Skip to main content
Earth, Planets and Space
Download PDF

Properties of matrices included in the calculation of geomagnetically induced currents (GICs) in power systems and introduction of a test model for GIC computation algorithms

Earth, Planets and Space volume 61, pages 263–272 (2009)Cite this article

Abstract

“Geomagnetically induced currents” (GICs) in ground-based networks are a manifestation of space weather and a potential source of problems to the systems. Exact matrix equations, which are summarized in this paper, for calculating GICs in a power system were formulated in the 1980s. These equations are reformulated here to show how they lead to a direct relation between GICs and the horizontal geoelectric field. Properties of the matrices, which enable the derivation of physical features of the flow of the GICs in a power system, are considered in detail. A specific aim of this study was to show that the ratio of the GICs obtained at a station under two different geophysical situations is independent of the total earthing resistance at that particular station. The behavior of the elements of the transfer matrix between geovoltages and GICs confirms the earlier result that it is sufficient to make a calculation of a small grid around the site if the GIC values at one site are of interest. Using the developed technique, I have calculated the GICs of the old configuration of the Finnish 400-kV grid.

References

  • Bolduc, L., GIC observations and studies in the Hydro-QuĂ©bec power system, J. Atmos. Sol.-Terr. Phys., 64(16), 1793–1802, 2002.

    Article  Google Scholar 

  • Boteler, D. H. and R. J. Pirjola, Modelling Geomagnetically Induced Currents produced by Realistic and Uniform Electric Fields, IEEE Trans. Power Delivery, 13(4), 1303–1308, 1998.

    Article  Google Scholar 

  • Boteler, D. H. and R. Pirjola, GIC Modelling, Technical Report for Real-Time GIC Simulator, ESA SpaceWeather Pilot Project, ESTEC Contract Number 16986/03/NL/LvH, European Space Agency (ESA), 27 pp., 2004.

    Google Scholar 

  • Boteler, D. H., R. J. Pirjola, and H. Nevanlinna, The effects of geomagnetic disturbances on electrical systems at the Earth’s surface, Adv. Space Res., 22(1), 17–27, 1998.

    Article  Google Scholar 

  • Elovaara, J., P. Lindblad, A. Viljanen, T. Mäkinen, R. Pirjola, S. Larsson, and B. KielĂ©n, Geomagnetically induced currents in the Nordic power system and their effects on equipment, control, protection and operation, CIGRÉ General Session 1992, (CIGRÉ = Inter-national Conference on Large High Voltage Electric Systems), Paris, France, August 31–September 5, 1992, Paper No. 36-301, 10 pp., 1992.

    Google Scholar 

  • Kappenman, J. G., Geomagnetic storms and their impact on power systems, IEEE Power Eng. Rev., May 1996, 5–8, 1996.

    Google Scholar 

  • Kappenman, J. G., An Overview of the Increasing Vulnerability Trends of Modern Electric Power Grid Infrastructures and the potential consequences of Extreme Space Weather Environments, in Effects of Space Weather on Technology Infrastructure, edited by I. A. Daglis, 257–286, NATO Science Series, Kluwer Academic Publishers, II. Mathematics, Physics and Chemistry, 176, Chapter 14: Space Weather and the Vulnerability of Electric Power Grids, 2004.

    Google Scholar 

  • Kappenman, J. G. and V. D. Albertson, Bracing for the geomagnetic storms, IEEE Spectrum, March 1990, 27–33, 1990.

    Google Scholar 

  • Lanzerotti, L. J., D. J. Thomson, and C. G. Maclennan, Engineering issues in space weather, in Modern Radio Science 1999, edited by M. A. Stuchly, 25–50, International Union of Radio Science (URSI), Oxford University Press, 1999.

    Google Scholar 

  • Lehtinen, M. and R. Pirjola, Currents produced in earthed conductor networks by geomagnetically-induced electric fields, Ann. Geophys., 3(4), 479–484, 1985.

    Google Scholar 

  • Mäkinen, T., Geomagnetically induced currents in the Finnish power transmission system, Finnish Meteorological Institute, Geophysical Publications, No. 32, Helsinki, Finland, 101 pp., 1993.

    Google Scholar 

  • Molinski, T. S., Why utilities respect geomagnetically induced currents, J. Atmos. Sol.-Terr. Phys., 64(16), 1765–1778, 2002.

    Article  Google Scholar 

  • Pirjola, R., Induction in power transmission lines during geomagnetic disturbances, Space Sci. Rev., 35(2), 185–193, 1983.

    Article  Google Scholar 

  • Pirjola, R., Effects of space weather on high-latitude ground systems, Adv. Space Res., 36(12), doi:10.1016/j.asr.2003.04.074, 2231–2240, 2005a.

    Article  Google Scholar 

  • Pirjola, R., Averages of geomagnetically induced currents (GIC) in the Finnish 400 kV electric power transmission system and the effect of neutral point reactors on GIC, J. Atmos. Sol.-Terr. Phys., 67(7), 701–708, 2005b.

    Article  Google Scholar 

  • Pirjola, R., Calculation of geomagnetically induced currents (GIC) in a high-voltage electric power transmission system and estimation of effects of overhead shield wires on GIC modelling, J. Atmos. Sol.-Terr. Phys., 69(12), 1305–1311, 2007.

    Article  Google Scholar 

  • Pirjola, R., Study of effects of changes of earthing resistances on geomagnetically induced currents in an electric power transmission system, Radio Sci., 43, RS1004, doi:10.1029/2007RS003704, 13 pp., 2008a.

    Article  Google Scholar 

  • Pirjola, R., Effects of interactions between stations on the calculation of geomagnetically induced currents in an electric power transmission system, Earth Planets Space, 60, 743–751, 2008b.

    Article  Google Scholar 

  • Pirjola, R. and M. Lehtinen, Currents produced in the Finnish 400 kV power transmission grid and in the Finnish natural gas pipeline by geomagnetically-induced electric fields, Ann. Geophys., 3(4), 485–491, 1985.

    Google Scholar 

  • Pulkkinen, A., S. Lindahl, A. Viljanen, and R. Pirjola, Geomagnetic storm of 29-31 October 2003: Geomagnetically induced currents and their relation to problems in the Swedish high-voltage power transmission system, Space Weather, 3, S08C03, doi: 10.1029/2004SW000123, 19 pp., 2005.

    Article  Google Scholar 

  • Watermann, J., The magnetic environment—GIC and other ground effects, in Space Weather, Research Towards Applications in Europe, edited by J. Lilensten, Springer, Chapter 5.0, 269–275, 2007.

    Chapter  Google Scholar 

  • Wik, M., A. Viljanen, R. Pirjola, A. Pulkkinen, P. Wintoft, and H. Lundstedt, Calculation of geomagnetically induced currents in the 400 kV power grid in southern Sweden, Space Weather, 6, S07005, doi:10.1029/2007SW000343, 11 pp., 2008.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Finnish Meteorological Institute, P.O. Box 503, 00101, Helsinki, Finland

    Risto Pirjola

Authors
  1. Risto Pirjola
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Risto Pirjola.

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

Pirjola, R. Properties of matrices included in the calculation of geomagnetically induced currents (GICs) in power systems and introduction of a test model for GIC computation algorithms. Earth Planet Sp 61, 263–272 (2009). https://doi.org/10.1186/BF03352906

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1186/BF03352906

Key words