Modeling and performance analysis of novel quad‐tied PV array configuration under partial shading conditions

A photovoltaic (PV) cell is the smallest unit in an array that exhibits nonlinear characteristic curves. To gather the maximum amount of energy from a PV array under partial shading conditions (PSCs), it is necessary to follow the largest peak in the power–voltage (P–V) curve. PV cells are partially or totally shaded due to atmospheric conditions, which show multiple peaks in the PV curve. To overcome the losses occurring due to PSCs, PV array reconfiguration action is advisable. The authors of this work proposed a novel 5×5 $5\times 5$ quad‐tied PV array configuration and compared its performance to that of other current configurations such as series‐parallel, total‐cross tied, and others in terms of global maximum power point tracking, mismatch loss, fill factor, and efficiency. The MATLAB/Simulink 2020a platform was used to generate PV array curves under various shading conditions.


| INTRODUCTION
With the rise in electricity consumption and recent changes in environmental conditions, such as global warming and greenhouse gas emissions, a modern, cheaper, and helpful sustainable energy source is required. 1Solar energy is plentiful and has emerged as a promising long-term energy source.It appears to be one of the most appealing research sources in recent years. 2 It is abundant, pollution-free, low-maintenance, dependable, and endless.It also has certain disadvantages, including a high installation cost and a low energy conversion efficiency. 3However, a key disadvantage of the photovoltaic (PV) system is the nonuniform distribution of illumination, often known as partial shading condition (PSC). 4,5PSCs are caused by a variety of circumstances, including solar PV-size constraints, structural issues, product faults, and the result of nonuniform irradiance. 6,7The PV modules in PSCs absorb less irradiance than the other modules, resulting in lower irradiance absorption. 8Due to less absorption of irradiance, the current produced in these modules is less than the current produced in other modules.Due to this change in magnitude, the shaded modules start absorbing the electricity, which results in the damage of the PV cell or module. 9Connecting bypass diodes across the terminals is one technique to safeguard modules from harm.Another reason for partial shading is that the PV array's P-V and I-V characteristics have several peaks, resulting in power losses in the system. 10][13][14] Some researchers have suggested the following methods to reduce PV system losses: • Patel and Agarwal 9 presented a comparison of PV arrays with series and series-parallel (SP) arrangements under PSCs.The performance was checked with the use of MATLAB/Simulink environment.According to the study, PV array topologies and shading schemes have an impact on the amplitude of global maximum power point. 9 Belhachat and Larbes 12 compared alternative PV array topologies with asymmetrical and equal-row shading patterns in great detail.As a result, the total-cross-tied (TCT) PV array architecture outperforms other PV array layouts when shading patterns are considered.PV array under six distinct shading scenarios.According to the findings, the efficiency of a PV array is highly dependent on the array configuration. 17,180][21] The paper 19 a TCT-SC hybridized voltage equalizer to mitigate the partial shading effect in PV arrays.The proposed equalizer showed improved performance compared to other voltage equalizers in terms of power loss and voltage balancing accuracy.However, the proposed system requires more maintenance and could be more difficult to integrate into existing PV systems.Rao et al. 20 and Sahu et al. 21a method to achieve maximum power from PV arrays under different shading conditions and partially shaded PV arrays, respectively.This method does not work optimally under extreme shading conditions, and the diodes can cause power loss and reduce the overall efficiency of the system.Authors in this paper presented a technique for the configuration of the physical positioning of the PV modules to alleviate losses that occurred due to partially shaded conditions.The modules are positioned in the array in accordance with the novel quadtied (QT) pattern, with the same power connections.The above arrangement makes it easier to spread the impact of shading throughout the array, lowering the proportion of shading on PV modules in the same row.The authors of this research work used the MATLAB/ Simulink platform to present a novel analysis and comparison of PV arrays with SP, bridge-link (BL), honeycomb (HC), triple tied, and TCT utilizing a 5 × 5 PV array under eight different shading conditions. 22he performance was investigated for different shading patterns and various parameters were considered, namely.Fill factor (FF), efficiency (η), and mismatch power loss (MMPL) exhibit the superiority of the proposed PV array structure.The authors have presented the paper as follows.In Section 2, the mathematical modeling of the PV module is shown.In Section 3, different shading patterns are given.Section 3 gives a description of the different topologies of PV arrays.Section 4 discusses the factors that influence the performance of a PV system.Section 5 examines the description of all topologies under the various shading patterns described in Section 3. In Section 6, the discussion's conclusion is described.

