An Optimization Model for Operations of Large scale Hydro Power Plants



Itaipú;, Hydraulic Head;, Operating Curves;, Electric Power Generation, Mixed Integer Linear Programming


Globally, there is an increase in the proportion of renewable sources for electricity generation. Among renewable sources, hydropower is the most widespread. For this reason, the improvements of their applications have been the focus of researches. Hydroelectric power plants have numerous aspects which might represent several economic advantages, if they are operated efficiently. Mathematical optimization models are interesting tools that help in the decision-making processes. In this context, this paper introduces a new Mixed Integer Lineal Programming model that determines the most convenient combination of units to operate a large-scale hydro power plant. Several aspects of reality are taken into account, which are sometimes not considered, such as the variation of the hydraulic head and the performance of other elements besides the turbines, as floodgates. To prove the effectiveness of the new model, the Itaipú Power Plant is selected as a case study. It has an installed power capacity of 14,000 MW and holds the world record in terms of annual generation with 103 million MWh. Three possible scenarios are evaluated in order to analyze the behavior of this plant in normal and extreme situations. The results indicate that the model effectively reduces computational times, and that power generation is influenced by market price variations and reservoir limitations.


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Author Biography

Gonzalo Exequiel Alvarez, CONICET

Gonzalo Exequiel Alvarez recibió el título de Ingeniero Electromecánico de la Universidad Tecnológica Nacional – Facultad Regional Paraná, Argentina, en 2011. Además recibió en título de Doctorado en Ingeniería, Mención Industrial en la Universidad Tecnológica Nacional – Facultad Regional Santa Fe, en 2019. Actualmente forma parte del Consejo Nacional de Investigaciones Científicos y Técnicas (CONICET), y su lugar de trabajo es el Instituto de Desarrollo y Diseño INGAR. Sus áreas de especialización están relacionadas con la optimización de Sistemas Interconectados de energía eléctrica y de Procesos Industriales.


International Energy Agency, “Key World Energy Statistics 2018,” 2018.

E. M. Rana Adib, Hannah E. Murdock, Fabiani Appavou, Adam Brown, , Anna Leidreiter , Christine Lins , Hannah E. Murdock , Evan Musolino, Ksenia Petrichenko, Timothy C. Farrell, Thomas Thorsch Krader, , Janet L. Sawin , Kristin Seyboth, Jonathan Skeen, , Freyr S, “Renewables 2016: Global Status Report,” 2016.

International Hydropower Association, “2019 Hydropower Status Report,” 2019.

M. Caballero, S. Lozano, and B. Ortega, “Efecto invernadero, calentamiento global y climático,” Rev. UNAM, p. 11, 2007.

B. K. Sovacool, “The intermittency of wind, solar, and renewable electricity generators: Technical barrier or rhetorical excuse?,” Util. Policy, vol. 17, no. 3–4, pp. 288–296, 2009.

S. Xia, K. W. Chan, X. Luo, S. Bu, Z. Ding, and B. Zhou, “Optimal sizing of energy storage system and its cost-benefit analysis for power grid planning with intermittent wind generation,” Renew. Energy, vol. 122, pp. 472–486, 2018.

M. Baumann, M. Weil, J. F. Peters, N. Chibeles-Martins, and A. B. Moniz, “A review of multi-criteria decision making approaches for evaluating energy storage systems for grid applications,” Renewable and Sustainable Energy Reviews. pp. 516–534, 2019.

J. A. Momoh, Electric Power System Applications of Optimization, Second Edition. 2017.

S. M. Naeem Nawaz and S. Alvi, “Energy security for socio-economic and environmental sustainability in Pakistan,” Heliyon, vol. 4, no. 10, 2018.

Chao-An Li, A. J. Svoboda, Chung-Li Tseng, R. B. Johnson, and E. Hsu, “Hydro unit commitment in hydro-thermal optimization,” IEEE Trans. Power Syst., vol. 12, no. 2, pp. 764–769, May 1997.

G. W. Chang et al., “ExperiencesWith Mixed Integer Linear Programming Based Approaches on Short-Term Hydro Scheduling,” IEEE Trans. Power Syst., vol. 16, no. 4, pp. 743–749, 2001.

