L-Shape Propagated Array Configuration With Dynamic Reconfiguration Algorithm for Enhancing Energy Conversion Rate of Partial Shaded Photovoltaic Systems

Partial shading is an unavoidable factor that reduces the performance of solar PV systems. The PV system receives uneven irradiation due to partial shading which causes the mismatch loss. The partial shading distracts the irradiation from the PV modules that makes the healthy modules as idle or low performing modules. The mismatch loss can be mitigated by uniformly distributing the partial shading over the PV array. In this work, L-shaped propagated array configuration method with a new dynamic reconfiguration algorithm have proposed for enhancing the energy conversion under the partial shading conditions. A new kind of array configuration is implemented in a $4\times 4$ PV array for the better shade dispersion. Further, a dynamic reconfiguration algorithm is employed to disperse the effect of partial shading. The combination of new array configuration and reconfiguration method is simulated in MATLAB/Simulink® and implemented in hardware. The outputs are measured under all possible shading patterns and validated with the outputs of convention methods for observing the enhanced energy conversion rate of the proposed system.


I. INTRODUCTION
Photovoltaic (PV) system accelerates its development in the global energy market in recent years because of its ecofriendly characteristics, reliability and renewability [1], [2]. Many countries prefer the solar PV plant for future energy demand. The structure of a PV cell is made with the bonding of n-type and p-type semiconductors with a PN-junction. The energy of photons in the sunlight breaks the bonding The associate editor coordinating the review of this manuscript and approving it for publication was Nagesh Prabhu . electrons in n-type and makes it flow to the load by through the p-type. The amount of free electrons liberated by the photons is the actual amount of current generated by the PV cell [3]. Some environmental factors like partial shading due to clouds, shadows of nearby objects, dust accumulation, dropping of birds, etc., will distract the rate of incident photons, which directly reduces current generation [4], [5]. The partial shading distributes non-uniform irradiation over the PV array which causes the mismatch losses. The power generation by the un-shaded PV cell will not be available at the load because of the shaded PV cells is the effect of VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ mismatch loss [6], [7]. The non-uniform distribution of the shading causes multiple peaks with multiple local maximum power points (LMPP) in the P-V and I-V characteristics of the PV array. Many approaches were proposed to obtain the maximum power from the partial shaded PV array. Bypass diode configuration is one of the earlier techniques to suppress the effect of partial shaded cell within it. At normal conditions, the internal resistance of the PV cell is lesser than the bypass diode. At partial shading conditions, the internal resistance of the PV cell is increased more than the bypass diode. So the current flows through the low resistance path of the diode. The bypass diodes will not allow the shaded cell to limit the current generation of the non-shaded PV cells and different approaches for using a bypass diode configuration is given in [8].
The global maximum power point (GMPP) is tracked and obtained from the various LMPP by incorporating the MPPT algorithm with the controller. The main concept of the MPPT algorithm is to maintain the resistance of source and load to be equal or approximately equal. The Perturb & Observe (P&O) algorithm [9], Incremental conductance (InC) algorithm [10] are the conventional MPPT algorithm used in the early days. In recent days, many types of MPPT algorithms are proposed in [11] by using the soft computing optimization techniques like artificial neural network (ANN), Particle swarm optimization (PSO), ant colony optimization (ACO) and, etc. for enhancing the accuracy of tracking GMPP. The fractional chaos based flower pollination algorithm is proposed in [12] to enhance the power generation of PV array under varying partial shaded conditions. The reduced PV current and PV voltage due to partial shading is compensated by using the converters. But this work requires more number of converters and sensor which increase the installation and maintenance cost of the PV system. The various array configurations such as Series-Parallel (SP), Bridge Link (BL), Total Cross Tied (TCT), Sudoku Pattern, Futoshiki Puzzle Pattern (FPP) are proposed in [13], [14]. The TCT, BL, HC, Sudoku, and FPP are dispersing the shading effect over the PV array to change the uneven current generating rows into even current generating row, which increases the power output. The level of partial shading is unpredictable and the effectiveness of array configuration is dumped by the complicated shading patterns.
Dynamic array reconfiguration techniques [15], [16] are changing the interconnection between the PV modules to equally disperse the effect of shading. In [17], authors proposed an innovative reconfiguration via multi objective grey wolf optimizer to mitigate the partial shading effect. Further, comprehensive study on different population based PV reconfiguration is introduced in [18] with an aim of row current minimization. In [19], current injection-based configuration method is been proposed for minimizing the mismatch losses in the PV system. A current source is connected in parallel with each row of the PV array, and it compensates the distorted current to the row. This method requires n number of converters and measuring units for compensating the current with the rows. A two-step reconfiguration method is been proposed in [20], at where the reconfiguration process is done in two steps. The PV array dimension is varied in each step. In step one the PV array operates in its original array size and in second step the PV system alters into the new dimension of rows with half of the size and columns with doubled size. Normal array configuration limits shade dispersing rate of this technique for some shading patterns, Where the proposed array configuration has high resistivity to the partial shading effect. The reconfiguration technique requires more number of sensors, where the reconfiguration method used in this work requires less number of sensors. In this work, L-shaped array configuration with dynamic reconfiguration method is proposed for uniformly dispersing all kind of shading patterns. The proposed array configuration can disperse the maximum amount of shading in the PV array. The remaining shading effect in the PV array can be completely or nearly nullified by the dynamic reconfiguration algorithm. This array reconfiguration algorithm does not require more number of data or sensor like the existing electrical array reconfiguration techniques. The current measurement is the only required data for measuring the shade dispersion rate and performing the reconfiguration algorithm. A switching circuit is incorporated with the PV array is executing the reconfiguration pattern which is generated by the algorithm. The work is simulated in MATLAB/Simulink and implemented in the hardware. The performance, shading dispersion rate, mismatch loss analysis and the percentage of error of the proposed work have been compared and analysed with the other configurations such as TCT, Sudoku, and FPP.
The rest of the paper is organized as follows. Section II presents the description of proposed array configuration and its structure. Section III presents the overview of the simulation, test models of the proposed configuration, the overall simulation flowchart and the results obtained from the simulation. Section IV summarizes and concludes the paper.

