Advertisement

Networks and Spatial Economics

, Volume 17, Issue 4, pp 1161–1184 | Cite as

Efficiency and Stability in Electrical Power Transmission Networks: a Partition Function Form Approach

  • Dávid CsercsikEmail author
  • László Á. Kóczy
Article

Abstract

The users of electricity networks are organized into groups where the production and consumption of electricity is in balance. We study the formation of these balancing groups using a cooperative game in partition function form defined over an ideal (lossless) DC load flow model of the power grid. We show that such games contain widespread externalities that can be both negative and positive. We study the stability of certain partitions using the concept of the recursive core. While the game is clearly cohesive, we demonstrate that it is not necessarily superadditive. We argue that subadditivity may be a barrier to achieve full cooperation.

Keywords

Partition function form games Power transmission networks Externalities Game theory Recursive core 

Notes

Acknowledgments

The authors thank Katalin Hangos, Dávid Raisz, Dániel Divényi, and seminar participants at IEHAS and LSU for their input. This work has been supported by the Fund PD 123900 of the Hungarian National Research, Development and Innovation Office, by the Momentum Program by the Hungarian Academy of Sciences (LP-004/2010), and by the Fund KAP17-61008-1.2-ITK of the Pázmány Péter Catholic University.

References

  1. Aumann RJ, Peleg B (1960) Von Neumann-Morgenstern solutions to cooperative games without side payments. Bull Am Math Soc 66:173–179CrossRefGoogle Scholar
  2. Bai X, Shahidehpour S, Ramesh V (1997) Transmission analysis by nash game method. IEEE Trans Power Syst 12:1046–1052CrossRefGoogle Scholar
  3. Bando K (2012) Many-to-one matching markets with externalities among firms. J Math Econ 48(1):14–20CrossRefGoogle Scholar
  4. Bondareva ON (1963) Some applications of linear programming methods to the theory of cooperative games. Problemy Kybernetiki 10:119–139. (In Russian)Google Scholar
  5. Chander P, Tulkens H (1997) The core of and economy with multilateral environmental externalities. Int J Game Theory 26(3):379–401CrossRefGoogle Scholar
  6. Contreras J (1997) A cooperative game theory approach to transmission planning in power systems. PhD thesis, University of California, BerkeleyGoogle Scholar
  7. Contreras J, Wu F (1999) Coalition formation in transmission expansion planning. IEEE Trans Power Syst 14:1144–1152CrossRefGoogle Scholar
  8. Contreras J, Gross G, Arroyo JM, Muñoz JI (2009) An incentive-based mechanism for transmission asset investment. Decis Support Syst 47:22–31.  https://doi.org/10.1016/j.dss.2008.12.005. http://dl.acm.org/citation.cfm?id=1519538.1519674 CrossRefGoogle Scholar
  9. Crucitti P, Latora V, Marchiori M (2004) A topological analysis of the italian electric power grid. Phys A: Stat Mech Appl 338(1):92–97CrossRefGoogle Scholar
  10. Csercsik D (2016) Competition and cooperation in a bidding model of electrical energy trade. Netw Spatial Econ 16(4):1043–1073.  https://doi.org/10.1007/s11067-015-9310-x CrossRefGoogle Scholar
  11. Csóka P, Herings PJJ, Kóczy LÁ (2007) Measures of risk from a general equilibrium perspective. J Banking Finance 31(8):2517–2534.  https://doi.org/10.1016/j.jbankfin.2006.10.026 CrossRefGoogle Scholar
  12. Evans F, Zolezzi J, Rudnick H (2003) Cost assignment model for electrical transmission system expansion: an approach through the kernel theory. IEEE Trans Power Syst 18:625–632CrossRefGoogle Scholar
  13. Funaki Y, Yamato T (1999) The core of an economy with a common pool resource: a partition function form approach. Int J Game Theory 28(2):157–171CrossRefGoogle Scholar
  14. Gabriel SA, Siddiqui SA, Conejo AJ, Ruiz C (2013) Solving discretely-constrained nash–Cournot games with an application to power markets. Netw Spatial Econ 13(3):307–326.  https://doi.org/10.1007/s11067-012-9182-2 CrossRefGoogle Scholar
  15. García-Bertrand R, Conejo AJ, Gabriel SA (2005) Multi-period near-equilibrium in a pool-based electricity market including on/off decisions. Netw Spatial Econ 5(4):371–393.  https://doi.org/10.1007/s11067-005-6209-y CrossRefGoogle Scholar
  16. Gately D (1974) Sharing the gains from regional cooperation: a game theoretic application to planning investment in electric power. Int Econ Rev 15:195–208CrossRefGoogle Scholar
  17. Gilbert R, Neuhoff K, Newbery D (2004) Allocating transmission to mitigate market power in electricity networks. RAND J Econ 35(4):691–709. http://www.jstor.org/pss/1593768 CrossRefGoogle Scholar
  18. Gillies DB (1959) Solutions to general non-zero-sum games. In: Tucker A W, Luce R D (eds) Contributions to the Theory of Games IV, no. 40 in Annals of Mathematics Studies. Princeton University Press, Princeton, pp 47–85Google Scholar
