A Novel Topology to Improve PV Module Efficiency under Partial Shading Conditions

In this paper, we investigate the power degradation in a novel photovoltaic (PV) cell recon ﬁ guration named KenDoKu (KDK) topology under di ﬀ erent shading patterns. We analyze how a modi ﬁ cation in the linkage between the PV cells within a shaded PV module can a ﬀ ect its e ﬀ ectiveness. The proposed approach relocates the physical position of the PV cells within the PV module without any change in electrical connections and redistributes the shading e ﬀ ects over the PV module for the improvement of the power generation. To achieve this purpose, modeling and simulation are performed for a set of various shading patterns such as homogeneous, sectional, and scattered shadings. The simulation model used is a combination of two-diode model and Bishop ’ s model. This model is applied to a PV module and is implemented in LTSpice software to quantify the impact of shading on P-V characteristics. The performance of the KDK topology is compared to other optimized con ﬁ gurations such as total-cross-tied (TCT), bridge link-total cross tied (BL-TCT), honey comb-bridge link (HC-BL), series parallel-total cross tied (SP-TCT) and existing odd-even (OE) and Latin square (LS) schemes of interconnection. The e ﬀ ectiveness of the KDK approach is evaluated in terms of the characteristics of P-V curves, global maximum power (GMP), mismatch power loss MPL (%), ﬁ ll factor FF (%), and performance ratio PR (%). The simulated results revealed that the KDK con ﬁ guration scheme performs better in terms of generating maximum power under the considered partial shading conditions. The proposed approach reduces the maximum power losses (MPL) and improves the ﬁ ll factor (FF) with respect to OE and LS con ﬁ gurations in the most of the cases. Moreover, experimental veri ﬁ cation is also carried out. The obtained results show that the KDK con ﬁ guration outperforms the other analyzed PV cell rearrangement in terms of increased power.