II. DESCRIPTION OF PROPOSED PV ARRAY CONFIGURATION A. PROPOSED ARRAY CONFIGURATION
The sudoku and futoshiki array configurations are applicable only for the square PV arrays and for the non-square PV arrays its logics were failed. The proposed array configuration is perfectly suitable for squared PV arrays, non-squared PV array with odd number of columns. For the non-squared PV array with even number of columns, the configuration may produce PV rows with repeated PV modules with the optimized location. The proposed PV array is generated by forming the rows with propagation of L from the starting node and it continues till reaching the final column or the previous to it. When it reaches the final or previous column of the PV array, the L propagation should end there and started again from the second column of the PV row and it continues to the end, which selects one panel from every PV row and column. This frames the PV rows with distinct PV panels from each row or the repeated PV panels with the optimized distance. Starting node and its corresponding column is the factors to consider in the propagation. This array configuration greatly reduces the mismatch losses in the PV system as compared to sudoku. The L-shape propagation of each rows for the 4 × 4 PV array is shown in Fig.2. For executing the reconfiguration algorithm, the PV panels are coupled as the individual units as flexible unit and static unit. For the n × m PV array, (2n) numbers of PV groups are formed and each PV group consists of (m/2) number PV modules. For the square PV arrays the PV row has been split into two equal parts with (m/2) PV panels for the fixed and adaptive parts. For the non-square PV arrays, each row has been splitter into ((m/2)+1) numbers of panels for the fixed part and ((m/2)-1) numbers of panels in the adaptive part. Two PV groups are connected in parallel to forms the m number of rows with n number of PV modules in each row. Further, these rows are connected in series to create an n × m proposed array configuration. For the 4 × 4 PV array, eight number of PV groups framed with the dimension of 2 × 1. Two PV groups which have no repeated PV modules in the same row or on its corresponding column have been connected in parallel to create a row 4×1 array size. The array formation is completed with connecting four number of 4 × 1 PV arrays in series. The fig.3.(d) shows the group formation diagram from TCT by the L-shape propagation with grouping and the fig.3.(e) shows the matrix configuration diagram of the proposed array configuration.

