## 4 Results and Discussion
### Multi-Step Ahead PV Power Forecasts  
Precise multi-step forecasts are essential to managing the operation of PV systems appropriately. Now, we assess the capability of the eight methods for multi-step ahead forecasting of PV power output using data from Data Set 1 (a 243 kW parking lot canopy array in the US) and Data Set 2 (a 9 MW PV system in Algeria). Based on the past measurements, \(x=[x_{1},x_{2},\ldots,x_{l}]\), the computed single-, two-, and multistep-ahead forecast are respectively \(x_{l+1}\), \(x_{l+2}\), and \(x_{l+n}\). The 5, 10, 15 steps-ahead forecastings of PV power data based on the testing data of the Parking lot canopy array dataset and the Adrar PV system are tabulated in Table 5.  
We can easily observe that, for all data sets, except BiLSTM and ConvLSTM, the other models performed consistently reasonable forecasting results five-, ten-, fifteen-step-ahead forecasting. Figure 10: NRMSE by method based on the testing datasets from the two considered PV systems. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & & & **Algerian** & **PV** & **System** & & **Parking** & **Lot** & **Canopy** & **Array** \\ \hline
**Model** & **Steps** & **Minutes** & **RMSE** & **MAE** & **R2** & **EV** & **RMSE** & **MAE** & **R2** & **EV** \\ \hline BiLSTM & 2 & 30 & 1591.639 & 1303.28 & 0.675 & 0.876 & 18.309 & 10.011 & 0.951 & 0.953 \\ CNN & 2 & 30 & 1007.54 & 613.344 & 0.87 & 0.888 & 24.105 & 16.534 & 0.915 & 0.916 \\ ConvLSTM2D & 2 & 30 & 359.128 & 262.526 & 0.983 & 0.991 & 17.31 & 7.786 & 0.956 & 0.956 \\ GRU & 2 & 30 & 910.589 & 770.907 & 0.894 & 0.936 & 17.454 & 7.897 & 0.955 & 0.955 \\ LSTM & 2 & 30 & 376.359 & 285.324 & 0.982 & 0.982 & 17.47 & 7.914 & 0.955 & 0.955 \\ RBM & 2 & 30 & 390.581 & 213.174 & 0.98 & 0.98 & 17.564 & 7.847 & 0.955 & 0.955 \\ RNN & 2 & 30 & 1448.063 & 1170.279 & 0.731 & 0.868 & 18.101 & 8.474 & 0.952 & 0.953 \\ SAE & 2 & 30 & 477.986 & 255.739 & 0.971 & 0.974 & 17.724 & 8.783 & 0.954 & 0.955 \\ VAE & 2 & 30 & 303.091 & 117.701 & 0.988 & 0.988 & 17.31 & 7.566 & 0.956 & 0.956 \\ BiLSTM & 3 & 45 & 374.303 & 186.576 & 0.982 & 21.855 & 12.028 & 0.93 & 0.93 \\ CNN & 3 & 45 & 1166.323 & 749.863 & 0.826 & 0.84 & 26.135 & 18.617 & 0.9 & 0.9 \\ ConvLSTM2D & 3 & 45 & 370.848 & 260.922 & 0.982 & 0.986 & 21.315 & 10.397 & 0.933 & 0.934 \\ GRU & 3 & 45 & 395.163 & 225.154 & 0.98 & 0.98 & 21.78 & 11.596 & 0.93 & 0.932 \\ LSTM & 3 & 45 & 367.048 & 194.691 & 0.983 & 0.983 & 21.485 & 9.707 & 0.932 & 0.932 \\ RBM & 3 & 45 & 579.104 & 341.511 & 0.957 & 0.958 & 21.76 & 10.434 & 0.931 & 0.931 \\ RNN & 3 & 45 & 428.615 & 284.6 & 0.976 & 0.977 & 22.458 & 11.99 & 0.926 & 0.93 \\ SAE & 3 & 45 & 521.723 & 255.686 & 0.965 & 0.969 & 21.823 & 10.335 & 0.93 & 0.93 \\ VAE & 3 & 45 & 344.468 & 164.635 & 0.985 & 0.985 & 21.461 & 9.878 & 0.932 & 0.932 \\ BiLSTM & 4 & 60 & 432.448 & 229.34 & 0.976 & 0.977 & 23.687 & 13.131 & 0.918 & 0.92 \\ CNN & 4 & 60 & 494.999 & 567.358 & 0.884 & 0.897 & 27.022 & 17.502 & 0.893 & 0.9 \\ ConvLSTM2D & 4 & 60 & 462.93 & 360.618 & 0.972 & 0.978 & 23.174 & 12.113 & 0.921 & 0.921 \\ GRU & 4 & 60 & 538.857 & 381.686 & 0.963 & 0.965 & 23.252 & 11.681 & 0.921 & 0.921 \\ LSTM & 4 & 60 & 533.916 & 355.042 & 0.963 & 0.966 & 23.298 & 11.912 & 0.92 & 0.921 \\ RBM & 4 & 60 & 614.722 & 379.406 & 0.951 & 0.951 & 23.321 & 11.605 & 0.92 & 0.92 \\ RNN & 4 & 60 & 476.67 & 297.196 & 0.971 & 0.971 & 24.152 & 13.208 & 0.914 & 0.918 \\ SAE & 4 & 60 & 554.917 & 274.536 & 0.96 & 0.961 & 23.604 & 11.768 & 0.918 & 0.918 \\ VAE & 4 & 60 & 420.029 & 193.157 & 0.977 & 0.978 & 23.134 & 11.664 & 0.921 & 0.921 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Validation metrics for multistep-step-ahead forecasts. For instance, the VAE model achieved R2 values of 0.902,0.873, 0.856 for five-, ten-, fifteen-step-ahead forecasting when using the first for Data Set 1, R2 values of 0.951,0.877, 0.818 for Data Set 2. The RNN, GRU, RBM, SAE, and VAE models performed about equally in terms of R2, MAPE, and RMSE in all cases.