MODALGasLab
The German highpressure gas pipeline network has an overall length of approximately 50,000 km. Each month, 120 billion kW/h of energy are transport via this network. This roughly corresponds to 10 times the electricity generation of all German nuclear power plants. Natural gas contributes more than 20% to the entire energy supply in Germany and is therefore, besides fuels, the most important source of energy. Thus, the gas transport system is of high social and political relevance. Expansion measures have a long time horizon and are as costintensive as maintenance and operation. The optimal use of existing capacities therefore offers high savings potentials. Suppliers and consumers involved currently have to inform the transport network operator about one day in advance about the gas purchase quantities expected. This process is called nomination. The network operators then control their network correspondingly, with security of supply being the factor with highest priority. At the same time, part of the gas in the network is used to supply the energy for transport. It is the network operators’ task to process a maximum number of orders with a minimum of internal energy consumption. Control of the network is highly nonlinearly complex and, due to the storage behavior of the network, very difficult to keep track of in terms of time. There is always the risk that a decision that has already been made will lead to a bottleneck at some point in the future. Thus, the most important aspect of the project is to identify potentially critical situations early and to initiate counter measures. MODAL aims at exploring the fundamentals for the development of a dynamic nomination validation. This would then calculate, on the basis of the current network condition and the existing nominations, an optimized control schedule for the network for the next 1 to 3 days. This would provide the foundation for an automated process for the control of gas networks. Such a process would entail various benefits: The security of supply would be increased considerably, since an early warning could be issued whenever a situation that cannot be operated threatens to arise in the network. Algorithms would be able to find solutions for control problems that are difficult or impossible to identify for human dispatchers. For the same reason, the capacity in the gas network would also be increased, so that it will be possible to process transport orders that at this point in time are out of reach. This would, in particular, be very welcome by the Federal Network Agency, since it would be possible to offer and use free capacities at very short notice. By calculating an optimized control schedule it will be possible to save costs of operation: Even a reduction of only 10% would correspond to the output of a nuclear power plant. Ultimately, such methods would also enable far better possibilities to react on geopolitical events such as reduced gas supplies from Russia. The online calculation of an optimized operation for a large gas transport network with a time horizon of 1 – 3 days is a task that can presently not be solved mathematically. The aim of GasLab is to develop a prototypical method that enables the automatic calculation of the control schedule with sufficient accuracy on the basis of realworld data. The challenge of this project lies equally in the design of suitable models, in the development of new optimization algorithms and in finding a way to make available the required but extremely voluminous data in a suitable manner.
Publications
2018 