B. RECONFIGURATION ALGORITHM
The reconfiguration algorithm gives the flexibility to the PV array to change its interconnection for equally disbursing the partial shading over it. For executing the reconfiguration algorithm m × n PV array has been splitter into two units as static unit and flexible units with (m/2) × n each for PV array with even numbers of column or ((m/2)-1) × n and (m/2) × n for PV array with odd number of columns. Static and flexible units were connected through the switching circuits which is capable to connect any flexible unit with the static unit based on the current generation. So that, each PV row can generate even current that leads to the minimum mismatch losses between the PV rows. The functional block diagram and the functional circuit diagram of the proposed reconfiguration algorithm is shown in Various steps involved for executing the reconfiguration algorithm. The entire PV array is splitter into two units as static and flexible unit. A switching circuit is placed between these units for connecting them. Short circuit current measurement for each row of static part and flexible part is obtained. Based on the short circuit current, rows in flexible unit are connected with the rows of static unit through switching circuit. This switching operation completes the reconfiguration algorithm. After the switching PV array will be operated with the even current generating rows. This entirely reduces the mismatch losses from the PV system.
The short circuit current of each rows in static and flexible unit is obtained as the following expression (1) and (2) where, I SCSU Ri is the short circuit current of static unit rows and I SCFU Ri is the short circuit current of flexible unit rows.  The short circuit currents of static and flexible units is ranked as the following expression (3) and (4), Ri (3) Static unit's short circuit current is ranked as maximum to minimum, whereas flexible unit's short circuit current is ranked as minimum to maximum. For the reconfiguration, Static unit's row with rank 1 should be connected to flexible unit's row with rank 1, i.e., the maximum power generating row of the static unit is connected with the minimum current generating row of the flexible unit.
The output current will be obtained by using the following equation (6) The dynamic reconfiguration algorithm for m × n PV array is performed by the following steps, Step-1: Splits PV array into two units as static and flexible unit.
Step-2: Measures short circuit current of each rows static and flexible units Step-3: Rank static unit's short circuit current from maximum to minimum Step-4: Rank the flexible unit's short circuit current from minimum to maximum.
Step-5: Connect the flexible unit's minimum current generating row with the maximum current generating row of the static unit.
Step-6: Repeat the same with a regular time interval.

III. RESULTS AND DISCUSSION
The The percentage of error is also a factor calculated to measure the uniformity between the current generations of each row in the PV array. The difference between the maximum generating row and the minimum current generating row gives the percentage of error so that it can be said as healthy or faulty operating condition. (7) The percentage of error denotes the uniform dispersion of shading over the PV array. For the high percentage of error, the mismatch loss in the PV array is high and for the minimum percentage of error the mismatch loss will be low. The panel rating is given in Table.1

A. PERFORMANCE ANALYSIS UNDER RANDOM SHADING CONDITION
Let consider the random shading pattern for the first case of analysis. The shading is not unique over the PV array. The shading pattern will not follow any kind of pattern like other shading condition. This kind of shading may occur in a random condition during the quick changing environmental conditions or the minor fault in the PV modules. The shading dispersion diagram and the P-V, I-V characteristic curves for the TCT, Sudoku, FPP, proposed array configuration and proposed array configuration after the reconfiguration is shown in Fig.6.

