Atom Search Optimization-Based PV Array Reconfiguration Technique under Partial Shading Condition

Li, Dahu; Zhou, Hongyu; Zhou, Yue; Rao, Yuze; Yao, Wei

doi:https://doi.org/10.1155/2023/8685976

International Transactions on Electrical Energy Systems

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Statistical Machine Learning for Uncertainty Modelling in Energy Systems

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Research Article | Open Access

Volume 2023 | Article ID 8685976 | https://doi.org/10.1155/2023/8685976

Atom Search Optimization-Based PV Array Reconfiguration Technique under Partial Shading Condition

Dahu Li,¹Hongyu Zhou,²Yue Zhou,¹Yuze Rao,¹and Wei Yao²

Academic Editor: Xueqian Fu

Received25 Oct 2022

Revised17 Nov 2022

Accepted23 Mar 2023

Published17 Apr 2023

Abstract

Photovoltaic (PV) reconfiguration is an effective solution for reducing the hot spot effect caused by partial shadows on PV arrays. This paper proposed an efficient atom search optimization- (ASO-) based PV reconfiguration method. The analysis and comparison with the other four reconfiguration methods were performed by three evaluation criteria, which are mismatch loss, fill factor, and standard deviation, respectively. The conclusion can be drawn that the efficiency, rapidity, and reliability of ASO are superior to those of other methods. Besides, a moving cloud shadow mode of 9 × 9-scaled PV array is designed in this paper, which can be widely recommended to thoroughly study a PV reconfiguration approach.

1. Introduction

With the continuous expansion of the scale of power construction, the problem of excessive energy consumption has reached an unprecedented level [1, 2]. As a nonrenewable resource, although fossil fuel has the advantages of strong flammability and high calorific values, its reserves are quite limited [3, 4]. The resulting deterioration of the ecological environment and global warming has brought a very serious threat to people’s survival and safety [5]. Due to the increasing demand for energy and the decreasing reserves of fossil energy [6], renewable energy sources are gaining more and more attention and are gradually replacing most fossil fuels [7], and one of the most promising energy sources is solar energy [8].

The solar cell is the core of the photovoltaic (PV) power generation system, and its conversion efficiency determines the practical application capability of the entire system [9, 10]. The application of PV power generation systems is complicated, and the single solar cell element cannot meet the conversion requirements of photovoltaic panels for power signal conversion [11]. Thus, it is necessary to connect multiple solar cell structures in series to form a solar cell array to ensure the smooth application of PV systems [12]. In the PV power generation system, the PV array can be understood as a combined connection form of solar cell elements [13]. Under the condition that the light intensity does not change, the more the number of solar cell elements connected in series, the more power the solar cell array has and the stronger the conversion ability [14].

PV arrays, as the most commonly used device to obtain solar energy, are widely used. PV cells are nonlinear devices at the core of PV power generation, and their output characteristics cause the PV array to work at a certain operating voltage to generate maximum output power [15]. However, some unavoidable destructive factors greatly reduce the efficiency of photovoltaic arrays. Partial shading condition (PSC) occlusion is one of them, which not only makes the output power curve appear multipeaks but also causes damage to a PV panel and may reduce its service life [16, 17]. In centralized PV systems, the series-parallel (SP) structure and total-cross-tied (TCT) structure are two commonly used structures in PV arrays [15]. The advantages of the SP structure are that the structure is relatively simple and that installation is convenient. In the TCT structure, modules are first connected in parallel to achieve the required output voltage, and then, these strings are connected in series to ensure that the output voltage reaches the voltage range required under normal operating conditions[18]. TCT is more stable and has higher efficiency than SP in most cases; thus, it is used in this paper to achieve better reconfiguration performance.

In recent years, some researchers have put forward a new idea to reduce the hot spot effect caused by partial shadows on PV arrays, which is called PV reconfiguration [19]. Specifically, reconfiguration means that the PV array changes the position or connection method of the corresponding components according to the type of shadow so as to balance the irradiance of each row or column and improve the output power of the array [20]. PV reconfiguration does not require manual intervention, and the whole process automatically achieves preset goals, which is more flexible and easier to implement [21]. Some researchers have developed a static PV reconfiguration technique to change the physical structure of PV panels. In this technique, PV modules that are shaded will be replaced by unshaded modules according to some established rules so as to keep the output current in different rows consistent, such as in the Sudoku method [22], zig-zag method [23], skyscraper puzzle [24], and Lo Shu method [25].

