and control of electric vehicle charging stations. IEEE Transactions on Transportation Electrification, 11(1):2897–2907, 2025. doi:10.1109/TTE.2024.3429545.
[7] N. Kastendiek, J. Niehues, R. Delabays, T. Gross, and F. Hellmann. Phase and gain stability for adaptive dynamical networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(5):053142, 2025-05-13. doi:10.1063/5.0249706.
[8] P. Kunkel and V. Mehrmann. Differential-Algebraic Equations. EMS Press, 2 edition, 2024.
[9] V. Mehrmann and B. Unger. Control of port-Hamiltonian differential-algebraic systems and applications. Acta Numerica, 32:395–515, 2023. doi:10.1017/S0962492922000083.
[10] V. Mehrmann and A. van der Schaft. Differential–algebraic systems with dissipative Hamiltonian structure. Mathematics of Control, Signals, and Systems, 35(3):541–584, 2023. doi: 10.1007/s00498-023-00349-2.
[11] U. von Wagner, L. Lentz, H. Dänschel, and N. Gräbner. On large amplitude vibrations of the softening duffing oscillator at low excitation frequencies—some fundamental considerations. Applied Sciences, 2024. doi:10.3390/app142311411.
[12] Y. Zhang, A. Palha, A. Brugnoli, D. Toshniwal, and M. Gerritsma. Decoupled structure-preserving discretization of incompressible MHD equations with general boundary conditions, 2025. URL: https://arxiv.org/abs/2410.23973, arXiv:2410.23973.
[13] H. Zwart and V. Mehrmann. Abstract dissipative Hamiltonian differential-algebraic equations are everywhere. DAE Panel, 2, 2024-08-23. doi:10.52825/dae-p.v2i.957.
[14] J. Niehues, A. Büttner, A. Riegler, and F. Hellmann. Complex phase analysis of power grid dynamics, 2025. URL: https://arxiv.org/abs/2506.22054, arXiv:2506.22054.