Introduction
For the past three decades, PV technology has become attractive for renewable energy. The PV modules are widely used in urban as well as rural electrification. However, the PV module or system was far from satisfactory due to their low efficiency and high installation cost [1,2]. The important current improvements have attracted the craze of researchers in the area of PV energy to deal with the problems presented in this field. Therefore, the enhancement of power is an open field of research, and therefore, the PV cell or module configuration technique is gaining more attention to address this problem [3].
The PV modules are often exposed to a number of factors that include wind, rain, heat, lightning, shading, and degradation effects over time, thus the performance of PV systems weather conditions dependent. In the literature, several studies have been carried out on the behavior of PV systems with various irradiances and temperatures to examine the change in solar irradiance and temperature effect on PV production systems [4]. The shading has predominant effect on the performance of PV modules, which thereby reduces significantly the generated power. Some PV cells or modules in the PV module/array receive various irradiance levels under partial shading conditions due to passing clouds, building, or trees, which may exhibit multiple local peaks (LP) and one global peak (GP) on the output characteristics [4,5]. The existence of multiple peaks may mislead the conventional maximum power point tracking technique by the local maximum power instead of global maximum power, which would add extra power loss to the PV module [1]. To extract the global maximum power, advanced MPP methodologies are employed [6,7]. Due to an eventual malfunction of PV modules, a change in physical conditions or partial shading conditions may result in a low performance of PV modules [8]. To resolve these issues, Chao et al. [9] and Chen et al. [10] have proposed alternative approaches to minimize the power losses, whether dividing a PV array into a fixed and adaptive bank with an array switch or connecting bypass diodes across each cell. However, the addition of bypass diodes can exhibit multiple peaks in the output characteristics of the PV module [11]. To overcome these issues, a reconfiguration technique was used. The main goal of reconfiguration is to disperse the shading effects for uniform row current.
Belhachat and Larbes [12] have proposed a numerical approach based on the MATLAB program to analyze and compare various topologies of PV arrays for different shading patterns to find the best configurations that minimize power losses under partial shading conditions. However, they focused their work on a single situation of shading pattern.
To overcome partial shading issues, different configurations of PV cells/modules such as SP, BL, HC, TCT, BL-TCT, and hybrid SRBL-TCT are analyzed to achieve the desired output characteristics [13]. This work shows that the hybrid configurations have the best performance results compared to the other configurations.
Some studies have been conducted on the comparison between various solar panel topologies such as SP, HC, BL, and TCT. The results obtained show that, in general, the TCT configuration provides the best efficiency under different partial shading conditions [14,15].
However, the TCT configuration has demerits, such as when the number of shaded PV cells are in the same row, that restricts the output characteristics of a PV module. To overcome this problem, Manna et al. [16] and Sai Krishna and Moger [17,18] have developed reconfiguration methodologies for the TCT topology to dispatch shading effects from one row into various rows, in order to reduce the mismatch losses under partial shading conditions. Reconfiguration methodologies can be classified into two parts: dynamic and static techniques. Sai Krishna and Moger [17][18][19] have analyzed and discussed dynamic reconfiguration approaches. In these methodologies, PV modules are dynamically reconfigured within the PV array to enhance the output power generation under different partial shading conditions. However, the aforementioned research show that the dynamic reconfiguration approach necessitates the use of sensors to locate the shading, a complex algorithm to enhance the output power and a switching circuit. As a result, the dynamic reconfiguration is found to be complex and economically not feasible for a large PV system [20,21]. Contrary to dynamic interconnection technique, the static methodology does not require any complex algorithms, sen-sors, and switching circuits. However, it requires an adequate design for organizing the location of PV cells to dispatch shading effects over the PV module. The authors [21][22][23] proposed novel interconnection schemes to eliminate partial shading effects over the PV array to enhance the PV power generation. However, all these proposed reconfigurations have one common demerit: they are not appropriate for PV arrays with unequal number of rows and columns. Therefore, to overcome these issues, the authors in [24] proposed zigzag reconfiguration scheme for TCT PV module configuration to enhance maximum power output under partial shading conditions. This reconfiguration technique alters the location of the PV modules in different columns. As a result, this complicates the interconnection scheme for a large PV module size. In ref [25], the authors introduced an improved permanent structuring technique named odd-even configuration to configure the PV module within the PV array in order to achieve maximum power output under partial shading conditions. The authors [26] presented a comprehensive and comparative study of the existing TCT configuration with a Latin square (LS) reconfiguration scheme to minimize shading effects. In this paper, the LS approach enables the reconfiguration scheme to redistribute shading effects over the PV array without altering the electrical connections. However, according to [25,26], when PV modules are shaded across the entire rows, the PV array is reorganized into two (2) rows; this means that if the shade falls on the diagonal side of the PV array (see Figures 1(a) and 1(b)), it will stay undispersed. Consequently, this causes a decrease in maximum power generation. Furthermore, after the PV module rearrangement, when the shade occurs on the diagonal side, the shading effects are displaced in the first row. As a result, the output current is reduced. According to the literature review [27], it is obvious that static interconnection considered as one time arrangement is superior to electric reconfiguration. It does not dynamically alter the location of the PV module, since the PV module position is set for all shading conditions. However, the one-time interconnection technique is limited to use in a small PV system; this should be improved. To overcome these issues, this paper introduces a physical location alternative using Kendoku (KDK) arrangement for TCT PV module configuration. The KDK technique redistributes the shading effect over the PV cells in a PV module, and therefore, mismatch losses are reduced. The proposed KDK arrangement approach minimalizes the number of shaded PV cells in a single row significantly and can be applied to PV module of any size. The effectiveness of the KDK arrangement is evaluated by analyzing the P-V characteristics under partial shading with other optimized arrangements techniques such as: (i) Total cross-tied (TCT) configuration as shown in Figure 2(a) (ii) Bridge-link total cross-tied (BL-TCT) configuration: it has the same number of components of TCT topology, but with an interconnection wiring as shown in Figure 2      3 International Journal of Photoenergy negative voltages. This is essential to be taken into account in the study of PV cells working partially shaded, forming part of a PV module. In this case, Bishop [28] proposed an equation in which the avalanche effect is expressed as a nonlinear multiplication factor that affects the shunt resistance current term, using the simple diode model. In the present work, we use a combination of the two-diode model and Bishop's model, to study the electrical behavior of solar cells working partially shaded. Figure 3 shows the PV cell equivalent circuit considering the avalanche effect.
Kirchhoff's first law carries the following relationship between PV cell current and voltage: Then, the photon-generated current can be calculated using Equation (2), which describes the I-V characteristics of a partially shaded PV cell considering the avalanche breakdown voltage.
where V T = kT/q is the thermal voltage, I PV is the current generated by the incident light, q is the electron charge, k is the Boltzmann constant, T is the temperature of the p − n junction, R S is the series resistance, and R Sh is the shunt resistance. I 01 and I 02 are the reverse saturation currents of diode 1 and diode 2, respectively. The extension term MðVÞ is added to the leakage current in the shunt resistance term modeled as a controlled current source: where V br is the avalanche breakdown voltage, m is the avalanche breakdown exponent (1 ≤ m ≤ 10), and a the correction factor.

