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Optimization and Engineering

, Volume 6, Issue 2, pp 163–176 | Cite as

A Stochastic Integer Programming Model for Incorporating Day-Ahead Trading of Electricity into Hydro-Thermal Unit Commitment

  • Matthias P. Nowak
  • Rüdiger SchultzEmail author
  • Markus Westphalen
Article

Abstract

We develop a two-stage stochastic integer programming model for the simultaneous optimization of power production and day-ahead power trading in a hydro-thermal system. The model rests on mixed-integer linear formulations for the unit commitment problem and for the price clearing mechanism at the power exchange. Foreign bids enter as random components into the model. We solve the stochastic integer program by a decomposition method combining Lagrangian relaxation of nonanticipativity with branch-and-bound in the spirit of global optimization. Finally, we report some first computational experiences.

Keywords

stochastic integer programming power optimization 

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References

  1. Amsterdam Power Exchange (APX). http://www.apx.nl/
  2. E. J. Anderson and A. B. Philpott, “Optimal offer construction in electricity markets,” Mathematics of Operations Research vol. 27, pp. 82–100, 2002.CrossRefGoogle Scholar
  3. E. J. Anderson and H. Xu, “Necessary and sufficient conditions for optimal offers in electricity markets,” SIAM Journal on Control and Optimization vol. 41, pp. 1212–1228, 2002.Google Scholar
  4. F. Bolle, “Supply function equilibria and the danger of tacit collusion: The case of spot markets for electricity,” Energy Economics vol. 14, pp. 94–102, 1992.Google Scholar
  5. C. C. Carøe and R. Schultz, “Dual decomposition in stochastic integer programming,” Operations Research Letters vol. 24, pp. 37–45, 1999.Google Scholar
  6. H.-P. Chao and H. G. Huntington, Designing Competitive Electricity Markets, Kluwer, Boston, 1998.Google Scholar
  7. Using the CPLEX Callable Library, CPLEX Optimization, Inc., 1999.Google Scholar
  8. R. Gollmer, M. P. Nowak, W. Römisch, and R. Schultz, “Unit commitment in power generation—A basic model and some extensions,” Annals of Operations Research vol. 96, pp. 167–189, 2000.Google Scholar
  9. R. J. Green and D. M. Newbery, “Competition in the British electricity spot market,” Journal of Political Economy vol. 100, pp. 929–953, 1992.Google Scholar
  10. N. Gröwe-Kuska, K. C. Kiwiel, M. P. Nowak, W. Römisch, and I. Wegner, “Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation,” in C. Greengard and A. Ruszczyński (Eds.), Decision Making under Uncertainty: Energy and Power, IMA volumes in Mathematics and its Applications, vol. 128, Springer-Verlag: New York, 2001, pp. 39–70.Google Scholar
  11. J. B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, Springer-Verlag: Berlin, 1993.Google Scholar
  12. B. F. Hobbs, “Network models of spatial oligopoly with an application to deregulation of electricity generation,” Operations Research vol. 34, pp. 395–409, 1986.Google Scholar
  13. K. C. Kiwiel, “Proximity control in bundle methods for convex nondifferentiable optimization,” Mathematical Programming vol. 46, pp. 105–122, 1990.Google Scholar
  14. K. C. Kiwiel, User’s Guide for NOA 2.0/3.0: A Fortran Package for Convex Nondifferentiable Optimization, Systems Research Institute, Polish Academy of Sciences: Warsaw, 1994.Google Scholar
  15. W. K. Klein Haneveld and M. H. van der Vlerk, “Stochastic integer programming: General models and algorithms,” Annals of Operations Research vol. 85, pp. 39–57, 1999.Google Scholar
  16. P. D. Klemperer and M.A. Meyer, “Supply function equilibria in oligopoly under uncertainty,” Econometrica vol. 57, pp. 1243–1277, 1989.Google Scholar
  17. F. V. Louveaux and R. Schultz, “Stochastic integer programming,” in A. Ruszczyński and A. Shapiro (Eds), Handbooks in Operations Research and Management Science, 10: Stochastic Programming, Elsevier, Amsterdam, 2003, pp. 213–266.Google Scholar
  18. G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization, Wiley, New York, 1988.Google Scholar
  19. M. P. Nowak and W. Römisch, “Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty,” Annals of Operations Research vol. 100, pp. 251–272, 2000.Google Scholar
  20. R. Nürnberg and W. Römisch, “A two-stage planning model for power scheduling in a hydro-thermal system under uncertainty,” Optimization and Engineering vol. 3, pp. 355–378, 2002.Google Scholar
  21. A. Rudkevich, M. Duckworth, and R. Rosen, “Modelling electricity pricing in a deregulated generation industry: The potential for oligopoly pricing in a poolco,” The Energy Journal vol. 19, pp. 19–48, 1998.Google Scholar
  22. R. Schultz, “Stochastic programming with integer variables,” Mathematical Programming vol. 97, pp. 285–309, 2003.Google Scholar
  23. G. B. Sheble and G. N. Fahd, “Unit commitment literature synopsis,” IEEE Transactions on Power Systems vol. 9, pp. 128–135, 1994.Google Scholar
  24. C. Supatgiat, R. Q. Zhang, and J. R. Birge, “Equilibrium values in a competitive power exchange market,” Computational Economics vol. 17, pp. 93–121, 2001.Google Scholar
  25. S. Takriti, J. R. Birge, and E. Long, “A stochastic model for the unit commitment problem,” IEEE Transactions on Power Systems vol. 11, pp. 1497–1508, 1996.Google Scholar
  26. S. Takriti, B. Krasenbrink, and L. S.-Y. Wu, “Incorporating fuel constraints and electricity spot prices into the stochastic unit commitment problem,” Operations Research vol. 48, pp. 268–280, 2000.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Matthias P. Nowak
    • 1
  • Rüdiger Schultz
    • 1
    Email author
  • Markus Westphalen
    • 2
  1. 1.SINTEF Industrial ManagementEconomics and LogisticsTrondheimNorway
  2. 2.Department of MathematicsUniversity Duisburg-EssenDuisburgGermany

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