Comparison of Bioinspired Techniques for Tracking Maximum Power under Variable Environmental Conditions

Yadav, Dilip; Singh, Nidhi; Giri, Nimay Chandra; Bhadoria, Vikas Singh; Sarker, Subrata Kumar

doi:https://doi.org/10.1155/2024/6678384

International Journal of Intelligent Systems

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Abstract Introduction Materials and Methods Results and Discussion Conclusions Abbreviations Data Availability Conflicts of Interest Authors’ Contributions Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2024 | Article ID 6678384 | https://doi.org/10.1155/2024/6678384

Comparison of Bioinspired Techniques for Tracking Maximum Power under Variable Environmental Conditions

Dilip Yadav,¹Nidhi Singh,¹Nimay Chandra Giri,²Vikas Singh Bhadoria,³and Subrata Kumar Sarker⁴

Academic Editor: Alexander Hošovský

Received17 Jun 2023

Revised25 Jan 2024

Accepted22 Mar 2024

Published12 Apr 2024

Abstract

This paper presents a comparative analysis of bioinspired algorithms employed on a PV system subject to standard conditions, under step-change of irradiance conditions, and a partial shading condition for tracking the global maximum power point (GMPP). Four performance analysis and comparison techniques are artificial bee colony, particle swarm optimization, genetic algorithm, and a new metaheuristic technique called jellyfish optimization, respectively. These existing algorithms are well-known for tracking the GMPP with high efficiency. This paper compares these algorithms based on extracting GMPP in terms of maximum power from a PV module running at a uniform (STC), nonuniform solar irradiation (under step-change of irradiance), and partial shading conditions (PSCs). For analysis and comparison, two modules are taken: 1Soltech-1STH-215P and SolarWorld Industries GmbH Sunmodule plus SW 245 poly module, which are considered to form a panel by connecting four series modules. Comparison is based on maximum power tracking, total execution time, and minimum number of iterations to achieve the GMPP with high tracking efficiency and minimum error. Minitab software finds the regression equation (objective function) for STC, step-changing irradiation, and PSC. The reliability of the data (P-V curves) was measured in terms of p value, R, , and VIF. The value comes out to be near 1, which shows the accuracy of the data. The simulation results prove that the new evolutionary jellyfish optimization technique gives better results in terms of higher tracking efficiency with very less time to obtain GMPP in all environmental conditions, with a higher efficiency of 98 to 99.9% with less time of 0.0386 to 0.1219 sec in comparison to ABC, GA, and PSO. The RMSE value for the proposed method JFO (0.59) is much lower than that of ABC, GA, and PSO.

1. Introduction

Photovoltaic (PV) technology is a promising one that sees annual capacity growth around the globe as it is a clean and convenient energy source. In recent years, renewable energy sources, such as solar, tidal, biogas, wind, and solar power, have become essential for power generation [1, 2]. One such potential innovation is the solar cell, which transforms solar energy into electrical energy that can be used directly in various ways. Although solar or PV cells are beneficial, they cannot convert all sun energy into electricity. Conversion efficiency refers to the proportion of solar energy a PV device turns into useable power [3]. The MPP is often reached by modifying the PV panel power, which is a function of voltage and current. Power electronic converters (DC-DC converters) [4] are vital in stabilizing the voltage in all conditions. According to the authors in [5], there are two types of MPPT control methods for PV systems: traditional methods and soft-computing approaches, which are further subdivided into artificial intelligence, bionature-inspired, and swarm-based MPPT techniques. Soft-computing, artificial intelligence (AI), and bioinspired (BI) techniques are the most powerful methods of tracking MPP, and they are highly effective and highly efficient when it comes to multiconstraint issues in solar PV optimization [3, 6]. Conventional MPPT algorithms fail to find the maximum point when environmental factors repeatedly vary; therefore, they are suitable for low-power and high-power applications [7]. The P-V characteristic curve exhibits a nonlinear, time-varying MPP problem due to the sudden changes in environmental variables, namely, sun irradiance and temperature. To overcome the problem of the conventional method, artificial intelligence was introduced, which could deal with the nonlinear behavior occurring in the PV system; moreover, they did not rely on the model or PV features. They could even use online follow-ups and self-learning to improve the algorithm [6, 7]. However, they are complex, costly, and take longer to determine the MPP. These MPPT algorithms are, unfortunately, more expensive to implement than traditional ones and need a specific training dataset.

Heuristic optimization methodologies are becoming more common as they can handle the challenges of traditional and AI-based. Moreover, bioinspired algorithms [8] involve fewer computations than AI algorithms. These heuristic approaches are beneficial and effective in finding the optimal solution for complicated problems in science and engineering, and they often do not need extensive mathematical expertise. Different applications of optimization techniques in variousfields of engineering are discussed in [8]. A few MPPT approaches have been suggested [6–8] and used recently to improve the PV yield under various atmospheric conditions. According to the authors in [9], MPPT problems are typically solved by considering five different techniques: the first approach employs techniques that consider constant variables, such as the PV current linear relationship with the short-circuit current; the traditional perturb and observe (P and O) strategy and its modified tactics are used in the second method, which involves the trial-and-error process; the third utilises comparison and measurement techniques, particularly the look-up table method; and the fourth employs mathematically based computation techniques such as incremental conductance (INC), while the last approach makes use of soft-computing techniques such as particle swarm optimization (PSO) or fuzzy logic controller (FLC) [6]. Bioinspired algorithms, such as swarm insight (SI) methodologies [6–9], have gained increased recognition as excellent optimization strategies for delivering the best responses and solving challenging issues during the PSC. The authors in [10] have given the classification of a few well-known MPP controllers with the advantages and disadvantages of conventional and optimization algorithms.

