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Energies 2020, 13, 6576 7 of 24 The simulations performed showed 63 ◦C as the minimum outlet condenser temperature that achieves this requirement stably. However, the variable-water-volume case needs also to control the volume of water stored inside the tank, thus requiring a switch to stop the filling and the SHP use when the tank is full, and to fill in and switch on the SHP when the tank reaches a low level limit, which could lead to emptying the tank if the DHW demand follows. For this purpose, a parameter alpha defined as the percentage of the minimum volume inside tank, respect to the tank total volume, at which the SHP is switched on, was introduced in the model as an optimization variable. 2.3. Model Restrictions and Energy Performance Indicators In order to compare the different systems, four indicators have been selected: the system global efficiency appointed as SPFuser (the system is designed to minimize this parameter), the SPF1, the total energy recovered at the BPHE, and the total energy used from the low temperature heat source: SPFuser = Quser , (2) WHP compressor + Wauxiliaries SPF1 = QHP condenser . WHP compressor (3) The seasonal performance factor for the user (SPFuser) is defined as the ratio between the useful heat supplied to the user (Quser) and the total energy consumption of the system (WHP compressor + Wauxiliaries) as stated in Equation (2). The seasonal performance factor of the SHP (SPF1) is defined as the ratio between the heat supplied by the SHP condenser (QHP condenser) and the energy consumed by the SHP compressor (WHP compressor) as stated in Equation (3). Finally, the total energy recovered accounts for the energy recovered in the HRU and the total energy used from the low temperature heat source for the energy extracted from the heat source considering the minimum system temperature as reference (10 ◦C). This study focuses on DHW production systems that employ a low temperature water stream as heat source, as for instance, grey water or a ULTDH. In order to reduce the number of input variables, the water temperature of the water stream has been considered as 30 ◦C and the temperature of the city water as 10 ◦C. Other combinations of temperatures could influence the absolute results but not the relative comparison among the options considered or the main conclusions. Several restrictions have been added in the model in order to guarantee that all optimal solutions found also satisfy the user comfort (water supply at 45 ◦C) and the system reliability. The restrictions are: • Maximum value for the annual percentage of discomfort of 0.05%, evaluated as shown in Equation (4). Where muser (T<45°C) corresponds with the mass flow rate over 45 ◦C and muser with the total mass flow rate: Annualdiscomfort = m user muser (T<45°C) <0.01. (4) • The total amount of minutes along the year during which the comfort was not reached is limited to a maximum value of 30 min per year, which corresponds to 5 s of discomfort per day for each hour of the day. This value is quite small compared to comfort requirements imposed in other applications like heating and cooling of spaces in which total time percentages along the year are defined, but it should be done in that way as the demand profile along the day is quite focused in certain periods. • Limitation of the number of starts per hour of the SHP to a maximum of 9. This is the usual limitation stated by the compressor manufacturers.PDF Image | Thermal Energy Storage Strategy Booster Heat Pump Low Temp
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