A Comprehensive Evaluation of Up-to-Date Optimization Algorithms on MPPT Application for Photovoltaic Systems

ABSTRACT Maximum Power Point Tracking (MPPT) plays a significant role in obtaining maximum power at PV system outputs. Recent research has focused on minimizing the adverse effects of partial shading and dynamic environmental conditions on MPPT. Metaheuristic optimization algorithms have attracted attention with their success in these issues. The growing body of literature lacks a study that comprehensively evaluates current metaheuristic algorithms. In this study, the performances of 20 metaheuristic algorithms under five different shading conditions, nonuniform temperature distribution, and variable irradiance conditions have been investigated. The successes of the algorithms in the convergence of the global maximum value and their convergence rates have been calculated through various statistical metrics with different aspects. This study provides a novel approach to objectively evaluating the performances of the algorithms by using the three-dimensional Pareto Front method. As the result of this multicriteria evaluation, RKO, MPA and CGO algorithms are able to provide non-dominated results. These three algorithms are further tested using case analysis designed for dynamic operating conditions, and the RKO algorithm exhibited the most favorable results. Additionally, the RKO algorithm exhibits remarkable performance by reaching the LMPP/GMPP point within an average time of 3.2 milliseconds in all cases. Moreover, it demonstrates an average efficiency value exceeding 0.999.


