Dynamic Competitive Equilibria in Electricity Markets

  • Gui Wang
  • Matias Negrete-Pincetic
  • Anupama Kowli
  • Ehsan Shafieepoorfard
  • Sean Meyn
  • Uday V. Shanbhag
Part of the Power Electronics and Power Systems book series (PEPS, volume 3)


This chapter addresses the economic theory of electricity markets, viewed from an idealized competitive equilibrium setting, taking into account volatility and the physical and operational constraints inherent to transmission and generation. In a general dynamic setting, we establish many of the standard conclusions of competitive equilibrium theory: Market equilibria are efficient, and average prices coincide with average marginal costs. However, these conclusions hold only on average. An important contribution of this chapter is the explanation of the exotic behavior of electricity prices. Through theory and examples, we explain why, in the competitive equilibrium, sample-paths of prices can range from negative values, to values far beyond the “choke-up” price—which is usually considered to be the maximum price consumers are willing to pay. We also find that the variance of prices may be very large, but this variance decreases with increasing demand response.


Smart Grid Equilibrium Price Electricity Market Competitive Equilibrium Demand Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Research supported in part by the Grainger Endowments to the University of Illinois, DOE awards DE-OE0000097 (TCIPG) and DE-SC0003879, and AFOSR Grant FA9550-09-1-0190.


