Abstract
In this work, we analyze the structural properties of the set of feasible bookings in the European entry–exit gas market system. We present formal definitions of feasible bookings and then analyze properties that are important if one wants to optimize over them. Thus, we study whether the sets of feasible nominations and bookings are bounded, convex, connected, conic, and star-shaped. The results depend on the specific model of gas flow in a network. Here, we discuss a simple linear flow model with arc capacities as well as nonlinear and mixed-integer nonlinear models of passive and active networks, respectively. It turns out that the set of feasible bookings has some unintuitive properties. For instance, we show that the set is nonconvex even though only a simple linear flow model is used.
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References
Alonso A, Olmos L, Serrano M (2010) Application of an entry-exit tariff model to the gas transport system in Spain. Energy Policy 38(9):5133–5140. https://doi.org/10.1016/j.enpol.2010.04.043
Aßmann D, Liers F, Stingl M, Vera J (2018) Deciding robust feasibility and infeasibility using a set containment approach: an application to stationary passive gas network operations. SIAM J Optim 28(3):2489–2517. https://doi.org/10.1137/17M112470X
Aßmann D, Liers F, Stingl M (2019) Decomposable robust two-stage optimization: an application to gas network operations under uncertainty. Networks 74(1):40–61. https://doi.org/10.1002/net.21871
Banda MK, Herty M (2008) Multiscale modeling for gas flow in pipe networks. Math Methods Appl Sci 31:915–936. https://doi.org/10.1002/mma.948
Banda MK, Herty M, Klar A (2006) Gas flow in pipeline networks. Netw Heterog Media 1(1):41–56. https://doi.org/10.3934/nhm.2006.1.41
Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton
Bermúdez A, González-Díaz J, González-Diéguez FJ, González-Rueda ÁM (2013) Gas transport networks: entry-exit tariffs via least squares methodology. Energy Policy 63:252–260. https://doi.org/10.1016/j.enpol.2013.08.095
Boucher J, Smeers Y (1985) Gas trade in the European community during the 1970s. Energy Econ 7(2):102–116. https://doi.org/10.1016/0140-9883(85)90025-8
Boucher J, Smeers Y (1987) Economic forces in the European gas market—a 1985 prospective. Energy Econ 9(1):2–16. https://doi.org/10.1016/0140-9883(87)90002-8
Carter RG (1996) Compressor station optimization: computational accuracy and speed. In: 28th annual meeting. Paper 9605
Carter RG (1998) Pipeline optimization: dynamic programming after 30 years. In: 30th annual meeting. Paper 9803
Chyong CK, Hobbs BF (2014) Strategic Eurasian natural gas market model for energy security and policy analysis: formulation and application to South Stream. Energy Econ 44:198–211. https://doi.org/10.1016/j.eneco.2014.04.006
Commission E (2001). First benchmarking report on the implementation of the internal electricity and gas market. Technical report, European Commission SEC (2001) 1957, https://ec.europa.eu/energy/sites/ener/files/documents/2001_report_bencmarking.pdf. Accessed 3 July 2019
Cremer H, Laffont J-J (2002) Competition in gas markets. Eur Econ Rev 46(4–5):928–935. https://doi.org/10.1016/S0014-2921(01)00226-4
Domschke P, Geißler B, Kolb O, Lang J, Martin A, Morsi A (2011) Combination of nonlinear and linear optimization of transient gas networks. INFORMS J Comput 23(4):605–617. https://doi.org/10.1287/ijoc.1100.0429
Ehrgott M (2005) Multicriteria optimization, vol 491. Springer, Berlin. https://doi.org/10.1007/3-540-27659-9
European Parliament and Council of the European Union (2009) Directive 2009/73/EC of the European Parliament and of the Council concerning common rules for the internal market in natural gas and repealing Directive 2003/55/EC
European Parliament and Council of the European Union (2009) Regulation No 715/2009 of the European Parliament and of the Council on conditions for access to the natural gas transmission networks and repealing Regulation No 1775/2005. July 13
