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.
| Date of Award | Apr 26 2021 |
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| Original language | English (US) |
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| Awarding Institution | - Computer, Electrical and Mathematical Sciences and Engineering
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| Supervisor | Raul Tempone (Supervisor) |
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- stochastic
- optimal
- control
- jump
- diffusion