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Mathematical Problems in Engineering
Volume 2010, Article ID 390940, 20 pages
Research Article

Stochastic Dynamic Programming Applied to Hydrothermal Power Systems Operation Planning Based on the Convex Hull Algorithm

1Department of Electrical Engineering, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), 22451-900, Rio de Janeiro, Brazil
2Department of Electrical Energy, Federal University of Juiz de Fora (UFJF), 36036-330, Juiz de Fora, Brazil
3Operador Nacional do Sistema Elétrico (ONS), 20091-005, Rio de Janeiro, Brazil

Received 16 October 2009; Revised 19 February 2010; Accepted 10 March 2010

Academic Editor: Joaquim J. Júdice

Copyright © 2010 Bruno H. Dias 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 presents a new approach for the expected cost-to-go functions modeling used in the stochastic dynamic programming (SDP) algorithm. The SDP technique is applied to the long-term operation planning of electrical power systems. Using state space discretization, the Convex Hull algorithm is used for constructing a series of hyperplanes that composes a convex set. These planes represent a piecewise linear approximation for the expected cost-to-go functions. The mean operational costs for using the proposed methodology were compared with those from the deterministic dual dynamic problem in a case study, considering a single inflow scenario. This sensitivity analysis shows the convergence of both methods and is used to determine the minimum discretization level. Additionally, the applicability of the proposed methodology for two hydroplants in a cascade is demonstrated. With proper adaptations, this work can be extended to a complete hydrothermal system.