Enhanced power generation of partial shaded photovoltaic fields by forecasting the interconnection of modules

Energy 95 (2016) 561e572

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Energy journal homepage: www.elsevier.com/locate/energy

Enhanced power generation of partial shaded photovoltaic fields by forecasting the interconnection of modules Smita Pareek a, *, Ratna Dahiya b a b

BK Birla Institute of Engineering and Technology, Pilani 333031, India National Institute of Technology, Kurukshetra 136119, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 May 2015 Received in revised form 17 October 2015 Accepted 11 December 2015 Available online xxx

SPV (solar photovoltaic) systems are often partially shadowed by passing cloud, neighboring building, chimney, tree, telephone pole etc. As a result, their produced power is lower than the expected value despite their size. This reduction in produced power is dependent on area of PVs under shade, shade scenario, module interconnection styles and also on the connection of shaded and non-shaded modules. This paper presents a novel method to forecast the interconnection of modules in a TCT (total-cross-tied) connected PV (photovoltaic) array. In this approach, the placement of shaded and non-shaded modules in array are done in such a way so as to distribute the shading effects evenly in each row thereby enhance the PV array power. The performance of this method is investigated for different shading patterns which are the approximations for the most common partial shading scenarios in PV fields and the results show that it can provide multiple solutions for reconfiguration of photovoltaic array to improve energy yield under partial shading conditions. In addition, the powerevoltage characteristic curve of these reconfigurable PV arrays are much smoother than that of TCT (total-cross-tied) configured PV arrays and thus ease the work of MPP (maximum power point) techniques. Also this method can easily be implemented for the design of large photovoltaic structures without tedious mathematical formulation. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Array Partial shading Photovoltaic Reconfiguration Series-parallel Total-cross-tied

1. Introduction SPV (solar photovoltaic) is steadily rising as a source of renewable energy. This is because of the depletion of fossil fuels, their negative effects on environment, noticeable decrease in the cost of solar panels and other associated advantages. However, according to the reports [1e3], there is a lack of confidence for this technology among users. The output power of SPV cells depends on insolation, temperature gradient, reflection, tilt, mismatch among modules, PS (partial shading) etc. [4e15]. Among the parameters listed above PS causes the major reduction in the output power. PS (partial shade) can be explained as when some modules in an array are receiving less insolation than others due to shading. It is a frequent phenomenon and ruins the energy yield of entire PV (photovoltaic) system. It is reported that shading causes a massive reduction in annual yields of large BIPV (building integrated PV) systems [16]. To

* Corresponding author. E-mail addresses: [email protected], (S. Pareek). http://dx.doi.org/10.1016/j.energy.2015.12.036 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

[email protected]

address this issue, this paper proposes a novel method to configure the modules in such a manner that can significantly reduce partial shading losses. The proposed method guarantee to provide a complete base for connection of shaded and non-shaded modules in case of large partially shaded photovoltaic fields for enhanced power generation and can also be used for fully reconfigurable and partial reconfigurable PV arrays. In addition, this method offers multiple reconfiguration possibilities in both HRPVA (half reconfigurable photovoltaic array) and FRPVA (full reconfigurable photovoltaic array) categories in comparison to the existing research [56], which provide only one solution in both the categories. This paper is organized as follows: Second 2 discusses the partial shading effects and hot spot phenomenon. Section 3 reviews the different techniques that are proposed to reduce the PS losses. Section 4 will be briefly discussing the different interconnections styles. In section 5, modeling of PV module and array is given. This section also deals with the investigation of small partially shaded TCT (total-cross-tied) configured PV fields (2*2 and 3*3) and based on the results, certain conclusions are drawn in terms of connection law and implementation of these results on large PV fields (4*4 and

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Nomenclature SPV PS PSC BIPV BL SP TCT IRA FRPVA HRPVA MPP MPPT G PA Pdc PR RPVA

solar photovoltaic partial shading partial shading conditions building integrated PV bridge-linked series-parallel total-cross-tied arrays' total irradiance level (W/m2) full reconfigurable photovoltaic array half reconfigurable photovoltaic array maximum power point maximum power point technique reference irradiance level (W/m2) array's output power (W) array's dc power rating (W) performance ratio reconfigurable photovoltaic array

above) shows that by connecting the shaded and unshaded modules according to the derived connection law can decrease PS losses and thus enhance power generation. However, the results of large PV fields (4*4 and above) are not shown due to limited space. Section 6 presents the application case studies of partially shaded PV fields for different shading patterns to verify the proposed connection law, followed by conclusion.

