*4.1. Test under STC*

Figure 6 shows the polycrystalline cell MSX60 performance using the four MPPT algorithms. All simulations are performed at an irradiance of 1000 W/m2 and 25 ◦C. According to the simulations observed in the figure, the MPP was reached using both traditional P&O and INC algorithms, but the output power had a high percentage of oscillations (see Figure 6a). In contrast, the efficiency of the cell performance can be enhanced using the modified versions of the classical methods, M-VSS-P&O and M-VSS-INC. As observed in the figure, the M-VSS-P&O algorithm (58% duty cycle) was the faster algorithm among the four algorithms to obtain the MPP with the same o/p power of P&O and INC techniques (see Figure 6b). While the Modified Variable Step Size INC algorithm (59% duty cycle) reached the MPP with a quicker response time (18.22 ms) than the classical methods, it was the only algorithm among the four algorithms that achieved 100% power efficiency with negligible steady-state oscillations.

**Figure 6.** STC test of MSX60 solar cell performance: (**a**) Output power and (**b**) duty cycle variation.

In the same manner, and according to the results presented in Figure 7, another solar cell (thin-film ST40) was used to test the four algorithms' performance. A comparison between the performances of the four MPPT algorithms using both cells is listed in Table 3. Accordingly, the performance efficiency of the traditional P&O in both cells can be noted as the lowest efficiency compared to the other algorithms. The algorithm also presents a higher level of oscillations to arrive at the MPP. Furthermore, the INC algorithm typically operates in the same way as P&O in the MSX60 panel in tracking the MPP. Nevertheless, corresponding to the ST40 cell simulations, it is obvious that all trackers could achieve a conversion efficiency of approximately 100%; both traditional techniques require a similar duration to operate at the same point (~34.0 ms). In contrast, the updated modified algorithms in MSX60 cell simulations were able to improve the efficiency of the solar cell to achieve the panel's full available power to hit the MPP with negligible oscillations quicker than traditional high oscillation algorithms. In addition, the M-VSS-INC improved the performance of the MPPT controller to 100% in 18.22 ms.

**Figure 7.** STC test of ST40 solar cell performance: (**a**) Output power and (**b**) duty cycle variation.


**Table 3.** Performance of the MPPT algorithms under STC conditions.

In summary, under STCs, the adjustments performed for both traditional P&O and INC algorithms increased the steady-state efficiency of both solar cells to achieve the full usable o/p power from the panel and grasp the MPP quicker than traditional algorithms that have low oscillations for both cells. However, according to the observations of both cells, the M-VSS-INC was proven to be the most efficient algorithm among the three algorithms.

#### *4.2. Test under an Abrupt Variation in Irradiance with Constant STC Temperature*

To extend our analysis to the four mentioned MPPT techniques under a constant STC temperature, a sudden variation in irradiance was examined for both solar cells as follows (Figure 8): The irradiance was initially 1000 W/m<sup>2</sup> but was unexpectedly reduced to 600 W/m<sup>2</sup> at *t* = 0.35 s; then, upon reaching 0.65 s, an extra variation from 600 W/m2 to 1000 W/m<sup>2</sup> was abruptly applied; eventually, the radiation remained steady at 1000 W/m<sup>2</sup> until the completion of the simulation time at *t* = 1 s.

**Figure 8.** Sudden Irradiance change at 25 ◦C.

In conjunction with [39], simulations were carried out to ensure the performance and efficiency of the algorithms, in particular, the updated algorithms to meet the MPP. Checking the MSX60 cell, as seen in Figure 9a, the four MPPTs were initially performed in the STC case addressed above. When the irradiance was abruptly reduced to 600 w/m2, both classical algorithms were able to detect the MPP but many oscillations occurred, exhibiting the same phenomena with a response time of 379.6 ms and an output power of 37.13 W, displaying an approximate error of 26.9 ms.

**Figure 9.** Cell performance under irradiance sudden variation for (**a**) MSX60 and (**b**) ST40.

In contrast, with a faster response time of 367.5 ms and a minor error of 17.5 ms, both modified strategies could congregate to 37.14 W, almost the equivalent MPP of the conventional algorithms. Moreover, the enhanced algorithms succeeded in minimizing the steady-state oscillations around the MPP. In comparison to both P&O and INC (60.14 W), both modified MPPTs can perceive the abrupt spike in solar irradiance even better and faster, with an inaccuracy of just 7.2 ms and a minor reduction in power (59.52 W) in 690.4 ms.

A similar evaluation of the four controllers on the ST40 solar cell is indicated in Figure 9b. Both P&O and INC algorithms were able to monitor and detect the MPP for solar radiation unexpectedly reduced to 600 W/m2, but with a high percentage of oscillations, demonstrating identical behavior with a performance power of 26.4 W in a response time of 381.8 ms, with almost 34.8 ms error. In comparison, both modified algorithms can converge

to an approximately identical highest power of 26.43 W but quicker than the classical algorithms with a response time of 363.4 ms and a smaller error of 13.4 ms.

Furthermore, the improved algorithms minimized steady-state oscillations all over the MPP. Furthermore, with a quicker reaction time, the enhanced algorithms could also recognize the abrupt rise in solar radiation with just a 25.2 ms error with an almost equivalent o/p power of 40.02 W related to P&O and INC with a time of 45.2 ms. Similar to the performance in the polycrystalline cell, the output power curves of the improved techniques showed better performance and fewer oscillation levels than the output power of the other conventional MPPT approaches. However, in the thin-film solar cell simulations, both modified algorithms were better in the MPP tracking process with a sudden increase and sudden reduction in irradiance. In contrast, the polycrystalline solar cell simulations showed different behavior in tracking as M-VSS-P&O and M-VSS-INC prospered in tracking the sudden increase in the irradiance, but they gave slightly less power than the conventional algorithms; however, they were very fast with almost no oscillations around the MPP.
