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, Volume 49, Issue 3, pp 193–200 | Cite as

Some applications of mathematical programming techniques in optimal power dispatch

  • J. Guddat
  • W. Römisch
  • R. Schultz
Article

Abstract

Some models for the economic dispatch of electric power are introduced and treated by mathematical programming techniques. In particular, our presentation includes (i) a short-term model for the optimal dispatch of thermal units, which is solved by a specific path following method, (ii) a daily model for a generation system consisting of thermal units, pumped storage plants and an energy contract, which can be solved by standard convex quadratic programming algorithms, and (iii) two stochastic programming models for the optimal daily dispatch, which depend on the (unknown) probability distribution of the electric power demand. One of the latter models can be solved efficiently by combining nonparametric estimation procedures and convex programming methods.

AMS Subject Classifications

90C15 90C25 

Key words

Nonlinear programming stochastic programming power dispatch 

Einige Anwendungen der mathematischen Optimierung bei der optimalen Lastverteilung

Zusammenfassung

In der Arbeit werden einige Modelle zur optimalen Lastverteilung von Elektroenergie diskutiert und mit Hilfe von Optimierungsmethoden behandelt. Insbesondere gehen wir ein auf (i) ein Modell der Momentan-Optimierung der Lastverteilung von Wärmerkraftwerden, das mit einer speziellen parametrischen Optimierungsmethode gelöst wird, (ii) ein Tagesmodell für ein Erzeugersystem bestehend aus Wärmekraftwerken, Pumpspeicherwerken und einem Energievertrag, welches mit Standardmethoden der quadratischen konvexen Optimierung behandelt wird, und (iii) zwei stochastische Optimierungsmodelle für die Optimierung im Tagesbereich, welche von der (unbekannten) Wahrscheinlichkeitsverteilung des Elektroenergiebedarfs abhängen. Eines dieser Modelle kann durch die Kombination nichtparametrischer Schätzmethoden mit Verfahren der konvexen Optimierung effizient numerisch behandelt werden.

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References

  1. [1]
    Bauer, W., Gfrerer, H., Lindner, E., Schwarz, A., Wacker, H.: Optimization of the Gosau hydroenergy powerplant system. Mathematical Engineering in Industry1, 169–190 (1987).Google Scholar
  2. [2]
    van den Bosch, P. P. J.: Optimal static dispatch with linear, quadratic and nonlinear functions of the fuel costs. IEEE Transactions on Power Apparatus and SystemsPAS-104, 3402–3408 (1985).Google Scholar
  3. [3]
    van den Bosch, P. P. J., Lootsma, F. A.: Scheduling of power generation via large-scale nonlinear optimization. Journal of Optimization Theory and Applications55, 313–326 (1987).Google Scholar
  4. [4]
    Bunn, D. W., Paschentis, S. N.: Development of a stochastic model for the economic dispatch of electric power. European Journal of Operational Research27, 179–191 (1986).Google Scholar
  5. [5]
    Gfrerer, H., Guddat, J., Wacker, H.: A globally convergent algorithm based on imbedding and parametric optimization. Computing30, 225–252 (1983).Google Scholar
  6. [6]
    Gröwe, N., Römisch, W.: A stochastic programming model for optimal power dispatch: Stability and numerical treatment. In: Marti, K. (ed.) Stochastic optimization. Berlin: Springer 1992 pp. 111–139 (Lecture Notes in Economics and Mathematical Systems Vol 379).Google Scholar
  7. [7]
    Gröwe, N., Römisch, W.: Numerical treatment of a stochastic programming model for optimal power dispatch. Proceedings of the Sixth Annual Conference of ECMI (Limerick, Ireland 1991; Hodnett, F. ed.), Dordrecht: Kluwer (to appear).Google Scholar
  8. [8]
    Guddat, J., Guerra Vasquez, F., Jongen, H. Th.: Parametric optimization: singularities, path-following and jumps. Chichester: Wiley 1990.Google Scholar
  9. [9]
    Kall, P.: Stochastic linear programming. Berlin: Springer 1976.Google Scholar
  10. [10]
    Kleinmann, P., Schultz, R.: A simple procedure for optimal load dispatch using parametric programming. Zeitschrift für Operations Research34, 219–229 (1990).Google Scholar
  11. [11]
    Prékopa, A.: Recent results in optimization of electro-energetic systems. In: Wacker, H. (ed.) Applied optimization techniques in energy problems. Stuttgart: Teubner 1985, pp. 354–383.Google Scholar
  12. [12]
    Römisch, W., Schultz, R.: Distribution sensitivity for certain classes of chance-constrained models with application to power dispatch. Journal of Optimization Theory and Applications71, 569–588 (1991).Google Scholar
  13. [13]
    Römisch, W., Schultz, R.: Stability analysis for stochastic programs. Annals of Operations Research30, 241–266 (1991).Google Scholar
  14. [14]
    Römisch, W., Schultz, R.: Lipschitz stability for stochastic programs with complete recourse, manuscript, Humboldt-Universität Berlin, Fachbereich Mathematik, 1992.Google Scholar
  15. [15]
    Wacker, H. (ed.): Applied optimization techniques in energy problems. Stuttgart: Teubner 1985.Google Scholar
  16. [16]
    Wets, R. J.-B.: Stochastic programming. In: Nemhauser, G. L., Rinnoy Kan, A. H. G., Todd, M. J. (eds.) Handbooks in operations research and management science, Vol. 1, Optimization. Amsterdam: North-Holland 1989, pp. 573–629.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • J. Guddat
    • 1
  • W. Römisch
    • 1
  • R. Schultz
    • 1
  1. 1.Fachbereich MathematikHumboldt-Universität BerlinBerlinFederal Republic of Germany

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