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Optimal Scenario Tree Reduction for Stochastic Streamflows in Power Generation Planning Problems

W.L. Oliveira (wlo***at***cepel.br)
C. Sagastizábal (sagastiz***at***cepel.br)
D.D.J. Penna (debora***at***cepel.br)
M.E.P. Mceira (elvira***at***cepel.br)
J.M. Damazio (damazio***at***cepel.br)

Abstract: The mid-term operation planning of hydro-thermal power systems needs a large number of synthetic sequences to represent accurately stochastic streamflows. These sequences are generated by a periodic autoregressive model. If the number of synthetic sequences is too big, the optimization planning problem may be too difficult to solve. To select a small set of sequences representing well enough the stochastic process, this work employs two variants of the Scenario Optimal Reduction technique. The first variant applies such technique at the last stage of a tree defined a priori for the whole planning horizon while the second variant combines a stage-wise reduction, preserving the periodic autoregressive structure, with re-sampling. Both approaches are assessed numerically on hydrological sequences generated for real configurations of the Brazilian power system.

Keywords: Scenario Reduction, Stochastic Programming, Mid-Term Operation Planning of Hydro-Thermal Systems.

Category 1: Stochastic Programming

Citation: G.E.P. Box; G.M. Jenkins, Time Series Analysis, Forecasting and Control, Holden-Day, 1994, San Francisco, Third Edition. T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to Algorithms. 2nd Edition. MIT Press and McGraw-Hill, 2001, Section 35.3, The set-covering problem, pp.1033-1038. J. Dupacová; N. Gröwe-Kuska; W. Römisch, Scenario reduction in stochastic programming: An approach using probability metrics, Mathematical Programming, 2003, Ser. A 95, 493-51. N. Gröwe-Kuska; H. Heitsch; W. Römisch, Scenario reduction and scenario tree construction for power management problems, IEEE Bologna Power Tech Proceedings, 2003, (A. Borghetti, C.A. Nucci, M. Paolone eds.), IEEE, pp. 2-4. D.N. Gujarati, Basic Econometrics, McGraw-Hill, 2000, 3th ed. H. Heitsch, W. Römisch, Scenarios Reduction Algorithms in Stochastic Programming, Computational optimization an Applications, 2003, 187-206. H. Heitsch, W. Römisch, C. Strugarek, Stability of Multistage Stochastic Programs, SIAM J.OPTIM, 2006, 551-525. H. Heitsch, W. Römisch, Scenario Tree for Multistage Stochastic Programs, Comput. Manag. Science 6 (2009), 117--133. M.E.P. Maceira; C.V. Bezerra, Stochastic Streamflow model for Hydroelectric Systems In: Proceedings of 5th International Conference on Probabilistic Methods Applied to Power Systems, 1997, Vancouver, Canada, Sep., pp. 305-310. M.E.P. Maceira; L.A. Terry; J.M. Damazio; F.S. Costa; A.C.G. Melo, Chain of Models for Setting the Energy Dispatch and Spot Price in the Brazilian System, Power System Computation Conference - PSCC'02, 2002, Sevilla, Spain, June 24-28. F.J. Massey, The Kolmogorov-Smirnov Test for Goodness of Fit, Journal of the American Statistical Association, 46 (March 1956), pp 68-77. S. Seigel, Nonparametric statistics for the behavioral sciences, New York. McGraw-Hill Book Company, 1956.

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Entry Submitted: 11/21/2008
Entry Accepted: 11/22/2008
Entry Last Modified: 10/20/2009

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