Introduction
Currently, photovoltaic systems have reached maturity to provide the conversion of solar energy to electrical energy in an economically viable manner and have become a widely used technology.In an atmosphere where economic and environmental concerns are on the rise, electricity generation from fossil fuels is becoming a worse option than each previous day.Photovoltaic systems are powered by the sun, which is a free energy source with a fair distribution on Earth.There is no waste or emission from photovoltaic energy conversion.In terms of being economical, sustainable, and environmentally friendly, photovoltaic systems are expected to have a very high share in the future electricity supply.
Although solar panels are a renewable energy source, their efficiency can be affected by factors such as temperature and shading.However, photovoltaic systems are sensitive to changes in ambient conditions.The voltage and current outputs have a nonlinear relationship defined over the ambient conditions and structural variables.Changes in environmental conditions modify this characteristic and cause the maximum power point to shift to a different voltage value.To obtain the highest possible power from photovoltaics systems, the output voltage must be brought closer to the maximum power point.Maximum Power Point Tracking (MPPT) techniques are used to determine the appropriate voltage value and drive the system to this value.
The history of the MPPT technique dates back to the 1950s, when the first practical photovoltaic cell was developed.From the past to the present, there has been a development process shaped by the needs and opportunities of the time, which continues.In a study by Abdel-Salam et al., the evolution of MPPT techniques from 1954 to 2018 has been quite successfully summarized (Abdel-Salam, EL-Mohandes, and Goda 2020).When the relevant literature is reviewed, it is observed that artificial intelligence has been widely used in MPPT techniques developed in recent years.In particular, very successful results have been obtained by adapting metaheuristic optimization algorithms to the MPPT problem.In recent years, MPPT studies have primarily focused on mitigating the effects of partial shading (Sarvi and Azadian 2022).
Partial shading is an important issue that affects the performance of photovoltaic (PV) systems.A panel with less irradiance (shaded) behaves like a load in the array and causes a reverse bias current.This may result in reduced system efficiency and the risk of hotspots.Bypass diodes are used in the system to prevent reverse bias currents from causing hotspots (Daliento et al. 2016).In this way, damage to the system is prevented, but the effect of the Partial Shading Condition (PSC) remains an issue.The power-voltage (P-V) characteristic of the system becomes a curve with multiple peaks under PSC (Teo et al. 2018).This leads to the challenge of determining the global maximum among the multiple peak points.Therefore, recent studies of MPPT techniques have focused on PSC.
In a review study conducted in 2019, 20 different optimization algorithms have been applied to the MPPT problem for PSC, and the results have been evaluated statistically (Rezk et al. 2019).In another study, 13 of which are based on optimization algorithms and one on artificial neural networks, 14 MPPT techniques have been examined (Pathak, Kumar Yadav, and Alvi 2022).The success of swarmbased optimization algorithms on MPP tracking under PSC has been examined.Twelve different optimization algorithms have been considered and their performances have been tested on a simulation setup (Wasim et al. 2022).Apart from the review studies, there is wide literature that includes research studies in which algorithms are specifically addressed.In these studies, the PSC performances of individual algorithms adapted to the MPPT problem or of the algorithms developed by hybridizing several have been investigated.Among the studies conducted in the last five years, the important ones in terms of their approaches and findings, are listed in Table 1.
In this study, MPPT performances of 20 meta-heuristic optimization algorithms have been comparatively examined.Seventeen of these algorithms have been developed over the last five years.Relatively older but highly cited algorithms, such as Differential Evolution, Gray Wolf Optimization, and Sine Cosine, have also been included in the study.Algorithms have been tested for seven different case scenarios in a system simulation formed by the five-parameter PV cell model.These cases are one for uniform irradiance, four for partial shading, one for non-uniform temperature, and one for dynamic irradiance.Case studies have been performed on a PV system modeled by four parallel connected identical strings consisting of four panels (16 PV modules in total).To examine the effect of PSC on the system more comprehensively, examinations have been performed on a system structure containing multiple strings.In each case study, algorithms have been evaluated over ten different criteria and the results obtained from the algorithms for each criterion have been compared.The criteria considered include various definitions for different attributes related to the algorithm's convergence speed, computational effort, and consistency of results.Pareto-front analysis has been used to systematically evaluate different attributes.The main motivation of this study is to present a current reference source for the convenience and competence of up-to-date optimization algorithms in the MPPT problem.This study is interesting in that it compares the up-to-date algorithms with those accepted in the literature on different criteria.The case scenarios have designed considering uniform and non-uniform irradiance and temperature distributions for the PV system provided a comprehensive evaluation.In particular, the case scenario has designed to examine dynamically varying irradiance levels is unique in terms of being studied with all-day-long irradiance-level transitions.On the other hand, the Pareto-front method has been effectively applied to the evaluation of different attributes of algorithms over various criteria.In the literature related with MPPT, an allinclusive approach has not been adopted in the examination and comparison of methods with multidimensional performance criteria, such as optimization algorithms.Each performance criterion used to be evaluated in itself.However, a method that is successful for one criterion may not show the same success as another criterion.In such cases, a clear measure of success cannot be presented.
A systematic evaluation has been achieved by applying the Pareto Front method.
The next section focuses on the system models and methods used in the analysis.In the third chapter, an overview of the meta-heuristic optimization algorithms and details of the Runge-Kutta optimization algorithm, which showed the highest success as a result of the analyses realized in the study, are shared.In the fourth section, details of the case studies are presented.The results obtained and the evaluations related to these results are presented in this section.The final section presents the conclusions of the study.In this section, a general evaluation is shared and remarkable findings are emphasized.

System description
Photovoltaic power plants cover large areas.The objects around the system or cloud transitions on the sky may cause partial shading on the PV array A sample system has been taken into consideration in the analyses to examine the partial shading on the PV system consisting of serial and parallel modules.The sample test system has been configured by parallel connection of four identical strings, consisting of four PV modules each, Figure 1.
The specification of the modules has been taken as given in the Table 2.

