Performance enhancement of partially shaded solar PV array using novel shade dispersion technique

Abstract

Solar photo voltaic array (SPVA) generates a smaller amount of power than the standard rating of the panel due to the partial shading effect. Since the modules of the arrays receive different solar irradiations, the P-V characteristics of photovoltaic (PV) arrays contain multiple peaks or local peaks. This paper presents an innovative method (magic square) in order to increase the generated power by configuring the modules of a shaded photovoltaic array. In this approach, the physical location of the modules in the total cross tied (TCT) connected in the solar PV array is rearranged based on the magic square arrangement pattern. This connection is done without altering any electrical configurations of the modules in the PV array. This method can distribute the shading effect over the entire PV array, without concentrating on any row of modules and can achieve global peaks. For different types of shading patterns, the output power of the solar PV array with the proposed magic square configuration is compared with the traditional configurations and the performance is calculated. This paper presents a new reconfiguration technique for solar PV arrays, which increases the PV power under different shading conditions. The proposed technique facilitates the distribution of the effect of shading over the entire array, thereby, reducing the mismatch losses caused by partial shading. The theoretical calculations are tested through simulations in Matlab/Simulink to validate the results. A comparison of power loss for different types of topologies under different types of shading patterns for a 4 × 4 array is also explained.

Keywords

photovoltaic cells / mismatch loss / shading patterns / partial shading / magic square / power enhancement / global peaks and total cross tied (TCT)

Introduction

Currently, the use of renewable energy sources has become more significant against the increasing energy need and the environmental effects of fossil fuels. Among all the renewable energy sources, solar energy is trustworthy, clean, eco-friendly, never-ending, easy to test, and faster to implement. Many countries such as, India, China, Britain, Italy, and USA are attaching more importance to install solar power to fulfil their energy requirement. The disadvantages of solar power are high installation expenditure, low energy conversion efficiency, and variation in the amount of power generation due to the change in weather conditions. In order to gain a higher power from PV systems, the PV arrays are formed by connecting the PV modules in series and parallel. The power generation of the PV array decreases under shading condition. The shades of objects such as clouds, birds, buildings, poles and trees are the main reason for partial shading. Because of this partial shading, there is a reduction in the output power yield [ 1] which significantly affects the efficiency of the system [ 2].

The power loss caused by partial shading depends upon the shading pattern and location of shaded modules [ 3]. So, in this proposed arrangement, the physical location of the modules is altered while the electrical connection remains unchanged. The modules of the PV panel receive different irradiation strengths under partial shading condition, which may give multiple local maxima in power-voltage characteristics. The multiple peaks in the solar PV characteristics arise and the global peak (GP) is settled at the local peak (LP) [ 4– 7].

There are three different types of configuration of the PV modules such as series-parallel (SP), bridge link (BL), and total cross tied (TCT). The power generated in TCT configuration of the PV array is higher than the other three configurations [ 8]. Villa et al. uses a technique to configure the physical location of modules in a TCT, connected solar PV array to boost up the output power under shaded conditions [ 9]. When the physical locations are changed from TCT to the Sudoku pattern, the power is increased by 6% [ 10]. However, the main drawback of Sudoku is that it can be performed only on a 9 × 9 array. The difference between actual powers and the obtained power (i.e., PV mismatch) for three different configurations such as SP, BL and TCT are presented [ 11]. In this proposed system, in order to overcome the disadvantage of Sudoku, the physical location of the TCT configured modules are changed by using a new technique called magic square.

The physical locations of the modules of the solar PV array are altered and the electrical connections are unchanged. This arrangement distributes the shading effect over the entire array and, hence, it reduces the affect of shaded modules in the row [ 12, 13]. In this paper, a comparison is made between the output powers of TCT and the magic square arrangement. The approach presented in this paper will help the PV plant (solar farms) to extract more power during partial shading of a PV array.

For different types of shading patterns, the performance is studied. The results exhibit that the magic square arrangement yields better results when it is compared with TCT in both theoretical values and simulation results.

The power electronics equalizer is used to eliminate the multiple maximum power points of the PV array under partial shading condition and, hence, increase the power generation of the PV array [ 14– 16]. But for a large PV plant, the application of the power electronics equalizer requires a large number of switches and a complex control algorithm. The output power of the PV array can be increased by using an electrical array reconfiguration strategy under partial shading condition [ 11, 17]. In the electrical reconfiguration strategy, the electrical connection of the PV modules is changed dynamically according to the shading condition. So, during practical implementation of the large PV system, a large number of sensors and switches are required to change the electrical connection of the PV array [ 17].

