Mathematical Analysis of Solar Photovoltaic Array Configurations with Partial Shaded Modules

Mathematical Analysis of Solar Photovoltaic Array Configurations with Partial Shaded Modules

Abstract: Solar photovoltaic (SPV) cells generate electricity from sunlight by the photovoltaic effect. The output voltage of a single PV cell is small, to increase the voltage by connecting PV cells in series known as PV module or panel. Solar PV array consists of series and parallel connections of modules in the matrix form with several columns and rows. The different types of SPV array configurations or topologies are formed by changing the number of electrical connections between module to module in an array. This paper presents the mathematical analysis of 6×6 size conventional SPV array configurations such as Total-Cross-Tied, Parallel, Honey-Comb, Series-Parallel, Series, Bridge-Linked types under un-shading case and various proposed shading cases mainly Short narrow and wide, Long narrow and wide shadings. The electrical equivalent circuit of each SPV array configurations is analyzed by Kirchhoff’s laws at different nodes and loops in a solar PV array. These conventional 6×6 size solar PV array topologies are simulated in Matlab/Simulink software and identified the maximum global power (GMPP) at different shading conditions.

Keywords– Photovoltaic cell, module, and array, configurations or topologies, Shaded modules, row currents, PV array power.

1. INTRODUCTION

The increased electrical energy demand worldwide, environmental problem, and global warming effect due to fossil fuels have resulted in the growing adoption of renewable energy for power generation. Renewable energy is an alternative source of electrical energy for supplying the required energy demand. Among all Renewable energy sources, the Photovoltaic (PV) system has more advantage than other sources due to latest development in PV technology and price drop of PV modules or panels, rugged and simple in design requiring very little maintenance, subsidies provided by the government, no pollution, etc.,[1]. Solar PV power is obtained by the direct conversion method of sunlight into electricity. The performance of the SPV system depends on solar irradiance, shading effect, ageing effect, temperature, and degradation effects, etc., and the most affecting factors are temperature and solar irradiance [2-3]. The solar PV system has a unique maximum power point (MPP) under uniform irradiance case, and multiple peaks occur under non-uniform irradiance cases such as local peaks, global peaks; from this global peak is considered on the output P-V characteristics [4].

Solar PV cells convert directly from solar power to electrical power and possible to connect them through different interconnections to attain more power. The solar PV panel or module is formed by connecting PV cells are in series, and the PV array is formed by series and parallel connection of PV panels. The number of interconnections between module to module in an array are changed to make the different SPV array connection topologies such as Series, Bridge-Link, Parallel, Total-Cross-Tied, Series-Parallel and Honey Comb types [5]. Among all topologies, TCT has minimum mismatch or shading power losses and high generating output power [6]. Many researchers have presented a literature review on solar PV array configurations under partial shading conditions [7-10].

This paper presents mathematical analysis 6×6 SPV array configurations under four shading cases, mainly Short narrow (SN), Long wide (LW), short wide (SW), long narrow (LN) shadings, and one un-shading case(U). The mathematical analysis of 6×6 size conventional configurations is derived from Kirchhoff’s laws, i.e., Kirchhoff’s current law (KCL) applied at nodes, and Kirchhoff’s voltage law (KVL) applied at closed loops.

This paper first discusses the modeling of a single diode photovoltaic cell, module, and array in section-2. Different conventional configurations are presented in section-3. In section-4 and 5, the mathematical analysis of conventional type configurations under the non-shading case and four shading cases and also simulation results for 6×6 array configurations are presented. In section-6, conclusions are presented.

II: MODELING OF SOLAR PHOTOVOLTAIC SYSTEM

2.1. Modeling of Photovoltaic Cell, Module, and Array

Solar Photovoltaic cells are direct convert photon energy from solar irradiance into DC electricity by the photovoltaic effect. Each cell generates a small amount of current, and these cells are connected in series to form a single panel or module and produce higher currents. The combination of series and parallel connected SPV panels are formed to PV array.

Fig-1: Formation of Solar PV cell to an array

Figure-1 shows the formation of SPV array with several cells and modules. The simplified model of single diode PV cell and PV array, as shown in fig-2 and fig-3, respectively. The solar PV array is made by series-connected (N_S) and parallels connected (N_P) PV panels.

