Mixed Integer Linear Programming Formulation for Sensible Thermal Energy Storages

In order to model the charging and discharging power of sensible thermal energy storages for the unit commitment problem with mixed integer linear programming more precisely, two extended formulations are proposed in this work. To this end, simulation data of a detailed simulation model, derived from measurement data of a fixed bed regenerator test rig, were investigated in order to determine the actual charging and discharging power of the storage in highly dynamic operation. The two formulations were derived from an original MILP storage model with fixed maximum charging and discharging power. The first proposed formulation adds linear constraints for charging and discharging power depending on the fill level. The second proposed formulation introduces auxiliary variables, taking into account the fill level at the end of the previous charging or discharging phase. The predicted operation for a test case of the original and the two proposed mixed integer linear formulations are compared with the achieved operation of the detailed simulation model. While the original formulation allows infeasible predictions for the storage operation, the two proposed formulations are able to describe the real operating behavior more detailed, therefore decreasing the infeasible predictions for operation as well as increasing the overall system performance.