The classification of different algorithms is illustrated in Figure 1. A few of the well-known optimization techniques are artificial immune system (AIS) [8], ant colony optimization (ACO) [5, 8, 12–14], moth-flame optimization (MFO) [12, 15], whale optimization algorithm (WOA) [12], butterfly optimization (BFO) algorithm [12], shuffled frog leaping algorithms (SFLA) [12], slap swarm algorithm [12], firefly algorithm (FA) [12, 16, 17], artificial bee colony (ABC) [5, 8, 9, 12, 13, 16–20], bat-search algorithm (BA) [12, 17], grey wolf optimization (GWO) [5, 12, 13, 15, 17, 21, 22], genetic algorithm (GA) [8, 12–14, 21, 23], flower pollination optimization (FPO) [12, 16, 24], JAYA [16], DE [8, 16], cuckoo search (CS) [5, 6, 12, 13, 15, 16, 24], particle swarm optimization (PSO) [5, 6, 8, 13–17, 19–29], seagull optimization algorithm (SOA) [27], Harris hawk optimization (HHO) [16, 20], African vultures optimization algorithm (AVOA) [30], AOA-based PI-IC-MPPT [21], grasshopper optimization algorithm (GOA) [15], Aquila optimizer (AO) [21], antlion optimizer (ALO) [21], tuna swarm optimization (TSO) [21], black widow spider (BWS), squirrel search algorithm (SSA) [15], yellow saddle goatfish algorithm (YSGA), and butterfly optimization algorithm (BOA) [29]. These are optimization techniques that have been utilized for comparing different factors in terms of tracking time [16, 21, 24, 29], tracking efficiency [13, 14, 16, 20, 22, 24, 29, 31], root mean square error [12, 14, 15, 18, 20], and mean absolute error [20]. Some of the new optimization techniques that have been recently introduced in the PV system analysis in 2022 and 2023 are specified as seagull optimization algorithm [27], African vulture optimization [30], jellyfish optimization algorithm [32], arithmetic optimization algorithm [21], reptile search algorithm [22], particle swarm optimization with butterfly optimization algorithm [29], DGBCO [33], EVO [34], GRNN-OPA [35], MRO [36], and many others that are utilized in different fields of engineering.

A Google Scholar study was conducted during the past five years, 2015–2020, on nonuniform solar irradiance and shading conditions [23]. Evolutionary algorithms (EAs) have emerged as the frontrunner for MPP tracking problems under shading circumstances [25]. These algorithms confirm that the PV system always runs at its GMPP, regardless of the change in the atmospheric condition (irradiation and temperature). Several approaches fail to determine the global point because they get trapped in local points or local maxima and minima. The paper [23, 24] focuses on classifications of optimization techniques, mathematical expressions, operational principles, and flowcharts [26]. This paper presents an attempt to highlight the present and future problems associated with developing high-performance PV systems. The determination of numerous parameters might cause the optimization approach to become challenging or complicated [27]. The literature research on finding popular optimization approaches is shown in Table 1. According to the authors in [20], the PSO gives optimum efficiency even under PSC, but it quickly falls into local optima, and as a result, determining MPP takes a long time. ABC has a strong exploration ability to follow MPP, though these approaches are highly prone to exploitation. [37] gives the modeling [38], electrical characteristics, and [39] parameter estimation of photovoltaic strings under PSC and explains the importance of bypass diodes The authors in [15, 19, 40–42] has reviewed and compared the performance of some well-known optimization algorithms under partially shaded conditions. The authors in [13] have reviewed and given the performance comparisons of conventional, artificial intelligence, and optimization-based MPPT in terms of tracking capability, convergence, implementation, tracking accuracy, tracking speed, efficiency, economy, and application and have given advantages and disadvantages of different optimization techniques used to track the GMPP. In [43], a comprehensive comparative analysis of the twenty-eight adaptive MPPT algorithms is performed based on the tracking time, steady-state oscillations, conversion efficiency, algorithm complexity, implementation cost, and the capability to perform on the partial shading conditions. This will help the readers to select the suitable MPPT methods. The authors in [44] focused on the use of jellyfish search optimizer in solving optimization problems. The authors in [32] have given a detailed explanation of the jellyfish optimization algorithm with its application in engineering. The authors in [11, 14] have shown a comparison of the different optimization techniques [28]. PSO and FPA are compared with ten (10) samples for PSC and it is concluded that the FPA produces 86.03 W power output compared to the power output in PSO of 85.5 W under PSC in the PV panel. The authors in [21] introduced AOA-based PI-IC-MPPT, which gives better results than MIC, GWO, GA, and PSO in terms of reducing rise time and settling time. The authors in [22] used the RAS optimization technique and proved that RSA gives better efficiency than DOA, GWO, WOA, and PSO. The authors in [29] used hybrid methods such as BOA-PSO-based algorithm and found that the PSO-BOA algorithm outperforms the PSO and BOA in terms of convergence accuracy, with a tracking accuracy of not less than 99.94%. The authors in [33] concluded that DGBCO has significantly less RMSE value than other algorithms. The authors in [45] reviewed some algorithms and proposed a SHTS algorithm that was compared with hybrid algorithms in terms of tracking speed and accuracy under partial shading conditions. Hybrid IABC + SHTS performs excellently in precisely identifying the GMPP of PV systems with phenomenal rapidity among multiple peaks. The authors in [34] introduced the energy valley optimizer (EVO) MPPT algorithm, showcasing 30% quicker tracking and 80% faster settling time. Research [35] also highlights the GRNN-OPA-based MPPT’s superior performance with 35% faster tracking, 90–110% quicker settling time, and 4–8% higher energy accumulation. In [36], the proposed controller achieves an average of 99.95% power output and 220 ms response time under dynamic thermal conditions, demonstrating 38–70% faster tracking of the maximum power point in dynamic operating conditions.

Many researchers [31, 46] have used regression analysis for forecasting PV power and concluded that one of the convenient ways to model PV performance is linear regression models. A multiple linear regression model was implemented for PV systems for MPPT, and regression analysis of a photovoltaic system in terms of RMSE was considered to generate the regression coefficient. The authors in [46] have given the application of regression analysis and machine learning for tracking the maximum power and the performance analysis of PV modules using regression analysis. According to the authors in [31], the accuracy obtainable for the prediction will depend on the value of the parameter , which lies between 0 and 1. The closer the value of to 1, the more accurately the PV module regression model is predicted to function [31, 46].

