## 4 Results and Discussion
### Distributed LHTS in DH Networks  
The 0D LHTS model is here applied to the reduction of the thermal power peak that is observed in DH networks at the beginning of their daily operation in some areas of the world (such as the Mediterranean area). In order to achieve this goal, the LHTS system follows the subsequent duty cycle, as detailed in Figure 7:  
* The charging phase of each LHTS unit lasts 3 h; thus, the whole LHTS bundle is charged between 1.20 and 5.40 am (due to the imposed delay between the activation of each unit);
* The discharging phase of each LHTS unit lasts 1.5 h; thus, the whole LHTS bundle is discharged between 6.30 am and 9.20 am (due to the imposed delay between the activation of each unit).  
Although all the energy absorbed by the LHTS during the charging phase is released in the discharging phase, the duration of these two processes is remarkably different. Since the HTF mass flow rate is constant, the thermal power is affected only by the temperature difference between the incoming HTF (48 \({}^{\circ}\)C or 75 \({}^{\circ}\)C) and the PCM average phase change temperature (70 \({}^{\circ}\)C) in both the operational phases. Consequently, the discharging phase is faster because the temperature difference is  
Figure 7: LHTS charge and discharge duty cycle to reduce DH morning peak.  
four times higher compared to the charging phase. Moreover, the spikes registered in the LHTS thermal power does not constitute a desirable feature from the point of view of the building heating system management. However, this highly unsteady behavior could be easily changed by a finer regulation of the HTF mass flow rate [16; 17] (that is out of the goals of the present analysis). Furthermore, as detailed in Section 2.2, a perfect LHTS insulation is assumed. Consequently, heat losses are negligible when the storage is fully charged.  
As shown in Figure 8, the time delay between the activation of each LHTS unit strongly affects the maximum power requested by the building to the DH network, whose reference value is 385 kW for this case study. Considering the LHTS system configuration analyzed, the peak thermal power of the DH supply is minimized when the activation of each LHTS unit is delayed by 16 min with respect to its preceding unit during the discharging phase. On the contrary, the minimization of the peak DH supply during the charge of the whole LHTS system would yield the obvious solution of charging each LHTS unit separately. However, this situation would not be compatible with the available time in the night. For this reason, an activation delay of 16 min was retained also for the charging phase.  
Finally, Figure 9 shows the DH supply curve when the LHTS system presented in this study is deployed. For consistency with the data of the building energy demand, the DH supply curve describes the average thermal power over 15-min intervals. The morning peak reduction is evident from the figure. The thermal energy supplied by the DH between 6.30 and 9 am is reduced by 25.5%, while the maximum value of the DH thermal power is decreased by 18%. This result is achieved by simply shifting the supplied thermal energy in the night hours. This shifting could also be extensively advantageous for DH users in case of different tariffs during the daytime and nighttime. As an example, in Turin, the heat during the night is sold at a price that is up to 50% lower than the daily price [25]. Furthermore, the overall volume occupied by the LHTS system proposed in this study amounts to 3.4 m\({}^{3}\), while a sensible water storage tank would require 7 m\({}^{3}\) for the same energy content (assuming also the same temperature difference 75-48 \({}^{\circ}\)C). Therefore, this feature constitutes a great advantage when the thermal energy storage is located in the small technical rooms available in the buildings.  
Figure 8: Minimization of DH peak thermal power through LHTS discharge delay.