Fügenschuh A, Geißler B, Gollmer R, Morsi A, Rövekamp J, Schmidt M, Spreckelsen K, Steinbach MC (2015) Chapter 2: physical and technical fundamentals of gas networks. In: Evaluating gas network capacities, pp 17–43. https://doi.org/10.1137/1.9781611973693.ch2
Fügenschuh A, Junosza-Szaniawski K, Kwasiborski S (2014) The reservation-allocation network flow problem. Technical report. https://www.researchgate.net/publication/265126185_The_Reservation-Allocation_Network_Flow_Problem. Accessed 3 July 2019
Gabriel SA, Kiet S, Zhuang J (2005) A mixed complementarity-based equilibrium model of natural gas markets. Oper Res 53(5):799–818. https://doi.org/10.1287/opre.1040.0199
Geißler B, Morsi A, Schewe L, Schmidt M (2015) Solving power-constrained gas transportation problems using an MIP-based alternating direction method. Comput Chem Eng 82:303–317. https://doi.org/10.1016/j.compchemeng.2015.07.005
Geißler B, Morsi A, Schewe L, Schmidt M (2018) Solving highly detailed gas transport MINLPs: block separability and penalty alternating direction methods. INFORMS J Comput 30(2):309–323. https://doi.org/10.1287/ijoc.2017.0780
Gotzes U, Heinecke N, Rövekamp J (2015) Chapter 3: regulatory rules for gas markets in Germany and other European countries. In: Evaluating gas network capacities, pp 45–64. https://doi.org/10.1137/1.9781611973693.ch3
Gotzes C, Heitsch H, Henrion R, Schultz R (2016) On the quantification of nomination feasibility in stationary gas networks with random load. Math Methods Oper Res 84(2):427–457. https://doi.org/10.1007/s00186-016-0564-y
Grimm V, Grübel J, Schewe L, Schmidt M, Zöttl G (2019) Nonconvex equilibrium models for gas market analysis: failure of standard techniques and alternative modeling approaches. Eur J Oper Res 273(3):1097–1108. https://doi.org/10.1016/j.ejor.2018.09.016
Grimm V, Schewe L, Schmidt M, Zöttl G (2019) A multilevel model of the European entry-exit gas market. Math Methods Oper Res 89(2):223–255. https://doi.org/10.1007/s00186-018-0647-z
Groß M, Pfetsch ME, Schewe L, Schmidt M, Skutella M (2019) Algorithmic results for potential-based flows: easy and hard cases. Networks 73(3):306–324. https://doi.org/10.1002/net.21865
Gugat M, Leugering G, Martin A, Schmidt M, Sirvent M, Wintergerst D (2018) MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems. Comput Optim Appl 70(1):267–294. https://doi.org/10.1007/s10589-017-9970-1
Gugat M, Leugering G, Martin A, Schmidt M, Sirvent M, Wintergerst D (2018) Towards simulation based mixed-integer optimization with differential equations. Networks 72(1):60–83. https://doi.org/10.1002/net.21812
Hante FM, Schmidt M (2019) Complementarity-based nonlinear programming techniques for optimal mixing in gas networks. EURO J Comput Optim 1:2–3. https://doi.org/10.1007/s13675-019-00112-w (pre-published)
Hayn C (2016) Computing maximal entry and exit capacities of transportation networks. Ph.D. thesis. Friedrich-Alexander Universität Erlangen-Nürnberg
Hiriart-Urruty J-B, Lemaréchal C (2001) Fundamentals of convex analysis. Springer, Berlin. https://doi.org/10.1007/978-3-642-56468-0
Humpola J, Fügenschuh A, Lehmann T, Lenz R, Schwarz R, Schweiger J (2015) The specialized MINLP approach. In: Evaluating gas network capacities, Chap 7, pp 123–143. https://doi.org/10.1137/1.9781611973693.ch7
Koch T, Hiller B, Pfetsch ME, Schewe L (2015) Evaluating gas network capacities. SIAM-MOS Ser Optim SIAM. https://doi.org/10.1137/1.9781611973693
Labbé M, Plein F, Schmidt M (2019) Bookings in the European gas market: characterisation of feasibility and computational complexity results. Optim Eng. https://doi.org/10.1007/s11081-019-09447-0
Leugering G, Martin A, Schmidt M, Sirvent M (2017) Nonoverlapping domain decomposition for optimal control problems governed by semilinear models for gas flow in networks. Control Cybern 46(3):191–225
Mahlke D, Martin A, Moritz S (2010) A mixed integer approach for time-dependent gas network optimization. Optim Methods Softw 25(4):625–644. https://doi.org/10.1080/10556780903270886