This paper uses a new metaheuristic JFO algorithm to track the PV panel’s GMPP with the help of regression analysis of the PV curve obtained by P-V curves. The objective function equation is formulated by using the regression analysis with the help of the Minitab software. The equation comprises of correlation factors that determine the power voltage and current relationship. This equation is optimized by using the JFO to find the voltage and current’s value corresponding to GMPP. Many authors [6, 10, 12, 16–19, 22, 23, 27, 29, 31, 43] have compared algorithms based on tracking capability, total execution time, tracking efficiency [16, 29], and accuracy. The authors in [25] compared in terms of population size, [14, 24] compared in terms of Iteration. The authors in [7] analysed the performance at different irradiation and PSC. Refrences [12, 14, 15, 18, 20, 33] compared RMSE and, the authors in [20] in terms of MAE. In this paper, three cases, STC, step-changing irradiation, and PSC, are taken to validate the performance of JFO in terms of maximum power tracking, total execution time, the minimum number of iterations to achieve the GMPP with high tracking efficiency, and RMSE for the same set of population and number of iterations. The analysis and comparison between the existing techniques (GA, ABC, and PSO) and the proposed technique (JFO) is carried out with a smaller population size (N_pop = 8) and maximum iterations (Ite_Max = 100). The module parameters, specification, irradiation, and temperature are kept the same for all cases. Also, the effect of air mass, wind, module heating, soiling, panel orientation, and humidity has not been considered in this research.

Section 2 briefly introduces the PV system description with the PV panel’s main equations, explains different optimization techniques with the flowchart, thoroughly explains how the JFO method works, and illustrates the critical phases in its execution. Finally, Section 3 gives the process of objective function formation with the help of Minitab software (regression model) in which power was made a function of voltage and current with coefficients that describe the P-V curve of the PV system for different environmental conditions, i.e., at STC, step-changing irradiations, and PSC. The MATLAB/simulation software was used to find the response of other optimization techniques. The results obtained in both case studies (1Soltech-1STH-215P and SolarWorld Industries GmbH Sunmodule plus SW 245 poly module) are compared with other optimization algorithms, i.e., PSO, GA, ABC, and JFO-based optimization at STC, step-changing irradiation, and PSC conditions for the same set of iterations and population size. Lastly, a comparison between the proposed technique and other optimization techniques is made. The results prove that the JFO-based optimization technique gives the desired output with less population and in less time with higher efficiency and lowest RMSE value. These findings and problem-solving techniques prove the novelty of the paper and JFO algorithm. Finally, conclusions are drawn in Section 4.

2. Materials and Methods

A photovoltaic cell is an energy-harvesting technology that converts solar energy into practical electricity through a photovoltaic effect [37]. The smallest unit is called a solar cell, the arrangement of cells in series and parallel combination forms module, arrangement of modules into series or parallel combination form panel, and a combination of modules form array. Irradiation and temperature significantly impact the performance of PV power generation, as solar irradiation is nonuniform in real life [38]. Tracking the real MPP is thus a crucial factor to consider while choosing the technique. The complexity of an algorithm’s design and efficiency significantly impacts how accurate and efficient the optimization techniques used for tracking GMPP are. The PV system’s constant steady-state response, tracking time, and efficiency were the primary deciding factors while evaluating the different optimization techniques. Considering all these factors, the design parameters of the PV module and other optimizations are illustrated in the subsections given as follows.

2.1. PV System Description

An antiparallel diode coupled to series resistance () and parallel resistance (R_sh) is used to represent the equivalent circuit of a single-diode PV cell (see Figure 2). The photovoltaic current generated (I_pv) is expressed as [27, 37] follows:

The total module current is calculated by using equation (1), where I_pv is the module current, V_pv is the module voltage, I_ph is the photogenerated current, is the diode reverse saturation current, I_sh is the current through shunt resistance, is the series resistance, R_sh is the shunt resistance, is the number of cells, is the junction’s thermal voltage and can be expressed as = (k α T)/q, where k is the Boltzmann’s constant 1.38 × 10⁻² J/K, q is the electron charge equal to 1.602 × 10^–19 C, T is the temperature in kelvin, and α is the ideality factor constant [44], and [ ()], where I_sc,ref is the solar cell short-circuit current, G_ref = 1000 W/m², T_ref = 25°C, is the solar cell short-circuit temperature coefficient, usually provided by the manufacturer (A/K), and G is the actual irradiance intensity (W/m²) [27].

When PV modules are exposed to high solar irradiation and low solar irradiation, they produce less current than unshaded modules, resulting in a phenomenon known as mismatch loss, which is also known as the partial shading condition (PSC). PSC affects the electrical characteristics of PV strings, so bypass diodes are coupled in parallel to every module to prevent this mismatch loss. The following equation [16] represents the bypass diode’s reverse bias saturation current (I_sat,bp) computed:

The simulation model is designed in MATLAB software to form a panel by combining four series modules (Figure 3(a)) that are connected by a bypass diode [38]. In PV modules, bypass diodes are utilized to avoid generating an excessive reverse voltage across the cells in the presence of shading. When one or more PV system cells are shaded and receive different solar radiation, it results in a partial shading condition [38]. The shadows projected by nearby trees, clouds, buildings, dust, and bird droppings are some causes of shading conditions. A frequent change in the irradiation level can permanently harm PV modules by generating cell mismatches, hotspots, and unexpected system losses in the PV system. Such a problem in the PV system can be avoided by connecting it to the PV module with a bypass diode. The P-V curve produced by these diodes exhibits various power peaks (Figure 3(b)), known as LMPP and GMPP.

(a)

(b)

2.2. Different Algorithms for Tracking GMPP

Solving challenging mathematical puzzles in various domains is one of the most difficult tasks for a human being. Nature is one of the excellent and extensive sources of inspiration that help lead the way in solving these complex problems efficiently. Optimization problems should keep the balance between the dependent variables while defining the objective functions. Many optimization methods have proved their importance in solving nondifferentiable and discontinuous problems in solar power generation to track the GMPP during the PSC and under step-change of irradiance conditions [6–10, 12, 16–20, 23–27, 30]. Due to some advantages [37] over conventional methods and intelligent techniques, heuristic approaches are usually used in the paper as they can quickly adapt to algorithm changes, and ample space for possible optimal solutions is available for different problems.

