# Power Prediction in Photovoltaic Systems with Neural Networks: A Multi-Parameter Approach
## 4 Power Prediction in Photovoltaic Systems with Neural Networks

Table 2: Monthly average value of meteorological data, and actual and estimated powers. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Radiation** & **Temperature** & **Wind** & **Average** & **Cloudiness** & **Average** \\  & **(W/m2)** & **(\({}^{\circ}\)C)** & **Speed (m/s)** & **Humidity (\%)** & **(Oktas)** & **Power (kW)** \\ \hline Radiation Effect & **8.1** & 27.7 & 3.0 & 30.5 & 0 & 7383.58 \\
5.7 & 26.5 & 2.8 & 30.4 & 0 & 6709.8 \\ \hline Temperature & 3.2 & \(\mathbf{-0.2}\) & 1.7 & 78.5 & 1.4 & 5015.01 \\ Effect & 3.2 & \(\mathbf{0.6}\) & 1.7 & 82.9 & 1.6 & 4413.85 \\ \hline Wind Effect & 2.4 & \(11.5\) & **3.1** & 50.8 & 5.8 & 3394.94 \\  & 2.4 & \(12.8\) & **1.8** & 51.4 & 5.7 & 2235.02 \\ \hline Cloud Effect & 6.9 & 15 & 2.0 & 51.8 & **1.5** & 7553.13 \\
5.9 & 15.5 & 2.1 & 49.8 & **0.8** & 7623.59 \\ \hline  & 8.1 & 27.7 & 3.0 & **30.5** & 0 & 7383.58 \\  & 8.1 & 28.0 & 2.8 & **28.2** & 0.3 & 7384.22 \\ Humidity Effect & 8.1 & 30.6 & 3.1 & **22.1** & 0.2 & 7256.56 \\  & 8.1 & 29.4 & 3.3 & **18.5** & 0 & 7450.05 \\  & 8.1 & 29.1 & 2.9 & **19.2** & 0.4 & 7290.49 \\ \hline \end{tabular}
\end{table} 
Table 3: Some data used in the study. negative impact of temperature on PV power generation is apparent. In the data selected to analyze the influence of wind, there is an almost two times difference in wind speed, and an increase in wind speed has positively affected power generation. In a system that generates power from solar irradiation, an increase in cloud cover naturally has a negative impact, which is clearly visible in the table. While the total radiation for both days is 6.9 W/m\({}^{2}\), as expected, the higher cloud cover has adversely affected power generation. However, no significant effect of humidity on the PV system has been identified. Finally, the graphs illustrating the variation of meteorological data for July and December, representing summer and winter months, are presented in Figure 8.  
Figure 8: Meteorological data for July and December (**a**) Radiation (**b**) Temperature (**c**) Wind Speed (**d**) Humidity (**e**) Cloudiness. From the data obtained in the study, the changes in daily average actual and estimated power for July and December are given in Figure 9a,b, respectively. In both graphs, it can be observed that the power predicted by the ANN closely follows the actual power values. As seen in Figure 9, the maximum difference between actual and estimated power values are 314.5 kW and 433.77 kW, which correspond to 5.5% and 11.5% for July and December, respectively. As seen in Figure 8, there is a rapid fluctuation in the meteorological data in December, which has yielded a high prediction error. As a final validation step, cross-validation was performed to ensure the reliability and generalizability of the proposed model. Cross-validation is a statistical technique that divides the dataset into multiple subsets, allowing the model to be trained and tested on different data splits [22]. In this study, 5-fold cross-validation was applied, where the dataset was divided into five equal parts. The model was trained on the 5-1 subset and tested on the remaining subset in each iteration, and the process was repeated five times. This approach helps reduce overfitting and provides a more robust assessment of the predictive performance of the model [22]. To further validate the performance of the proposed ANN model, a comparative analysis was conducted using cross-validation with alternative machine learning techniques, including SVM, GPR, LR, Ensemble methods, and DT, as presented in Figure 10.  
As summarized in Figure 10, the results show that the ANN model achieved the lowest MSE of 0.13676 and the highest R value of 0.98. This confirms that the proposed ANN model outperforms the traditional methods in PV power prediction. Figure 10: R and MSE values of alternative machine learning techniques. Figure 9: Estimated and actual daily average power values (**a**) July (**b**) December.