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Modelling and Optimizing the General Power System


Project team leaders: Prof. Peter Gritzmann, Dr. René Brandenberg, Dr. Michael Ritter
Ph.D. Students: Dipl.-Math. Matthias Silbernagl, M. Sc. (hons) Paul Stursberg
Research partners Lehrstuhl für Energiewirtschaft und Anwendungstechnik (Fakultät für Elektrotechnik und Informationstechnik, TUM)
Fachgebiet Elektrische Energieversorgungsnetze (Fakultät für Elektrotechnik und Informationstechnik, TUM)


The efficient integration of renewable energy into the existing infrastructure poses a multitude of challenges, many of which have not been brought to a satisfactory conclusion so far, such as the power grid and its expansion, unit commitment in systems with intermittent renewable energy units, and the impact of renewable energy on the power market.


DecEnSys - Dekomposition von Energiesystemen zur Modellierung dezentraler Stromversorgungssysteme

The number of renewable energy sources integrated into the German power system is increasing, which leads to changes in the structure of the system. The centralised and hierar- chical system is becoming more and more decentralised. Mutual dependencies grow between energy sources, network regions and system levels which leads to additional uncertainty. On the other hand, the energy system is analysed and evaluated mostly on separate system levels (from municipalities to entire nations) with specifically adapted modelling techniques on different levels of detail. The changes mentioned require a more integrated perspective on the energy system that connects these different approaches.

The project DecEnSys aims to further develop methods for modelling and optimisation of energy systems to couple the various system levels in a reliable way. This will serve to represent the mentioned properties of the future energy system more appropriately. The project is based on modern methods of mathematical optimisation and aims to develop these further. Decomposition methods, which will be adapted explicitly to problems of energy system analysis, allow a more detailed representation of the decentralised future energy system including the existing uncertainties. Using this representation, reliable demand analyses will be carried out. Furthermore, detailed models for municipalities and larger regions can be incorporated using suitable interfaces.

Based on the developed methods, economically optimal expansion and development plans for power plant, grid and bmwe 4c gef en.pngstorage infrastructure will be computed. For the computation, relevant uncertain factors as well as existing policies on all system levels can be taken into account. The results will be published and the improved methods will be implemented and made accessible under an open-source license to simplify public access.

The project is carried out in cooperation with the Chair of Renewable and Sustainable Energy Systems of TUM and funded by the German Federal Ministry for Economic Affairs and Energy as part of the Forschungsnetzwerk Energiesystemanalyse 

Integration of Renewable Electricity Generation

g16.png Investment decisions in the energy sector such as the construction of new power lines and generators typically have to be taken years or decades in advance. Therefore, choices have to be made now in order to be ready for an energy system dominated by renewables twenty years from now. In order to evaluate these options, our partners from the Institute for Energy Economics and Application Technology use large-scale optimisation models that compute economically optimal investment decisions for the next decades.

Because of the long time horizon, these optimisation problems quickly become huge in size, even while using only highly simplified technological constrains. In some places, these simplifications can be justified because the omitted details hardly play a role in the long-term perspective. In other places, such as the transmission grid, details become increasingly important: The constraints of the grid determine to what extent generation facilities can be moved away from load centres and to places with better availability of renewable resources. Furthermore, transmission between different geographical regions enables the system to balance load peaks in one region with generation peaks in a different region.

In this project, we are searching for ways to include detailed physical properties of the transmission grid into the large-scale optimisation models used for investment planning. Among the mathematical tools used are decomposition techniques and convex duality theory.

The project is funded by the International Graduate School of Science and Engineering (IGSSE).

Concluded Subprojects

Unit Commitment in Systems with Intermittent Renewable Energy

Production fluctuations are intrinsic to the widely used kinds of renewable energy, solar and wind energy. To match the power consumption, these fluctuations have to be counteracted by the remaining units, exposing them to irregular load patterns with higher ramps and lower baseload. Consequentially, the start-up and ramping process gains importance when scheduling power units. We are researching new start-up process models, and improving the existing ramping and start-up cost models.

Modelling the Power Market

Power markets - supply and demand

Renewable energy production, especially wind and solar power, is characterised by intermittency. The production volume can be predicted, but not controlled. Increased investments in such intermittent production capacity will influence the electricity markets whereby balancing supply and demand will have to be satisfied by thermal units.