Jonas Schweiger, Frauke Liers  A Decomposition Approach for Optimal Gas Network Extension with a Finite Set of Demand Scenarios  Optimization and Engineering, 19(2), pp. 297326, 2018 
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Benjamin Hiller, Thorsten Koch, Lars Schewe, Robert Schwarz, Jonas Schweiger  A System to Evaluate Gas Network Capacities: Concepts and Implementation  European Journal of Operational Research, 270(3), pp. 797808, 2018 (preprint available as ZIBReport 1811) 
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Kai Helge Becker, Benjamin Hiller  ASTS Orientations on Undirected Graphs: Structural analysis and enumeration  ZIBReport 1831 
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Manuel Radons, Lutz Lehmann, Tom Streubel, Andreas Griewank  An Open Newton Method for Piecewise Smooth Systems  ZIBReport 1843 
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Benjamin Hiller, René Saitenmacher, Tom Walther  Analysis of operating modes of complex compressor stations  ZIBReport 1765 
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Felix Hennings  Benefits and Limitations of Simplified Transient Gas Flow Formulations  Operations Research Proceedings 2017, pp. 231237, Vol.Operations Research Proceedings, 2018 (preprint available as ZIBReport 1739) 
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Richard Hasenfelder, Lutz Lehmann, Manuel Radons, Tom Streubel, Christian Strohm, Andreas Griewank  Computational aspects of the Generalized Trapezoidal Rule  ZIBReport 1823 (submitted to Optimization Methods and Software) 
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Jonas Schweiger  Exploiting structure in nonconvex quadratic optimization  ZIBReport 1835 
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Tom Streubel, Christian Strohm, Philipp Trunschke, Caren Tischendorf  Generic Construction and Efficient Evaluation of Network DAEs and Their Derivatives in the Context of Gas Networks  Operations Research Proceedings 2017, pp. 627632, 2018, isbn: 9783319899206 (preprint available as ZIBReport 1741) 
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Benjamin Hiller, Tom Walther  Improving branching for disjunctive polyhedral models using approximate convex decompositions  ZIBReport 1768 
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Benjamin Hiller, Kai Helge Becker  Improving relaxations for potentialdriven network flow problems via acyclic flow orientations  ZIBReport 1830 
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Benjamin Hiller, Tom Walther  Modelling compressor stations in gas networks  ZIBReport 1767 
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Ralf Lenz, Kai Helge Becker  Optimization of Capacity Expansion in Potentialdriven Networks including Multiple Looping  A comparison of modelling approaches  ZIBReport 1844 
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Tom Streubel, Caren Tischendorf, Andreas Griewank  Piecewise Polynomial Taylor Expansions – The Generalization of Faà di Bruno’s Formula  ZIBReport 1824 (submitted to Modeling, Simulation and Optimization of Complex Processes HPSC2018) 
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James Luedtke, Claudia D'Ambrosio, Jeff Linderoth, Jonas Schweiger  Strong Convex Nonlinear Relaxations of the Pooling Problem  ZIBReport 1812 
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James Luedtke, Claudia D'Ambrosio, Jeff Linderoth, Jonas Schweiger  Strong Convex Nonlinear Relaxations of the Pooling Problem: Extreme Points  ZIBReport 1813 
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Uwe Gotzes, Claudia Gotzes  The Jeep Problem: A Flexible MIP Formulation  Journal of Nepal Mathematical Society, Vol.1, pp. 1117, 2018 
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2017 

Benjamin Hiller, Thorsten Koch, Lars Schewe, Robert Schwarz, Jonas Schweiger  A System to Evaluate Gas Network Capacities: Concepts and Implementation  ZIBReport 1703 
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Jonas Schweiger  Exploiting structure in nonconvex quadratic optimization and gas network planning under uncertainty  Doctoral thesis, Technische Universität Berlin, Thorsten Koch, Andrea Lodi (Advisors), 2017 
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Peter Benner, Sara Grundel, Christian Himpe, Christoph Huck, Tom Streubel, Caren Tischendorf  Gas Network Benchmark Models  ZIBReport 1773 (submitted to DifferentialAlgebraic Equations Forum) (accepted for publication on 20180523) 
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Martin Schmidt, Denis Assmann, Robert Burlacu, Jesco Humpola, Imke Joormann, Nikolaos Kanelakis, Thorsten Koch, Djamal Oucherif, Marc E. Pfetsch, Lars Schewe, Robert Schwarz, Matthias Sirvent  GasLib – A Library of Gas Network Instances  Optimization Online, 2017 
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Andreas Griewank, Richard Hasenfelder, Manuel Radons, Lutz Lehmann, Tom Streubel  Integrating Lipschitzian dynamical systems using piecewise algorithmic differentiation  Optimization Methods and Software, pp. 119, 2017 (epub ahead of print, preprint available as ZIBReport 1744) 
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Kai Hoppmann, Robert Schwarz  On Finding Maximum Minimum Cost Flows  OR Proceedings 2017, 2017 (accepted for publication, preprint available as ZIBReport 1668) 
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Andreas Griewank, Tom Streubel, Lutz Lehmann, Manuel Radons, Richard Hasenfelder  Piecewise linear secant approximation via algorithmic piecewise differentiation  Optimization Methods and Software, pp. 119, 2017 (epub ahead of print, preprint available as ZIBReport 1654) 
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Tom Walther, Benjamin Hiller, René Saitenmacher  Polyhedral 3D Models for compressors in gas networks  ZIBReport 1766 
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2016 

