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Mathematics 2022, 10, 3167 19 of 27 Figure 11 shows a proposed operating mode scheduling for the specific demand profile introduced in Figure 7, according to the power constraints analysed in Section 5.2 and the energy price profile shown in Figure 9. Operating mode scheduling Cooling demand satisfied at the evaporator and at the TES tank Cooling demand TES tank discharging Cooling demand satisfied at the evaporator Cooling deman d satisfied at the evaporator TES tank char ging satisfied at the evaporator TES tank in stand-by TES tank charging 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 Time [h] Figure 11. Proposed operating mode scheduling. As observed in Figure 11, the TES tank is scheduled to be charged during the off-peak periods at the beginning and at the end of the day, when the cost of cooling power produc- tion is lower. Given that the demand is low but not zero during these periods, operating mode 1 is scheduled, in such a way that the cooling demand is satisfied exclusively at the evaporator. Furthermore, the cold-energy stored in the TES tank is scheduled to be released during the peak period, complementing the cooling power provided to the secondary fluid at the evaporator to meet the cooling demand (operating mode 3). Two intermediate periods when the TES tank is not charged nor discharged, but in stand-by (operating mode 2), have been inserted between the charging and discharging periods, given that the cooling demand can be satisfied at the evaporator and it is certainly more interesting from an economic point of view to ensure the cooling demand satisfaction during all the peak period, when the contribution of the TES tank is imperative. Moreover, once the peak period is finished, it might be more interesting to concentrate the TES tank charging during the central hours of the off-peak period, when the economic cost of cooling power production is lowest. 5.5. Simulation Results Some simulation results of the proposed scheduling strategy are presented in this subsection, where they are also compared to the performance of the original refrigeration system without energy storage, regarding both economic cost and constraint meeting. Given the cooling demand shown in Figure 7 and the energy price profile shown in Figure 9, the references of the cooling powers are computed every hour. However, the dynamics related to heat transfer within the TES tank require an internal sampling time of the prediction model of 10 min. The latter could be reduced to increase accuracy, at the expense of greater computational load of the predictive scheduling strategy. Safety limits γmin = 0.05 and γmax = 0.95 have been considered, while a prediction horizon PH = 4 is TES TES Figure 12 shows the performance of both the proposed scheduling strategy for the TES-backed-up system and the refrigeration cycle without TES, concerning the satisfaction of the cooling demand. Furthermore, Figure 13 shows the three references of the relevant cooling powers, whereas Figure 14 represents the charge ratio of the TES tank in the proposed scheduling strategy. Moreover, Figure 15 shows the temperature of the intermediate fluid, set. At the initial state of the TES tank, the intermediate fluid is assumed to be in thermal equilibrium with the PCM cylinders (T (t = 0) = Tlat ), whereas the initial enthalpy int distribution of the latter is such that γTES(t = 0) = 0.35. pcm Operating modePDF Image | Refrigeration Systems with Thermal Energy Storage
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