The paper first discusses the system configuration, different types of topologies of the solar PV arrays and different types of shading patterns. It, then, presents the experimental results. After that, it gives a comparison of power mismatch losses for different traditional configurations and the proposed configuration.

System configuration

Photovoltaic model

An easy method to collect solar energy is photovoltaic conversion. This consists of the transformation of solar energy to electric energy using solar cells. Solar cells are manufactured from pure silicon with some impurities of other chemical elements, using solar radiation as the source. They capture both direct and diffuse radiation. This means that energy can be generated even on cloudy days. The cells are mounted in series to form PV modules in order to reach a suitable voltage for electrical applications. The PV modules collect the solar energy and transform it directly into electric energy as direct current. It is necessary to store the electric energy in batteries in order that it may be used at the time when there is no sunlight [ 18].

The solar cell can be seen as a current generator which generates the current I_m. The current in the diode I_D flows in the opposite direction and is caused by a potential between the+ and ‒ terminals. In addition, two resistances, one in series (R_s) and the other in parallel (R_sh), represented in the equivalent circuit diagram, are shown in Fig. 1. The series resistance is caused by the fact that a solar cell is not a perfect conductor. The parallel resistance is caused by the leakage of current from one terminal to the other due to poor insulation. For an ideal solar cell, R_s= 0 and R_sh= ∞.

The equation describes the model, where the output current and the voltage of a PV module at an irradiance ‘G’ can be given as

(1) {{\displaystyle I}}_{\mathrm{m}}={{\displaystyle I}}_{\mathrm{p}\mathrm{h}}-{{\displaystyle I}}_{\mathrm{0}}\left[\exp \left({\displaystyle \frac{{{\displaystyle V}}_{\mathrm{p}}+{{\displaystyle R}}_{\mathrm{s}}{{\displaystyle I}}_{\mathrm{m}}}{A}}\right)-1\right]-\frac{V_{\mathrm{p}}+{{\displaystyle R}}_{\mathrm{s}}{I}_{\mathrm{m}}}{{{\displaystyle R}}_{\mathrm{s}\mathrm{h}}},

(2) A={\displaystyle \frac{nkT}{q}}.

The photovoltaic current is obtained as

(3) {{\displaystyle I}}_{\mathrm{p}\mathrm{h}}={{\displaystyle I}}_{\mathrm{s}\mathrm{c}\mathrm{o}}\left({\displaystyle \frac{G}{{{\displaystyle G}}_{\mathrm{0}}}}\right)(\mathrm{1}+{\mathrm{\alpha }}_{\mathrm{1}}(T-{{\displaystyle T}}_{\mathrm{0}})){\displaystyle \frac{{{\displaystyle R}}_{\mathrm{s}}+{{\displaystyle R}}_{\mathrm{s}\mathrm{h}}}{{{\displaystyle R}}_{\mathrm{s}\mathrm{h}}}}.

The specifications of the module at standard test conditions are given in Table 1.

The simulation of the solar PV module [ 19– 20]] is done for irradiations of 1000 W/m², 600 W/m², 400 W/m² and 200 W/m² [ 21– 25]. The current vs. voltage and power vs. voltage characteristics for different irradiations at a constant temperature of 25 °C are illustrated in Fig. 2 and the current vs. voltage and power vs. voltage characteristics for different temperatures at a constant irradiation of 1000 W/m² are demonstrated in Fig. 3.

Different types of topologies

This paper explains three basic topologies, series-parallel (SP), bridge-link (BL), and total cross tied connection (TCT), as depicted in Fig. 4 [ 26– 28].

Series-parallel (SP): In this arrangement, the panels are connected in series with one another while the series connected panels are connected in parallel to obtain the series-parallel configuration.

Bridge-link (BL): This connection is inspired by the wheat-stone bridge connection. The BL interconnection scheme is derived from the connections in a bridge rectifier.

