Abstract
This chapter formulates and solves an optimal resource allocation problem of thermal and hydropower plants with multiple basins and multiple connected reservoirs. The stochastic factors of the problem are here represented by natural hydro inflows. A multivariate scenario tree is in this case obtained taking into account the stochastic inputs and their spatial and temporal dependencies. The hydropower plant efficiency depends on its water head and the reservoir volume depends nonlinearly on the headwater elevation, leading to a large-scale stochastic nonlinear optimization problem, whose formulation and solution are detailed in the case study. An analysis of exhaustive alternatives of computer implementation is also discussed.
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M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming. Theory and Algorithms, 2nd ed. New York, NY: Wiley, 1993.
J. R. Birge and F. Louveaux, Introduction to Stochastic Programming, 1st ed. New York, NY: Springer, 1997.
A. Brooke, D. Kendrick, A. Meeraus, and R. Raman, GAMS: A User’s Guide. Whashington, DC: GAMS Development Corporation, 2008.
R. H. Byrd, J. Nocedal, and R. A. Waltz, KNITRO: An Integrated Package for Nonlinear Optimization, in Large-Scale Nonlinear Optimization, G. di Pillo and M. Roma, Ed., Berlin: Springer, 2006, pp. 35–59.
J. Cabero, A. Baillo, S. Cerisola, M. Ventosa, A. Garcia-Alcalde, F. Peran, and G. Relano, A Medium-Term Integrated Risk Management Model for a Hydrothermal Generation Company, IEEE Transactions on Power Systems, 20: 1379–1388, 2005.
R. S. Dembo, A. Chiarri, J. G. Martin, and L. Paradinas, Managing Hidroelectrica-Espanola Hydroelectric Power-System, Interfaces, 20: 115–135, 1990.
A. L. Diniz, P. P. I. Esteves, and C. A. Sagastizabal, A Mathematical Model for the Efficiency Curves of Hydroelectric Units, Ieee Power Engineering Society General Meeting, 1–10: 200–206, 2007.
A. Drud, CONOPT: A Large-Scale GRG Code, INFORMS Journal on Computing, 6: 207–216, 1994.
J. Jacobs, G. Freeman, J. Grygier, D. Morton, G. Schultz, K. Staschus, and J. Stedinger, Socrates – A System for Scheduling Hydroelectric Generation under Uncertainty, Annals of Operations Research, 59: 99–133, 1995.
J. W. Labadie, Optimal Operation of Multireservoir Systems: State-of-the-Art Review, Journal of Water Resources Planning and Management-Asce, 130: 93–111, 2004.
J. M. Latorre, S. Cerisola, A. Ramos, R. Bellido, and A. Perea, Creation of Hydroelectric System Scheduling by Simulation, in Complex Decision Making: Theory and Practice, H. Qudrat-Ullah, J.M., Spector, P., Davidsen, Ed., New York, NY: Springer, 2007a, pp. 83–96.
J. M. Latorre, S. Cerisola, and A. Ramos, Clustering Algorithms for Scenario Tree Generation: Application to Natural Hydro Inflows, European Journal Of Operational Research, 181: 1339–1353, 2007b.
B. A. Murtagh and M. A. Saunders, MINOS 5.1 User’s Guide, Stanford University Report SOL 83-20R, 1987.
M. V. F. Pereira and L. M. V. G. Pinto, Multistage Stochastic Optimization Applied to Energy Planning, Mathematical Programming, 52: 359–375, 1991.
A. Seifi and K. W. Hipel, Interior-Point Method for Reservoir Operation with Stochastic Inflows, Journal of Water Resources Planning and Management-Asce, 127: 48–57, 2001.
F. Stein-Erik and K. Trine Krogh, Short-Term Hydropower Production Planning by Stochastic Programming, Computers Operations Research, 35: 2656–2671, 2008.
A. Wchter and L. T. Biegler, On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming, Mathematical Programming, 106: 25–57, 2006.
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Ramos, A., Cerisola, S., Latorre, J.M., Bellido, R., Perea, A., Lopez, E. (2011). A Decision Support Model for Weekly Operation of Hydrothermal Systems by Stochastic Nonlinear Optimization. In: Bertocchi, M., Consigli, G., Dempster, M. (eds) Stochastic Optimization Methods in Finance and Energy. International Series in Operations Research & Management Science, vol 163. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9586-5_7
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