Load Flow Estimation in a Transmission Network

  • Alexander KrylatovEmail author
  • Victor Zakharov
  • Tero Tuovinen
Part of the Springer Tracts on Transportation and Traffic book series (STTT, volume 15)


This chapter includes an investigation on a power smart grid with multiple suppliers and consumers. The first section is devoted to the corresponding model description. The power load flow estimation is presented in a form equivalent to a link-flow traffic assignment problem. The second section concentrates on the competition of consumers, while the third section concentrates on the cooperation of suppliers. From mathematical perspectives, both defined models of economic interaction imply bi-level optimization problems. Thus efficient computational algorithms are required. The last section is devoted to pricing mechanisms for transmission networks with multiple suppliers and consumers. Possible techniques for the arising complex problem of transmission cost sharing are proposed.


  1. 1.
    Duffin R (1947) Nonlinear networks. IIa. Bull Am Math Soc 53, 963–971MathSciNetCrossRefGoogle Scholar
  2. 2.
    Patriksson M (2015) The traffic assignment problem: models and methods. Dover Publications Inc, MineolaGoogle Scholar
  3. 3.
    Popov I, Krylatov A, Zakharov V, Ivanov D (2017) Competitive energy consumption under transmission constraints in a multi-supplier power grid system. Int J Syst Sci 48(5):994–1001MathSciNetCrossRefGoogle Scholar
  4. 4.
    Schweppe FC, Caramanis MC, Tabors RD, Bohn RE (1988) Spot pricing of electricity. Kluwer Academic Publishers, NorwellCrossRefGoogle Scholar
  5. 5.
    Hogan WW (1992) Contract networks for electric power transmission. J Regul Econ 4:211–242CrossRefGoogle Scholar
  6. 6.
    O’Neill RP, Helman U, Hobbs BF, Stewart WR, Rothkopf MH (2002) A joint energy and transmission rights auction: proposal and properties. IEEE Trans Power Syst 17(4):1058–1067CrossRefGoogle Scholar
  7. 7.
    Bertsekas DP (1999) Nonlinear programming, 2nd edn. Athena Scientific, Belmont, MassachusettszbMATHGoogle Scholar
  8. 8.
    Rosen JB (1965) Existence and uniqueness of equilibrium points for concave \(n\)-person games. Econometrica: J Econ Soc 520–534MathSciNetCrossRefGoogle Scholar
  9. 9.
    Roth AE (1988) The Shapley value: essays in honor of Lloyd S. Cambridge University Press, ShapleyCrossRefGoogle Scholar
  10. 10.
    Popov I, Krylatov A, Zakharov V (2016) Integrated smart energy system based on production-oriented consumption. IFIP Adv Inf Commun Technol 480:265–273CrossRefGoogle Scholar
  11. 11.
    Veit A, Xu Y, Zheng R, Chakraborty N, Sycara KP (2013) Multiagent coordination for energy consumption scheduling in consumer cooperatives. In: 27th AAAI conference on artificial intelligence, pp 1362–1368Google Scholar
  12. 12.
    Mohsenian-Rad A-H, Wong VW, Jatskevich J, Schober R, Leon-Garcia A (2010) Autonomous demand-side management based on game-theoretic energy consumption scheduling for the future smart grid. IEEE Trans Smart Grid 1(3):320–331CrossRefGoogle Scholar
  13. 13.
    Popov IV, Krylatov AYu, Lukina AA (2017) Pricing mechanisms for day-ahead demand management in multi-generator power grid. In: 2016 International conference on recent advances and innovations in engineering (ICRAIE)Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Transport ProblemsRussian Academy of SciencesSaint PetersburgRussia
  2. 2.Faculty of Applied Mathematics and Control ProcessesSaint Petersburg State UniversitySaint PetersburgRussia
  3. 3.Faculty of Information TechnologyUniversity of JyväskyläJyväskyläFinland

Personalised recommendations