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

Finished Projects

Optimization of Hybrid Energy Systems

Hybrid 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.

A gas network basically consists of compressors and valves, connected by pipes. The aim of gas network optimization is to operate the network in such a way that the consumer's demands are satisfied and the compressors are set in cost-efficiently. This leads to a complex mixed integer nonlinear optimization problem. We develop approximation techniques for the nonlinearities, which are suitable for a mixed integer linear programming model.

A fundamental task in gas transportation is the validation of nomination (or nomination validation) problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, ﬁnd operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. The validation of nominations problem is a complex and numerical difficult mixed-integer nonconvex nonlinear problem.

Integrated Regenerative Energy Concepts in Urban Areas

The construction sector offers a high potential for increasing its energy efficiency by using renewable energies combined with a strong interconnection of different energy carriers. The planning of efficient energy supply concepts within the building sector requires the integrated consideration of decentralized energy generation, energy storages, and combined energy networks. Technologies such as photovoltaics, geothermal power, and combined heat and power as well as biomass from urban open spaces are included in the planning process.

For the optimal planning of dispersed generation systems, multiple energy carriers such as electricity, gas, and heat have to be considered simultaneously. The aim of this project is the optimization of the network layout and the dimension of the cables and pipes, respectively. Here the consumer demands can be satisfied by the public supply network as well as by dispersed combined heat and power plants. Mathematically, this problem results in a complex nonlinear mixed integer program.

Optimal Use of Energy Storages and Power Plants in Power Generation including Regenerative Energy Supply

Integrating an offshore wind park into a public electricity network leads to the problem of fluctuating energy supply. Therefore, energy storages and conventional power plants are used to compensate the imbalance of the regenerative energy supply and the consumers' demand. The aim of this project is to operate the storages and plants cost-efficiently over a period of one day.

The 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.