Improving Photovoltaic MPPT Performance through PSO Dynamic Swarm Size Reduction

Abstract

Efficient energy extraction in photovoltaic (PV) systems relies on the effective implementation of Maximum Power Point Tracking (MPPT) techniques. Conventional MPPT techniques often suffer from slow convergence speeds and suboptimal tracking performance, particularly under dynamic variations of environmental conditions. Smart optimization algorithms (SOA) using metaheuristic optimization algorithms can avoid these limitations inherent in conventional MPPT methods. The problem of slow convergence of the SOA is avoided in this paper using a novel strategy called Swarm Size Reduction (SSR) utilized with a Particle Swarm Optimization (PSO) algorithm, specifically designed to achieve short convergence time (CT) while maintaining exceptional tracking accuracy. The novelty of the proposed MPPT method introduced in this paper is the dynamic reduction of the swarm size of the PSO for improved performance of the MPPT of the PV systems. This adaptive reduction approach allows the algorithm to efficiently explore the solution space of PV systems and rapidly exploit it to identify the global maximum power point (GMPP) even under fast fluctuations of uneven solar irradiance and temperature. This pioneering ultra-fast MPPT method represents a significant advancement in PV system efficiency and promotes the wider adoption of solar energy as a reliable and sustainable power source. The results obtained from this proposed strategy are compared with several optimization algorithms to validate its superiority. This study aimed to use SSR with different swarm sizes and then find the optimum swarm size for the MPPT system to find the lowest CT. The output accentuates the exceptional performance of this innovative method, achieving a time reduction of as much as 75% when compared with the conventional PSO technique, with the optimal swarm size determined to be six.

1. Introduction

The demand for sources of sustainable energy has risen significantly over the last few years, with sustainable energy being ranked as one of the most popular and widely used options. The conversion of solar energy into practical electrical power is often achieved through the use of PV systems. One of the critical aspects of PV systems is the efficient extraction of maximum power output amidst varying environmental conditions and situations of partial shading. Partial shading, while having a detrimental effect on the shaded modules/arrays, also curtails the overall power output harvested from the complete PV system [1]. MPPT techniques function as a major element in enhancing the performance of PV systems by ensuring that the point at which the system operates is kept proximate to the Maximum Power Point (MPP) [2]. Conventional MPPT methods, including Perturb and Observe (P&O) [3], Incremental Conductance [4], Hill Climbing (HC) [5], and others, have demonstrated success in pursuing the MPP under steady-state circumstances; however, they may exhibit slow convergence and poor performance under rapidly changing environmental circumstances such as inconsistent irradiance and temperature variations [6]. Given this, the need for smart optimization algorithms (SOA) arises to tackle this issue. There have been several applications of soft computing techniques aimed at tracking the GMPP of a PV system, including PSO [7], genetic algorithm (GA) [8], gray wolf optimization (GWO) [9], cuckoo search algorithm (CSA) [10], bat algorithm (BA) [11], ant colony algorithm (ACA) [12], etc. These approaches diverge in aspects such as intricacy, cost, performance, reaction time, and robustness [13]. In each of these soft computing techniques, efficient tracking of the PV array’s GMPP was observed [14].

The social behavior seen in bird flocks or schools of fish serves as the inspiration for PSO, a population-centered optimization algorithm [15]. The PSO technique is recognized as one of the strongest and most effective search algorithms for tackling non-linear optimization issues [16]. A broad spectrum of optimization problems has seen extensive usage of it, including MPPT. Recognized widely as a robust, simple, effective, and highly popular swarm optimization technique, the PSO method has consequently been extensively used for MPPT in PV systems [17,18,19,20]. The primary advantage of using PSO for MPPT in PV system applications is its ability to converge quickly to the global optimum without the hindrance of being caught in local optima, which is common in gradient-based optimization techniques [21]. The convergence time (CT) and failure rate (FR) of PSO-based MPPT methods are critical factors that determine the overall effectiveness of the algorithm [22]. CT refers to the duration required for the algorithm to reach an acceptable proximity to the global optimum, while FR represents the likelihood of the algorithm not converging to the optimal solution [23]. The CT and FR are influenced by several factors, including the initial population, parameter settings, and the termination criteria of the PSO algorithm.

