## Optimization of Energy Systems

The EDOM group has been active in the optimization of energy systems for several years. In a number of projects we have cooperated with electrical and civil engineers, architects, economists, and other mathematicians from universities, research institutes, and industry alike. We investigate problems arising from the planning and operation of energy networks as well as from the analysis of energy markets. We model these as optimization problems, where we can tackle discrete (e.g., yes/no) decisions but also the physical and technical restrictions. In addition, we include stochastic components and multilevel structures in the models where appropriate.

If you have further questions regarding our projects; please contact Alexander Martin (alexander.martin[at]fau.de), Martin Schmidt (mar.schmidt[at]fau.de), or Lars Schewe (lars.schewe[at]math.uni-erlangen.de).

### Current Projects

## Optimal Control of Electrical Distribution Networks with Uncertain Solar Feed-InThe objective of this project is to develop innovative techniques for modelling, simulation and optimization of electrical distribution networks with regard to uncertain solar feed-in. We want to study and optimize fluctuating energy feed and corresponding power flows. Therefore new mathematical approaches will be combined to guarantee a efficient design and stable real-time operation. Details |

## MINOA: Mixed-Integer Non-Linear Optimization: Algorithms and ApplicationsMINOA will train a new generation of scientists in the rather young but fast growing field of mixed-integer nonlinear optimisation applications and algorithms, by enhancing research-related and transferable competences and exposure to the non-academic sector. Through self-organizing training events, the young researchers take responsibility at an early stage of their career. The settings provided by the hosting institutions empower the ESRs to become independent and creative researchers, which increases their employability. Mobility and internationality is provided through secondments within our international consortium that includes institutions from 6 European countries. Furthermore, network-wide events take place regularly. |

### Finished Projects

## Optimization of Hybrid Energy SystemsHybrid energy systems usually consist of two or more energy sources with at least one renewable source and one completely controllable source. In our case the hybrid system also comprises of energy storages, different types of energy consumers and a mini-grid connecting a small number of households. The aim of the project is the optimization of the internal and external power distribution, i. e. inside the individual households as well as between the different households, in order to minimize the energy costs while satisfying the demands. |

## Clearing Coupled Day-Ahead Electricity MarketsThe European power grid can be divided into several market areas where the price of electricity is determined in a day-ahead auction. Market participants can provide continuous hourly bid curves and combinatorial bids with associated quantities given the prices. The goal of the auction is to determine cross-border flow and market clearing prices. Whereas this can be done rather efficiently in the absence of combinatorial structure, in the case of electricity markets the determination of a market clearing price is hard. We solve a non-discriminatory market model to determine clearing prices that maximize the economic surplus of all participants. The determined prices are consistent throughout the market areas. |