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The impact of potential-based physics models on pricing in energy networks

  • Lars Schewe
  • Martin SchmidtEmail author
Original Article

Abstract

Pricing of access to energy networks is an important issue in liberalized energy sectors because of the natural monopoly character of the underlying transport infrastructures. We introduce a general pricing framework for potential-based energy flows in arbitrarily structured transport networks. In different specifications of our general pricing model we discuss first- and second-best pricing results and compare different pricing outcomes of potential-free and potential-based energy flow models. Our results show that considering nonlinear laws of physics leads to significantly different pricing results on networks and that these differences can only be seen in sufficiently complex, e.g., cyclic, networks as they can be found in real-world situations.

Keywords

Energy networks Pricing Gas networks Electricity networks 

JEL Classification

C61 L94 L95 

Notes

Acknowledgements

The authors thank the Deutsche Forschungsgemeinschaft for their support within projects A05, B07, and B08 in the Sonderforschungsbereich/Transregio 154 “Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks”. This research has been performed as part of the Energie Campus Nürnberg and is supported by funding of the Bavarian State Government. Finally, we thank Veronika Grimm and Gregor Zöttl for numerous discussions on the topic of this paper.

References

  1. Ambrosius M, Grimm V, Kleinert T, Liers F, Schmidt M, Zöttl G (2018). Endogenous price zones and investment incentives in electricity markets: an application of multilevel optimization with graph partitioning. Tech. rep. http://www.optimization-online.org/DB_HTML/2018/10/6868.html
  2. Arnott R, Yan A (2000) The two-mode problem: second-best pricing and capacity. Rev Urban Reg Dev Stud 12(3):170–199CrossRefGoogle Scholar
  3. Bollobás B (1998). Modern graph theory. vol. 184. Graduate Texts in Mathematics. Springer, New York, pp. xiv+394.  https://doi.org/10.1007/978-1-4612-0619-4
  4. Burgschweiger J, Gnädig B, Steinbach MC (2009) Optimization models for operative planning in drinking water networks. Optim Eng 10(1):43–73.  https://doi.org/10.1007/s11081-008-9040-8 CrossRefGoogle Scholar
  5. Cardell JB, Hitt CC, Hogan WW (1997) Market power and strategic interaction in electricity networks. Resour Energy Econ 19(1–2):109–137.  https://doi.org/10.1016/S0928-7655(97)00006-7 CrossRefGoogle Scholar
  6. Chao H-P, Peck SC (1996) A market mechanism for electric power transmission. J Regul Econ 10(1):25–59.  https://doi.org/10.1007/BF00133357 CrossRefGoogle Scholar
  7. Chao H-P, Peck SC (1998) Reliability management in competitive electricity markets. J Regul Econ 14(2):189–200.  https://doi.org/10.1023/A:1008061319181 CrossRefGoogle Scholar
  8. Cremer H, Laffont J-J (2002) Competition in gas markets. Eur Econ Rev 46(4):928–935.  https://doi.org/10.1016/S0014-2921(01)00226-4 CrossRefGoogle Scholar
  9. Cremer H, Gasmi F, Laffont J-J (2003) Access to pipelines in competitive gas markets. J Regul Econ 24(1):5–33.  https://doi.org/10.1023/A:1023943613605 CrossRefGoogle Scholar
  10. Deng S-J, Oren S (2001) Priority network access pricing for electric power. J Regul Econ 19(3):239–270.  https://doi.org/10.1023/A:1011107106649 CrossRefGoogle Scholar
  11. Facchinei F, Kanzow C (2007) Generalized Nash equilibrium problems. 4OR 5(3):173–210.  https://doi.org/10.1007/s10288-007-0054-4 CrossRefGoogle Scholar
  12. Facchinei F, Fischer A, Piccialli V (2007) On generalized Nash games and variational inequalities. Oper Res Lett 35(2):159–164.  https://doi.org/10.1016/j.orl.2006.03.004 CrossRefGoogle Scholar
  13. Fügenschuh A, Geißler B, Gollmer R, Morsi A, Pfetsch ME, Rövekamp J, Schmidt M, Spreckelsen K, Steinbach MC (2015) Physical and technical fundamentals of gas networks. In: Koch T, Hiller B, Pfetsch ME, Schewe L (eds) Evaluating gas network capacities. SIAM-MOS series on optimization. Chap. 2. SIAM, University City, pp 17–44.  https://doi.org/10.1137/1.9781611973693.ch2 CrossRefGoogle Scholar