1) ANALYSIS OF ROW CURRENT GENERATION
The array configuration is made up of TCT connection. The current generation of each row can be calculated For the TCT configuration, Current generation of each row can be VOLUME  The current generation of the proposed method after the reconfiguration is measured in two steps. The current generation of the fixed part rows and the adaptive part rows have been measured separately. Based on the reconfiguration algorithm, the fixed part row is connected with the adaptive part row. Then the current generation of the entire row is calculated. The current generation of the flexible unit rows are measured as, The reconfiguration algorithm connects the maximum power generating row of Flexible unit with the minimum power generation row of adaptive unit for executing the reconfiguration as shown in the Fig.9. The current generation of each row after the reconfiguration can be measured as, From equation (7), the percentage of error is calculated for analyzing the effectiveness of each configuration under the random shading condition. The purpose of the proposed array configuration is to uniformly disperse the shading effect to make each row with nearly even current generation. The percentage of error shows the uniformity of shade dispersion. The performance analysis is given in Table.2.
The TCT configuration has the error rate of 57.9% which has the rank of the third position. The percentage of error of the proposed configuration is 15.7% and after reconfiguration is 12% which lowers than all other configurations where the FPP configuration has the 44.3% of error rate which is higher in this random shading pattern. The random shading pattern may occur on any part of the PV array but the proposed method could distribute the effect of shading evenly in the PV array. The power output of the proposed configuration will be higher than other configuration because of the low percentage of error. The power generation and the shade dispersion matrix of the TCT, Sudoku, Futoshiki Configurations has shown in Fig.8. The High current generating row in the fixed part has been connected with the low current generating row of the adaptive part. The P-V and I-V characteristic curves of the reconfigured PV array has shown in Fig.8. The characteristic curve of all configurations has the multiple peaks i.e., many local maximum power points but the proposed configuration curve has nearly a smooth curve. It is also inferred that the proposed configuration has the global maximum power point as compared with other configurations.  The power loss analysis is carried out to find the amount of power enhanced during the shading pattern. The short circuit current, open-circuit voltage, and the maximum power for all configurations have been derived from the Simulink output. Table.2 shows the power output and the power loss for each array configuration. The power loss can be calculated by using the following equation (8),

B. PERFORMANCE ANALYSIS UNDER UNEVEN COLUMN SHADING CONDITION
The rows in the PV array are availed with irregular irradiation in the type of uneven column shading. The nearby objects are the main cautions for this kind of shading pattern. In this kind of shading pattern, TCT array configuration has very low power generation due to the shading in a single row. The shading pattern and the shade dispersion diagram of the all-array configuration under this shading pattern is shown in Fig.9. The first PV module in each row has affected by the shading that causes uneven shading pattern. The TCT is highly losing its performance in this shading whereas the other configurations disperse the shading evenly over the PV array that observed from the matrix dispersion diagram. The percentage of error is given in Table.2.

C. PERFORMANCE ANALYSIS UNDER UNEVEN ROW SHADING CONDITION
The UR shading occurs in the PV array that causes the uneven irradiance in each row of the PV array. This generally occurs due to the nearby objects or the environmental changes. The TCT configuration could withstand this kind of shading. The matrix dispersion diagram under UR shading pattern is shown in Fig.10. All configurations have an equal shade dispersion rate that also reflects in the percentage of error. Generally, this kind of shading does not cause more power loss in TCT but in Series parallel configuration this causes severe power loss. The percentage of error under UR shading is given in Table.2 All array configurations have an equal percentage of error that shows that all configurations had equally dispersed the shading over the PV array

D. PERFORMANCE ANALYSIS UNDER DIAGONAL SHADING CONDITION
In diagonal shading pattern, the PV modules in the diagonal position of the square or rectangular PV array has experiencing the shading due to the nearby taller narrow objects like towers, chimneys or by the clouds. The PV modules in the diagonal positions like P11, P22, P33, and P44 have received the irregular irradiation such as 800W/m2, 200W/m2, 400W/m2 and 800W/m2 whereas another PV module receives the irradiation as 950W/m2. The shading dispersion diagram of each array configuration is shown in Fig.11. The Sudoku configuration failed to disperse the shading evenly over the PV array. The shading is not completely dispersed in the Futoshiki and proposed array configuration which reflects the limitation of the static array configuration. This limitation of the static configuration has overcome by the proposed dynamic reconfiguration algorithm. The proposed configuration after reconfiguration shows the ability to overcome the limitation and disperse the shading as much as possible over the PV array.  The efficiency of the proposed array configuration is given in Table.2 with the percentage of error. The Futoshiki and Sudoku pattern has the highest percentage of error as compared to others. The proposed array configuration is also had a high percentage of error but this can be further reduced by the reconfiguration. The characteristic curve of all configurations under the diagonal shading is shown in Fig.12. Whereas the TCT and the configuration after the reconfiguration have a similar P-V and I-V curves. The Futoshiki and Sudoku patterns had the uneven shade dispersion over the PV array that reflects in the P-V curve as the multiple peaks. Whereas the proposed array configuration had less number of peaks that shows the power enhancement over the existing configurations.

