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Mathematics 2022, 10, 3167 25 of 27 References model previously developed, a simplified model focused on the slower dynamics related to heat transfer within the storage tank has been proposed to act as the prediction model in the scheduling optimization. A layered scheduling and control strategy has been proposed, where a non-linear predictive scheduler computes the references of the main cooling powers involved, whereas the low-level controller ensures the achievement of the required cooling powers. The pre- dictive scheduling problem is posed as a non-linear optimization with constraints due to cooling demand satisfaction, power feasibility, and latency limits, while considering economic criteria in the objective function. A case study has been analysed, where a challenging load forecast that requires scheduling of different operating modes must be satisfied. The proposed strategy has been shown to ensure the cooling demand satisfaction and meeting of constraints while reducing the daily operating cost by up to 28% when compared to the refrigeration cycle without TES. Moreover, the latter fails in satisfying the cooling load during the entire day. A sensitivity analysis of the proposed strategy has shown it to provide satisfactory performance even when significant uncertainty in the prediction model is considered. As future work, the application of the proposed strategy to the experimental plant is scheduled to be performed as soon as the upgrading process undertaken on the facility is finished. Furthermore, the development of an economic NMPC strategy is devised [33], as well as the stability analysis of the proposed NMPC-based scheduling strategy. Author Contributions: Conceptualization, G.B., J.M.L. and M.G.O.; methodology, G.B., J.M.L., J.R.-A. and M.G.O.; software, G.B.; validation, G.B., J.M.L. and M.G.O.; formal analysis, G.B.; investigation, G.B.; resources, F.R.R. and M.G.O.; data curation, G.B.; writing—original draft preparation, G.B.; writing—review and editing, G.B., J.M.L., J.R.-A., F.R.R. and M.G.O.; visualization, G.B.; supervision, J.M.L., F.R.R. and M.G.O.; project administration, M.G.O.; funding acquisition, F.R.R. and M.G.O. All authors have read and agreed to the published version of the manuscript. Funding: Grant RTI2018-101897-B-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. Institutional Review Board Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results Abbreviations The following abbreviations are used in this manuscript: HVAC Heating, Ventilating, and Air Conditioning EEV Electronic expansion valve PMV Predicted Mean Vote TES Thermal energy storage PCM Phase change material COP Coefficient of Performance HTF Heat transfer fluid MPC Model Predictive Control NMPC Non-linear Model Predictive Control CAPEX Capital Expenditure 1. Raveendran, P.S.; Sekhar, S.J. Performance studies on a domestic refrigerators retrofitted with building-integrated water-cooled condenser. Energy Build. 2017, 134, 1–10. https://doi.org/10.1016/j.enbuild.2016.11.013. 2. Ruz, M.L.; Garrido, J.; Vázquez, F.; Morilla, F. A hybrid modeling approach for steady-state optimal operation of vapor compression refrigeration cycles. Appl. Therm. Eng. 2017, 120, 74–87. https://doi.org/10.1016/j.applthermaleng.2017.03.103.PDF Image | Refrigeration Systems with Thermal Energy Storage
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