  1. 1.
    Aliprantis CD, Cornet B, Tourky R (2002) Economic equilibrium: optimality and price decentralization. Positivity 6:205–241MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Anderson EJ, Philpott AB (2002) Using supply functions for offering generation into an electricity market. Oper Res 50(3):477–489 MR 1910284 (2003f:91069)Google Scholar
  3. 3.
    Arrow KJ, Hahn F (1971) General competitive analysis. Holden-Day, San FranciscoMATHGoogle Scholar
  4. 4.
    Baldick R, Grant R, Kahn E (2004) Theory and application of linear supply function equilibrium in electricity markets. J Regul Econ 25(2):143–167CrossRefGoogle Scholar
  5. 5.
    Chen M, Cho I-K, Meyn SP (2006) Reliability by design in a distributed power transmission network. Automatica 42:1267–1281 (invited)Google Scholar
  6. 6.
    Cho I-K, Meyn SP (2009) A dynamic newsboy model for optimal reserve management in electricity markets. SIAM J Contr Optim (Submitted for publication)Google Scholar
  7. 7.
    Cho I-K, Meyn SP (2010) Efficiency and marginal cost pricing in dynamic competitive markets with friction. Theoret Econ 5(2):215–239MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Chow GC (1997) Dynamic economics: optimization by the lagrange method. Oxford University Press, USAGoogle Scholar
  9. 9.
    Chow JH, De Mello W, Cheung KW (2005) Electricity market design: an integrated approach to reliability assurance. Proc IEEE 93(11):1956 –1969CrossRefGoogle Scholar
  10. 10.
    Day CJ, Hobbs BF, Pang J-S (2002) Oligopolistic competition in power networks: a conjectured supply function approach. IEEE Trans Power Syst 17:597–607CrossRefGoogle Scholar
  11. 11.
    Epstein PR, Buonocore JJ, Eckerle K, Hendryx M, Stout III BM, Heinberg R, Clapp RW, May B, Reinhart NL, Ahern MM, Doshi SK, Glustrom L (2011) Full cost accounting for the life cycle of coal. Ann NY Acad Sci 1219(1):73–98CrossRefGoogle Scholar
  12. 12.
    FERC (1998) Staff Report to the Federal Energy Regulatory Commission on the Causes of Wholesale Electric Pricing Abnormalities in the Midwest During June 1998, FERC study, September 22, 1998Google Scholar
  13. 13.
    Hobbs BF (2001) Linear complementarity models of Nash–Cournot competition in bilateral and POOLCO power markets. IEEE Trans Power Syst 16(2):194–202CrossRefGoogle Scholar
  14. 14.
    Hobbs BF, Helman U (2004) Complementarity-Based Equilibrium Modeling for Electric Power Markets. Modeling Prices in Competitive Electricity Markets, Wiley Series in Financial Economics. Wiley, West Sussex, England, pp 69–98Google Scholar
  15. 15.
    Houston Chronicle Editorial (2011) Rolling blunder statewide blackouts raise the question: who really runs the lone star power grid?, Feb. 12, 2011
  16. 16.
    Hu X, Ralph D (2007) Using EPECs to model bilevel games in restructured electricity markets with locational prices. Oper Res 55(5):809–827. MR MR2360950Google Scholar
  17. 17.
    Johari R, Tsitsiklis JN (2009) Efficiency of scalar-parameterized mechanisms. Oper Res 57:823–839MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Kizilkale AC, Mannor S (2010) Volatility and efficiency in markets with friction. In: 48th Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, pp 50–57Google Scholar
  19. 19.
    Klemperer PD, Meyer MA (1989) Supply function equilibria in oligopoly under uncertainty. Econometrica 57:1243–1277MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Kowli A, Meyn SP (2011) Supporting wind generation deployment with demand response. In: IEEE PES 11: power energy society general meeting, Detroit, MichiganGoogle Scholar
  21. 21.
    Luenberger DG (1969) Optimization by vector space methods. Wiley, New YorkMATHGoogle Scholar
  22. 22.
    Mas-Colell A, Whinston MD, Green JR (1995) Microeconomic theory. Oxford University Press, New YorkMATHGoogle Scholar
  23. 23.
    Metzler C, Hobbs B, Pang J-S (2003) Nash–Cournot equilibria in power markets on a linearized DC network with arbitrage: formulations and properties. Network Spatial Econ 3(2):123–150CrossRefGoogle Scholar
  24. 24.
    Meyn S, Negrete-Pincetic M, Wang G, Kowli A, Shafieepoorfard E (2010) The value of volatile resources in electricity markets. In: Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, Georgia, pp 1029–1036Google Scholar
  25. 25.
    Mookherjee R, Friesz T, Hobbs BF, Ringdon M (2008) Dynamic oligopolistic competition on an electric power network with ramping costs and joint sales constraints. J Ind Manage Org 4(3):425–452MATHGoogle Scholar
  26. 26.
    Negrete-Pincetic M, Meyn SP (2011) Intelligence by design for the entropic grid. In: IEEE PES 11: Power energy society general meeting, Invited lecture for PES panel: deploying tomorrow’s electric power systems: low carbon, efficiency and security, Detroit, MichiganGoogle Scholar
  27. 27.
    Robinson S (2005) Math model explains volatile prices in power markets. SIAM NewsGoogle Scholar
  28. 28.
    Shanbhag UV, Infanger G, Glynn PW (2011) A complementarity framework for forward contracting under uncertainty. Oper Res 59(4):810–834MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Smith JC, Beuning S, Durrwachter H, Ela E, Hawkins D, Kirby B, Lasher W, Lowell J, Porter K, Schuyler K, Sotkiewicz P (2010) The wind at our backs. IEEE Power Energ Mag 8(5):63–71CrossRefGoogle Scholar
  30. 30.
    Wang G, Kowli A, Negrete-Pincetic M, Shafieepoorfard E, Meyn S (2011) A control theorist’s perspective on dynamic competitive equilibria in electricity markets. In: Proceedings of 18th world congress of the international federation of automatic control (IFAC), Milano, ItalyGoogle Scholar
  31. 31.
    Wang G, Negrete-Pincetic M, Kowli A, Shafieepoorfard E, Meyn S, Shanbhag UV (2012) Real-time prices in an entropic grid. IEEE Conference on Decision and Control. To appear in the Proceedings of the 2012 PES Innovative Smart Grid Technologies Conference. (Invited), Jan 2012Google Scholar
  32. 32.
    Electricity Authority strikes down Genesis price spike. Business Desk Report, New Zealand Herald, May 6, 2011. c_id=3&objectid=10723856
  33. 33.
    Wilson R (2002) Architecture of power markets. Econometrica 70(4):1299–1340MATHCrossRefGoogle Scholar
  34. 34.
    Wood AJ, Wollenberg BF (1996) Power generation, operation, and control. Wiley, New YorkGoogle Scholar
  35. 35.
    Yao J, Adler I, Oren S (2008) Modeling and computing two-settlement oligopolistic equilibrium in a congested electricity network. Oper Res 56(1):34–47. MR MR2402216Google Scholar
  36. 36.
    Zavala VM, Anitescu M (2010) On the dynamic stability of electricity markets. Math Program (submitted for publication)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Gui Wang
    • 1
  • Matias Negrete-Pincetic
    • 1
  • Anupama Kowli
    • 1
  • Ehsan Shafieepoorfard
    • 1
  • Sean Meyn
    • 1
  • Uday V. Shanbhag
    • 2
  1. 1.CSL and the ECE DepartmentUniversity of IllinoisUrbana-ChampaignUSA
  2. 2.ISE DepartmentUniversity of IllinoisUrbana-ChampaignUSA

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