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Scientific Reports volume 15, Article number: 6963 (2025)
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Among the most sustainable forms of energy, solar energy delivers clean, dependable, and limitless power. However, the PV arrays experience uneven irradiance as a result of partial shadowing situations, which causes several peaks in their PV characteristics. Reconfiguration alleviates mismatch loss and enhances power generation in partial shading. Compared to normal conditions, this partial shade scenario results in less power generation. In this proposed work, a 4 × 4 solar PV array is exposed to different partial shading conditions to identify the optimal arrangement, and various parameters like power losses, mismatch losses, and fill factors are found and compared with existing methods. The results of the comparisons and examines revealed that the reconfigured arrays deliver improved maximum global power values. This reconfiguration technique enhances an average power output by 18.37% thereby increasing in energy output of 293.2 kWh even under different partial shading conditions when compared to other conventional configuration methods.
In the globe nearly 75% of carbon dioxide emission is due to the emissions from the power generating sectors. The overall temperature of the planet is significantly increased due to burning of fossil fuels, Petrol, Diesel and coal. Energy demand has increased exponentially in last two decades. To reduce greenhouse gas emission, to reduce the effect of climate change due to global warming it is necessary to generate electrical power in clean and friendly environment. Many developing countries are looking for electric power generation using renewable energy sources because of increasing energy demand, pollution and exhaustion of coal reserves. As per International Renewable Energy Agency the installed capacity of solar is around 1200 GW in 2022 whereas it was less than 40 GW in 2010. India has planned to generate 175 gigawatts of electrical power through renewable energy sources. Even though there are several renewable energy sources, power generation through solar is widely preferred because of source availability1,2.
Non-polluting nature, low skilled requirements. and less maintenance make solar PV system surged as a solution to meet out the increase in demand for sustainable energy. However, the PV generating system has few drawbacks like environment dependent and nonlinear characteristics. Additionally, partial shading is produced by inevitable natural phenomena including the presence of clouds, dust particles deposition and the shading of trees, obstruction particles and the buildings. The partial shading results mismatch among the modules and thereby results less power output. Owing to this unbalance. larger current flows through the shaded modules which act as load instead of generating, results less output current3,4,5. The effects of partial shading are. hotspots. mislead to maximum power point tracking (MPPT). Power losses multiple power peaks and low efficiency. The partial shading effects can be reduced by suitable maximum. PowerPoint tracking methods. by using bypass diodes, dust cleaning. periodically and PV array configuration methods. Numerous strategies have been implemented to reduce energy losses. Earlier simple power tracking systems were implemented for power enhancement. Perturb and observe and incremental conductance methods were implemented for power enhancement. The power output curve became unstable and have multiple peaks in partial shading condition. In PV array reconfiguration method, researchers looked for the ways to reduce shade dispersion over the PV arrays by rearranging the PV modules, physical location and using the fixed electrical connection technique6,7,8,9. Under different shading cases the Su do Ku Puzzle and L-shaped is used to reconfigure the PV array and compared with series parallel, bridge link and honeycomb and TCT configuration8,10,11,12,13,14,15,16. The cross-diagonal pattern is considered for reconfiguration and the results are compared with conventional methods17,18,19. Conventional techniques fail to track maximum power under different partial shading conditions. To address this, new approach called dynamic configuration have been devised20. In this approach advanced sensors and switching systems are required for shade dispersion makes increase in overall cost21,22,23,24,25,26,27,28. Dynamic configurations require continuous monitoring for optimal performance20,29. Machine learning, Fuzzy logic algorithms and binary firefly algorithms were used for tracking maximum power point, however these systems were complex and require more processing power than simpler systems30,31,32,33,34. Static configurations offer several advantages over dynamic configuration due to lower investment cost, maintenance cost, no real time monitoring requirement and reduced management needs26–30,35. Voltage equalization through multi string differential power processing is performed to mitigate the impacts of partial shading solely in series parallel configurations36.
Static reconfiguration techniques are novel for their predictability, simplicity, and cost-effectiveness. Predictability: Best suited for environments with static or predictable shading conditions. Simplicity: It requires less computational power and is easier to implement than dynamic methods. Cost-effectiveness: Lower hardware and maintenance requirements make them ideal for resource-limited setups. Table 1 shows the summary of the various techniques.