Fig-2: Simplified model of a single diode solar cell

The mathematical representation of the PV cell is given in equation-1[11].

Figure-3: Circuit of Solar Photovoltaic Array

The mathematical representation of the PV module given in Eq. (2),

Where I_L is module light generated current, represented as

Where K_isc: module short circuit co-efficient, I_LSTC: module light generated current at STC. G is the incident irradiance, and Go is standard irradiation.

The simplified mathematical equation of PV array [10-11] is given by

Where N_P and N_S are the total number of parallel and series connected panels in SPV array, R_SH and R_S are parallel and series resistances of the module, V_a and I_a are the voltage and current of the SPV array. I_Lcell denotes the photo-electric current, I_o: reverse saturation current, q: charge, a: diode ideality factor, k: Boltzmann constant and T is the temperature of the solar cell at STC.

The above set of equations is used to model the PV array to simulate I-V and P-V characteristics with the help of parameters in the datasheet of a solar PV cell.

III: SOLAR PV ARRAY CONFIGURATIONS

3.1. Conventional Solar PV Array Configuration:

There are six PV array configurations are available, known as a conventional type of configurations or topologies. From this conventional type, hybrid PV array topologies are developed by combining any two conventional type configurations. The main conventional configurations of PV array are [12],

1. Simple Series (SS) connection
2. Series-Parallel (S-P) connection
3. Bridge-Linked (B-L) connection
4. Simple Parallel (SP) connection
5. Total-Cross-Tied (T-C-T) connection
6. Honey-Comb (H-C) connection configuration.

Figure-4 shows the conventional array configurations of a 6×6 size solar PV array.

Simple-Series (SS): In this connection, one module connected to another module like a series connection, as shown in fig-4(a). In a series connection, the total voltage is the sum of each module voltages, so the output array voltage is high in SS topology.

Simple-Parallel (P): In this connection, all SPV modules are parallelly connected, as shown in fig-4(b). In a parallel connection, the total current is the sum of each module currents, so the output array current is high in Parallel topology.

Series-Parallel (SP): In this type, the number of series-connected modules called strings are connected to form series-parallel (SP) topology, as displayed in fig-4(c).

Bridge-Link (BL): This BL topology is adapted from a wheat-stone bridge, and this scheme is derived from the bridge rectifier connections, as shown in fig-4(e).

Honey-Comb (HC): In this connection, Solar PV panels are connected in hexagon shape by the honeycomb architecture, as shown in fig-4(f).                                                                   Total-Cross-Tied (TCT): This TCT connection is formed by establishing the electrical contacts or ties among the rows and columns of S-P connection topology, as shown in fig-4(d).

In this TCT connection, SPV modules are connected in matrix form. For example, in 6×6 connected SPV array 1^st row consists of PV modules labeling from 11 to 16, and the 1^st column consists of modules from 11 to 61, as shown in fig-4.

Figure-4: 6×6 Solar PV Array Conventional Configurations

1. MATHEMATICAL ANALYSIS OF SPV ARRAY CONFIGURATIONS

4.1 Generation of power across the solar PV array:

In this paper, mathematical analysis is performed for a 6×6 size PV array configuration, as shown in figures-5(a) to 5(f). In order to analyze the performance of 6×6 conventional SPV array topologies, different shading cases are considered [9-12]. The mathematical analysis of conventional topologies is performed with the help of Kirchhoff’s laws, i.e., Kirchhoff’s current law applied at nodes and Kirchhoff’s voltage law applied at closed loops.

The current I generated by a single solar module at any irradiance G is given as

Where G is irradiance at shading condition, and G₀ is the standard irradiance of 1000 W/m². If the solar module receives full irradiance, the output current of the module is more and vice-versa. The PV Array voltage V_PV is given as the summation of individual module voltages in the rows in an array, i.e.,

Where V_pq is the module voltage at q^th row. Total array voltage of 6×6 SPV array by neglecting the voltage drop across diodes is given as,

By applying the Kirchhoff’s current law, the current across each node is given by,

For 6×6 solar PV array configuration, array current is given as,

For the 6×6 Solar PV array under un-shaded conditions, the power output of the array is given as,

4.2: Different interconnection configurations:

(i). Simple Series Configuration

The simplest topology or configuration of the PV system is Simple Series connection type, as shown in figure-5(a). Where I_PV and V_PV are current and voltage of the PV array.

