MATH+ Project AA4-3

Title

Equilibria for Energy Markets with Transport

Project Heads

Michael Hintermüller, Volker Mehrmann, Carlos Rautenberg

Project Members

N.N. (HU Berlin)

Project Duration 01.01.2019 - 31.12.2021

Located at Humboldt Universität zu Berlin

Description. Motivated by efficient energy distribution, we develop theory and solution algorithms for a new class of generalized Nash equilibrium problems (GNEPs) arising in game theoretic formulations of energy markets. As agents of the GNEP measure data along the underlying equilibrium process, we establish model predictive control (MPC) and closed loop strategies to target realistic control scenarios. The pertinent transport physics together with additional system constraints are considered within a hierarchy of models and with possible stochastic perturbations.

References
  • D. Gahururu, M. Hintermüller, S.M. Stengl, and T.M. Surowiec. Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms, and risk aversion, preprint, 2019.
  • J. J Stolwijk and V. Mehrmann. Error analysis and model adaptivity for flows in gas networks. Analele Stiintifice ale Universitatii Ovidius Constanta. Seria Matematica, Accepted for publication, 2017.
  • M. Hinterüller, C. N. Rautenberg, M. Mohammadi, and M. Kanitsar. Optimal sensor placement: A robust approach. SIAM Journal on Control and Optimization, 55(6):3609-3639, 2017.
  • M. Hintermüller, T. Surowiec, and A. Kämmler. GNEPs in Banach spaces: theory, Nikaido-Isoda-based path-following methods, and applications. SIAM J. Optim., 25(3):1826-1856, 2015.


Poster (thanks to Olivier Huber)