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Center for Nonlinear Studies |
As the transfer from non-renewable to renewable energy resources has become increasingly widespread, certain assumptions regarding power grid efficiency have changed. Power generators have become cheaper to build and install, but may be situated large distances from demand, as for instance in the case of wind power. We consider the problem of optimal transmission line placement and conductance assignment, given the combined costs of resistive power loss and line construction. We adopt the DC model of Johnson and Chertkov, with a single generator and multiple loads, all at known locations. Transmission line construction costs are made up of a fixed cost for each line present, as well as variable costs proportional to each line’s conductance, leading to a nonconvex optimization problem. We have developed a novel two-part discrete and continuous hybrid algorithm for this problem. The discrete method, genetic algorithms, is used to sample over the space of grid topologies. As the topologies are sampled, they are sent to a continuous optimization procedure that uses Newton’s method to determines the optimal line conductance values for a related convex optimization problem. We have studied, implemented and tested this hybrid algorithm, obtaining results compatible with those of Johnson and Chertkov. We will discuss possible modifications to the algorithm that may improve upon these results.
Host: Misha Chertkov, chertkov@lanl.gov, 665-8119