Various techniques (TCT, Sudoku, Futoshiki) demonstrate varying strengths in addressing shading losses and mismatch effects49. For instance, TCT is known for its simplicity and reliability, while Sudoku and Futoshiki leverage mathematical optimization to achieve higher performance under non-uniform irradiation. This diversity allows for a comprehensive evaluation of our proposed technique relative to different types of existing approaches. In this proposed work, the PV arrays are configured into different static nineteen configurations and their performance under different partial shading conditions are analyzed.
In this research work, the PV modules are exposed to different irradiation of 250 W/m2, 500 W/m2, 750 W/m2, and 1000 W/m2 respectively. The PV arrays are coupled in various configurations and they are exposed to different 18 shading patterns.
The experimental one of four PV modules connected in a total cross-tied configuration is shown in Fig. 1. The PV modules have ratings of 24.8 V, and 6 A for open circuit voltage and short circuit current respectively, and peak power voltage and current of 20 V and 0.5 A.
Experimental setup of 4 × 4 Solar PV array.
The experiments were carried out in Academic Block IV (D-Block) of Kamaraj College of Engineering and Technology, Virudhunagar. In this experimental study, the partial shading scenario is created with the help of cardboard sheets in a photovoltaic module. The cardboard sheets will limit the sun intensity level on that particular module. The flow chart of the proposed work is shown in Fig. 2. In this proposed work, various Partial shading conditions like (A) diagonal and long, (B) short and long, (C) inverse diagonal (D) short, (E) long and short, (F) inverse diagonal and long, (G) inverse short and long, (H) diagonal, (I) inverse long and diagonal, (J) inverse long and short, (K) inverse short, (L) centre, (M) double ladder, (N) L-corner, (O) column left, (P) two corners, (Q) one corner and (R) random two corners are shown in Fig. 3.
Flow chart of the proposed work.
Shading pattern for the proposed work.
Step-by-Step Methodology of the Proposed Reconfiguration Technique:
The first step involves monitoring the photovoltaic (PV) array to identify shading patterns using real-time irradiation data collected.
Based on the shading information, the mismatch losses across the PV modules are calculated using a mathematical model. This step quantifies the power reduction caused by partial shading.
The PV modules are physically reconfigured according to the various configuration techniques analyzed in this study.
The reconfigured system’s performance is analyzed in real-time by comparing key metrics such as power output, mismatch loss, and power loss against the various configuration techniques (e.g., TCT, Sudoku, or Futoshiki configurations).
Step 1: Start.
Step 2: Enter the size of the PV array mXn.
Step 3: Initialise i, j and k variables. In array (mXn)ij represents the position of PV array.
Step 4: Start from left top corner through diagonal wise and move up to “n” steps.
Step 5: Increment K by 1 and then enter through the (mxn)i+1,jth position and proceed to n steps. Increment “k” by 1.
Step 6: Start from (mXn)in, jn−2th position up to “n” steps and increment k by 1.
Step 7: Start from (mXn)in−2,jnth position up to “n” steps and increment k by 1.
Step 8: Stop.
mXn represent the size of an array.
This section describes the parameter analysis of PV modules under different partial shader conditions. The power loss, mismatch loss and fill factor are used to assess their PV modules performance31.
The effectiveness of converting incident solar radiation to electrical power in PV panel is measured by fill factor. It is the ratio of product of maximum power to the product of open circuit voltage and short circuit current.
The mismatch loss is the difference between maximum and actual output power at partial shader conditions (PSC).
The power loss in photovoltaic arrays is the difference between maximum output power at Standard Test Conditions (STC’s) and actual output power at partial shading conditions.
Experimental investigation of different configuration under various partial shading conditions is shown in Figs. 4 and 5.
(A) Configuration-I, (B) Configuration-II (C) Configuration-III (D) Configuration-IV (E) Configuration-V (F) Configuration-VI (G) Configuration-VII (H) Configuration-VIII (I)Configuration-IX (J) Configuration-X.
(A) Configuration-XI (B) Configuration-XII (C) Configuration-XIII (D) Configuration-XIV (E) Configuration-XV (F) Configuration-XVI (G) Configuration-XVII (H) Configuration-XVIII.
