*4.1. Parametric Study*

The impact of daily solar radiation, average daily outdoor air temperature, and ventilation air flow rate on the static thermal transmittance *Ust* was analyzed and shown in Figure 9a. The *Ust* was determined from measured data, gathered between 23:00 and 6:00 the next morning. It can be concluded that the *Ust* is practically independent of daily solar radiation *Hglob,90* (c2), and values in the middle of the air flow rate range are ~ 0.04 <sup>W</sup>/m2K lower when compared to that of the reference composite façade wall (c1) due to the increased thermal resistances of the BIPV and air gap. No significant impact of mid-range daily average outdoor air temperatures *Te,av* can be seen either. This result corresponds to the fact that composite wall is light-weight with limited potential for storing the (solar) heat. This also confirms that the thermal response through the previous day does not affect the heat response of the BIPV the next day, leading to the conclusion that energy efficient indicators can be determined by averaging data over the proposed time period (6:00 to 6:00+). The impact of the air flow rate *Va,i* can be noticed only when the air gap was not ventilated (*Ust* is lowered to the range between 0.80 to 0.85 <sup>W</sup>/m2K) and at its highest air flow rate, at which *Ust* increases to 10 <sup>W</sup>/m2K (c3). Some additional data would increase the credibility of this finding.

**Figure 9.** Static thermal transmittance *Ust* of the glazed BIPV façade structure with a forced ventilated air gap; (**a**) impact of the daily solar radiation *Hglob,90* received by the BIPV façade structure and average daily outdoor air *Te,avg* (equal to the temperature of the ventilation air at the inlet of the air gap); (**b**) impact of the solar radiation and ventilation air flow rate *Va,i*.

The dynamic thermal transmittance *Ue*ff shows a significantly greater dependence on the influencing parameters (Figure 10). In theory, at low daily solar radiation (*Hglob,90* < 300 Wh/day) dynamic thermal transmittance approaches static one (c1) regardless of the outdoor air temperature. At higher daily solar radiation *Ue*ff decrease linearly (c4), while it increases with the decreasing of the outdoor air temperature *Te,avg* (c2). The dynamic thermal transmittance *Ue*ff of BIPV is 0.2 <sup>W</sup>/m2K or lower if daily average outdoor temperature is above ~ 9 ◦C and the solar radiation is above 4000 Wh/day, and when the outdoor temperature *Te,avg* is above ~ 5 ◦C, the daily solar radiation *Hglob,90* will be not less than 2500 Wh/day, if BIPV is not ventilated (c3). The slope of *Ue*ff decrease is higher in case of non-ventilated BIPV (c5) when compared to the slope of *Ue*ff decrease in the case of ventilated BIPV (c4). The decrease of the *Ue*ff with increased ventilation air flow rate *Va,i* is more evident at higher air flow rates (C6), while it is not seen at daily solar radiation below 2000 Wh/day. Negative *Ue*ff were observed at the highest air flow rates. The wind velocity *vw* at the experiment location was so low (Table 1) during the whole period of experiment that it cannot be treated as impact parameter.

**Figure 10.** Dynamic thermal transmittance *Ue*ff of the BIPV façade structure with a forced ventilated air gap; (**a**) impact of the daily solar radiation Hglob,90 received by the BIPV façade structure and average daily outdoor air *Te,avg*; (**b**) impact of the solar radiation and ventilation air flow rate *Va,i*.

The average daily e fficiency of electricity production is shown in Figure 11. One must note that values are defined for the BIPV façade structure as whole, while PV cells only cover 60% of BIPV structure. The daily e fficiency η*PV,BIPV* increases slightly (c2) with daily solar radiation Hglob,90 above 2500 Wh/day, while at such conditions e fficiency is almost temperature independent (c1). The reason can be in the design of glazed BIPV, which contains two relatively thick glass panes (2 × 4 mm). By measurement it was determined that absorptivity of the transparent area of BIPV is ~ 19.5%. It was also discovered that an increase of the ventilation air flow rate *Va,i* causes only minor increase of efficiency because of the PV cells cooling (c3). It can be that at higher air flow rate the fully developed flow occurs at a larger distance from the inlet opening. Nevertheless, as mentioned before, the di fference between PV cell temperatures (meaning as measured—the temperature of the inner glass of the BIPV behind the PV cell) in the 2nd and 6th rows only di ffer for < 1–1.5 ◦C during clear sky conditions at air flow rates above 15 m<sup>3</sup>/h, while temperature di fferences up to 5.5◦C were noticed in similar weather conditions in case of buoyancy convection in closed air gap. This finding indicates that additional research will be useful in the future. In this case as well, we found no evidence of impact of the wind velocity *vw* on the PV cell e fficiency as well.

