Skip to main content
SpringerLink
Log in

A mixed integer programming approach for optimal power grid intentional islanding

  • Original Paper
  • Published:
Energy Systems Aims and scope Submit manuscript

Abstract

A power grid island is a self-sufficient subnetwork in a large-scale power system. In weakly connected islands, limited inter-island power flows are allowed. Intentional islanding of a power grid is helpful for the analysis of distributed generation systems connected to a power grid, and valuable for power system reliability of extreme emergency states. In this paper, we use graph partitioning methods to form islands in a power grid and formulate these problems as mixed integer programs. Our models are based the optimal power flow model to minimize the load shedding cost. With these mathematical programming models, optimal formation of islands can be obtained and the different approaches can be compared. Through experiment on IEEE-30-Bus system, computational results are analyzed and compared to provide insight for power grid intentional islanding.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Nkwetta, D.N., Smyth, M., Thong, V.V., Driesen, J., Belmans, R.: Electricity supply, irregularities, and the prospect for solar energy and energy sustainability in Sub-Saharan Africa. J. Renew. Sustain. Energy 2, 023102 (2010)

    Article  Google Scholar 

  2. IEEE/CIGRE joint task force on stability terms and definitions: definition and classification of power system stability. IEEE Trans. Power Syst. 19(2), 1387–1401 (2004)

    Google Scholar 

  3. Rebennack, S., Pardalos, P.M., Pereira, M.V.F., Iliadis, N. (eds.): Handbook of Power Systems (2 volumes). Springer, Berlin (2010)

    Google Scholar 

  4. Zeineldin, H.H., Bhattacharya, K., El-Saadany, E.F., Salama, M.M.A.: Impact of intentional islanding of distributed generation on electricity market prices. IEE Proc., Gener. Transm. Distrib. 153(2), 147–154 (2006)

    Article  Google Scholar 

  5. Ropp, M., Bower, W.: Evaluation of islanding detection methods for photovoltaic utility interactive power systems. International Energy Agency Implementing Agreement on Photovoltaic Power Systems, Tech. rep. IEA PVPS T5–09 (2002)

  6. IEEE Std 1547-2003. IEEE standard for interconnecting distributed resources with electric power systems (2003)

  7. Liu, Y., Liu, Y.: Aspects on power system islanding for preventing widespread blackout. In: Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control (ICNSC ’06), pp. 1090–1095 (2006)

    Google Scholar 

  8. Tiptipakorn, S.: A spectral bisection partitioning method for electric power network applications. Ph.D. dissertation. Department of Electrical and Computer Engineering, University of Wisconsin (2001)

  9. Bi, T., Ni, Y., Shen, C.M., Wu, F.F.: Efficient multiway graph partitioning method for fault section estimation in large-scale power networks. IEE Proc., Gener. Transm. Distrib. 149(3), 289–294 (2002)

    Article  Google Scholar 

  10. Sen, A., Ghosh, P., Vittal, V., Yang, B.: A new min-cut problem with application to electric power network partitioning. Eur. Trans. Electr. Power 19(6), 778–797 (2009)

    Article  Google Scholar 

  11. Li, J., Liu, C.C.: Power system reconfiguration based on multilevel graph partitioning. In: Proceedings of 2009 IEEE Bucharest Power Tech Conference, Bucharest, Romania (2009)

    Google Scholar 

  12. Wang, X., Vittal, V.: System islanding using minimal cutsets with minimum net flow. In: Proceeding of the 2004 IEEE PES Power System Conference and Exposition, October, New York, USA (2004)

    Google Scholar 

  13. You, H., Vittal, V., Yang, Z.: Self-healing in power systems: an approach using islanding and rate of frequency decline based load shedding. IEEE Trans. Power Syst. 18(1), 174–181 (2003)