PSO [5, 6, 8, 11, 13, 14, 16, 17, 19, 23–26], GA [8, 11–14, 23], and ABC [5, 8, 11–13, 16–19] are the most widely used optimization algorithms because of some advantages [5, 16, 17] such as their simple structure, independence of a mathematical model, capability to solve nonlinear and challenging mathematical problems, easy understanding, and high reliability. Each optimization technique considers a few deciding factors such as the number of populations and a few particles/food sources/chromosomes/jellyfish. The stopping criteria of each optimization technique are based on the previous best optimal solution compared with the current optimal solution such that the current solution should be greater than the last optimal solution value. The optimal solution can be in terms of P_max or less error or any parameter (cost function) that can be maximized or minimized. Each algorithm has some stopping criterion that helps determine the problem’s optimal solution. Root mean square error (RMSE) is an essential metric for assessing the effectiveness of MPPT methodologies. The following equation is used for this statistical analysis [33, 34].where P_pvi represents the power at STC, P_pv is the power tracked, and n represents the number of samples.

Regression analysis is a statistical approach that obtains the best coefficients to model the system with a minimum cumulative least square error. The accuracy obtainable for the prediction will depend on the value of the parameter , which lies between 0 and 1, and the nearer this value is to 1, the better the predicted accuracy of the regression model designed for the PV module [31, 46]. value is a statistical test that determines the probability of extreme results of the statistical data where its coefficient turns out to be zero, i.e., for a lower value of <0.05 [31]. In the literature, some researchers have tried to apply linear regression to model PV systems. The goodness of fit is defined as [46] follows:where is the mean value of and ns is the sample count. The value of and RMSE closer to zero represents the model with greater prediction strength [46].

A multiple linear regression model for PV can be denoted as follows [31]:where and , …, are the input variables (1 to n). The coefficient is the intercept, while values of , …, denote the slope coefficient of each input (explanatory) variable and the error e (the amount by which the predicted value is different from the actual value). The regression model estimates the best values, leading to the least error “R.” R is known as the correlation coefficient, and its value determines the strength and direction of linear association between the two variables under examination. Building a model with a small dataset and a high number of predictors leads to a model with low performance, and the correlation between predictors could increase, leading to high values of VIF (variance inflation factor) for predictors [31]. A VIF of <5 for their predictors makes them the potential models for independent variables. The collinearity of variables is checked through the VIF. The VIF of a predictor is low when it is <5, and the VIF of a predictor is moderate when it is <10 [31]. The values of the correlation coefficient R near 1 or 1 indicate a strong correlation between the two variables. In this paper, the value of R is 0.95, which shows the excellent correlation between the variables V and I with P_max. After using the regression analysis of the PV curve, an objective function is formed that is tested by calculating its RMSE value.

Different algorithms can find the GMPP at STC, under step-changing irradiation, and PSC [8–20, 23–27, 30, 37–43]. Artificial jellyfish optimization (JFO) [44] is a new novel swarm-based optimization algorithm with some advantages over other algorithms. JFO can balance exploration and exploitation strategies well and reach optimal solutions in less time [32, 44]. A comparative analysis is performed for the two panels for STC, step-change of irradiances, and PSC conditions. JFO is compared among the PSO, ABC, and GA. A brief introduction of these algorithms is as follows.

2.2.1. Genetic Algorithm (GA)

It is one of the most influential evolutionary algorithms based on the theory that living things have evolved biologically and Darwin’s principle of “survival of the fittest” [8]. A function optimizer is another name for it [12, 23]. GA commonly uses a fixed population size. Three genetic processes are employed: mutation, cross-over, and selection. The process begins with developing a random population of solutions, after which it uses the fitness function or objective function to assess the fitness of each chromosome. Then, the best chromosome is picked for the mating pool, and a new set of solutions known as offspring are produced when these chromosomes encounter cross-over and mutation (switches from 1 to 0). To improve the solution selected from the present generation, we choose the most suitable offspring to transmit to future generations. The method is repeated until the requirements are met (P_max). Finally, the overview of the genetic algorithm’s [8, 12, 13, 23] working principle is displayed in Figure 4(a) [13].

(a)

(b)

2.2.2. Artificial Bee Colony (ABC)

Karaboga proposed the artificial bee colony (ABC) method to optimize numerical challenges in 2005 [17, 44]. The ABC algorithm is a swarm-based metaheuristic algorithm. It was influenced by how honeybees used intelligence in their foraging. The algorithm is based explicitly on the model used for honeybee colony foraging behavior [5, 8, 12, 16–19]. Its operation is based on three phases [17]: the employed bee’s phase, the onlooker bee’s phase, and the scouting phase. The ABC working method is shown in Figure 4(b).

In ABC, the artificial bees update each position over time using equation (6). The bee’s primary goal is finding the best food source to produce the most nectar [8]. Then, the scout bees randomly pick the food sources and fly around the searched area. Finally, the observing bees choose the food source based on the expected amount of nectar [16]. They only consider the location of the leading food source during the greedy search process. Whenever a food source is fully utilized, an employed bee transforms into a scout bee and investigates a new area. While creating a new position, the position that best matches the previously created one is chosen. In equation (6) [16], i^th is the food source in the swarm (), where x_maxj and x_minj are the bounds in the j^th dimension and a random number (rand) range from 0 to 1.

The dependency of random food source () is on selection probability () that is represented in terms of food source () with the food source number () given in the following equation [16]:

By comparing a probability factor associated with several food areas, the location of the food source is determined [5]. The primary objective of the algorithm is to substitute a source of nectar with a higher level of food source. The main advantages are simplicity, high flexibility, strong robustness, few control parameters, ease, and combination with other methods.

2.2.3. Particle Swarm Optimization (PSO)

V. Kennedy and Eberhart gave this algorithm structure in 1995 [16]. Like many optimization algorithms, PSO draws inspiration from the natural life cycle and the behaviors during this period. Fish, insect, and bird herd behavior were studied during the development of the PSO and incorporated into the algorithm. Every particle has a velocity updating equation (8) and location updating equation (9), resulting in a change in variable according to the local best solution P_best,i and the globally best solution G_best, which are modified after each iteration by learning from the local best point [12, 16, 17, 23–26]. The PSO working flowchart is given in Figure 5(a). Each particle’s position refers to a set point for a variable. The best position is identified by using the following equation [23]:where is the velocity component used to represent the MPPT step size. The value of is calculated by using the following equation [23]:where is the velocity of the i^th swarm, is the learning factor, and , , , and are the position constant and random number, respectively. To use it in the script file (MATLAB), a few steps are needed to get the optimized value of the function. As a result, an algorithmic replacement program model is created to find the optimal solution for the parties.