TCT: A TCT configuration is obtained by connecting ‘n × n’ branches, in series and parallel with one another. Now cross ties are connected across the branches after each row of panels. All the panels in a column are connected in series and each panel in a row is connected in parallel. The bypass diodes are also connected across each solar panel to allow the current to be bypassed, when the solar panel is shaded. This solar PV array consists of n rows and n columns totally of n² modules in an ascending order of numbers in column wise.

For example, when 4 × 4 connected panel is considered, column 1 consists of modules labelling from 01 to 04, and column 3 consists of modules from 09 to 12, as displayed in Fig. 5 [ 29].

Different types of shading patterns

Based on the number of shaded columns (width (wide or narrow)) and shaded modules per column (length (short or long)), to verify the proposed technique, four different shading conditions for solar PV arrays [ 30]] which are short wide (SW), long wide (LW), short narrow (SN) and long narrow (LN), are employed, as exhibited in Fig. 6.

For each shading condition, the PV characteristics are obtained for both TCT and magic square. The results are presented in Section 3.

Magic square configured structure of a solar PV array

A magic square is an arrangement of the numbers from 1 to n² in an ‘n × n’ matrix, with each number occurring exactly once, such that the sum of the entries of any row, any column, or any main diagonal is the same.

This technique is applied for the 4 × 4 square matrix. Consider a square matrix as shown in Fig. 5. All the elements in the diagonal elements of TCT configuration is filled up first, leaving all the remaining elements (Fig. 7(a)). As this paper proposes a 4 × 4 configuration, there exist 16 elements. Starting from the last, i.e., 16th element, in a descending order, all the unused numbers are arranged column-wise to fill all the remaining ones left out (Fig. 7(b)).

In this arrangement, the physical locations of modules are changed, without affecting the electrical connections. As the electrical connections are unaltered, the current and voltage equations also remain the same as in the TCT connection. The panels in the row in the TCT configuration are now in different rows in the magic square technique. The bypass diodes are also connected across each solar panel in the magic square technique. When the solar panel is shaded, these diodes allow the current to be bypassed through them. This proposed magic square technique for this paper is shown in Fig. 8 (a) and its arrangement is represented in Fig. 8 (b). This makes it possible to reduce the shading effect on a single row by distributing the shade over the entire array. Thus, using this technique in the partial shaded conditions, the incoming current at a particular node is increased and reduces the bypassing of panels. Therefore, the generated power is increased for the identical shading pattern.

Simulations and results

In order to evaluate the performance of the proposed system, a 4 × 4 solar PV array, as shown in Fig. 8, is subjected to four types of different shading patterns.

Case 1 Short wide

In this case, four different irradiations are considered to calculate the performance of the system. Group one receives an irradiation of 900 W/m², group two receives an irradiation of 600 W/m². and group three and four receives an irradiation of 400 W/m² and 200 W/m², respectively.

The shading pattern can be observed in Fig. 9. So to calculate the location of global peak (GP), first the current which is generated in each row of the array should be calculated.

In the traditional system, all the panels in row 1 and row 2 receive an irradiation of 900 W/m².

The current equation for row 1 is expressed as

(4) {{\displaystyle I}}_{\mathrm{R}\mathrm{I}}={{\displaystyle k}}_{\mathrm{1}}{{\displaystyle I}}_{\mathrm{1}}+{{\displaystyle k}}_{\mathrm{2}}{{\displaystyle I}}_{\mathrm{2}}+{{\displaystyle k}}_{\mathrm{3}}{{\displaystyle I}}_{\mathrm{3}}+{{\displaystyle k}}_{\mathrm{4}}{{\displaystyle I}}_{\mathrm{4}}

where k₁ = G₁/G_o = 0.9 in which G₁ is the solar irradiance of panel 1 and I₁ is the current generated by panel 1.

Assuming the current generated by all panels as I_m

(5) {{\displaystyle I}}_{R\mathrm{1}}={{\displaystyle I}}_{R\mathrm{2}}=\mathrm{4}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{3.6}{{\displaystyle I}}_{\mathrm{m}}

In row 3, two panels receive an irradiation of 900 W/m² and the remaining two receives 600 W/m². The current generated in the other rows is given as

(6) {{\displaystyle I}}_{\mathrm{R}\mathrm{3}}=\mathrm{2}\times \mathrm{0.6}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{2}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{3.0}{{\displaystyle I}}_{\mathrm{m}}

