Optimal Su-Do-Ku based interconnection scheme for increased power output from PV array under partial shading conditions

Abstract

Partial shading is a common phenomenon in PV arrays. They drastically reduce the power output because of mismatch losses, which are reliant on the shape of the shade as well as the locations of shaded panels in the array. The power output can be improved by distributing the shade over various rows to maximize the current entering the node. A Su-Do-Ku configuration can be used to rearrange the physical locations of the PV modules in a total cross tied PV array with the electrical connections left unchanged. However, this arrangement increases the length of the wire required to interconnect the panels thus increasing the line losses. In this paper, an improved Su-Do-Ku arrangement that reduces the length of the wire required for the connection is proposed. The system is designed and simulated in a Matlab/Simulink environment for various shading patterns and the efficacies of various arrangements are compared. The results prove that the power output is higher in the proposed improved Su-Do-Ku reconfiguration technique compared to the earlier proposed Su-Do-Ku technique.

Graphical abstract

Keywords

array configuration / mismatch losses / partial shading / line losses / Su-Do-Ku arrangement

1 Introduction

The use of solar energy has grown significantly in the past decades [1]. This can be attributed to the increasing energy demand, environmental threats from the existing conventional sources and rapidly falling cost of photovoltaic cells over the past few decades [2,3]. Solar power generation also has several advantages; it is renewable, eco-friendly, has free fuel source, is maintenance free, etc [4,5].

Many panels are connected in series and parallel to form a PV array. Mismatch loss is the difference in maximum power output of the array and the sum of maximum power outputs of the constituent modules [6]. This phenomenon causes large power losses in PV arrays. Module parameter mismatch or partial shading may lead to mismatch losses [7]. Partial shading may result from shadows of various structures, passing clouds, trees, etc. [8]. Some common effects of this include development of multiple peaks in PV curves [9,10] which mislead some MPPT algorithms to track a local peak [11–13].

The array structure, pattern and irradiation level of the shade add to the mismatch losses. The array structure will determine the interconnection between rows and columns. Configurations such as series parallel, bridge linked and total cross tied (TCT) have been proposed and their performance has been studied [14,15]. Adding crossties between columns in a simple series parallel configuration leads to the development of TCT and BL structures. Crossties across each row of the junction results in a TCT connected array whereas a BL structure has half of such crossties. TCT configuration has improved power output with lesser mismatch losses compared to other configurations during partial shading [16].

Various papers [17–23] have dealt with the use of switching strategies to improve power output under partial shading. These reconfiguration strategies require switches and sensors to implement switching to minimize the losses. An optimal TCT interconnection scheme that was computed based on the available shading data was proposed [24]. A fixed (onetime) physical arrangement was proposed to enhance the power generation under partial shaded conditions [25]. The modules are physically rearranged based on the Su-Do-Ku puzzle pattern without altering their electrical connection. The shading effect is dispersed over the array due to the physical rearrangement thereby increasing the generated PV power. Nevertheless, these systems do not consider the line losses for evaluating the system. Further, both these techniques increase the length of the wire required to connect the modules, thereby causing increased line losses. In this paper, the line losses are included in the analysis, and subsequently an improved Su-Do-Ku configuration is proposed. The line losses depend on the length of the wire required for connection, and hence on the Su-Do-Ku puzzle pattern, which determines the interconnection scheme. The system is studied and its performance is simulated for different shading patterns. The obtained results affirm that the proposed Su-Do-Ku configured structure has reduced line losses and thus an improved power output as compared to that of any random Su-Do-Ku pattern without compromising the improvement in mismatch losses under partial shaded conditions.

2 System description

2.1 Model of a PV cell

A PV cell can be viewed as a current source with a diode in parallel and some shunt and series resistances (R_sh and R_s) as depicted in the equivalent circuit [26] in Fig. 1. The characteristics of the PV module can be obtained by connecting a number of PV cells in series. The relation between the output current and the voltage of a PV module is given by

(1)I_{\mathrm{m}}=I_{\mathrm{ph}}-I_{\mathrm{0}}\left[\exp \left({\displaystyle \frac{V_{\mathrm{pv}}+I_{\mathrm{m}}{R}_{\mathrm{s}}}{A}}\right)-\mathrm{1}\right]-\left[{\displaystyle \frac{V_{\mathrm{pv}}+I_{\mathrm{m}}{R}_{\mathrm{s}}}{R_{\mathrm{sh}}}}\right],

where I_m, V_pv, and T are the PV current, voltage and the temperature (in Kelvin) of the module. Constant A = nKT/q, where n is the number of series connected cells, K is the Boltzmann’s constant and q is the electric charge. The photoelectric current I_ph [26] is expressed as