2. PS (partial shading) effects Generally SPV panels are connected in series and parallel to meet the load power requirement and thus, there is a chance that some of the panels are often partially or completely shadowed by nearby buildings, trees, chimneys, clouds, towers etc. [17,18]. Partial shading causes the reduction in the insolation received by cell under shade compared to other non-shaded cells. The short circuit current of solar cells depend on the insolation received and thus shaded cells have less current compared to non-shaded cells. Since in a series connected string, the string current must equally flow through cells, the result is that shaded cells operate in reverse bias region to conduct same current as that of non-shaded cells. The shaded cell will then consume power as it is operating in reverse bias region. This may lead to high bias voltage and breakdown of the shaded cell which in turn create hot-spot [14,19e21]. The effect of partial shading is such severe that it need not to fall on an entire panel to deteriorate its output. Rather it is something that if blocks or cast on even small portion of the panels in a string, the output of the entire string will be reduced to almost zero. However, if there is another string which is non-shaded, then this string will continue to produce power. It is reported that the losses

occur due to partial shading are not proportional to the of PV's area under shade but also depends on the shading pattern, array interconnection style like SP (series-parallel), TCT (total cross tied), BL (bridged linked)etc. and the location of shaded and non-shaded module within the array [22e24]. 3. PS loss reduction techniques PS losses can be reduced by the addition of bypass diodes. This is the conventional way to reduce the destructive effects of PS. Bypass diodes are connected in antiparallel to PV cells/modules [25e28]. However, the incorporation of bypass diodes increases the complexity of the PV characteristic curve with multiple peaks and thus mislead the conventional MPP (maximum power point) techniques [29,30]. In addition a) the PV cells with bypass diode do not produce any power under PSC (partial shading conditions) because of being bypassed; b) the production of SPVA (solar photovoltaic array) with bypass diodes is costly and c) not applicable for low voltage applications. Although several techniques has been reported to find global MPP out of all local MPPs but the operator may face a challenge when choosing the most suitable technique among them. All techniques differ in terms of accuracy, tracking speed, total cost, number and type of sensors required (complicated measuring system for the insolation, open circuit voltage, short circuit current etc.), complexity of the algorithm. Further some techniques works for a particular shading patterns and fails for other shading patterns [31,32]. Another technique to reduce PS losses is reported in Refs. [33e39] in which a separate dc/dc power convertor with MPP controller is combined to each PV module in order to extract maximum power from each module thus enable module level MPPT. AC modules [40e43] have also been used to reduce the PS losses by providing separate dc-to-ac conversion to each module and thus the shading of any module only affects its output power. In addition, there are also other advantages associated with this technique like a) the DC installation is replaced by an AC installation thus there is reduced danger of arcs, b) simple plug and play device because of standardized AC output (220 V), c) easily upgradeable etc. In other works, short strings operating separately [1], parallel connection of modules [44], multi-level converters [45e48], multiinput converter [49,50] are preferred to reduce the negative effects of PSC. The common drawback of all above techniques are high cost because of the requirements of separate components with each module. Also, some techniques works only for low power applications [1,44], some require that modules should be connected in parallel connection and are mostly used in portable applications [49,50], some require independent voltage control for each PV module and also has high power loss in switching [45e48]. Another method reported to overcome the negative effects of PS is reconfiguration of PV arrays [51e54], which is also being addressed in this work, with an intention to cover the limitations of the work done in this area. Although this technique could not

Fig. 1. Interconnection styles for a 6*4 PV field. (a) SP interconnection (b) TCT interconnection (c) BL interconnection [61].

