Thermal storage facilities help to mitigate and to manage temporal fluctuations of heat supply and demand for heating and cooling systems of single buildings as well as for district heating systems. We focus on a heating system equipped with several heat production units using also renewable energies and an underground thermal storage. The thermal energy is stored by raising the temperature of the soil inside that storage. It is charged and discharged via heat exchanger pipes filled with a moving fluid.

Besides the numerous technical challenges and the computation of the spatio-temporal temperature dis- tribution in the storage also economic issues such as the cost-optimal control and management of such systems play a central role. The latter leads to challenging mathematical optimization problems. There we incorporate uncertainties about randomly fluctuating renewable heat production, environmental conditions driving the heat demand and supply.

The dynamics of the controlled state process is governed by a PDE, a random ODE, and SDEs modeling energy prices and the difference between supply and demand. Model reduction techniques are adopted to cope with the PDE describing the spatio-temporal temperature distribution in the geothermal storage. Finally, time- discretization leads to a Markov decision process for which we apply numerical methods to determine a cost-optimal control.

This is joint work with Paul Honore Takam (BTU Cottbus-Senftenberg) and Olivier Menoukeu Pamen (AIMS Ghana, University of Liverpool).