Medium-Term Operational Planning for Hydrothermal Systems

  • Raphael E. C. Gonçalves
  • Michel Gendreau
  • Erlon Cristian Finardi
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 199)


The planning of operations of hydrothermal systems is, in general, divided into coordinated steps which focus on distinct modeling details of the system for different planning horizons. The medium-term operation planning (MTOP) problem, one of the operation planning steps and the focus of this chapter, aims at defining weekly generation for each power plant with the minimum expected operational cost over a specific planning horizon, with regard especially to the uncertainties related to reservoir inflows. Consequently, it is modeled as a stochastic problem and solving it requires the use of multistage stochastic optimization algorithms. In this sense, the objective of this chapter is to discuss the problem features, its particularities, and its importance in the overall operational planning. The stochastic methods usually used to solve this problem and some applications are also presented.


Scenario Tree Bender Decomposition Stochastic Problem Stochastic Programming Problem Stochastic Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Wood AJ, Wollenberg BF (1996) Power generation, operation, and control, 2nd edn. Wiley, New YorkGoogle Scholar
  2. 2.
    Pereira MVF (1989) Optimal stochastic operations scheduling of large hydroelectric systems. Electr Power Energ Syst 11:161–169CrossRefGoogle Scholar
  3. 3.
    Sjelvgren D et al (1989) Large-scale non-linear programming applied to operations planning. Int J Electr Power Energ Syst 11:213–217CrossRefGoogle Scholar
  4. 4.
    Pereira MVF, Pinto LMVG (1984) Operation planning of large-scale hydroelectrical systems. In: 8th power system computation conference (PSCC), HelsinkiGoogle Scholar
  5. 5.
    Redondo NJ, Conejo AJ (1999) Short-term hydro-thermal coordination by lagrangian relaxation: solution of the dual problem. IEEE Trans Power Syst 14:89–95CrossRefGoogle Scholar
  6. 6.
    Cabero J et al (2005) A medium-term integrated risk management model for a hydrothermal generation company. IEEE Trans Power Syst 20:1379–1388CrossRefGoogle Scholar
  7. 7.
    Morton D (1996) An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling. Ann Oper Res 64:211–235CrossRefGoogle Scholar
  8. 8.
    Escudero LF (2000) WARSYP: a robust modeling approach for water resources system planning under uncertainty. Ann Oper Res 95:313–339CrossRefGoogle Scholar
  9. 9.
    Watchorn CW (1967) Inside hydrothermal coordination. IEEE Trans Power Apparat Syst PAS-86:106–117CrossRefGoogle Scholar
  10. 10.
    Terry LA et al (1986) Coordinating the energy generation of the brazilian national hydrothermal electrical generating system. Interfaces 16:16–38CrossRefGoogle Scholar
  11. 11.
    Sherkat VR et al (1988) Modular and flexible software for medium and short-term hydrothermal scheduling. IEEE Trans Power Syst 3:1390–1396CrossRefGoogle Scholar
  12. 12.
    Enamorado JC et al (2000) Multi-area decentralized optimal hydro-thermal coordination by the Dantzig–Wolfe decomposition method. In: IEEE in Power Engineering Society Summer Meeting, Seattle, WA, vol 4, pp 2027–2032Google Scholar
  13. 13.
    Zambelli M et al (2006) Deterministic versus stochastic models for long term hydrothermal scheduling. In: IEEE in Power Engineering Society General Meeting, Montreal, QC, pp 7Google Scholar
  14. 14.
    Dias BH et al (2010) Stochastic dynamic programming applied to hydrothermal power systems operation planning based on the convex hull algorithm. Math Probl Eng 2010:20CrossRefGoogle Scholar
  15. 15.
    Aouam T, Zuwei Y (2008) Multistage stochastic hydrothermal scheduling. In: IEEE International Conference on Electro/Information Technology, EIT, pp 66–71Google Scholar
  16. 16.
    Bortolossi HJ et al (2002) Optimal hydrothermal scheduling with variable production coefficient. Math Methods Operations Res 55:11–36CrossRefGoogle Scholar
  17. 17.
    Gjelsvik A, Wallace SW (1996) Methods for stochastic medium-term scheduling in hydro-dominated power systems. Report EFI TR A 4438, Electric Power Research InstituteGoogle Scholar
  18. 18.
    Johannesen A, Flataboe N (1989) Scheduling methods in operation planning of a hydro-dominated power production system. Int J Electr Power Energ Syst 11:189–199CrossRefGoogle Scholar
  19. 19.
    Labadie J (2004) Optimal operation of multireservoir systems: state-of-the-art review. J Water Resour Plann Manag 130:93–111CrossRefGoogle Scholar
  20. 20.
    Botnen OJ et al (1992) Modelling of hydropower scheduling in a national/international context. Proceedings Hydropower ’92, A.A. BalkemaGoogle Scholar
  21. 21.
