Skip to main content
SpringerLink
Log in

Economic analysis of the N−k power grid contingency selection and evaluation by graph algorithms and interdiction methods

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

Abstract

Contingency analysis is important for providing information about the vulnerability of power grids. Many methods have been purposed to use topological structures of power grids for analyzing contingency states. Considering failures of buses and lines, we present and compare several graph methods for selecting contingencies in this paper. A new method, called critical node detection, is introduced for selecting contingencies consisting of failures on buses. Besides these methods, we include an interdiction model which provides the worst case contingency selection. Our measurement for contingency evaluation is to maximize the social benefit, or to minimize the generating and load shedding cost. Comparing with other measurements for contingency selection, our model is based on economic analysis and is reasonable for evaluating the selected contingency state. Additionally, a contingency consisting of both buses and lines is also studied.

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

Similar content being viewed by others

Abbreviations

I::

set of buses, including substations, generators and load consumers

Let \(\mathbf{1}^{g}_{i}\) for i∈I be the indicator such that \(\mathbf {1}^{g}_{i}=1\) if i is a generator, and \(\mathbf{1}^{g}_{i}=0\) otherwise

(i,j)∈L::

power lines, i,j∈I

N=(I,L)::

an undirected network representing a power grid where I is the set of buses/nodes and L is the set of power lines/edges

D i ::

load at bus i

\(\bar{F}_{ij}\)::

transmission capacity for line (i,j)∈L

\(\bar{G}_{i}\)::

generation capacity at bus i∈I

b ij ::

susceptance of line (i,j); b ij is computed from the resistance and the reactance of line (i,j)∈L

h i ::

generation cost at bus i∈I

r i ::

penalty cost for load-shedding at i∈I

k::

the number of components (buses or lines) to be failed

g i ::

power generation at node i∈I

f ij ::

power flow on line (i,j)∈L

s i ::

load shed at node i∈I

θ i ::

phase angle at node i∈I

δ i ::

δ i =1 if the bus i is selected as one of k components for failures; δ i =0 otherwise

σ ij ::

σ ij =1 if the line (i,j) is selected as one of k components for failures; σ ij =0 otherwise

References

  1. Albert, R., Albert, I., Nakarado, G.L.: Structural vulnerability of the North American power grid. Phys. Rev. E 69, 025103(R) (2004)

    Article  Google Scholar 

  2. Arulselvan, A., Commander, C.W., Elefteriadou, L., Pardalos, P.M.: Detecting critical nodes in sparse graphs. Comput. Oper. Res. 36(7), 2193–2200 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bienstock, D., Verma, A.: The N−k problem in power grids: new models, formulations and numerical experiments. SIAM J. Optim. 20(5), 2352–2380 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Brande, U.: A faster algorithm for betweenness centrality. J. Math. Sociol. 25, 163–177 (2001)

    Article  Google Scholar 

  5. Carreras, B.A., Lynch, V.E., Dobso, I., Newman, D.E.: Critical points and transitions in an electric power transmission model for cascading failure blackouts. Chaos 12(4), 985–994 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, Q., McCalley, J.D.: Identifying high risk N−k contingencies for online security assessment. IEEE Trans. Power Syst. 20(2), 823–834 (2005)

    Article  Google Scholar 

  7. Chen, Y., Jin, S., Chavarria-Miranda, D., Huang, Z.: Application of Cray XMT for power grid contingency selection. In: Proceedings of Cray User Group 2009, Atlanta, GA, May 2009

    Google Scholar 

  8. Donde, V., Lopez, V., Lesieutre, B., Pinar, A., Chao, Y., Meza, J.: Severe multiple contingency screening in electric power systems. IEEE Trans. Power Syst. 23(2), 406–417 (2008)

    Article  Google Scholar 

  9. Freeman, L.C.: A set of measures of centrality based on betweenness. Sociometry 40, 35–41 (1977)

    Article  Google Scholar 

  10. Hedman, K.W., Ferris, M.C., O’Neill, R.P., Fisher, E.B., Oren, S.S.: Co-optimization of generation unit commitment and transmission switching with N−1 reliability. IEEE Trans. Power Syst. 24(2), 1052–1063 (2010)

    Article  Google Scholar 

  11. Hines, P., Cotilla-Sanchez, E., Blumsack, S.: Do topological models provide good information about electricity infrastructure vulnerability? Chaos 20, 033122 (2010)

    Article  Google Scholar 

  12. IEEE reliability test data [online]. Available at http://www.ee.washington.edu/research/pstca/

  13. Li, F., Chegu, A.: High order contingency selection using particle swarm optimization and Tabu search. In: Proceedings of 15th International Conference on Intelligent System Applications to Power Systems, 2009, ISAP ’09 (2009)

    Google Scholar 

  14. Mori, H., Goto, Y.: A tabu search based approach to (N−k) static contingency selection in power systems. In: Proceedings of 2001 IEEE International Conference on Systems, Man, and Cybernetics, vol. 3, pp. 1954–1959 (2001)

    Google Scholar 

  15. O’Neill, R.P., Hedman, K.W., Krall, E.A., Papavasiliou, A., Oren, S.S.: Economic analysis of the ISOs multi-period N−1 reliable unit commitment and transmission switching problem using duality concepts. Energy Syst. 1(2), 165–195 (2010)

    Article  Google Scholar 

  16. Pinar, A., Meza, J., Donde, V., Lesieutre, B.: Optimization strategies for the vulnerability analysis of the electric power grid. SIAM J. Optim. 20(4), 1786–1810 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Salmerón, 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 

  18. Salmerón, J., Wood, K., Baldick, R.: Worst-case interdiction analysis of large-scale electric power grids. IEEE Trans. Power Syst. 24(1), 96–104 (2009)

    Article  Google Scholar 

  19. Wang, J.-W., Rong, L.-L.: Cascade-based attack vulnerability on the US power grid. Saf. Sci. 47, 1332–1336 (2009)

    Article  Google Scholar 

  20. Wu, L., Shahidehpour, M., Li, T.: Cost of reliability analysis based on stochastic unit commitment. IEEE Trans. Power Syst. 23(3), 1364–1374 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Decision Applications Division, Los Alamos National Laboratory, Los Alamos, NM, USA

    Neng Fan & Feng Pan

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

    Neng Fan, Hongsheng Xu & Panos M. Pardalos

Authors
  1. Neng Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongsheng Xu
    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

Corresponding author

Correspondence to Neng Fan.

Additional information

This work was supported in part by the Defense Threat Reduction Agency through the grant BRCALL08-A-2-0030.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fan, N., Xu, H., Pan, F. et al. Economic analysis of the N−k power grid contingency selection and evaluation by graph algorithms and interdiction methods. Energy Syst 2, 313–324 (2011). https://doi.org/10.1007/s12667-011-0038-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12667-011-0038-5

Keywords

Search

Navigation