For diagonal and long partial shading conditions, a power output of 110 W was obtained using the proposed method for configurations 4, 6, 7, 11, 15, 18, and 19. In contrast, for other configurations, it was 80 W, 90 W, and 100 W, and for the conventional TCT method, it was 100 W; for sudoku and Futoshiki, it was 80 W, and for the L- shape it was 90 W, as represented in Fig. 6A. The proposed method attains fill factor, mismatch loss, and power loss of 0.46, 7.5 W, and 50 W, for configurations 4, 6, 7, 11, 15, 18, and 19. The experimental results are presented in Table 2. In contrast, it was 0.42, 17.5 W, and 60 W for the conventional method. For sudoku and futoshiki, it was 0.34, 37.5 W, and 80 W. For the L-shape, it was 0.38, 27.5 W, and 70 W, as represented in Fig. 6A.
(A) Diagonal and long, (B) Short and long, (C) Inverse diagonal (D) short.
For short and long partial shading conditions, a power output of 60 W was obtained for the conventional method (TCT). For sudoku and Futoshiki, it was 80 W. In contrast, a power output of 90 W was obtained using the proposed method for configurations 3, 5, 8, 12, 13, and 16 which is the same as the L-shape partial shading conditions. The proposed method attains mismatch loss, power loss, and fill factor of 10 W, 70 W, and 0.38, for configurations 3, 5, 8, 12, 13, and 16 which is the same as the L-shape partial shading conditions. In Table 2, the experimental results are shown. For conventional TCT, it was 40 W, 100 W, and 0.25. For sudoku and Futoshiki, it was 20 W, 80 W, and 0.34 respectively, as represented in Fig. 6B.
Owing to the nature of the inverse diagonal partial shading conditions, the output power, mismatch loss, power loss, and fill factor in configurations 3, 5, 8, 13, 17, and 19 are 80 W, 20 W, 80 W, 0.34 respectively, which is the same as the L-shape partial shading conditions, whereas for the TCT, it was 70 W, 30 W, 90 W, 0.29. Table 2 shows the experimental assessment parameters for inverse diagonal partial shading conditions. For sudoku, Futoshiki method, it was 40 W, 60 W, 120 W, 0.17, as shown in Fig. 6C.
Due to the nature of the short partial shading conditions, the output power, mismatch loss, power loss, and fill factor in sudoku, Futoshiki, and L-shape configurations are 110 W, 0 W, 50 W, 0.46 respectively, which is better compared to the all-other proposed configurations, whereas for the TCT, it was 40 W, 70 W, 120 W, 0.17.In contrast, a power output of 90 W was obtained using the proposed method for configurations 6, 18, and 19. The proposed method attains mismatch loss, power loss, and fill factor of 20 W, 70 W, and 0.38, for configurations 6, 18, and 19 and it is shown in Fig. 6D. Table 2 shows the experimental assessment parameters for short partial shading conditions.
Owing to the nature of the long and short partial shading conditions, the output power, mismatch loss, power loss, and fill factor in configuration 9 are 130 W, 0 W, 30 W, and 0.55 respectively. Whereas, for the TCT, sudoku, Futoshiki method, and L-shape it was 120 W, 10 W, 40 W, and 0.50 as shown in Fig. 7A, which is the same for all the conventional methods. Table 2 shows the experimental assessment parameters for long and short partial shading conditions.
(A) Long and short (B) Inverse diagonal and long (C) Inverse short and long (D) diagonal.
For inverse diagonal and long partial shading conditions, a power output of 120 W was obtained using the proposed method for configurations 7, 8, 9, 10, 11, 14, 17, 18, and 19, which is the same as for the conventional TCT method, sudoku, Futoshiki, and L-shape as represented in Fig. 7B. The proposed method attains fill factor, mismatch loss, and power loss of 0.50, 10 W, and 40 W, for configurations 7, 8, 9, 10, 11, 14, 17, 18, and 19, which is same as well as for the conventional TCT method, sudoku, Futoshiki, and L-shape. The experimental results are presented in Table 2. Partial shading conditions in configurations 7, 8, 9, 10, 11, 14, 17, 18, and 19 results in low levels of mismatch.
Due to the nature of the inverse short and long partial shading conditions, the output power, mismatch loss, power loss, and fill factor in configurations 3, 8, and 17 are 80 W, 15 W, 80 W, and 0.34 respectively which is better compared to sudoku, and Futoshiki configurations. For sudoku, and Futoshiki, it was 70 W, 25 W, 90 W, 0.29 respectively, whereas for the TCT, it was 60 W, 35 W, 100 W and 0.25 and it is shown in Fig. 7C. Table 2 shows the experimental assessment parameters for short partial shading conditions.
