Energy
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.unierlangen.de).
Current Projects
CRC/Transregio 154 – Mathematical Modelling, Simulation and Optimization using the Example of Gas NetworksGas transport through pipeline systems has been an important research area in applied mathematics since several decades. In particular, the disciplines of mathematical modelling, simulation, and optimization have been applied to problems from gas transport. However, newdevelopments related to the gas market demand further progress in these mathematical disciplines. The work on these challenges will also extend the range of the yet known mathematical methods. Recently, the necessary fundamental research for this is funded by the Deutsche Forschungsgemeinschaft by implementing the Collaborative Research Center/Transregio 154 “Mathematical Modelling, Simulation, and Optimization using the Example of Gas Networks” in October 2014. The research will include not only progress in each of the mentioned areas. Rather, the main goal is a tighter linkage as a key to answer theoretical as well as applied questions associated to gas transport. Spokesperson of this CRC/Transregio is Alexander Martin. For more details visit trr54.fau.de 

Energie Campus NürnbergThe structurally adjusted treatment of diverse forms of energy, their availability on different scales in time and space, and their feedin and transportation through a holistically designed “energy grid” are among the major challenges for the power industry and powerrelated sciences. The Energie Campus Nürnberg (EnCN) is an interdisciplinary research center that combines scientific work from the areas engineering and natural sciences, computer sciences, socioeconomic, architecture, and mathematics. Its goal is to put to the vision of a sustainable power society based on renewable energy into practice. Currently, the EnCN is divided into ten research projects that strongly interact with each other. The chair of EDOM is active in the project EnCN Simulation that acts as a link between the other EnCN projects Transport, Networks, Process, Building, and (in particular) Economy. Examples of encompassing goals are the optimal layout, planning, and coupling of networks or the development of models and methods to increase robustness against fluctuating availability of energy forms, quantities, market economies and consumption. For more details visit encn.de 

EWave – Water Supply Energy Management SystemOver the past few years, requirements for drinking water supply in Germany have become more and more demanding. While the secure supply of highquality drinking water for the public was the priority during the past decades, rising energy costs and the energy reform being implemented by the German Federal Government now also require that energy is used efficiently. The joint research project EWave aims to develop an innovative energy management system. The objective is to devise energyoptimized operating plans for plants for water collection, treatment, and distribution within the supply system by using stateoftheart methods, algorithms and software from discrete and continuous optimization. 

Robustification of Physical Parameters in Gas NetworksIn many realworld optimization problems, not every model parameter can be measured precisely. With the help of robust optimization, uncertain problems can be immunized against perturbations of the input parameters. We focus on the nomination validation problem under uncertain roughness values of the networks’ pipes. As the simple strict robustification is too conservative for this setting, a more flexibel twostage approach is developed. A particular challenge is the incorporation of binary decision variables in this framework. The goal of this research project is the development of tractable robust counterparts for global optimization problems, with a focus on gas networks. More details can be found here. 

Adaptive MIPRelaxations for MINLPsGoal of the project is the analysis and solution of largescale MINLPs, especially from the application of instationary gas network optimization, using adaptive MIP models. We approximate the nonlinearities with piecewiselinear functions to construct MIP relaxations of the underlying MINLP. In addition, theoretical results linking the complexity of the relaxations to structural properties of the nonlinear functions and the linearization error shall be derived, whereby known statements of approximation theory are to be combined with techniques of polyhedral combinatorics. Furthermore the polyhedral structure of the resulting MIP relaxations shall be investigated. Mor details can be found here. 

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 minigrid 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. 

Transient Gas Network OptimizationA 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 costefficiently. 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. 

Validation of Nominations in Gas NetworksA 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 mixedinteger nonconvex nonlinear problem. 

Integrated Regenerative Energy Concepts in Urban AreasThe 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. 

Optimal Design of Coupled Energy Carrier NetworksFor 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 SupplyIntegrating 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 costefficiently over a period of one day. 

Clearing Coupled DayAhead Electricity MarketsThe European power grid can be divided into several market areas where the price of electricity is determined in a dayahead 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 crossborder 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 nondiscriminatory market model to determine clearing prices that maximize the economic surplus of all participants. The determined prices are consistent throughout the market areas. 

Sustainable Business Models in Energy MarketsThe liberalization of electricity markets and the increasing advancement of renewable energy sources pose important new challenges and requirements for our energy system with regard to grid expansion, energy production, transmission, distribution, and innovative storage systems. A successful transformation into a smart energy system thereby crucially depends on adequate investment incentives and the attractiveness of the business models of involved stakeholders. The purpose of the research project “Sustainable Business Models in Energy Markets: Perspectives for the Implementation of Smart Energy Systems” is to provide a comprehensive analysis of the energy system, including the specific economic incentives and business models of all relevant stakeholders, the institutional environment and the technological perspectives. The aim of the project is to develop new and urgently needed insight into the interaction between business models and regulation while taking into account the technological framework, and to allow a more informed discussion and advice regarding political and regulatory frameworks to ensure a successful transition towards a smart energy system. 