E. C. Finardi, R. D. Lobato, V. L. de Matos, C. Sagastizábal, and A. Tomasgard, “Stochastic hydro-thermal unit commitment via multi-level scenario trees and bundle regularization,” Optim. Eng., 2019.

R. Taktak and C. D’Ambrosio, “An overview on mathematical programming approaches for the deterministic unit commitment problem in hydro valleys,” Energy Syst., vol. 8, no. 1, pp. 57–79, 2017.

E. Finardi, E. Silva, and C. Sagastizábal, “Solving the unit commitment problem of hydropower plants via Lagrangian relaxation and sequential quadratic programming,” Comput. Appl. Math., vol. 24, no. 3, pp. 317–341, 2005.

C. a. Floudas and X. Lin, “Mixed integer linear programming inprocess scheduling: Modeling, algorithms, and applications,” Ann. Oper. Res., vol. 139, no. 1, pp. 131–162, 2005.

G. Alvarez, M. Marcovecchio, and P. Aguirre, “Hydrothermal Unit Commitment with Deterministic Optimization : Generation and Transmission Including Pumped Storage Units,” Electron. J. Informatics Oper. Res. SADIO - Spec. Issue Dedic. to JAIIO 2017, vol. 17, no. 1, pp. 92–115, 2018.

C. Cheng, J. Wang, and X. Wu, “Hydro Unit Commitment with a Head-Sensitive Reservoir and Multiple Vibration Zones Using MILP,” IEEE Trans. Power Syst., vol. 31, no. 6, pp. 4842–4852, 2016.

C. Cheng, C. Su, P. Wang, J. Shen, J. Lu, and X. Wu, “An MILP-based model for short-term peak shaving operation of pumped-storage hydropower plants serving multiple power grids,” Energy, vol. 163, pp. 722–733, 2018.

Sala de Prensa ITAIPU, “ITAIPU BINACIONAL. La mayor hidroeléctrica del mundo en producción de energía.” [Online]. Available: [Accessed: 30-Aug-2019].

L. M. Cardenas and C. J. Franco, “Structure and Current State of the Wholesale Electricity Markets,” IEEE Lat. Am. Trans., vol. 15, no. 4, pp. 669–674, 2017.

V. Hinojosa, O. Ticuna, and G. Gutierrez, “Improving the Mathematical Formulation of the Unit Commitment with Transmission System Constraints,” IEEE Lat. Am. Trans., vol. 14, no. 2, pp. 773–781, 2016.

G. Alvarez, M. Marcovecchio, and P. Aguirre, “Security-Constrained Unit Commitment Problem including thermal and pumped storage units: An MILP formulation by the application of linear approximations techniques,” Electr. Power Syst. Res., vol. 154, pp. 67–74, 2018.

A. Arce, T. Ohishi, and S. Soares, “Optimal dispatch of generating units of the Itaipú hydroelectric plant,” IEEE Trans. Power Syst., vol. 17, no. 1, pp. 154–158, 2002.

J. M. P. Filipe, “Optimization strategies for pump-hydro storage and wind farm coordination including wind power uncertainty,” 2014.

E. Lehtonen, “Production Planning of a Pumped-storage Hydropower Plant,” MS-E2108 Independent Research Projects in Systems Analysis. p. 23, 2015.

E. A. B. Guillén, “Estimación de la potencia eléctrica teórica disponible en Río Copinula, Jujutla, Ahuachapán,” ING-NOVACIÓN, vol. 4, pp. 33–50, 2012.

C. Mataix Plana, Hydraulic Turbomachines: Hydraulic Turbines, Pumps, Fans. Universidad Pontificia Comillas, 2009.

C. T. Cheng, X. Cheng, J. J. Shen, and X. Y. Wu, “Short-term peak shaving operation for multiple power grids with pumped storage power plants,” Int. J. Electr. Power Energy Syst., vol. 67, pp. 570–581, 2015.

C. Liu, M. Shahidehpour, and J. Wang, “Application of augmented Lagrangian relaxation to coordinated scheduling of interdependent hydrothermal power and natural gas systems,” IET Gener. Transm. Distrib., vol. 4, no. July, pp. 1314–1325, 2010.

IBM Corp. and IBM, “V12. 1: User’s Manual for CPLEX,” Int. Bus. Mach. Corp., vol. 12, no. 1, p. 481, 2009.


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