(a)

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2.2.4. Jellyfish Optimization (JFO)

JFO is a new metaheuristic optimization algorithm based on jellyfish behavior. This method is inspired by the exploration behavior and movement patterns of Jellyfish [44]. In JFO, the amount of food at different locations varies. Therefore, jellyfish movement occurs by comparing the food proportions in an ocean. Its exploration and exploitation approach helps to reach optimal solutions in less time [32, 44]. A flowchart of the JFO algorithms is shown in Figure 5(b). This algorithm follows these rules for operation.(i)A “time control mechanism”(ii)Maximum food availability in that ocean area(iii)Active and passive motions of jellyfish

The ocean current can be calculated by using the following equation [44]:where the relevant updated position is determined by and γ is the motion coefficient.

Equation (11) [44] is considered to calculate the direction of motion, and equation (12) [44] is used to update the location. In equation (14), c (t) value varies between 0 and 1, is a constant value of 0.5, and t represents the time period at a particular instant [32].

The population initialization is performed by using the following equation [32]:

The logistic chaotic () value of i^th jellyfish, ∈ (0, 1), and the value of “a” are chosen as 4.0 [32, 44]. To use it in the script file (MATLAB), a few steps are needed to get the optimized value of the function.

Equation (14) represents the time control mechanism in the JFO, and equation (15) [32] describes the “initialization phase” [32, 44], the first step in JFO optimization. The second step is setting the boundary condition for different functions. The boundary condition is essential so that the jellyfish does not move outside the boundary search area. Equation (16) [32, 44] gives the limit of jellyfish in a search space area or boundary condition to jellyfish [32]. A jellyfish is located at in the d^th dimension.

The best location for the food is determined by the jellyfish, where the quantity of food is more. As a result, an algorithmic replacement program model is created that replicates the ocean jellyfish’s search patterns and movement. Due to the c (t) functions, it takes more iterations to track the maximum power, as it must find a new direction in every iteration.

3. Results and Discussion

For the analysis purpose and comparison purposes, two modules of different specifications are taken such as 1Soltech-1STH-215P (case 1) and SolarWorld Industries GmbH Sunmodule plus SW 245 poly panel (case 2) that is available in MATLAB R2021a software. Four modules are connected in series to design a panel. With the help of Minitab software, a regression equation or objective function is obtained in terms of voltage and current values obtained from the P-V curves at STC under step-change of irradiance and PSC condition. For step-change of irradiance conditions, different irradiation values are taken at constant temperatures at different time frames.

A similar environmental condition for STC is considered in the simulation model, having an air mass of 1.5, maximum irradiation of 1000 W/m^2, and a fixed temperature of 25°C. For PSC, a set of irradiations is taken and operated simultaneously, and the irradiation dataset values lie between 100 W/m² and 1000 W/m². The effect of air pressure, dust, humidity, and other losses are neglected in this paper. A simulation model is made with the help of MATLAB software. The panel output is taken in terms of V_max, I_max, and P_max, and the comparison of the optimization algorithm is based on parameters such as maximum iterations, number of populations, number of iterations to achieve the GMPP, execution time (sec), tracking efficiency, and RMSE.

3.1. Case Study 1: 1Soltech-1STH-215P Module

For analysis and comparison purposes, a single PV module of 213.15 watts is considered to form a panel; its specifications are given in Table 2. Four modules are taken and connected in series to form a panel with an output of approximately 852.6 watts, with a maximum voltage and current rating of 116 volts and 7.35 amperes to improve the power rating of the PV system.

The simulation model of a panel (four series connected modules) has irradiation and temperature as input parameters (Figure 6). The irradiation values are taken in such a way that the change in the response (I-V and P-V curves) can be analysed at STC (1000 watt/m²), and for step-change of irradiance (200, 400, 500, 600, 700, 800, and 1000 watt/m²) at a constant temperature of 25°C. The I-V and P-V curves for the same is given (Figures 7(a) and 7(b)). The effect of change in irradiation is given in terms of maximum voltage, current, and power (Table 3). The curve at 1000 W/m² represents the STC condition of the panel V_max, I_max, and P_max reading for the STC and step-change of irradiances (Table 3 and Figures 7(a) and 7(b)).

(a)

(b)

From the results, it can be observed that with the change in the value of irradiation, there is a significantly less fluctuation in the V_max value, but a significant variation is found in the I_max and P_max values, which shows that the panel’s I_max and P_max values are more sensitive toward the irradiation value.

Irradiance variations affect the overall performance of solar cells/modules/panels. The power the PV panel receives from the sun varies with the time of the day, which impacts solar cell efficiency and its fill factor (FF). For analysing the effect on the panel under step-change of irradiance, in the model (Figure 6), the irradiation values are changed continuously with the time period of 0, 2, 3, 4, and 5 secs for the irradiation value of 500, 700, 800, and 1000 corresponding to the curves shown in Figures 8(a) and 8(b). In addition, the P_max, V_max, and I_max values are given in Table 3 for the step-change of irradiance conditions. The partial shading condition (PSC) arises when panels are subjected to different irradiation levels caused by nonuniform shading. As a result, the PV array’s unshaded module receives higher solar irradiation, while the shaded module receives lesser solar irradiation. From an analysis point of view, a panel is designed by connecting four modules (1Soltech-1STH-215P) in series with the help of a bypass diode (Figure 9). Then, its I-V and P-V curves are analysed for PSC. Irradiation values range from 400 W/m² to 1000 W/m² (Figures 10(a) and 10(b)). In PSC, the input is in terms of irradiation values, and its output is in terms of V_max, I_max, and P_max values (Table 4) for different cases. For case 4, irradiation values of 400, 500, 700, and 1000 W/m² have been considered, for which each module is given different irradiation while showing the shading condition. The P-V curve for the PSC condition is shown in Figure 10(b).

