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Scenario Reduction In The Stochastic Hydropower Planning Operation

Congress: 2015
Author(s): Frederico Vilhena, Mario Barros
POLI - USP1

Keyword(s): Sub-theme 10: Management of water resources,
Abstract

ABSTRACT

Introduction

The optimization of water uses plays a key role in the water resources engineering. In countries like Brazil where water demands are increasing exponentially this is a very important issue due to water demand for electrical generation. Planning the operation of a large hydrothermal system is a complex problem that involves a large number of random variables and parameters. Among them are the inflows to the Brazilian National Interconnected System (SIN - Sistema Interligado Nacional in Portuguese) composed of more than 150 hydropower plants, which are responsible for most of the Brazilian electrical power generation. An approach to forecasting mean monthly flows consists of adopting stochastic models, a possibility to consider the random influences. The series of synthetic mean monthly flows generated by stochastic models can be connected through scenario trees whose assumption, that, in this context, represents the universe of possibilities of the occurrence of streamflows. However, the dimension of the stochastic optimization process of hydropower generation grows exponentially when trees are used with many scenarios, making it necessary to employ specific techniques that will reduce the dimensionality of the problem. One way of handling with these problems consists of using scenario reduction techniques.

Thus, the purpose of this paper is to apply a scenario reduction technique on the hydropower generation of an individualized power plant to the stochastic optimization process, aiming to analyze the validity and stability of this process and its effect on the results of the stochastic optimization of hydropower generation.

Methods/Materials

The hydropower analysis was done using the algorithm developed by Zambon (2008) for the HIDROTERM Decision Support System (DSS). This DSS can optimize the planning operation of the Brazilian SIN considering the inflows stochasticity. The stochastic methodology consists of constructing "fork"shaped trees with up to 1000 equiprobable scenarios, using an autoregressive stochastic model PAR(p). The scenario reduction was done by SCENRED model developed for the GAMS package by Heitsh et Romish (2001).

The Três Marias hydropower plant, on the São Francisco River in the state of Minas Gerais, Brazil, was chosen as a case study.

For this, a historical series of monthly natural flows on this site was used, and it covers the period from January 1931 to December 2012. The data were provided by the SIN National Operator (ONS -- Operador Nacional do Sistema Elétrico in Portuguese).

Based on this historical series, an auto-regressive stochastic model PAR(3) was adjusted to generate synthetic flow series. The model was adjusted using SAMS (Stochastic Analysis Modeling and Simulation) software, developed by the Colorado State University and the US Bureau of Reclamation (SAMS, 2003). With this stochastic model, 1000 synthetic series of mean monthly flows were generated, each one corresponding to a possible scenario of occurrence of the scenario tree. The scenario reduction tool aimed to reduce the number of initial scenarios is such way that the main statistical information of the initial tree can be maintained.The tool called SCENRED was chosen because it consists of a collection of scenario reduction tools that determines optimal scenario sub-trees according to the cardinality or required precision, using probabilistic metrics, such as the Fourtet-Mourier metric, to determine the optima scenario reduction. The stochastic optimization was based on the formulation contained in the SSD HIDROTERM, adjusted to the specific conditions of SCENRED.

The analyses based on the stochastic optimization algorithm had two main objectives: - Analyze the stochastic optimization taking into account different scenario trees and validation of the stochastic optimization model; - Analyze the stochastic optimization considered different reduced trees of scenarios.

Results and Discussion

The Três Marias hydropower plant has a well-defined hydrological regime, with rainy the season between November and March. The historical series proved to be stationary and due to this was possible to adjust a stochastic model for scenario generation.

In terms of planning the operation for a hydropower system, a key set of decision variables is the turbine flow for the first month of the planning horizon. The impact of the scenarios was analyzed considering this variable.

The first analysis dealt with different scenario trees, without applying scenario reduction tools. It indicated that the more scenarios are contained in the tree, the smaller thevariability and the greater the solution stability.

The second analysis always began with a tree with 1000 initial scenarios to which SCENRED was applied, aiming at different reduced trees. The results highlighted the exponential increase in the computer time required to solve the stochastic optimization when increasing the number of reduced tree scenarios, as well as the greater stability of the solution when considering a high number of scenarios, respectively.

Conclusion

The results indicate that the larger the scenario tree, the more precise and stable tend to be the results. On the other hand, the more scenarios are involved, the greater the dimensionality of the problem and, consequently, the processing time required. In this context, the SCENRED reduction tool enabled significant reductions in scenarios tree, without, however, causing significant reductions in the information contained in the initial tree. The analyses also indicate that, beginning with an initial tree with 1000 scenarios and reducing it to about 50 scenarios, a point of equilibrium is reached between the computational effort involved and the quality of the solution.

1. Heitsch, H., Romisch, W. Scenario reduction algorithms in stochastic programming. Preprint 01-8, Institutf¨urMathematik, Humboldt-Universit¨atzu Berlin, 2001.

2. SAMS, Stochastic Analisys Modeling and Simulation,, 2013.

3. Zambon, R.C. Planejamento da operação de sistemas hidrotérmicos de grande porte, 2008.

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