    Belsnes MM et al (2003) Quota modeling in hydrothermal systems. In: IEEE bologna power tech conference proceedings, bologna (italy), vol 3. p 6Google Scholar
  22. 22.
    Gonçalves REC et al (2011) Applying different decomposition schemes using the progressive hedging algorithm to the operation planning problem of a hydrothermal system. Electr Power Syst Res 83:19–27CrossRefGoogle Scholar
  23. 23.
    Santos MLL et al (2009) Practical aspects in solving the medium-term operation planning problem of hydrothermal power systems by using the progressive hedging method. Int J Electr Power Energ Syst 31:546–552CrossRefGoogle Scholar
  24. 24.
    Gonçalves REC et al (2011) Exploring the progressive hedging characteristics in the solution of the medium term operation planning problem. In: 17th power systems computation conference (PSCC), Sweden, 2011Google Scholar
  25. 25.
    Santos MLL et al (2008) Solving the short term operating planning problem of hydrothermal systems by using the progressive hedging method. In: 16th power system computation conference (PSCC), Glasgow, 2011Google Scholar
  26. 26.
    Gonçalves REC et al (2011) Comparing stochastic optimization methods to solve the medium-term operation planning problem. Comput Appl Math 30:289–313CrossRefGoogle Scholar
  27. 27.
    Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer, New YorkGoogle Scholar
  28. 28.
    Greengard C, Ruszczynski AP (2002) Decision making under uncertainty: energy and power. Springer, New YorkCrossRefGoogle Scholar
  29. 29.
    Cunha SHF et al (1997) Modelagem da Produtividade Variável de Usinas Hidrelétricas com base na Construção de uma Função de Produção Energética,” in XII Simposio Brasileiro de Recursos Hidricos, ABRH, pp 391–397Google Scholar
  30. 30.
    Rosa C, Ruszczyinski A (1996) On augmented lagrangian decomposition methods for multistage stochastic programs. Ann Oper Res 64:289–309CrossRefGoogle Scholar
  31. 31.
    Ruszczynski A (1999) Some advances in decomposition methods for stochastic linear programming. Ann Oper Res 85:153–172CrossRefGoogle Scholar
  32. 32.
    Benders JF (1962) Partitioning procedures for solving mixed variables programming problems. Numer Math 4:238–252CrossRefGoogle Scholar
  33. 33.
    Jacobs J et al (1995) SOCRATES: a system for scheduling hydroelectric generation under uncertainty. Ann Oper Res 59:99–133CrossRefGoogle Scholar
  34. 34.
    Anukal Chiralaksanakul BS (2003) Monte carlo methods for multi-stage stochastic programs. Doctorate, Department of Philosophy, University of Texas at Austin, AustinGoogle Scholar
  35. 35.
    Liu H et al (2009) Portfolio management of hydropower producer via stochastic programming. Energ Convers Manag 50:2593–2599CrossRefGoogle Scholar
  36. 36.
    Shapiro A (2011) Analysis of stochastic dual dynamic programming method. Eur J Oper Res 209:63–72CrossRefGoogle Scholar
  37. 37.
    da Costa JP et al (2006) Reduced scenario tree generation for mid-term hydrothermal operation planning. In: International conference on probabilistic methods applied to power systems, PMAPS, Stockholm - Sweden, pp 1–7Google Scholar
  38. 38.
    Ruszczyinski A (1992) Augmented lagrangian decomposition for sparse convex optimization. Ann Oper ResGoogle Scholar
  39. 39.
    Mulvey J, Vladimirou H (1991) Applying the progressive hedging algorithm to stochastic generalized networks. Ann Oper Res 31:399–424CrossRefGoogle Scholar
  40. 40.
    Watson J-P, Woodruff D (2011) Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. Comput Manag Sci 8(4): 355–370CrossRefGoogle Scholar
  41. 41.
    Rockafellar RT, Wets RJB (1991) Scenarios and policy aggregation in optimization under uncertainty. Math Oper Res 16:119–147CrossRefGoogle Scholar
  42. 42.
    Shapiro A, Philpott A (2007) A tutorial on stochastic programming. Technical report. INFORMS Tutorials in Operations Research, Technical report 2007Google Scholar
  43. 43.
    Fourer R, Lopes L (2006) A management system for decompositions in stochastic programming. Ann Oper Res 142:99–118CrossRefGoogle Scholar
  44. 44.
    Medina J et al (1998) A comparison of interior-point codes for medium-term hydro-thermal coordination. IEEE Trans Power Syst 13:836–843CrossRefGoogle Scholar
  45. 45.
    Ruszczyinski A, Shapiro A (2003) HandBooks in operations research and management science. 1st edn. vol 10, Elsevier Science B.V., NetherlandsGoogle Scholar
  46. 46.
