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Complex dynamics of Cournot game with bounded rationality in an oligopolistic electricity market

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Abstract

In order to accurately simulate the dynamic decision-making behaviors of market participants, a novel dynamic Cournot game model with bounded rationality of electricity market that considers the constraints of realistic power networks is proposed in this paper. This model is represented by discrete difference equations embedded within the optimization problem of consumption benefits. The Nash equilibrium of electricity market and its stability are quantitatively analyzed. It is found that there are different Nash equilibriums with different market parameters corresponding to different operating conditions of power network, i.e. congestion and non-congestion, and even in some cases there is no Nash equilibrium at all. Numerical simulations with the 2-node and IEEE 30-node systems are carried out to evaluate the dynamic behaviors of electricity market, especially the periodic and chaotic behaviors when the market parameters are beyond the stability region of Nash equilibrium.

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References

  • Agiza HN, Hegazi AS, Elsadany AA (2001) The dynamics of Bowley’s model with bounded rationality. Chaos Solitons Fractals 12:1705–1717

    Article  MathSciNet  MATH  Google Scholar 

  • Agliari A, Gardini L, Puu T (2000) The dynamics of a triopoly Cournot game. Chaos Solitons Fractals 11:2531–2560

    Article  MathSciNet  MATH  Google Scholar 

  • Alsac O, Stott B (1974) Optimal load flow with steady-state security. IEEE Trans Power Apparatus Syst 93(3):745–751

    Article  Google Scholar 

  • Alvarado FL (1999) The stability of power system markets. IEEE Trans Power Syst 14(2):505–511

    Article  MathSciNet  Google Scholar 

  • Alvarado FL, Meng J, DeMarco CL (2001) Stability analysis of interconnected power systems coupled with market dynamics. IEEE Trans Power Syst 16(4):605–701

    Article  Google Scholar 

  • Bischi GI, Naimzada A (2000) Global analysis of a dynamic duopoly game with bounded rationality. In: Filar JA, Gaitsgory V, Mizukami K (eds) Advances in dynamic games and applications, pp 361–385

  • Branch WA, McGough B (2008) Replicator dynamics in a Cobweb model with rationally heterogeneous expectations. J Econ Behavior Organ 65:224–244

    Article  Google Scholar 

  • Facchinei F, Pang JS (2003) Finite-dimensional variational inequalities and complementarity problems. Springer, New York

    Google Scholar 

  • Gao J, Sheng Z (2003) Evolutionary game theory and its application in electricity market. Autom Electr Power Syst 27(18):18–21

    Google Scholar 

  • Hamdy NA, Gian IB, Michael K (1999) Multistability in a dynamic Cournot game with three oligopolists. Math Comput Simul 51:63–90

    Article  Google Scholar 

  • Herdrik R, Arco S (2004) Control of the triple chaotic attractor in a Cournot triopoly model. Chaos Solitons Fractals 29:409–413

    Google Scholar 

  • Hogan WW (2002) California market design breakthrough. Harvard University Press, Cambridge

    Google Scholar 

  • Lance BC, Ross B, Martin LB (2002) An empirical study of applied game theory: transmission constrained Cournot behavior. IEEE Trans Power Syst 17(1):166–172

    Article  Google Scholar 

  • Liu Y, Ni YX, Wu FF (2004) Control theory application in electricity market stability analysis. In: IEEE international conference on electric utility deregulation, restructuring and power technologies, vol 2. IEEE, New York, pp 562–569

    Google Scholar 

  • Maiorano A, Song YH, Trovato M (2000) Dynamics of non-collusive oligopolistic electricity markets. In: IEEE power engineering society winter meeting, vol 2. IEEE, New York, pp 838–844

    Google Scholar 

  • Medio A, Lines M (2001) Nonlinear dynamics: a primer. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Tang Y, Wu J, Zou Y (2001) The research on the stability of electricity market. Autom Electr Power Syst 25(4):11–16

    Google Scholar 

  • Varian HR (1992) Microeconomic analysis, 3rd edn. Norton & Company, London, pp 180–250

    Google Scholar 

  • Xie S (2002) Economic game theory, 2nd edn. Fudan University Press, Shanghai

    Google Scholar 

  • Yang W, Sheble GB (2002) Modeling generation company decisions and electric market dynamics as discrete systems. In: IEEE power engineering society summer meeting, vol 3. IEEE, New York, pp 1385–1391

    Chapter  Google Scholar 

  • Yang Z, Liu Y, Tang Y (2005) Analysis of electricity market stability. Proc Chin Soc Electr Eng 25(2):1–5

    MathSciNet  Google Scholar 

  • Younes Z, Ilic M (1998) Generation strategies for gaming transmission constraints: will the deregulated electric power market be an oligopoly? In: Proceedings of the 31th Hawaii international conference on system sciences, vol 3, Hawaii, USA 1998, pp 112–121

  • Zhang Y, Luo X, Xue J (2003) Adaptive dynamic Cournot model of optimizing generating units’ power output under nonlinear market demand. Proc Chin Soc Electr Eng 23(11):80–84

    Google Scholar 

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Authors and Affiliations

  1. College of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha, Hunan, 410114, PR China

    Hongming Yang & Meng Zhang

  2. Key Laboratory of Logistics Information and Simulation Technology, Hunan University, Changsha, Hunan, 410079, PR China

    Hongming Yang & Mingyong Lai

  3. College of Economics and Trade, Hunan University, Changsha, Hunan, 410079, PR China

    Mingyong Lai

Authors
  1. Hongming Yang
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  2. Meng Zhang
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  3. Mingyong Lai
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Correspondence to Hongming Yang.

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Yang, H., Zhang, M. & Lai, M. Complex dynamics of Cournot game with bounded rationality in an oligopolistic electricity market. Optim Eng 12, 559–582 (2011). https://doi.org/10.1007/s11081-010-9122-2

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  • DOI: https://doi.org/10.1007/s11081-010-9122-2

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