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 jumpdiffusion 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
HamiltonJacobiBellman partial differential equation associated with the system.
We discretize the HamiltonJacobiBellman partial differential equation using finite
differences and a time splitting operator technique, providing a stability analysis.
Finally, we solve a onedimensional minimization problem to determine the battery's
optimal capacity.
Date of Award  Apr 26 2021 

Original language  English (US) 

Awarding Institution   Computer, Electrical and Mathematical Science and Engineering


Supervisor  Raul Tempone (Supervisor) 

 stochastic
 optimal
 control
 jump
 diffusion