| MATHEMATICAL MODELING OF PV UNIT
Mathematical modeling of PV modules is essential for a better understanding of how they work.The PV cell converts the incident light energy directly to electricity.The amount of energy produced by a PV cell is proportional to the amount of irradiance and temperature.Figure 1A shows the equivalent circuit of an ideal and practical PV cell. 23,24Single-diode PV cell models are used for higher accuracy and computational simplicity. 25igure 1B shows a PV array made up of N S series and N P parallel-linked diodes in multiple diode PV architectures.
The output current of a PV cell (I t cell , ) is given by [26][27][28] VERMA ET AL.
| 3435 PV module's output current (I ) is given by 29,30 The output current (I o ) of PV array is given by where is the thermal voltage, a is the ideality factor, R S is the series resistance, R SH is the shunt resistance, n S is the number of cells in series (per module), N S is the number of PV modules in series, N P is the number of PV modules in parallel, k is Boltzmann's constant (1.3806503 × 10-23 J/K), T is cell operating temperature, q is the charge of electron (1.60217646 × 10-19 C), and I o and V o are the terminal current and voltage, respectively.

| Description of different shading patterns
The efficiency is mostly affected by PSCs and also creates a variety in the production of power according to the pattern of shading.In this section, there are eight different patterns of shading that are discussed, which affect the power production.The presentation of each shading pattern is described using a PV array of a 5 × 5 PV module system.The patterns are classified as: • random shading (RS), • diagonal shading (DS), • center shading (CS), • full frame shading (FF).
In Figure 2, different shading patterns are featured using blocks, in which the horizontal section presents the number of rows and the vertical section presents the number of columns.

| Random shading
Any randomly picked modules in a 5 × 5 PV array are influenced by shading and come across irradiance of decreased magnitude under this shading pattern, referred to as half-frame shading, as seen in Figure 2A.The shaded modules are: • PV21 and PV54 are shaded at 250 W/m 2 .
• The continuing modules are each shaded at 1000 W/m 2 .
F I G U R E 1 PV models: (A) single diode and (B) multiple diode.PV, photovoltaic.

| Center shading
The center-positioned modules in a 5 × 5 PV array are shaded and receive lower irradiance under this shading pattern, referred to as CS, as seen in Figure 2C.The modules that have been darkened are: • PV22, PV23, and PV24 are shaded at 250 W/m 2 .
• The continuing modules are each shaded at 1000 W/m 2 .

| DESCRIPTION OF PV ARRAY TOPOLOGIES
The power current and voltage production from PV array setups is very much dependent on the configuration of their connections.In this study, the authors have analyzed and compared five different PV array topologies using a 5 × 5 PV module system.The topologies for analysis are: • series-parallel, • bridge-link, • honeycomb, • total-cross tied, • quad tied.It is the most widely employed PV array configuration due to its simple structure and advantages in economical operations.In this design, five modules are connected in series to obtain the requisite voltage, and five similar configurations are connected in parallel to generate the required current.Because the number of modules in a series is smaller than the number of modules connected in a series topology, mismatch losses are reduced.Figure 3A depicts the SP topology for a 5 × 5 PV array system.

| Bridge-link
The bridge rectifier structure connects all of the modules in this PV array design.Because there are a large number of modules connected in series in an SP configuration, there is a considerable decrease in voltage under PSCs.Two modules are connected in series and then further connected in series in this configuration.Figure 3B depicts the bridge link structure for a 5 × 5 PV array system.

| Honeycomb
Bees create HC, which is the inspiration for this design.
In this PV array layout, the PVs are joined in a hexagonal form, similar to an HC. Figure 3C depicts the HC topology for a 5 × 5 PV array system.