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gather a significant reliability in past because of high cost and lack of suitable hardware for switches implementation but now-a-days with the advances in hardware and software, researchers and others have a renewed interest in reconfigurable solar arrays [55]. Also reconfigurable PV arrays avoids the use of complex MPPT algorithms and reduces the extra power consumption of the bypass diodes. To reduce the negative effect of PS, another method is to connect the modules in different style, which is being elaborated in the next section. 4. Interconnection schemes

Fig. 2. PV Array (31*3) arranged in three series assemblies, connected in parallel, each having thirty-one modules.

The interconnection schemes represents the method to connect PV modules to each other within the array. Many configurations are reported for the connection of PV modules within the array like SP (series-parallel), TCT (total-cross-tied) BL (bridged-link), etc. In a series-parallel connection, all modules are first connected in series to form string and then these series connection are connected in parallel fashions. In a TCT style, each module is in series and parallel to each other whereas in BL style, half of the interconnections of the TCT style are removed. Thus the negative effects of PS can be reduced by connecting the modules in TCT styles in place of SP and BL styles [57e60]. This is because TCT style has more number of parallel paths as compared to SP and BL style as shown in Fig. 1. Thus in the paper, TCT connected PV arrays are analyzed, which can alleviate the negative effects of PS. Although TCT is superior under PSC but it is not capable to produce maximum possible power under all PSC [61] and also this interconnection scheme is investigated only for small PS-PV (partially shaded photovoltaic fields) [62] and the generalized connection laws for large PS-PV fields are still need research. 5. System description This section describes the procedure for developing the proposed method for the connection of modules in a TCT- configured partially shaded PV array. All the simulation models are built in the MATLAB/SIMULINK environment and a bypass diode is connected across each PV module. 5.1. Model of a PV module In this work, singleediode PV model developed in Ref. [63] is used because of numerous associated advantage with this model. This model can take into consideration the effects of bypass diodes and the variation of the equivalent circuit parameters with respect to operating conditions [64] and thus the role of every module can be easily identified in power production and hence ease the study and effects of PS on large PV arrays. The PV module data is given in the Appendix I. 5.2. Model of a PV array

Fig. 3. Characteristics of PV array arranged in three series assemblies, connected in parallel, each having thirty-one modules.

a) shaded modules are in series

A PV array is formed by connecting modules in series and parallel to increase voltage and current capacity respectively. A large

b) shaded modules are diagonally opposite Fig. 4. Shade scenarios in 2*2 PV array.

c) shaded modules are parallel

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, a) shaded modules are in series

b) shaded modules are diagonally opposite

c) shaded modules are parallel

Fig. 5. Shade scenarios in 3*3 PV array.

31*3 PV array (arranged in three series assemblies, connected in parallel, each having thirty-one modules) is simulated by using above simulated module as shown in Fig. 2. The IeV and PeV characteristics of the array at STC (standard test conditions) is shown in Fig. 3. As expected, the maximum output power, open circuit voltage and short circuit current of this array at STC is 18826.92 W, 1000 V and 24.63 A respectively. The simulation of this large PV array, consisting of ninety-three module is given in this paper to ratify that PV array comprising of more number of modules can be simulated by using this simulated PV module.

5.3. TCT configured PV array To evaluate the performance of partially shaded PV arrays, a TCT configured photovoltaic array consisting of four modules those are arranged into two series assemblies, connected in parallel, each having two modules is simulated. It is assumed that a) the PV module that consists of several series connected solar cells is lumped together as a single solar cell for simplicity b) all modules used are considered to be identical. Further, this array is assumed to be under partial shade in which only two modules are shaded (shown grey and black) and rest two are non-shaded (shown white). The possible shading scenarios (with two modules shaded out of four modules) can be categorized in three parts: i) shaded modules are in series, ii) shaded modules are diagonally opposite and iii) shaded modules are parallel to each other as shown in Fig. 4(a), (b), and (c) respectively. The output power received in first two categories are same (486 W) and more compared to third category (320 W).