  14. Gabriel SA, Conejo AJ, Fuller JD, Hobbs BF, Ruiz C (2012) Complementarity modeling in energy markets, vol 180. Springer, BerlinGoogle Scholar
  15. Gabriel SA, Conejo AJ, Ruiz C, Siddiqui S (2013) Solving discretely constrained, mixed linear complementarity problems with applications in energy. Comput Oper Res 40(5):1339–1350.  https://doi.org/10.1016/j.cor.2012.10.017 CrossRefGoogle Scholar
  16. Galiana FD, Conejo AJ, Gil HA (2003) Transmission network cost allocation based on equivalent bilateral exchanges. IEEE Trans Power Syst 18(4):1425–1431CrossRefGoogle Scholar
  17. Gasmi F, Oviedo JD (2010) Investment in transport infrastructure, regulation, and gas-gas competition. Energy Econ 32(3):726–736.  https://doi.org/10.1016/j.eneco.2009.10.008 CrossRefGoogle Scholar
  18. German TSOs (2014) Netzentwicklungsplan Strom 2014. Tech. rep, Zweiter Entwurf der ÜbertragungsnetzbetreiberGoogle Scholar
  19. German TSOs (2017) Netzentwicklungsplan Strom 2030, Version 2017. Tech. rep, Erster Entwurf der ÜbertragungsnetzbetreiberGoogle Scholar
  20. Gil HA, Galiana FD, Conejo AJ (2005) Multiarea transmission network cost allocation. IEEE Trans Power Syst 20(3):1293–1301CrossRefGoogle Scholar
  21. Grimm V, Martin A, Schmidt M, Weibelzahl M, Zöttl G (2016) Transmission and generation investment in electricity markets: the effects of market splitting and network fee regimes. Eur J Oper Res 254(2):493–509.  https://doi.org/10.1016/j.ejor.2016.03.044 CrossRefGoogle Scholar
  22. Grimm V, Schewe L, Schmidt M, Zöttl G (2017) Uniqueness of market equilibrium on a network: a peak-load pricing approach. Eur J Oper Res 261(3):971–983.  https://doi.org/10.1016/j.ejor.2017.03.036 CrossRefGoogle Scholar
  23. Grimm V, Schewe L, Schmidt M, Zöttl G (2018) A multilevel model of the european entry-exit gas market. Math Methods Oper Res.  https://doi.org/10.1007/s00186-018-0647-z CrossRefGoogle Scholar
  24. Grimm V, Grübel J, Schewe L, Schmidt M, Zöttl G (2019a) 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 CrossRefGoogle Scholar
  25. Grimm V, Kleinert T, Liers F, Schmidt M, Zöttl G (2019b) Optimal price zones of electricity markets: a mixed-integer multilevel model and global solution approaches. Optim Methods Softw. 34(2):406–436.  https://doi.org/10.1080/10556788.2017.1401069 CrossRefGoogle Scholar
  26. Groß M, Pfetsch ME, Schewe L, Schmidt M, Skutella M (2019) Algorithmic results for potential-based flows: easy and hard cases. Networks.  https://doi.org/10.1002/net.21865 CrossRefGoogle Scholar
  27. Harker PT (1991) Generalized Nash games and quasi-variational inequalities. Eur J Oper Res 54(1):81–94.  https://doi.org/10.1016/0377-2217(91)90325-P CrossRefGoogle Scholar
  28. Hogan WW (1992) Contract networks for electric power transmission. J Regul Econ 4(3):211–242.  https://doi.org/10.1007/BF00133621 CrossRefGoogle Scholar
  29. Hogan WW (1997) A market power model with strategic interaction in electricity networks. Energy J 18(4):107–141CrossRefGoogle Scholar
  30. Johansson RC, Tsur Y, Roe TL, Doukkali R, Dinar A (2002) Pricing irrigation water: a review of theory and practice. Water Policy 4(2):173–199CrossRefGoogle Scholar
  31. Joskow PL (1997) Restructuring, competition and regulatory reform in the U.S. electricity sector. J Econ Perspect 11(3):119–138.  https://doi.org/10.1257/jep.11.3.119 CrossRefGoogle Scholar
  32. Joskow PL (2008) Incentive regulation and its application to electricity networks. Rev Netw Econ 7(4):1–14CrossRefGoogle Scholar
  33. Kirschen D, Strbac G (2004) Transmission networks and electricity markets. In: Kirschen DS, Strbac G (eds) Fundamentals of power system economics. Chichester, England, pp 141–204CrossRefGoogle Scholar
  34. Kleinert T, Schmidt M (2019) Global optimization of multilevel electricity market models including network design and graph partitioning. Discrete Optim. (forthcoming)Google Scholar
  35. Koch T, Hiller B, Pfetsch ME, Schewe L (2015) Evaluating gas network capacities. SIAM-MOS series on optimization. SIAM, University City, p xvi + 364.  https://doi.org/10.1137/1.9781611973693 CrossRefGoogle Scholar
