A Local Relaxation Approach for the Siting of Electrical Substations |
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Authors: | Walter Murray Uday V Shanbhag |
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Institution: | (1) Department of Management Science and Engineering, Stanford University, Stanford, CA, 94305-4026;(2) Department of Mechanical and Industrial Engineering, Urbana, IL, 61801 |
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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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