# Probabilistic Analysis of Low-Emission Hydrogen Production from a Photovoltaic Carport
## 4 Results
### Probability of Monthly Energy Production Levels in Italy  
Identical calculations were performed for the monthly energy production of the photovoltaic system with a peak power of 6.3 kWp operating in Italy. The amounts of monthly energy production by photovoltaic systems in Italy also depend to a very large extent on seasonality related to the shift to different seasons. The highest energy production occurs in the spring and summer months, exceeding 700 kWh per month, similarly to Poland. The basic statistical data presented in Table 4 indicate that the highest monthly energy production by the photovoltaic system with a peak power of 6.3 kWp took place in July and amounted to 1132.73 kWh of energy. The lowest value of energy production took place in January and amounted to only 251.033 kWh. This means that in Italian geographic and climatic conditions, there is a more than 4-fold difference in energy production between the best and worst months of the year. Let us recall that this value was more than 16-fold for Poland. In Italy, in this region, snow falls very rarely in the winter months, and it does not often accumulate on photovoltaic panels. Energy production by the 6.3 kWp photovoltaic system is characterized by an average value of monthly energy production of 711.584 kWh with a standard deviation of 324.064 kWh. In comparison, these values for Poland were 529.221 kWh and 350.765 kWh, respectively. Thus, in the average approach, the system located in Italy produced almost 200 kWh more electricity per month than its counterpart located in Poland. The data from the Italian photovoltaic system also indicate a large difference in the amount produced in individual months. Additionally, the extended statistics presented in Table 5 clearly present that the energy production probabilities corresponding to the individual quantiles are very different.  
Afterward, an advanced probability analysis using the Metalog probability distribution family was also performed. The Cumulative Distribution Function (CDF) and Probability Density Function (PDF) generated by Genie 4.1 software for the monthly energy production of the 6.3 kWp peak of the photovoltaic system located in Italy are shown in Figure 11. Described by a fourth-degree polynomial, the PDF has a bimodal course. The first optimum (maximum) occurs for small amounts of monthly energy production of about 300 kWh. The second optimum (maximum) occurs for large amounts of monthly energy production of over 1100 kWh.  
Based on the data on the monthly energy production of the Italian photovoltaic system (presented in Figure 7), the Genie 4.1 software also created the models that constitute the knowledge base. The following question was asked: What is the probability of generating monthly energy equal to or less than 400 kWh by the tested photovoltaic system? Based  
\begin{table}
\begin{tabular}{c c} \hline  & **Energy Production [kWh]** \\ \hline Count & 12 \\ Minimum & 251.033 \\ Maximum & 1132.73 \\ Mean & 711.584 \\ StdDev & 324.064 \\ \hline \end{tabular}
\end{table}
Table 4: Basic statistical analysis of the energy generated monthly by a 6.3 kWp photovoltaic system in Italy.  
\begin{table}
\begin{tabular}{c c} \hline
**Probability** & **Energy Production [kWh]** \\ \hline
0.05 & 251.0330047607 \\
0.25 & 485.2600097656 \\
0.5 & 780.6019897461 \\
0.75 & 1028.311035156 \\
0.95 & 1132.729003906 \\ \hline \end{tabular}
\end{table}
Table 5: Extended statistical analysis of the energy generated monthly by a 6.3 kWp photovoltaic system in Italy.  
on the models available in the form of CDF and PDF, the database provides an answer: 0.25. Therefore, the probability of generating monthly energy greater than 400 kWh by the tested photovoltaic system is \(1-0.25=0.75\). The results of knowledge acquisition from the knowledge base are presented in Table 6.