Efficient Game for Vehicle-to-Grid Coordination Problems

  • Zhongjing MaEmail author


PEVs, as distributed energy sources, are promising to provide vehicle-to-grid (V2G) services for power grid, like frequency and voltage regulations, by coordinating their active and reactive power rates. However due to the autonomy of PEVs, it is challenging how to efficiently schedule the coordination behaviors among these units in a decentralized way. In this chapter it formulates the underlying coordination problems as a novel class of VCG-style auction games where players, power grid and PEVs, do not report a full cost or valuation function but only a multi-dimensional bid signal: the maximum active and reactive power quantities that power grid wants and the maximum per-unit prices it is willing to pay, the maximum active and reactive power quantities that a PEV can provide and the minimum per-unit prices it asks. We show the existence of the efficient Nash equilibrium for the underlying auction games, though there may exist other inefficient Nash equilibria. In order to deal with large-scale PEVs, in this chapter, it designs games with aggregator players each of which submits bid profiles representing the overall utility for a collection of PEVs, and extends the so-called quantized-PSP mechanism to the underlying auction games to implement the efficient Nash equilibrium.


  1. 1.
    I. Cvetkovic, T. Thacker, Future home uninterruptible renewable energy system with vehicle-to-grid technology, in 2009 IEEE Energy Conversion Congress and Exposition, 2009. ECCE 2009 (2009), pp. 2675–2681Google Scholar
  2. 2.
    M. Erol-Kantarci, H. Mouftah, Management of PHEV batteries in the smart grid: towards a cyber-physical power infrastructure, in 2011 7th International Wireless Communications and Mobile Computing Conference (IWCMC) (2011), pp. 795–800Google Scholar
  3. 3.
    C. Wu, H. Mohsenian-rad, J. Huang, Vehicle-to-aggregator interaction game. IEEE Trans. Smart Grid (2011)Google Scholar
  4. 4.
    D. Infield, J. Short, C. Home, L. Frerism, Potential for domestic dynamic demand-side management in the uk. 2007 IEEE Power Engineering Society General Meeting (2007), pp. 1–6Google Scholar
  5. 5.
    S. Jang, Optimal decision on contract size for V2G aggregator regarding frequency regulation, in Optimization of Electrical and Electronic Equipment (OPTIM) (2010), pp. 54–62Google Scholar
  6. 6.
    H. Sekyung, H. Soohee, K. Sezaki, Development of an optimal vehicle-to-grid aggregator for frequency regulation. IEEE Trans. Smart Grid 1(1) (2010)Google Scholar
  7. 7.
    C. Hutson, G. Venayagamoorthy, K. Corzine, Intelligent scheduling of hybrid and electric vehicle storage capacity in a parking lot for profit maximization in grid power transactions, in Energy 2030 Conference (2008), pp. 1–8Google Scholar
  8. 8.
    M. Baran, F. Wu, Optimal sizing of capacitors placed on a radial distribution system. IEEE Trans. Power Deliv. 4(1), 735–743 (1989)Google Scholar
  9. 9.
    R. Gallego, A. Monticelli, R. Romero, Optimal capacitor placement in radial distribution networks. IEEE Trans. Power Syst. 16(4), 630–637 (2001)Google Scholar
  10. 10.
    S. Sundhararajan, A. Pahwa, Optimal selection of capacitors for radial distribution systems using a genetic algorithm. IEEE Trans. Power Syst. 9(3), 1499–1507 (1994)Google Scholar
  11. 11.
    Y.C. Huang, H.T. Yang, C.L. Huang, Solving the capacitor placement problem in a radial distribution system using tabu search approach. IEEE Trans. Power Syst. 11(4), 1868–1873 (1996)Google Scholar
  12. 12.
    C. Wu, H. Mohsenian-Rad, J. Huang, J. Jatskevich, PEV-based combined frequency and voltage regulation for smart grid, in Innovative Smart Grid Technologies (ISGT) (2012), pp. 1–6Google Scholar
  13. 13.
    A. Lazar, N. Semret, The progressive second price auction mechanism for network resource sharing, in 8th International Symposium on Dynamic Games (1998)Google Scholar
  14. 14.
    A.A. Lazar, N. Semret, Design and analysis of the progressive second price auction for network bandwidth sharing, in Telecommunication Systems - Special issue on Network Economics (1999)Google Scholar
  15. 15.
    W. Vickrey, Counterspeculation, auctions, and competitive sealed tenders. J. Financ. 16(1), 8–37 (1961)Google Scholar
  16. 16.
    E.H. Clark, Multipart pricing of public goods. Public Choice 11(1), 19–33 (1971)Google Scholar
  17. 17.
    T. Groves, Incentives in teams. Econometrica 41(4), 617–631 (1973)Google Scholar
  18. 18.
    L. Ausubel, P. Cramton, Demand reduction and inefficiency in multi-unit auctions. Working papers, University of Maryland (2002)Google Scholar
  19. 19.
    G. Federico, D. Rahman, Bidding in an electricity pay-as-bid auction. J. Regul. Econ. 24(2), 175–211 (2003)Google Scholar
  20. 20.
    F. Wen, A. Kumar David, Optimal bidding strategies and modeling of imperfect information among competitive generators. IEEE Trans. Power Syst. 16(1), 15–21 (2001)Google Scholar
  21. 21.
    Rahul Jain, Jean Walrand, An efficient nash-implementation mechanism for network resource allocation. Automatica 46, 1276–1283 (2010)Google Scholar
  22. 22.
    P. Jia, P. Caines, Analysis of decentralized decision processes in competitive markets: quantized single and double-sided auctions, in 49th IEEE Conference on Decision and Control (2010), pp. 237–243Google Scholar
  23. 23.
    P. Jia, P. Caines, Analysis of decentralized quantized auctions on cooperative networks. IEEE Trans. Autom. Control 58, 529–534 (2013)Google Scholar
  24. 24.
    P. Jia, P. Caines, Analysis of quantized double auctions with application to competitive electricity markets. INFOR: Inf. Syst. Oper. Res. 48(4), 239–250 (2010)Google Scholar
  25. 25.
    S. Bashash, S. Moura, J. Forman, H. Fathy, Plug-in hybrid electric vehicle charge pattern optimization for energy cost and battery longevity. J. Power Sources 196(196), 541–549 (2011)CrossRefGoogle Scholar
  26. 26.
    S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004)Google Scholar
  27. 27.
    J. Orr, A. Emanuel, Current harmonics generated by a cluster of electric vehicle battery chargers. IEEE Trans. Power Appar. Syst. 101(3), 691–700 (1982)CrossRefGoogle Scholar
  28. 28.
    Z. Luo, Z. Hu, Y. Song, Z. Xu, H. Lu, Optimal coordination of plug-in electric vehicles in power grids with cost-benefit analysis — part i: Enabling techniques, To appear in IEEE Transactions on Power Systems (2013)Google Scholar
  29. 29.
    Z. Luo, Z. Hu, Y. Song, Z. Xu, H. Lu, Optimal coordination of plug-in electric vehicles in power grids with cost-benefit analysis — part ii: a case study in china, To appear in IEEE Transactions on Power Systems (2013)Google Scholar
  30. 30.
    S. Yang, E.B. Hajek, VCG-Kelly mechanisms for allocation of divisible goods: adapting VCG mechanisms to one-dimensional signals. IEEE J. Sel. Areas Commun. 25(6), 1237–1243 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.School of AutomationBeijing Institute of TechnologyBeijingChina

Personalised recommendations