Optimal Control of Electrical Storage

The project is concerned with electrical networks with random energy production and consumption as well as electrical storage. More specifically, given processes characterizing energy production and consumption, which strategy will optimally drive an electrical storage facility?
Advances in the design of renewal energy production such as solar and wind power as well in battery design allow to create small self-sustaining electrical networks at reasonable cost, which satisfy basic adequacy and reliability requirements. An example would be a network for a remote field hospital.
A challenge is that inefficient charge/discharge cycles can lead to accelerated ageing of the relatively costly battery storage. In such a scenario it might be optimal not to use excess renewable energy for charging, even if that leads to increased conventional energy use, e.g. diesel. This sets battery storage apart from other more traditional storage technologies such as compressed gas and hydro storage, for which mathematically rigorous studies exist, we refer for instance to Peter Forsyth and his co-authors.
The core research aims of the project are:
- to extend the existing dynamic programming models for electrical networks with
storage to storage with ageing,
- to numerically study the resulting Hamilton-Jacobi-Bellman equation with semi-
Langrangian schemes within relevant parameter ranges.
In addition it would be desirable to
- prove well-posedness of the Hamilton-Jacobi-Bellman equation in the viscosity
sense,
- prove convergence of the semi-Langrangian method via the Barles-Souganidis
argument.