    Article  Google Scholar 

  14. Yusof, S.B., Rogers, G.J., Alden, R.T.H.: Slow coherency based network partitioning including load buses. IEEE Trans. Power Syst. 8(3), 1375–1382 (1993)

    Article  Google Scholar 

  15. You, H., Vittal, V., Wang, X.: Slow coherency based islanding. IEEE Trans. Power Syst. 19(1), 483–491 (2004)

    Article  Google Scholar 

  16. Yang, B., Vittal, V., Heydt, G.T.: Slow-coherency-based controlled islanding—a demonstration of the approach on the August 14, 2003 blackout scenario. IEEE Trans. Power Syst. 21(4), 1840–1847 (2006)

    Article  Google Scholar 

  17. Senroy, N., Heydt, G.T., Vittal, V.: Decision tree assisted controlled islanding. IEEE Trans. Power Syst. 21(4), 1790–1797 (2006)

    Article  Google Scholar 

  18. Vittal, V., Heydt, G.T.: The problem of initiating controlled islanding of a large interconnected power system solved as a Pareto optimization. In: Proceedings of the 2009 IEEE PES Power System Conference and Exposition, Seattle, WA, USA (2009)

    Google Scholar 

  19. Peiavi, A., Ildarabadi, R.: A fast algorithm for intentional islanding of power systems using the multilevel Kernel k-means approach. J. Appl. Sci. 9(12), 2247–2255 (2009)

    Article  Google Scholar 

  20. Du, P., Nelson, J.K.: Two-step solution to optimal load shedding in a micro-grid. In: IEEE/PES Power Systems Conference and Exposition (2009)

  21. Fan, N., Pardalos, P.M.: Linear and quadratic programming approaches for the general graph partitioning problem. J. Glob. Optim. 48(1), 57–71 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. IEEE reliability test data. Online available at http://www.ee.washington.edu/research/pstca/

  23. Wood, A.J., Wollenberg, B.F.: Power Generation, Operation and Control, 2nd edn. Wiley, New York (1996)

    Google Scholar 

  24. Salmeron, J., Wood, K., Baldick, R.: Analysis of electric grid security under terrorist threat. IEEE Trans. Power Syst. 19(2), 905–912 (2004)

    Article  Google Scholar 

  25. Dilkina, B., Gomes, C.P.: Solving connected subgraph problems in wildlife conservation. In: CPAIOR-10: 7th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, Bologna, Italy (2010)

    Google Scholar 

  26. Fan, N., Pan, F.: Locating phasor measurements and detecting cutset angles in power systems. In: IEEE PES Innovative Smart Grid Technologies (ISGT 2011) Conference, Anaheim, CA, USA (2011)

    Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Defense Threat Reduction Agency through the grant BRCALL08-A-2-0030. N. Fan is currently with Sandia National Laboratories, which is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Author information

Authors and Affiliations

  1. D-6 Risk Analysis and Decision Support Systems, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Neng Fan

  2. Discrete Math & Complex Systems, Sandia National Laboratories, Albuquerque, NM, 87185, USA

    Neng Fan

  3. D-6 Risk Analysis and Decision Support Systems, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    David Izraelevitz & Feng Pan

  4. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611, USA

    Panos M. Pardalos

  5. Laboratory of Algorithms and Technologies for Networks Analysis (LATNA), Higher School of economics, National Research University, 20 Myasnitskaya st., Moscow, 101000, Russia

    Panos M. Pardalos

  6. Center for Energy, Environmental, and Economic Systems Analysis, Argonne National Laboratory, Argonne, IL, 60439, USA

    Jianhui Wang

Authors
  1. Neng Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Izraelevitz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Feng Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Panos M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jianhui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Neng Fan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fan, N., Izraelevitz, D., Pan, F. et al. A mixed integer programming approach for optimal power grid intentional islanding. Energy Syst 3, 77–93 (2012). https://doi.org/10.1007/s12667-011-0046-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12667-011-0046-5

Keywords

Search

Navigation