# Enhancing Photovoltaic Power Predictions with Deep Physical Chain Model
## 4 Discussion  
The challenge of predicting solar power generation demands advanced approaches. In this context, the present study uses modern deep modeling techniques and, through data adjustments, exhibits promising results according to Table 15, where it can be seen that our model is superior to the state-of-the-art results in most cases of photovoltaic stations.  
The errors of stations 4 and 5 have a particular behavior, although in each block they are the stations that presented the greatest improvements in the forecasts, as well as being the stations with the lowest performance compared to the other stations. In Section 3.7, a possible reason for this particularity is already mentioned, but without more detail about the state and maintenance of the sensors, nothing conclusive can be stated.  
In any case, despite these possible errors, we see that the proposed model gives less priority to these stations to adjust to the rest of the stations. The above could mean that the model is overfitting to these plants, so we apply the latter on stations not seen in the training phase, the results of which are shown in Table 16. It is seen that the errors are by the results of the other stations, demonstrating that the good results of the proposed module do not correspond to overfitting, but rather derive from a correct generalization.  
Our proposed deep chain model outperforms state-of-the-art performance metrics, especially at stations with less accurate forecasts, highlighting the effectiveness of the Transformer Bi-LSTM in mitigating prediction errors. However, the deep chain model also faces a major challenge, the main being susceptible to cumulative errors.  
Although the feature engineering process helps by improving the forecasts of the chain blocks corresponding to GHI and decomposition, this does not have a great impact on the final intra-hour power forecasting, with the proposed model being mainly responsible for the good results.  
It should be remembered that this methodology has been developed without irradiance measurements in the array plane, so there is still a large margin for optimization in the transposition block, although most of the error comes from the NWP forecasts, which agrees with what is seen in the literature.  
In summary, both the deep chain model and the direct approach offer benefits and limitations, and the selection between them will depend on the particular requirements of the project and the available resources.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Metric** & \multicolumn{2}{c}{**Station**} & \multicolumn{1}{c}{**Mean**} \\  & **6** & **7** & **9** & \\ \hline MAE & 0.4774 & 0.7730 & 0.3705 & 0.5403 \\ RMSE & 0.8555 & 1.3770 & 0.6668 & 0.9664 \\ \(R^{2}\) & 0.9070 & 0.9078 & 0.9153 & 0.9100 \\ \hline \hline \end{tabular}
\end{table}
Table 16: Results of the deep chain model in stations not present during training. RMSE and MAE are measured in \([MW]\), and \(R^{2}\) is unitless.  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Model** & **Metric** & \multicolumn{6}{c}{**Station**} & \multicolumn{3}{c}{**Mean**} \\  & & **0** & **1** & **2** & **3** & **4** & **5** & **8** & \\ \hline Our best method & MAE & 0.192 & 0.850 & 0.671 & 0.711 & 1.318 & 1.712 & 0.783 & 0.891 \\ Best\({}_{Ipota}\) NWP\({}_{\text{Ipoa}}\) & RMSE & 0.362 & 1.610 & 1.272 & 1.317 & 2.433 & 3.233 & 1.457 & 1.669 \\ \hline Reference & MAE & 1.36 & 1.09 & 1.07 & 1.36 & 1.24 & 1.29 & - & 1.24 \\ GSTANN [22] & RMSE & 1.89 & 1.51 & 1.56 & 1.85 & 1.74 & 1.91 & - & 1.74 \\ \hline Reference & MAE & - & 1.286 & 0.961 & - & 1.391 & - & 1.030 & 1.167 \\ PSC-SVR [21] & RMSE & - & 2.152 & 1.521 & - & 2.337 & - & 1.699 & 1.927 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Comparison of obtained results with those present in the state of the art. RMSE and MAE are measured in \([MW]\).