*3.1. Electricity Production*

The amount of diurnal produced electricity was determined by analytical model considering the measured values of influenced parameters in each time step of observation Δ*tmeas*. Daily amount of produced electricity is determined by equation:

$$E\_{PV} = \frac{1}{60} \sum\_{\text{tsr}}^{\text{tss}} A\_{PV} \cdot n\_{PV} \cdot \text{K}\_T \cdot \text{K}\_G \cdot G\_{\text{glab},\emptyset} \Delta t\_{\text{meas}} \left(\frac{\text{Wh}}{\text{day}}\right) \tag{3}$$

where *tsr'* and *tss'* are sunrise and sunset time relative to the BIPV structure, respectively, indicating the time frame when PV cells produce electricity. *KT* is the efficiency factor that corresponds to corrected PV cell efficiency and includes temperature coefficient β, which depends on PV cell technology. Value −0.46%/K was assumed for m-Si cells [28–30]. *APV* and *nPV* are the area of an individual PV cell (0.156 × 0.156 m) and the number of PV cells in the BIPV [15,19]. Because BIPV has relatively thick glass layers (4 + EPA + 4 mm, λ 0.76 W/mK), the PV cell temperature *TPV* was modelled by combining the heat transfer model and measurements of surface temperature on the outer and inner glass. The surface glass temperatures were measured behind the 2nd row and 6th row of the PV cell (*TBIPV,2*, *TBIPV,6*). It was found that in the case of ventilated air gap, there was not a significant difference between both temperatures, and an average value was used as the representative surface glass temperature. According to the CFD computer simulations, the combined surface heat transfer coefficient *hr*+*c,e* 15 <sup>W</sup>/m2K and *hr*+*c,i* 6 <sup>W</sup>/m2K were assumed and PV cell temperature *TPV* is approximated in the following way:

$$K\_T = \eta\_{ref} \cdot \left( 1 + \beta \cdot \left( \left( \overbrace{T\_{PV,si} + 0.0064 + 0.0013 \cdot G\_{glab,\theta}}^{T\_{PV}} \right) - 25 \right) \right) \tag{4}$$

where *TPV,si* is temperature of the BIPV surface behind the PV cell towards the air gap. The reference efficiency η*ref* was taken from producer data [19] and is equal to 0.185. Solar irradiation correction factor *KG* considers the decrease of PV cell efficiency at low level of solar irradiation [15]:

$$K\_{\mathcal{S}} = 1 \text{ if } G\_{\mathcal{glab};90} \ge 200 \frac{\text{W}}{\text{m}^2} \text{ and } \frac{0.029 \cdot \ln\left(G\_{\mathcal{glab};90}\right) - 0.0037}{\eta\_{\text{ref}}} \text{ if } G\_{\mathcal{glab};90} < 200 \frac{\text{W}}{\text{m}^2}. \tag{5}$$

To investigate the impact of ventilation of the air gap on PV cell overheating, diurnal overheating hours *OHH* was introduced. *OHH* is defined as diurnal sum of the difference between modeled PV cell temperature and PV cell reference temperature 25 ◦C:

$$
\delta \mathcal{O} HH = \frac{1}{60} \sum\_{\text{tsr}}^{\text{tss}} \delta \cdot (T\_{PV} - 25) \cdot \Delta t\_{\text{mass}} \,\delta = 1 \,\text{if} \,(T\_{PV} - 25) > 0 \,\text{otherwise} \,\delta = 0 \,\left(\frac{\text{Kh}}{\text{day}}\right) . \tag{6}
$$

As an example, Figure 5 shows measured data for two selected days—the clear sky and overcast cloudy day, and diurnal variables involved in energy efficiency modeling—daily solar radiation received by BIPV *Hglob,90*, average daily outdoor air temperature during PV cell operation *Te,avg,PV*, average wind velocity during PV cell operation time *vW,avg,PV* (m/s), and . *Va*,*in* ventilation air flow rate.

