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    Optimal policies for battery operation and design via stochastic optimal control of jump diffusions

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    Type
    Thesis
    Authors
    Rezvanova, Eliza cc
    Advisors
    Tempone, Raul cc
    Committee members
    Boffi, Daniele cc
    Bolin, David
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2021-04-26
    Embargo End Date
    2022-04-26
    Permanent link to this record
    http://hdl.handle.net/10754/668996
    
    Metadata
    Show full item record
    Access Restrictions
    At the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis will become available to the public after the expiration of the embargo on 2022-04-26.
    Abstract
    To operate a production plant, one requires considerable amounts of power. With a wide range of energy sources, the price of electricity changes rapidly throughout the year, and so does the cost of satisfying the electricity demand. Battery technology allows storing energy while the electric power is lower, saving us from purchasing at higher prices. Thus, adding batteries to run plants can significantly reduce production costs. This thesis proposes a method to determine the optimal battery regime and its maximum capacity, minimizing the production plant's energy expenditures. We use stochastic differential equations to model the dynamics of the system. In this way, our spot price mimics the Uruguayan energy system's historical data: a diffusion process represents the electricity demand and a jump-diffusion process - the spot price. We formulate a corresponding stochastic optimal control problem to determine the battery's optimal operation policy and its optimal storage capacity. To solve our stochastic optimal control problem, we obtain the value function by solving the Hamilton-Jacobi-Bellman partial differential equation associated with the system. We discretize the Hamilton-Jacobi-Bellman partial differential equation using finite differences and a time splitting operator technique, providing a stability analysis. Finally, we solve a one-dimensional minimization problem to determine the battery's optimal capacity.
    Citation
    Rezvanova, E. (2021). Optimal policies for battery operation and design via stochastic optimal control of jump di usions. KAUST Research Repository. https://doi.org/10.25781/KAUST-Y3Z26
    DOI
    10.25781/KAUST-Y3Z26
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-Y3Z26
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; MS Theses; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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