(2)I_{\mathrm{ph}}=I_{\mathrm{sco}}\left({\displaystyle \frac{G}{G_{\mathrm{0}}}}\right)\left(\mathrm{1}+{\alpha }_{\mathrm{1}}\left(T-T_{\mathrm{0}}\right)\right)\left({\displaystyle \frac{R_{\mathrm{s}}+R_{\mathrm{sh}}}{R_{\mathrm{sh}}}}\right),

where I_sco is the short circuit current at a standard irradiation and temperature of G₀ (1000 W/m²) and T₀ (25°C) respectively. α₁ is the temperature coefficient for current of the module. The nonlinear output characteristic of the PV module results in a unique MPP on its power-voltage characteristics. Table 1 gives the specifications of the module used under standard test conditions.

2.2 PV array configured using TCT interconnection scheme

A TCT configured PV array with nine rows and nine columns totaling 81 modules is utilized for this analysis (Fig. 2). The modules are marked as “pq” where p and q denote the row and column in which the module is connected, respectively. R_pq denotes the resistance of the wire used for connection in the pth row and qth column. The impact of resistances of the crossties on the power loss is minimal because the crossties carry negligible current compared to the PV current and is also shorter in length, and hence is neglected. The voltage of the array can be written as

(3)V_{\mathrm{array}}={\displaystyle \sum _{p=\mathrm{1}}^{\mathrm{9}}{V}_{\mathrm{m}p}},

where V_mp is the voltage of the pth row which can be given by

(4)V_{\mathrm{m}p}=V_{pq}-I_{pq}{R}_{pq}q=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{...},\mathrm{9},

where V_pq, I_pq and R_pq are the voltage of the panel, the current and the resistance values respectively in the pth row and qth column. The total power loss is given by

(5){\displaystyle \sum _{p=\mathrm{1}}^{\mathrm{9}}{\displaystyle \sum _{q=\mathrm{1}}^{\mathrm{9}}\left(I_{pq}^{\mathrm{2}}\times R_{pq}\right)}}.

The value of R_pq depends on the length of the wire used for interconnecting the module to the previous module or the DC bus.

2.3 PV array configured using Su-Do-Ku arrangement

The mismatch loss caused by partial shading depends not just on the shading area but also on the position of the shaded modules with respect to other shaded modules in the array. The shade occurring over a module limits the current entering the node to which the module is connected. Consider the current and voltage at MPP at STC to I_m and V_m for each panel. A shade occurring over an entire row (9 panels per row in 9×9 array) would limit the current entering that node for all columns, and hence would drastically reduce the power output. Therefore, the array current can be approximately computed as

(6)I=\mathrm{9}x{I}_{\mathrm{m}},

where x = shade irradiation/1000.

A current by-pass of the entire row might occur in such a situation. If a shade occurs across an entire column (9 panels), the node current would be limited for only one panel per row and is approximately

(7)I=\mathrm{8}{I}_{\mathrm{m}}+x{I}_{\mathrm{m}}.

Consequently, the output power would be higher in the latter situation. Similarly, a shade occurring across a small portion of the array would cause lesser losses if it was split across various rows, rather than a single row. Hence, the objective of any reconfiguration scheme would be to relocate the shaded panels to various rows to distribute the effect of shading. The scheme proposed in Ref. [25] involves a fixed (one-time) rearrangement to reduce mismatch losses. The modules are physically rearranged without disturbing the electrical connection. Hence, a shade occurring physically across a row would be electrically dispersed across various rows. The technique used for determining this rearrangement pattern is determined using Su-Do-Ku puzzle.

Su-Do-Ku is a logic puzzle in which numbers are placed in a grid based on certain constraints [27]. The grid should be filled such that every row, column, and region contains only one occurrence of each number. Such a logic puzzle pattern inherently has the ability to avoid repetition in each row and each region. Hence, the row number of each panel in the array is replaced with the corresponding number from the puzzle pattern. This would ensure that a shade occurring over a group panel is physically distributed across various rows. The column number remains the same as in the TCT configuration. The electrical connections of the modules remain unaltered as in a normal TCT structure whereas the physical positions of the modules are alone altered.

A Su-Do-Ku arrangement used in Ref. [25] is shown in Fig. 3(a). For example, panel 93 (9th row, 3rd column) is physically moved to the 5th row. However, electrical connections remain the same, and hence the connection of this panel is undisturbed in the 9th row. Even though such an arrangement facilitates reduction of mismatch losses, the increase in the length of wire required for the interconnection of modules in each column causes additional line losses.