In a series connection, the same current flowing through the 36 modules in the array. Apply KVL for one closed loop in the Simple Series topology and the KVL equation is written as,

Where n is a number of modules in an array co figuration. It is noted that a 6×6 array of SS connection has 36 module voltages and the one array current.

i.e.,           

               Figure-5(a): 6×6 Simple Series Configuration  

(ii). Simple Parallel configuration

The simple parallel configuration, as shown in figure-5(b).

Figure-5(b): 6×6 Simple Parallel Configuration

Where, I_PV and V_PV are array current and voltage.

In a parallel configuration, all the modules have the same voltage (In any parallel circuit voltages are equal), i.e., V₁=V₂=………. = V₃₆ =V shown in figure-5(b) and different currents. Apply KCL at different nodes, then

Where n is a number of modules in an array configuration. It is noted that a 6×6 array of parallel connection has 36 module currents and the one array voltage.

i.e.,           

(iii). Series-Parallel configuration

The circuit of Series-Parallel (S-P) configuration of modules in an array, as shown in figure-5(c). This topology has four parallel strings, and each contains nine series-connected modules.

Figure-5(c): 6×6 Series-Parallel Configuration

The total array current I_PV is equal to the sum of the six-string currents.

i.e.,           

The six parallel string voltages are equal to the array voltage. Apply KVL at parallel strings, then the equations are given by,

In SP configuration has 36 module voltages and four-string currents. SP configuration voltages and currents in 1^st, 2^nd,3^rd, 4^th,5^th, 6^th columns are V₁ to V₆, V₇ to V₁₂, V₁₃ to V₁₈, V₁₉ to V₂₄, V₂₅ to V_30, V₃₁ to V₃₆ and I₁, I₂, I_3, I₄, I₅, I₆ respectively are shown in figure-5(c).

(iv). Total-Cross-Tied configuration

The solar PV array with TCT configuration, as shown in figure-5(d).

Figure-5(d): 6×6 Total-Cross-Tied Configuration

The voltage of 6 parallel modules at the m^th row is V_m. where,

The array voltage V_PV is equal to the sum of six rows of individual module voltages:

Apply KCL at nodes 1 to 5 as shown in figure-5(d).

The TCT topology has 36 module currents and 6 module voltages, as shown in figure-5(d). TCT configuration has currents in 1^st,2^nd,3^rd,4^th,5^th,6^th columns are I₁ to I₆, I₇ to I₁₂, I₁₃ to I₁₈, I₁₉ to I₂₄, I₂₅ to I_30, I₃₁ to I₃₆ and voltages in 1^st row to 6^th rows are V₁ to V₆.

(v). Bridge-linked connection configuration

Figure-5(e) shows the PV array with BL configuration. The module currents and voltages are I_m and V_p, respectively. The subscripts m, p is related to module number n.

Where,

;

In this BL type connection topology, 30 module currents and 32 voltages across modules. Figure-5(e) shows the 12 nodes in BL topology.

The node numbers 3 and 8 at the left column, apply the KCL at node points:

Where the subscript q is related to m by

Figure-5(e): 6×6 Bridge-Linked Configuration

Similarly, apply KCL for the nodes 1,6,11 between 2^nd & 3^rd column and nodes 4 & 9 between 3^rd & 4^th columns,

For the node numbers 5 and 10 between 5^th and 6^th columns, apply the KCL at node points:

in which the subscripts q and m relate to each other by

Figure-5(e) shows the loops and each loop containing four modules, apply KVL for the loops:

Finally, apply the KVL for six modules loop in the 1^st column is given by

The 6×6 BL configuration has 32 voltages, and 30 currents are shown in figure-5(e). BL configuration voltages and currents in 1^st, 2^nd,3^rd, 4^th, 5^th,6^th columns are V₁ to V₆, V₇ to V₁₂, V₁₃ to V₁₆, V₁₇ to V₂₂, V₂₃ to V₂₆, V₂₇ to V₃₂  and I₁ to I₃, I₄ to I₉, I₁₀ to I₁₅, I₁₆ to I₂₁, I₂₂ to I₂₇, I₂₈ to I₃₀  respectively.

