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7 pump, whose evaporator uses the recovered air in the ventilation channel as a heat source。 The same model is also adopted for assessing the performances of a conventional system where the ambient air is used。 The heat pump works with R-134a and is designed for an evaporation temperature of -5 °C and a condensation temperature of 40 °C, high enough to supply water at 35 °C to the radiant heating system。 A different fluid as HFO-1234yf would have very similar performances and results of R 134a as also discussed in [27–29]。 Other assumptions are summarized in Table 2。 At each time step (one minute), the model calculates the evaporation temperature assuming a constant overall heat transfer coefficient in the evaporator, which is a generally accepted simplification。 Consequently, the heat pump heating capacity, the compressor power and the heat pump COP can be calculated as: (24) A more detailed simulation of the evaporator could have been carried out with advantages on results accuracy but with higher computational efforts。 Since the aim of this work is the assessment of the overall system performances, the detailed simulation was not included in the model。 In the reference case, a constant air temperature difference of 6 °C is assumed whenever the minimum evaporation temperature is respected。 For the solar driven heat pump, when the air temperature variation is higher than 6°C, the ambient temperature is kept as air condition at the outlet of the evaporator。 This assumption implies the presence of an inverter to control the compressor rotation speed, which is typically installed in commercial products。 Taking the ambient temperature at the evaporator outlet will outline the differences in terms of COP thanks to the higher air temperature at the inlet of the evaporator, even though the thermal power generated will be different between the two cases (i。e。 higher for the reference case as consequence of the higher pressure ratio across the compressor)。 Examples of heat pump performances and thermodynamic cycle in the p-h diagram for the two different evaporation conditions are shown in Figure 3。 The COP increases by 17% with solar irradiance on the tile of 311 W/m2。 Finally, the pressure losses across the evaporator are in the range of one Pa, which correspond to about 1% the natural convection driving force。 Therefore, the impact of the evaporator on the natural convection can be considered negligible。 Moving to the electric energy produced by the PV panel, it is calculated starting from the datasheet performances at STC (Standard Test Conditions) provided by the manufacturer and then corrected for the actual radiation and the operating cell temperature as follows: (25) Where is the nominal electric power of the PV cell at STC, is the cell power temperature coefficient, Gtile is the actual solar irradiance on the cell, GSTC is the one at STC (1000 W/m2), and

Ttile and TSTC are the actual and reference cell temperatures (25 °C)。 Ttile results from the thermal model。 In the lump approach used in this work, the cell and the tile temperatures coincides, hence Eq。 (25) could be expressed as function of tile conditions。 The electric energy generated by the PV cell is taken into account into the thermal model。 Overall result of this analysis is the energy performance index (EPI) index of the under-slating ventilation system (Inn HP) with reference to conventional air-water heat pump system (Ref HP) to

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8 cover the thermal load of the house。 (26) The primary energy consumption is calculated as follows: (27) Where indicates the primary energy consumptions for the Inn HP and Ref HP respectively, Qload is the thermal energy generated, COP,I is the average coefficient of performance of the heat pump (Inn HP or Ref HP), ηel is the reference conversion efficiency for electricity generation (it depends on the location and assumed equal to 45% [30]。 The electricity produced by the PV panel is included in the PEC calculation as well。 When the Inn HP is not able to cover the heat demand and the thermal energy storage is empty, the auxiliary heat pump (which coincides with Ref HP) will cover the heat demand with no EPI variation with respect to the Ref HP case。 The overall methodology adopted in this work is summarized in Figure 4。 The calculations are performed for an entire year featured by 12 typical days, one for each month, with a single minute time-step。 Accordingly, both ambient conditions (Tamb, GDNI, GDIFF) and loads are defined with this time-step starting from the measurement at the Solartech lab [31]