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Scientific Reports volume 15, Article number: 27787 (2025)
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Among the key challenges in utilizing solar photovoltaic arrays comprising multiple series-connected modules, is achieving its operation at the global maximum power point under partial shading conditions (PSCs). Partial shading is a common occurrence in large PV installations due to obstructions such as poles, trees, chimneys, clouds, and fences. Consequently, the output power generated by partially shaded panels often falls short of the expected levels and thus user has less reliability in this technology. To mitigate the adverse effects of PSCs related to power generation, modifications to the interconnection schemes of PV arrays are frequently employed. Numerous interconnection strategies have been proposed and incorporated in the literature. Among them, the most popular ones are series–parallel (SP) and total-cross-tied (TCT). A performance comparison between SP and TCT under various shade patterns are analysed in this paper. The findings show that TCT typically performs better than SP, generating more power in the majority of situations. SP is a good substitute for TCT, though, because it can produce more or the same amount of electricity under specific shading conditions. Because SP has less complicated wiring, requires less time to install, and performs just as well, hence it is preferred. In order to maximize power generation, the paper also contains experimental validation of simulation results, highlighting the fact that the number of shaded rows and columns should determine the interconnection scheme selection. PV systems can increase dependability and efficiency by choosing the right interconnection approach, guaranteeing peak performance even in partial shading conditions.
Although several renewable energy sources are available, solar energy are acquiring special attention because it has wide spectrum on earth which is available almost everywhere. Further, solar energy can be used from small scale to large installations and require very less maintenance1. On global level, energy received from the sun in an hour is more than the energy consumed by entire population on earth in a year i.e., it is very high compared to our overall energy requirements and consumption. Thus, by knowing that solar energy has the potential to meet a large portion of the worlds’ growing demands for energy, it is important to make efficient use of electricity generated by this way2.
In solar photovoltaic (PV) systems, the solar panels are connected to each other to match the requirements by the grids or loads and thus panels may be illuminated in a non-uniform manner due to shading caused by clouds, nearby trees, neighbor’s houses etc.3,4,5,6,7,8,9.
The shading on a panel may causes some unwanted effect and decreases the output of whole PV system. Therefore, the extracted output is usually less than the expected output under partial shading conditions (PSC)10,11,12. This results in a lack of reliability for this technology among consumers/users. Due to space limitations, partial shading (PS) is unavoidable in many cases. In contrast to PV farms, the rooftops installations or building integrated photovoltaic systems has more probability of encountering some obstacles such as nearby trees, chimney, towers etc. In many cases, the obstacles cannot be removed and moreover, the shadow could appear on PV panels after their installation because of a new building constructed nearby. In addition, the output power under partial shading conditions is not only dependent on shaded area but also on the array interconnection scheme used and the geometry as well as intensity of the shade13,14,15,16.
Sources of partial shading are of two types. One is easy-to-predict shadows and other one is difficult-to-predict shadows. In easy-to-predict shadows, the pattern of shadow may be forecast and is almost known17,18,19,20. For example, when modules are mounted on the roof of a building and source of shade possible are nearby fixture, building, chimney, pole, tower, tree etc. In these types of cases solutions may be provided during the designing stage of a PV system to reduce PS losses20,21,22,23. For example, PS from nearby installed modules may be reduced by increasing the distance between the modules to have for larger distances between adjacent arrays and thus to avoid shading. In difficult-to-predict shadows, sources of shadows may be clouds, dust, snow etc. The effects of these types of shade are not easily predictable and thus their solutions. Minimizing the impact of partial shading (PS) and enhancing energy production are significant challenges in photovoltaic (PV) systems24,25,26.
An interconnection scheme, or configuration, refers to method of arranging or connecting PV panels within an array27. Several arrangements have been reported in literature for connection/linking of modules in the array28. Some of them are series–parallel (SP), honeycomb (HC), bridged-link (BL) and total-cross-tied (TCT) configuration29. As name specifies; in SP arrangement, panels are tied in series to get the necessary voltage; then, theses series connected panels are connected in parallel to get the necessary power. TCT arrangement may be achieved from SP arrangement by attaching links in between30. In BL arrangement, all panels are arranged such that four panels constitute a bridge. HC arrangement may be obtained from BL arrangement with few changes.
Among all, SP arrangement is very simple with few interconnections among panels. Due to less interconnections, SP arrangement has less cable loss and minimum wiring time of installation. However, this arrangement malfunctions under PSCs. On the other hand, other arrangements like TCT, BL and HC have a greater number of links/ties/connections among panels and these arrangements reported to have higher reliability under PSCs31. However, these arrangements suffer from the drawback of increased links/ties/connections in between modules and thus increases complexity and in turn wiring time during installation32,33. Several other works are also given and summarized in Table 1.
