## 3 Results and Discussion
This fact has been analysed in depth by authors who proposed specific models for spectral effects in facades [92]. In addition, the boundary atmospheric conditions (aerosol optical depth and water vapour content) have to be taken into account. In future works, we aim to explore the range of surface tilt angles for which air mass-based spectral models are valid and when specific spectral models similar to those developed for facades in the mentioned reference need to be applied. In consequence, the spectral impact on the \(PR\) was not considered in this paper. Applying the proposed methodology to Building 42 leads to an estimated \(PR\) of 0.78 for 2019, which results in a deviation of less than 3% from the experimental \(PR\). The methodology was then applied to similar BIPV systems, but allowing for any possible tilt angle and orientation of the modules. Polar graphs for yearly irradiation and \(PR\) in Madrid were developed to aid in designing BIPV systems. To obtain more representative results for the case site, \(G_{\text{POA}}\) estimations were based on a Typical Meteorological Year (TMY) from Meteororm ([[https://meteonorm.com/en/](https://meteonorm.com/en/)]([https://meteonorm.com/en/](https://meteonorm.com/en/)), accessed on 5 March 2025), a global climatological database widely used as meteorological input for the simulation of solar applications and buildings (Figure 4). Figure 4: Annual solar irradiation heatmap for Madrid (from Meteororm TMY3 data). Figures 5 and 6 show the effects of temperature and angular losses, respectively. Losses related to temperature shift southwestward due to solar heat accumulation in the modules throughout the day. The lowest temperature power loss factor of 0.89 corresponds to temperature losses of 0.11, obtained at the optimal tilt angle for photovoltaic conversion and southwest orientation. On the other hand, angular losses are symmetrical with respect to the north-south direction, given that the sun's trajectory is similar before and after solar noon (i.e., the sun's zenith). Lower angular power loss factors occur at vertical positions and azimuths far from the south orientation. The maximum value of 0.97, which means minimum annual angular losses of 0.003, is obtained at a 35-degree tilt towards the Equator. The combination of temperature and angular losses with the other power loss factors (Table 2) leads to the total performance ratio of the system, shown in Figure 7. This heatmap represents the final performance ratio for Madrid using data from 2019, though it can be  
Figure 5: Annual temperature power loss factor (1-L\({}_{\text{temp}}\)) heatmap for Madrid in 2019 (based on CAMS and PVGIS irradiance data). Figure 6: Annual angular power loss factor (1-L\({}_{\text{AOI}}\)) heatmap for Madrid in 2019 (based on CAMS and PVGIS irradiance data). calculated for any desired timeframe using other input data (e.g., a TMY). As observed, the annual performance ratio in Madrid ranged 2019 between 0.74 and 0.82 as a function of the modules' positions. This graph helps evaluate the expected performance losses of a BIPV system depending on the azimuth and tilt angles of the module. The irradiation map (Figure 4), together with the \(PR\) map (Figure 7), allow the designer to estimate the PV generation of the BIPV system based on the position of the modules, which is also helpful when renovating buildings, as the PV potential for roofs and facades is assessed based on their orientation and tilt angle. This methodology can be applied to any other location worldwide. As an example, Figure 8 shows the obtained \(PR\) heatmap for an equivalent facade in Stockholm. In this case, the \(PR\) varies between 0.79 and 0.85.