(a)

(b)

(a)

(b)

Optimization techniques are well-known for solving nonlinear problems under step-change of irradiance and PSC. So, for performance and comparison purposes, a few well-known optimization techniques, such as PSO, GA, ABC, and the proposed JFO technique, are used to track the panel’s maximum power. First, the “Minitab” software calculates the regression equation (objective function). The predictor’s coefficients, along with the p values, the coefficient of correlation (R), the coefficient of determination (), and the root mean squared error (RMSE) are determined. Summary statistics are taken in terms of , (adj.), p values, and VIF performance score with the values of 0.9, 0.98, 0.01e − 10, and 0.23, which shows that the data collected are reliable and regression analysis is possible on the chosen date of the P-V curve. With the help of the regression equation, a MATLAB code is written for different optimization techniques to solve this regression equation calculated for STC, step-changing irradiation, and PSC.

The regression equation values for STC condition, under step-change of irradiance, and PSC condition can be obtained by choosing the voltage and current values as input variables and the output in terms of the maximum power generated at a particular irradiation value. Equation (17) represents the regression equation for the STC taken from the P-V curve for 1000 W/m² irradiation (Figure 7(b)). Equation (18) represents the regression equation for the step-change of irradiance values taken from the P-V curve (Figure 8(b)), and equation (19) gives the regression equation for PSC taken from the P-V curve for case 4 (Figure 10(b)).

The regression equation at STC condition is

The regression equation for the condition is

The regression equation for the partial shading condition iswhere x1 represents the voltage and x2 represents the current of the PV panel. As per the best knowledge, constant parameters [14, 19, 23, 25, 44] are assigned for different optimization techniques (Table 5). Equations (17)–(19) are the three objective functions for STC, under step-change of irradiance and PSC, that need to be maximized using ABC, PSO, GA, and JFO.

As the parameters are set (Table 5) for ABC, GA, PSO, and JFO, few of the parameters are kept the same, i.e., the number of populations, maximum iteration, and lower and upper limit boundary conditions so that the comparison can be made in terms of maximum power (P_max) and the number of iterations at which the maximum power is obtained.

The graphical results and magnified view of maximum power tracked vs. maximum iterations for the different optimization techniques for the STC condition are shown in Figure 11. The response is taken in terms of the maximum iteration at which the maximum power is obtained with the total execution time (Table 6). From the results, it can be concluded that the JFO technique gives the desired maximum power of 851.986 watts in less than 0.0391 sec, with a tracking efficiency of 99.8%. PSO attained the maximum power of 850.987 watts in a time period of 0.0506 sec. Still, it could not track the desired output of the panel, which was 852.4 watts, where ABC takes much execution time (1.0287 sec.) compared to other techniques. From the point of view of overall performance, JFO > PSO > ABC > GA.

The graphical results of the different optimization techniques for the step-change of irradiance conditions are shown in Figure 12. As per the results obtained (Table 7), it can be concluded that the JFO-based optimization technique can track the maximum power of approximately 835.274 watts with a significantly less time of 0.086 sec. In contrast, PSO was able to track the maximum capacity of 836.114 watts in 10 iterations.

The efficiency of PSO is slightly less than that of JFO, where ABC could track 826.346 watts, and the total executing time of the algorithm was 0.983 seconds, the highest of all algorithms. GA has the least maximum power with an execution time of 0.091 sec. Considering that the tracking efficiency and maximum power are attained in less time, the JFO performance is more accurate and efficient than other optimization techniques. The performance shows the tracking efficiency of JFO > PSO > ABC > GA for step-change of irradiance values.

The partial shading condition can be obtained by taking four series connected modules (Figure 9). To analyse the response of PSC, case 4 has been considered (Figure 10(b)). Equation (19) is the partial shading condition’s regression equation or objective function. The response of different optimization techniques is given in Figure 13. The results (Table 8) show that JFO can track the maximum power of 359.460 watts/m² in less than 0.1219 sec. In contrast, the execution time of other optimization techniques is more than JFO, and the maximum power is less than JFO. Regarding performance, it can be concluded that JFO can track the maximum power in less time with maximum power tracking efficiency.

3.2. Case Study 2: SolarWorld Industries GmbH Sunmodule plus SW 245 Poly Panel

The panel must operate at its P_max point to achieve maximum output in the PV system. Multiple PV modules can be connected in series or parallel combinations to increase the system’s power rating to form a panel. The simulation model (Sunmodule plus SW 245 poly panel) of the panel having a single module can obtain the maximum power of 245.168 watts at STC conditions. The SolarWorld Industries GmbH Sunmodule plus SW 245 poly specification for module and panel (four series connected) is given in Table 9. The I-V and P-V curves for the panel are provided for different irradiation values in Figure 14(a) and 14(b).

(a)

(b)

We suppose that the configuration (Figure 6) is a four series connected module. In that case, the maximum power tracking capability increases to 980.6 watts with the maximum voltage and current rating of 123.2 volts and 7.96 amps. The response for the single module and the panel (4-series connected) for different irradiation values, i.e., 400, 500, 700, 800, 900, and 1000 W/m², is given in Table 10. The maximum power for a panel with a maximum wattage is 980.6 watts. For analysing the panel for step-change of irradiance, in the model (Figure 6), the irradiation values are changed continuously with the time of 0, 2, 3, 4, and 5 secs, for the irradiation values of 500, 700, 800, 1000, and 1000 corresponding to the I-V and P-V curves shown in Figures 15(a) and 15(b). In addition, the panel’s P_max, V_max, and I_max values are given in Table 10 for the step-change of irradiance conditions.

(a)

(b)

A PSC is created by choosing the different irradiations, i.e., 400, 500, 700, and 1000 W/m², falling on the panel, i.e., four series connected modules (Figure 9), in such a way that multiple peaks can be obtained in the I-V and P-V curves (Figure 16) if nonuniform irradiation falls on the panel at the same time (shaded). Case 1 refers to STC, while cases 2, 3, and 4 refer to PSC (see Table 11). The PV module should operate at GMP for better panel performance. Cases 1 and 4, which represent the STC and PSC conditions (Figure 16(b)), are analysed.

(a)

(b)

The regression equation for the STC, PSC, and step-change of irradiance values can be obtained by choosing two input parameters, voltage and current. In contrast, the output is in terms of power from the panel. The Minitab software is used to derive the regression equation for STC, PSC, and step-change of irradiances.