Fig. 6. Proposed connection laws.

1000 1000 1000 1000 1000 500

1000 1000 1000 1000 1000 500

1000 1000 1000 1000 1000 500

1000 1000 1000 1000 1000 500

Fig. 7. Application example 1: single-row shading.

Table 1 Possible solutions for HRPVA in single erow shading.

Half reconfigurable photovoltaic array (columns II and IV are reconfigurable) Reported solution Proposed solutions (n) (m) [56] 1000 1000 1000 1000 1000 500

1000 1000 1000 1000 500 1000

1000 1000 1000 1000 1000 500

500 1000 1000 1000 1000 1000

1000 1000 1000 1000 1000 500

1000 1000 1000 1000 500 1000

1000 1000 1000 1000 1000 500

1000

1000 1000

1000 1000 1000 1000 1000 500

1000 500 1000 1000 1000 1000

1000 1000 1000 1000 1000 500

500 1000 1000 1000 1000 1000

(a, b, c)

1000 1000 1000 1000 1000 500

1000 1000 1000 500 1000 1000

1000 1000 1000 1000 1000 500

1000 1000 500 1000 1000 1000

1000 1000 1000 1000 1000 500

1000 1000 1000 1000 1000 500

1000

20 (m=1;n=19)

1000

(l, m, n, o)

1000 1000

(d, e, f, g)

1000 1000 1000 1000 1000 500

Total solutions (m+n)

1000 1000 1000 1000 1000 500

1000

1000

(p, q, r, s)

1000

1000

(h, I, j, k)

possible location of shaded module depending on the location of shaded modules in I, II, III columns

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Table 2 Possible solutions for FRPVA in single erow shading.

Full reconfigurable photovoltaic array Reported solution [56] 1000 1000 1000 1000 1000 500

1000 1000 1000 1000 500 1000

1000 1000 1000 500 1000 1000

Some of the possible solutions

500 1000 1000 1000 1000 1000

1000 1000 1000 1000 1000 500

1000 1000 1000 1000 500 1000

1000 1000 500 1000 1000 1000

1000 1000 1000 1000 1000 500

1000 1000 1000 1000 500 1000

1000 1000 1000 500 1000 1000

1000 1000 1000 1000 500 1000

1000 1000 1000 500 1000 1000

1000 500 1000 1000 1000 1000

1000 1000 1000 1000 500 1000

1000 1000 1000 500 1000 1000

1000 1000 500 1000 1000 1000

1000 1000 1000 500 1000 1000

1000 1000 1000 1000 500 1000

1000 500 1000 1000 1000 1000

1000 1000 500 1000 1000 1000

1000 500 1000 1000 1000 1000

(a)

(c)

500 1000 1000 1000 1000 1000

(d)

( b)

1000 1000 500 1000 1000 1000

1000 1000 500 1000 1000 1000 1000 1000 1000 1000 1000 500

500 1000 1000 1000 1000 1000

(e)

500 1000 1000 1000 1000 1000

1000 1000 1000 1000 1000 500

(f)

................and many more

Another TCT configured photovoltaic array consisting of nine modules those are arranged into three series assemblies, connected in parallel, each having three modules is simulated. Further, this array is assumed to be under partial shade in which only two modules are shaded and all seven are non-shaded. The MPP power obtained in series and diagonally opposite connection of shaded modules [Fig. 5(a) & (b)] is same and equal to 1400 W and the MPP power obtained in parallel connected shaded modules is 1220 W [Fig. 5(c)]. Thus it can be concluded that series and diagonally opposite connected shaded modules yields more power as compared to parallel connected shaded modules. To further verify these laws, TCT configured PV arrays consisting of large number of Table 3 Application example 1: array and modules' MPP powers. Individual module's MPP (W)

TCT

201.97 201.97 201.97 201.97 201.97
3.3 HRPVA (for 175.46 solution a) 194.35 175.46 175.46 194.35 96.69 FRPVA (for 193.57 solution a) 201.03 201.03 193.57 201.03 98.65