Modeling of the PV Module.
A PV module is a combination of PV cells in series or parallel to enhance the required electrical power. In the case of series connected PV cells, the I-V characteristic is derived by adding the induced voltages at the same output current, whereas, in the case of parallel connected PV cells, the induced currents will be added at the same terminal voltage [29]. Theoretically, the parameters to be added will be a multiple of one parameter and the number of cells assuming identical PV cells. The experience has shown that this assumption is not always valid. Although the PV cells are characterized with the same specifications, there are slight differences during the manufacturing points under the same insolation level. This phenomenon is known as mismatched operation of PV cells. Thus, the model described in Section 2.1 for a PV cell can be extended to a PV module consisting of Ns series PV cells and Np parallel PV cells [29]. The numerical equation for the current I of a PV module arranged in N P parallel and N S series PV cells becomes: where γ = N S /N P ; GðVÞ is given as follows:

Experimental Setup
3.1. Procedure for Parameter Extraction. The PV cell model used in this research work is based on the model presented in the reference [13]. The proposed topology KDK consists of n parallel strings; each string contains n series components. Each component is protected by antiparallel bypass diode. Basically, we assume that all PV cells in the PV module are homogeneous, and there is no mismatch between them. We used, for the simulation, LTSpice software to implement the relationships described in the previous Equation (4). LTSpice is a high-performance simulation program with integrated circuit emphasis (SPICE) simulator. Different scenarios are simulated for various PV cell sizes. The current-voltage (I-V) curve for each component cell in the PV module is characterized by PV cell specific parameters' values. The parameters of a typical solar cell named KX0B22-12X1F are used for our modeling and simulation [30]. It is a complementary study of a previous work in which the parameters of the PV cell extracted under dark/ International Journal of Photoenergy light conditions by using a nonlinear least squares method [30,31]. For Bishop Parameter's extraction, a fit of the I-V characteristic is carried out under dark condition by using the measurement data as shown in Figure 4. The data are measured in forward and reverse direction. The values of the extracted parameters are presented in Table 1.
The photocurrent source is influenced by four parameters, such as irradiation, temperature, the area of the PV cell, and short circuit current. For this study, the PV cell used has an area of 270 mm 2 and a short circuit current density of 42, 4 mA/cm 2 .

Shading Patterns
Used in the Simulation. The shading models used for the experiment are presented and categorized into three parts. Besides, the defined solar irradiance levels or shading rates of each PV cell are described in Figure 1(j), in which 1000 W/m 2 means that there are not shaded PV cells in the module. On the other hand, 500 W/m 2 means that 50% of the area of the PV cells is covered by shade.