Boost converter model
The converter types used for MPPT at the outputs of PV systems are Buck, Boost and Buck-Boost configurations.The voltage at the output of the PV array is regulated by adjusting the duty cycle over the modulation of the signals and sending to the switches in the converter.As can be seen from Table 1, the Boost converter is widely used in MPPT studies.Boost converters consist of an inductor, a diode, input and output capacitors, a load resistor, and semiconductor switching elements.
In this study, a boost converter model specially designed for MPPT applications has been used.This model is based on the resistance value defined over the maximum power point voltage and current (Ayop and Wei Tan 2018).The determination of the rate between the input and output voltages for boost converters is given in Eq. ( 1).
The values for the maximum power point resistance R max , the load (output) resistance R, the capacitance values at the input C in and output C O and inductor value L are defined by the following Eq.(2-8).
The relationship between the R max , R and d is given in Eq. ( 3) From the definition of capacitance, the relationship between the maximum power point voltage ripple ΔV mp and the change of the charge ΔQ in the capacitor C in has been given in Eq. ( 4).
where C in is the input capacitance, and γ V mp is the maximum power point voltage ripple factor.The definition for C in has been given as in Eq. ( 5).A small change in V mp may result in a significant change in I mp .The maximum power point voltage ripple γ V mp should be small to keep the process close to the maximum power point.
The output capacitance C o is defined by the expression in Eq. ( 6) derived from the voltage waveform on the output capacitor (Hart 2011).
where γ V O is the output voltage ripple factor.Eq. ( 7) is used to calculate the minimum inductance L required for a boost converter,  where f is the switching frequency, γ I L is the inductor current ripple factor and R o is the fixedoutput-resistance.The formula of Eq. 7 ensures that the inductor is sufficiently large to avoid the current from reaching zero during the switch's ON time.
where, d min and d max indicate lower and upper limits of the duty cycle, which have been chosen as 0,2 and 0,8, respectively.

Overview of optimization algorithms
Optimization algorithms can be classified under two main categories, deterministic and stochastic.Generally, deterministic approaches fail to obtain the global optimum solution for non-convex or highly non-linear problems that are difficult to distinguish and trap in the local optimum (Yang 2010).Stochastic approaches are more preferable for the MPPT problem, which is the search for the global optimum point on a nonlinear characteristic that changes under the influence of ambient conditions.In particular, meta-heuristic optimization algorithms are superior to their alternatives in terms of computation speed and consistency in results.Many optimization algorithms have been developed in the literature using different approaches (evolutionary, swarm, physics-based, etc).According to the free lunch (NFL) theorem, not all meta-heuristic methods are likely to perform best in solving all optimization problems (Cikan and Kekezoglu 2022).In other words, any meta-heuristic method may exhibit very promising results on a number of problems, but the same search algorithm may not show the same success for different problems.From this point of view, the adaptation of twenty metaheuristic optimization algorithms to the MPPT problem and the success of these algorithms under various operating conditions are examined.Attention has been paid to the fact that the selected algorithms are up-to-date algorithms developed in recent years.Besides, relatively older algorithms such as Differential Evaluation (DE), Sine-Cosine Algorithm (SCA) and, Gray Wolf Optimization (GWO) have been included due to their high citation count and acceptance in the literature.In Table 3, the references to the publications where the algorithms were proposed and the years belonged are listed.
As a result of the examinations within the scope of the study, the RKO optimization algorithm has performed with the highest success.For this reason, it has been needed to open a subsection for the algorithm.

Runge-Kutta Optimizer Algorithm (RKO)
RKO optimization is a new meta-heuristic search algorithm introduced by Ahmadianfar et all (Ahmadianfar et al. 2021).RKO is a population-based technique that uses the Runge-Kutta approach.A mathematical search mechanism has been given in between Eq. ( 9) and Eq. ( 22).
X n;l is initial swarm-population position and where l ¼ 1; 2; 3 . . .; D. D presents the dimension of the optimization problem.Upper i and Lower i show maximum and minimum limits of ith variable of the problem, respectively.
x worst andx best are the worst and best solution that calculated at each iteration.Δ x is position difference and defined as follows: According to the Runge-Kutta method, k i coefficients and its variables are calculated as follows: where rand no ; rand no;1 and rand no;2 are random numbers and distributed in the range of [0,1].