201.97 201.97 201.97 201.97 201.97
3.3 175.46 194.35 175.46 175.46 90.95 195.88 193.57 201.03 201.03 193.57 98.65 201.03

201.97 201.97 201.97 201.97 201.97
3.3 175.46 194.35 175.46 175.46 194.35 96.69 193.57 201.03 98.65 193.57 201.03 201.03

PV modules (4*4 and above) are also simulated and investigated under PSCs and the inferences drawn large PV fields are in close agreement with the inferences obtained for small PV fields (not shown here to avoid complexity and due to limited space). The MPP power obtained for 4*4 TCT configured PV fields is 2840 W for series or diagonally connected shaded modules and 2540 W for parallel connected shaded modules. Thus, the following inferences can be drawn for connection of modules in TCT configured PV arrays, to reduce the negative effects of PSC conditions: ➢ In a string, the shaded modules should be connected in series to enhance produced power. ➢ In different strings, the shaded modules should be diagonally opposite to each other to enhance produced power.

Array's PR Power MPP (W) (app II) change w.r.t. TCT (%)

201.97 4013.4 201.97 201.97 201.97 201.97
3.3 175.46 4037.4 90.95 175.46 175.46 194.35 195.88 193.57 4354.3 98.65 201.03 193.57 201.03 201.03

0.9

e

0.906

þ0.598

0.977

þ8.49

Fig. 8. Application example 1: arrays' PeV characteristic curves.

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1000 1000 1000 1000 500 500

1000 1000 1000 1000 500 500

1000 1000 1000 1000 500 500

6. Application examples

1000 1000 1000 1000 500 500

It is a general practice in PV farms that shading analysis is performed in the planning stage, i.e., before the construction of the PV field. Based on this analysis, an optimum connection of modules is selected to reduce PS losses in accordance with the shade scenario and reconfiguration possibilities. In all the following applications, the four shading patterns which are the approximations for the most common partial shading scenarios in PV fields are considered [56]. These patterns are single-row, double-row shading, quarterarray shading and oblique shading. All the following application examples will be considering a 6*4 PV array in TCT interconnection, a HRPVA (half reconfigurable photovoltaic array) and a FRPVA (full reconfigurable photovoltaic array). In HRPVA, first and third columns are fixed and the second and fourth columns are reconfigurable to form a HRPVA (half reconfigurable photovoltaic array). It is assumed the irradiance of the shaded modules are 50% as that of the unshaded modules. Thus in the array, the MPP of the module receiving 1000-W/m2 and 500 W/m2 irradiance is 202.44 W and 99.468 W respectively and the 6*4 PV array's overall MPP power in TCT configuration is 4857.4 W, when all modules are receiving 1000-W/m2 irradiance. While designing the HRPVA and FRPVA, it should be taken into consideration that the shaded modules (if belong to different strings) must be diagonally opposite to each other and not parallel.

Fig. 9. Application example 2: double-row shading.

➢ The parallel connection of shaded module should be avoided in TCT configured PV arrays.

5.4. Proposed rules for TCT configured partially shaded PV arrays Based on the inferences obtained in previous section, the proposed rules for the connection of modules in TCT configured PV array are explained using a 4*4 TCT configured PV array (Fig. 6). Thus to achieve more power, if a shaded module is located at position (4*1), then, the preferred location of another shaded module in any other string should be diagonally opposite to this shaded module and these positions are given by (1*2), (2*2), (3*2) in string 2, (1*3), (2*3), (3*3) in string 3 and (1*4), (2*4), (3*4) in string 4 as shown by green dots (in the web version). These locations redistribute the effect of shading evenly. Further, the non-preferred location of another shaded module is in parallel to this shaded module and its position can be (4*2), (4*3) and (4*4) in string 2, string 3 and string 4 respectively as shown by blue dots. These locations are called as non-preferred locations because in these cases the received output power is less compared to preferred locations. These proposed rules (for the connection of modules) should be taken into account in designing the optimum connections for the following application case studies.