Benjamin Hiller, René Saitenmacher, Tom Walther  Analysis of operating modes of complex compressor stations  ZIBReport 1661 (Appeared in Proceedings of Operations Research 2016, Springer, 2017.) 
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Ralf Lenz, Robert Schwarz  Optimal Looping of Pipelines in Gas Networks  ZIBReport 1667 
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Stephen Maher, Matthias Miltenberger, Joao Pedro Pedroso, Daniel Rehfeldt, Robert Schwarz, Felipe Serrano  PySCIPOpt: Mathematical Programming in Python with the SCIP Optimization Suite  ZIBReport 1664 (Appeared in: Mathematical Software – ICMS 2016, Volume 9725, Pages 301307) 
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Jesco Humpola, Felipe Serrano  Sufficient pruning conditions for MINLP in gas network design  EURO Journal on Computational Optimization, 2016 (epub ahead of print) 
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2015 

Benjamin Hiller, Jesco Humpola, Thomas Lehmann, Ralf Lenz, Antonio Morsi, Marc E. Pfetsch, Lars Schewe, Martin Schmidt, Robert Schwarz, Jonas Schweiger, Claudia Stangl, Bernhard M. Willert  Computational results for validation of nominations  Evaluating Gas Network Capacities, SIAM, 2015, isbn: 9781611973686 
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Jesco Humpola, Armin Fügenschuh  Convex reformulations for solving a nonlinear network design problem  Computational Optimization and Applications, 2015 (preprint available as ZIBReport 1331) 
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Thorsten Koch, Benjamin Hiller, Marc Pfetsch, Lars Schewe  Evaluating Gas Network Capacities  SIAM, 2015, isbn: 9781611973686 
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Jesco Humpola, Imke Joormann, Djamal Oucherif, Marc E. Pfetsch, Lars Schewe, Martin Schmidt, Robert Schwarz  GasLib  A Library of Gas Network Instances  Optimization Online, 2015 
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Thorsten Koch, Marc E. Pfetsch, Jessica Rövekamp  Introduction  Evaluating Gas Network Capacities, Society for Industrial and Applied Mathematics, pp. 316, 2015, isbn: 9781611973686 
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Lars Schewe, Thorsten Koch, Alexander Martin, Marc E. Pfetsch  Mathematical optimization for evaluating gas network capacities  Evaluating Gas Network Capacities, Society for Industrial and Applied Mathematics, pp. 87102, 2015, isbn: 9781611973686 
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Pia Domschke, Martin Groß, Falk M. Hante, Benjamin Hiller, Lars Schewe, Martin Schmidt  Mathematische Modellierung, Simulation und Optimierung von Gastransportnetzwerken  gwf  Gas+Energie, 156(11), pp. 880885, 2015 
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Benjamin Hiller, Christine Hayn, Holger Heitsch, René Henrion, Hernan Leövey, Andris Möller, Werner Römisch  Methods for verifying booked capacities  Evaluating gas network capacities, Society for Industrial and Applied Mathematics, pp. 291315, 2015 
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Christine Hayn, Jesco Humpola, Thorsten Koch, Lars Schewe, Jonas Schweiger, Klaus Spreckelsen  Perspectives  Evaluating Gas Network Capacities, SIAM, 2015, isbn: 9781611973686 
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Uwe Gotzes, Nina Heinecke, Benjamin Hiller, Jessica Rövekamp, Thorsten Koch  Regulatory rules for gas markets in Germany and other European countries  Evaluating gas network capacities, Society for Industrial and Applied Mathematics, pp. 4564, 2015, isbn: 9781611973686 
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Dagmar Bargmann, Mirko Ebbers, Nina Heinecke, Thorsten Koch, Veronika Kühl, Antje Pelzer, Marc E. Pfetsch, Jessica Rövekamp, Klaus Spreckelsen  Stateoftheart in evaluating gas network capacities  Evaluating Gas Network Capacities, Society for Industrial and Applied Mathematics, pp. 6584, 2015, isbn: 9781611973686 
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Jesco Humpola  Sufficient Pruning Conditions for MINLP in Gas Network Design  ZIBReport 1504 (Appeared in: EURO Journal on Computational Optimization) 
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Jesco Humpola, Armin Fügenschuh, Benjamin Hiller, Thorsten Koch, Thomas Lehmann, Ralf Lenz, Robert Schwarz, Jonas Schweiger  The Specialized MINLP Approach  Evaluating Gas Network Capacities, SIAM, 2015, isbn: 9781611973686 
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Jesco Humpola, Armin Fügenschuh, Thorsten Koch  Valid inequalities for the topology optimization problem in gas network design  OR Spectrum, 2015 (preprint available as ZIBReport 1306) 
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2014 