Exploration and exploitation phase
Exploration and exploitation phases are related to global and local search, respectively.The mathematical expressions of variables have been defined in Eq. ( 18).
where μ is a random number and presents in Eq. ( 19).
x m and x c are defined as follows: where ψ is a random number in the range [0,1].x best show the best solution so far and x best;l is the best solution at the end of each iteration.x s and x s are defined in Eq. ( 21).
x s ¼ rand no : SM is the search mechanism of the RKO optimizer algorithm based on the Runge-Kutta approach.SF is an adaptive factor and is expressed as: where, a and b are constant integers and have been taken as 20 and 12, respectively.

Case study
In order to measure the performance of the algorithms in the detection of the global maximum power point, the operation of the test system under different conditions has been examined.At first, the case where all the modules in the system have the same irradiance 1000W=m 2 ð Þ and temperature (25°C) values to represent Standard Reference Condition (SRC) is considered.This case has been addressed as Case 0. The P-V characteristic of the system has only a single maximum power point in these conditions.Partial shading condition causes local minimums to occur in the P-V characteristic.Four different cases have been designed to examine the performance of the algorithms in MPPT at partial shading with varying levels or intensities.
Cases have been set with different irradiance distributions for each one, while a uniform temperature (25°C) is valid.The irradiance distribution on the system for each case have been shared in Table 4. Another case scenario has been designed to observe the effect of non-uniform temperature distribution on the MPPT performance of the algorithms.This case is labeled as Case 5 and has the same irradiance distribution as Case 3. The temperature distribution is designed as given in Table 4.
For each case shared in Table 4, the P-V characteristics have been generated separately from the test system modeled in the MATLAB environment.P-V characteristics of each case have been plotted on the same axes, Figure 2. Thus, the effect of the ambient conditions on the characteristics and the differences in the characteristics have been able to be visualized.As can be seen from the figure, there are two peak points in Case 1, three peaks in Case 2, four peaks in Case 3 and Case 5 and more in Case 4. In Case 3, Case 4, and Case 5 local maximums are high in number and these peaks are close to each other and to global maximum point.This is challenging for the algorithms in terms of detecting the global maximum power point (GMPP).

Case 0
Case 0 is the most fundamental case for MPPT, representing SRC and having a single maximum point in the system characteristic.All the modules have 1000W=m 2 irradiance on their surfaces, and the temperature is uniformly distributed as 25 o C. As seen in the P-V characteristic of Case 0 given in Figure 2, it has an obvious peak of about 3202.17Watts.Most algorithms may efficiently perform MPPT over a characteristic with a single peak.In order to have a better understanding of the superiority of the algorithms to each other, the algorithm parameters are limited to certain values.In all of the algorithms, the population number has been chosen as four and the number of iterations has been limited to 25.For this reason, although the problem is simple, the performance of some algorithms    the other hand, the highest elapsed time also belongs to CGO.In light of this information, it can be deduced that an iteration step of the CGO algorithm takes longer than other algorithms.

Case 1
Case 1 is based on the fact that half of the modules in the test system are shaded to have 500W=m 2 irradiance.The other half of the modules in the system have 1000W=m 2 radiation on their surface.Under this partial shading condition, the P-V characteristic of the test system has two peaks, as given in Figure 2. One of these peaks is the global maximum, and the other is the local maximum.The global maximum power point is approximately 1765.83W. All of the analyzes performed for case 0 have been applied here in the same order as in all other case analyses.As can be seen, there is a general decrease in the number of global optimum detections in Case 1 compared to Case 0, Figure 6.It is clear that the local optimum formed in the P-V characteristic due to partial shading affects the success of the algorithms.According to the results, the most successful algorithm is MPA with 990 detections.MPA is followed by the RKO algorithm with 988 detections.Considering the criteria given in Figure 7, MPA algorithm has the best values here as well.MPA is followed by the CGO algorithm.Although it is behind RKO in detecting the optimum value, it is more successful in statistical performance.Thus, it means that the values obtained for Case 1 over CGO are more stable than for RKO.
The temporal performance of the algorithms on the computations realized in Case 1 can be seen from the data shared in Figure 8. AOA, EO, GWO, and SCA algorithms have shorter elapsed times and low amounts of outliers.Still, their success in detecting global optima and their stability is lower than other algorithms.

