# 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).

## Current 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

### EWave – Water supply energy management system

### Description

The joint research project EWave, supported by the German ministry of education and research (BMBF), aims to develop and implement a prototype for an energy management decision support system based on mathematical optimization.

Over the past few years, requirements for drinking water supply in Germany have become more and more demanding. While the secure supply of high-quality 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. Water suppliers must therefore rise to the challenge of continuing to prioritize a secure supply of high-quality drinking water while coping with the increasing demand for energy efficiency.

A core feature developed and implemented in the EWave project is a mixed-integer nonlinear programming model for the optimization of operative planning including the processes of water collection, treatment, and distribution. This includes a detailed hydraulic model to adequately describe the predicted state of the network as well as further technical and especially operational restrictions. The main objective is to minimize overall energy consumption mainly arising from active raw and pure water pumps. The computation of an energy efficient proposal of the network control is performed for a fixed time period by a receiding horizon strategy, e.g., every 15 minutes for the next 24 hours. To obtain solutions for the resulting mixed-integer nonlinear nonconvex programming problem we combine state of the art methods from the fields of discrete and continuous optimization. On the one hand mixed-integer linear programming relaxations are computed and solved, which draw on piecewise linear approximation of nonlinear nonconvex functions with a predefined error tolerance. Resulting discrete controls such as on/off switching states of pumps and open/closed states of valves are fixed in a complementary stage where optimal control based methods and continuous nonlinear programming techniques are applied.

For more information, please visit our joint project website.

### People involved

Alexander Martin (EWave project coordinator)

Björn Geißler

Antonio Morsi

### Supported by

The research collaboration EWave is supported within the funding program “Future-oriented Technologies and Concepts for an Energy-efficient and Resource-saving Water Management – (ERWAS)” by the German Federal Ministry of Education and Research (BMBF) from 2014 to 2017 under the grants 02WER1323A – 02WER1323F.

### Partners

Academic partners

Angewandte Mathematik 2 (FAU Erlangen-Nuernberg)

Numerik und wissenschaftliches Rechnen (Technische Universität Darmstadt)

Elektrotechnik, Maschinenbau und Technikjournalismus (Hochschule Bonn-Rhein-Sieg)

Industrial partners

RWW Rheinisch-Westfälische Wasserwerksgesellschaft mbH

Bilfinger GreyLogix Aqua GmbH

Siemens AG

Associated partner

Wissenschaftliches Rechnen, Universität Mannheim

### Related Publications

A. Morsi.

Solving MINLPs on Loosely-Coupled Networks with Applications in Water and Gas Network Optimization.

Ph.D. thesis, University of Erlangen-Nuremberg, 2013.

A. Morsi, B. Geißler, A. Martin.

Mixed Integer Optimization of Water Supply Networks.

In A. Martin, K. Klamroth, J. Lang, G. Leugering, A. Morsi, M. Oberlack, M. Ostrowski, R. Rosen (Eds), Mathematical Optimization of Water Networks, Vol. 162 of International Series of Numerical Mathematics, pp 35-54, Springer Basel, 2012.

O. Kolb, A. Morsi, J. Lang, A. Martin.

Nonlinear and Mixed-Integer Linear Programming.

In A. Martin, K. Klamroth, J. Lang, G. Leugering, A. Morsi, M. Oberlack, M. Ostrowski, R. Rosen (Eds), Mathematical Optimization of Water Networks, Vol. 162 of International Series of Numerical Mathematics, pp 55-65, Springer Basel, 2012.

A. Martin, K. Klamroth, J. Lang, G. Leugering, A. Morsi, M. Oberlack, M. Ostrowski, R. Rosen (Eds).

Mathematical Optimization of Water Networks.

Vol. 162 of International Series of Numerical Mathematics, Springer Basel 2012.

B. Geißler, A. Martin, A. Morsi, L. Schewe.

Using Piecewise Linear Functions for Solving MINLPs.

In Jon Lee and Sven Leyffer (Eds), Mixed Integer Nonlinear Programming, Vol. 154 of The IMA Volumes in Mathematics and its Applications, pp 287-314, Springer, 2012.