However, complex PSC will cause worse accuracy, efficiency, and performance of PV reconfiguration. Therefore, using the dynamic reconfiguration to dynamically balance each row of the photovoltaic array can facilitate the tracking of the maximum power point and lay a foundation for further improving the efficiency of PV systems [26]. Existing dynamic reconfiguration usually uses heuristic algorithms to gain the best reconfiguration solution, thus achieving fast and accurate optimization [27]. The switch matrix changes the electrical connection between modules according to the optimal configuration of the algorithm output, thus realizing photovoltaic reconfiguration. Figure 1 shows a schematic diagram of a switch matrix consisting of a single-pole multiple-throw switch. Some researchers proposed different matrix switches for photovoltaic arrays of different scales, which can reconfigure the array quickly and flexibly and effectively improve the average output power and conversion efficiency of the array [28]. The immediate purpose of PV array reconfiguration is to evenly distribute uneven shadows across the whole array. The premise of reconfiguration is to obtain the key parameters and data of PV arrays. In the static reconfiguration technique, irradiance and temperature as well as voltage and current through PV cells are collected and then transmitted to the computational model of PV arrays. Afterward, the control unit deduces the optimal configuration following certain strategies and then shifts the modules using mechanical devices. Similar to the static reconfiguration technique, the first step of a dynamic reconfiguration technique is to acquire the data by using various sensors. Subsequently, these data are imported into the computational model of PV arrays that can simulate the operation characteristics of the array. Then, the central control unit deduces the optimal configuration with the help of the reconfiguration algorithm. After that, the optimal configuration is transmitted to the switch matrix. As the execution unit, the switch matrix alters the electrical connection among panels or modules according to the new configuration. Through such a set of actions, the target of mitigating the impact of PSC and improving the power output is realized. The general structure of the reconfiguration technique is exhibited in Figure 2.

In [29, 30], detailed discussions of reconfiguration techniques that have been developed are given. In [31], the engineering practicability of the PV reconfiguration technique is illustrated. This paper proposed an atom search optimization-based PV reconfiguration method, which has better performance than other PV reconfiguration methods in this paper.

2. Modelling of PV Systems under the Shadow of Moving Clouds

2.1. Total-Cross-Tied PV System Modelling

A 9 × 9 TCT-interconnected PV array is used in this work, which is shown in Figure 3. TCT configuration is the most widely used connection and has been proved to be the most stable topology of PV arrays. It is worth noticing that this configuration technology does not change the original position of the PV array but changes its electrical connection. The total output voltage of the PV array can be written as follows:where is the output voltage of the PV array, is the output current of the PV array, is the maximum voltage of ath row, and is the node current at the ath row and bth column.

In particular, Figure 4 shows the flowchart of PV reconfiguration based on ASO.

2.2. Shadow of Moving Cloud Modelling

In real projects, the shielding of large-scale PV arrays is mostly caused by clouds and the shape and position of clouds change continuously with time [32]. The output characteristics of the PV array are seriously affected by cloud covering situations. On this basis, the PV system needs to research and design the reconfiguration method, maximum power point tracking (MPPT), inverter, grid connection, and other measures to promote the efficiency of the PV array. Therefore, it is necessary to establish the output characteristics model of the PV array in the case of moving cloud shading. By describing the moving cloud shadow itself and its motion factors, the target shadow of the object to be studied can be modelled [33]. Shadows blocking the PV array can be seen as projections on the horizontal plane of the PV array; hence, the movement of shadows can be regarded as the movement of particles.

This paper considered the shape of cloud and moving cloud shadows in 9 minutes with different irradiation values from 300 W/m² to 1000 W/m², which can offer reference for researchers in related fields.