| TCT PV configuration
All modules are connected in parallel to reduce the number of modules connected in series, resulting in less mismatch loss.All of the modules are connected in series as well as in parallel with their neighboring modules in this setup.Figure 3D depicts the overall cross-tied architecture for a 5 × 5 PV array system.
T A B L E 1 Performance of PV array topologies under uniform isolation.
Global peak values Local peak values | 3439

| Quad-tied PV configuration
This layout is inspired by park entry gates, which open from one end, and the next opening is on the opposite side of the first, creating a zig-zag pattern.Figure 3E depicts the QT architecture for a 5 × 5 PV array system.

| FACTORS CONSIDERED TO QUANTIZE THE PERFORMANCE OF PV ARRAY
Under various shading situations, the five specified PV topologies, namely, SP, BL, HC, TCT, and QT, are compared.FF, efficiency, and mismatch loss are some of the factors evaluated while analyzing the performance and output of electricity under specific situations.

| Fill factor
FF is defined as the ratio of P GPP power generated under the given condition to the product of V OC open circuit voltage and I SC short circuit current.The ideal value of PV module FF is unity.This can be calculated by

GPP OC SC
(4) T A B L E 5 Performance of PV array topologies under full frame shading condition.
Global peak values Local peak values

| Cumulative distribution function (CDF)
The CDF finds the cumulative probability for the given value. 31The CDF of a real-valued random variable X is the function given by

| RESULTS AND DISCUSSION
This section enumerates the results for PV array topologies, namely, SP, BL, HC, TCT, and QT under different conditions.The results are generated with the MATLAB/Simulink platform.The performance graph of each shading condition is given in Tables 1-5.

| Under uniform isolation
At this shading, all the modules are provided with full irradiance.It is observed that the output from all the configurations is approximately equal to GPPs of 1966.467W at 91.226 V and 21.556 A. The performance graph under this condition is given in Figure 4.The configurations and their respective performances are enumerated in Table 1.On the basis of the results, it is evident that the proposed algorithm exhibits a similar FF, maximum efficiency, and reduced mismatch losses under the considered shading cases.The study provides evidence that the proposed algorithm can extract maximum power from the PV array even in the presence of partial shading, thus improving the overall efficiency and reliability of the system.

| Under RS condition
In RS conditions, PV modules in an array are shaded randomly to check the efficiency of the proposed QT connection.The QT configuration is providing the maximum GPP at this shading condition of 1566.924W at 92.219 V and 16.991A with one local maximum power point (LMPP).The BL configuration is producing the lowest GPP of 1389.605W at 94.057 V and 15.947 A. The performance graph under RS conditions is given in Figure 5. From the result, it is clear that the proposed algorithm has the highest FF, maximum efficiency, and reduced mismatch losses under considered shading cases.The configurations and their respective performances are enumerated in

| Under DS condition
In DS condition, PV modules in an array are diagonally shaded to establish the superiority of the proposed QT connection.The QT configuration is providing the maximum GPP at this shading condition of 1137.791W at 91.834 V and 12.389 A with one LMPP.The lowest GPP is provided by the SP configuration of 804.781W at 76.914 V and 10.463 A. A performance graph under this condition is given in Figure 6.From the result, it is clear that the proposed algorithm has the highest FF, maximum efficiency, and reduced mismatch losses under considered shading cases.The configurations and their respective performances are enumerated in Table 3. FF obtained from QT connection is 59.283 which is higher than other conventional connections.Mismatch loss is 30.546% and efficiency under this shading condition is 57.633%.FF, efficiency, and mismatch loss under the DS condition are provided in Tables 6-8, respectively.

| Under CS condition
In the CS condition, PV modules in an array are shaded in the center to establish the superiority of the proposed QT connection.The SP configuration is providing the maximum GPP at this shading condition of 1241.051W at 76.756 V and 16.168A with one LMPP.The TCT configuration is producing the lowest GPP of 1195.048W at 96.115 V and 12.434 A. The performance graph under this condition is given in Figure 7.The configurations and their respective performances are enumerated in Table 4. FF obtained from QT connection is 39.040 which is higher than other conventional connections.Mismatch loss is 44.718% and efficiency under this shading condition is 60.959%.FF, efficiency, and mismatch loss under CS conditions are provided in Tables 6-8, respectively.