B. Geißler, O. Kolb, J. Lang, G. Leugering, A. Martin, A. Morsi.

Mixed Integer Linear Models for the Optimization of Dynamical Transport Networks.

Mathematical Methods of Operations Research, Volume 73, Number 3, pp 339-362, 2011

### 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

### Adaptive MIP-Relaxations for MINLPs

### Description

Goal of this project B07 inside of the TRR 154 is the analysis and solution of large-scale MINLPs, especially from the application of instationary gas network optimization, using adaptive MIP models. We approximate the nonlinearities with piecewise-linear 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.

### People involved

Robert Burlacu

Alexander Martin

Lars Schewe

### Contact

For further details about this project please contact Robert Burlacu (robert.burlacu[at]fau.de)

### Supported by

Deutsche Forschungsgemeinschaft, Sonderforschungsbereich/Transregio 154

### Related Talks

2nd September, 2015, OR, Wien

Robert Burlacu (Co-Authors: Bjoern Geissler, Antonio Morsi and Lars Schewe): Computational studies on solving Mixed-Integer Nonlinear Programs by Mixed-Integer Linear Program relaxations

### 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.

### MIP-based Alternating Direction Methods for High-Detail Stationary Gas Transport MINLPs

### Description

The goal of this project is to develop problem-tailored alternating direction methods (ADMs) for highly detailed stationary gas transport models. The theoretical and practical achievements should be used to solve mixed-integer nonlinear models incorporating mixing models for specific gas quality parameters and, especially, highly detailed models of compressor stations (see, e.g., Schmidt et al. 2015).

In recent years, significant advances in the algorithmic optimization of mixed-integer nonlinear and non convex models of stationary gas transport have been made (see, e.g., Koch et al. 2015 or Pfetsch et al. 2015). These advances are mainly based on the decoupling of discrete and nonlinear aspects of the models.

The discrete aspects are typically addressed by using mixed-integer linear (MILP) approaches that are capable of handling switching decisions of the active network elements (like valves, control valves, and compressor stations) as well as of handling approximating formulations of nonlinear functions via piecewise linear modeling techniques. The advances of the last years in this area made it possible to solve MILP models of networks of national scale in a reasonable time limit (see, e.g., Geißler et al. 2013, Geißler et al. 2012, or Domschke et al 2010).

On the other hand, highly detailed nonlinear models (NLPs) have been developed for the description of gas flows in pipes and for the description of compressor stations including compressor drives. These models can also be solved efficiently.

The coupling of these two approaches has been mainly realized by a single-stage approach that does not incorporate a reasonable feedback loop between the MILP and NLP models. To be more specific, the MILP models yield discrete controls of the active network elements together with an approximation of the resulting physical gas flow. These outcomes are then fixed and serve as input for the highly detailed NLP models that are then able to validate the physical and technical feasibility of the given discrete controls. After a positive validation this yields a feasible solution of the underlying highly detailed mixed-integer nonlinear model. Unfortunately, there are only a few strategies of how to proceed if this is not the case.

The strategy of this project is the coupling of the MILP and NLP models by using ADMs. However, in order to use these kinds of methods it is necessary to reformulate the underlying MINLP model in an appropriate way.

### People involved

Björn Geißler

Antonio Morsi

Lars Schewe

Martin Schmidt

### Contact

For further details about this project please contact Lars Schewe (lars.schewe[at]math.uni-erlangen.de).

### Supported by

Deutsche Forschungsgemeinschaft, Sonderforschungsbereich/Transregio 154

### Publications

Solving power-constrained gas transportation problems using an MIP-based alternating direction method. Björn Geißler, Antonio Morsi, Lars Schewe, and Martin Schmidt. In Computers & Chemical Engineering, 2015, Vol. 82, pages 303-317. DOI: 10.1016/j.compchemeng.2015.07.005. Preprint (11/2014): Optimization Online.

