AA4 – Energy and Markets



Energy-Based Modeling, Simulation, and Optimization of Power Systems under Uncertainty

Project Heads

Volker Mehrmann, Caren Tischendorf, Matthias Voigt

Project Members

Lena Scholz (TU) 

Project Duration

01.01.2019 – 31.12.2021

Located at

TU Berlin


Modern power systems need to be controlled and optimized as dynamical systems in real time, rather than as stationary systems as is the case today. To properly deal with strong decentralization, new long distance DC transmission lines, and the increased randomness in power generation, we plan to set up complete model hierarchies of different modeling granularity that can be used for different simulation, control, and optimization tasks. As basis we will use energy-based models (port-Hamiltonian systems) of partial differential-algebraic equations that also allow the appropriate treatment of stochasticity and time-delay.

Project Webpages

Selected Publications

  1. V. Mehrmann  and P. Van Dooren: Optimal robustness of discrete time passive systems. Preprint 09-2019, Institute of Mathematics, TU Berlin, 2019. (http://arxiv.org/abs/1909.06871)
  2. K. Cherifi, V. Mehrmann, and K. Hariche: Numerical methods to compute a minimal realization of a port-Hamiltonian system. Preprint 08-2019, Institute of Mathematics, TU Berlin, 2019. (http://arxiv.org/abs/1903.07042)
  3. L. Scholz: Condensed forms for linear port-Hamiltonian descriptor systems. Electronic Journal of Linear Algebra, vol. 35, pp. 65-89, 2019.
  4. R. Krug, V. Mehrmann, and M. Schmidt: Nonlinear Optimization of District Heating Networks, 2020. Submitted for Publication. (https://arxiv.org/abs/1910.06453)
  5. V. Mehrmann and P. Van Dooren: Structured backward errors for eigenvalues of linear port-Hamiltonian descriptor systems, 2020. Submitted for publication. (http://arxiv.org/abs/2005.04744)
  6. C. Mehl, V. Mehrmann, and M. Wojtylak: Distance problems for dissipative Hamiltonian systems and related matrix polynomials. Preprint 01-2020, Institute of Mathematics, TU Berlin, 2020. (http://arxiv.org/abs/2001.08902)
  7. S. Hauschild, N. Marheineke, and V. Mehrmann: Model reduction techniques for linear constant coefficient port-Hamiltonian differential-algebraic systems, Preprint 02-2019, Institute of Mathematics, TU Berlin. (http://arxiv.org/abs/1901.10242). To appear in Control and Cybernetics, 2020.
  8. V. Mehrmann and P. Van Dooren: Optimal robustness of port-Hamiltonian systems, SIAM Journal Matrix Analysis and Applications, Vol. 41, 134-151, 2020. (http://arxiv.org/abs/1904.13326)
  9. N. Aliyev, V. Mehrmann and E. Mengi: Computation of Stability Radii for Large-Scale Dissipative Hamiltonian Systems, Advances in Computational Mathematics, Vol. 46, 6, 2020. (http://arxiv.org/abs/1808.03574)
  10. C. A. Beattie, S. Gugercin and V. Mehrmann: Structure-preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems. Preprint 10-2019, Institute of Mathematics, TU Berlin, 2019. (http://arxiv.org/abs/1910.05674)
    To appear in Festschrift to honor the 70th birthday of A. Antoulas, 2020.
  11. V. Mehrmann and R. Morandin: Structure-preserving discretization for port-Hamiltonian descriptor systems. Proceedings of the 58th IEEE Conference on Decision and Control (CDC), 9.-12.12.19, Nice, pp. 6863–6868, 2019. (http://arxiv.org/abs/1903.10451)
  12. S.-A. Hauschild, N. Marheineke, V. Mehrmann, J. Mohring, A. Moses Badlyan, M. Rein, and M. Schmidt: Port-Hamiltonian modeling of district heating networks. To appear in DAE Forum. (http://arxiv.org/abs/1908.11226)
  13. D. Bankmann, V. Mehrmann, Y. Nesterov, and P. Van Dooren: Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis. To appear in Vietnam Journal of Mathematics, 2020. (http://arxiv.org/abs/1904.08202)

Selected Pictures

A simple DC power network
Evolution of the states of a controlled port-Hamiltonian power system model
Evolution of the Hamiltonian of a controlled port-Hamiltonian power system model

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