Case 2
In case 2, a partial shading situation with three different radiation levels is studied.The P-V characteristic of the system is a curve consisting of three peaks as given in Figure 2 and its global maximum value is 1519.20 W. MPA and RKO algorithms have achieved to detect the global maximum with the highest number for Case 2, as in previous cases.In the horizontal plane of Figure 9, it can be observed that some of the data points have been concentrated around 1000W.This indicates that some algorithms have been trapped in the local maximum of the P-V characteristic.
Other performance criteria for Case 2 are given in Figure 10.Although CGO has a lower global optimum detection number than JO and BES algorithms, it has higher average efficiency and lower error metric values than these two algorithms.According to the cumulative evaluation of the performance data, MPA, RKO, and CGO are the three most successful algorithms for Case 2. As can be seen from Figure 11(a), the highest elapsed time belongs to CGO and the third highest is MPA.Although it may seem like a disappointment at first glance, it does not constitute a significant disadvantage in today's technology.It should be noted that the difference between the average elapsed time values of the fastest and the slowest algorithms is 6 ms.This value does not mean a serious issue in MPPT applications.

Case 3
In case 3, four different irradiance values have been systematically distributed over the system modules.The irradiance values of 750, 300, 450, and 950 W=m 2 have been distributed so that the module in the same row of each array has the same irradiance.As a result, the P-V characteristics have become a curve with four peaks as shown in Figure 2. The global maximum value is 1244.75W. The local maximum value closest to the global is around 1100 W. Considering the data points concentrated on this value on Figure 12, it is obvious that most of algorithms have been trapped at this value.MPA, RKO, and CGO algorithms proved their superiority in detecting the maximum power point by far, Figure 12.The success of these three algorithms can also be confirmed by the statistical values given in Figure 13.The CGO algorithm has been the algorithm that showed the most successful results in all metrics.Although AHA and HGSO algorithms had very low global optimum detection rate, these algorithms had remarkable results on statistical metrics.It can be deduced that for the case of AHA and HGSO cannot fully detect the global optimum value, these algorithms have achieved to give close values to the global.CGO and MPA algorithms have the longest elapsed time values in this case as well.Among the most successful algorithms for Case 3, the algorithm with the best temporal performance is RKO, Figure 14.

Case 4
In case 4, each module of the test system has a different irradiance value, as given in the fifth column of Table 4.The aim of designing the case study in this way is to increase the number of  peaks in the P-V curve and obtain local maximums close to the global value.By the inclusion of such a challenging case in the study, it has been thought that it could provide definite conclusions about the persistence of the success of the algorithms.The P-V curve for Case 4 is given in Figure 2. The curve has five peaks and the global maximum point is 1167.20 W. RKO, MPA, JO and BES stand out in the analyzes performed for Case 4 with a global optimum detection success of over 900 per 1000, Figure 15.
The performance criteria of the algorithms are given in Figure 16.Considering the error metrics, RKO is the first and CGO is the second-best algorithm.Especially, in root mean square error the lowest value belongs to CGO.In light of this information, it can be deduced that the CGO, which has a high detection number of 868, has given values very close to the global optimum in the remaining 132 executions.These results remark the consistency of CGO.On the other hand, BES algorithm has given high values in error metrics.Returning to the horizontal plane in Figure 15, it can be observed that values far from the global optimum give results.
Case 3 has a global maximum and three locals; Case 4 contains more local maximums.When the values of both case studies of the algorithms are examined, it has been understood that they have higher success in Case 4 and more difficulty in Case 3. From here, it can be deduced that being close the local maximums to each other and to the global maximum, rather than the excess of local maximums in a problem, corresponds to a bigger challenge for algorithms.According to the results given in Figure 17(a), it has a lower elapsed time than JO, RKO, and MPA algorithms, and it also has a lower mean iteration value, Figure 17(b).

