Nonconvex and nonsmooth economic dispatch
(2022)
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- Abstract
- Large gas power plants are—and will be in the years to come—a major element of power system operations. On one hand, for the flexibility they offer, which is most valuable for the massive integration of renewable energy sources in the energy mix and the associated uncertainty linked to the production of such sources. On the other hand, they can serve as a replacement for nuclear power plants, following the policy of some European countries like Germany and Belgium. These large gas power plants often obey the valve point effect. This physical effect is due to the increase of throttling losses when operating a unit off a valve point, that is, just after opening one of the several fuel admission valves. We show how the consideration of this physical effect makes the dispatch a nonconvex and nonsmooth optimization problem and propose algorithms that aim at efficiently finding a solution as close as possible to the global optimum, along with some guarantees. In the first part of the thesis, we present a three-step algorithm. The first step solves a relaxation of the problem to obtain an infeasible solution that we expect to be close to the feasible set, along with a lower bound to the global optimum. Then, the second step projects this infeasible solution onto the feasible set. Finally, the last step amounts to locally improving the feasible solution that is obtained in the second step via a Riemannian subgradient descent scheme. In the second part of the thesis, we further analyze the second step. The problem is posed abstractly as the projection of a given point onto the intersection of a quadratic hypersurface—or quadric—and a box. We show how to compute the exact projection onto a central non-cylindrical quadric and use splitting methods for the projection onto the full set.
- Affiliations
UCLouvain SST/ICTM/INMA - Pôle en ingénierie mathématique
Citations
Van Hoorebeeck, L. (2022). Nonconvex and nonsmooth economic dispatch. https://hdl.handle.net/2078.5/103377