## 4 Simulation Results and Discussion
Figure 8:6 Response of the P&O algorithm to fast irradiance change (5000 W/m\({}^{2}\)/s) from medium (500 W/m\({}^{2}\)) to low (100 W/m\({}^{2}\)) irradiance and back; (**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 8:7 Response of the Td-MPPT 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). In Figures 23-25, inverted profiles proceeding from 500 W/m\({}^{2}\) to 100 W/m\({}^{2}\) at a change rate of 5000 W/m\({}^{2}\)/s were tested for the three algorithms proposed. This change rate is the same as the fastest presented in the EN50530 test (Figures 17-19). However, during this test the irradiance starts at a medium value (500 W/m\({}^{2}\)) and drops to a low value (100 W/m\({}^{2}\)). A profile such as this could be observed if irradiance is blocked by an obstacle, e.g., a moving cloud. It can be observed that the P&O (Figure 23) becomes confused only when irradiance rises from a low to a medium value. This simulation is consistent with the behavior observed in the literature [1; 2; 19]. The efficiency of the P&O was similar to the standard test with a changing rate of 5000 W/m\({}^{2}\)/s (98.05%). The dP-P&O (Figure 24) displayed a better efficiency under this test than under the standard one (99.39%). Moreover, Td-MPPT (Figure 25) showed a slightly lower efficiency than the observed under the standard test (99.59%). It must be noted that these results were very similar to the standard test with a changing rate of 5000 W/m\({}^{2}\)/s (98.05%). Figure 8:8 Response of the dP-P&O algorithm to fast irradiance change (5000 W/m\({}^{2}\)/s) from medium (500 W/m\({}^{2}\)) to low (100 W/m\({}^{2}\)) irradiance and back; (**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 8:9 Response of the Td-MPPT algorithm to fast irradiance change (5000 W/m\({}^{2}\)/s) from medium (500 W/m\({}^{2}\)) to low (100 W/m\({}^{2}\)) irradiance and back; (**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). similar to the ones observed in Figures 23-25, with the P&O showing the worst performance of the three algorithms tested and Td-MPPT performing the best. Partial shading is not addressed in this work since it would need a different approach and methodology since EN50530 only considers uniform irradiance in the test ramps. However, a modification to Td-MPPT would be relatively simple. For example, in [37], the authors propose a novel probability algorithm to track the global maximum power point (GMPP), and then a variable step-size P&O performs fine tracking.