  36. Krebs V, Schmidt M (2018) Uniqueness of market equilibria on networks with transport costs. Oper Res Perspect 5:169–173.  https://doi.org/10.1016/j.orp.2018.05.002 CrossRefGoogle Scholar
  37. Krebs V, Schewe L, Schmidt M (2018) Uniqueness and multiplicity of market equilibria on DC power flow networks. Eur J Oper Res 271(1):165–178.  https://doi.org/10.1016/j.ejor.2018.05.016 CrossRefGoogle Scholar
  38. Laffont J-J, Tirole J (1994) Access pricing and competition. Eur Econ Rev 38(9):1673–1710.  https://doi.org/10.1016/0014-2921(94)90046-9 CrossRefGoogle Scholar
  39. Larock BE, Jeppson RW, Watters GZ (2010) Hydraulics of pipeline systems. CRC Press, Boca RatonGoogle Scholar
  40. Léautier T-O (2001) Transmission constraints and imperfect markets for power. J Regul Econ 19(1):27–54.  https://doi.org/10.1023/A:1008143528249 CrossRefGoogle Scholar
  41. Lochner S (2011) Identification of congestion and valuation of transport infrastructures in the European natural gas market. Energy 36(5):2483–2492.  https://doi.org/10.1016/j.energy.2011.01.040 CrossRefGoogle Scholar
  42. McCarl BA (2009) GAMS User Guide. Version 23Google Scholar
  43. Meran G, von Hirschhausen C, Neumann A (2010) Access Pricing and Network Expansion in Natural Gas Markets. Zeitschrift für Energiewirtschaft 34(3):179–183.  https://doi.org/10.1007/s12398-010-0028-7 CrossRefGoogle Scholar
  44. Micola AR, Bunn DW (2007) Two markets and a weak link. Energy Econ 29(1):79–93.  https://doi.org/10.1016/j.eneco.2006.08.009 CrossRefGoogle Scholar
  45. Midthun KT, Bjørndal M, Tomasgard A (2009) Modeling optimal economic dispatch and system effects in natural gas networks. Energy J 30(4):155–180CrossRefGoogle Scholar
  46. Midthun KT, Fodstad M, Hellemo L (2015) Optimization model to analyse optimal development of natural gas fields and infrastructure. Energy Procedia 64:111–119CrossRefGoogle Scholar
  47. Ramsey FP (1927) A contribution to the theory of taxation. Econ J 37(145):47–61.  https://doi.org/10.2307/2222721 CrossRefGoogle Scholar
  48. 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.  https://doi.org/10.1007/s10589-019-00085-x (forthcoming)
  49. Rosendahl KE, Sagen EL (2009) The global natural gas market: will transport cost reductions lead to lower prices? Energy J 30(2):17–39Google Scholar
  50. Ruiz C, Conejo AJ, Gabriel SA (2012) Pricing non-convexities in an electricity pool. IEEE Trans Power Syst 27(3):1334–1342.  https://doi.org/10.1109/TPWRS.2012.2184562 CrossRefGoogle Scholar
  51. Schmidt M (2013) A generic interior-point framework for nonsmooth and complementarity constrained nonlinear optimization. Ph.D. thesis. Leibniz Universität HannoverGoogle Scholar
  52. 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 CrossRefGoogle Scholar
  53. 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 CrossRefGoogle Scholar
  54. Schrijver A (2003) Combinatorial optimization. Polyhedra and Efficiency. Vol. A: Paths, flows, matchings. Springer, Berlin, pp. xxxviii+647Google Scholar
  55. Schweppe FC, Tabors RD, Caraminis M, Bohn RE (1988) Spot pricing of electricity. Springer, Berlin.  https://doi.org/10.1007/978-1-4613-1683-1 CrossRefGoogle Scholar
  56. Spulber N, Sabbaghi A (2012) Economics of water resources: from regulation to privatization, vol 13. Springer, BerlinGoogle Scholar
  57. Tawarmalani M, Sahinidis NV (2005) A polyhedral branch-and-cut approach to global optimization. Math Progr 103(2):225–249.  https://doi.org/10.1007/s10107-005-0581-8 CrossRefGoogle Scholar
  58. Verhoef ET (2002) Second-best congestion pricing in general static transportation networks with elastic demands. Reg Sci Urban Econ 32(3):281–310CrossRefGoogle Scholar
  59. Winston C (1985) Conceptual developments in the economics of transportation: an interpretive survey. J Econ Lit 23(1):57–94Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Discrete OptimizationFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  2. 2.Energie Campus NürnbergNurembergGermany
  3. 3.Department of MathematicsTrier UniversityTrierGermany

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