The work in this paper aims to investigate SP and TCT topologies of PV array under PSCs to get the best topology for various easy-to-predict shading patterns. Among SP, TCT, BL and HC interconnection schemes, the most exploited are TCT and SP and thus considered and studied in this work28. In “Modeling of photovoltaic module and array” section of paper, modeling of PV module is mentioned and in the “Performance analysis of 2*3 PV array” section, results of PV array (4*4) simulated in SP as well as TCT interconnections are shown under uniform irradiance conditions and PSCs. In “Experimental validation” section elaborates about the experimental validation of the work done.
For simulation of solar cell/module/array several models are available in literature and each model is an improvement over other. However, with each improvement an additional component is added and thus with each improvisation the complexity of model increases. Due to simplicity and less component, one-diode model is considered in this work to simulate solar module. This one-diode PV model developed using three general equations3,30,38,39.
All simulations are done in MATLAB/Simulink and the parameters required for simulation is taken from Table 2. The current–voltage (I–V) characteristics and power–voltage (P–V) characteristics of simulated panel is given ref.3,30 which also shows the validation of simulated model by comparing its characteristics curves with existing model.
A 2*3 photovoltaic array including six modules is simulated for the analysis using SP and TCT arrangements (Figs. 1 and 2 respectively). For all analysis carried out during this work, the PV module is considered as lumped for simplicity, however it consists of several solar cells connected in series38. All the modules in both the configurations are equipped with bypass diodes and are identical. The maximum power obtained under STC is given in Table 3. Uniform irradiance conditions, both the interconnections are delivering equal power.
Various interconnections (SP).
Various interconnections (TCT).
This section includes comparative analysis of SP and TCT configurations under various shading pattern scenarios. Thus, based on the analysis, appropriate configuration of PV array is suggested for each shading scenario. For all analysis carried out during this work, the shadow is cast upon all cells of a module with the same intensity. Two moving shade patterns are considered to study the relation between the interconnection schemes, shading scenario and the MPP power obtained. These shade patterns are vertical shade pattern and horizontal shade pattern as shown in Fig. 3. These shade patterns are common in PV farms and many BIPVs. In all the following simulations, non-shaded modules and shaded modules are shown as white and green respectively. Four moving shade scenarios are considered in each vertical and horizontal shade pattern.
Various shade patterns.
The vertical shade pattern (VSP) shades the columns of PV array in such a manner that shade can appear either on one column or on multiple columns of the PV array, while progressing from bottom to top. Four moving shades are considered: The shadow is moving up covering one by one all modules of first, second, third and all four columns of PV array. Various irradiance levels considered are if (a) No Shading (shown white) that means it’s a fully exposed panel and irradiance level is 1000 W/m2; (b) Heavily shaded panel (shown green) that means it’s a case of dense shading and irradiance level is 200 W/m2.
In this shading scenario, the shade is moving up from bottom-to-top, covering leftmost column of the PV array as shown in Fig. 4i.
Vertical shade patterns.
Eight various simulations have been performed to get the influence of shade on both topologies. Table 4 shows MPP power for each case of this shading scenario for both SP and TCT topologies. Figure 5 shows the comparison of MPPs for various cases together with the MPP power without PS for reference. The best topology suggested for this moving shade scenario with reference to MPP power obtained is TCT. However, for shadow covering all modules of leftmost column (Illustration 4), any topology can be selected because both topologies yield same MPP power. However, SP is suggested as it has a smaller number of interconnections.
MPP power for different cases of VSP 1.
In this shading scenario, shade is moving up from bottom-to-top, covering two left columns of the PV array (Fig. 4ii). Eight various simulations have been performed to determine the impact of shadow.
Table 5 shows MPP power for each case of this shading scenario for both topologies. Figure 6 shows the comparison of MPPs for various cases together with the MPP power without PS for reference. For shadow covering two bottom modules of leftmost columns (Illustration 1), SP topology can be selected, as it is yielding more MPP power. For shadow covering two leftmost columns entirely (Illustration 4), any topology can be selected, because both topologies yield same MPP power. However, SP is suggested as it has a smaller number of interconnections. For rest two cases (Illustration 2 and Illustration 3), TCT is performing better.
MPP power for different cases of VSP 2.
In this shading scenario, the shade is moving up from bottom-to-top, covering three left columns as shown in Fig. 4iii. Eight various simulations have been performed. Table 6 shows MPP power for each case of this shading scenario for both topologies. Figure 7 shows the comparison of MPPs for various cases together with the MPP power without partial shading for reference. The topology suggested for this moving shade scenario according to MPP power obtained is SP, as it is yielding more MPP power in these cases. However only in Illustration 3, TCT yields more MPP power as compared to SP. Therefore, for Illustration 3, TCT topology can be selected. For Illustration 4, any topology can be selected, because both topologies yield same MPP power in this PS situation. However, SP is suggested as it has a smaller number of interconnections as compared to TCT.
