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Optimization in the Energy Industry pp 321–346Cite as

Scenario Tree Approximation and Risk Aversion Strategies for Stochastic Optimization of Electricity Production and Trading

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Part of the book series: Energy Systems ((ENERGY))

Summary

Dynamic stochastic optimization techniques are highly relevant for applications in electricity production and trading since there are uncertainty factors at different time stages (e.g., demand, spot prices) that can be described reasonably by statistical models. In this paper, two aspects of this approach are highlighted: scenario tree approximation and risk aversion. The former is a procedure to replace a general statistical model (probability distribution), which makes the optimization problem intractable, suitably by a finite discrete distribution. Our methods rest upon suitable stability results for stochastic optimization problems. With regard to risk aversion we present the approach of polyhedral risk measures. For stochastic optimization problems minimizing risk measures from this class it has been shown that numerical tractability as well as stability results known for classical (nonrisk-averse) stochastic programs remain valid. In particular, the same scenario approximation methods can be used. Finally, we present illustrative numerical results from an electricity portfolio optimization model for a municipal power utility.

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Authors and Affiliations

  1. Department of Mathematics, Humboldt-University Berlin, Berlin, 10099, Germany

    Andreas Eichhorn, Holger Heitsch & Werner Römisch

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  1. Andreas Eichhorn
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  2. Holger Heitsch
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  3. Werner Römisch
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Editors and Affiliations

  1. Am Mahlstein 8, 67273, Weisenheim, Germany

    Josef Kallrath

  2. Department of Industrial & Systems Engineering, University of Florida, 303 Weil Hall, 116595, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos  & Steffen Rebennack  & 

  3. ProCom GmbH, Luisenstraße 41, 52070, Aachen, Germany

    Max Scheidt

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Eichhorn, A., Heitsch, H., Römisch, W. (2009). Scenario Tree Approximation and Risk Aversion Strategies for Stochastic Optimization of Electricity Production and Trading. In: Kallrath, J., Pardalos, P.M., Rebennack, S., Scheidt, M. (eds) Optimization in the Energy Industry. Energy Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88965-6_14

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  • DOI: https://doi.org/10.1007/978-3-540-88965-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88964-9

  • Online ISBN: 978-3-540-88965-6

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