Modeling and Simulation of PV Module under Shading
Conditions. As defined previously, the model of Bishop is adopted in this research paper to analyze PV modules operating in uniform, partial or full shading conditions. Figure 5 presents the output characteristics (current-voltage (I-V) and puissance-voltage (P-V)) of an example of PV module topology operating in normal (uniform) and abnormal or partial shading conditions. In normal conditions,  5 International Journal of Photoenergy temperature and irradiance are defined in the standard test condition (STC) (at 25°C and 1000 W/m 2 ) while in abnormal conditions, various levels of irradiance are defined: two PV cells are exposed to 500 W/m 2 and 700 W/m 2 , respectively.
As seen in Figure 5, the shading increase in the rate of the cell produces a higher reduction of short circuit current I SC , which causes a reduction in the maximum power. It clearly demonstrates that the cell-generated current is a function of the rate of light transmittance. Under normal conditions, the maximum power of a PV module is 0.37 W at a maximum voltage equal to 1.93 V. When shading occurs, a considerable reduction of the power is observed. The P-V curve also presents two local maximum peaks. The first maxima localized very far from the normal maxi-mum power point (at P = 0:80 W and V oc = 0:14 V) zone is independent of the irradiance or shaded PV cell area, as the number of shaded PV cells is short-circuited. On the other hand, the second maxima is the function of the number of shaded PV cells and their irradiance.

Proposed KDK Topology.
Our method used a rebus to a power production. KDK is a rebus which requires the use of the digits to supplement a collection of cells named cages. It involves n × n or m × n grid which is divided into irregular cages. In each cage, a number and an arithmetic operation are affected as shown in Figure 6.
The principle is described as follows: (i) Each square cell in the grid will contain a digit between 1 and the size of the grid. For the 4 × 4 grid, we use the digits 1, 2, 3, and 4  Whether there is no arithmetic operation denoted in a 1 × 1 cage, this digit is to be inserted into the cage. The operations such as sum or product of the digits in a cage have to yield the goal digit when the operation is (+) or ( × ). On the other hand, when the operation is (−) or ( ÷ ), the cage must consist to two squares, and the difference or quotient of the two digits must yield the goal digit. The complete solution of 4 × 4 KDK rebus is presented in Figure 7.

Proposed KDK Arrangement.
The considered PV module consists of 16 cells with 4 rows and 4 columns. In the traditional system of interconnection, the PV cells (forming a PV module) or modules (forming a PV array) are settled as in Figure 8(a). The puzzle settlement of the KDK topology is presented in Figure 8(b), in which the first number in each lodge indicates the row number and the second digit refers to the column number of the 4 × 4 PV module.
The electrical nexus of PV cells for the TCT topology is shown in Figure 9(a). According to the KDK pattern, the reconfiguration of TCT topology is presented in Figure 9(b).

Simulation and
Analysis of the Proposed Topology of the PV Module Operating in Partial Shading Conditions. In this section, we evaluate the P-V output characteristics for various topologies operating in partial shading conditions. As     Figure 10.  Figure 11 shows the P-V characteristics obtained by simulating the different topologies under the DS condition. We can see that most of the topologies exhibit some maxima on the P-V characteristics. Among all topologies, KDK topology generates a better profile. We can see from the P-V curves presented in Figure 12(a) that the rate of power degradation is much higher when the shading is flat for all topologies except the KDK topology, which shows a better performance in homogeneous shading conditions. However, in VS condition as shown in Figure 12(b), all topologies demonstrate a similar profile that generates the same maximum power point.

Case 2. Sectional shading pattern condition.
From Figures 13(a) and 13(b), it can clearly see that KDK topology is still better under sectional shading conditions, particularly in CS condition. Meanwhile, the HC-BL and SP-TCT topologies provide the lowest efficiency, in CS-pattern and CLS-pattern, respectively. Indeed, the more number of series connections in a string involves some mismatching losses under CLS-pattern condition.
Case 3. Scattered shading (SS) pattern condition. Figure 14 shows the P-V characteristics of various PV module typologies operating in SS-pattern condition. The results show that KDK topology is greater in terms of maximum output power compared to other topologies under different shading patterns such as SS-pattern A, SS-pattern B, SS-pattern C, and SS-pattern D. KDK topology provides the best efficiency with low power dissipation compared to the others. From the obtained results, it is seen that the  Figure 14(c)) and SP-TCT topology (in Figures 14(a), 14(b), and 14(d)) are less interesting no matter the shading pattern. Among all the configurations, KDK topology is seen to be the most adequate in providing the optimal power by attenuating the power losses under SSpattern condition.