(vi). Honeycomb connection configuration

The PV array with HC connection configuration, as shown in Figure-5(f). The module currents and voltages are I_m and V_p, respectively. The subscripts m, p is related to module number n.

Where,

In HC connection type topology, the total number of nodes is 13. Apply KCL for each node,

and the subscript q is related to m given by

Figure-5(f): 6×6 Honey-Comb Configuration

Then apply KVL for the six or four modules in a loop,

Finally, apply KVL for the six modules loop in the left column is given as,

In 6×6, HC configuration has 25 module voltages and 32 currents shown in figure-5(f). HC configuration has voltages and currents in 1^st, 2^nd, 3^rd, 4^th, 5^th, 6^th  columns are V₁ to V₆, V₇ to V₉, V₁₀ to V₁₄, V₁₅ to V₁₇, V₁₈ to V₂₂, V₂₃ to V₂₅ and I₁ to I₄, I₅ to I₁₀, I₁₁ to I₁₆, I₁₇ to I_22, I₂₃ to I_28, I₂₉ to I₃₂ respectively.

Mathematical analysis of 6×6 PV connection configurations is tabulated in Table-1. Where V, I, and P are the total voltage, current, and power of solar PV array, respectively.

Table-1: Parameters of 6×6 PV Array Topologies

V: MATHEMATICAL ANALYSIS OF PARTIAL SHADED PV ARRAY TCT CONFIGURATIONS

5.1: Row currents and output powers of the SPV array:

The figure-9 shows the partially shaded modules in the 6×6 PV array with TCT configurations [13-14]. For mathematical analysis of 6×6, TCT configuration calculates the currents in each row, array voltage, and array power [12]. The row currents are given as

Where

Where  is row number, G₀ is standard irradiance of 1000 W/m²,  is the 1^st-row 1^st column irradiance value in W/m²

The 1^st-row current is given as,

The 2^nd, 3^rd,4^th, 5^th, and 6^th-row currents are given as,

Since the currents are different in each row, so two or more peaks occur in output characteristics (P-V curves). In TCT

SPV array configuration, the global MPP, is the product of voltage and current of each row. The array current depends on the irradiance, and the array voltage is the same for all the rows by neglecting the voltage drop across the diodes. Solar PV array output voltage and power is given as,

The theoretical calculations of current, voltage, and power of TCT array topology are tabulated in Table-2.

5.2: Generation and location of Global MPP for TCT PV Array topology:

The output power of 6×6 TCT SPV array configuration under different shading cases are shown in figure-9 [13]. For mathematical analysis of partially shaded conventional TCT configuration [15], four partial shading patterns, as shown in fig-8, are considered. There are mainly,

(a) Short Narrow shading (SNS)

(b) Short Wide shading (SWS)

(c) Long Narrow shading (SNS)

(d) Long Wide shading (SNS)

(e) Un-shaded Case (U)

Figure-8. Types of shading cases

(a) Short Narrow shading (SNS)

The short narrow type of shading scenario is observed in figure-9(a). For formulating the location of Global Maximum Power Point (GMPP) in the output P-V characteristics theoretically, first calculate the currents in each row of the SPV array. From figure- 9(a), the 1^st-row current is expressed as from the equation-30,

Where,  irradiances at shading and G₀ is standard irradiance of 1000W/m².

From figure-9(a): In short Narrow shading, PV panels in 1^st, 2^nd and 3^rd rows are under full uniform irradiation level of 1000 W/m² while the remaining rows are under different irradiance of 500 W/m². The current generated by the 1^st, 2^nd, and 3^rd rows are calculated as follows:

Modules in row 4^th, 5^th and 6^th are shaded. Corresponding row currents are given by,

From Equations-i and ii, it is observed that the currents in different rows are changing from 4.5 I_m to 6 I_m. Due to these varying currents, multiple peaks are generated in the output characteristics.

