1. Introduction
Worldwide, the increased awareness of the drawbacks of fossil fuels raised up the interest in developing renewable energy-based power plants. Lately, the drawbacks of fossil power plants were proved to be a beyond developed and sustained industry. The environment is highly harmed by fossil fuels through the enormous emissions of carbon dioxide, global warming, depleted ozone, and more. That is why replacing fossil resources by renewable energy resources has become a necessity in order to lessen these global environmental difficulties. It is always preferable to use renewable energy resources since they are ecological and accessible to everyone and everywhere.
Recently, the most popular and trendy renewable energy resources are wind and solar energies due to their significant availability and easy set-up. Moreover, solar energy had a lot of research interest globally since it depends on ever-lasting resource, which is the sun. Moreover, because it is power electronic based, it is dependent on the speedy electronics field development. Researchers are keen on continuously developing solar power plants, to maximize its benefits as much as possible. Researchers are mainly challenged by the conversion efficiency of PV and output power generated as it is required to keep it at its predictable maximum value [
1,
2,
3]. Therefore, several maximum power point tracking (MPPT) approaches are proposed [
1,
4]. The most important part of PV’s control system is MPPT controlling unit, where the maximum power point (MPP) is variable with the sun’s irradiance which is changeable along the day.
Various MPPT approaches were proposed in the past decade [
5]. Perturb and observe (P&O) is not only the most well-known and the most used method, but also the oldest and most elementary method. However, with the growing interest in improving MPPT techniques, P&O is shown to be the least effective approach. More functioning techniques are recommended, such as incremental conductance (INC) method, constant voltage (CV) method, hill climbing (HC) method, constant current (CC) method, and others [
2]. Lastly, INC is proved to be a relatively desirable technique since it is characterized by low complexity and high tracking accuracy [
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15]. Various MPPT approaches are generally compared and introduced in [
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18]. There are many challenges that face the process of MPPT, and one of these major challenges is partial shading (PS). PS takes place when a part of the PV array is shaded by a body or a cloud leading to a huge drop in the output power in addition to a distortion in the power-voltage characteristics, as shown in
Figure 1 [
19], which make PS quite an important issue for MPPT control.
The distorted power–voltage characteristics result in multiple peaks on the curve. Having multiple peaks means that there are several local maximum power points. This can confuse the MPPT control unit in its search for the global MPP, where it may be trapped in a local MPP region, not the global one. Consequently, the P&O approach is absolutely ineffective in PS condition, while the INC method is more recommended. It is suggested to numerically scan power–voltage characteristics so that it is easier and more accurate to find the MPP. Several research works are introduced considering tracking the MPP for PV systems under the PS condition.
Moreover, several MPPT approaches are applied to PS conditions, such as meta-heuristics [
20,
21,
22,
23,
24,
25], fuzzy logic [
26,
27], numerical methods [
28,
29,
30,
31], modified conventional methods [
32,
33,
34], hardware-based methods [
35,
36,
37,
38,
39,
40], and more detailed MPPT approaches are studied in [
41,
42]. Currently, the research work is more oriented towards optimization techniques that are inspired from nature. Generally, most of the optimization algorithms would reach an optimum solution in a relatively short time with minimum complexity. With their continuous improvement in the last few years, a fitting solution is always expected. The authors of [
43] presented some of the nature-inspired optimization algorithms such as cuckoo search algorithm, genetic algorithm, ant colony optimization, bat optimization, particle swarm optimization, bee colony optimization, firefly optimization, and more.
Nearly all of the meta-heuristics are popular and well-known. All of them have mainly the same flow cycle, as shown in
Figure 2 [
43], in addition to being employed in a lot of applications and subjects [
44]. General reviews for applying various optimization algorithms for MPPT are presented in [
45,
46,
47]. In this paper, the emperor penguin optimizers (EPO) algorithm is proposed to optimize the parameter of the boost converter used for MPPT. In addition, the proposed EPO algorithm is utilized to optimize the gains of the PI controller used for grid-connected inverter to regulate the DC-link voltage. The performance of the proposed EPO algorithm is compared with the particle swarm optimization (PSO) [
32] and cuttlefish algorithm (CFA) under different PS patterns and dynamic changes in irradiance levels.
4. Results and Comparison
Three different PS patterns are considered. The irradiance of one PV array is set at the maximum value of 1000 W/m
2, while the irradiance of the second PV array is set to a specific profile according to the case under study. The performance of the system is evaluated under each PS pattern when the parameters are optimized using either the PSO, the CFA or the proposed EPO algorithm. Five scenarios are presented. In the first and second scenarios, only the initial value of the duty cycle Dc is optimized. The third and fourth scenarios are dedicated to evaluate dynamic performance of the system under changing the PS pattern. In these cases, the system is fully optimized, where the gains of the PI controller and SOA are optimized in addition to the initial duty cycle. The last scenario is dedicated to check the dynamic performance of the system under different PS pattern than that used to obtain optimized parameters utilizing the proposed EPO algorithm.