2.3. Evaluation Criteria

There are three evaluation criteria to measure the simulation results of proposed ASO and other comparison methods. They are, respectively, (a) mismatch loss [20], (b) fill factor [20], and (c) standard deviation [34].(i)Mismatch loss The mismatch loss is defined as where is the global maximum power of the unshaded PV system and is the global maximum power of the partially shaded PV system.(ii)Fill factor The fill factor (ff) is a critical criterion to denote the power loss of PV systems under PSC, which is given in the equation: where and are the voltage and current of PV systems at the local maximum power point, respectively, and and are the open-circuit voltage and short-circuit current of the PV array, which are usually given by manufacturers.(iii)Standard deviation In this paper, standard deviation (STD) is used to evaluate the reconfiguration stability of heuristic algorithms.

2.4. Problem Formulation

When series-connected PV panels are all working properly under PS conditions, they will operate at points which are deviated from their maximum power point, respectively, resulting in a decrease in the obtained power. In order to impair the influence of mismatch loss caused by the occurrence of PSC, reconfiguration technologies are used to equalize the irradiation of each column and thus realize the maximization of output power, which can be written aswhere and represent the output current and output voltage of each row.

3. Atom Search Optimization-Based Reconfiguration Method

3.1. Mathematical Formulation of ASO

Atom search optimization is an efficient heuristic algorithm that was proposed by Zhao in 2019 [35]. It simulates the interatomic displacement caused by atomic attractive and repulsive forces in molecules. The mechanism of optimization is based on the specific mass and acceleration of different atoms, including update acceleration of atoms, update velocity of atoms and update position of atoms.

In the ASO algorithm, in order to strengthen the global exploration ability at the initial stage of iteration, each atom needs to interact with more neighboring atoms with better fitness. In the later stage of iteration, in order to enhance local development and promote algorithm convergence, each atom needs to interact with fewer neighboring atoms with better fitness.

It is assumed that an atom represents a PV module. The entire population consists of several atoms. It is worth noting that PV array reconfiguration changes the modules’ electrical connection with different rows in the same column and hence balances the current of each line of modules. Atomic motion follows Newton’s second law: the acceleration of the atom is related to its mass and is generated by the interaction between atoms and the geometric constraint of the optimal atom on it. Therefore, the acceleration of the ith atom at iteration t is as follows:where is the acceleration of the ith PV module, is the constraint force between atoms determined by positions and fixed bond length at kth iteration, is the mass of the ith atom at kth iteration, and is the total force acting on the ith atom at kth iteration, which can be expressed as follows:where is the Lagrangian multiplier, which changes with the number of iterations, expressed by , is the multiplier weight, and are the position of the ith atom and the best position among all atoms, respectively, r is a random number between [0, 1], (k) determines whether an atom is attracted or repulsed, which can be expressed by , is a weight factor, is the distance between two atoms, and , , and are the ith fitness value, best fitness value, and worst fitness value at kth iteration, respectively.

The velocity of the ith atom at kth iteration will be updated by the following equation:

The position of the ith atom at kth iteration will be updated by the following equation:

3.2. Overall Process of ASO-Based PV Reconfiguration

The algorithm pseudocode of ASO-based PV reconfiguration is as follows (Table 1).

4. Case Studies

4.1. Classical 9 × 9 PV Array

To verify the effectiveness of the reconfiguration algorithm, various sizes of PV arrays and different shading modes are often simulated. In this section, the most frequently used 9 × 9 PV array is used to verify the effect of ASO, and the shadow of moving cloud in 9 minutes has been carried out to cooperate with the simulation experiment in this paper. The simulation tool used is MATLAB 2020a. Besides, the PV model and its parameters are provided in Table 2, and several reconfiguration methods, e.g., Sudoku [22], ant colony optimization (ACO) [36], genetic algorithm (GA) [37], and particle swarm optimization (PSO) [38], are also constructed for performance comparison. Run times, iteration, and the population number of each algorithm are set to be 20, 100, and 10, respectively. α and β of ASO are set to be 50 and 0.2, respectively. Figure 5 shows the shading mode of moving clouds in 9 minutes before reconfiguration. Figure 6 shows the best reconfiguration results of ASO in 9 minutes under the shadow of moving clouds. It can be seen that the shadow is spread evenly compared to before reconfiguration.