Martin A, Möller M, Moritz S (2006) Mixed integer models for the stationary case of gas network optimization. Math Program Ser B 105(2):563–582. https://doi.org/10.1007/s10107-005-0665-5
Martin A, Geißler B, Hayn C, Morsi A, Schewe L, Hiller B, Humpola J, Koch T, Lehmann T, Schwarz R, Schweiger J, Pfetsch M, Schmidt M, Steinbach M, Willert B, Schultz R (2011) Optimierung Technischer Kapazitäten in Gasnetzen. In: Optimierung in der Energiewirtschaft. VDI-Berichte 2157, pp 105–114. https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1512. Accessed 3 July 2019
Mehrmann V, Schmidt M, Stolwijk JJ (2018) Model and discretization error adaptivity within stationary gas transport optimization. Vietnam J Math 1:2–3. https://doi.org/10.1007/s10013-018-0303-1
Meran G, von Hirschhausen C, Neumann A (2010) Access pricing and network expansion in natural gas markets. Z für Energiewirtschaft 34(3):179–183. https://doi.org/10.1007/s12398-010-0028-7
Pfetsch ME, Fügenschuh A, Geißler B, Geißler N, Gollmer R, Hiller B, Humpola J, Koch T, Lehmann T, Martin A, Morsi A, Rövekamp J, Schewe L, Schmidt M, Schultz R, Schwarz R, Schweiger J, Stangl C, Steinbach MC, Vigerske S, Willert BM (2015) Validation of nominations in gas network optimization: models, methods, and solutions. Optim Methods Softw 30(1):15–53. https://doi.org/10.1080/10556788.2014.888426
Ríos-Mercado RZ, Borraz-Sánchez C (2015) Optimization problems in natural gas transportation systems: a state-of-the-art review. Appl Energy 147:536–555. https://doi.org/10.1016/j.apenergy.2015.03.017
Robinius M, Schewe L, Schmidt M, Stolten D, Thürauf J, Welder L (2019) Robust optimal discrete arc sizing for tree-shaped potential networks. Comput Optim Appl 73(3):791–819. https://doi.org/10.1007/s10589-019-00085-x
Schewe L, Koch T, Martin A, Pfetsch ME (2015) Chapter 5: mathematical optimization for evaluating gas network capacities. In: Evaluating gas network capacities, pp 87–102. https://doi.org/10.1137/1.9781611973693.ch5
Schmidt M (2013) A generic interior-point framework for nonsmooth and complementarity constrained nonlinear optimization. Ph.D. thesis. Gottfried Wilhelm Leibniz Universität Hannover
Schmidt M, Steinbach MC, Willert BM (2015) High detail stationary optimization models for gas networks. Optim Eng 16(1):131–164. https://doi.org/10.1007/s11081-014-9246-x
Schmidt M, Steinbach MC, Willert BM (2015). The precise NLP model. In: Koch T, Hiller B, Pfetsch ME, Schewe L (eds) Evaluating gas network capacities. SIAM-MOS Series on Optimization SIAM, Chap 10, pp 181–210. https://doi.org/10.1137/1.9781611973693.ch10
Schmidt M, Steinbach MC, Willert BM (2016) High detail stationary optimization models for gas networks: validation and results. Optim Eng 17(2):437–472. https://doi.org/10.1007/s11081-015-9300-3
Schrijver A (2003) Combinatorial optimization–polyhedra and efficiency. Springer, Berlin
Siddiqui S, Gabriel SA (2017) Modeling market power in the U.S. shale gas market. Optim Eng 18(1):203–213. https://doi.org/10.1007/s11081-016-9310-9
Willert B (2014) Validation of nominations in gas networks and properties of technical capacities. Ph.D. thesis. Gottfried Wilhelm Leibniz Universität Hannover
Wong PJ, Larson RE (1968) Optimization of tree-structured natural-gas transmission networks. J Math Anal Appl 24:613–626. https://doi.org/10.1016/0022-247X(68)90014-0
Acknowledgements
This research has been performed as part of the Energie Campus Nürnberg and is supported by funding of the Bavarian State Government. The first and second author also thank the DFG for their support within Projects A05, B07, and B08 in CRC TRR 154. Finally, we want to thank Fränk Plein for carefully reading a former version of this manuscript and for his comments that helped to improve the quality of the paper.
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Schewe, L., Schmidt, M. & Thürauf, J. Structural properties of feasible bookings in the European entry–exit gas market system. 4OR-Q J Oper Res 18, 197–218 (2020). https://doi.org/10.1007/s10288-019-00411-3
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DOI: https://doi.org/10.1007/s10288-019-00411-3