Case 5
Considering the results obtained in Cases 3 and 4, it has been seen that the algorithms were more successful in Case 4. The P-V characteristic in Case 4 has more peaks than in Case 3.However, in Case 4, the global maximum is more distinctive than the local maximum.In Case 3, the local and global values are closer together.Therefore, it is concluded that the positions of local and global maximums relative to each other are more effective on the computational effort of the algorithms rather than the number of peaks in the characteristic curve.From this point of view, another case called Case 5 is examined as a case analysis with the peaks closer to each other.In Case 5, the irradiance data of the partial shading conditions considered for Case 3 have been taken exactly, and the temperature values of the modules are arranged as given in Table 4. Increasing temperature has a negative effect on the efficiency of PV cells.In the case of long-term partial shading, the temperature values of the modules may differ.In such a case, the value of characteristic open circuit voltage decreases, and therefore the maximum power value is lower.The P-V characteristic curve for Case 5 is given in Figure 2 and it can be seen there, the global maximum and local maximums are closer to each other than in Case 3.
Considering the results for case 5, as predicted, the ability of the algorithms to detect the maximum power point has decreased.According to the number of detecting the global maximum value (Figure 18), MPA has given better results than other algorithms.However, RKO and CGO algorithms have been able to give statistically more consistent results than MPA, Figure 19.
According to Figure 20(a), the RKO algorithm has the lowest elapsed time value among the successful algorithms.The CGO algorithm has the lowest iteration number and the longest elapsed time as in all of the Cases, Figure 20(b).

Case 6
In Case 6, the performances of algorithms under dynamic operation have been investigated.For this purpose, irradiance data with one minute resolution has been taken into account, and the calculated energy outputs for different algorithms have been examined.As seen in the results from previous case studies, all the algorithms are able to determine the global maximum in a time that very less than a minute.In Figure 21, the power variation for a sample processing step has been given.The point τ 1 is the settling time which corresponds to the moment when the global or local maximum is reached.The success of the algorithms is related to the short settling time and the consistency of the convergence value with the global maximum.
The energy calculation for each minute has been realized as in the equations shared below.where i is the number of the time step and k is the amount of the required step for reaching the settling time.P i and P k are instantaneous power at i th iteration and global/local maximum power, respectively.E minute is the amount of energy obtained with operation in a minute.E hour is the amount of energy obtained from the one-hour operation.
Using the findings obtained in the previous six case analysis, three algorithms with the highest success have been determined for all cases.Instead of examining the performance of all algorithms under dynamic operation, it has been thought that it would be more functional to compare CGO, MPA and RKO algorithms, which have proven their success in quite comprehensive evaluations.Pareto front method has been used in the determination of the three most successful algorithms.
In the study, the algorithms have been examined on multi-criteria evaluation such as the number of detecting the maximum power point, six different statistical metrics, and elapsed time.Algorithms may not have the same performance in all criteria.The Pareto Front method has been used in order to obtain a systematic approach for considering all the criteria.A three-dimensional evaluation has been taken as the basis: number of the global maximum detection, statistical performance, and elapsed time.Number of the global maximum detection and statistical performance metric are normalized to be between [0,1] values in order to provide an equivalent evaluation.The Pareto Front method has been applied separately for each case study.Each algorithm is included in the Pareto frontier as a feasible choice.Algorithms that give non-dominated results from all of the Pareto Frontiers are CGO, MPA, and RKO algorithms.These algorithms have been run 500 times with daily irradiance data.The data has a one-minute resolution, which corresponds to 900 data points (for 21 June, Istanbul).The efficiency values of each execution of the algorithms are given in the Figure 22.The figure has been plotted with identical axis ranges for having an understandable illustration.As can be seen, the RKO algorithm has given the most consistent results.
In Table 5, the average efficiency values of the algorithms are given.Considering the results, the most successful algorithm is RKO, the second is MPA, and the third is CGO.

