Skip to main content
Log in

On computational complexity of the electric power flow optimization problem in market environment

Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

Under consideration is the electric power flow optimization problem for an electric power system which typically arises in calculation of electrical power auctions in the “day-ahead” and balancing markets. It was established that the problem of finding a feasible flow in the balancing market is NP-hard in the strong sense even in case of one generator. The problem of finding an optimal flow in the day-ahead market is proved to be NP-hard even with one generator and without controlled cuts.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price includes VAT (Canada)

Instant access to the full article PDF.

Institutional subscriptions

References

  1. G. I. Atabekov, Theoretical Foundations of Electrical Engineering. Linear Circuits (Lan’, St. Petersburg, 2009) [in Russian].

    Google Scholar 

  2. V. M. Gornshtein, D. S. Miroshnichenko, and A. V. Ponomarev, Methods for Optimization of Power System States (Energiya, Moscow, 1981) [in Russian].

    Google Scholar 

  3. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NPCompleteness (Freeman, San Francisco, 1979; Mir,Moscow, 1982).

    MATH  Google Scholar 

  4. M. R. Davidson, Yu. V. Dogadushkina, E.M. Kreines, N.M. Novikova, Yu. A. Udal’tsov, and L. V. Shiryaeva, “Mathematical Model of the Competitive Wholesale Power Market in Russia,” Izv. Ross. Akad. Nauk Teor. Sist. Upravl. No. 3, 72–83 (2004) [J. Comput. Syst. Sci. Intern. 43 (3), 394–405 (2004)].

    MATH  Google Scholar 

  5. M. R. Davidson, Yu. V. Dogadushkina, E. M. Kreines, N. M. Novikova, A. V. Seleznev, Yu. A. Udal’tsov, and L. V. Shiryaeva, “Mathematical Model of Power System Management in Conditions of a Competitive Wholesale Electric Power (Capacity) Market in Russia,” Izv. Ross. Akad. Nauk Teor. Sist. Upravl. No. 2, 84–94 (2009) [J. Comput. Syst. Sci. Intern. 48 (2), 243–253 (2009)].

    MATH  Google Scholar 

  6. M. C. Caramanis, R. E. Bohn, and F. C. Schweppe, “Optimal Spot Pricing: Practice and Theory,” IEEE Trans. Power Appar. Syst. 101 (9), 3234–3245 (1982).

    Article  Google Scholar 

  7. W. W. Hogan, “Contract Networks for Electric Power Transmission,” J. Regul. Econ. 4 (3), 211–242 (1992).

    Article  Google Scholar 

  8. R. Palma-Benhke, A. Philpott, A. Jofré, and M. Cortés-Carmona, “Modelling Network Constrained Economic Dispatch Problems,” Optim. Eng. 14 (3), 417–430 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  9. M. River, I. J. Pérez-Arriaga, and G. Luengo, “JUANAC: A Model for Computation of Spot Prices in Interconnected Power Systems,” in Proceedings of 10th Power Systems Computations. Conference, Graz, Austria, August 19–24, 1990 (Butterworths, London, 1990), pp. 254–261.

    Google Scholar 

  10. F. C. Schweppe, M. C. Caramanis, R. D. Tabors, and R. E. Bohn, Spot Pricing in Electricity (Kluwer Acad. Publ., Norwell,MA, 1988).

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Eremeev.

Additional information

Original Russian Text © A.V. Eremeev, 2017, published in Diskretnyi Analiz i Issledovanie Operatsii, 2017, Vol. 24, No. 4, pp. 47–59.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eremeev, A.V. On computational complexity of the electric power flow optimization problem in market environment. J. Appl. Ind. Math. 11, 500–505 (2017). https://doi.org/10.1134/S1990478917040068

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478917040068

Keywords

Navigation