When the PV array is optimized by ASO, the inner connection of the PV array is changed according to the best optimization result gained by the algorithm. The maximum optimized output power and the minimum output power of each heuristic algorithm in 20 run times and the mismatch loss and the fill factor of each method are presented in Table 3. It is apparent that heuristic algorithms get the best optimistic effect and that Sudoku takes second place. Among all algorithms, P_max and P_min gained by ASO are both higher than those obtained by other algorithms, and the STD of ASO is smaller than that of other algorithms, which illustrates the high stability of ASO. It is obvious that the mismatch loss and ff of ASO behave better in performance among all algorithms. The optimal mismatch loss gained by ASO is 38.13%, 20.93%, 2.49%, 3.75%, and 0.51% lower than that of before optimization, Sudoku method, ACO, GA, and PSO, respectively, and optimal ff gained by ASO is 20.70%, 7.95%, 0.71%, 1.15%, and 0.13% higher than that of before optimization, Sudoku method, ACO, GA, and PSO, respectively.

Figure 7 shows the output I-U curves and P-U curves of before optimization, Sudoku method, GA, and ASO in 9 minutes. It is observed that, when there are more shadows, output characteristic curves get less smooth. The output I-U curves usually have a lot of inflection points, and the output P-U curves have a lot of peaks. Taking the 4^th minute as an example, there are 6 power peaks before reconfiguration. After optimization, power peaks have, respectively, decreased to 3 and 2 by the Sudoku method and GA. ASO has reduced the number of power peaks to one, which completely clears the local peaks. Hence, ASO has achieved a remarkable reconfiguration effect compared to other methods in this paper.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

A timely provided PV array reconfiguration scheme is a significant evaluation criterion of the PV reconfiguration approach [39]. Table 4 provides the simulation time (s) of different reconfiguration methods compared with TCT configuration including ASO and other algorithms. The provided time data are calculated by each algorithm’s averaged running time in the presented three cases. To ensure the fairness of each algorithm’s simulation time, the population size and the max iteration number are all set to be 25 and 200, respectively. The provided data have shown that the operating speed of ASO is the highest, while GA ranks second. So it is obvious that the proposed approach is preferable to the other algorithms used in this paper.

4.2. Hardware-in-the-Loop Experiment

To ensure the real-time response capability of the used PV array, this paper proposed real-time hardware-in-the-loop experiment based on the RTLAB platform to evaluate the output characteristics under different temperatures and irradiance which is shown in Figure 8. For comparison, a simulation based on the MATLAB 2020a platform is introduced. Figures 9 and 10, respectively, show that the simulation results under different temperatures and irradiation obtained by the RTLAB platform and MATLAB platforms basically coincide. These results illustrated that the maximum output power of the PV array is linearly rated to input irradiation. By contrast, the input temperature has little influence on the maximum output power. Because the above two platforms remain consistent through the simulation, all the case studies in this paper are undertaken in MATLAB R2020a by using a desktop computer with Intel(R) Core TM i7-8650U CPU at 2.11 GHz with 8 GB of RAM.

(a)

(b)

(a)

(b)

5. Conclusions

This paper proposed an ASO-based PV array reconfiguration technique. This approach is realized by discretizing the original ASO algorithm and combining it with a PV reconfiguration approach. ASO can provide the optimal solution in real time; thus, the local optimal solution can be avoided. By comparing the output power, mismatch loss, fill factor, standard deviation, and output characteristic curves of ASO, Sudoku, ACO, GA, and PSO quantitatively, the superiority of ASO is proved. Moreover, the HIL experiment has proved the hardware feasibility of the ASO-based PV reconfiguration method. Besides, a novel shading mode of moving clouds is proposed, which can be applied in related studies for researchers. Future research will address the practical problems of ASO, the defects of ASO should be improved to improve the efficiency of algorithm optimization, and ASO should be applied to larger photovoltaic arrays [40].

Data Availability

The constraint and parameter data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Authors’ Contributions

Dahu Li was responsible for conceptualization and writing and editing the manuscript. Hongyu Zhou was responsible for writing the original draft and investigation. Yue Zhou was responsible for reviewing the manuscript and supervision. Yuzhe Rao was responsible for conceptualization and resources. Wei Yao was responsible for writing and reviewing the manuscript and supervision.

Acknowledgments

This work was jointly supported by the Science and Technology Project of State Grid Hubei Electric Power Co., Ltd. (Research on Key Technologies of Operation and Control of Hubei New Power System for Multi UHVDC Feed in and New Energy Base Development, No. 52150521000W).

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Copyright © 2023 Dahu Li 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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