A significant number of studies have been conducted to improve and analyze the CT and FR in MPPT approaches based on PSO. For instance, a new adaptive PSO (NA-PSO) reduced the CT by 50% and had zero FR [14]. Similarly, two nested PSOs are used in a newly proposed scheme (NESTPSO), which shows its supercity in reducing the CT from 442.7% to 86.9% [24]. Another study showed a reduction of the CT up to 650% by applying the anticipated peak position idea [25]. In the research conducted by [26], an Enhanced Particle Swarm Optimization (EPSO) method is introduced that demonstrates a remarkable improvement in CT. Moreover, the Particle Swarm Optimization with Targeted Position-Mutated Elitism (PSO-TPME) technique exhibits a 45% enhancement in CT [27]. This improvement in CT can be attributed to the utilization of hybrid techniques, which have been employed in various studies to boost the effectiveness of MPPT algorithms. For instance, Ref. [28] introduces an Incremental Conductance-based Particle Swarm Optimization (ICPSO) algorithm; a unique PSO-PID algorithm is proposed in [29], while Grey Wolf Optimization and Particle Swarm Optimization (GWO–PSO) technique is discussed in [30], Particle Swarm Optimization and Salp Swarm Optimization (PSOSSO) is presented in [31], Incremental Conductance with Particle Swarm Optimization and Model Predictive Control (IncCond-PSO-MPC) is introduced in [32], the Tunicate Swarm Algorithm with the Particle Swarm Optimization technique (TSA-PSO) is detailed in [33], and Particle Swarm Optimization and Incremental Conductance (PSO + IC) is described in [34]. All these hybrid techniques can achieve MPP in just a fraction of a second, exhibiting a marked improvement in comparison to conventional PSO algorithms.

The starting population size plays a crucial role in determining the CT. A larger population size may require more time to converge, as there are more individuals to evaluate and update. Conversely, a smaller population size has the potential for faster convergence but also runs the risk of getting caught in local optima, which are suboptimal solutions. Therefore, this study aims to investigate the delicate balance between CT and population size, as striking the right equilibrium is essential for efficient optimization.

In this research article, an innovative PSO-based MPPT algorithm was presented, designed to overcome the limitations of existing methods by incorporating a sophisticated optimization strategy. The approach was specifically geared toward significantly improving CT and minimizing FRs, allowing the algorithm to promptly adapt to changing irradiance and temperature conditions. Results from a comprehensive simulation revealed that the advocated strategy surpassed other PSO-based MPPT algorithms in terms of tracking speed, accuracy, and dependability, establishing it as a practical solution for real-world PV applications. The primary innovation in the method was the employment of an SSR strategy in each iteration to attain a fast-converging system. The reduction was implemented by decreasing one particle per iteration and then comparing the outcomes with those achieved using conventional PSO. The aim was to show the efficacy of the suggested system. This study aims to address a topic that, from the author’s perspective, has not been previously covered in the literature. The goal is to identify the optimal swarm size for achieving the best performance in real-world PV applications. Therefore, by employing the SSR and experimenting with a range of swarm sizes, the optimal swarm size can be determined, ultimately leading to a reduction in convergence time.

The subsequent sections of this paper are designed to present the methodology of the research, which includes a detailed discussion of both conventional Particle Swarm Optimization (C-PSO) and the newly proposed PSO when employed as MPPT techniques for PV systems. Next, a comprehensive description of the components of the PV system and their operational principles is provided. Following this, a simulation study aiming to contrast the effectiveness of the suggested PSO technique with C-PSO when employed for MPPT in PV systems is introduced. Through this comparative analysis, the advantages and improvements offered by our novel approach are presented. Lastly, the conclusions drawn from this research offer recommendations for future work in this area, providing insights and suggestions for further enhancements and exploration in the realm of MPPT applied to PV systems.

2. Methodology

In this section, a comprehensive examination of the PSO method is presented. Initially, the intricacies of the C-PSO are explored, followed by an in-depth presentation of the novel proposed PSO method. The research’s PV system, which includes a trio of PV panels configured in series, a DC-DC converter, and a PSO-based MPPT for managing the boost converter’s duty ratio to track the GMPP, is demonstrated in Figure 1.

