## 4 Simulation Results and Discussion
On the other hand, dP-P&O (Figure 18) becomes confused at the beginning of the trapezoid and corrects the search direction by reaching MPP shortly after. The efficiency achieved by it during this test was 99.22%. In contrast, the Td-MPPT (Figure 19) keeps perturbing in the correct direction almost every time, and the actual operation point (solid-blue) does not drift away from MPP. The system only becomes confused when the irradiance changing rate shows a significant enough change, i.e., when the edges of the trapezoidal irradiance profile occur between a cycle of the MPPT. However, the system corrects the trajectory and effectively follows MPP. Because of this, the efficiency of Td-MPPT for this section is 99.69% (average). Figure 8:1 Response of the Td-MPPT 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). Figure 8:2 Response of the dP-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). Lastly, the behavior of the algorithms during steady irradiance of 300 W/m\({}^{2}\) is displayed in Figure 8:3 It can be observed that both P&O (Figure 16a) has to perturb three times around the MPP while dP-P&O (Figure 16b) performs only two. This difference could be caused by the fact that dP-P&O obtains additional information at \(T_{MPPT}/2\) since the system has not reached a steady state when it is being measured. In contrast, Td-MPPT (Figure 16c) perturbs only one time in the same direction, reducing steady-state oscillations. Accordingly, P&O achieved 99.35% and dP-P&O achieved 99.38% efficiency during the steady irradiance settling time (3 s) of the first part of the test. In comparison, Td-MPPT (99.42) achieved 99.82% efficiency. Figure 8:4 Response of the dP-P&O algorithm to steady irradiance at (300 W/m\({}^{2}\)); (**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 8:5 Response of the P&O algorithm to steady irradiance at (300 W/m\({}^{2}\)); (**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). For the behavior of the algorithms during steady irradiance of 300 W/m\({}^{2}\) displayed in Figures 20-22, the P&O (Figure 20) has to perturb three times around the MPP, while the dP-P&O (Figure 21) performs only two. This difference could be caused by the fact that dP-P&O obtains additional information at \(T_{MPPT}/2\) since the system has not reached a steady state when it is being measured. In contrast, Td-MPPT (Figure 22) perturbs only one time in the same direction, reducing steady-state oscillations. Accordingly, during the steady irradiance settling time (3 s) of the first part of the test, the P&O obtained 99.35% efficiency, the dP-P&O achieved 99.38% efficiency, and the Td-MPPT reached 99.82% efficiency.