Equation (20) represents the regression equation for the STC obtained from the PV curve at 1000 W/m² (Figure 15(b)). Equation (21) represents the regression equation for the step-change of irradiance values (Figure 15(b)) for the step-change of irradiances condition, and equation (22) represents the regression equation for a PSC from the P-V curve for case 4 (PSC) (Figure 16(b)).

The regression equation for STC is

The regression equation for the step-change of irradiance values is

The regression equation for PSC is

In the abovementioned equations (20–22), x1 represents the panel voltage, x2 represents the panel current, and Fx is the maximum power obtained from the panel under different environmental conditions. All the dependent parameters for ABC, PSO, GA, and JFO algorithms are given in Table 5, in which many of the parameters are kept the same as it was in case study 1 (1Soltech-1STH-215P module), except the upper limit taken for the case study 2 (SolarWorld Industries GmbH Sunmodule plus SW 245 poly) at STC, PSC, and step-change of irradiances. Voltage and current values express the upper limit (Ub) at STC, PSC, and step-change of irradiances.

By utilizing equation (20) for the STC condition and putting the parameters of different optimization techniques (Table 5), an optimal solution in terms of maximum power tracked by the panel versus the number of iterations can be plotted for ABC, GA, PSO, and JFO-based algorithms (Figure 17). The response of different algorithms is taken in terms of maximum iterations, number of populations, number of iterations to achieve the GMP, maximum power tracked, time to reach GMPP, and the tracking efficiency (Table 12).

The findings indicate that the JFO approach offers superior tracking performance with much shorter execution times, i.e., 0.0386 sec, to reach the global maximum power point of 980.4 watts, with a total efficiency of 99.9%. However, PSO takes only five iterations. Still, the execution time (0.1233 sec) is higher than JFO and reached the maximum power of 975.992 watts, where ABC’s tracking power is higher (979.8014 watts) than PSO, but the execution time (2.1722 sec) is more than PSO. GA was unable to track the GMPP in a given time period. Regarding tracking maximum power, JFO > ABC > PSO > GA. In terms of executing time, JFO > PSO > ABC > GA. Regarding tracking efficiency, JFO > PSO > ABC > G.A. The overall analysis and performance show that JFO is better than PSO, ABC, and GA.

Regarding step-change of irradiances, equation (21) is the regression equation (objective function) used to compare ABC, PSO, GA, and JFO algorithms. The algorithm’s response is given in Table 13 and Figure 18. The results prove that JFO is more efficient than the other optimization techniques, PSO, ABC, and GA, in tracking the maximum power of 960.43 watts in less than 0.0767 seconds. PSO and ABC have tracked the maximum power of 958.727 watts and 952.5 watts at 12 and 32 iterations, but they could not track the desired maximum power of 980.6 watts. The findings indicate that the JFO approach offers superior tracking performance with much shorter execution times than other optimization techniques. In terms of overall performance, JFO > PSO > ABC > GA, and in terms of execution time, JFO > PSO > ABC > GA at step-change of irradiance.

In the case of the partial shading condition, equation (22) is the regression equation (objective function) used for all different optimization techniques. PSO, ABC, GA, and JFO responses were obtained as shown in Figure 19 and Table 14. The results prove that the new bioinspired jellyfish optimization technique is more efficient in tracking the maximum power of 415.699 watts with a significantly less execution time of 0.041 sec than the PSO, ABC, and GA. PSO, ABC, and GA have tracked the maximum power of 414.7002 watts, 412.677 watts, and 395.42 at 13, 32, and 97 iterations. Still, they could not track the desired maximum power of 415.7 watts. The results indicate that the JFO performs better than PSO, ABC, and GA. In terms of overall performance, JFO > PSO > ABC > GA. Regarding execution time, JFO > PSO > ABC > GA at PSC.

The overall performance of the JFO was better in both the case studies in all environmental conditions, i.e., at STC, step-change of irradiance, and PSC conditions (Figure 20 and Table 15). Performance analysis and comparison are made on the following outcome, i.e., maximum power tracked, the execution time of an algorithm, iteration at which the maximum power is tracked, efficiency, and RMSE. The RMSE value of JFO (0.594) is much less than PSO, ABC, and GA (Table 16). Module/panel specifications for testing 1Soltech-1STH-215P and SolarWorld Industries GmbH Sunmodule plus SW 245 poly were considered (Tables 2 and 9). The effect of irradiation on the module/panel for STC, under step-change of irradiance and PSC, is shown in Tables 3, 4, 10, and 11. The PSC-supported MPP techniques are compared based on the selection parameters (Table 17), which helps to determine the most suitable method.

The comparison of different optimization techniques, JFO, PSO ABC, and GA, is given for case study 1 (Tables 6–8) and case study 2 (Tables 12–14). From these different comparison tables, it can be concluded that the JFO technique is better than the other three optimization techniques in terms of tracking maximum power, less execution time, and higher efficiency. JFO tracking efficiency in all environmental conditions lies from 98 to 99.9% with a significantly less execution time of 0.0386–0.1219 sec., which proves that the JFO technique can be utilized for tracking the maximum power in all environmental conditions. The JFO technology can also be used for various applications, such as MPPT techniques with converters, stand-alone solar systems, hybrid solar systems with diesel generators, wind turbines, and grid-connected systems.

Findings of other related research work on different PV solar modules are given in Table 16. The results are not compared with other researchers’ work because of the different specifications of solar modules from the ones available in the literature. According to the authors in [16, 17], PSO has better fitness value and efficiency than ABC. According to the authors in [14, 43], PSO has a better response than GA. In [11], a comparison between ABC, PSO, and GA has been made, and the ABC algorithm performs better than PSO in tracking speed and efficiency, and PSO shows better response than GA.

As per the study, analysis, and comparison performed in this paper, among the different optimization techniques for obtaining the GMPP with higher efficiency and tracking time, JFO is relatively better in tracking the maximum power with higher accuracy and efficiency, with very less execution time than PSO, GA, and ABC algorithms at step-change of irradiance and for PSC. JFO tracking efficiency in all environmental conditions lies from 98 to 99.9% with significantly less execution time of 0.0386 to 0.1219 sec. As per the result obtained in the paper, the performance of JFO > PSO > ABC > GA proves the effectiveness of the JFO technique over other techniques. As every researcher has used different specifications of panels and different environmental conditions, only a few parameters, such as efficiency, execution time, maximum power tracked, number of iterations needed to track the power, and RMSE, have been considered as the comparison parameters.