Owing to the nature of the diagonal partial shading conditions, the output power, mismatch loss, power loss, and fill factor for the sudoku, and Futoshiki method is 70 W, 40 W, 90 W, and 0.29 respectively. Whereas, for the L-shape, it was 80 W, 30 W, 80 W, and 0.34 as shown in Fig. 7D Compared to all the other configurations TCT method showed better results (110 W, 50 W, 0.46, and 0 mismatch loss) which is due to the nature of the diagonal partial shading conditions. Table 2 shows the experimental assessment parameters for long and short partial shading conditions.
For inverse long and diagonal partial shading conditions, a power output of 120 W was obtained using the proposed method for configurations 3, 6, 7, 10, 11, 14, 15, 18, 19, and also for TCT, and the L- shape configurations with the mismatch loss of 30 W, power loss of 60 W, and fill factor of 0.50. In contrast, for other configurations (sudoku and Futoshiki method), it was 20 W, 50 W, and 0.46 with the output power of 110 W as represented in Fig. 8A. The experimental results are presented in Table 2.
(A) Inverse long and diagonal (B) Inverse long and short (C) Inverse short, (D) Centre.
Due to the nature of the inverse long and short partial shading conditions, the output power, mismatch loss, power loss, and fill factor in configurations 2, 3, 4, 5, 6, 8, 12, 13, 16, 17, sudoku, Futoshiki, and L-shape configurations are 70 W, 20 W, 90 W, 0.29 respectively, which is better compared to the TCT method and it is represented in Fig. 8B. For TCT, it was 60 W, 30 W, 100 W, 0.25. Table 2 shows the experimental assessment parameters for short partial shading conditions.
Due to the nature of the inverse short partial shading conditions, the output power, mismatch loss, power loss, and fill factor in sudoku, Futoshiki, and L-shape configurations are 110 W, 0 W, 50 W, 0.46 respectively, which is better compared to the all-other proposed configurations, whereas for the TCT, it was 40 W, 70 W, 120 W, 0.17.In contrast, a power output of 90 W was obtained using the proposed method for configurations 1, 2, 3, 5, 8, 12, 13, 16, and 17. The parameters are represented in Fig. 8C. Table 2 shows the experimental assessment parameters for short partial shading conditions.
Due to the nature of the centre partial shading conditions, the output power, mismatch loss, power loss, and fill factor in configurations 7, 10, 11, and 14 are 130 W, 5 W, 30 W, 0.55 respectively, which is same as that of the L-shape method which is better compared to the all-other proposed configurations, whereas for the TCT, sudoku, and Futoshiki, it was 110 W, 25 W, 50 W, 0.46. The parameters output power, mismatch loss and fill factor under centre partial shading are represented in Fig. 8D. Table 2 shows the experimental assessment parameters for short partial shading conditions.
For double ladder partial shading conditions, a power output of 110 W was obtained using the proposed method for configurations 7, and 11. In contrast, for the conventional TCT method, sudoku, Futoshiki, and L- shape it was 100 Was represented in Fig. 9A. The experimental results are presented in Table 2.
(A) Double ladder (B) L-corner (C) Column left (D) Two corners.
Due to the nature of the L- corner partial shading conditions, the output power, mismatch loss, power loss, and fill factor in configurations 1, 12, and 16 are 80 W, 10 W, 80 W, 0.34 respectively, which is same as that of the L-shape method, sudoku, and Futoshiki which is better compared to the all-other proposed configurations, whereas for the TCT, it was 40 W, 50 W, 120 W, 0.17. Table 2 shows the experimental assessment parameters for short partial shading conditions and they are represented in Fig. 9B.
For column left partial shading conditions, a power output of 100 W was obtained using the proposed method for configurations 9, 12, and 16, which is the same as that of the conventional TCT, sudoku, Futoshiki, and L-shape method is shown in Fig. 8C. The mismatch loss, power loss, and fill factor were 0, 60 W, and 0.42 respectively, as represented in Fig. 9C The experimental results are presented in Table 2.
Due to the nature of the two corner partial shading conditions, the output power, mismatch loss, power loss, and fill factor for L-shape configurations are 110 W, 0 W, 50 W, and 0.46 respectively, which is better compared to the other proposed configurations. Whereas, for the TCT, it was 100 W, 10 W, 60 W, 0.42. Figure 9D shows the experimental assessment parameters for two corner partial shading conditions.