To facilitate understanding of the proposed method, a flowchart illustrating the sequence of steps involved in the proposed approach is provided, elucidating the workflow and its underlying principles, as shown in Figure 2.

2.1. Application of the PSO Technique in PV MPPT

The PSO technique, a kind of metaheuristic algorithm, mimics the actions of animals or fish in their search for food. Utilizing this technique, particles randomly roam through the search space. When a particle finds the most food, it shares its knowledge with the others, steering them towards the most fruitful feeding spot [25]. This method can function as an MPPT strategy within PV systems. Initially, particles acquire duty ratio values and then evaluate the corresponding output power. The particle with the highest power output becomes a reference for the other particles, which adjust their movements to move toward this optimal position. Each particle keeps track of its best solution, known as its “personal best”, achieved during its journey. Through the application of Equation (1), the path and speed of particles towards their updated locations can be ascertained. Additionally, the particles’ new positions can be deduced by adding their velocity, as computed from Equation (1), to their existing positions, as expressed in Equation (2) [35].

$$v_{i+1}^k={\omega }_i{v}_i^k+c_1{r}_1\left(P_{best,i}^K-d_i^k\right)+c_2{r}_2(G_{best,i}-d_i^k)$$

(1)

$$d_{i+1}^k=d_i^k+v_{i+1}^k$$

(2)

where, ω represents the inertia weight, $c_1$ and $c_2$ denote the acceleration coefficients, $P_{best,i}$ signifies the personal best solution of particle $i$, $G_{best,i}$ stands for the global best of $P_{best,i}$, $k$ is the particle order within the swarm, and $r_1$ and $r_2$ are random values ranging between [0, 1].

The classical PSO algorithm typically employs a fixed value for the inertia weight [36]. However, to enhance its performance, researchers set forth the principle of time-varying inertia weight (TVIM) [37,38]. This approach involves a linear decrease in the inertia weight over time. Specifically, a larger inertia weight is recommended during the initial stages of the search process to promote the ease of global exploration; while finalizing, a decreased inertia weight is leveraged to refine the area of investigation at present (local exploitation) [36]. The PSO-TVIM formula is expressed mathematically as follows:

$$\omega ={(\omega }_1-{\omega }_2)(\frac{N-T}{N})+{\omega }_2$$

(3)

where ${\omega }_1$ represents the initial value of the inertia weight, ${\omega }_2$ stands for the final value of the inertia weight, $T$ corresponds to the current iteration, whereas $N$ is indicative of the maximum number of iterations that are permissible.

The PSO-TVIW approach can rapidly identify a favorable solution compared to other evolutionary optimization techniques. It may have difficulty fine-tuning the optimal solution as the diversity in the search process tends to diminish towards the conclusion [14]. Throughout previous studies, researchers have emphasized the importance of problem-based parameter tuning in the PSO algorithm to achieve precise and efficient solutions [39]. To overcome these limitations, Ref. [40] proposes the Time-Varying Acceleration Coefficients (TVAC) approach to enhance the PSOs effectiveness, as shown in Equations (4) and (5).

$$c_1=\left(c_{1f}-c_{1i}\right)\frac{T}{N}{+c}_{1i}$$

(4)

$$c_2=\left(c_{2f}-c_{2i}\right)\frac{T}{N}{+c}_{2i}$$

(5)

where $c_{1i}$, $c_{1f}$, $c_{2i}$ and $c_{2f}$ are fixed constants, $T$ signifies the count of the current iteration, while $N$ represents the upper limit on the number of iterations that can be performed.

Several research studies have proposed diverse approaches for estimating the optimal values of the control parameters for the PSO [41,42,43,44,45]. Many strategies of this kind involve adjusting the parameters through a trial-and-error process or using empirical formulas to enhance the PSO’s performance. However, some approaches have succeeded in specific applications but failed to deliver desirable results in others. As a result, the demand for finely tuning the control parameters of the PSO for various applications is on the rise [24].

