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mathematics Article Energy Management of Refrigeration Systems with Thermal Energy Storage Based on Non-Linear Model Predictive Control Guillermo Bejarano 1,* , João M. Lemos 2 , Javier Rico-Azagra 3 , Francisco R. Rubio 4 and Manuel G. Ortega 4 1 2 3 4 * Correspondence: gbejarano@uloyola.es Abstract: This work addresses the energy management of a combined system consisting of a refriger- ation cycle and a thermal energy storage tank based on phase change materials. The storage tank is used as a cold-energy buffer, thus decoupling cooling demand and production, which leads to cost reduction and satisfaction of peak demand that would be infeasible for the original cycle. A layered scheduling and control strategy is proposed, where a non-linear predictive scheduler computes the references of the main powers involved (storage tank charging/discharging powers and direct cooling production), while a low-level controller ensures that the requested powers are actually achieved. A simplified model retaining the dominant dynamics is proposed as the prediction model for the scheduler. Economic, efficiency, and feasibility criteria are considered, seeking operating cost reduction while ensuring demand satisfaction. The performance of the proposed strategy for the system with energy storage is compared in simulation with that of a cycle without energy storage, where the former is shown to satisfy challenging demands while reducing the operating cost by up to 28%. The proposed approach also shows suitable robustness when significant uncertainty in the prediction model is considered. Keywords: refrigeration system; thermal energy storage; phase change materials; non-linear model predictive control; scheduling MSC: 93-10 1. Introduction Vapour-compression refrigeration systems represent the most used technique world- wide to provide cooling power, including freezing, cooling, and air conditioning applica- tions. The amount of energy involved in such processes is huge, both for industrial and commercial/residential purposes [1]. It is reported that up to 30% of total energy needs around the world are due to Heating, Ventilating, and Air Conditioning (HVAC) systems, among which refrigeration processes represent a significant share [2]. Energy efficiency of current mechanical compression refrigeration systems has been highly improved over time, while their environmental impact has been reduced due to diverse factors. Firstly, more effective design of heat exchangers, variable-speed compres- sors, and electronic expansion valves (EEV) have improved heat transfer efficiency and controllability. Secondly, more efficient control strategies have been applied to satisfy cooling demand while rejecting disturbances and achieving the highest energy efficiency possible with a direct environmental impact. For instance, Jain and Alleyne developed a Departamento de Ingeniería, Escuela Técnica Superior de Ingeniería, Universidad Loyola Andalucía, Avda. de las Universidades s/n, 41704 Dos Hermanas, Spain INESC-ID—Instituto de Engenharia de Sistemas e Computadores, Investigação e Desenvolvimento em Lisboa, Instituto Superior Técnico, University Lisboa, Rua Alves Redol, 9, 1000-029 Lisbon, Portugal Departamento de Ingeniería Eléctrica, Universidad de la Rioja, Calle San José de Calasanz, 31, 26004 Logroño, Spain Departamento de Ingeniería de Sistemas y Automática, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Seville, Spain Citation: Bejarano, G.; Lemos, J.M.; Rico-Azagra, J.; Rubio, F.R.; Ortega, M.G. Energy Management of Refrigeration Systems with Thermal Energy Storage Based on Non-Linear Model Predictive Control. Mathematics 2022, 10, 3167. https://doi.org/10.3390/ math10173167 Academic Editor: Nicu Bizon Received: 6 August 2022 Accepted: 31 August 2022 Published: 2 September 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Mathematics 2022, 10, 3167. https://doi.org/10.3390/math10173167 https://www.mdpi.com/journal/mathematicsPDF Image | Refrigeration Systems with Thermal Energy Storage
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