Performance Evaluation.
To select the best PV module topology which provides the highest efficiency, we compare the various topologies in terms of power loss percentage (Δθ Loss ) operating in different shading conditions, by using the equation below: in which P max and P Sha max are, respectively, the maximum power produced under normal (unshaded) and partial shading conditions.  Figure 15 bar chart form, the KDK topology presents better performance compared to TCT, BL-TCT, HC-BL, HC-TCT, SP-TCT, and TCT. Most power dissipations are related to FS-pattern in which the shading has covered the entire PV module row. According to the VS-pattern, all topologies are found to be better in most of the shading models under homogeneous shading conditions. This implies that once the shading is distributed over the important part of the PV module area, the topologies do not con-stitute an alternative to power loss issues no matter the shading pattern. For the sectional shading shown in Figure 16, BL-TCT and KDK are considered as the topologies with the best efficiency in comparison to the others under CS-pattern condition. On the other hand, under CLS-pattern conditions, TCT and KDK are the most interesting. The results obtained demonstrate that the KDK topology gives the best efficiency, whereas the SP-TCT typology presents lower efficiency. This indicates that the junctions among the PV cells may have an effect over power generation. Figure 17 presents the simulated results of power losses for different topologies as a function of the defined scattered shading pattern. For these shading patterns, the power losses are quite drastic for the SP-TCT topology.

Comparison with Existing Reconfigurations Topologies
In this section, the proposed KDK approach and existing reconfiguration topologies such as odd-even OE [25] and Latin square LS [26] are compared to evaluate their applicability under different partial shading conditions.

Factors Impacting the Effectiveness of PV Module
Topologies. The main factors considered to test the effectiveness of these various topologies are global maximum power (GMP), mismatch power losses (MPL), fill factor (FF), and performance ratio (PR).

Mismatch Power Losses (MPL)
. MPL is defined as the difference in GMP under the standard test condition (STC) from partial shading conditions and can be formulated as where P GMP (STC) and P GMP (PSc) are the generated GMP at STC and PSc, respectively.

Fill Factor (FF).
Fill factor can be defined as the ratio of GMP to the product of module's open-circuit voltage (V OC ) and short circuit current (I SC ) given by   [25], LS [26], and KDK arrangement schemes of configuration under different partial shading conditions. OE [25] LS [26] Table 2. The improved effectiveness is carried out after the novel arrangement of PV cells according to the KDK approach. The calculated power is found higher or equal. Indeed, in the KDK configuration, the repositioning of PV cells disperses the PSc effects over the PV module, which results in improved maximum power.

FS Pattern Condition.
As illustrated in Figure 1(b), the PV cells in rows 2 and 3 are completely shaded. The calcu-lated row current, voltage, and power of OE, LS, and KDK configurations under this shading pattern are tabulated in Table 2. It is obvious that after the rearrangement of PV cells according to the KDK approach, the KDK topology increased power generation compared to OE and LS configurations.

VS Pattern Condition.
Under this shading pattern, the PV cells in columns 2 and 3 are completely shaded, as shown in Figure 1(c). Table 2 presents the calculated current, voltage, and power of the OE, LS, and KDK configurations. In    Table 2 shows the calculated current, voltage, and power of OE, LS, and KDK configurations. The results shows that OE, LS, and KDK generated maximum power by dispersing more shades over the PV module.  Table 2 presents the calculated row current, voltage, and power of the OE, LS, and KDK configurations. According to the obtained results, the KDK configuration shows improved performance when compared to OE and LS configurations. 5.2.7. SS Pattern B Condition. As described in Figure 1(g), the positioned PV cells are subjugated to different irradiance levels. The shaded PV cells receive irradiance of 0 W/m 2 , 100 W/m 2 , 200 W/m 2 , and 900 W/m 2 . The rest of the PV cells receive 1000 W/m 2 irradiance. The calculated row current, voltage, and power for OE, LS, and KDK configurations are shown in Table 2. From this table, it is clearly noted that the KDK and LS configurations show improved performance as compared to OE PV cell arrangement.   Table 3 under different partial shading conditions. After implementing the different approaches named OE, LS, and KDK to reconfigure the PV cells and distribute shades on its area to extract maximum power, the obtained results of each in terms of GMP are analyzed and compared. Figure 18 shows the effects of shading on power generation.
The results show that the KDK approach generates the best GMP for most of the considered shading patterns com-pared to OE and Ls methods. Analysis of results by MPL, FF, and PR factors under different shading patterns is shown in Figures 19 and 20.
Based on the analysis performed in Figure 20, it can be noted that the KDK method is able to generate the best results in performance analysis via fill form (FF) factor compared to OE and LS methods. Evaluations also show that the KDK approach has the lowest of MPL compared to the other.

