Multi-leader–follower game theory for modelling interaction between virtual power plants and distribution company

Multi-leader–follower game theory for modelling interaction between virtual power plants and distribution company

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Virtual power plant (VPP) is an entity that aggregates generation of distributed generation units. Thus, it is important to design a competitive framework which models the participation of the VPPs in the electricity market along with their trading with distribution company (DisCo). This study proposes a bilevel programming framework using the concept of multi-leader–follower game theory to determine the optimal contract prices of VPPs which compete against each other in the distribution network. The optimal prices are used for setting annual bilateral contracts with VPPs. The leader layer of the proposed bilevel problem includes VPPs, which try to maximise their profits, while the follower problem corresponds to the cost function of the DisCo, which aims to minimise the payments of supplying the forecasted demand. The DisCo optimisation problem is transferred by its Karush–Kuhn–Tucker optimality conditions, turning each VPP problem into an equivalent single-level optimisation problem. Some case studies are defined and implemented to assess the performance of the proposed scheduling model.


    1. 1)
      • 1. Chiradeja, P., Ramakumar, R.: ‘An approach to quantify the technical benefits of distributed generation’, IEEE Trans. Energy Convers., 2004, 19, pp. 764773.
    2. 2)
      • 2. Algarni, A.A.S., Bhattacharya, K.: ‘A generic operations framework for discos in retail electricity markets’, IEEE Trans. Power Syst., 2009, 24, pp. 356367.
    3. 3)
      • 3. Ackermann, T., Andersson, G., Söder, L.: ‘Distributed generation: a definition’, Electr. Power Syst. Res., 2001, 57, (3), pp. 195204.
    4. 4)
      • 4. Pudjianto, D., Ramsay, C., Strbac, G.: ‘Virtual power plant and system integration of distributed energy resources’, IET Renew. Power Gener., 2007, 1, pp. 1016.
    5. 5)
      • 5. Ochoa, L.F., Padilha-Feltrin, A., Harrison, G.P.: ‘Evaluating distributed generation impacts with a multiobjective index’, IEEE Trans. Power Deliv., 2006, 21, pp. 14521458.
    6. 6)
      • 6. Ghavidel, S., Li, L., Aghaei, J., et al: ‘A review on the virtual power plant: components and operation systems’. 2016 IEEE Int. Conf. Power System Technology (POWERCON), Wollongong, NSW, Australia, 28 September - 1 October 2016, pp. 16.
    7. 7)
      • 7. Morais, H., Kadar, P., Cardoso, M., et al: ‘Vpp operating in the isolated grid’. 2008 IEEE Power and Energy Society General Meeting – Conversion and Delivery of Electrical Energy in the 21st Century, Pittsburgh, PA, USA, July 2008, pp. 16.
    8. 8)
      • 8. Mashhour, E., Moghaddas-Tafreshi, S.M.: ‘Bidding strategy of virtual power plant for participating in energy and spinning reserve markets – part i: problem formulation’, IEEE Trans. Power Syst., 2011, 26, pp. 949956.
    9. 9)
      • 9. Shayegan-Rad, A., Badri, A., Zangeneh, A.: ‘Day-ahead scheduling of virtual power plant in joint energy and regulation reserve markets under uncertainties’, Energy, 2017, 121, (Suppl. C), pp. 114125.
    10. 10)
      • 10. Peik-Herfeh, M., Seifi, H., Sheikh-El-Eslami, M.: ‘Decision making of a virtual power plant under uncertainties for bidding in a day-ahead market using point estimate method’, Int. J. Electr. Power Energy Syst., 2013, 44, (1), pp. 8898.
    11. 11)
      • 11. Dempe, S.: ‘Foundations of bilevel programming, vol. 61’ (Kluwer Academic, Dordrecht, The Netherlands, 2002).
    12. 12)
      • 12. Carrion, M., Arroyo, J.M., Conejo, A.J.: ‘A bilevel stochastic programming approach for retailer futures market trading’, IEEE Trans. Power Syst., 2009, 24, pp. 14461456.
    13. 13)
      • 13. Nazari, F., Zangeneh, A., Shayegan-Rad, A.: ‘A bilevel scheduling approach for modeling energy transaction of virtual power plants in distribution networks’, Iranian J. Electr. Electron. Eng., 2017, 13, (1), pp. 19.
    14. 14)
      • 14. Fudenberg, D., Tirole, J.: ‘Game theory’ (MIT Press, Cambridge, MA, USA, 1991, 5th edn.), pp. 145160.
    15. 15)
      • 15. Kulkarni, A.A., Shanbhag, U.V.: ‘A shared-constraint approach to multi-leader multi-follower games’, Set-Valued Variational Anal., 2014, 22, (4), pp. 691720.
    16. 16)
      • 16. Kulkarni, A.A., Shanbhag, U.V.: ‘An existence result for hierarchical stackelberg v/s stackelberg games’, IEEE Trans. Autom. Control, 2015, 60, pp. 33793384.
    17. 17)
      • 17. Mobarakeh, A.S., Rajabi-Ghahnavieh, A., Zahedian, A.: ‘A game theoretic framework for dg optimal contract pricing’. IEEE PES ISGT Europe 2013, Lyngby, Denmark, October 2013, pp. 15.
    18. 18)
      • 18. Leyffer, S., Munson, T.: ‘Solving multi leader common follower games’, Opt. Meth. Softw., 2010, 25, (4), pp. 601623.
    19. 19)
      • 19. Haghighat, H., Seifi, H., Kian, A.R.: ‘Gaming analysis in joint energy and spinning reserve markets’, IEEE Trans. Power Syst., 2007, 22, pp. 20742085.
    20. 20)
      • 20. El-Khattam, W., Bhattacharya, K., Hegazy, Y., et al: ‘Optimal investment planning for distributed generation in a competitive electricity market’, IEEE Trans. Power Syst., 2004, 19, pp. 16741684.
    21. 21)
      • 21. Lopez-Lezama, J.M., Padilha-Feltrin, A., Contreras, J., et al: ‘Optimal contract pricing of distributed generation in distribution networks’, IEEE Trans. Power Syst., 2011, 26, pp. 128136.
    22. 22)
      • 22. Operador del Mercado Ibérico de Energía (OMEL) – Polo Español S.A. [Internet]. Available at
    23. 23)
      • 23. The GAMS Development Corporation Website [Online]. Available at, 2009.

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