## 4 Simulation Results and Discussion  
The proposed Td-MPPT algorithm is simulated in MATLAB/Simulink to compare it with the traditional P&O and dp-P&O to contrast their performance and illustrate the differences between them. The algorithms are simulated using irradiance profiles based on the ones defined in the efficiency test of the EN50530 standard [30] to compare their performance under different scenarios (Table 1). \begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|} \hline \multicolumn{8}{|c|}{**a. Irradiance low to medium (100 W/m\({}^{2}\)-500 W/m\({}^{2}\))**} \\ \hline
**Settling** & **Rep.** & **Slope** & **Rise** & **Wait** & **Fall** & **Wait** & **Duration** \\
[s] & [n] & [W/m\({}^{2}\)/s] & [s] & [s] & [s] & [s] & [s] \\ \hline
300 & 2 & 0.5 & 800 & 10 & 800 & 10 & 3540 \\ \hline
300 & 2 & 1 & 400 & 10 & 400 & 10 & 1940 \\ \hline
300 & 3 & 2 & 200 & 10 & 200 & 10 & 1560 \\ \hline
300 & 4 & 3 & 133 & 10 & 133 & 10 & 1444 \\ \hline
300 & 6 & 5 & 80 & 10 & 80 & 10 & 1380 \\ \hline
300 & 8 & 7 & 57 & 10 & 57 & 10 & 1372 \\ \hline
300 & 10 & 10 & 40 & 10 & 40 & 10 & 1300 \\ \hline
300 & 10 & 14 & 29 & 10 & 29 & 10 & 1080 \\ \hline
300 & 10 & 20 & 20 & 10 & 20 & 10 & 900 \\ \hline
300 & 10 & 30 & 13 & 10 & 13 & 10 & 760 \\ \hline
300 & 10 & 50 & 8 & 10 & 8 & 10 & 660 \\ \hline  & & & & & & Total & 15,936 \\ \hline  & & & & & & & 04:25:39 \\ \hline \multicolumn{8}{|c|}{**b. Irradiance medium to high (300 W/m\({}^{2}\)-1000 W/m\({}^{2}\))**} \\ \hline
**Settling** & **Rep.** & **Slope** & **Rise** & **Wait** & **Fall** & **Wait** & **Duration** \\
[s] & [n] & [W/m\({}^{2}\)/s] & [s] & [s] & [s] & [s] & [s] \\ \hline
300 & 10 & 10 & 70 & 10 & 70 & 10 & 1900 \\ \hline
300 & 10 & 14 & 50 & 10 & 50 & 10 & 1500 \\ \hline
300 & 10 & 20 & 35 & 10 & 35 & 10 & 1200 \\ \hline
300 & 10 & 30 & 23 & 10 & 23 & 10 & 960 \\ \hline
300 & 10 & 50 & 14 & 10 & 14 & 10 & 780 \\ \hline
300 & 10 & 100 & 7 & 10 & 7 & 10 & 640 \\ \hline  & & & & & & Total & 6980 \\ \end{tabular}
\end{table} 
Table 1: Irradiance profile as described in the EN50530 standard. As shown in Figure 7, the irradiance profile can be divided into three regions: a low to medium irradiance region (where it fluctuates between 10% and 50% of the G\({}_{\rm STC}\)), a medium to high irradiance region (where it fluctuates between 30% and 100%), and a startup region (where it fluctuates between 1% and 10%). Each one comprises a given number of trapezoidal waveforms with varying slopes. The irradiance described in the EN50530 standard is presented in Table 1. For example, during the first trapezoidal waveform, irradiance rises during 800 s at a rate of 0.5 W/m\({}^{2}\)/s from 100 W/m\({}^{2}\) to 500 W/m\({}^{2}\), and then it remains steady at 500 W/m\({}^{2}\) during 10 s. Then, it decreases at a rate of 0.5 W/m\({}^{2}\)/s until it reaches 100 W/m\({}^{2}\). Lastly, it remains steady for another 10 s. The test also includes an additional settling period of 300 s between each cluster of repetitions with the same slope. The startup region consists of a single trapezoidal profile with an ascending and descending slope of 0.1 W/m\({}^{2}\)/s with 30 s settling periods before the first ramp and after each one. To further test the Td-MPPT response under very fast-changing irradiance, a speed multiplier of 10\({}^{2}\) was introduced to the standard EN50530 efficiency test, and the startup test was not included in the simulations. The resulting profiles are shown in Table 2.  
The model provided with MATLAB/Simulink of a solar panel UP-M155M made by Upsolar was chosen due to its low series resistance. It includes 72 cells, a temperature coefficient of V\({}_{\rm OC}\) = \(-\)0.40122%/\({}^{\circ}\)C, a temperature coefficient of I\({}_{\rm SC}\) = 0.057535%/\({}^{\circ}\)C, a light-generated current (I\({}_{\rm L}\)) = 5.0443 A, a diode saturation current (I\({}_{\rm 0}\)) = 6.41 \(\times\) 10\({}^{-10}\), a diode ideality factor = 0.98551, a shunt resistance (R\({}_{\rm SH}\)) = 111.1072 \(\Omega\), and a series resistance (R\({}_{\rm S}\)) = 0.31595 \(\Omega\).