## Decomposition methods for mixed-integer optimal control

### Description

The objective of this project A05 inside of the TRR 154 is the development of mathematical algorithms to find an optimal control for mixed-integer problems on transport networks with the help of decomposition methods. For the sake of synergy inside of the TRR 154 the focus is on gas networks, but the methods should also be useful for water networks or other energy networks. The optimization problems are planned to be decomposed with respect to variables but also with respect to subsystems, with the result that we are getting a time-expansive MINLP with a hierarchic structure. On the upper level, there are integer decisions, while on the lower level the focus is on continuous variables. Eventually the continuous variables are discretized for the numerical realization. This approach investigates the whole range from totally discrete MINLPs to PDE-based MINLPs in the Banach space. While we use well-known finite-volume methods to simulate the gas equations at the beginning, we want to include methods from the sub-project C02 inside of TRR 154 during the progress. The same holds for the inclusion of MINLP-Solvers from the sub-project B07. So the focus of this project is on the mathematical analysis of structured MINLPs in the light of hierarchic models. The methods of many classical decomposition approaches like Benders, Outer Approximation or Dantzig-Wolfe focus on a generation of cutting planes in the subproblem, which tighten the relaxed set in the masterproblem to achieve a convergence between the values of the objective functions of the masterproblem (dual bound) and the subproblem (primal bounds). In this sub-project we want the subproblem to provide disjunctions for the masterproblem as well, because such an approach enables the algorithm to find global optima for non-convex problems as well.

### People involved

- Alexander Martin
- Martin Schmidt
- Mathias Sirvent

### Contact

For further details about this project please contact Mathias Sirvent (mathias.sirvent[at]fau.de).

### Supported by

Deutsche Forschungsgemeinschaft, Sonderforschungsbereich/Transregio 154

### Partners

This project is part of the Sonderforschungsbereich/Transregio 154. Collaborative researchers in this project are

Prof. Dr. Günter Leugering (FAU, Applied Mathematics 2)

Prof. Dr. Martin Gugat (FAU, Applied Mathematics 2)

David Wintergerst (FAU, Applied Mathematics 2)

### Related Talks

May 24th, 2017 by Mathias Sirvent

SIOPT: SIAM Conference on Optimization, Vancouver, Canada

MIP-Based Instantaneous Control of Mixed-Integer PDE-Constrained Gas Transport Problems

http://www.siam.org/meetings/op17/

September 2nd, 2015 by Mathias Sirvent

OR: International Conference on Operations Research, Vienna, Austria

A Decomposition Method for Mixed-Integer Programs with Differential Equations (Version 2015)

http://or2015.univie.ac.at/

July 5th, 2016 by Mathias Sirvent

EURO: European Conference on Operational Research, Poznań, Poland

A Decomposition Method for Mixed-Integer Programs with Differential Equations (Version 2016)

http://www.euro2016.poznan.pl/

July 19th, 2016 by Mathias Sirvent

7ECM: 7th European Congress of Mathematics, Berlin, Germany

A Decomposition Method for Mixed-Integer Programs with Differential Equations (Version 2016)

http://www.7ecm.de/

### Publications

### Submitted work / Preprints

The Cost of Not Knowing Enough: Mixed-Integer Optimization with Implicit Lipschitz Nonlinearities. Martin Schmidt, Mathias Sirvent, and Winnifried Wollner. Submitted. Preprint (4/2018): Optimization Online, TRR154 Preprint Server.

A Decomposition Method for MINLPs with Lipschitz Continuous Nonlinearities. Martin Schmidt, Mathias Sirvent, and Winnifried Wollner. Submitted. Updated Preprint (3/2018): Optimization Online, TRR154 Preprint Server.

### Journal Articles

MIP-Based Instantaneous Control of Mixed-Integer PDE-Constrained Gas Transport Problems. Martin Gugat, Günter Leugering, Alexander Martin, Martin Schmidt, Mathias Sirvent, and David Wintergerst. In Computational Optimization and Applications, Volume 70, Issue 1, pp. 267-294, May 2018. DOI: 10.1007/s10589-017-9970-1.