E. PERFORMANCE ANALYSIS UNDER SHORT & NARROW SHADING CONDITION
The short and narrow shading may occur in the PV array due to the nearby objects that covers 25% of PV array size. The P11, P12, P13, and P22 have experienced the shading in S&N. Shading dispersion diagram and the shading pattern under the short and narrow is shown in Fig.13.  It is inferred that the shading has uniformly dispersed in the Futoshiki configuration. The power output by the Futoshiki configuration, proposed configuration and after reconfiguration is the same due to the third and fourth column has an equal irradiation level. The percentage of error under the short and narrow shading condition has given in Table.2.
The TCT and Sudoku pattern has a high-level percentage of error in this shading pattern. The P-V and I-V characteristics of all configurations under the short and narrow shading pattern are shown in Fig.14. The characteristic curve of TCT and Sudoku configurations has multiple peaks due to the uneven shade dispersion. The Futoshiki and the proposed configurations had the less no of peaks and also had the maximum power points as compared to the existing configurations.

F. PERFORMANCE ANALYSIS UNDER SHORT & WIDE SHADING CONDITION
The shading dispersion under the short and wide shading pattern is discussed in this section. This kind of shading affects 75% of the PV area. The shade dispersion is much required for this shading condition due to the high power loss. The shade dispersion can enhance more power in this kind of shading but it depends on the uniformity. The proposed reconfiguration method uniformly disperses the shading over the PV array. The matrix diagram of the shade dispersion is shown in Fig.15.  The percentage of error compared in Table.2. TCT configuration is not efficient in highly shaded PV array that also reflects in the percentage of error. The proposed reconfiguration allows the PV array to disperse the shading uniformly even under the high shading condition like short and wide. The Futoshiki and Sudoku configuration has a high percentage of error that was minimized in the proposed configuration.
The P-V and I-V characteristics of all configurations under the short and wide shading pattern are shown in Fig.16. The red colour curve shows the characteristics of the proposed reconfiguration method which has one small peak in the centre where the Futoshiki, Sudoku and the TCT pattern has multiple peaks in the P-V curve. It is inferred that the proposed reconfiguration method can produce the minimum number of peaks in the characteristic curve with maximum power generation.

G. PERFORMANCE ANALYSIS UNDER LONG AND NARROW SHADING CONDITION
The long and narrow shading affects the irradiance of PV array around 50% which reduced half of the power generation in TCT configuration. The proposed reconfiguration algorithm is more effective for this kind of shading pattern. At first, the proposed reconfiguration disperses the shading as much as possible later the reconfiguration algorithm disperse the effect of shading evenly over the PV array. The matrix dispersion diagram of shading is shown in Fig.17. The Futoshiki   and Sudoku configuration has a high percentage of error where the proposed configuration minimized the percentage of error more than half of the existing. It shows the ability of the proposed configuration to disperse the shading evenly in all rows.
The P-V and I-V characteristic curves under the L&N shading pattern have shown in Fig.18. The Sudoku, TCT, and Futoshiki configurations had the more no of peaks in the characteristic curves. The proposed configuration has the one up and down in the characteristic curve that closes to the smooth curve. The characteristic curves of the PV system before and after reconfiguration nearly close to each other.

H. PERFORMANCE ANALYSIS UNDER LONG AND WIDE SHADING CONDITION
The long and wide shading pattern affects around 75% to 80% of irradiation of the PV array. This kind of shading is  mostly possible by the clouds, by the unavoidable objects and by the temporary constructions. The PV array requires the uniform shade dispersion to minimize the mismatch losses. In this proposed method the PV can disperse the shading based on the power generation. It makes the even power generating row so that the maximum power can be extracted as much as possible. The matrix dispersion diagram of the array configurations under the L&W shading pattern is shown in Fig.18. The TCT, Sudoku and FPP configurations have a high percentage of error in the L&W shading pattern. That also reduces power output. The proposed configuration has less than 10% of error that allows the rows in PV array to generate nearly equal current with each other. The Power output the amount of power loss in each array configuration has given in Table.2.
The P-V and I-V characteristics of the PV array configurations in L&W shading pattern is shown in Fig.20. It is inferred that the proposed method after reconfiguration has a smooth P-V and I-V curve whereas all other configurations have the curve with multiple peaks. This difference shows the effectiveness of the proposed method for power enhancement under the various shading conditions.