2.4 Selection of the Su-Do-Ku pattern

The length of wire required for interconnection of modules depends on the Su-Do-Ku pattern. Different patterns have different wire lengths depending on the dispersion of numbers in a column. A puzzle with more dispersed numbers in each column requires a longer length of the wire than a puzzle with no dispersion. Thus, a pattern where the numbers are lesser dispersed in each column needs to be formed. The numbers are lesser dispersed when the subsequent elements in the column are consecutively numbered. Hence, in each column the numbers are formed such that they are mostly consecutive. Another constraint involved is that, the puzzle must also be a Su-Do-Ku puzzle. If all columns contain numbers that are consecutive, it will lead to the formation of nine columns each numbered from ‘1’ to ‘9’ consecutively; hence, it is impossible to form a Su-Do-Ku pattern. Therefore, a quantum of shift is made in each column to ensure that the pattern remains a Su-Do-Ku pattern and the numbers are mostly consecutive. In each column, the numbers start with a shift compared to a fully consecutive column. The magnitude of shift is adjusted in every column to formulate a Su-Do-Ku puzzle pattern. The procedure for shift and the method of applying this technique to a PV array are explained as a flowchart in Fig. 4.

The pattern thereby obtained is depicted in Fig. 3(b). This pattern is still a Su-Do-Ku pattern and hence the distribution of shading effect is possible. After obtaining the puzzle pattern, the row numbers in the TCT connected PV array are replaced by the number from the Su-Do-Ku puzzle and physical rearrangement is done without altering it electrically as demonstrated in Fig. 3(c). The wiring diagram for implementing the Su-do-ku arrangement is illustrated in Fig. 5. It is observed that the panels are placed sequentially and the wiring length is much shorter. To shorten the wire length in the proposed configuration, the equivalent circuit diagram can be constructed for both patterns as displayed in Fig. 6. The resistance of the wire is considered to be ‘R’ per length of one panel. The difference in total resistance of the wiring between both configurations is computed as 72R and hence the reduction in line losses is transparent.

The reconfiguration techniques usually employed in large PV systems require a large number of sensors and switches and a complex control circuit to dynamically change the connection depending on the shading pattern. The proposed rearrangement technique as per the Su-Do-Ku puzzle pattern is a one-time fixed arrangement that can be employed to reduce the mismatch and wire losses and this arrangement is profitable for all shading patterns. The system is analyzed and studied for the shading conditions of short wide, short narrow, long wide and long narrow as defined in literature [28] (Fig. 7). The maximum power output is obtained for each shading condition, with and without line losses for the TCT, normal Su-Do-Ku and the improved Su-Do-Ku arrangements.

2.5 Wiring considerations

The wire used for interconnections can be designed based on the maximum current passing through the wire. The short circuit current of the module used amounts to 4.7 A. The National Electric code prescribes that the ampacity of the wire must be 1.56 times the maximum current passing through it [29], and hence suitable American wire gauge (AWG) rating of the wires are chosen [30]. The length of module can be obtained from the specifications, and thereby can be used to find the resistance of the wire per unit panel length (R). For the 20 AWG rating and a panel length of 1.21 m, the resistance is obtained as R = 0.039 Ω. This circuit is used for modeling the system as per the circuit in Fig. 6.

3 Results and discussion

The PV array is exposed to the following four shading patterns and the characteristics are obtained for the TCT, the normal Su-Do-Ku and the improved Su-Do-Ku arrangements and the results obtained are presented. The improvement in power output in the proposed pattern due to the power loss reduction is presented for each shading pattern.

3.1 Case 1: short wide

The PV array is divided into four different groups with each group receiving a different irradiation. The first group receives an irradiation of 900 W/m², while the second, third and fourth group receive irradiation of 600 W/m², 400 W/m² and 200 W/m ² respectively. The shading pattern is depicted in Fig. 8 (a). After physically positioning the panels in the Su-Do-Ku pattern earlier proposed, the shade on the array would be as depicted in Fig. 8 (b). The electrical connection shown in Fig. 8 (c) can be obtained by ordering the panels sequentially (as per the actual electrical wiring) with the same shade for each panel as in Fig. 8 (b). Thus, it can be seen that the shade is dispersed across various rows in the electrical connection. Figure 8 (d) and (e) demonstrates the physical positioning of panels and the electrical connections respectively, for the short wide shade. Figure 8 (f) shows the PV characteristics as obtained in each of the three configurations namely the TCT, the Su-Do-Ku arrangement, and the improved Su-Do-Ku arrangement. The position of the global peak is higher and shifted toward the right in the Su-Do-Ku pattern when compared to the TCT. However, the position of the peak remains nearly the same for both Su-Do-Ku configurations. The maximum power output of the simple TCT configured array is only 3520 W. The power output increases when the modules are connected as per Su-Do-Ku pattern due to distribution of the shading effect over the entire array.

