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Mathematics 2022, 10, 3167 17 of 27 Table 4. Cooling power ranges corresponding to operating modes 1 to 4. Mode 1 650 550 450 350 250 150 50 50 Steady-state power map with boundary at the PCM cylinder centre Freezing/Melting Boundary Location Edge Halfway Centre Freezing/Melting Boundary Location Edge Halfway Centre Freezing/Melting Boundary Location Edge Halfway Centre Freezing/Melting Boundary Location Edge Halfway Centre Q ̇e,sec[W] [138, 759] [142, 695] [144, 621] Mode 2 Q ̇e,sec[W] [128, 810] [128, 810] [128, 810] Mode 3 Q ̇e,sec[W] [128, 810] [128, 810] [128, 810] Mode 4 Q ̇e,sec[W] – – – Q ̇TES[W] [103, 808] [82, 705] [71, 611] Q ̇TES[W] – – – Q ̇TES[W] – – – Q ̇TES[W] – – – Q ̇ TES,sec [W] – – – Q ̇ TES,sec [W] – – – Q ̇ TES,sec [W] [610, 1036] [483, 704] [327, 406] Q ̇ TES,sec [W] [610, 1036] [483, 704] [327, 406] 150 250 350 450 550 650 Figure 8. Steady-state cooling power map for mode 1 when the freezing/melting boundary locates at the PCM cylinder centre. Similar plots have been obtained for different locations of the freezing boundary, which are not included here for the sake of brevity. Notice that the cooling demand Q ̇ sec in operating mode 1 must be completely satisfied by Q ̇ e,sec, since Q ̇ TES,sec is zero. Therefore, the maximum charging power Q ̇ TES is shown to be constrained by the cooling demand. 5.3. Energy Price Realistic energy price evolution throughout the day is applied to the optimization problem. Figure 9 depicts the electricity prices corresponding to a given day (29 May 2019) in the Spanish spot market [31]. These prices, once scaled, are considered as the cost of the cooling power production at the evaporator, we,sec in Equation (22), as well as the cost of the TES charging power, wTES. However, wTES,sec is assumed to be zero, given that no extra cost is involved when using the previously produced cold energy, beyond the electric power devoted to pumping the secondary fluid, which is not considered in the objective function detailed in Equation (22).PDF Image | Refrigeration Systems with Thermal Energy Storage
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