Sampling strategies and stopping criteria for stochastic dual dynamic programming: A case study in long-term hydrothermal scheduling

Tito Homem-De-Mello, Vitor L. De Matos, Erlon C. Finardi

Research output: Contribution to journalArticlepeer-review

86 Scopus citations

Abstract

The long-term hydrothermal scheduling is one of the most important problems to be solved in the power systems area. This problem aims to obtain an optimal policy, under water (energy) resources uncertainty, for hydro and thermal plants over a multi-annual planning horizon. It is natural to model the problem as a multistage stochastic program, a class of models for which algorithms have been developed. The original stochastic process is represented by a finite scenario tree and, because of the large number of stages, a sampling-based method such as the Stochastic Dual Dynamic Programming (SDDP) algorithm is required. The purpose of this paper is two-fold. Firstly, we study the application of two alternative sampling strategies to the standard Monte Carlo-namely, Latin hypercube sampling and randomized quasi-Monte Carlo-for the generation of scenario trees, as well as for the sampling of scenarios that is part of the SDDP algorithm. Secondly, we discuss the formulation of stopping criteria for the optimization algorithm in terms of statistical hypothesis tests, which allows us to propose an alternative criterion that is more robust than that originally proposed for the SDDP. We test these ideas on a problem associated with the whole Brazilian power system, with a three-year planning horizon.

Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalEnergy Systems
Volume2
Issue number1
DOIs
StatePublished - Mar 2011
Externally publishedYes

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