Towards Simulation Based Mixed-Integer Optimization with Differential Equations. Martin Gugat, Günter Leugering, Alexander Martin, Martin Schmidt, Mathias Sirvent, and David Wintergerst. In Networks, 2018. DOI: 10.1002/net.21812.

GasLib – A Library of Gas Network Instances. Jointly with Martin Schmidt, Denis Aßmann, Robert Burlacu, Jesco Humpola, Imke Joormann, Nikolaos Kanelakis, Djamal Oucherif, Marc E. Pfetsch, Lars Schewe, Robert Schwarz, and Mathias Sirvent. In Data, Volume 2, Issue 4, December 2017. DOI: 10.3390/data2040040.

Nonoverlapping Domain Decomposition for Optimal Control Problems governed by Semi-Linear Models for Gas Flow in Networks. Jointly with Günter Leugering, Alexander Martin, Martin Schmidt, and Mathias Sirvent. In Control and Cybernetics, Volume 46, Issue 3, pp. 191-225, 2017.

A Linearized Model for the Optimization of the Coupled Electricity and Natural Gas System. Mathias Sirvent, Nikolaos Kanelakis, Björn Geißler, and Pandelis Biskas. In Journal of Modern Power Systems and Clean Energy, Volume 5, Issue 3, pp. 364-374, May 2017. DOI: 10.1007/s40565-017-0275-2.

### Optimal allocation of gas network capacities

### Description

Due to regulations gas network operators face the new challenge of allocating free capacity at all entry and exit points. Customers may then book within the reported capacity intervals separately at the entry and exit points. Operators have to guarantee that all expected requests within these intervals (called nominations) can be transported through the network. Where no historical withdrawal data is applicable, the worst-case request situation has to be considered. However, due to gas physics and active elements like compressors, the underlying question whether a nomination can be transported through the network, called nomination validation, already is far from being trivial and is modelled as a non-convex MINLP. Thus, it is not obvious what the operating limits of the network are.

We develop an algorithm for solving a relaxed variant. Therein a nomination validation tool is used as black box.

This project is part of the industrial research project ForNe (Forschungskooperation Netzoptimierung). Please have also a look at the related software project LaMaTTO++.

### People involved

Lars Schewe

### Contact

Christine Hayn (christine.hayn[at]fau.de)

### Partners

Open Grid Europe GmbH

Leibniz Universität Hannover, Institut für Angewandte Mathematik

Contact: Marc Steinbach

Universität Duisburg-Essen, Diskrete Mathematik und Optimierung

Contact: Rüdiger Schultz

Humboldt-Universität zu Berlin, Institut für Mathematik

Contact: Werner Römisch

Technische Universität Darmstadt, Arbeitsgruppe Optimierung

Contact: Marc Pfetsch

Weierstraß-Institut für Angewandte Analysis und Stochastik, Nichtlineare Optimierung und Inverse Probleme

Contact: René Henrion

Zuse-Institut Berlin

Contact: Thorsten Koch

### Partners

Open Grid Europe GmbH

Leibniz Universität Hannover, Institut für Angewandte Mathematik

Contact: Marc Steinbach

Universität Duisburg-Essen, Diskrete Mathematik und Optimierung

Contact: Rüdiger Schultz

Humboldt-Universität zu Berlin, Institut für Mathematik

Contact: Werner Römisch

Technische Universität Darmstadt, Arbeitsgruppe Optimierung

Contact: Marc Pfetsch

Weierstraß-Institut für Angewandte Analysis und Stochastik, Nichtlineare Optimierung und Inverse Probleme

Contact: René Henrion

Zuse-Institut Berlin

Contact: Thorsten Koch

### Publications Related to ForNe and Network Capacities

B. Hiller, C. Hayn, H. Heitsch, R. Henrion, H. Leövey, A. Möller, W. Römisch. Methods for verifying booked capacities In: Thorsten Koch, Benjamin Hiller, Marc E. Pfetsch, and Lars Schewe, eds.Evaluating Gas Network Capacities. SIAM-MOS series on Optimization. SIAM, 2015. xvii + 364. isbn: 978-1-611973-68-6