The maximum generated power of SPV array configuration under uniform irradiance of 1000 W/m² is given as

Where V_m is the maximum voltage. In TCT topology, there are six series-connected modules, the voltage across the PV Array is 6V_m and the array current is 4.5I_m, due to the limitation of array current in series-connected modules in array topology. There is no module bypassed through the bypass diode, so the array voltage is 6V_m.

In TCT topology under short narrow shading case without bypassing the solar modules, the total array output power is given as

Figure-9: 6×6 Solar array with TCT configuration under partial shading conditions

(b) Short Wide shading (SWS)

The Short wide shading pattern can be observed in figure-9(c). In this shading case, PV modules in 1^st, 2^nd, 3^rd rows receive an irradiance of 1000 W/m² while the remaining modules in rows are under shaded with solar insolation of 500 W/m². The current generated by the 1^st, 2^nd, and 3^rd rows are calculated as follows:

Modules in row 4^th, 5^th and 6^th are shaded. Corresponding row currents are given by,

(c) Long Narrow shading (LNS)

The Long Narrow shading pattern can be observed in figure-9(c). In this shading case, PV modules in 1^st row receive irradiance of 1000 W/m² while the remaining modules in rows are shaded with an irradiance of 500 W/m². Then the current in 1^st row is calculated as follows:

PV Modules in 2^nd,3^rd,4^th,5^th and 6^th rows are under shading, corresponding row currents are given by,

(d) Long Wide shading (LWS)

The LWS shading case is observed in Figure-9(d). Assume shading modules have irradiance of 500 W/m². In this type of shading case, all rows are shaded. Row current is expressed as from equation-30,

From figure-9(d): In long wide shading, PV modules in all rows are under shaded with solar insolation of 500 W/m². The current generated by the 1^st, 2^nd, 3^rd, 4^th, 5^th, and 6^th rows are calculated as follows:

The PV Modules in 4, 5, 6^th rows are shaded, corresponding row currents are given by,

The currents generated in six rows in an array configuration are different due to non-uniform irradiance falling on the modules in an array configuration, it results in the multiple peaks occur on the output P–V characteristics. The location of global MPP in output PV characteristics of conventional array topologies under different shading cases are tabulated in Table-2 and 3, and the module currents in each row are based on the order in which modules were bypassed. By neglecting the voltage drops across the diodes and voltage variations across individual rows, then the voltage of PV array is given as V_PV=6 V_m. Total Array power is given as P_PV =V_PV. I_PV. In Table-2, the array current I_PV^* denotes the minimum of six-row currents due to series connection of six modules the current is limited to minimum row current; only that minimum current will flow through the array configurations.

(e) Un-Shaded Case-U:

In the un-shade case, 36 PV modules in 6×6 array configurations receive uniform irradiance of 1000 W/m². From equation-8, array current, array voltage, and array power are 6 I_m, 6 V_m, and 36 V_mI_m.

5.3: Theoretical calculations and Discussions

In this paper, a mathematical analysis of 6×6 size, solar PV array configuration is performed under four shading cases such as short narrow, short wide, long narrow, and long wide types of partial shadings, as shown in figures-9(a) to 9(b). Table-3 shows the theoretical calculation to determine the maximum global power for Total-Cross-Tied PV array configuration. Under uniform irradiance means the non-shading case, the TCT configuration has maximum array power 36 V_mI_m, and in shading cases, the currents in each row are different due to change in irradiance on the PV modules in an array and corresponding power also changed. In the case of short narrow shading (SNS), the minimum current is 4.5 I_m from the rows 4^th, 5^th, 6^th, and remaining row currents are equal to 6 I_m. Modules are connected in series due to this; the current is limited to the minimum current of rows, so the array current is 4.5 I_m, and array voltage is 6 Vm. The resultant array power is 27 V_mI_m. Remaining three shading cases output power of PV array TCT configuration is less than the short narrow shading case. The theoretical results are tabulated in Table-3 for the TCT 6×6 PV array configuration. In a series connection, high voltages, and in parallel connection, high currents are generated by the PV modules. In S-P and TCT connection, under the short narrow case, the output power of array is more compared to other shading cases.