(7) {{\displaystyle I}}_{\mathrm{R}\mathrm{4}}=\mathrm{2}\times \mathrm{0.4}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{2}\times \mathrm{0.2}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{1.2}{{\displaystyle I}}_{\mathrm{m}}

As the currents in the 4 rows are different from each other, there will be multiple peaks in PV characteristics. They are tabulated in Table 2. The power produced by the array is given by

{{\displaystyle P}}_{\mathrm{a}}=\mathrm{4}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}{{\displaystyle V}}_{\mathrm{a}}=\mathrm{4}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}(\mathrm{4}{{\displaystyle V}}_{\mathrm{m}});

(8)

{{\displaystyle P}}_{\mathrm{a}}=\mathrm{14.4}{{\displaystyle V}}_{\mathrm{m}}{{\displaystyle I}}_{\mathrm{m}}; if no panel is bypassed [ 31].

For the magic square arrangement, the panels are rearranged for shade dispersion, and the current in each row is calculated as

(9) \begin{array}{l}{{\displaystyle I}}_{\mathrm{R}\mathrm{1}}={{\displaystyle I}}_{\mathrm{R}\mathrm{4}}=\mathrm{2}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.4}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.2}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{2.4}{{\displaystyle I}}_{\mathrm{m}},\\ {{\displaystyle I}}_{\mathrm{R}\mathrm{2}}={{\displaystyle I}}_{\mathrm{R}\mathrm{3}}=\mathrm{3}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.6}{{\displaystyle I}}_{\mathrm{m}}=3.3{{\displaystyle I}}_{\mathrm{m}}.\end{array}

The calculated voltage and power are noted down in Table 2. The results are verified with the simulations in Matlab/Simulink and are compared with theoretical results. The comparison clearly indicates that the maximum power generated is 643 W for TCT and that of magic square is 898 W, with an increase of 28.4%. This increase in power results from the changing of the physical locations of the array which distributes the shading effect from a row to the entire array.

Case 2 Long wide

A solar PV array with five distinct groups is taken in this case of shading pattern, as shown in Fig. 10. Group one receives an irradiation of 900 W/m² and the remaining groups receive an irradiation of 600 W/m², 500 W/m², 400 W/m² and 200 W/m².

The current in each row is calculated as

(10) \begin{array}{l}{{\displaystyle I}}_{\mathrm{R}\mathrm{1}}={{\displaystyle I}}_{\mathrm{R}\mathrm{2}}=\mathrm{3}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{1}\times \mathrm{0.5}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{3.2}{{\displaystyle I}}_{\mathrm{m}},\\ {{\displaystyle I}}_{\mathrm{R}\mathrm{3}}=\mathrm{3}\times \mathrm{0.6}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{1}\times \mathrm{0.4}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{2.2}{{\displaystyle I}}_{\mathrm{m}},\\ {{\displaystyle I}}_{\mathrm{R}\mathrm{4}}=\mathrm{2}\times \mathrm{0.4}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{2}\times \mathrm{0.2}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{1.2}{{\displaystyle I}}_{\mathrm{m}}.\end{array}

The shade dispersion is done by using the magic square method and the current in each row is determined by

(11) \begin{array}{l}{{\displaystyle I}}_{\mathrm{R}\mathrm{1}}=\mathrm{1}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.5}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.4}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.2}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{2}{{\displaystyle I}}_{\mathrm{m}},\\ {{\displaystyle I}}_{\mathrm{R}\mathrm{2}}=\mathrm{2}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.4}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.6}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{2.8}{{\displaystyle I}}_{\mathrm{m}},\\ {{\displaystyle I}}_{\mathrm{R}\mathrm{3}}=\mathrm{1}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{2}\times \mathrm{0.6}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.4}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{2.6}{{\displaystyle I}}_{\mathrm{m}},\\ {{\displaystyle I}}_{\mathrm{R}\mathrm{4}}=\mathrm{2}\times \mathrm{0.9}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.4}{{\displaystyle I}}_{\mathrm{m}}+\mathrm{0.2}{{\displaystyle I}}_{\mathrm{m}}=\mathrm{2.4}{{\displaystyle I}}_{\mathrm{m}}.\end{array}

The maximum power obtained from TCT is 501 W and that from magic square is 791 W. There is a hike of 36.7% due to the dispersion of shaded modules. The location of GP in both TCT and magic square is tabulated in Table 3.