| Under FF shading condition
The QT configuration is providing the maximum GPP at this shading condition of 1148.002W at 92.114 V and 12.462 A with one LMPP.The lowest GPP is provided by the SP configuration of 1088.966W at 91.506 V and 11.900 A. The performance graph under this condition is given in Figure 8.The configurations and their respective performances are enumerated in Table 5. FF, mismatch power obtained from QT connection is 44.905 which is higher than other conventional connections.Mismatch loss is 52.452% and efficiency under this shading condition is 58.150%.FF, efficiency, and mismatch loss under the FF condition are provided in Tables 6-8, respectively.

| Comparison using CDF
The data of the five PV array topologies taken into consideration have been analyzed for the different shading patterns using the CDF to investigate their behavior in terms of mismatch losses.The CDF of mismatch losses of the five PV topologies is shown in Figure 9.The analysis shows that the QT topology is the optimal configuration.Tables 6-8 show FF, MMPL, and efficiency for each shading condition, respectively.
The ability of a solar panel to convert sunlight into electrical energy is reflected in its FF, which is an important parameter.Table 6 displays the FF values ranging from 41.8% to 44.9% for different shading conditions and configurations, highlighting that the shading condition and configuration significantly affect the FF.Configuration DS exhibits the highest FF across all shading conditions except for SP, where RS has the highest value.This implies that the DS configuration is the most effective in converting sunlight into electrical energy.
Table 7 showcases the mismatch loss for various shading conditions and configurations.Mismatch loss occurs when the current-voltage characteristics of solar cells in the panel do not match, resulting in power loss.The mismatch loss percentages range from 54.7% to 57.3%.Configuration QT experiences the highest mismatch loss under all shading conditions, while BL has the lowest mismatch loss.Therefore, the BL configuration is deemed the most dependable regarding the current-voltage characteristics of the solar cells.
Table 8 presents the efficiency of the panels under different shading conditions and configurations, which varies from 55.1% to 79.4%.QT has the highest efficiency under all shading conditions, while BL has the lowest.As a result, the QT configuration is the most efficient in converting sunlight into electrical energy.
To sum up, the DS configuration has the highest FF, while the BL configuration has the lowest mismatch loss.The QT configuration has the highest efficiency in converting sunlight into electrical energy.Shading conditions significantly affect the performance of solar panels, and the optimal configuration may vary depending on the shading conditions.

| CONCLUSION
This paper presents a thorough description of the influence and production of maximum power by PV panels when connected with different topologies under PSCs.A novel configuration is proposed, namely, a QT PV configuration.The testing is done on a 5 × 5 PV array and validated for PSCs, namely, RS, DS, CS, and FF shading conditions.Further, a comparative analysis is provided for the proposed configuration with pre-existing configurations, like, SP, BL, HC, and TCT under all PSCs using the MATLAB/Simulink platform.The proposed configuration displayed maximum GPP for shading conditions RS, DS, and FF.The proposed technique finds its supremacy in comparison to the simulation method adhering to the fact that the former technique holds the capability to instantly predict the exact and detailed output of the extensive and large-size PV arrays, which results in efficient time management during the designing phase.

F I G U R E 6
Performance graph under diagonal shading condition.BL, bridge-link; HC, honeycomb; QT, quad-tied; SP, series-parallel; TCT, total-cross tied.F I G U R E 7 Performance graph under center shading condition.BL, bridge-link; HC, honeycomb; QT, quad-tied; SP, series-parallel; TCT, total-cross tied.

F
I G U R E 8 Performance graph under full frame shading condition.BL, bridge-link; HC, honeycomb; QT, quad-tied; SP, series-parallel; TCT, total-cross tied.F I G U R E 9 Cumulative distribution function of relative power losses.BL, bridge-link; HC, honeycomb; QT, quad-tied; SP, seriesparallel; TCT, total-cross tied. 12 15 Performance of PV array topologies under random shading condition.
Performance of PV array topologies under center shading condition.