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A Local Relaxation Approach for the Siting of Electrical Substations

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Abstract

The siting and sizing of electrical substations on a rectangular electrical grid can be formulated as an integer programming problem with a quadratic objective and linear constraints. We propose a novel approach that is based on solving a sequence of local relaxations of the problem for a given number of substations. Two methods are discussed for determining a new location from the solution of the relaxed problem. Each leads to a sequence of strictly improving feasible integer solutions. The number of substations is then modified to seek a further reduction in cost. Lower bounds for the solution are also provided by solving a sequence of mixed-integer linear programs. Results are provided for a variety of uniform and Gaussian load distributions as well as some real examples from an electric utility. The results of gams/dicopt, gams/sbb, gams/baron and cplex applied to these problems are also reported. Our algorithm shows slow growth in computational effort with the number of integer variables.

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Authors and Affiliations

  1. Department of Management Science and Engineering, Stanford University, Stanford, CA, 94305-4026

    Walter Murray

  2. Department of Mechanical and Industrial Engineering, Urbana, IL, 61801

    Uday V. Shanbhag

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  1. Walter Murray
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  2. Uday V. Shanbhag
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Correspondence to Walter Murray.

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Murray, W., Shanbhag, U.V. A Local Relaxation Approach for the Siting of Electrical Substations. Comput Optim Applic 33, 7–49 (2006). https://doi.org/10.1007/s10589-005-5957-4

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  • DOI: https://doi.org/10.1007/s10589-005-5957-4

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