## 4 Simulation Results and Discussion
It must be noted that the efficiency axis for both the dP-P&O and the Td-MPPT are zoomed-in compared  
Figure 12: Plotted MPPT efficiency for every sequence of the trapezoidal shapes described in Table 2 organized according to the Irradiance slope of every section for the P&O (**a**), dP-P&O (**b**), and the Td-MPPT (**c**): efficiency for the low to medium irradiance test section (solid blue) and efficiency for the medium to high irradiance test section (dashed red). Figure 13: Behavior of the classical P&O during irradiance trapezoidal profiles tested with an irradiance slope of 700 W/m\({}^{2}\)/s (**a**) and 5000 W/m\({}^{2}\)/s (**b**); simulated PV voltage (solid-blue) and corresponding V\({}_{\text{MPP}}\) (dotted-red). to the P&O. This was used to observe the differences in efficiency between these two algorithms better. In Figures 14-25, the response of the algorithms is displayed in more detail for some sections of the test or specific irradiance profiles. First, the case of the slightest slope (50 W/m\({}^{2}\)/s) of the first section (low to medium irradiance) is considered (Figures 14-16) as an example of the performance under a slowly changing rate of irradiance. Second, the fastest-changing rate (5000 W/m\({}^{2}\)/s) of the first test section (low to medium irradiance) is displayed (Figures 17-19) as an example of the performance under a very rapidly changing rate of irradiance. Then, a steady irradiance (300 W/m\({}^{2}\)) case is considered to validate the steady-state oscillations in Figures 20-22. Lastly, a specific irradiance profile is proposed that takes irradiance down from a medium (500 W/m\({}^{2}\)) to a low irradiance (100 W/m\({}^{2}\)) at a fast-changing rate (5000 W/m\({}^{2}\)/s). This specific profile was designed to validate how the platform would react to irradiance on the PV panel being rapidly decreased by a passing obstacle. In Figures 14-16 it can be noted that both algorithms track the MPPT (dotted-red) very similarly for the slightest slope scenario. During this test section, the P&O (Figure 14) obtained an efficiency of 99.61%, the dP-P&O (Figure 15) achieved 99.53%, and lastly, Td-MPPT (Figure 16) reached the highest efficiency at 99.75%. For the fastest irradiance changes in the low to medium section of the test, it can be observed that the P&O (Figure 17) shows the characteristic drift reported in the literature. The operating point determined by the MPPT (As in Equation (10)) can be observed in Figure 17a. Even when MPPT perturbs in the correct direction at the beginning of the trapezoidal form, it cannot detect that it has passed the MPP. Furthermore, when the irradiance profile begins its descent, the P&O attributes the measured power reduction to the effect of the perturbations introduced and keeps perturbing around the same operating point until irradiance reaches a steady state. In Figure 17c, it can be observed that the  
Figure 16: Response of the Td-MPPT algorithm to slow irradiance change (50 W/m\({}^{2}\)/s) from the low to medium irradiance section of the test; (**a**) Simulated PV power (solid-blue) and P\({}_{\rm MPP}\) (dotted-red), (**b**) PV voltage simulated (solid-blue) and V\({}_{\rm MPP}\) (dotted-red), (**c**) simulated PV current (solid-blue) and I\({}_{\rm MPP}\) (dotted-red), and (**d**) irradiance (solid blue) and duty cycle (solid red). Figure 8:0 Response of the P&O algorithm to fast irradiance change (5000 W/m\({}^{2}\)/s) from the low to medium irradiance section of the test; (**a**) Simulated PV power (solid-blue) and P\({}_{\rm MPP}\) (dotted-red), (**b**) PV voltage simulated (solid-blue) and V\({}_{\rm MPP}\) (dotted-red), (**c**) simulated PV current (solid-blue) and I\({}_{\rm MPP}\) (dotted-red), and (**d**) irradiance (solid blue) and duty cycle (solid red). current of the system drops under the theoretical maximum because of this behavior. Also, this produces a decrease in the power output that can be noted in Figure 17a. Because of this, P&O reaches an efficiency of 98.12% (average).