Case 3 Short narrow

In this case, the array is subjected to three different irradiations, viz. 900 W/m², 600 W/m², and 200 W/m², as shown in Fig. 11. The location of GP in both TCT and magic square is tabulated in Table 4.

The maximum power obtained form TCT is 878 W and that from magic square is 960 W. After the physical locations of the modules are changed, the power generated in the array is increased by 8.54% from magic square than that generated from TCT.

Case 4 Long narrow

In this case, the partial shading array is subjected to three different irradiations, viz. 900 W/m², 600 W/m², 400 W/m², and 200 W/m², as shown in Fig. 12, and the location of GP in TCT and magic square is tabulated in Table 5.

The simulation shows that the power generated by the TCT method is 760 W while that generated by magic square is 920 W which is 17.40% greater than that of TCT. Hence, by changing the configuration of the solar PV array from TCT to the magic square pattern, the output power of the array is enhanced.

As seen from Tables 6 and 7, in all the four cases, the power generated by the magic square configuration is higher than that generated by the TCT arrangement.

Power losses of different configurations

The simulations are conducted by using Matlab/Simulink. The specifications of the module under standard test conditions are given in Table 1. Under partial shading conditions, the power mismatches of the above mentioned topologies, i.e., SP, BL, TCT, and the proposed magic square technique are compared.

1) Short wide shading conditions. Figure 13 (a) shows the simulation results between the power loss and the shading level of short wide shading condition. In order to simulate different configurations, two different irradiations are needed, viz., shaded modules and unshaded modules. The unshaded module is fixed up at 1000 W/m² while the shaded module is altered from 200 W/m² to 1000 W/m². The power loss in each case is observed and plotted.

It is observed that the SP configuration shows a maximum power loss of 983 W at 200 W/m² and the performance of TCT is found to be better than that of SP and BL. TCT has a power loss of 966 W at 200 W/m². The proposed configuration (magic square) yields a very minimum power loss of 473 W at 200 W/m².

2) Long wide shading conditions. In this case, 1, 2, 5, 6, 9, 10 are the panels that remain unshaded. At 400 W/m², SP has a power loss of 744W while BL and TCT have a power loss of 725 W and 726 W, respectively. The proposed magic square technique has the minimum power loss of 548 W, because the shaded modules are dispersed over the entire array by changing the physical locations of the modules without altering the electrical connections, as shown in Fig. 13(b).

3) Short narrow shading conditions. Only 11, 12, 15 and 16 are the panels that are shaded in this case. The power loss of this case is shown in Fig. 13(c). It is clearly observed that in SP, BL and TCT configurations, there is a significant increase in the losses with increase in shading level and the maximum power loss of the SP configuration at 600 W/m² is 224 W. However, the minimum power loss of 132 W is obtained by the proposed new magic square technique.

4) Long narrow shading conditions. Figure 13(d) shows the simulation results of a long and narrow shading condition. The power loss is observed at an irradiation of 800 W/m² for different types of topologies. The SP configuration has the highest power loss of 108 W, while the BL scheme has a power mismatch of 103 W, TCT is found to have a power loss of only 93 W, and the proposed magic square technique has a power loss of only 63 W which is the least of all the configurations.

From above mentioned cases, it is clearly observed that the performance of SP experiences a maximum power loss at different irradiations for various partial shading conditions, followed by BL and TCT. The proposed magic square technique is found to be the best method of all the different configurations which are discussed earlier. This magic square technique has the minimum power loss under various partial shading conditions at any irradiations.

Conclusions

This paper proposed a novel approach to distribute the shadows over the entire PV array to enhance the power generation under partial shading condition. In this approach, only the physical location of PV modules is changed, but the electrical connection of panels remains the same. The location of global peaks in TCT and the magic square configuration of a PV array are calculated theoretically. The power-voltage characteristics of a 4 × 4 PV array are obtained by using Matlab/Simulink and are presented for four different shading conditions in TCT and the proposed magic square configuration. The power-voltage characteristics of the proposed configuration is smoother and contains less number of local maxima, hence the accurate tracking of global maximum is simpler. It is verified that, for a PV array, there is a significant power enhancement in the proposed magic square configuration with respect to the TCT configuration. The validation of the simulation and theoretical results also guarantees the successful working of this technique in hardware implementation.

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