Suchergebnisse

.

This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of steps it can be composed of and on the minimum step length. Our algorithm relies on dynamic programming and is built on the basis that said curve-fitting task can be tackled as a shortest-path type of problem. Numerical results on synthetic and realistic data sets reveal that our algorithm is able to provide the globally optimal monotone stepwise curve fit for samples with thousands of data points in less than a few hours. Furthermore, the algorithm gives a certificate on the optimality gap of any incumbent solution it generates. From a practical standpoint, this piece of research is motivated by the roll-out of smart grids and the increasing role played by the small flexible consumption of electricity in the large-scale integration of renewable energy sources into current power systems. Within this context, our algorithm constitutes an useful tool to generate bidding curves for a pool of small flexible consumers to partake in wholesale electricity markets. ; This research has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 755705). This work was also supported in part by the Spanish Ministry of Economy, Industry and Competitiveness and the European Regional Development Fund (ERDF) through project ENE2017-83775-P. Martine Labbé has been partially supported by the Fonds de la Recherche Scientifique - FNRS under Grant(s) no PDR T0098.18.

In an attempt to speed up the solution of the unit commitment (UC) problem, both machine-learning and optimization-based methods have been proposed to lighten the full UC formulation by removing as many superfluous line-flow constraints as possible. While the elimination strategies based on machine learning are fast and typically delete more constraints, they may be over-optimistic and result in infeasible UC solutions. For their part, optimization-based methods seek to identify redundant constraints in the full UC formulation by exploring the feasibility region of an LP-relaxation. In doing so, these methods only get rid of line-flow constraints whose removal leaves the feasibility region of the original UC problem unchanged. In this paper, we propose a procedure to substantially increase the line-flow constraints that are filtered out by optimization-based methods without jeopardizing their appealing ability of preserving feasibility. Our approach is based on tightening the LP-relaxation that the optimization-based method uses with a valid inequality related to the objective function of the UC problem and hence, of an economic nature. The result is that the so strengthened optimization-based method identifies not only redundant line-flow constraints but also inactive ones, thus leading to more reduced UC formulations. ; The work of Álvaro Porras was supported in part by the Spanish Ministry of Science, Innovation and Universities through the university teacher training program with Fellowship under Grant FPU19/03053. This work was supported in part by the Spanish Ministry of Science and Innovation under Grant AEI/10.13039/501100011033 through project PID2020-115460GB-I00, in part by the European Research Council (ERC) through the European Union's Horizon 2020 Research and Innovation Programme under Grant 755705, in part by the Junta de Andalucía (JA), and in part by the European Regional Development Fund (FEDER) through the research project under Grant P20_00153.