C. Hayn, J. Humpola, T. Koch, L. Schewe, J. Schweiger, K. Spreckelsen. Perspectives In: Thorsten Koch, Benjamin Hiller, Marc E. Pfetsch, and Lars Schewe, eds.Evaluating Gas Network Capacities. SIAM-MOS series on Optimization. SIAM, 2015. xvii + 364. isbn: 978-1-611973-68-6

A. Fügenschuh, B. Geißler, R. Gollmer, C. Hayn, R. Henrion, B. Hiller, J. Humpola, T. Koch, T. Lehmann, A.Martin, R. Mirkov, A. Morsi, W. Römisch, J. Rövekamp, L. Schewe, M. Schmidt, R. Schultz, R. Schwarz, J.Schweiger, C. Stangl, M. Steinbach, B. Willert. Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets. In: Energy Systems 5.3 (2014), pp. 449–473

A. Martin, B. Geißler, C. Hayn, A. Morsi, L. Schewe, B. Hiller, J. Humpola, T. Koch, T. Lehmann, R. Schwarz, J. Schweiger, M. Pfetsch, M. Schmidt, M. Steinbach, B. Willert, R. Schultz. Optimierung Technischer Kapazitäten in Gasnetzen (Optimizing Technical Capacities in Gas Networks). VDI Bericht 2157, Optimierung in der Energiewirtschaft, pp. 105-114, 2011.

### Energy System Analysis

### Description

The problem of Energy Systems is as follows. The power market faces increasing challenges toward inegrating the growing share of Renewable Energy Sources (RES) due to the fluctuating nature of wind and solar insolation. Hence the conventional power plants must provide the flexibility to adjust to the fluctuating residual load resulting from the gap between power demand and the preferential feed-in from RES. Since the peak power production of renewable energy carriers such as solar power or wind power do not coincide with peak demands, the occurance of times with overproduction and time periods where fossile power plants are needed to cover power demand are unavoidable. To compensate overproductions, we include energy storages, such as batteries, pumped hydro storages or power to gas storages. This leads to a time expanded tuning of the charging and discharging of storages and the control of the fossile power plants to cover the fluctuating residual load, with the objective to minimize the electricity price resulting from the power production costs according to the merit order effect. In order to ensure system security we must include balancing power which must be held available by conventional power plants. Under the restrictions of the just explained unit commitment problem and the targets set by the government such as, at least 50% of the power demand must be satisfied by renewable energy carriers, we further suggest a power capacity expansion plan for the given planning period. The capacity expansion problem arises due to the fact that the nuclear plants will be turned off at specific times during the planning period. For extension power plants we include integrated gasification combined cycle power plants, gas turbines, wind power, hydro power, solar power and geothermal power. Mathematically this problem leads to a stochastic mixed integer nonlinear program, where the stochasticity results form the fluctuating feed in of renewable energy carriers. The nonlinearity results from the efficiency factors of the power plants and storages. The combinatorial aspects arise due to the switching processes of the conventional plants the charging status of the energy storages and the extension decisions.

### People involved

Alexander Martin

Christoph Thurner

### Contact

For further details about this project please contact Christoph Thurner (christoph.thurner [at] fau.de)

### Supported by

Bayerisches Staatsministerium für Wirtschaft und Medien,Energie und Technologie

Bayern Innovativ / Cluster Energietechnik

### Partners

FAU Erlangen-Nürnberg Lehrstuhl Informatik 7

FAU Erlangen-Nürnberg Lehrstuhl für Elektrische Energiesysteme

E.ON

AÜW (Allgäuer Überlandwerk GmbH)

Thüga AG

infra Fürth

AREVA

SIEMENS

OMV

SWU Stadtwerke Ulm/Neu-Ulm GmbH

VERBUND AG

WVV (Würzburger Versorgungs- und Verkehrs-GmbH)

### Publications

A. Bärmann, A. Heidt, A. Martin, S. Pokutta, C. Thurner: Polyhedral Approximation of Ellipsoidal Uncertainty Sets via Extended Formulations — a computational case study –, Tech. Report. (submitted 2013)

M. Pruckner, C. Thurner, A. Martin, R. German: A Coupled Optimization and Simulation Model for the Energy Transition in Bavaria, MMB & DFT 2014 (Veranst.): Proceedings of the International Workshop on Demand Modeling and Quantitative Analysis of Future Generation Energy Networks and Energy Efficient Systems (FGENET 2014, Bamberg, Germany, March 19, 2014).