**Figure 11.** Average daily e fficiency of electricity production by glazed BIPV determined considering that surface area of PV cell in glazed BIPV is 60%; (**a**) impact of the daily solar radiation *Hglob,90* and average daily outdoor air *Te,avg*; (**b**) impact of the solar radiation and ventilation air flow rate . *Va*,*in*.

If supply air is predominantly preheated by heat losses through composite façade wall (c1 in Figure 12), the e fficiency of solar energy utilization η*a,BIPV* for preheating of the supply air for space ventilation may rise over the value of one. In practice, this is the case in days with low daily solar radiation *Hglob,90* (threshold is at ~500 Wh/day). Such cases appear at daily average outdoor air temperatures Te,avg below 8 ◦C (c2). Where daily solar radiation *Hglob,90* is above that threshold value, the η*a,BIPV* is in the range 0.50 to 0.75 showing a slightly negative trend due to the increased heat losses of the BIPV glazed façade structure (c3). Consequently, at daily solar radiation above 4000 Wh/day, it will be slightly below the 0.5. This means that the decrease of ventilation heat losses is comparable to the mechanical ventilation with heat recovery. Results also show a slight increase of e fficiency with the ventilation air flow rate . *Va*,*in* (c4), while no significant impact of the wind velocity *vw* on the η*a,BIPV* can be found from experimental results.

**Figure 12.** Average daily efficiency of solar radiation utilization for preheating of the supply air for space ventilation; (**a**) impact of the daily solar radiation *Hglob,90* and average daily outdoor air *Te,avg*; (**b**) impact of the solar radiation and ventilation air flow rate . *Va*,*in*.

Solar radiation that passed through glazed BIPV façade structure was absorbed on the opaque composite façade wall. Consequently, heat loss decreased or even turned into the heat gain. If solar heat gains exceed steady-state heat loss on the daily basis, the value of η*i,sol,BIPV* will be greater than zero. The heat gains are defined by the product of the ηi,sol,BIPV and daily solar radiation Hglob,90. Figure 13 shows how η*i,sol,BIPV* depends on influence parameters: daily solar radiation *Hglob,90*, daily average outdoor temperature *Te,avg*, and ventilation air volume flow rate *Va,i*. One must note, that only 40% of the total BIPV structure is transparent. The η*i,sol,BIPV* slightly rises with daily solar radiation if Hglob,90 is larger than 500 Wh/day, where it will be in the range between 0.06 and 0.08 (c1). In case of non-ventilated BIPV, it is significantly higher (c2)—between 0.10 and 0.12. The efficiency rise varies slightly with the outdoor air temperature *Te,avg* as well (c3). At lower solar radiation, the η*i,sol,BIPV* rises up to 0.30. Obviously, at such low solar energy potential, increased thermal resistance of the BIPV structure contributes more significantly to decreased heat losses than solar radiation itself. Ventilation air flow rate has a negative and quite small impact on the η*i,sol,BIPV*, but it must be considered in a multi-parametric regression model. A small negative impact of wind velocity *vw* was also noticed. Furthermore, it was noticed that heat flux that enters the building has a small-time delay because of the low thermal capacity of the composite façade wall (Figure 6b).

**Figure 13.** Average daily solar heat gains through composite façade wall behind the glazed BIPV façade structure expressed by efficiency η*i,sol,BIPV*; (**a**) impact of the daily solar radiation *Hglob,90* and average daily outdoor air *Te,avg*; (**b**) impact of the solar radiation and ventilation air flow rate . *Va*,*in*.

