Modeling, simulation, and optimization are important methodological pillars of digital engineering and have triggered a revolution in the way we approach things. Spearheaded by applications in mechanical engineering and logistics, also chemical engineering and information technologogy have been witnessing an explosion of computational approaches. This trend is further accelerated by availability of data, open source software, hardware improvements, and interdisciplinary approaches and cooperations. At the same time, we have been entering a transition phase towards a sustainable energy policy using several fluctuating energy sources.

Electricity load in Germany for two exemplary weeks, showing the impact of renewable energy.

Power2X is the name for a number of electricity conversion, energy storage, and reconversion pathways that use surplus electric power, typically during periods where fluctuating renewable energy generation exceeds load, as indicated in the example illustration above.

It is important to do this conversion efficiently, as massive installations and import of renewable energies are necessary to reduce CO2 emissions. Here E-Fuels (H2, CH4, CH3OH, OME) made from renewable energy and CO2 are an attractive option. The flexible design and operation of Power2X processes by optimization and optimal control can give insight into the most promising solutions.

However, there are many challenges to a computational approach. Usually, there are many different units / processes involved, often modeled via complicated partial differential equation (PDE) models and involving still unknown/unmodeled mechanisms. In addition there are uncertainties in the fluctuating inputs (electricity, products of biogas plants) and demand imposing intelligent storage solutions. The design of novel processes is impaired by many combinatorial choices.

The following figure from the paper CO2 Methanation Process Synthesis by Superstructure Optimization shows an optimal Power2Methane choice for particular assumptions on available processes in a preimposed order (one choice per column possible) and particular purity constraints and objective function specifications. It was calculated based on steady-state assumptions with an optimization-driven software solution developed in my group. An extension to transient processes and a clever interaction between detailed PDE models and underestimating surrogate models is ongoing work.

Discrete choices in Power2Methane.

We have been working on storage capacities in electricity grids and on the optimal design and control of Power2X processes, with a focus on Methane and Methanol as energy carriers.

@article{Schweidtmann2021,
    author = {Schweidtmann, A.M. and Esche, E. and Fischer, A. and Kloft, M. and Repke, J. and Sager, S. and Mitsos, A.},
    title = {Machine Learning in Chemical Engineering: A Perspective},
    publisher = {Wiley Online Library},
    year = {2021},
    volume = {93},
    number = {12},
    pages = {2029--2039},
    doi = {10.1002/cite.202100083}
}

@article{Uebbing2021,
    author = {Uebbing, J. and Biegler, L.T. and Rikho-Struckmann, L. and Sager, S. and Sundmacher, K.},
    title = {Optimization of Pressure Swing Adsorption via a Trust-Region Filter Algorithm and Equilibrium Theory},
    journal = {Computers \& Chemical Engineering},
    year = {2021},
    volume = {151},
    pages = {107340},
    doi = {10.1016/j.compchemeng.2021.107340}
}

@incollection{Garmatter2020,
    author = {Garmatter, D. and Maggi, A. and Wenzel, M. and Monem, S. and Hahn, M. and Stoll, M. and Sager, S. and Benner, P. and Sundmacher, K.},
    title = {Power-to-Chemicals: A Superstructure Problem for Sustainable Syngas Production},
    booktitle = {Mathematical Modeling, Simulation and Optimization for Power Engineering and Management},
    publisher = {Springer},
    year = {2020},
    pages = {145--168}
}

@article{Himmel2020,
    author = {Himmel, A. and Sager, S. and Sundmacher, K.},
    title = {Time-minimal set point transition for nonlinear SISO systems under different constraints},
    journal = {Automatica},
    year = {2020},
    volume = {114},
    pages = {108806},
    url = {http://www.sciencedirect.com/science/article/pii/S0005109820300042},
    doi = {10.1016/j.automatica.2020.108806}
}

@misc{Rackauckas2020,
    author = {Rackauckas, C. and Ma, Y. and Martensen, J. and Warner, C. and Zubov, K. and Supekar, R. and Skinner, D. and Ramadhan, A.},
    title = {Universal differential equations for scientific machine learning},
    year = {2020},
    note = {arXiv preprint arXiv:2001.04385}
}

@article{Uebbing2020,
    author = {Uebbing, Jennifer and Rihko-Struckmann, Liisa and Sager, Sebastian and Sundmacher, Kai},
    title = {CO2 methanation process synthesis by superstructure optimization},
    journal = {Journal of CO2 Utilization},
    publisher = {Elsevier},
    year = {2020},
    volume = {40},
    pages = {101228}
}

@inproceedings{Buerger2018a,
    author = {Buerger, A. and Zeile, C. and Altmann-Dieses and A., Sager, S. and Diehl, M.},
    title = {An Algorithm for Mixed-Integer Optimal Control of Solar Thermal Climate Systems with MPC-capable runtime},
    journal = {Proceedings of the European Control Conference (ECC)},
    year = {2018},
    url = {https://ieeexplore.ieee.org/document/8550424}
}

@incollection{Himmel2017,
    author = {Himmel, Andreas and Sager, Sebastian and Sundmacher, Kai},
    title = {Set point tracking of a biogas plant coupled to a methanation reactor},
    booktitle = {Computer Aided Chemical Engineering},
    publisher = {Elsevier},
    year = {2017},
    volume = {40},
    pages = {1645--1650}
}

@inproceedings{Matke2017,
    author = {Matke, C. and Bienstock, D. and Munoz, G. and Yang, S. and Kleinhans, D. and Sager, S.},
    title = {Robust optimization of power network operation: storage devices and the role of forecast errors in renewable energies},
    booktitle = {Studies in Computational Intelligence: Complex Networks and Their Applications V},
    year = {2017},
    number = {693},
    pages = {809--820},
    doi = {10.1007/978-3-319-50901-3}
}

@inproceedings{Matke2017a,
    author = {Matke, Carsten and Medjroubi, Wided and Kleinhans, David and Sager, Sebastian},
    title = {Structure Analysis of the German Transmission Network Using the Open Source Model SciGRID},
    booktitle = {Advances in Energy System Optimization},
    publisher = {Springer International Publishing},
    year = {2017},
    editor = {Bertsch, Valentin and Fichtner, Wolf and Heuveline, Vincent and Leibfried, Thomas},
    pages = {177--188},
    address = {Cham}
}

@inbook{Gruene2010,
    author = {Gr\"une, L. and Sager, S. and Allg\"ower, F. and Bock, H.G. and Diehl, M.},
    title = {{P}roduction {F}actor {M}athematics},
    publisher = {Springer},
    year = {2010},
    editor = {Gr\"otschel, M. and Lucas, K. and Mehrmann, V.},
    pages = {9--38},
    note = {ISBN 978-3-6421-1247-8}
}