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Optimal Power Generation under Uncertainty via Stochastic Programming

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Stochastic Programming Methods and Technical Applications

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 458))

Abstract

A power generation system comprising thermal and pumpedstorage hydro plants is considered. Two kinds of models for the cost-optimal generation of electric power under uncertain load are introduced: (i) a dynamic model for the short-term operation and (ii) a power production planning model. In both cases the presence of stochastic data in the optimization model leads to multi-stage and two-stage stochastic programs respectively. Both stochastic programming problems involve a large number of mixed-integer (stochastic) decisions but their constraints are loosely coupled across operating power units. This is used to design Lagrangian relaxation methods for both models which lead to a decomposition into stochastic single unit subproblems. For the dynamic model a Lagrangian decomposition based algorithm is described in more detail. Special emphasis is put on a discussion of the duality gap the efficient solution of the multi-stage single unit subproblems and on solving the dual problem by bundle methods for convex nondifferentiable optimization.

This research is supported by the Schwerpunktprogramm “Echtzeit-Optimierung großer Systeme” of the Deutsche Forschungsgemeinschaft

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Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Darinka Dentcheva & Werner Römisch

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  1. Darinka Dentcheva
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  2. Werner Römisch
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Editors and Affiliations

  1. Fakultät für Luft- und Raumfahrttechnik, Universität der Bundeswehr München, D-85577, Neubiberg/München, Germany

    Kurt Marti

  2. Institut für Operations Research, Universität Zürich, Moussonstraße 15, CH-8044, Zürich, Switzerland

    Peter Kall

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Dentcheva, D., Römisch, W. (1998). Optimal Power Generation under Uncertainty via Stochastic Programming. In: Marti, K., Kall, P. (eds) Stochastic Programming Methods and Technical Applications. Lecture Notes in Economics and Mathematical Systems, vol 458. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45767-8_2

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  • DOI: https://doi.org/10.1007/978-3-642-45767-8_2

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  • Print ISBN: 978-3-540-63924-4

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