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Mathematical Problems in Engineering
Volume 2012, Article ID 856178, 18 pages
Research Article

Solving the Short-Term Scheduling Problem of Hydrothermal Systems via Lagrangian Relaxation and Augmented Lagrangian

1Departamento de Eletrotécnica, Instituto Federal de Santa Catarina, 88020-300 Florianópolis, Brazil
2LabPlan, Departamento de Engenharia Elétrica, Universidade Federal de Santa Catarina, 88040-970 Florianópolis, Brazil

Received 8 April 2011; Revised 4 July 2011; Accepted 26 September 2011

Academic Editor: Alexei Mailybaev

Copyright © 2012 Rafael N. Rodrigues et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper addresses the short-term scheduling problem of hydrothermal power systems, which results in a large-scale mixed-integer nonlinear programming problem. The objective consists in minimizing the operation cost over a two-day horizon with a one-hour time resolution. To solve this difficult problem, a Lagrangian Relaxation (LR) based on variable splitting is designed where the resulting dual problem is solved by a Bundle method. Given that the LR usually fails to find a feasible solution, we use an inexact Augmented Lagrangian method to improve the quality of the solution supplied by the LR. We assess our approach by using a real-life hydrothermal configuration extracted from the Brazilian power system, proving the conceptual and practical feasibility of the proposed algorithm. In summary, the main contributions of this paper are (i) a detailed and compatible modelling for this problem is presented; (ii) in order to solve efficiently the entire problem, a suitable decomposition strategy is presented. As a result of these contributions, the proposed model is able to find practical solutions with moderate computational burden, which is absolutely necessary in the modern power industry.