Conclusion
In this study, the performances of 20 optimization algorithms in solving the MPPT problem have been examined.The study has up-to-date content the aspect of selecting nineteen algorithms proposed in the last three years.It is aimed to determine the most competent algorithms for the solution of the MPPT problem.Analyses have been conducted on a total of seven cases in this context.These cases include one scenario with   uniform irradiance, four scenarios with different partial shading conditions, one scenario with nonuniform temperature distribution, and one scenario for dynamic operation.The performances of the algorithms have been examined over ten different criteria for each case.In the analysis of six cases, MPA and RKO algorithms always yielded results as the two most successful algorithms, according to the detection value of the global maximum point.The best performances of these two algorithms in global maximum point detection were in Case 0 with a success of over %99.Even in case 5, where the lowest values were obtained in terms of the global maximum detection, MPA and RKO were able to show the two best performances with a high success rate of above 86%, and 78%, respectively.The rest of the success ranking according to this criterion differs in each case analysis.Considering the error metrics, the values obtained for the CGO algorithm are impressive.In the dynamic MPPT operating analysis, the three most successful algorithms have been determined by the Pareto Front method applied with the results obtained from the other six case analyses.CGO, MPA and RKO algorithms gave non-dominated results in all of the Pareto frontiers obtained for each case.The application of the Pareto Front method has provided a systematic approach to the evaluation of the performances of the algorithms.In this respect, the study makes an important contribution to the literature and presents a new approach that can be taken as an example in future studies.
Another unique aspect of the study is the comprehensive analysis of the dynamic performance of the optimization algorithms with a one-minute resolution daily irradiance data.The daily energy yield by the MPPT methods based on the determined algorithms has been estimated.The results have proven the success of the RKO algorithm.Although significant advances have been experienced in microcontroller technology in recent years, the hardware used in practical MPPT applications does not have as high computational power as computers.Therefore, an experimental study in the future will contribute to obtaining more reliable information on the use of metaheuristic optimization algorithms in practice.The knowledge and findings obtained in the study provide a comprehensive theoretical background on the subject.The study is expected to be an important reference for practical studies planned to be realized in the future.In addition, due to the fact that up-to-date algorithms have been examined within the scope of the study, it is thought that it will benefit researchers from different disciplines.

Figure 1 .
Figure 1.Configuration of the test system.

Figure 2 .
Figure 2. P-V characteristics of each case.

Figure 3 .
Figure 3. Results on the performance of the algorithms on detecting global optima for Case 0.

Figure 6 .
Figure 6.Results on the performance of the algorithms on detecting global optima for Case 1.

Figure 8 .
Figure 8.(a) Box plot for the Algorithms' elapsed time in Case 1, (b) Average number of iterations of the algorithms to reach the local/global point in Case 1.

Figure 9 .
Figure 9. Results on the performance of the algorithms on detecting global optima for Case 2.

Figure 11 .
Figure 11.(a) Box plot for the Algorithms' elapsed time in Case 2, (b) Average number of iterations of the algorithms to reach the local/global point in Case 2.

Figure 12 .
Figure 12. Results on the performance of the algorithms on detecting global optima for Case 3.

Figure 14 .
Figure 14.(a) Box plot for the Algorithms' elapsed time in Case 3, (b) Average number of iterations of the algorithms to reach the local/global point in Case 3.

Figure 15 .
Figure 15.Results on the performance of the algorithms on detecting global optima for Case 4.

Figure 18 .
Figure 18.Results on the performance of the algorithms on detecting global optima for Case 5.

Figure 21 .
Figure 21.(a) Daily Solar Irradiation, (b) Power output for a sample processing step.

Table 1 .
Related studies in the literature for last few years.

Table 2 .
Specification of PV module used in simulations.

Table 3 .
Algorithms considered in the study and the years.

Table 4 .
Partial shading and temperature values for the analyzed cases.

Table 5 .
Algorithms efficiency for dynamic MPPT problem.