  19. Guo Z, Fan Y (2017) A stochastic multi-agent optimization model for energy infrastructure planning under uncertainty in an oligopolistic market. Netw Spatial Econ 17(2):581–609.  https://doi.org/10.1007/s11067-016-9336-8 CrossRefGoogle Scholar
  20. Habis H, Csercsik D (2015) Cooperation with externalities and uncertainty. Netw Spatial Econ 15(1):1–16.  https://doi.org/10.1007/s11067-014-9265-3 CrossRefGoogle Scholar
  21. Habis H, Herings PJ (2011) Transferable utility games with uncertainty. J Econ Theory 146:2126–2139CrossRefGoogle Scholar
  22. Hobbs B (1992) Using game theory to analyze electric transmission pricing policies in the united states. Eur J Oper Res 56:154–171CrossRefGoogle Scholar
  23. Kaltenbach J, Hajdu L (1971) Optimal corrective rescheduling for power system security. IEEE Trans power Apparatus Syst 90:843–851CrossRefGoogle Scholar
  24. Kirschen D, Strbac G (2004) Fundamentals of power system economics. Wiley, Chichester.  https://doi.org/10.1002/0470020598 CrossRefGoogle Scholar
  25. Kóczy LÁ (2007) A recursive core for partition function form games. Theor Decis 63(1):41–51.  https://doi.org/10.1007/s11238-007-9030-x CrossRefGoogle Scholar
  26. Kóczy LÁ (2009) Sequential coalition formation and the core in the presence of externalities. Games Econ Behavior 66(1):559–565CrossRefGoogle Scholar
  27. Kóczy LÁ (2010) Strategic aspects of the 1995 and 2004 EU enlargements. Group Decis Negot 19(3):267–277.  https://doi.org/10.1007/s10726-009-9161-2 CrossRefGoogle Scholar
  28. Lange F, Grabisch M (2009) Values on regular games under Kirchhoff’s laws. Math Social Sci 58(3):322–340.  https://doi.org/10.1016/j.mathsocsci.2009.07.003. http://linkinghub.elsevier.com/retrieve/pii/S0165489609000729 CrossRefGoogle Scholar
  29. Leuthold FU, Weigt H, von Hirschhausen C (2012) A large-scale spatial optimization model of the european electricity market. Netw Spatial Econ 12(1):75–107.  https://doi.org/10.1007/s11067-010-9148-1 CrossRefGoogle Scholar
  30. Metzler C, Hobbs B, Pang JS (2003) Nash-Cournot equilibria in power markets on a linearized dc network with arbitrage: formulations and properties. Netw Spatial Econ 3(2):123–150.  https://doi.org/10.1023/A:1023907818360 CrossRefGoogle Scholar
  31. Neto PA, Friesz TL, Han K (2016) Electric power network oligopoly as a dynamic stackelberg game. Netw Spatial Econ 16(4):1211–1241.  https://doi.org/10.1007/s11067-016-9337-7 CrossRefGoogle Scholar
  32. Neuhoff K, Barquin J, Boots M, Ehrenmann A, Hobbs B, Rijkers F, Vázquez M (2005) Network-constrained Cournot models of liberalized electricity markets: the devil is in the details. Energy Econ 27:495–525CrossRefGoogle Scholar
  33. Oggioni G, Smeers Y, Allevi E, Schaible S (2012) A generalized Nash equilibrium model of market coupling in the european power system. Netw Spatial Econ 12(4):503–560.  https://doi.org/10.1007/s11067-011-9166-7 CrossRefGoogle Scholar
  34. Shapley LS (1967) On balanced sets and cores. Naval Res Logistics Quarterly 14(4):453–460.  https://doi.org/10.1002/nav.3800140404 CrossRefGoogle Scholar
  35. Shenoy PP (1979) On coalition formation: a game-theoretical approach. Int J Game Theory 8(3):133–164CrossRefGoogle Scholar
  36. Smeers Y (2003a) Market incompleteness in regional electricity transmission. part i: The forward market. Netw Spatial Econ 3(2):151–174.  https://doi.org/10.1023/A:1023959902430 CrossRefGoogle Scholar
  37. Smeers Y (2003b) Market incompleteness in regional electricity transmission. part ii: The forward and real time markets. Netw Spatial Econ 3(2):175–196.  https://doi.org/10.1023/A:1023916120177 CrossRefGoogle Scholar
  38. Thrall R, Lucas W (1963) n-person games in partition function form. Naval Res Logistics Quarterly 10:281–298CrossRefGoogle Scholar
  39. Van Cutsem T, Vournas C (1998) Voltage stability of electric power systems. Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar
  40. Wu F, Varaiya P, Spiller P, Oren S (1996) Folk theorems on transmission access: proofs and counterexamples. J Regul Econ 10(1):5–23.  https://doi.org/10.1007/BF00133356 CrossRefGoogle Scholar
  41. Yi SS (1997) Stable coalition structures with externalties. Games Econ Behavior 20:201–237CrossRefGoogle Scholar
  42. Zerrahn A, Huppmann D (2017) Network expansion to mitigate market power. Netw Spatial Econ 17(2):611–644.  https://doi.org/10.1007/s11067-017-9338-1 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Faculty of Information Technology and BionicsPázmány Péter Catholic UniversityBudapestHungary
  2. 2.Game Theory Research GroupCenter for Economic and Regional Studies of the Hungarian Academy of SciencesBudapestHungary
  3. 3.Keleti Faculty of Business and ManagementÓbuda UniversityBudapestHungary

Personalised recommendations