## 4 Model Validation  
The developed model was validated using the experimental data from a testing campaign carried out for a complete system, including the heat pump and the embedded thermal energy storage. A detailed description of the system, testing conditions, and results is presented in [30]. The testing rig used for the experimental activity consisted of three water storages units connected to different heat sources, to supply the different temperature levels needed for the operation of thermal systems. The inlet and outlet HTF flows of each storage were mixed through the use of high-speed mixing valves to guarantee a constant inlet and the precise regulation of the desired set-point. Heat storage units with charge/discharge power up to 30 kW can be tested. A picture of the system (heat pump + heat storage) connected to the testing rig and the layout of the latent storage are shown in Figure 3. The uncertainty of measurements for this setup was \(\pm\)0.5 \({}^{\circ}\)C for the temperatures and \(\pm\)700 W for the thermal power [30]. Different operating modes are possible for the storage unit [30]:  
* charge mode: the refrigerant of the heat pump is used to solidify the PCM, there is no flow in the HTF circuit;
* discharge mode: the heat pump is off, the HTF is circulated, and the PCM is melted by subtracting the latent heat from the HTF, which is cooled down and delivered to the user;
* parallel charging/discharging mode: the PCM is charged and discharged at the same time. Hence, the heat pump is on and at the same time the HTF circuit is connected to the load. In order to validate the model, reference tests for each of the investigated operating modes were considered. For the charge process, the case of a test with the PCM starting at an average temperature of 15 \({}^{\circ}\)C and fully charged until 0 \({}^{\circ}\)C with the heat pump at a part load of 60% was considered. The results are shown in Figure 4a, where a direct comparison between the average measured PCM temperature and the simulated one is presented. It is possible to notice that there was a good agreement between the experiments and the simulation, with deviations lower than 0.5 K. An exception is represented by the temperature range 0-2 \({}^{\circ}\)C, corresponding to the material in a fully solid state. In this case, a deviation of 1.2 K was shown, probably due to the enthalpy formulation of the implemented model in Dymola. However, under the designed operating conditions, it is not beneficial to reach such temperatures, also due to a too high reduction in the temperature of the refrigerant of the heat pump, with a, consequently, strong penalization  
Figure 3: (**a**) heat pump and latent heat storage system installed in the lab during the testing campaign. (**b**) schematic representation of the three-fluid heat exchanger. of its efficiency. Accordingly, it is possible to state that the validation in the designed range was successful. For the discharge process, a test with the PCM starting at \(-2\)\({}^{\circ}\)C and ending at 12 \({}^{\circ}\)C, with a discharge flow rate of 0.2 kg/s for the HTF was selected. A comparison of the average PCM temperature from the experiments and the simulation is shown in Figure 4b. In this case, the average deviation between the experiments and simulation was about 16%. The larger difference being due to the larger thermal gradient in the heat exchanger, as  
Figure 4: Model validation for the different operating modes. (a) charge; (b) discharge; (c) parallel operation. a consequence of the turbulent flow of the HTF and its uneven distribution, which is more complex to reproduce in lumped parameter modeling. However, considering that this measurement error is in the order of 10%, the error introduced by the simulation for this operating mode can also be considered acceptable for simulation-aided design purposes. Finally, the validation for parallel operation is shown in Figure 4c. During this operating mode, as described in detail in [30], the temperature of the PCM is almost constant.