Experimental
Analysis. An experimental setup has been carried out by using the PV cell configured with the proposed KenDoKu technique and the OE and the LS techniques. The electrical parameters of the PV cells under consideration are tabulated in Table 4. We have considered all shading patterns defined in Section 3.2. Figure 21 displays the experimental setup which consists in a Keithley 2701 multimeters, a simulator, and an arc lamp source. The data were recorded with a computer. To provide nonuniform insolation to the PV module, light-emitting diode lamps are used over each PV cell as independent source. The illumination of each lamp is controlled by using potentiometers connected across a light-emitting diode lamp. This allowed us to create partial shading conditions for the PV module. Table 5 summarizes the experimental powers obtained by the proposed KDK reconfiguration and OE and LS reconfigurations under different shading conditions.
For the DS condition, the proposed KDK configuration has increased the maximum power by 8% compared to OE and LS techniques. For FS condition, the KDK configuration has raised the maximum power by 40.7% and 13.8% compared to OE and LS configurations, respectively. For VS and CS conditions, all the three KDK, OE, and LS configurations have generated the same maximum power of 105 mW (VS pattern) and 162.85 mW (CS pattern). For CLS condition, the KDK configuration has increased the maximum by 21.43% and 13.2% compared to OE and LS configurations, respectively. For the SS pattern A condition, the KDK and LS configurations have generated the best maximum power (163.85 mW) and raised the maximum power by 16.30% compared to the OE configuration. For the remaining partial shading conditions, the KDK configuration has generated the best maximum power output as compared to other OE and LS configurations. Overall, the  17 International Journal of Photoenergy experimental data show that the proposed KDK technique resulted in a significant improvement in the maximum power of the PV module. Indeed, the KDK technique has reduced the shading loss by scatting more shades in all rows of the PV module. Besides, the KDK technique reorients the physical position of the PV cell within the PV module without altering the electrical interconnection. As the KDK technique does not use neither a complex algorithm nor a sensor and switching circuit, it can also be economical compared to other OE and LS configurations.

Conclusion
In this research paper, the effectiveness of TCT, BL-TCT, HC-BL, HC-TCT, SP-TCT, OE, and LS configurations is evaluated, analyzed, and compared with the proposed KDK arrangement scheme of configuration under defined partial shading conditions. The proposed KDK technique redistributed shading effects over the PV module without any change in the electrical connections of the PV cells. The effectiveness of the KDK approach is evaluated in terms of P-V curve characteristics, GMP, ML (%), FF (%), and PR (%). The simulation model is developed using the bishop model and is implemented in LTSpice software. The simulated results showed that the proposed KDK configuration scheme exhibited better performance to generate maximum power output under the considered partial shading conditions. In most of the cases, the GMP of the KDK configuration is found to be superior as compared to the existing OE and LS configurations. In short, the proposed KDK scheme of configuration has more efficiency as compared to the TCT, BL-TCT, HC-BL, HC-TCT, SP-TCT, OE, and LS schemes of interconnection, with an increasing maximum performance. In addition, the proposed approach reduced the maximum power losses (ML) and improved the fill factor (FF) with respect to the OE and LS configurations in most cases. Moreover, experimental verification is also carried out. The results obtained showed that the KDK configuration scheme outperforms other analyzed PV cell/module arrangement pattern of interconnection in terms of power increasing.

Data Availability
Data are available on request.

Conflicts of Interest
The authors declare that there is no conflict of interests regarding the publication of this paper.