Jesco Humpola, Thomas Lehmann, Armin Fügenschuh  A primal heuristic for optimizing the topology of gas networks based on dual information  EURO Journal on Computational Optimization, 2014 (preprint available as ZIBReport 1349) 
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Jesco Humpola  Gas Network Optimization by MINLP  Doctoral thesis, Technische Universität Berlin, Martin Grötschel (Advisor), 2014 
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2013 

Armin Fügenschuh, Björn Geißler, Ralf Gollmer, Christine Hayn, René Henrion, Benjamin Hiller, Jesco Humpola, Thorsten Koch, Thomas Lehmann, Alexander Martin, Radoslava Mirkov, Antonio Morsi, Werner Römisch, Jessica Rövekamp, Lars Schewe, Martin Schmidt, Rüdiger Schultz, Robert Schwarz, Jonas Schweiger, Claudia Stangl, Marc C. Steinbach, Bernhard M. Willert  Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets  Energy Systems, 5(3), pp. 449473, 2013 (preprint available as ZIBReport 1313) 
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2012 

Jácint Szabó  The set of solutions to nomination validation in passive gas transportation networks with a generalized flow formula  ZIBReport 1144 
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Marc E. Pfetsch, Armin Fügenschuh, Björn Geißler, Nina Geißler, Ralf Gollmer, Benjamin Hiller, Jesco Humpola, Thorsten Koch, Thomas Lehmann, Alexander Martin, Antonio Morsi, Jessica Rövekamp, Lars Schewe, Martin Schmidt, Rüdiger Schultz, Robert Schwarz, Jonas Schweiger, Claudia Stangl, Marc C. Steinbach, Stefan Vigerske, Bernhard M. Willert  Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions  ZIBReport 1241 (Appeared in: Optimization Methods and Software 30 (2015) pp. 1553) 
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2011 

Armin Fügenschuh, Benjamin Hiller, Jesco Humpola, Thorsten Koch, Thomas Lehmann, Robert Schwarz, Jonas Schweiger, Jacint Szabo  Gas Network Topology Optimization for Upcoming Market Requirements  International Conference on the European Energy Market (EEM), pp. 346351, 2011 (preprint available as ZIBReport 1109) 
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Alexander Martin, Björn Geißler, Christine Heyn, Benjamin Hiller, Jesco Humpola, Thorsten Koch, Thomas Lehmann, Antonio Morsi, Marc Pfetsch, Lars Schewe, Martin Schmidt, Rüdiger Schultz, Robert Schwarz, Jonas Schweiger, Marc Steinbach, Bernhard Willert  Optimierung Technischer Kapazitäten in Gasnetzen  Optimierung in der Energiewirtschaft, pp. 105114, VDIBerichte 2157, 2011 (preprint available as ZIBReport 1156) 
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