Optimal policies for battery operation and design via stochastic optimal control of jump diffusions
Type
ThesisAuthors
Rezvanova, Eliza
Advisors
Tempone, Raul
Committee members
Boffi, Daniele
Bolin, David
Date
2021-04-26Embargo End Date
2022-04-26Permanent link to this record
http://hdl.handle.net/10754/668996
Metadata
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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-Y3Z26ae974a485f413a2113503eed53cd6c53
10.25781/KAUST-Y3Z26