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Optimal control of electricity input given an uncertain demand

  • Simone GöttlichEmail author
  • Ralf Korn
  • Kerstin Lux
Original Article
  • 6 Downloads

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.

Keywords

Stochastic optimal control Jump diffusion processes Transport equation 

Mathematics Subject Classification

93E20 60H10 65C20 

Notes

Acknowledgements

The authors are grateful for the support of the German Research Foundation (DFG) within the Project “Novel models and control for networked problems: from discrete event to continuous dynamics” (GO1920/4-1) and the BMBF within the Project ENets.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MannheimMannheimGermany
  2. 2.Department of MathematicsTU KaiserslauternKaiserslauternGermany
  3. 3.Department of Financial MathematicsFraunhofer ITWMKaiserslauternGermany

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