# Neural Network Approach to MPPT Control and Irradiance Estimation
## 4 Simulation Results
### Experimental Data  
The NN is trained for 500 different values of \(G\) and \(T\), distributed in the ranges \(\{50,1100\}\) and \(\{5,50\}\), respectively (Figure 10). Each \(I\)-\(V\) curve contains 180 operating points. Figure 11 represents the \(P\)-\(V\) curves for values of irradiance and temperature which were not included in the training dataset. The subscripts \(e\) and \(s\) denote the NN models/NMPPT algorithms trained by experimental/simulated data, respectively. It can be seen that the \(P\)-\(V\) curves of the NN\({}_{e}\) model coincide very well with the measured curves. The MSE for training data equals 0.0027, while the testing MSE is 0.0028. On the other hand, the MSE between the current generated by the NN\({}_{s}\) model and measured current equals 0.0612.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(k\) & \(G\) & \(P_{max}\) & \multicolumn{4}{c}{**Prediction Error (\%)**} \\ \hline  & & & **NMPPT** & **P\&O** & **EMPPT** & **CNNMPT** \\ \hline
20 & 140 & 59.429 & 18.881 & 32.397 & 56.772 & 0.251 \\
40 & 240 &  
In the first example, we performed a comparison between the considered algorithms under a sudden change in irradiance and temperature. Until the 100 th iteration, the irradiance and the temperature are \(G=320\,\mathrm{W}/\mathrm{m}^{2}\) and \(T=10\,^{\circ}\mathrm{C}\), when they change to the values \(G=725\,\mathrm{W}/\mathrm{m}^{2}\) and \(T=50\,^{\circ}\mathrm{C}\). It can be perceived from Figure 12a that the CNNMMPT provides the optimal voltage instantaneously, while the \(\mathrm{NMPPT}_{e}\), \(\mathrm{NMPPT}_{s}\), \(\mathrm{EMPPT}\) and P&O algorithm need 20, 23, 40 and 75 iterations to reach the steady-state, respectively. Note also that the \(\mathrm{NMPPT}_{e}\) has the smallest steady-state error, followed by the \(\mathrm{NMPPT}_{s}\), \(\mathrm{EMPPT}\), P&O and CNNMPPT. This behavior can be explained by the fact that EEST and \(\mathrm{NNEST}\) have lower accuracy, which can be observed from Figure 12b.  
Eventually, the last example focuses on the two time-varying irradiance and temperature profiles. Corresponding simulation results are presented in Figures 13 and 14. A similar conclusion as in the previous example can be drawn here. The NMPPT algorithm and NI&I estimator, which are based on the experimental data, provide the best steady-state performance. On the other hand, both the \(\mathrm{NMPPT}_{s}\) and \(\mathrm{EMPPT}\) exhibit acceptable performance. It can also be seen that the NI&I\({}_{s}\) has greater accuracy than the EEST and \(\mathrm{NNEST}\). The P&O algorithm has the slowest tracking speed and exhibits oscillations in the steady-state. Finally, the CNNMPT for some irradiance levels has good accuracy, while for some irradiance levels exhibits the worst performance. The relative error between the predicted and true maximal power for different irradiance level is shown in Table 2. Observe that the \(\mathrm{NMPPT}_{e}\) tracks the maximal power point with error less than 0.1%. Note also that in the \(\mathrm{NMPPT}_{s}\), \(\mathrm{EMPPT}\), \(\mathrm{P\&O}\) and CNNMMPT the relative error reaches the values 0.2259%, 0.408%, 1.856% and 2.586%, respectively.  
Figure 11: Comparison between measured _P-V_ curves and _P-V_ curves generated by NN models.  
Figure 10: The experimental data used for the training of the NMPPT.  
Figure 12: Comparison of the algorithms under sudden change in irradiance.  
Figure 13: Comparison of the algorithms under time varying profile of the solar irradiance.