In this paper, the values have been chosen to ensure the best performance of the PSO operation across all examined case studies, as; $c_{1i}$ = 1, $c_{1f}$ = 0.0015, $c_{2i}$ = 0.3, $c_{2f}$ = 1.4, ${\omega }_1$ = 0.1, ${\omega }_2$ = 0.2 and $N$ = 50.

Moreover, randomly initializing the swarms can result in longer CT and a higher probability of failure. To overcome this issue, the swarms can be equally distributed within the range of [0.1, 0.9], as demonstrated in Equation (6) [14].

$$d_0^k=\raisebox{1ex}{$k$}\!\left/ \!\raisebox{-1ex}{$(ss+1)$}\right.$$

(6)

where $d_0^k$ stands for the initial particle (duty ratio) with the rank of $k$ in the swarm, where $ss$ refers to the swarm size, and the letter $k$ serves as a counter denoting the particle’s number in the swarm ($k$ = 1, 2, ….$ss$). The use of the suffix 0 in $d_0^k$ is to signify the initial values of particles.

2.2. Proposed Strategy (New Adaptive PSO Technique)

The key input provided by the new adaptive PSO strategy is the gradual reduction of the swarm size during each iteration, leading to faster CT. However, reducing the swarm size may increase the FR; therefore, the optimal swarm size value will be carefully analyzed and discussed in the results section. This approach enables a fast tracker to be implemented under fluctuating and uneven irradiance as well as fast temperature change conditions, which, as far as the authors are aware, has not been realized in earlier studies. The proposed technique can benefit not only the PSO method but also other metaheuristic techniques facing similar challenges. In this study, the proposed approach involves reducing the swarm size, which leads to a faster CT to the MPP compared to existing methods. The increased quantity of search agents at the start of the optimization process aids in exploring convergence. Meanwhile, through the continual reduction of the count of search agents (particles), exploitation is supported and the accuracy of the GMPP value is improved. The performance parameters, initialization of the PSO, and termination criteria are critical factors that need to be carefully considered to ensure the effective implementation of the approach.

The stopping criterion was discussed in the literature [24]. In this study, two conditions need to be satisfied to calculate the CT. The difference in power should be less than a predefined tolerance ${\epsilon }_p=0.01$, and the duty cycle difference at each iteration should be less than another predefined tolerance ${\epsilon }_d=0.0001$. These values were empirically selected following a performance study of the convergence of the proposed PSO. Figure 2 illustrates the adaptive PSO logic in a flowchart, which can be detailed in the succeeding steps:

Step 1:

Start with particle initialization to be equally distributed within the range of [0.1,0.9].

Step 2:

Send each particle at each step to the MPPT system and obtain the respective power assigned to each particle.

Step 3:

Check the current position of each particle if it is better than $P_{best}$ update $P_{best}$ otherwise, go to Step 4.

Step 4:

Check each $P_{best}$ with $G_{best}$ if $G_{best}$ is less than $P_{best}$, then update $G_{best}$ else go to Step 5.

Step 5:

Apply the reduction technique. If swarm size >min swam size, remove particles with the lowest cost function; otherwise, go to Step 6.

Step 6:

For each particle, update the velocity.

Step 7:

For each particle, update the position based on the global and personal bests.

Step 8:

Updated parameters of $c_1$, $c_2$ and ω based on the current iteration, go to Step 2.

3. PV System Modeling

The suggested setup includes a DC-DC boost converter linked to PV arrays to optimize power output under varying irradiance conditions. Boost converters, commonly utilized in PV systems that incorporate MPPT, can be implemented in either single or interleaved configurations [7]. The PV system insulated for the simulation comprises three series-connected PV panels, each with the capacity to generate a maximum of 83.28 W. In this system, Figure 1 presents a control mechanism that ensures a PSO algorithm tracks the GMPP by regulating the boost converter’s duty ratio. Figure 3 illustrates the connection between the power and voltage from the PV under both uniform shading and varying shading conditions. Similarly, Figure 4 illustrates the relationship between the power from the PV and the boost converter’s duty ratio under both uniform shading and varying shading scenarios. The P-V curve shows a clear MPP during uniform irradiance (SPO [1000 1000 1000]), an aspect easily managed by conventional MPPT techniques. However, under non-uniform irradiance (SP1 [700 1000 1000]), the P-V curve exhibits several Local Peaks (LPs) and the Global Peak, as shown in Figure 3.

