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Optimal control of electricity input given an uncertain demand

Author

Listed:
  • Simone Göttlich

    (University of Mannheim)

  • Ralf Korn

    (TU Kaiserslautern
    Fraunhofer ITWM)

  • Kerstin Lux

    (University of Mannheim)

Abstract

We consider the problem of determining an optimal strategy for electricity injection that faces an uncertain power demand stream. This demand stream is modeled via an Ornstein–Uhlenbeck process with an additional jump component, whereas the power flow is represented by the linear transport equation. We analytically determine the optimal amount of power supply for different levels of available information and compare the results to each other. For numerical purposes, we reformulate the original problem in terms of the cost function such that classical optimization solvers can be directly applied. The computational results are illustrated for different scenarios.

Suggested Citation

  • Simone Göttlich & Ralf Korn & Kerstin Lux, 2019. "Optimal control of electricity input given an uncertain demand," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 301-328, December.
    • Handle: RePEc:spr:mathme:v:90:y:2019:i:3:d:10.1007_s00186-019-00678-6
    DOI: 10.1007/s00186-019-00678-6
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    References listed on IDEAS

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    1. Tim Breitenbach & Mario Annunziato & Alfio Borzì, 2018. "On the Optimal Control of a Random Walk with Jumps and Barriers," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 435-462, March.
    2. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    3. Souvik Roy & Mario Annunziato & Alfio Borzì & Christian Klingenberg, 2018. "A Fokker–Planck approach to control collective motion," Computational Optimization and Applications, Springer, vol. 69(2), pages 423-459, March.
    4. René Aïd & Luciano Campi & Adrien Nguyen Huu & Nizar Touzi, 2009. "A Structural Risk-Neutral Model Of Electricity Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 925-947.
    5. Andreas Wagner, 2014. "Residual Demand Modeling and Application to Electricity Pricing," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    6. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, August.
    7. M. T. Barlow, 2002. "A Diffusion Model For Electricity Prices," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 287-298, October.
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