In the case presented in Figure 5a, BIPV was not ventilated, while in the case shown in Figure 5b BIPV was ventilated with air flow rate . *Va*, *in*. Concerning the surface glass temperature behind the PV cells (*TBIPV,2* and *TBIPV,6*), it can be seen that temperatures differ only in the case of non-ventilated (closed) air gap (mark c) as consequence of buoyancy driven convection—by solar irradiation during day-time and by heat flux due heat losses during the night-time. This causes counter flow pattern during the night-time and higher *TBIPV,6* when compared to *TBIPV,1*.

**Figure 5.** Graphs showing instant η*PV* and average diurnal PV cell efficiency η*PV,avg*, instant electricity power . *EPV*, and diurnal production of electricity *EPV* (**a**), PV cell temperatures (glass surface temperatures behind PV cell towards ventilated air gap) in the 2nd (*TBIPV,2*) and the 6th row (*TBIPV,6*) in BIPV, overheating hours (*OHH)* and selected meteorological data—solar irradiation *Gglob,90*, diurnal solar radiation *Hglob,90*, and instant and daily average outdoor air temperature (*Te*, *Te,avg*) (**b**).

#### *3.2. Preheating of Ventilation Air*

The air gap formed by BIPV was force ventilated by outdoor air. Two by two temperature sensors were installed at the outlet openings, on both sides of fans. It was found that an increase of the air temperature caused by fans can be neglected. Data on air velocity in the center of the supply pipe, gathered by a hot-wire anemometer, was used to determine volumetric air flow using a continuity equation. Because air flow is turbulent even in case of lowest flow rate set, the volume (and mass) air flow rate was determined by averaging velocity using the Blasius formula and continuity equation. Daily heat transferred into the building by preheated air was determined by the sum of one-minute experimental data over the 24-hour period starting each day at 6:00 in the morning:

$$Q\_{a,in} = \frac{1}{60} \sum\_{\text{fe00}}^{+\text{ef00}} \frac{1}{3600} \cdot \rho\_a \cdot c\_{p,a} \cdot \dot{V}\_{a,in} \cdot (T\_{a,in} - T\_e) \cdot \Delta t\_{\text{man}} \left(\frac{\text{Wh}}{\text{day}}\right) \tag{7}$$

.

where ρ*a* is air density, *cp,a* specific heat capacity of air, *Va*,*in* is volume air flow rate, *Ta,in* is supply air temperature, and *Te* is outdoor temperature. Preheating efficiency of ventilation air, value that can be compared to the heat recovery efficiency in case of mechanical ventilation with recovery unit, is defined by averaging supply air, outdoor air, and indoor air temperatures over the occupied office hours (8:00–17:00), assuming constant ventilation air flow rate during observation period:

$$
\kappa\_{\nu} = \left(\frac{T\_{a,\text{in.avy}} - T\_{c,\text{avy}}}{T\_{i,\text{avy}} - T\_{c,\text{avy}}}\right)\_{8\,\text{k}0}^{17\,\text{k}0} \cdot 100 \, (\%). \tag{8}
$$

Preheating efficiency ε*v* can be above 100% if *Ta,in,avg* > *Ti,avg,* and *Te,avg* < *Ti,avg*. Figure 6 shows an example of experimental data for the selected days. The average air inlet temperature during work-hours *Ta,in,avg*, the integrated solar radiation *Hglob,90* received by the BIPV, and heat transferred by air into the building . *Qa*,*in* are shown as well. Because average supply air temperature *Ta,in,avg* in Figure 6b is above average indoor air temperature *Ti,avg* while average outdoor temperature *Te,avg* is below *Ti,avg*, the air preheating efficiency is above 100%.

**Figure 6.** Graphs showing outdoor and indoor air temperatures and the temperature of supplied preheated air (*Te*, *Ti*, and *Ta,in*); velocity, ventilation air volume flow rate, and heat flux by preheated air (*va*, . *Va*,*in*, and . *Qa*,*in*); average ventilation air temperature during office occupant hours *Ta,in,avg*; air preheating efficiency (<sup>ε</sup>*v*); as well as solar irradiation *Gglob,90*; and diurnal solar radiation *Hglob,90*; as well as diurnal heat transferred into the ventilated space by preheated air *Qa,in*; (**a**) for 14 January 2020 and (**b**) for 28 February 2020.