Due to the nature of the one corner partial shading conditions, the output power, mismatch loss, power loss, and fill factor in configurations 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, TCT, L-shape method, sudoku, and Futoshiki are 110 W, 15 W, 50 W, and 0.46 respectively, which is better compared to the all-other proposed configurations 17, 18, and 19. Figure 10A shows the experimental assessment parameters for short partial shading conditions.
Due to the nature of the random two corner partial shading conditions, the output power, mismatch loss, power loss, and fill factor in configurations 7, 11, 15, 18, 19, TCT, and L-shape method are 110 W, 5 W, 50 W, and 0.46 respectively, which is better compared to the all-other proposed configurations. Table 2 shows the experimental assessment parameters for short partial shading conditions. For different configurations, parameters like Im, Isc, Output power, Mismatch loss, Power loss and fill factor are shown in Fig. 10B. Figure 11A,= shows the P-V curve under normal conditions and Fig. 11B–D shows the P-V curve under different shading conditions like short, diagonal and column left shading pattern.
(A) One corner (B) Random two corner.
(A) Normal condition. (B) Short shading condition. (C) Diagonal shading condition. (D) Column left shading condition.
In this proposed work, PV panels connected in different configuration under different partial shading conditions are discussed. There is an power enhancement of 25% in diagonal and long shading pattern for the PV arrays connected in configuration IX and XVII. Configuration XVI enhances power by 40% in inverse diagonal shading pattern. In long and short shading pattern, configuration XVI, XVII, XVIII and XIX enhances power by 20%. 37.5% power is enhanced for configurations I, II and XVI in inverse diagonal and long shading pattern. In diagonal shading pattern 57% power is enhanced for configuration I, XII and XIII. For inverse diagonal and long shading pattern the power is enhanced by 9% and 10% for centre shading pattern. For double ladder shading pattern the power is enhanced by 42% for configuration XVII which is higher than conventional configuration methods. In this configuration the average power is enhanced by 16.54% under short and long shading pattern, 12.31% under long and shading pattern, 8.15% under inverse long and shading pattern, 10.76% under inverse long and diagonal shading pattern and maximum average power is enhanced by 44.18% under inverse short shading pattern.
This configuration helps to enhance an average output power by 18.37% when compared to other conventional methods. In this proposed work static configuration is preferred as novelty over dynamic configuration like socio inspired political algorithm, Ramanujan reconfiguration, Hybrid red deer with moth flame, dynamic leader based collective intelligence, grey wolf optimizer and artificial rabbit algorithm because the former is capable to provide cost effective, reliable solution and less computational power than the latter. These dynamic configurations have high computational complexity, complex configuration and the requirement of continuous processing. When compared with the proposed method the static configurations like black widow reconfiguration, optimal mileage configuration, ancient Chinese magic square, fixed electrical configuration, novel prime numbers and knights tour technique have the drawback like complex implementation, challenging for real time, limited flexibility and adaptability. Advances in PV materials, hybrid configurations and AI powered predictive modelling make static configurations are suitable for cost effective projects and suitable for further expansion.
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
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The authors declare that no funds, grants or other support were received during the preparation of this manuscript.
Department of Electrical and Electronics Engineering, Kamaraj College of Engineering and Technology, Vellakulam, Tamilnadu, India
Sakthivel Ganesan & Prince Winston David
Department of Electrical and Electronics Engineering, M. Kumarasamy College of Engineering, Thalavapalayam, Tamilandu, India
Hariharasudhan Thangaraj
Department of Electrical and Electronics Engineering, Vardhaman College of Engineering, Kacharam, Telangana, India
Praveen Kumar Balachandran
Department of CSE, Kebri Dehar University, Kebri Dehar, Somali, Ethiopia
Shitharth Selvarajan
Department of Electrical and Electronics Engineering, Chennai Institute of Technology, Chennai, 600069, Tamilnadu, India
Praveen Kumar Balachandran
Centre for Research Impact and Outcome, Chitkara University, Chandigarh, 140401, Punjab, India
Praveen Kumar Balachandran
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All the authors have contributed equally. All authors reviewed the manuscript.
Correspondence to Praveen Kumar Balachandran or Shitharth Selvarajan.
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Ganesan, S., David, P.W., Thangaraj, H. et al. Power enhancement of PV arrays in different configurations under different partial shaded condition. Sci Rep 15, 6963 (2025). https://doi.org/10.1038/s41598-025-91508-9
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