Keywords

• Stochastic optimal control
• Dynamic programming
• Hamilton-Jacobi-Bellman equation
• Hidden Markov model
• Energy storage
• Regularization

Project description

Energy storage enables the temporal balancing of energy supply and demand. During periods of low demand or overproduction, they can store energy and feed it back into the energy grid when demand is higher. Storage is becoming increasingly important with the growing share of renewable energies, as their production is subject to strong fluctuations that are difficult to predict and control.

In addition to many technical issues related to security of supply, it makes sense to also consider the economic aspects of energy storage. This involves exploiting the inherent optionality of storage, which allows energy to be transferred over time. This enables the owner of an energy storage facility to benefit from fluctuating energy prices and generate profits by trading on the energy markets and actively managing storage.

The basic idea behind the economic evaluation is to maximize the expected cash flow, which includes the costs of purchasing energy (charging) and the profits from selling energy (discharging), by choosing a suitable storage strategy.

The mathematical contribution of this project is the investigation of the resulting stochastic optimal control problems with partial information.

Energy prices are described by a regime switching model, which captures changing economic conditions through a Markov chain that cannot be directly observed. By applying filtering techniques, the optimal control problem with partial information is transformed into one with full information. Using dynamic programming methods, the Hamilton-Jacobi-Bellman equation (HJB equation) associated with the new problem is formulated and investigated.

This HJB equation is degenerate in the diffusion part of the differential operator. This classical existence and uniqueness results for the solution of the HJB equation and verification theorems based on it cannot be applied to the optimal control problem. These difficulties are to be overcome by using a regularization technique.

Another focus of the project is the numerical solution of the HJB equation. For this purpose, difference schemes based on the semi-Lagrange method and the policy improvement method are being developed.

Project-related publications

A.A. Shardin and R. Wunderlich: Partially Observable Stochastic Optimal Control Problems for an Energy Storage. Stochastics, 89 (1), 280-310 (2017)

A.A. Shardin and M. Szölgyenyi: Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information. International Journal of Theoretical and Applied Finance, 19(4):1-27 (2016)