# Enhancing Photovoltaic Power Predictions with Deep Physical Chain Model
## 3 Results
### GHI Deep Model  
The Transformer Bi-LSTM model applied on the GHI block gives encouraging performance results under various conditions. When compared to the base error of NWP\({}_{\text{GHI}}\), which has a MAE of 120 [W/m\({}^{2}\)] and a RMSE of 175 [W/m\({}^{2}\)], two methods are implemented. In the first method, the variable NWP\({}_{\text{GHI}}\) is employed, and in the second one, Best\({}_{\text{GHI}}\) is added. It should be remembered that the variables \(\cos(\theta_{\text{zenith}})\) and \(\sin(\theta_{\text{azimuth}})\) are used as the basis for all models. The results are listed in Table 9. \begin{table}
\begin{tabular}{c l c c c c c c c} \hline \hline
**Metric** & **Model** & \multicolumn{6}{c}{**Station**} & \multicolumn{3}{c}{**Mean**} \\  & & **0** & **1** & **2** & **3** & **4** & **5** & **8** & \\ \hline MAE & Skartveit & 107 & 57 & 112 & 107 & 149 & 85 & 67 & 98 \\  & Abreu & 115 & 60 & 124 & 108 & 136 & 93 & 62 & 100 \\  & Erbs & 112 & 58 & 121 & 108 & 179 & 90 & 62 & 104 \\  & BRL & 102 & 62 & 99 & 124 & 209 & 81 & 91 & 110 \\  & Dirindex & 129 & 79 & 130 & 103 & 158 & 103 & 67 & 110 \\  & NWP\({}_{\text{DHI}}\) & 104 & 99 & 125 & 142 & 155 & 110 & 90 & 118 \\  & Engerer & 109 & 194 & 102 & 113 & 227 & 155 & 210 & 158 \\  & DISC & 139 & 182 & 101 & 181 & 183 & 167 & 230 & 169 \\  & Dirntnt & 144 & 182 & 103 & 186 & 187 & 164 & 230 & 171 \\ \hline RMSE & Skartveit & 167 & 87 & 166 & 145 & 217 & 120 & 97 & 143 \\  & Abreu & 185 & 94 & 188 & 159 & 207 & 136 & 92 & 152 \\  & BRL & 149 & 90 & 139 & 155 & 302 & 118 & 122 & 154 \\  & Erbs & 181 & 92 & 182 & 156 & 260 & 131 & 92 & 156 \\  & Dirindex & 203 & 111 & 191 & 156 & 222 & 142 & 103 & 161 \\  & NWP\({}_{\text{DHI}}\) & 174 & 138 & 198 & 204 & 244 & 157 & 115 & 176 \\  & DISC & 193 & 235 & 142 & 246 & 249 & 221 & 283 & 224 \\  & Dirntnt & 199 & 237 & 145 & 251 & 252 & 218 & 283 & 226 \\  & Engerer & 163 & 287 & 144 & 144 & 326 & 256 & 294 & 231 \\ \hline \(R^{2}\) & Skartveit & 0.31 & 0.53 & 0.52 & 0.45 & 0.30 & 0.47 & 0.28 & 0.41 \\  & BRL & 0.39 & 0.51 & 0.60 & 0.45 & 0.02 & 0.48 & 0.29 & 0.39 \\  & DISC & 0.47 & 0.21 & 0.63 & 0.33 & 0.23 & 0.37 & 0.25 & 0.36 \\  & Dirntnt & 0.43 & 0.21 & 0.62 & 0.30 & 0.23 & 0.37 & 0.24 & 0.34 \\  & Abreu & 0.17 & 0.48 & 0.37 & 0.35 & 0.33 & 0.38 & 0.23 & 0.33 \\  & Erbs & 0.20 & 0.50 & 0.41 & 0.38 & 0.17 & 0.42 & 0.23 & 0.33 \\  & Dirindex & 0.11 & 0.46 & 0.39 & 0.37 & 0.31 & 0.41 & 0.18 & 0.32 \\  & Engerer & 0.43 & 0.10 & 0.61 & 0.48 & 0.29 & 0.08 & 0.19 & 0.31 \\  & NWP\({}_{\text{DHI}}\) & 0.18 & 0.03 & 0.21 & 0.01 & 0.16 & 0.17 & 0.07 & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of physical decomposition models with NWP\({}_{\text{DHI}}\) reference. RMSE and MAE are measured in [W/m\({}^{2}\)], and \(R^{2}\) is unitless. \begin{table}
\begin{tabular}{l l c c c c c c c c} \hline \hline
**Predictors** & **Metric** & \multicolumn{6}{c}{**Station**} & \multicolumn{3}{c}{**Mean**} \\  & & **0** & **1** & **2** & **3** & **4** & **5** & **8** & \\ \hline NWP\({}_{\text{GHI}}\) & MAE & 39 & 44 & 54 & 46 & 80 & 59 & 58 & 54 \\  & RMSE & 73 & 93 & 98 & 88 & 159 & 114 & 109 & 105 \\  & \(R^{2}\) & 0.82 & 0.89 & 0.88 & 0.87 & 0.93 & 0.91 & 0.86 & 0.88 \\ \hline NWP\({}_{\text{GHI}}\) & MAE & **39** & **44** & **53** & **45** & **79** & **59** & **57** & **54** \\ Calibration\({}_{\text{MAE}}\) & RMSE & 73 & 94 & 98 & 86 & 158 & 115 & 108 & 105 \\  & \(R^{2}\) & 0.93 & 0.89 & 0.87 & 0.91 & 0.82 & 0.86 & 0.88 & 0.88 \\ \hline Reference NWP\({}_{\text{GHI}}\) & MAE & 81 & 93 & 108 & 102 & 217 & 127 & 114 & 120 \\  & RMSE & 123 & 162 & 149 & 140 & 310 & 186 & 158 & 175 \\  & \(R^{2}\) & 0.81 & 0.72 & 0.71 & 0.79 & 0.55 & 0.66 & 0.76 & 0.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results of deep GHI model block. RMSE and MAE are measured in [W/m\({}^{2}\)], and \(R^{2}\) is unitless. Both methods achieve an average MAE of 54, an RMSE of 105, and an \(R^{2}\) of 0.88.