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Mathematics 2022, 10, 3167 12 of 27 which retains the dominant dynamics while allowing a much greater sampling time, comes handy. Therefore, the computational complexity of the proposed model is not compared with the one in [25] due to impracticability, but the benefits provided in terms of computational cost are evident. 3.2. Operating Modes Diverse operating modes can be defined, according to all possible combinations of the three main cooling powers involved in the problem: the cooling power provided to the secondary fluid at the evaporator Q ̇ e,sec, the TES charging cooling power Q ̇ TES, and the TES discharging cooling power Q ̇ TES,sec [25]. Up to eight operating modes have been defined and discussed in the aforementioned work, though the most useful operating modes might be modes 1 to 4, since modes 5 and 8 require no cooling demand, whereas modes 6 and 7 involve simultaneous TES tank charging and discharging, which may not make sense from the operating point of view. The most interesting operating modes are graphically described in Figure 5. Cycle TES Chamber Mode 1 Cycle T E S Q ̇ T ES,sec Chamber Mode 3 Cycle TES Q ̇ e,sec Chamber Mode 2 Cycle T E S Q ̇ T E S Q ̇ e,sec Q ̇ e , s e c Q ̇ T ES,sec Mode 4 Chamber Figure 5. Most useful operating modes of the TES-backed-up refrigeration system. Mode 1 may be scheduled when the cooling demand can be satisfied by using only the refrigeration cycle and it is interesting to simultaneously charge the TES tank. Mode 2 might be scheduled in the same situation, but when the TES tank is fully charged or it is not economically interesting to continue charging it. Mode 3 is useful when the cooling demand is greater than the maximum power achievable by using only the refrigeration cycle. Mode 4 requires that the demand can be satisfied by only discharging the TES tank, thus the refrigeration cycle is stopped. 4. Scheduling and Control Strategy 4.1. Overview Figure 6 represents the proposed scheduling and control strategy. The main objective is to track a certain reference of the chamber temperature Tre f , which, by means of the chamber so-called outer controller, may result in a reference of the overall cooling power that must be provided to the secondary fluid Q ̇ re f , since an electric resistance transfers a certain heat sec Q ̇ R to the secondary fluid to simulate the thermal load. This controller is not addressed in this work due to its simplicity, since it tackles a single reference Tre f and a single chamber control action Q ̇ re f . A simple PID control could be applied without difficulty, thus the sec development of such a control law has not been considered of interest for this work.PDF Image | Refrigeration Systems with Thermal Energy Storage
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