The power output in both Su-Do-Ku and improved Su-Do-Ku arrangements remain the same if line losses are not considered. The reason for this is that both Su-Do-Ku patterns equally disperse the shading effect. However, when line losses are taken into consideration, the proposed pattern reduces the length of the wire required for interconnection, thus leading to an improved power output. The power output is higher in the proposed Su-Do-Ku arrangement (4419 W) as compared to the normal Su-Do-Ku arrangement (4407 W).

3.2 Case 2: long wide

A PV array with three groups receiving three different irradiations is considered. The first group receives an irradiation of 900 W/m², while the second and third groups receive an irradiation of 500 W/m² and 200 W/m² respectively.

The shading pattern is depicted in Fig. 9 (a). The shading pattern is applied to each of the three arrangements. The PV characteristics corresponding to these shading patterns are shown in Fig. 9 (e). The maximum power generated by the array is 3717 W in the TCT configuration. The rearrangement of modules in both Su-Do-Ku arrangements gives the same power output of 4623 W when line losses are neglected. However, the power output is 4507 W in the improved Su-Do-Ku arrangement compared to 4493 W in the normal Su-Do-Ku arrangement when line losses are considered. This is resulted from the reduction in line losses as per the proposed arrangement.

3.3 Case 3: short narrow

The PV array is divided into three different groups which receive irradiations of 900 W/m², 600 W/m², 400 W/m² respectively (Fig. 10(a)). It is observed that the TCT configured array provides a maximum power of 4789 W under this shading condition.

The improved Su-Do-Ku configuration produces a maximum power output of 5168 W whereas it is 5156 W in the normal Su-Do-Ku arrangement when line losses are neglected. This slight improvement in power is caused by the fact that the proposed pattern better disperses the shading effect compared to the normal Su-Do-Ku pattern. The maximum power generated is further increased in the improved Su-Do-Ku configuration with a value of 5044 W relative to 5003 W in the normal Su-Do-Ku configuration when line losses are also considered. This is caused by the improved dispersion of shaded modules as well as the reduction in line losses.

3.4 Case 4: long narrow

The PV array is subjected to different irradiations of 900 W/m², 700 W/m², 400 W/m² and 300 W/m² as shown in Fig. 11(a). The maximum power generated is 4713 W in the TCT configured array. When line losses are neglected, the maximum power generated is 4980 W in the Su-Do-Ku configured array compared to 4965 W in the improved Su-Do-Ku configured array.

This decrease in power resulted from the normal Su-Do-Ku configuration which better disperses the shading effect compared to the proposed improved Su-Do-Ku configuration. However when line losses are also accounted for, the proposed improved Su-Do-Ku configuration produces a maximum power output of 4850 W compared to 4833 W in normal Su- Do-Ku configuration. This reveals that the power output reduction caused by lesser dispersion is more than that compensated by the reduction in line losses by the improved pattern. Thus, the arrangement of PV modules according to the improved Su-Do-Ku puzzle pattern improves the power output under partially shaded conditions. It can be observed in Table 2 that the power generated is higher compared to both the normal Su-Do-Ku and the TCT configurations. This is caused by the dispersion of shaded modules and the reduction in line losses as per the new Su-Do-Ku configuration.

4 Conclusions

An improved Su-Do-Ku configuration for structuring the PV array to reduce mismatch losses due to partial shading and to reduce line losses is proposed in this paper. The physical positions of panels are fixed once according to the improved Su-Do-Ku pattern without altering the electrical arrangement. The Su-Do-Ku pattern disperses the shading effect over the entire array, thereby increasing the power output. Further, the proposed Su-Do-Ku arrangement reduces the length of the wire required for the interconnection of modules compared to any random Su-Do-Ku pattern, thereby reducing the line losses incurred. The efficacy of this system for different shading patterns is tested using simulations and it is observed that the proposed Su-Do-Ku arrangement has a better energy yield under partially shaded conditions compared to normal Su-Do-Ku arrangement or TCT arrangement. The Su-Do-Ku pattern can also be formulated and applied to other large sized PV arrays (i.e 12 × 12, 16 × 16, etc.) to reduce the mismatch and line losses. Further, for a very large array the array can be viewed as set of equally sized sub-arrays. The panels in each sub-array are arranged as per the improved Su-Do-Ku configuration and the array on the whole is arranged as per the improved Su-Do-Ku configuration. For example, a 54×54 array can be divided into 6×6 sub-arrays, where each sub-array is of the dimensions of 9×9. The panels in the 9×9 sub-array are arranged as per the improved Su-Do-Ku arrangement and the whole array can be viewed as a 6×6 array and can be arranged as per the improved Su-Do-Ku configuration. Such arrangement using sub-arrays can further reduce the wire length and the wiring complexity, which becomes a major issue otherwise.

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