A. Bärmann, F. Liers, A. Martin, M. Merkert, C. Thurner, D. Weninger: Solving Network Design Problems via Iterative Aggregation, Mathematical Programming Computation: Volume 7, Issue 2 (2015), Page 189-217

## Robust Power Load Balancing in Railway Networks

### Description

This project is part of the German research initiave “E-Motion”, which aims at organizing mobility in motorized passenger and freight traffic in Germany more energy-efficient. Exemplarily, it considers the fields of air traffic and railway traffic. Mathematical analysis and optimization of fundamental planning steps deliver the tools to investigate the energy-efficiency of the two means of transport in order to recognize and to make full use of the potentials – within each means of transport as well as in their interconnection.

E-Motion adresses an optimized choice of flight routes to minimize fuel consumption and emissions in air traffic and an optimal energy management in railway traffic. For the latter, we enable a significant reduction of energy consumption and energy cost by an optimized routing and and optimized schedules. Furthermore, we investigate the optimal expansion of transfer capacities from road to rail.

The project “Robust Power Load Balancing in Railway Networks” is conducted at the FAU Erlangen-Nürnberg. It aims at the optimal adaption of a given train schedule to reduce peak power demands in the power supply stations of the railway network. This allows for a significant reduction of the necessary power reserve, which is responsable for a considerable part of the energy costs. Further it leads to stabilization of the electric power supply system.

### People involved

Andreas Bärmann

Alexander Martin

### Contact

For further details on this project, please contact Andreas Bärmann (Andreas.Baermann[at]math.uni-erlangen.de).

### Supported by

German Ministry of Education and Research (BMBF).

### Partners

Zuse Institut Berlin

HSU Hamburg

TU Braunschweig

TU Chemnitz

Fraunhofer SCS

Lufthansa Systems AG

Deutsche Bahn Mobility Logistics AG

Kombiverkehr GmbH & Co. KG

## Smart Grid Optimization

### Description

Decentralized power generation requires planning and scheduling for residential microgrids connected to the main public supply grid. We develop highly detailed models for smart grids including a photovoltaic module, a wind energy generator, a combined heat and power unit together with a battery and a heat storage unit. Our goal is to optimize day-ahead operation of this smart grid considering weather forecasts with regard to solar and wind power as well as to the electrical and heat power demand. The objective is minimization of costs to cover energy demand. In case surplus electrical energy is produced it can be sold to the public network operator, and then we aim to maximize profit of the microgrid owner. Possible further questions concern the planning of layouts of such grids.

Mathematically this problem results in a MIP problem, where the discrete aspects deal with switching processes of the combined heat and power unit. The whole problem includes uncertainties which can be handled with techniques of robust optimization.

This project is part of an EnCN Simulation Project at Energie Campus Nürnberg.

### Contact

For further details about this project please contact Galina Orlinskaya (galina.orlinskaya[at]fau.de).

#### Smart Grid Solar

The partners in “Smart Grid Solar” are implementing and field-testing components of a smart grid in the region of Upper Franconia. With a special focus on photovoltaics, simulation and optimisation is used to study the integration of large power production in low-voltage grids using both small private and larger proximity storages.

Several storage systems are analysed and evaluated according to seasonal or short-term electrical storage potentials. Furthermore a common framework is used to derive strategies for optimal (dis)charge schedules that exploit a great variety of input data including residual loads, weather forecasts, market prices for electricity and storage properties. The research project ”Smart Grid Solar” is co-financed by the European Union through the European Regional Development Fund and by the Free State of Bavaria.

For more details visit http://www.smart-grid-solar.de

## 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

### 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

#### 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.