I. OUTPUT ANALYSIS
The maximum current and the power output of the 4 × 4 PV array is measured by the Arduino controller, current sensor and the potential divider. Based on the measured values the P-V and I-V characteristic curves were plotted and the power output comparison were discussed in the result and discussion VOLUME 9, 2021 section. It is observed that the proposed configuration has the consi1stency of shade dispersion in all kind of shading pattern, whereas the other configuration is good in some specific shading pattern and failed to perform in others. The Futoshiki and the Sudoku configurations have the good power generation near to the proposed method in UCS, URS, SN, Diagonal shading patterns. But the proposed array configuration and reconfiguration algorithm has dispersed the maximum level of shading in all cases of shading pattern. The proposed method has the unique performance in all kind of shading patterns. The percentage of error and the power output shows the effectiveness of the proposed configuration over the other array configurations and it has plotted as the bar chart shown in Fig.21(a) and Fig.21. (b).

IV. CONCLUSION
The five types of array configurations including the proposed method have been analyzed with the eight kinds of possible shading patterns. The shading patterns like UR, UC, and Diagonal were considered as the minor shadings that do not highly affects the power output. In these shadings, the existing configurations such as TCT, Sudoku and the FPP could disperse the shading uniformly over the PV array whereas the proposed method disperses too. While considering the major shading patterns like random, S&N, S&W, L&N and L&W the existing array configurations failed to disperse the shading evenly. The percentage of error under the major shading patterns is more than 35% in the existing configurations where the proposed configuration had less than 20% for the all-kind shading patterns. It is inferred that the existing configurations are good in the minor shading patterns but failed to perform under the major shading patterns. The proposed L-shape array configuration performs better than the all-other array configurations. The performance of the L-shape configuration is further enhanced by the proposed reconfiguration scheme. Shading level and its pattern are not a constraint for the proposed method because it makes the even current generating rows by reconfigure the PV modules. The implementation of the proposed L-Shape propagated array configuration is very simple as like the existing array configurations and it can be implemented on any sized PV systems. This method will be commercial solution to the PV system for overcoming the mismatch losses. The initial cost is higher than the existing configurations (not much higher); however, the payback period is very low from the power generation of the PV array.  THANIKANTI SUDHAKAR BABU (Senior Member, IEEE) received the B.Tech. degree from Jawaharlal Nehru Technological University at Ananthapur, Ananthapur, India, in 2009, the M.Tech. degree in power electronics and industrial drives from Anna University, Chennai, India, in 2011, and the Ph.D. degree from VIT University, Vellore, India, in 2017.

ACO
From 2019 to 2020, he was associated with the Institute of Power Engineering, Universiti Tenaga Nasional (UNITEN), Malaysia, as a Postdoctoral Researcher. He is currently working as an Associate Professor with the Department of Electrical Engineering, Chaitanya Bharathi Institute of Technology, Hyderabad, India. He has published more than 60 research articles in various renowned international journals. His research interests include the design and implementation of solar PV systems, renewable energy resources, power management for hybrid energy systems, storage systems, fuel cell technologies, electric vehicles, and smart grids. He has been acting as an Editorial Board Member and a Reviewer of various reputed journals, such as the IEEE and IEEE ACCESS, IET, Elsevier, and Taylor and Francis.
HASSAN HAES ALHELOU (Senior Member, IEEE) is currently a Faculty Member with Tishreen University, Lattakia, Syria. He is also with University College Dublin, Ireland. He has published more than 130 research articles in the high-quality peer-reviewed journals and international conferences. He has participated in more than 15 industrial projects. His major research interests include power systems, power system dynamics, power system operation and control, dynamic state estimation, frequency control, smart grids, micro-grids, demand response, load shedding, and power system protection.