MPP power for different cases of VSP 3.
In this shading scenario, the shade is moving up from bottom-to-top, covering all columns of the PV array (Fig. 4iv). Eight various simulations have been performed to get the influence of shade on both topologies. Table 7 shows MPP power for each case. Figure 8 shows the comparison of MPPs for various cases together. Both topologies yield same MPP power in this PS situation. Thus, any topology can be selected. However, SP is suggested as it has a smaller number of interconnections as compared to TCT.
MPP power for different cases of VSP 4.
The horizontal shade pattern (HSP) shades the rows of the PV array. In this PS situation, the shade appears either on single row or multiple rows of PV array. In this analysis, four moving shades are considered: The shadow is moving from left to right covering one by one all modules of one, two, three and all four rows of the PV array.
In this shading scenario, the shade is moving towards covering last line of the PV array as shown in Fig. 9i. Table 8 shows MPP power for each case. Figure 10 shows comparison of MPPs for various cases together with the MPP power without PS for reference. The topology suggested for this moving shade scenario according to MPP power obtained is SP, as it is yielding more or equal MPP power in three cases. However, for shadow covering only one module (Illustration 1), TCT topology can be selected as it is yielding more MPP power.
Horizontal shade patterns.
MPP power for different cases of HSP 1.
In this shading scenario, the shade is moving to right from left, covering two rows (Fig. 9ii). Eight various simulations have been performed. Table 9 shows MPP power for each case of this shading scenario for both topologies. Figure 11 shows the comparison of MPPs for various cases together with the MPP power without partial shading for reference. The topology suggested for Illustration 1 and Illustration 2 is TCT. However for shadow covering three modules (Illustration 3), SP is performing better. For Illustration 4, any topology can be selected because both topologies yield same MPP power. However, SP is suggested as it has less number of interconnections compared to TCT.
MPP power for different cases of HSP 2.
In this shading scenario, the shade is moving from left to right, covering three rows (Fig. 9iii). Eight various simulations have been performed. Table 10 shows MPP power for each case of this shading scenario for both SP and TCT topologies. The topology suggested for this moving shade scenario according to MPP power obtained is TCT. However, for shadow covering all rows, any topology can be selected. However, SP is suggested as it has a smaller number of interconnections as compared to TCT. Figure 12 shows the comparison of MPPs for various cases together with the MPP power without partial shading for reference.
MPP power for different cases of HSP 3.
In this shading scenario, shade is moving from left to right, covering all rows of the PV array (Fig. 9iv). Eight various simulations have been performed. Table 11 shows MPP power for each case of this shading scenario for both SP and TCT topologies. Figure 13 illustrates the comparison of MPPs for various cases together with the MPP power without partial shading for reference. The topology suggested for this moving shade scenario according to MPP power obtained is SP, because both topologies are yielding same MPP power and SP has fewer interconnections.
MPP power for different cases of HSP 4.
SP and TCT topologies have been simulated with most common shade scenarios i.e., vertical shade pattern, horizontal shade pattern and diagonal shade pattern. The best topology is also identified for all the possible cases of these shade patterns, based on the MPP power obtained. The results obtained for vertical and horizontal shading pattern are also summarized in Table 12, in terms of number of rows and columns affected by shadow and preferred interconnection. The analysis is done to contribute more qualitative conclusions for PV array of any size under partial shading condition. It can be concluded that:
When the number of columns affected by shade is more than the number of rows affected by shade, then MPP power received is more with SP interconnections. However, both topologies produce same MPP power when either full column (VSP 1: Illustration 4) or full row (HSP 1: Illustration 4) is shaded. For these shade scenarios, SP is suggested as it has a smaller number of interconnections.
In contrast to this, when number of rows affected by shade is more than the number of columns affected by shade, then MPP power received is more with TCT and thus preferred in these cases.
To get the preferred topology for PV array of any size and consisting of any number of rows and columns affected by shadow, a flowchart (Fig. 14) is made using above conclusions.
Flowchart showing preferred interconnections.
In beginning the number of strings, modules in each string, number of columns affected by shadow and number of rows affected by shadow is taken as input. SP interconnection is preferred in two situations: (a) the number of columns affected by shade is more than the number of rows and (b) either full row or full column is shaded. In rest of the cases, TCT yield better results. This is so because under shading modules in TCT forces relatively less output current and in turn forces its other host row modules to generate slightly more currents, in such a way that the overall current supplied by the row is equal to the output current of each non-shaded row. Thus shading on any module causes very little change in the operating point of the modules which are not under shade and in turn the global maximum power drop would be small.
