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Mathematics 2022, 10, 3167 5 of 27 power constraints. The economic performance and demand satisfaction of the scheduling strategy are compared to that of the original cycle without energy storage in simulation. Finally, Section 6 summarises the main conclusions and some future work is proposed. 2. Combined System Description 2.1. Terminology All abbreviations, symbols, and subscripts/superscripts used in the work are detailed in Table 1. The CoolProp tool [26] has been used to compute the thermodynamic properties of all involved fluids. Table 1. Abbreviations, symbols, and subscript/superscript notation. Italic Symbols Subscripts Description refrigerated chamber coating economic cost evaporator inlet/input intermediate fluid cylindrical layer outlet/output PCM electric resistance related to the charge ratio refrigerant superheating secondary fluid surroundings tank Thermal Energy Storage expansion valve Symbol Description A Opening CAPEX Capital Expenditure Units Symbol % chamber e coat – cost J kg−1 K−1 e COP Coefficient of Performance cp Specific heat at constant pressure D Diameter m in EEV Electronic Expansion Valve – int e Thickness m lay g Non-linear dynamic model of the TES tank HVAC Heating, Ventilating, and Air Conditioning HTF Heat Transfer Fluid h Specific enthalpy J Objective function k Discrete step time L Length m sec MPC Model Predictive Control m ̇ Mass flow rate m Mass N Compressor speed NMPC Non-linear Model Predictive Control n Number of elements – SH – surr kg s−1 tank kg TES – out – pcm – R J kg−1 ratio – refr Hz v – Superscripts – cond P Pressure Pa conv thermal conduction convection external latent state maximum latency point minimum latency point maximum minimum reference uncertain wall PCM Phase Change Material PH Prediction horizon Q ̇ Cooling power R Thermal resistance – ext – lat W lat+ K W−1 lat− T Temperature K max TES Thermal Energy Storage t Time U Internal energy V Volume m3 wall w Weight in the objective function x State vector e MWh−1 – W m−2 K−1 – W m−1 K−1 kg m−3 – min h ref J uncer Greek Symbols α Coefficient of thermal losses γ Charge ratio κ Thermal conductivity ρ Density 2.2. TES Tank Embedding The designed TES tank is intended to complement a two-compression-stage, two- load-demand experimental refrigeration facility located at the Department of SystemsPDF Image | Refrigeration Systems with Thermal Energy Storage
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