From the mathematical analysis of 6×6 size solar PV array configurations, it can be concluded that:

* In simple series connection type of configuration, under uniform irradiance case maximum current (I_m) is generated in each row of the array and under shading cases, limitation due to a minimum current of 0.5I_m with an irradiance of 500W/m² is calculated from equation-(30), and array voltage is V_m, neglect voltage drops across diodes. The resultant array power is only 18 V_mI_m, whereas in uniform case 36 V_m.I_m.

* In simple Parallel connection type of configuration, under uniform irradiance case maximum current (I_m) is generated in each parallel connection in the PV array, and under shading cases, different currents are generated calculated from equation-(30). In short narrow case, the array current is 31.5I_m, and array voltage is V_m, neglect voltage drops across diodes. The resultant array power is only 31.5 V_mI_m, whereas in uniform case 36 V_mI_m.

* In Series-Parallel connection type of configuration, under uniform irradiance case array current is the sum of six-string currents (series connection of modules), i.e., 6 I_m, array voltage is 6 V_m and the resultant array power is 36 V_mI_m. Under the short narrow case, due to shading irradiance of 500 W/m², the array current is 4.5 I_m, and array voltage across 6 PV modules is 6 V_m then the resulting power is 27 V_mI_m.

* In TCT connection type of configuration, under uniform irradiance case array current, voltage and power are 6 I_m,6 V_m, and 36 V_mI_m, respectively. In short narrow shading case row 4, 5, 6 has a minimum current of 4.5 I_m, and voltage is 6 V_m (neglecting voltage drop across the diodes). Due to the limitation of minimum current in the array, the resultant power is 27 V_mI_m.

* In B-L connection type of configuration, under uniform irradiance case maximum current of the array in parallel strings is 6 I_m, voltage is 6 V_m and array power is 36 V_mI_m. Under shading cases, the output power of the array is changed.

* In H-C connection type of configuration, under uniform irradiance case array configuration current of 6 I_m, voltage 6 Vm and power is 36 V_mI_m. The output power of an array configuration is changed, and it depends on the shading pattern.

Theoretical calculations of different solar PV array configurations are presented in Table-2 and 3.

Table-2: Theoretical calculations of Location / Position of GMPP in PV Array S, P, S-P configurations:

Table-3: Theoretical calculations of Location of GMPP in SPV Array TCT configuration:

5.4: Simulation Results:

The 6×6 solar PV array conventional topologies mainly S-P, TCT, BL, HC type of models are developed and simulated in Matlab/Simulink software. The simulation results are tabulated in Table-4, and the maximum PV array powers are 7714W, 5478W, 6865W, and 5284W are observed in TCT topology compared to other topologies under proposed four shading cases. The output characteristics (P-V) of array configurations are shown in figures 10 to 13.

Table-4: Simulation results of 6×6 solar PV array configurations under different shading cases

1. S-P Configuration P-V Characteristics

Figure-10: PV Curves for S-P type connection

1. TCT Configuration P-V Characteristics

Figure-11: PV Curves for TCT type connection

iii.  B-L Configuration P-V Characteristics

Figure-12: PV Curves for B-L type connection

1. H-C Configuration P-V Characteristics

Figure-13: PV Curves for HC type connection

1. CONCLUSIONS

In this paper, mathematical analysis of conventional solar PV array configurations namely SS, P, SP, TCT, BL and HC types under uniform irradiance case, i.e., non-shading case and proposed partial shading cases such as short narrow, short wide, long narrow and long wide shading cases are presented. The 6×6 size solar PV array configurations are considered for analyzing the non-shading cases and different partial shading cases. Under different shading cases, each row currents are calculated based on the order of row currents in which the modules are bypassed for the identification of a global peak power position in the output characteristics of different PV array configurations. The mathematical analysis is based on the KVL and KCL equations of module connections in a PV array. From the theoretical calculations and simulation analysis, the array output power is more in TCT configurations under short narrow shading conditions, and it depends on the shading pattern in the PV array configurations.