Screenshot of MATLAB window showing the program to obtain the preferred topology.
Once the shaded panels in any row increase, maximum power of array decreases. With the help of this flowchart, preferred topology may be obtained for PV arrays by writing a small program (Program 1), which shows the screenshot of MATLAB command window. Figures 15 and 16 shows the result of the programs for 4*4 and 20*10 PV arrays respectively. The number of rows affected by shadow is four and seven in program 1 and 2 respectively and the number of columns affected by shadow is one and six in program 1 and 2 respectively.
Simulation results on 4*4 array.
Simulation results on 20*10 array.
Experimental validation of proposed interconnections are carried out and the outcomes are compared with the simulation results. Six modules (2*3 photovoltaic array) are used as shown in Fig. 17 and all practical setup conditions including datasheet of the array are given in3,30.
Practical setup.
Measurements were carried out with (a) panel 1 and panel 2 shaded to represent the case: number of row shaded (i.e. 2 in number) is greater than number of column shaded (i.e. 1 in number); (b) panel 1, panel 4 and panel 5 are shaded to represent the case: number of column shaded (i.e. 3 in number) is greater than number of row shaded (i.e. 1 in number). The results obtained are in agreement with the simulation results and the results of both interconnections are given in Tables 13 and 14. The results obtained are also summarized in Figs. 18 and 19, for SP and TCT interconnection respectively.
Output power of SP configuration for various cases.
Output power of TCT configurations for various cases.
It may be seen that the voltage reading is slightly varying in both the interconnections under same insolation condition. The reason is change in time at which the readings were taken and in turn changes in insolation condition. The huge difference in output power of both the interconnections under PSC may also be seen.
In experimental investigations, the intrinsic uncertainty of measurement instruments, such as multimeters, constitutes a significant source of error. For a typical multimeter, this uncertainty may be approximately ± 1.75% of the reading. When integrating such measurements into large-scale systems, the aggregation of these individual uncertainties can propagate, leading to a demonstrable reduction in the overall output of the system. Consequently, it is imperative to quantify and account for these instrument-specific uncertainties in the comprehensive error analysis to ensure the reliability and validity of experimental findings.
Partial shading (PS) is a common issue in photovoltaic (PV) installations. While large land areas can reduce shading losses, this solution is impractical. This work compares series–parallel (SP) and total cross-tied (TCT) interconnection schemes under two shading scenarios: vertical shading and horizontal shading.
The results reveal that different shading conditions impact maximum power point (MPP) power differently. In some cases, both interconnections show similar performance, while in others, one performs better than the other. TCT generally produces higher power compared to SP, but there are cases where SP matches or outperforms TCT.
Since SP has a simpler wiring configuration, it is the preferred choice when both interconnections yield equal power. On the other hand, TCT is more complex and does not always guarantee superior performance. Therefore, the selection of an optimal module configuration depends on the most likely shading scenario.
By analyzing various shading patterns and their impact on power output, this study highlights the importance of selecting the appropriate interconnection scheme to maximize efficiency while minimizing complexity.
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
Bridge-linked
Global maximum power point
Global maximum power point technique
Honey-comb
Maximum power point
Maximum power point technique
Partial shading
Partial shading conditions
Solar photovoltaic array
Solar photovoltaic
Series–parallel
Total-cross-tied
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BK Birla Institute of Engineering and Technology, Pilani, Rajasthan, India
Smita Pareek
Department of Electrical Engineering, Graphic Era Deemed to be University, Dehradun, India
Md Fahim Ansari
Maharshi Dayanand University, Rohtak, Haryana, India
Neha Khurana
Department of Electronics and Communication, GLA University, Mathura, India
Md. Manzar Nezami
Department of Electrical Engineering, Al-Baha University, Alaqiq, Saudi Arabia
Salah S. Alharbi & Saleh S. Alharbi
IIMT, College of Engineering, Greater Noida, India
Gopal Krishan
NIT , Kurukshetra, Haryana, India
Ratna Dahiya
Department of Electronics and communication engineering,, SR University, Warangal, Telangana, India
Mohammad Junaid Khan
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Smita Pareek: Technical writing, results analysis; Md Fahim Ansari: Technical writing, results analysis, conceptualization, investigation and data analysis; Neha Khurana: Technical writing, system modelling; Manzar Nezami: Problem formulation and technical writing; Salah S. Alharbi: Data collection paragraph writing; Saleh S. Alharbi: Results analysis; Gopal Krishan: Problem formulation and technical writing; Ratna Dahiya: Problem formulation and result analysis; Mohammad Junaid Khan: Results analysis and technical check.
Correspondence to Md Fahim Ansari.
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