Table 17 compares the proposed jellyfish optimization with some existing techniques. Different users have used different parameters and specifications to prove that their technique is better than the existing one, so different comparison parameters are considered such as tracking time [16], RMSE [14, 15, 18], efficiency [13, 17, 22, 24, 27, 29, 31, 34–36], MAE [20], accuracy [41], reduced rise time [21], settling time/tracking time [21, 29, 35], and maximum power [28, 35, 36]. In this paper, maximum power tracked, maximum efficiency, total execution time, convergence speed, complexity, parameter, steady-state oscillation, stability, sensitivity, tracking ability, and economy have been compared [10, 12, 13, 23, 27]; FPA performs better with a small margin than PSO in terms of maximum power [28]. In comparison to a recent 2023 research article [13], M-PSO has the highest efficiency of 99.87, [22] RAS 99.85%, and [29] PSO-BOA 99.7% with 0.47 sec tracking time. As per the proposed JFO algorithm, they have attained the highest efficiency of 99.941% with a tracking time of 0.0386 sec; in terms of RMSE, the error between the predicted and calculated value of JFO was found to be significantly less than 0.5940 in comparison to PSO, ABC, and GA that has been calculated for 100 points at steady-state value (Table 16).

4. Conclusions

This paper comprehensively analyses the bioinspired method used for tracking the GMPP. Comparison and analysis are made under different environmental conditions, such as STC, step-change of irradiance, and partial shading conditions. This paper validates the recently developed jellyfish optimization technique by comparing its performance with PSO, ABC, and GA for smaller population size (N_pop = 8) for 100 iterations (Ite_Max). These algorithms were implemented to track the maximum power for different case studies and environmental conditions. Minitab software was used to obtain regression equation (objective function) and check the data’s reliability. Summary statistics are taken in terms of , (adj.), p values, and VIF performance regression that comes out to be 0.9, 0.98, 0.01e − 10, and 0.23, which shows that the data collected are reliable. Regression analysis is possible on the chosen date of the P-V curves for STC, step-changing irradiation, and PSC. MATLAB/simulation software was used to assess the effectiveness of these algorithms. The comparison and analysis are made in terms of tracking capability, total time of execution, tracking efficiency, accuracy, and RMSE value. The result shows that JFO is relatively better in tracking the maximum power with higher accuracy and efficiency, with significantly less execution time than PSO, GA, and ABC algorithms in all environmental conditions, i.e., at STC conditions, at step-change of irradiance and PSC. The RMSE value of JFO is much less than that of other optimization algorithms. PSO and ABC were close to the desired value of the panel but were less efficient than JFO. GA was unable to track the desired output with higher efficiency. JFO tracking efficiency in all environmental conditions lies from 98 to 99.9% with very less execution time of 0.0386–0.1219 sec. In terms of overall performance, JFO > PSO > ABC > GA. The results obtained from all three cases showed the superiority of the proposed novel algorithm over the other MPPT algorithms.

Abbreviations

ABC:	Artificial bee colony
ACO:	Ant colony optimization
ALO:	Antlion optimizer
AO:	Aquila optimizer
AOA:	Arithmetic optimization algorithm
AVOA:	African vultures optimization algorithm
BOA:	Butterfly optimization algorithm
BWS:	Black widow spider
CS:	Cuckoo search
DE:	Different evolution
DGBCO:	EVO dynamic group-based optimization algorithm energy valley optimizer
FPO:	Flower pollination optimization
GA:	Genetic algorithm
GMPP:	Global maximum power point
GOA:	Grasshopper optimization algorithm
GRNN-OPA:	General regression neural network orca predation algorithm
GWO:	Grey wolf optimization
HHO:	Harris Hawk’s optimization
INR:	Incremental resistance
I-V:	Current-voltage
JFO:	Jellyfish optimization
LMPP:	Local maximum power point
LFO:	Levy flight optimization
MFO:	Moth-flame optimization
MRO:	Mud ring optimization algorithm
MSFLA:	Modified shuffled frog leaping algorithm
NN_ML:	Neural network-trained machine learning
P and O:	Perturb and observation
PSC:	Partial shading condition
PSO:	Particle swarm optimization
P-V:	Power voltage
RSA:	Reptile search optimization algorithm
RMSE:	Root mean square error
SIOA:	Swarm intelligence optimization algorithm
SOA:	Seagull optimization algorithm
SSA:	Salp swarm algorithm
SSA:	Squirrel search algorithm
STC:	Standard test condition
TLABC:	Teaching-learning and artificial bee colony
TSO:	Tuna swarm optimization
VIF:	Variance inflation factor
YSGA:	Yellow saddle goatfish algorithm
SHTS:	Simultaneous Heat transfer search algorithm
/:	Cognitive acceleration factor
/:	Social acceleration factor
:	Time control function
D:	Dimension
I_max:	Maximum current
I_sc:	Short-circuit current
Ite_Max:	Maximum iterations
:	Lower limit
N_pop:	Number of populations
:	Mutation rate (uniform)
:	Cross-over probability
P_max:	Maximum power
:	Series resistance
R_sh:	Shunt resistance
S:	Selection rate
:	Upper limit
V_max:	Maximum voltage
V_oc:	Open circuit voltage
W:	Inertia weight
Α:	İdeality factor
α′:	Logistic chaotic constant
Β:	Distribution coefficient
Γ:	Motion coefficient
Λ:	Coefficient position update
Φ:	Selection probability.

Data Availability

The data that support the findings of this study are available from the corresponding author upon request. The data are not publicly available due to privacy or ethical restrictions.

Conflicts of Interest

The authors declare that they have no conflicts of interest regarding the publication of this paper.

Authors’ Contributions

All authors have contributed to completing the research work and agreed to the published version of the manuscript.

Acknowledgments

The authors thank the Management of Gautam Buddha University, India, for supporting this research.

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Copyright © 2024 Dilip Yadav et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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