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Mathematics 2022, 10, 3167 4 of 27 As previously mentioned, cold-energy storage allows decoupling of cooling demand and production. Moreover, given the parallel arrangement between the evaporator and the TES tank, the cooling demand at the refrigerated chamber may be satisfied using both secondary fluid streams. It implies that the TES-backed-up refrigeration system is able to satisfy peak cooling demand that might be infeasible for the original standard refrigeration cycle, due to the double contribution provided by both secondary fluid streams. The economic and feasibility potential offered by the addition of the TES tank to the original refrigeration cycle is explored by proposing a scheduling and control strategy based on non-linear MPC to satisfy the cooling demand while minimizing the daily operating cost. The main contribution of this work regarding the scheduling is the application of non- linear model predictive control (NMPC) to this hybrid system, where the computational cost of the prediction model is also considered. A non-linear model describing the dominant dynamics of the TES tank is proposed to be used as the prediction model. The latter is developed from the frequency analysis performed in the work by Rodríguez et al. [25], where it is stated that two very different time scales arise in the combined system: one related to the fastest dynamics of the refrigeration cycle, and another, slower one, related to heat transfer within the TES tank. In that work, a detailed model of the TES-backed-up refrigeration cycle was presented, focusing on the faster dynamics caused by the refrigerant circulation, which must be integrated using a small sampling time, in the order of a few seconds. However, such complexity is not affordable or even necessary when addressing the scheduling stage, according to the desired sampling time of several minutes, given the slower dynamics related to heat transfer within the TES tank. Therefore, in this work a simplified non-linear model is proposed, focusing on the dominant dynamics related to the TES tank, which turns out to be far from trivial but more suitable to model-based predictive strategies, especially concerning computational load. This is one of the main contributions of the work, since the reduced computational cost of the prediction model allows direct application of a non-linear model predictive control strategy while ensuring reasonable computation times. The performance of the proposed scheduler for the TES-backed-up system is compared in simulation with the refrigeration cycle without energy storage, while an analysis on the operating cost and constraint meeting is also performed, even when considering significant parametric uncertainty in the prediction model. Therefore, the main contributions of the work are summarised below: • A novel setup of a TES-backed-up refrigeration system is presented, where the TES tank is inserted within the refrigeration cycle, causing the heat transfer fluid to dif- fer between charging and discharging processes. This is an essential and relevant difference with respect to the dominant packed bed technology [13,14]. • A layered NMPC-based scheduling and control strategy is applied to the TES-backed- up refrigeration system, which explores the economic and feasibility potential of such a setup, where the control of the compressor and expansion valves is directly affected by the embedding of the TES tank within the refrigeration cycle, in contrast with the packed bed technology, where the refrigerant circulation is not affected by the state of the storage tank [13]. Thus, the existing control strategies previously detailed [17,18,21–23] cannot be applied to the configuration under study. • A simplified and computationally efficient non-linear prediction model describing the dominant dynamics of the system is presented, which allows the application of the previously mentioned non-linear predictive strategy with reasonable computa- tional load, when compared with the accurate but computationally expensive existing dynamic model [25]. The work is organised as follows. Section 2 describes the main characteristics of the designed TES tank and its embedding in the existing facility. Section 3 addresses the modelling of the combined system, focusing on the dominant dynamics related to heat transfer within the TES tank. The overall control strategy is presented in Section 4, focusing on the NMPC-based scheduling algorithm. Section 5 describes a case study for a demanding load profile, where the need for operating mode scheduling is justified according to thePDF Image | Refrigeration Systems with Thermal Energy Storage
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