#### *4.2. Multi-Parametric Model of Overall E*ffi*ciency of Solar Energy Utilization*

In the previous section it was shown which variables have the greatest impact on the overall efficiency of solar energy utilization of the BIPV façade structure. To be able to predict energy efficiency of such structure in different climate conditions based on the diurnal data, multiple linear regression models were developed for each component of overall efficiency of solar energy utilization—η*PV,BIPV*, η*a,BIPV*, and η*i,sol,BIPV*. Statistical regression analysis was made within MS Excel using built-in LINEST function, which fits the data using the least squares method. The level of significance for the regression coefficients of each predictor (independent variable) were tested using Student's t-tests with built-in T.DIST.2T function. Only terms with *p*-value < 0.05 were used in the final multiple linear regression models. Developed models are of the form:

$$\ln p\_{PV,BIPV} = 0.01207 \cdot \ln \left( H\_{glab,90} \right) - 0.000414 \cdot \left( \overbrace{T\_{PV,ref} - T\_{e,\text{avg}}}^{25^{\circ}C} \right) - 0.000147 \cdot \dot{V}\_{a,i,\text{avg}} \tag{15}$$

$$
\eta\_{\text{fl,BIPV}} = \frac{340.775}{H\_{\text{glab,90}}} - 0.0783 \cdot T\_{\text{c,avg}} + 0.02807 \cdot \dot{V}\_{a\text{,avg},\text{\textdegree}} \tag{16}
$$

$$\eta\_{i, \text{sol,RIPV}} = \frac{7.867}{H\_{\text{g1ob,90}}} + 0.00152 \cdot \left(T\_i - T\_{e, \text{avg}}\right) + 0.0078 \cdot \ln\left(\dot{V}\_{a, i, \text{avg}}\right) - 0.0072 \cdot v\_{\text{w,avg}} \tag{17}$$

where all independent variables are daily integrals or average values. The accuracy of the developed multiple linear regression models of solar energy utilization efficiencies was tested with widely used indices [31,32]: the adjusted coefficient of determination *<sup>R</sup>2adj*, the normalized mean bias error *(NMBE)* and the coefficient of variation of the root-mean-square error *CV(RMSE)* which are defined by the following equations:

$$R^2\_{\
u \, \rm adj} = 1 - \frac{n-1}{n - (p+1)} \cdot \left(1 - R^2\right),\tag{18}$$

$$NMBE = \frac{1}{\overline{M}} \cdot \frac{\sum\_{i=1}^{n} (M\_i - P\_i)}{n - p} \cdot 100,\tag{19}$$

$$CV(RMSE) = \frac{1}{\overline{\overline{M}}} \cdot \sqrt{\frac{\sum\_{i=1}^{n} \left(M\_i - P\_i\right)^2}{n - p}} \cdot 100. \tag{20}$$

Detailed explanation as well as calibration criteria of ASHRAE and other agencies can be found in [31]. Figure 14 presents the comparison of individual efficiencies of overall efficiency of solar energy utilization obtained from measured values and determined with developed multiple linear regression models (Equations (15)–(17)). The statistical parameters are also shown on the figures.

It can be seen that *R2adj* exceeds the recommended value of 0.75 for all three regression models. Also, *NMBE* is within ± 5%, which is the calibration criteria in the case of monthly calculation methods. Only *CV(RMSE)*, which should be below 15%, is slightly higher in the case of η*a,BIPV*, which is probably is the consequence of the narrow range of ventilation air flow rates. Nevertheless, we can conclude that the developed multi-parametric regression models are adequate and can be used to evaluate the energy efficiency performance of the analyzed BIPV façade structure within the ranges of meteorological conditions that appeared during the experiments. It should be noted that the conditions during the experiment were quite typical for a moderate and continental climate.

**Figure 14.** Correlation of components of overall efficiency of solar energy utilization η*sol,BIPV* determined by experimental results and multi-parametric regression models; statistical indicators are also shown for (**a**) η*PV,BIPV*, (**b**) η*a,BIPV*, and (**c**) η*i,sol;BIPV*.