4. Analysis of the Simulation Results

This section presents the simulation of the proposed PV system employing the novel adaptive approach for the PSO method, which functions as an MPPT system. The simulation integrated MATLAB code, incorporating the PSO algorithm, with Simulink, which contained the PV system and the DC-DC converter.

Table 1. Characteristics of the PV Module Utilized in the Research.

Specification	Value
$\mathrm{Maximum}\mathrm{Power}\mathrm{per}\mathrm{module}(P_{MP}$)	83.28 W
$\mathrm{Open}\mathrm{Circuit}\mathrm{voltage}(V_{OC}$)	12.64 V
$\mathrm{Short}\mathrm{Circuit}\mathrm{current}(I_{SC}$)	8.62 A
$\mathrm{Voltage}\mathrm{at}\mathrm{MPP}(V_{MP}$)	10.32 V
$\mathrm{Current}\mathrm{at}\mathrm{MPP}(I_{MP}$)	8.07 A

showcases the module parameters showcased in the simulation. The system featured three series-connected PV modules. Each module had differing radiation levels, with the set-up being [700, 1000, 1000]. The study aims to implement a swarm size reduction technique in each iteration. Two different scenarios were examined: first, the C-PSO without reduction; second, the application of the reduction method with a step of 1. In both cases, the Initial Swarm Size (ISS) starts from 20 until 3, with results collected at each swarm size. As a result, the optimum swarm size for the two cases was selected based on the optimum CT and FR percentages.

Table 2. Simulation results of the CT and FR at each Initial swarm size (ISS).

ISS	Reduction = 0		Reduction = 1
	CT	FR	CT	FR
20	3.66	0%	1.972	0%
19	3.591	0%	1.809	0%
18	3.456	0%	1.667	0%
17	3.043	0%	1.51	0%
16	2.976	0%	1.324	0%
15	2.73	0%	1.182	0%
14	2.688	0%	1.06	0%
13	2.379	0%	0.91	0%
12	2.172	0%	0.824	0%
11	1.958	0%	0.682	0%
10	1.79	0%	0.584	0%
9	1.602	0%	0.472	0%
8	1.36	0%	0.422	0%
7	1.065	0%	0.342	0%
6	1.02	0%	0.258	0%
5	0.97	50%	0.2	100%
4	0.915	60%	0.11	100%
3	0.708	80%	0.07	100%

shows the results of CT and FR for the two scenarios.

As demonstrated in Table 2, the SSR method demonstrates exceptional performance in attaining the MPP with remarkable speed, a reality that is particularly evident in multi-ISS scenarios. A consistent and systematic decrease in CT is observed when executing the algorithm with varying swarm sizes. This trend is to be expected, given that fewer particles in the swarm would typically result in faster computation. The impact of reducing the swarm size is particularly prominent for the proposed particle PSO algorithm, as the CT continues to exhibit a decreasing pattern until the swarm is reduced to a mere two particles.

Upon conducting a detailed analysis of the results, it becomes evident that when the swarm size lies within the range of 20 to 6 particles, the algorithm exhibits an impressive zero-FR across 10 separate executions. However, when the swarm size is further reduced to five, four, or three particles, the FRs begin to appear. This can primarily be attributed to a decline in the exploration performance of the C-PSO algorithm. The consequences of this diminished exploration efficiency become even more pronounced in the context of the newly proposed PSO algorithm, as the limited number of particles available for exploration hinders the algorithm’s ability to effectively locate the MPP. Despite these challenges, it is crucial to highlight that the CT remains consistently shorter when using the proposed PSO algorithm; this becomes evident when contrasted with the conventional method. The limitation linked to the utilization of the SSR strategy was pronounced when the swarm size was minimized, consequently affecting the performance of exploration. As detailed in this research, a rigorous assessment of 18 different swarm sizes was performed to pinpoint the ideal size for optimal exploration.

The findings presented in Table 2 offer valuable insights into the relationship between swarm size and CT for both the C-PSO and the proposed PSO algorithms. Furthermore, they underscore the potential advantages of the newly proposed PSO algorithm, particularly about achieving faster CTs, while also emphasizing the need for an optimal balance between swarm size and exploration efficiency to ensure reliable performance in locating the MPP.

