Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information

TL;DR

This paper develops a method for optimizing energy storage in a changing economic environment with partial information, using filtering theory and solving a complex stochastic control problem.

Contribution

It introduces a novel approach combining filtering and stochastic control for energy storage optimization under partial information and changing conditions.

Findings

Derived a Hamilton-Jacobi-Bellman equation for the problem

Proved existence and uniqueness of solutions for complex SDEs involved

Validated the admissibility of the proposed optimal control

Abstract

In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage manager and the energy price process, which is a diffusion process the drift of which is assumed to be unobservable. We apply filtering theory to find an alternative state process which is adapted to our observation filtration. For this alternative state process we derive the associated Hamilton-Jacobi-Bellman equation and solve the optimization problem numerically. This results in a candidate for the optimal policy for which it is a-priori not clear whether the controlled state process exists. Hence, we prove an existence and uniqueness result for a class of time-inhomogeneous stochastic differential equations with discontinuous drift and singular diffusion coefficient. Finally, we apply our result to prove admissibility of the candidate optimal control.