# Neural Network Approach to MPPT Control and Irradiance Estimation
## 4 Simulation Results
### Simulated Data  
The neural network is trained with 200 pairs of \(G\) and \(T\), uniformly distributed within the ranges \(G\in\{50,1100\}\) and \(T\in\{5,50\}\). Each \(I\)-\(V\) curve consists of 100 operating points. Figure 6 shows the \(P\)-\(V\) curves of PV module and NN model for irradiance and temperature values which were not included in the training dataset. It can be seen that the \(P\)-\(V\) curves of the NN model coincide very well with those of the simulated model. The MSE for training data equals \(2.92\times 10^{-5}\), while the testing MSE is \(3.81\times 10^{-5}\).  
In the first MPPT example, the performance of the proposed algorithm is assessed for different values of \(G\). Precisely, during the first 30 iterations, the irradiance has value \(G=900\) W/m\({}^{2}\), after which it is changed to \(G=600\) W/m\({}^{2}\). In the first scenario, the NI&I algorithm is applied for the irradiance estimation. It may be observed from Figure 7b that the NI&I estimator converges in 15 iterations for \(P=1\). On the other hand, the convergence speed of both the NI&I and NMPPT algorithm is increased as \(P\) reaches higher values (Figure 7a). In the second scenario, the gradient irradiance estimator is coupled with the NMPPT algorithm. It can be seen from Figure 7b that the NGE has faster convergence speed than the NI&I, which, additionally, causes the slightly faster convergence speed of the NMPPT algorithm. Considering the trade-off between the computational complexity and performance, in the remaining analysis, we used the NMPPT and NI&I estimator for \(P=2\).  
Figure 6: Comparison between \(P\)-\(V\) curves of PV module generated by the equivalent circuit and NN model of the photovoltaic.  
Figure 7: Performance of the proposed algorithm for different values of \(P\).  
The second MPPT example describes the comparison between the NMPPT, P&O, EMPPT and CNNMMPT algorithm. 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 \(T=50\,^{\circ}\mathrm{C}\). Observe from Figure 8(a) that the CNNMMPT provides the optimal voltage instantaneously, while the NMPPT, EMPPT and P&O algorithm need 8, 20 and 75 iterations to reach the steady-state, respectively. On the other hand, the NMPPT exhibits the smallest steady-state error, without oscillations. The reason for this is that the NI&I has greater accuracy than the EEST and CNNEST irradiance estimators, as can be seen from Figure 8(b). Finally, in the P&O, the operating point oscillates about the MPP.  
In the last example, the irradiance and the temperature are linearly changed within the ranges \(G\in\{50,1050\}\), and \(T\in\{5,55\}\). By observing the Figure 9(a), it is possible to note that the NMPPT, EMPPT and CNNMPPT exhibit good tracking ability. The P&O has the slowest convergence speed, while the EMPPT has the largest steady-state error. It also can be seen that the NI&I estimator tracks the irradiance with the smaller error than the EEST and CNNEST (Figure 9(b)). The relative error between the predicted and true maximal power is shown in Table 1. Observe that, after the convergence, the proposed algorithm tracks the maximal power point with error less than 0.001%. Note also that in the EMPPT, P&O and CNNMMPT the relative error reaches the values 1.138%, 2.118% and 0.171%, respectively.  
Figure 8: Comparison of the algorithms under sudden change in irradiance.