In the current study, to optimize the system’s performance, it is crucial to select the swarm size that yields the best CT and FR. It has been determined that the optimal swarm size for the algorithm being examined is six particles, accompanied by a reduction size of 1. This configuration leads to a CT of just 0.258 s, which constitutes a substantial 75% improvement when compared to the 1.02 s CT observed with the C-PSO method. This significant reduction in CT serves as a testament to the capability of the designed PSO algorithm and emphasizes its potential for delivering enhanced performance across a variety of applications. The discovery of the optimal swarm size for improved performance offers valuable insights into the underlying dynamics of the proposed PSO algorithm. By meticulously adjusting the swarm size to consist of six particles and adopting a reduction size of 1, researchers have been able to achieve a remarkable improvement in the algorithm’s CT, rendering it more efficient and effective compared to the conventional approach. The optimization of swarm size, as evidenced by the notable 75% improvement in CT, demonstrates the potential of the proposed PSO algorithm to provide superior performance in diverse applications, especially those that require swift convergence toward an optimal solution. This accomplishment not only contributes to the growing body of research on PSO techniques but also lays the groundwork for future investigations aimed at further refining and enhancing the performance of PSO algorithms in various contexts.

Figure 5 and Figure 6 display the outcomes for power, duty cycle, and swarm size in both scenarios, emphasizing the use of a swarm size consisting of 6 particles. Figure 7 illustrates the behavior of particles converging towards the MPP using the C-PSO method with a swarm size of 6. The figure clearly shows that particle traffic is a significant factor, as the algorithm requires 19 iterations to achieve convergence. In each iteration, 6 particles are dispatched to search for the MPP, resulting in a combined count of 114 particles for the search process, which leads to increased particle traffic surrounding the MPP as the iterative process progresses. This leads to the conclusion that a higher number of particles to be assessed would require an extended amount of time. In contrast, Figure 8 presents the particle behaviors converging towards the MPP when employing the proposed PSO algorithm. This method requires only seven iterations to achieve convergence and incorporates a swarm size of 6. In this scenario, the number of particles decreases with each iteration, resulting in diminished particle traffic and expedited convergence, necessitating fewer iterations overall. The approach utilizes six particles in the first iteration, followed by five in the second, four in the third, three in the fourth, and two in both the fifth and sixth iterations, as well as the seventh iteration. This results in a total of 24 particles for searching. Clearly, the SSR strategy utilizes a substantially reduced number of particles in comparison to the C-PSO approach for reaching the MPP, resulting in swifter convergence. To facilitate improved visualization of the graphical representations, a color scale is employed, which assigns a unique color to each iteration, thereby enabling a more effective interpretation of the convergence process and the associated particle traffic patterns.

5. Conclusions

Maximum Power Point Tracker (MPPT) methods utilizing PSO show considerable advantages over conventional MPPT methods, particularly in dynamically varying and partial shading conditions. Factors such as CT and FR significantly influence the efficacy of PSO-based MPPT techniques. In this research, a novel PSO method involving the reduction of swarm size is put to work in tracing the GMPP of partially shaded PV systems. This new technique is designed to facilitate a rapid response in the system. Various swarm sizes, ranging from 20 to 3, were tested in two scenarios each to obtain a comprehensive understanding of the system and select the optimal swarm size according to the shortest conversion time (CT) and zero failure rate (FR) criteria.

As far as the author’s experience extends, this marks the inaugural instance where the ideas of diminishing swarm size and identifying the optimal swarm size for the system have been employed to enrich the functionality of PSO. In this research, the optimal swarm size was determined to be six, as it exhibited excellent CT and a zero-FR. The results highlight the superiority of this innovative technique, which achieves up to a 75% reduction in time compared to the conventional PSO method. However, some failures were observed at the swarm sizes of 5, 4, and 3 in both cases, and this is due to fewer particles being available for the exploration to find the MPP. Future research will compare this proposed method with other metaheuristic techniques as well as explore the applicability of swarm size reduction to other metaheuristic approaches.