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Optimization of Transmission Systems for Chain-Type Markets

  • Alexander VasinEmail author
  • Nikita Tsyganov
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)

Abstract

We consider a market for a homogeneous good with a chain-type transmission network. Every node corresponds to a local market with a perfect competition characterized by supply and demand functions. The initial transmission capacity, the cost of the capacity expansion and the unit transmission cost are given for every transmission line. The cost of the capacity expansion includes fixed and variable components. We examine the social welfare optimization problem for such a market. The welfare corresponds to the difference between the total consumption utility and the costs of production, transportation, and expansion of the transmission lines. Due to fixed costs of lines expansion, the problem is in general NP-hard with respect to the number of the nodes. We generalize the concept of supermodularity of the welfare function on the set of expanded lines and propose an algorithm for the solution of the problem. Results of computer simulation confirm the statistical efficiency of the algorithm.

Keywords

Mixed optimization problem Social welfare Transmission network 

References

  1. 1.
    Vasin, A.A., Grigoryeva, O.M., Tsyganov, N.I.: Optimization of an energy market transportation system. Doklady Math. 96(1), 411–414 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Guisewite, G.M., Pardalos, P.M.: Minimum concave-cost network flow problems: applications, complexity, and algorithms. Ann. Oper. Res. 25(1), 75–99 (1990)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Gasnikov, A.V.: A note on effective computability of competitive balances in transportation economic models. Math. Model. 27(12), 121–136 (2015)MathSciNetGoogle Scholar
  4. 4.
    Vasin, A.A., Dolmatova, M.: Optimization of transmission capacities for multinodal markets. Procedia Comput. Sci. 91, 238–244 (2016)CrossRefGoogle Scholar
  5. 5.
    Stoft, S.: Power System Economics: Designing Markets for Electricity. IEEE/Wiley, New York (2002)CrossRefGoogle Scholar
  6. 6.
    Magnus, Y.R., Katyshev, P.K., Peresetsky, A.A.: Econometrics. Beginner’s Course. Tutorial. Delo, Moscow (2004)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia

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