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Distributed Nash Equilibrium Seeking for a Dynamic Micro-grid Energy Trading Game with Non-quadratic Payoffs

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  • Bhatti, Bilal Ahmad
  • Broadwater, Robert

Abstract

To model energy trading interactions among prosumers, a generic non-quadratic dynamic game model is proposed and solved for a stable Nash equilibrium. The framework is modeled as a non-cooperative, infinite strategy, multiplayer game where the participating players can possess a non-quadratic payoff function. Moreover, the market framework realizes a dynamic mapping from strategy set to payoffs of the participating players. It also carries an embedded notion of reliability and fairness by utilizing the concept of market reputation index. The existence of multiple Nash equilibria is discussed as well as the criteria for stability of Nash equilibrium. It is demonstrated that when an extremum seeking approach is used to model Nash seeking behavior of the players, the system converges to one of the stable Nash equilibriums depending on the initial condition. Simulation results are presented to verify the theoretical results, and a complete day with multiple prosumers is simulated to demonstrate effectiveness of the approach. The results are evaluated using several reliability matrices to show that the proposed framework results in an increased local generation, increased payoffs for prosumers, lower market clearing prices, and higher reliability.

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  • Bhatti, Bilal Ahmad & Broadwater, Robert, 2020. "Distributed Nash Equilibrium Seeking for a Dynamic Micro-grid Energy Trading Game with Non-quadratic Payoffs," Energy, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:energy:v:202:y:2020:i:c:s0360544220308161
    DOI: 10.1016/j.energy.2020.117709
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    1. Theo Offerman & Jan Potters & Joep Sonnemans, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(4), pages 973-997.
    2. Naimzada, Ahmad K. & Sbragia, Lucia, 2006. "Oligopoly games with nonlinear demand and cost functions: Two boundedly rational adjustment processes," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 707-722.
    3. Yu, Mengmeng & Hong, Seung Ho, 2017. "Incentive-based demand response considering hierarchical electricity market: A Stackelberg game approach," Applied Energy, Elsevier, vol. 203(C), pages 267-279.
    4. Tushar, Wayes & Saha, Tapan Kumar & Yuen, Chau & Morstyn, Thomas & McCulloch, Malcolm D. & Poor, H. Vincent & Wood, Kristin L., 2019. "A motivational game-theoretic approach for peer-to-peer energy trading in the smart grid," Applied Energy, Elsevier, vol. 243(C), pages 10-20.
    5. Wei, F. & Jing, Z.X. & Wu, Peter Z. & Wu, Q.H., 2017. "A Stackelberg game approach for multiple energies trading in integrated energy systems," Applied Energy, Elsevier, vol. 200(C), pages 315-329.
    6. Wu, Qiong & Ren, Hongbo & Gao, Weijun & Ren, Jianxing, 2017. "Benefit allocation for distributed energy network participants applying game theory based solutions," Energy, Elsevier, vol. 119(C), pages 384-391.
    7. Mei, Jie & Chen, Chen & Wang, Jianhui & Kirtley, James L., 2019. "Coalitional game theory based local power exchange algorithm for networked microgrids," Applied Energy, Elsevier, vol. 239(C), pages 133-141.
    8. Motalleb, Mahdi & Annaswamy, Anuradha & Ghorbani, Reza, 2018. "A real-time demand response market through a repeated incomplete-information game," Energy, Elsevier, vol. 143(C), pages 424-438.
    9. Su, Wencong & Huang, Alex Q., 2014. "A game theoretic framework for a next-generation retail electricity market with high penetration of distributed residential electricity suppliers," Applied Energy, Elsevier, vol. 119(C), pages 341-350.
    10. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    11. Bhatti, Bilal Ahmad & Broadwater, Robert, 2019. "Energy trading in the distribution system using a non-model based game theoretic approach," Applied Energy, Elsevier, vol. 253(C), pages 1-1.
    12. Zhang, Ni & Yan, Yu & Su, Wencong, 2015. "A game-theoretic economic operation of residential distribution system with high participation of distributed electricity prosumers," Applied Energy, Elsevier, vol. 154(C), pages 471-479.
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