    Christoforidis M et al (1996) Long-term/mid-term resource optimization of a hydrodominant power system using interior point method. IEEE Trans Power Syst 11:287–294CrossRefGoogle Scholar
  47. 47.
    Fuentes-Loyola R et al (2000) A performance comparison of primal-dual interior point method vs lagrangian relaxation to solve the medium term hydro-thermal coordination problem. In: IEEE power engineering society summer, Seattle, pp 2255–2260Google Scholar
  48. 48.
    Dupacova J et al (2000) Scenarios for multistage stochastic programs. Ann Oper Res 100:25–53CrossRefGoogle Scholar
  49. 49.
    Garcia-Gonzalez J, Castro GA (2001) Short-term hydro scheduling with cascaded and head-dependent reservoirs based on mixed-integer linear programming. In: IEEE Portugal power tech proceedings, Porto - Portugal, vol 3, p 6Google Scholar
  50. 50.
    Diniz AL, Maceira MEP (2008) A four-dimensional model of hydro generation for the short-term hydrothermal dispatch problem considering head and spillage effects. IEEE Trans Power Syst 23:1298–1308CrossRefGoogle Scholar
  51. 51.
    Finardi EC, da Silva EL (2006) Solving the hydro unit commitment via dual decomposition and sequential quadratic programming. IEEE Trans Power Syst 21:835–844CrossRefGoogle Scholar
  52. 52.
    Breton M et al (2004) Accounting for losses in the optimization of production of hydroplants. IEEE Trans Energ Convers 19:346–351CrossRefGoogle Scholar
  53. 53.
    Ruszczyinski A (1997) Decomposition methods in stochastic programming. Math Program 79:333–353Google Scholar
  54. 54.
    Pennanen T, Kallio M (2006) A splitting method for stochastic programs. Ann Oper Res 142:259–268CrossRefGoogle Scholar
  55. 55.
    Gorenstin BG et al (1991) Stochastic optimization of a hydro-thermal system including network constraints. In: Conference proceedings on power industry computer application conference, Baltimore, MD, pp 127–133Google Scholar
  56. 56.
    Pereira MVF, Pinto LMVG (1985) Stochastic optimization of a multireservoir hydroelectric system: a decomposition approach. Water Resour Res 21:779–792CrossRefGoogle Scholar
  57. 57.
    Philpott AB, de Matos VL (2012) Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion. Eur J Oper Res 218:470–483CrossRefGoogle Scholar
  58. 58.
    Matos VLD, Finardi EC (2012) A computational study of a stochastic optimization model for long term hydrothermal scheduling. Int J Electr Power Energ Syst 43:1443–1452CrossRefGoogle Scholar
  59. 59.
    Al-Agtash S (2001) Hydrothermal scheduling by augmented lagrangian: consideration of transmission constraints and pumped-storage units. IEEE Power Eng Rev 21:58–59CrossRefGoogle Scholar
  60. 60.
    Cristian Finardi E, Reolon Scuzziato M (2013) Hydro unit commitment and loading problem for day-ahead operation planning problem. Int J Electr Power Energ Syst 44:7–16CrossRefGoogle Scholar
  61. 61.
    Diniz AL et al (2007) Assessment of lagrangian relaxation with variable splitting for hydrothermal scheduling. In: IEEE power engineering society general meeting, pp 1–8.Google Scholar
  62. 62.
    Helgason T, Wallace SW (1991) Approximate scenario solutions in the progressive hedging algorithm: a numerical study. Ann. Oper. Res. 31:425–444CrossRefGoogle Scholar
  63. 63.
    LeMaréchal C et al (1996) Bundle methods applied to the unit commitment problem. Syst Model Optim, IFIP – The International Federation for Information Processing, 395–402Google Scholar
  64. 64.
    Berger AJ et al (1994) An extension of the DQA algorithm to convex stochastic programs. SIAM J Optim 4:735–753CrossRefGoogle Scholar
  65. 65.
    Nocedal J, Wright SJ (2006) Numerical optimization, 2nd edn. Springer, New YorkGoogle Scholar
  66. 66.
    Slyke RMV Wets R (1969) L-Shaped linear programs with applications to optimal control and stochastic programming. SIAM J Appl Math 17:638–663CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Raphael E. C. Gonçalves
    • 1
    • 2
  • Michel Gendreau
    • 1
    • 2
  • Erlon Cristian Finardi
    • 3
    • 4
  1. 1.NSERC/Hydro-Québec Industrial Research Chair on the Stochastic Optimization of Electricity Generation CIRRELTUniversité de MontréalMontréalCanada
  2. 2.Department of Mathematics and Industrial EngineeringÉcole Polytechnique de MontréalMontrealCanada
  3. 3.Universidade Federal de Santa Catarina - UFSCFlorianópolisBrazil
  4. 4.Laboratório de Planejamento de Sistemas de Energia Elétrica - LabPlan, EEL, CTC, UFSCFlorianópolisBrazil

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