"Slow" thermal units, like for example nuclear and lignite units, produce at low costs, but are not able to cost-efficiently adjust energy output. On the other hand, "fast" thermal units like modern coal units, and in particular gas units, have higher production costs, but are able to ramp their production up and down fast and efficiently. This suggests that a higher share of renewable energy will depend on "fast" thermal units, and thus increase the demand for natural gas in the electricity sector.

Our cooperation partner Statoil, the main Norwegian energy company, has an interest in an accurate assessment of the consequences of such a development, because:

  • It influences the market potential of natural gas, and
  • It influences the profitability of gas-to-power
To prove and quantize the increased market potential of natural gas, we model the electricity market with a so-called Unit Commitment problem. Each unit is modelled by its basic physical and economical properties, placing special care on its ramping speed and on its start-up and shutdown costs. Using historical data and forecasted power demands, a cost-optimal, time-dependent production schedule for all units is calculated.

From this schedule and from the derived electricity prices, the profitability of different unit types can be deduced. This includes, in particular, the profitability of gas units and the market potential of natural gas.

The major drawback of this approach is the missing consideration of the market composition. Most electricity markets, however, are dominated by a relatively small number of electricity generating companies satisfying the bulk of the electricity demand. Such companies arguably would be able to influence the electricity price significantly.

Therefore, we are developing a model based on a game theoretical approach with the goal of capturing this market power.

Publications and Preprints

/abs/1408.2644][arXiv version]]
  • R. Brandenberg, P. Stursberg - Cut Selection for Benders Decomposition, submitted, arXiv version .
  • R. Brandenberg, P. Stursberg - A Generalization of Spanning Trees for Network Flows with Differential Constraints, in preparation.

Related student theses and projects

Supervised Dissertations

  • Paul Stursberg - Integration of Renewable Electricity Generation
  • Matthias Silbernagl - Discrete optimization approaches for modelling the european power market

Completed Theses and Projects

Completed Master's Theses

  • Franziska Penk - Optimizing Power Plant and Storage Dispatch under Uncertainty of Renewable Energy - A Solution Based on Stochastic Dual Dynamic Programming (2014)
  • Eva Bammann - Central Management of Flexible Loads for Ancillary Services Provision (2014)
  • Ludwig Jäntschi - Robuste Optimierung für die Modellierung von Energiesystemen (2013)

Completed Bachelor's Theses

  • Antonia Demleitner - On optimizations problems in generalized networks (2016)
  • Sarah Frank - Auswirkungen von Veränderungen des Übertragungsnetzes auf das Verhalten von Stromerzeugern (2015)
  • Barnabas Arvay - Optimization of power storage for regional electricity networks: A realistic model for production planning (2011)

Completed Projects

  • Daniel Opritescu - Optimaler Speichereinsatz in der Stromerzeugung: Zufällige Schwankungen im Verbrauch (2010)

Completed Case Studies Projects

  • Christian Biefel, Anja Kirschbaum, Benedikt Plank, Martin Sutter - Scheduling in Smart Grids (2016)
  • Eva Bammann, Vincent Bates, Franziska Penk - Decomposition Methods on a Smart Grid Optimization Model (2012)
  • Julia Bergbauer, Anna Sanden, Pascal Schambach, Andrej Winokurow - The New Age of Power Supply (2011)
  • Barnabas Arvay, Dominik Billing, Alexander Breuer, Thomas Fischer, Lisa Henkel, Thomas Himmelstoß - We’ve got the power! (2011)

Research Unit M9

Department of Mathematics
Boltzmannstraße 3
85748 Garching b. München
phone:+49 89 289-16858
fax:+49 089 289-16859


Prof. Dr. Peter Gritzmann
Applied Geometry and Discrete Mathematics

Prof. Dr. Andreas S. Schulz
Mathematics of Operations Research
(affiliated member of M9)

Prof. Dr. Stefan Weltge
Discrete Mathematics


Jan 25th, 2019
Case Studies 2019: Preliminary Meeting on Wed, Feb 6th, at 16:00 in room MI 03.06.011.