Power Flow Tracing in Complex Networks

  • Mirko SchäferEmail author
  • Sabrina Hempel
  • Jonas Hörsch
  • Bo Tranberg
  • Stefan Schramm
  • Martin Greiner
Part of the FIAS Interdisciplinary Science Series book series (FIAS)


The increasing share of decentralized renewable power generation represents a challenge to the current and future energy system. Providing a geographical smoothing effect, long-range power transmission plays a key role for the system integration of these fluctuating resources. However, the build-up and operation of the necessary network infrastructure incur costs which have to be allocated to the users of the system. Flow tracing techniques, which attribute the power flow on a transmission line to the geographical location of its generation and consumption, represent a valuable tool set to design fair usage and thus cost allocation schemes for transmission investments. In this article, we introduce a general formulation of the flow tracing method and apply it to a simplified model of a highly renewable European electricity system. We review a statistical usage measure which allows to integrate network usage information for longer time series, and illustrate this measure using an analytical test case.


Power Flow Transmission Capacity Network Usage Renewable Generation Admittance Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Mirko Schäfer gratefully acknowledges support from Stiftung Polytechnische Gesellschaft Frankfurt am Main. Sabrina Hempel and Jonas Hörsch acknowledge support from the German Federal Ministry of Education and Research under grant no. 03SF0472C.


  1. 1.
    European Commission. A Roadmap for moving to a competitive low carbon economy in 2050 (2011)Google Scholar
  2. 2.
    G7. Leader’s Declaration G7 Summit, 7–8 Jun 2015Google Scholar
  3. 3.
    Mark A. Delucchi, Mark Z. Jacobson, Providing all global energy with wind, water, and solar power, part ii: reliability, system and transmission costs, and policies. Energy Policy 39(3), 1170–1190 (2011)CrossRefGoogle Scholar
  4. 4.
    M.Z. Jacobson, M.A. Delucchi, A path to sustainable energy by 2030. Sci. Am. 301, 58–65 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    ENTSO-E. 10-Year Network Development Plan 2014 (2014)Google Scholar
  6. 6.
    R.A. Rodriguez, S. Becker, G.B. Andresen, D. Heide, M. Greiner, Transmission needs across a fully renewable European power system. Renew. Energy 63, 467–476 (2014)CrossRefGoogle Scholar
  7. 7.
    S. Becker, R.A. Rodriguez, G.B. Andresen, S. Schramm, M. Greiner, Transmission grid extensions during the build-up of a fully renewable pan-European electricity supply. Energy 64, 404–418 (2014)CrossRefGoogle Scholar
  8. 8.
    CONSENTEC and Frontier Economics. Study on the further issues relating to the inter-TSO compensation mechanism (2006)Google Scholar
  9. 9.
    M. Aguado, R. Bourgeois, J.Y. Bourmaud, J. Van Casteren, M. A. Ceratto, M. Jäkel, W. Van den Reek, M. Rohleder, P.H. Schavemaker, S. Scolari, O. Weis, J. Wolpert, Flow-based market coupling in the Central Western European region—on the eve of implementation (2012)Google Scholar
  10. 10.
    Tom Brown, Transmission network loading in Europe with high shares of renewables. Renew. Power Gener. 9, 57–65 (2015)CrossRefGoogle Scholar
  11. 11.
    B. Tranberg, A. Thomsen, R. Rodriguez, G. Andresen, M. Schäfer, M. Greiner, Power flow tracing in a simplified highly renewable European electricity network. New J. Phys. 17, 105002 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    J. Bialek, Tracing the flow of electricity. IEE Proc.- Gener. Transmi. Distrib. 143 (1996)Google Scholar
  13. 13.
    A.J. Wood, B.F. Wollenberg, G.B. Sheblé, in Power Generation, Operation, and Control, 3rd edn. (Wiley, 2014)Google Scholar
  14. 14.
    P. Van Mieghem, in Graph Spectra for Complex Networks. (Cambridge, 2011)Google Scholar
  15. 15.
    J. Hörsch, M. Schäfer, S. Becker, S. Schramm, M. Greiner, Applications of a generalized flow tracing formalism. IEEE Trans. Power Syst. (2016)Google Scholar
  16. 16.
    G.B. Andresen, A.A. Søndergaard, M. Greiner, Validation of Danish wind time series from a new global renewable energy atlas for energy system analysis. Energy 93, 1074–1088 (2015)CrossRefGoogle Scholar
  17. 17.
    R.A. Rodriguez, M. Dahl, S. Becker, M. Greiner, Localized vs. synchronized exports across a highly renewable pan-European transmission network. Energy, Sust. Soc. 5 (2015)Google Scholar
  18. 18.
    EC. Commission Regulation (EU) No 838/2010 of 23 Sept 2010 on laying down guidelines relating to the inter-transmission system operator compensation mechanism and a common regulatory approach to transmission charging (2010)Google Scholar
  19. 19.
    Delberis A. Lima, Antonio Padilha-Feltrin, Javier Contreras, An overview on network cost allocation methods. Electr. Power Syst. Res. 79, 750–758 (2009)CrossRefGoogle Scholar
  20. 20.
    D. Heide, M. Greiner, L. von Bremen, C. Hoffmann, Reduced storage and balancing needs in a fully renewable European power system with excess wind and solar power generation. Renew. Energy 36, 2515–2523 (2011)CrossRefGoogle Scholar
  21. 21.
    D. Heide, L. von Bremen, M. Greiner, C. Hoffmann, M. Speckmann, S. Bofinger, Seasonal optimal mix of wind and solar power in a future, highly renewable Europe. Renew. Energy 35, 2483–2489 (2010)CrossRefGoogle Scholar
  22. 22.
    H. Rudnick, R. Palma, J.E. Fernandez, Marginal pricing and supplement cost allocation in transmission open access. IEEE Trans. Power Syst. 10(2), 1125–1142 (1995)CrossRefGoogle Scholar
  23. 23.
    S. Hempel, Using virtual injection patterns to allocate power flows in renewable electricity networks. Master’s thesis, Goethe Universität Frankfurt (2016)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Mirko Schäfer
    • 1
    Email author
  • Sabrina Hempel
    • 1
  • Jonas Hörsch
    • 1
  • Bo Tranberg
    • 2
  • Stefan Schramm
    • 1
  • Martin Greiner
    • 2
  1. 1.Frankfurt Institute for Advanced StudiesFrankfurt am MainGermany
  2. 2.Department of EngineeringAarhus UniversityAarhusDenmark

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