# 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.uni-erlangen.de).

*Ongoing Projects*

### CRC/Transregio 154 – Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks

Gas 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 Nürnberg

The structurally adjusted treatment of diverse forms of energy, their availability on different scales in time and space, and their feed-in and transportation through a holistically designed “energy grid” are among the major challenges for the power industry and power-related sciences. The Energie Campus Nürnberg (EnCN) is an interdisciplinary research center that combines scientific work from the areas engineering and natural sciences, computer sciences, socio-economic, 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

### Robustification of Physical Parameters in Gas Networks

### Description

The goal of research project B06 within the CRC 154 is the development of tractable robust counterparts for global optimization problems, with a focus on gas networks. The motivation stems from the fact that for many real-life problems some parameters can only be estimated roughly. A well-known example in gas network optimization is the roughness value of the pipe that influences the friction of the gas and thereby effects the pressure loss between the endpoints of the pipe. However, the roughness depends on the contamination of the pipe and can only be measured with great effort. Another example is the real gas factor which depends on the gas mixture. Since gases with different chemical composition are mixed within the network, usually the exact gas mixture is unknown, and the real gas factor has to be estimated. Moreover, different formulas are used that describe the function for determining the friction from the pipe roughness. Finally, there are methodological uncertainties from the approximation of nonlinear functions in the context of mixed-integer linear optimization problems (MIPs). Similar situations are found in a wide range of applications. Therefore, results of this research project may be used for other optimizations problems under uncertainty, e.g. for water-network optimzation. In our robust optimization setting, continuous state variables are categorized as adjustable (“wait-and-see”), whereas binary decision variables are modeled as static or “here-and-now” variables. The robustification of the mentioned problem leads to mixed-integer linear, conic quadratic or positive semidefinite optimization problems, depending on the given uncertainty set and the occurance of the uncertain data. These different modeling options are adapted for gas-network optimization. A major goal will be the development of exact methods that use positive semidefinite subproblems. Initially, only the stationary case is considered. However, an extension to straight-forward transient models is a mid-term goal.

### People involved

Denis Aßmann

Frauke Liers

Michael Stingl

### Contact

For further details about this project please contact Denis Aßmann (denis.assmann [at] fau.de)

### Supported by

Deutsche Forschungsgemeinschaft, CRC/Transregio 154

**Finished Projects**

**Finished Projects**

### Analysis of the German Electricity Market

### Description

### People involved

Frauke Liers

Alexander Martin

### Contact

For further details about this project please contact Martin Schmidt (mar.schmidt[at]fau.de).

### Partners

This project is part of the Energie Campus Nürnberg. Collaborative researchers in this project are

Prof. Dr. Veronika Grimm (FAU, Chair of Economic Theory)

Prof. Dr. Gregor Zöttl (FAU, Chair of Regulation and Energy Markets)

### Publications

Veronika Grimm, Alexander Martin, Martin Schmidt, Martin Weibelzahl, Gregor Zöttl: Transmission and Generation Investment in Electricity Markets: The Effects of Market Splitting and Network Fee Regimes. 2015. Preprint

Lars Schewe, Martin Schmidt: The Impact of Physics on Pricing in Energy Networks. 2015. Preprint

Veronika Grimm, Lars Schewe, Martin Schmidt, Gregor Zöttl: Peak-Load Pricing on a Network. 2015. Preprint

Veronika Grimm, Alexander Martin, Martin Weibelzahl, Gregor Zöttl: More Price Zones May Lead to Worse Locational Price Signals. 2015. In Preparation.

## Optimal Control of Electrical Distribution Networks with Uncertain Solar Feed-In

“Areic modelling, simulation and optimization of solar feed-in, power flow and control of electrical distribution networks with uncertain feed” is a collaborative project of the BMBF-funding measure “Mathematics for Innovations”. The project will be funded from January 01, 2018 to Dezember 31, 2020.

## Description

- Kevin-Martin Aigner
- Frauke Liers
- Alexander Martin

### Contact

For further details about this project please contact Kevin-Martin Aigner (kevin-martin.aigner@fau.de).

Partners

*Academic Partners*

- Universität Ulm, Institut für Stochastik (Prof. Dr. Volker Schmidt, project coordinator)
- Universität Duisburg-Essen, Lehrstuhl für Energiewissenschaft (Prof. Dr. Christoph Weber)

*Industrial Partners*

- Deutscher Wetterdienst (Dr. Bernhard Reichert)

## MINOA: Mixed-Integer Non-Linear Optimization: Algorithms and Applications

MINOA 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.

Details

**Participants:** Frauke Liers, Martin Schmidt, Dennis Adelhütte

#### 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

#### Transient Gas Network Optimization

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.

#### Validation of Nominations in Gas Networks

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.

#### Optimal Design of Coupled Energy Carrier Networks

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.

#### Clearing Coupled Day-Ahead Electricity Markets

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.

#### Sustainable Business Models in Energy Markets

The 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.