Table 2 and
Table 3 show comparisons between the PSO, CFA, and EPO algorithms used for optimizing Dc for case 1 and case 2, respectively. The shaded PV array used for case 1 and case 2 is exposed to an irradiance of 800 W/m
2 and 400 W/m
2, respectively. For case 1,
Figure 7a shows the duty cycle. Meanwhile,
Figure 7b shows the extracted power from the PV system using the default initial Dc compared to that optimized by CFA and EPO algorithms. As should be expected, the duty cycle is inversely proportional to the PV power.
Figure 8a,b illustrates the current fed to grid and the DC-link voltage. It is obvious from these results that using the optimized initial setting of the duty cycle obtained from the proposed EPO algorithm improves the harvested PV power and consequently the current fed to the grid. Additionally, the load current is increased with the decrease of duty cycle as the PV power is increased, while the DC voltage is tightly regulated at a specific level for all cases. Moreover, the tracking efficiency for the three algorithms is compared in
Figure 9. By observing it, the three algorithms reach very close results at the end of the last iteration; despite the search region of each one which is detected randomly within fixed pre-specified ranges for all of them.
Figure 10 and
Figure 11 give comparisons of case study 2, where the irradiance levels of the PV arrays are set to 1000 W/m
2 and 400 W/m
2. It is clear from the results that the proposed EPO algorithm succeeds to set the initial setting of the duty cycle to harvest more power from the PV arrays than that obtained from using the CFA. It is worth mentioned that the DC-link voltage is tightly regulated regardless the setting of the initial duty cycle since the parameters of the PI based voltage regulator is kept constant during the tests.
Figure 12 illustrates the tracking efficiency for case 2. It is obvious that all algorithms converge to close optimum solutions despite their different search region.
In the first two cases, static PS patterns are considered. Practically, this may occur if the PV array is installed near a fixed body, which may block the sunlight during certain period of the day. Despite it can rarely happen, these cases are considered to analyze the response of the system to the change in the initial setting of the duty cycle even in static mode. Case study 3 is dedicated to study the performance of the proposed PV system under dynamic PS pattern, shown in
Figure 13a, where the irradiance of the shaded array is changed from 1000 W/m
2 to 800 W/m
2 to 400 W/m
2 to 800 W/m
2 to 1000 W/m
2. These dynamic changes require that all the control parameters such as PI and SOA gains beside initial Dc value to be optimized. Results are recorded in
Table 4 and optimized parameter values are given in
Table 5. Moreover, the time needed for each algorithm—PSO, CFA, and EPO—to find the best solution is presented in
Table 4. While the PSO takes the longest time to reach optimum setting, the EPO shows a little improvement compared to the CFA.
Figure 13b shows the duty cycle, while
Figure 13c illustrates the harvested PV power using the default Dc, PSO-optimized, CFA-optimized, and EPO-optimized parameters. This result reveals that using the optimized parameters of the proposed EPO algorithm results in more accurate operation of the MPPT compared to the CFA even under dynamic PS conditions. It is observed that PSO results are quite divergent to that of EPO.
Figure 14a indicates that using the PSO algorithm results in severe oscillations in the grid current during transition from mode to another. Consequently, the DC link voltage may experience a severe overshoot as illustrated in
Figure 14b. However, using the proposed EPO algorithm results in the best performance compared to the other techniques. Despite the PSO results in slightly higher power and energy harvesting than the EPO, its corresponding grid current and DC voltage are not acceptable.
Figure 15 illustrates the tracking efficiency of case 3 and shows how close the solutions of EPO and PSO at the end of last iteration.
Case 4 is dedicated to evaluate the proposed objective function. The irradiance profile is the same as in case 3. However, a comparison is made between two objective functions given in
Table 6. The first one obj
1 is given in Equation (5). The second objective function Obj
2 given in Equation (14), where the optimization process is focused only on maximizing power value, without taking into account the harvested energy.
Figure 16 and
Figure 17 present the results of this case. It is obvious that eliminating the energy term from the objective function deteriorate the dynamic system performance. Using the optimized parameters, when the energy term is considered in the objective function, results in fast dynamic response without oscillations.
The last case is dedicated to check the robustness of using the optimized parameters using the proposed EPO algorithm under a PS profile different than used in the optimization process. The irradiance at the second PV array is set to a dynamic profile shown in
Figure 18a, where it is set at 300 W/m
2, then it is abruptly raised to 600 W/m
2, then to 900 W/m
2, and it falls again in reverse manner.
Figure 18b illustrates the duty cycle. A comparison is made for the harvested power between the optimized initial duty cycle found by EPO and the default value in
Figure 18c. Furthermore, the grid current and the DC-link voltage are shown in
Figure 19a,b, respectively. It is obvious from these results that using the optimized parameters obtained from the proposed EPO algorithm improve the harvested PV power and consequently the current fed to the grid.