Unit commitment in power generation – a basic model and some extensions | Annals of Operations Research Skip to main content
Log in

Unit commitment in power generation – a basic model and some extensions

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

For the unit commitment problem in the hydro-thermal power system of VEAG Vereinigte Energiewerke AG Berlin we present a basic model and discuss possible extensions where both primal and dual solution approaches lead to flexible optimization tools. Extensions include staggered fuel prices, reserve policies involving hydro units, nonlinear start-up costs, and uncertain load profiles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J.R. Birge and F. Louveaux, Introduction to Stochastic Programming(Springer, New York, 1997).

    Google Scholar 

  2. C.C. Carøe and R. Schultz, Dual decomposition in stochastic integer programming, Operations Research Letters 24 (1999) 37–45.

    Article  Google Scholar 

  3. C.C. Carøe and R. Schultz, A two-stage stochastic program for unit commitment under uncertainty in a hydro-thermal system, Preprint SC 98–11, Konrad-Zuse-Zentrum für Informationstechnik Berlin (1998). Downloadable as SC 98–11 from http://www.zib.de/bib/pub/pw/index.en. html.

  4. Using the CPLEX Callable Library, CPLEX Optimization, Inc. 1994.

  5. P. Carpentier, G. Cohen, J.-C. Culioli and A. Renaud, Stochastic optimization of unit commitment, a new decomposition framework, IEEE Transactions on Power Systems 11 (1996) 1067–1073.

    Article  Google Scholar 

  6. D. Dentcheva, R. Gollmer, A. Möller, W. Römisch and R. Schultz, Solving the unit commitment problem in power generation by primal and dual methods, in: Progress in Industrial Mathematics at ECMI 96, eds. M. Brøns, M.P. Bendsøe and M.P. Sørensen (Teubner, Stuttgart, 1997) pp. 332–339.

    Google Scholar 

  7. D. Dentcheva and W. Römisch, Optimal power generation under uncertainty via stochastic programming, in: Stochastic Programming Methods and Technical Applications, eds. K. Marti and P. Kall, Lecture Notes in Economics and Mathematical Systems, Vol. 458 (Springer, Berlin, 1998) pp. 22–56.

    Google Scholar 

  8. J. Dupa?cov´a, G. Consigli and S.W. Wallace, Scenarios for multistage stochastic programs, Working Paper, Charles University Prague (1998). Submitted to Annals of Operations Research.

  9. S. Feltenmark and K.C. Kiwiel, Dual applications of proximal bundle methods, including Lagrangian relaxation of nonconvex problems, SIAM Journal on Optimization (to appear).

  10. S. Feltenmark, K.C. Kiwiel and P.O. Lindberg, Solving unit commitment problems in power production planning, in: Operations Research Proceedings 1996, eds. U. Zimmermann et al. (Springer, Berlin, 1997) pp. 236–241.

    Google Scholar 

  11. M. Fischer, Gestaffelte Brennstoffpreise in der Kraftwerkseinsatzoptimierung, Diplomarbeit, Technische Universität Berlin (1997).

    Google Scholar 

  12. R. Gollmer, A. Möller, W. Römisch, R. Schultz, G. Schwarzbach and J. Thomas, Optimale Blockauswahl bei der Kraftwerkseinsatzplanung der VEAG, in: Optimierung in der Energieversorgung II(VDI-Berichte 1352, 1997) pp. 71–85.

  13. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms II(Springer, Berlin, 1993).

    Google Scholar 

  14. 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 (1995) 99–133.

    Article  Google Scholar 

  15. N. Jiménez Redondo and A.J. Conejo, Short-term hydro-thermal coordination by Lagrangian relaxation, Solution of the dual problem, IEEE Transactions on Power Systems 14 (1999) 89–95.

    Article  Google Scholar 

  16. K.C. Kiwiel, Proximity control in bundle methods for convex nondifferentiable minimization, Mathematical Programming 46 (1990) 105–122.

    Article  Google Scholar 

  17. K.C. Kiwiel, User's Guide for NOA 2.0/3.0: A Fortran package for convex nondifferentiable optimization, Polish Academy of Science, System Research Institute, Warsaw (1993/1994).

    Google Scholar 

  18. C. Lemaréchal and A. Renaud, Dual equivalent convex and nonconvex problems, Research Report, INRIA, Rocquencourt (1996).

