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Transmission system repair and restoration

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Abstract

This paper studies the use of mathematical programming for the repair and restoration of a transmission system after a significant disruption (e.g., a natural disaster). Such blackouts may last several days and have significant impact on human and economic welfare. The transmission system repair and restoration problem (TSRRP) consists in dispatching crews to repair damaged electrical components in order to minimize the size of the blackout. The TSRRP can be modeled as a large-scale mixed nonlinear, nonconvex program, including both routing components and the nonlinear steady-state power flow equations. To tackle its daunting computational complexity, this paper proposes a 2-stage approach, decoupling the restoration and repair aspects. The first step is a restoration ordering problem, a mixed nonlinear, nonconvex program which is approximated by a mixed integer program. The approximation does not use the traditional DC power flow approximation which is plagued by convergence issues and inoperable dispatches; rather, it uses the recent LPAC approximation that captures reactive power and voltage magnitudes. The second stage is a pickup and repair routing problem which is solved using a constraint-programming model, large neighborhood search, and a randomized adaptive decomposition. Experimental results on benchmarks based on the US electrical infrastructures and state-of-the-art damage scenarios indicate that the 2-stage approach provides significant improvements over the “best practice” in the field.

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Notes

  1. The algorithms presented in this paper were deployed through our collaboration with the Los Alamos National Laboratory and activated during hurricanes Irene and Sandy to help federal agencies in the United States.

  2. Note that the combination of delaying an activation and enforcing that a line remains activated provide a practical and acceptable way to address Braess paradox.

  3. We use maximum values for the last three measures because the summation and the mean are not particularly meaningful, since the E-DC-ROP algorithm fails to converge to an AC solution on numerous occasions.

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Acknowledgments

We would like to thank the reviewers for many interesting comments and suggestions that improve the paper significantly. NICTA is funded by the Australian Government through the Department of Commu- nications and the Australian Research Council through the ICT Centre of Excellence Program.

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  1. National ICT Australia (NICTA), Australian National University, Canberra, Australia

    P. Van Hentenryck & C. Coffrin

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  1. P. Van Hentenryck
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  2. C. Coffrin
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Correspondence to P. Van Hentenryck.

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Van Hentenryck, P., Coffrin, C. Transmission system repair and restoration. Math. Program. 151, 347–373 (2015). https://doi.org/10.1007/s10107-015-0887-0

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