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Mathematics 2022, 10, 3167 23 of 27 Obviously, the achieved reduction on the operating cost would come at a certain price in terms of CAPEX (capital expenditure). The economic analysis performed in this work is not intended to be comprehensive, but to throw some light on the high economic potential of such energy storage systems, which not only can ensure the satisfaction of demanding cooling load profiles, but they can also lead to significant cost reduction when properly operated. However, the simulation results highlight the need for suitable predictive scheduling strategies to manage the stored cold energy within the latent zone and fit the cooling power limits of a given facility. Indeed, the latter have been shown to vary significantly when the energy storage system is added to the original refrigeration cycle, both in charging and discharging processes. 5.6. Sensitivity Analysis Some simulations of the proposed scheduling strategy considering parametric un- certainty are presented in this subsection. Given the design of the TES tank described in Section 2, minor uncertainty is expected to be devoted to geometry, constructive materials, working fluids, and their thermodynamic properties. Nevertheless, a simple heat transfer model is used to compute the cooling power transferred between the PCM cylinders and the intermediate fluid Q ̇ pcm, where a probably uncertain heat transfer coefficient computed by classical correlations for natural convection [32] has been considered to compute the thermal resistance Rconv,ext in Equation (3). Moreover, the assumption of homogeneous pcm heat transfer between the PCM cylinders and the intermediate fluid could lead to some degree of uncertainty regarding the cooling power calculation and then the evolution of the temperature of the intermediate fluid Tint. In order to assess the robustness of the proposed scheduling strategy against this kind of uncertainty, the latent temperature Tlat considered pcm by the prediction model will be artificially modified. The latter is usually precisely known by design, but if an uncertain value was considered in the prediction model, it would strongly affect the calculation of both TES charging and discharging cooling powers, which in turn determine how the intermediate fluid evolves. Therefore, the consideration of some uncertainty in the latent temperature Tlat is just a simplified way of inducing uncertainty pcm in all cooling power calculation within the TES tank. Figure 16 shows the references of the TES charging/discharging cooling powers Q ̇ TES and Q ̇ , when some uncertainty in Tlat is considered. This temperature has been TES,sec pcm increased/decreased in 1 K from the nominal value in the prediction model. Given the variations of the intermediate temperature for the nominal case shown in Figure 15a, the considered increment/decrement is high enough to cause significant uncertainty in the prediction model with respect to the accurate model used for the plant simulation. Furthermore, Figure 17 compares the TES charge ratio for the three cases. It is shown in Figure 17 that the proposed scheduling strategy provides very similar results for the references of the charging and discharging cooling powers, in spite of the significant uncertainty in the cooling power calculation and thus in the estimated charge ratio. In the case of Q ̇ TES,sec, the references are identical, as shown in Figure 16b, but some appreciable differences appear in Figure 16a regarding the charging power. The latter variations are due to the greater closeness to the upper limit imposed on the charge ratio in the case of the charging process, as represented in Figure 17. Therefore, the proposed scheduling strategy presents a suitable degree of robustness to significant modelling errors, ensuring cooling demand is satisfied and that the limits of the latent zone are met even if significant errors are introduced in the cooling power calculation.PDF Image | Refrigeration Systems with Thermal Energy Storage
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