    Google Scholar 

  19. C. Lemaréchal, C. Sagastizćbal, F. Pellegrino and A. Renaud, Bundle methods applied to the unit commitment problem, in: System modelling and optimization, eds. J. Doležal and J. Fiedler (Chapman & Hall, London, 1996) pp. 395–402.

    Google Scholar 

  20. P.B. Luh, R.N. Tomastik and D. Zhang, An algorithm for solving the dual problem of hydrothermal scheduling, IEEE Transactions on Power Systems 13 (1998) 593–600.

    Article  Google Scholar 

  21. A. Möller and W. Römisch, A dual method for the unit commitment problem, Preprint Nr. 95–1, Humboldt-Universität Berlin, Institut für Mathematik (1995). Downloadable from http:// taylor.mathematik.hu-berlin.de/publ/pre/1995/p-95–1.ps.

    Google Scholar 

  22. M.P. Nowak, A fast descent method for the hydro storage subproblem in power generation, Working Paper WP-96–109, IIASA, Laxenburg (Austria) (1996). Downloadable from http://www. iiasa.ac.at/Publications/Documents/WP-96–109.ps.

    Google Scholar 

  23. M.P. Nowak, Stochastic Lagrangian relaxation applied to power scheduling of a hydro-thermal system under uncertainty, Forthcoming dissertation, Humboldt-Universität Berlin, Institut für Mathematik (1999).

    Google Scholar 

  24. M.P. Nowak and W. Römisch, Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty, Preprint Nr. 98–24, Humboldt-Universität Berlin, Institut für Mathematik (1998). Submitted to Annals of Operations Research. Downloadable from http:// www.mathematik.hu-berlin.de/publ/pre/1998/M-98–24.

    Google Scholar 

  25. M.V.F. Pereira and L.M.V.G. Pinto, Multi-stage stochastic optimization applied to energy planning, Mathematical Programming 52 (1991) 359–375.

    Article  Google Scholar 

  26. G.Ch. Pflug and A. Świetanowski, Optimal scenario tree generation for multiperiod fi-nancial optimization, Technical Report, AURORA TR 1998–22, Universität Wien (1998). Downloadable from ftp://ftp.par.univie.ac.at/projects/aurora/reports/ auroratr1998–22.ps.gz.

  27. W. Römisch and R. Schultz, Decomposition of a multi-stage stochastic program for power dispatch, ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik 76(3) (1996) 29–32.

    Google Scholar 

  28. R. Schultz, On structure and stability in stochastic programs with random technology matrix and complete integer recourse, Mathematical Programming 70 (1995) 73–89.

    Google Scholar 

  29. G.B. Sheble and G.N. Fahd, Unit commitment literature synopsis, IEEE Transactions on Power Systems 9 (1994) 128–135.

    Article  Google Scholar 

  30. S. Takriti, The unit commitment problem, in: Operations Research in Industry, eds. T.A. Ciriani, S. Gliozzi and E.L. Johnson (Macmillan Press, 1999) (to appear).

  31. S. Takriti, J.R. Birge and E. Long, A stochastic model for the unit commitment problem, EEE Transactions on Power Systems 11 (1996) 1497–1508.

    Article  Google Scholar 

  32. S. Takriti, B. Krasenbrink and L.S.-Y. Wu, Incorporating fuel constraints and electricity spot prices into the stochastic unit commitment problem, Operations Research (to appear).

  33. S. Takriti, C. Supatgiat and L.S.-Y. Wu, Coordinating fuel inventory and electric power generation under uncertainty, IBM Research Report RC 21152, Yorktown Heights, New York (1998). Downloadable from http://domino.watson.ibm.com/library/CyberDig.nsf/Papers?SearchView&Query=RC21152.

    Google Scholar 

  34. I. Wegner, Erzeugung von Szenariobäumen für die Kraftwerks-Einsatzoptimierung, Diplomarbeit, Humboldt-Universität Berlin, Institut für Mathematik (1999).

    Google Scholar 

  35. A.J. Wood and B.F. Wollenberg, Power Generation, Operation and Control, 2nd ed. (Wiley, New York, 1996).

    Google Scholar 

  36. F. Zhuang and F.D. Galiana,Towards a more rigorous and practical unit commitment by Lagrangian relaxation, IEEE Transactions on Power Systems 3(1988) 763–773.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gollmer, R., Nowak, M.P., Römisch, W. et al. Unit commitment in power generation – a basic model and some extensions. Annals of Operations Research 96, 167–189 (2000). https://doi.org/10.1023/A:1018947401538

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018947401538

Keywords

Navigation