# Some Applications of ANN to Solar Radiation Estimation and Forecasting for Energy Applications
## 5 Estimation of Tilted Global Irradiation (GTI) from Horizontal Global Irradiation (GHI)
### Results  
The five error metrics are presented in Table 5 (calculated on the basis of eight runs (each run corresponds to a different random weight initializing). The first column contains the number of neurons in the hidden layer.  
The nRMSE mean values and its corresponding standard deviation are presented in Figure 7 as an error-bar graph. An improvement appears until reaching four hidden neurons, then the nRMSE becomes almost constant and no improvement was observed. The dash points define the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Hidden Neurons**} & **MAE** & **nMAE** & **RMSE** & **nRMSE** & **MBE** \\ \cline{2-6}  & **Wh.m\({}^{-2}\)** & **\%** & **Wh.m\({}^{-2}\)** & **\%** & **Wh.m\({}^{-2}\)** \\ \hline
1 & 5.94 & 16.32 & 6.89 & 18.93 & \(-0.97\) \\
2 & 2.95 & 8.12 & 3.81 & 10.48 & \(-0.29\) \\
3 & 2.80 & 7.71 & 3.65 & 10.04 & \(-0.50\) \\
**4** & **2.41** & **6.63** & **3.21** & **8.81** & \(-\mathbf{0.31}\) \\
5 & 2.56 & 7.04 & 3.47 & 9.54 & \(-0.80\) \\
6 & 2.75 & 7.56 & 3.77 & 10.36 & \(-1.14\) \\
7 & 2.68 & 7.38 & 3.68 & 10.12 & \(-1.09\) \\
8 & 2.70 & 7.43 & 3.69 & 10.14 & \(-1.12\) \\ \hline \end{tabular}
\end{table}
Table 5: Average statistical parameters between measured and estimated global solar 5 min-irradiation on a 36.8\({}^{\circ}\) tilted plane for the station of Bouzareah. The bold line is the results for the best architecture.  
Figure 6: ANN architectures for the estimation of ETI.  
95% confidence interval of the prediction errors (calculated based on eight runs per architecture), the triangles and squares are the minimum and maximum observed errors, respectively. We observed the same trend for the variation of the nMAE. The best configuration is encircled in red.  
We conclude that an ANN with one hidden layer of four neurons is the best model. Moreover, it appears that the use of the azimuth does not provide any improvement. Thus, we will retain an ANN with four inputs and one hidden layer of four neurons, which have an average nRMSE of 8.81%, the best simulation with this ANN structure conduced to an nRMSE of 8.27%.  
To illustrate the good reliability of this optimized MLP, a period of seven days unknown to the network was plotted with measured and calculated data in Figure 8.  
A good relationship is observed between the modelled and measured data whatever the state of the sky is (clear, partially cloudy, and cloudy) because the nRMSE was under 10%, which is a good value for an nRMSE for such a short time step (5-min).  
Forecasting of Hourly Direct Normal (DNI) and Horizontal Global (GHI) Irradiation for a Time Horizon from 1 h to 6 h  
This forecasting work was realized from global horizontal (GHI) and normal beam (BNI) data measured at Odeillo, Pyrenees Orientales, located in the south of France (42\({}^{\circ}\)29 N, 2\({}^{\circ}\)01 E, 1550 m asl).  
Figure 8: Validation of the model for seven randomly chosen days (Bouzareah site).  
Figure 7: nRMSE evolution vs the number hidden neurons (Bouzareah site).