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A two stage stochastic equilibrium model for electricity markets with two way contracts

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  • Dali Zhang
  • Huifu Xu
  • Yue Wu

Abstract

This paper investigates generators’ strategic behaviors in contract signing in the forward market and power transaction in the electricity spot market. A stochastic equilibrium program with equilibrium constraints (SEPEC) model is proposed to characterize the interaction of generators’ competition in the two markets. The model is an extension of a similar model proposed by Gans et al. (Aust J Manage 23:83–96, 1998) for a duopoly market to an oligopoly market. The main results of the paper concern the structure of a Nash–Cournot equilibrium in the forward-spot market: first, we develop a result on the existence and uniqueness of the equilibrium in the spot market for every demand scenario. Then, we show the monotonicity and convexity of each generator’s dispatch quantity in the spot equilibrium by taking it as a function of the forward contracts. Finally, we establish some sufficient conditions for the existence of a local and global Nash equilibrium in the forward-spot markets. Numerical experiments are carried out to illustrate how the proposed SEPEC model can be used to analyze interactions of the markets. Copyright Springer-Verlag 2010

Suggested Citation

  • Dali Zhang & Huifu Xu & Yue Wu, 2010. "A two stage stochastic equilibrium model for electricity markets with two way contracts," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 1-45, February.
    • Handle: RePEc:spr:mathme:v:71:y:2010:i:1:p:1-45
    DOI: 10.1007/s00186-009-0283-8
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    2. Holmberg, Pär & Willems, Bert, 2015. "Relaxing competition through speculation: Committing to a negative supply slope," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 236-266.
    3. M. Sarfati & M.R. Hesamzadeh & P. Holmberg, 2018. "Increase-Decrease Game under Imperfect Competition in Two-stage Zonal Power Markets – Part II: Solution Algorithm," Working Papers EPRG 1838, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
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    5. Hesamzadeh, Mohammad Reza & Holmberg, Pär & Sarfati, Mahir, 2018. "Simulation and Evaluation of Zonal Electricity Market Designs," Working Paper Series 1211, Research Institute of Industrial Economics.
    6. Kovacevic, Raimund M. & Pflug, Georg Ch., 2014. "Electricity swing option pricing by stochastic bilevel optimization: A survey and new approaches," European Journal of Operational Research, Elsevier, vol. 237(2), pages 389-403.
    7. Javad Khazaei & Golbon Zakeri & Shmuel S. Oren, 2017. "Single and Multisettlement Approaches to Market Clearing Under Demand Uncertainty," Operations Research, INFORMS, vol. 65(5), pages 1147-1164, October.
    8. Sarfati, Mahir & Hesamzadeh, Mohammad Reza & Holmberg, Pär, 2018. "Increase-Decrease Game under Imperfect Competition in Two-stage Zonal Power Markets –​ Part II: Solution Algorithm," Working Paper Series 1254, Research Institute of Industrial Economics.
    9. Escudero, Laureano F. & Monge, Juan F. & Rodríguez-Chía, Antonio M., 2020. "On pricing-based equilibrium for network expansion planning. A multi-period bilevel approach under uncertainty," European Journal of Operational Research, Elsevier, vol. 287(1), pages 262-279.
    10. Huifu Xu & Dali Zhang, 2013. "Stochastic Nash equilibrium problems: sample average approximation and applications," Computational Optimization and Applications, Springer, vol. 55(3), pages 597-645, July.

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