## 4 Conclusions  
The PV modules utilized in this study showed very high energy efficiency, but only in months with favorable conditions. This is a typical situation for temperate climates, as well as for most countries in the middle latitudes. The ANN is an efficient and precise method for predicting the output of PV systems in Poland. The proposed methodology, with an MRE of around 10.78%, is a good starting point for the optimization of energy generation and consumption and provides competitive accuracy compared with other similar works [55, 56]. The case study indicated that the application of the ANN leads to a significant increase in profits (annually) and results in the reduction of CO\({}_{2}\) emission. The most significant benefits can be seen for months with moderate energy production. The ANN created in this study indicates significant advantages compared to similar approaches that can be found in the literature [57]. Besides typical parameters such as average daily solar irradiation, it also takes into account additional factors that affect the effectiveness of photovoltaic panels, such as ambient temperature, precipitation (water on PVs left over after rain muddies its works), or even the day of the year, as the latter indirectly carries information about the angle of the sun. The last aspect is especially uncommon compared with similar studies [59]. This allowed for modeling much more comprehensive and sensitive subtleties in the process.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Month** & & **March** & **May** & **December** &
\begin{tabular}{c} **Annual** \\ **(Approximated)** \\ \end{tabular} \\ \hline Energy coverage & Optimized & 98.13 & 98.90 & 36.85 & 996.03 \\ (\%) & Unoptimized & 84.25 & 94.41 & 36.74 & 898.95 \\ Installation gain & Optimized & 31.73 & 67.08 & \(-\)52.18 & 235.08 \\ (\(\xi\)) & Unoptimized & 29.42 & 66.34 & \(-\)52.20 & 218.94 \\ Emission reduction & Optimized & 452.26 & 455.81 & 169.83 & 4590.49 \\ (kgCO\({}_{2}\)) & Unoptimized & 388.29 & 435.12 & 169.33 & 4143.07 \\ \hline \end{tabular}
\end{table}
Table 1: Summary of economic analysis of case studies.  
**Supplementary Materials:** The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app14072764/s1](https://www.mdpi.com/article/10.3390/app14072764/s1)]([https://www.mdpi.com/article/10.3390/app14072764/s1](https://www.mdpi.com/article/10.3390/app14072764/s1)), Table S1: Summary of case study data in [kWh].  
**Author Contributions:** K.P.: Conceptualization, Methodology, Formal analysis, Writing--Original Draft; M.C.: Investigation, Formal analysis, Writing--Original Draft; E.W.-J.: Conceptualization, Data Curation; W.L.: Investigation, Resources; M.K.: Supervision, Resources. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was financed by a statutory activity from the Polish Minister of Science and Higher Education.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are available on request due to restrictions.  
**Conflicts of Interest:** Author [PERSON] was employed by the company Innovation and Implementation Company Ekomotor Ltd., 1A Wyscigowa Street, 53-011 Wroclaw, Poland. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.