VII. REFERENCES

[1] Alan L. Fahrenbruch, Richard H. Bube, “Fundamentals of Solar Cells: Photovoltaic Solar Energy Conversion,” Academic Press, 1983.

[2] Dir k Assmann, Ulrich Laumanns, Dieter U, “Renewable Energy: A Global Review of Technologies, Policies, and Markets,” 1844072614, 9781844072613 Earthscan Publications Ltd. 2016.

[3] Kumar, A., Pachauri, R.K., Chauhan, Y.K., 2016. “Experimental analysis of SP/TCT PV array configurations under partial shading conditions”. In: IEEE Conference on Power Electronics, Intelligent Control and Energy Systems, pp. 1648–1653.

[4] Bingol Okan, Ozkaya Burçin. “Analysis and comparison of different pv array configurations under partial shading conditions”. Sol Energy 2018; 160: 336-43.

[5] Pendem Suneel Raju, Suresh Mikkili. “Modelling and performance assessment of pv array topologies under partial shading conditions to mitigate the mismatching power losses”. Sol Energy 2018; 160:303-21.

[6] Nguyen Dzung, Lehman Brad “A reconfigurable solar photovoltaic array under shadow conditions. 2008. p. 980-6.

[7] S¸  Parlak Koray. “PV array reconfiguration method under partial shading Conditions”. Int J Electr Power Energy Syst 2014; 63:713-21.

[8] Rani B Indu, Saravana Ilango G, Nagamani Chilakapati “Enhanced power generation from pv array under partial shading conditions by shade dispersion using su do ku configuration”, IEEE Trans Sustain Energy 2013;4(3): 594-601.

[9] Yaw-Juen Wang, Po-Chun Hsu “An investigation on partial shading of PV modules with different connection configurations of PV cells”, Energy 36 (2011) 3069-78.

[10] Venkata Madhava Ram Tatabhatla, Anshul Agarwal, Tirupathiraju Kanumuri “Improved power generation by dispersing the uniform and non-uniform partial shades in a solar photovoltaic array”, Energy Conversion and Management 197 (2019) 111825.

[11] G.Sai Krishna, Tukaram Moger “Enhancement of maximum power output through reconfiguration techniques under non-uniform irradiance conditions”, Energy 187 (2019) 11591.

[12] V. Bala Raju, Ch. Chengaiah, “Performance Analysis of Conventional, Hybrid and Optimal PV Array Configurations of Partially Shaded Modules”, International Journal of Engineering and Advanced Technology (IJEAT) ISSN: 2249 – 8958, Volume-9 Issue-1, October 2019.

[13] Kuei-Hsiang Chao, Pei-Lun Lai, Bo-Jyun Liao “The optimal configuration of photovoltaic module arrays based on adaptive switching controls”, Energy Conversion and Management 100 (2015) 157–167.

[14] Zhu L, Li Q, Chen M, Cao K, Sun Y. “A simplified mathematical model for power output predicting of Building Integrated Photovoltaic under partial shading conditions”, Energy Convers Manage 2019;180:831–43.

[15] Belhachat F, Larbes C. “Modeling, analysis and comparison of solar photovoltaic array configurations under partial shading conditions. Sol Energy”, 2015; 120:399–418.

Authors’ Profiles

Mr V.Balaraju received a B.Tech degree in 2010 from SV University, Tirupati, and M.Tech degree in 2013 from JNTU Anantapur. Currently pursuing a PhD in the Department of Electrical and Electronics Engineering, SV University, Tirupati. His research interests include Reconfigurations of Solar PV arrays, Power quality, and grid integration of renewable energy systems.

Dr Ch. Chengaiah is a Professor of the Department of Electrical and Electronics Engineering at SV University College of Engineering, Tirupati. He completed his PhD in power system operation and control from SV University, Tirupati, in 2013. He obtained his ME in power systems from NIT Trichy in 2000 and B.Tech in Electrical and Electronic Engineering from SV University in 1999. His research interests include Renewable energy systems, power system operation, and control.

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