## 5 Digital Simulation Experiments and Analysis  
### Simulation Case 1  
The purpose of testing the rapidity and effectiveness of tracking the MPP voltage of PV arrays under PSC is to verify the GMPPT nonlinear control method proposed in simulation case 1. The performance of the proposed MPPT method based on nonlinear control is evaluated under conditions where the irradiance changes rapidly, by using Matlab/Simulink. The PV array model proposed in this paper is shown in Figure 2b, where \(N_{s}=6\), \(N_{p}=12\), and \(N_{s1}=3\) is region A, and \(N_{s2}=3\) is shown as area B. The parameters of the solar module are presented in Table 1. The irradiances of regions A and B are shown in Figure 9. The simulation parameters are presented in Appendix B, and the simulation results are shown in Figures 9-14. The peaks under 200 V in Figure 9 are defined as the left peaks and the peaks above 200 V are defined as the right peaks. It can be seen from Figure 9 that during the simulation the irradiance can change gradually or abruptly. The amplitude of the MPP voltage also deviates frequently by more than 150 V; that is, the MPP keeps moving between the left and right peaks with changes in irradiance. The MPP is on the right peak in area a of Figure 9A. As the irradiance increases, the MPP moves to the left peak at 0.16 s and keeps increasing, as shown in Figure 9B. At 0.35 s, the MPP is still on the left peak when the irradiance decreases from 1000 W/m\({}^{2}\) to 550 W/m\({}^{2}\) suddenly. At 0.4 s, the MPP on the left peak shifts to the right peak when the irradiance decreases from 550 W/m\({}^{2}\) to 250 W/m\({}^{2}\), as shown in area d of Figure 9A. At 0.45 s, 0.5 s, 0.55 s, and 0.74 s, the irradiance changes as shown in Figure 9a, accompanied by a shift of the MPP from the left peak to the right peak. In order to verify the method proposed in this paper, the simulation conditions are designed to simulate a variety of changes in the PV array. The simulation conditions are consistent with the analysis in Section 2.3. It can be observed from Figure 10 that, in areas a, b, c, e, g, and h, the AFL method can track the MPP voltage quickly and without steady-state errors, under conditions where the irradiance changes slowly or rapidly; this is obviously superior to the FL method. In areas (A) to (B) and stages d-h, even if the MPP voltage changes in a wide range and the dynamic tracking process produces a large overshoot, the controller can still respond within 0.03 s to the new voltage reference. As can be observed in Figure 10, the AFL method can track the MPP voltage quickly, accurately, and statically. Figure 10: _Cont._  
Figure 9: (**a**) Irradiances of different parts of the PV array; (**b**) voltage of the PV array. At the same time, the hybrid control method (ANN + AFL) proposed in this paper can achieve MPPT and eliminate the possibility of GMPPT failures, regardless of the changes in the PV shielding conditions. The control effect of MPPT focuses on the output power of the PV system, as shown in Figure 11. It can be seen from Figure 11 that the AFL controller can realize the MPP with high efficiency and can accurately track the MPP voltage. Figure 10: Output voltage of PV systems with AFL (augmented state feedback precise linearization) and FL (state feedback precise linearization) controller: (**A**) Output voltage (overall); (**B**) output voltage (detailed): (**a**) output voltage (0.05–0.15 s); (**b**) output voltage (0.15–0.35 s); (**c**) output voltage (0.35–0.40 s); (**d**) output voltage (0.40–0.45 s); (**e**) output voltage (0.45–0.50 s); (**f**) output voltage (0.50–0.55 s); (**g**) output voltage (0.55–0.74 s); (**h**) output voltage (0.74–0.95 s).