6.1. Application example 1: single-row shading The PS situation as shown in Fig. 7, known as single erow shading is considered, where numbers in boxes indicate modules' irradiance levels in W/m2. 6.1.1. Partial reconfigurable photovoltaic array The reported solution [56] is shown in Table 1 and Table 2 for HRPVA and FRPVA respectively. By applying the above proposed rules, the other configurations which are also possible and yields same MPP power in both the categories are also shown. Thus there are twenty possible solutions for HRPVA while many solutions can

Table 4 Possible solutions for HRPVA in double-row shading.

Half reconfigurable photovoltaic array Reported Proposed solutions (n) solution (m)[56] 1000 1000 1000 500 1000 500 1000 1000 500 1000 500 1000

1000 1000 1000 1000 500 500

500 1000 1000 500 1000 1000

1000 1000 1000 1000 500 500

500 500 1000 1000 1000 1000

1000 1000 1000 1000 500 500

500 1000 500 1000 1000 1000

1000 1000 1000 1000 500 500

500 1000 1000 500 1000 1000

1000 1000 1000 1000 500 500

1000 1000 500 500 1000 1000

1000 1000 1000 500 1000 500 1000 1000 500 1000 500 1000

1000 500 1000 500 1000 1000

1000 1000 1000 500 1000 1000 1000 500 500 1000 500 1000

1000 500 500 1000 1000 1000

1000 1000 1000 1000 1000 500 1000 500 500 1000 500 1000

(a)

1000 1000 1000 1000 500 500

(c)

1000 1000 1000 1000 500 500

500 1000 1000 500 1000 1000

(d)

(b)

1000 1000 1000 1000 500 500

Total solutions (m+n+o)

1000 1000 1000 1000 500 500

500 1000 500 1000 1000 1000

(e)

1000 1000 1000 1000 500 500 (f)

500 500 1000 1000 1000 1000

7 (m=1;n=6)

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Table 5 Possible solutions for FRPVA in double-row shading.

Full reconfigurable photovoltaic array Some of the possible solutions

Reported Solution[56] 1000 1000 500 1000 500 1000 1000 500 1000 500 1000 1000 500 1000 500 1000 500 1000

1000 1000 500 1000 1000 1000

1000 1000 500 500 1000 1000 500 500 1000 500 1000 1000 1000 500 1000 1000 500 1000 1000 1000 500 1000 1000 1000

1000 1000 1000 1000 500 500

1000 500 1000 500 1000 1000

1000 1000 1000 1000 500 500

500 1000 500 1000 1000 1000

1000 1000 1000 1000 500 500

500 500 1000 1000 1000 1000

1000 1000 1000 1000 500 500

1000 1000 500 500 1000 1000

1000 1000 1000 1000 500 500

500 1000 1000 500 1000 1000

1000 1000 500 1000 500 1000

1000 500 500 1000 1000 1000

1000 1000 1000 1000 500 500

500 1000 500 1000 1000 1000

1000 1000 1000 1000 500 500

1000 500 1000 500 1000 1000

1000 500 1000 1000 1000 500 1000 500 1000 1000 500 1000 1000 1000 500 500 500 1000 1000 1000 500 1000 1000 1000 ................and many more

be proposed for FRPVA for this shade scenario. These proposed solutions will be very useful for designers, researchers etc.

6.1.2. Full reconfigurable photovoltaic array By applying the above proposed rules, many other configurations are possible which yield same MPP power in FRPVA. Some of the possible fully reconfiguration possibilities are shown in Table 2 together with the reported solution. The array and modules' MPP powers are as shown in Table 3 together with the array's overall PR (performance ratio) [56].

Table 6 Application example 2: array and modules' MPP powers. Individual module's MPP (W)

TCT

199.72 199.72 199.72 199.72
3.3
3.3 HRPVA (for 195.7 solution a) 195.7 195.7 195.7 93.695 93.695 FRPVA (for 189.27 solution a) 189.27 195.7 195.7 92.05 92.05

199.72 199.72 199.72 199.72
3.3
3.3 92.05 92.05 195.7 195.7 189.27 189.27 189.27 189.27 92.05 92.05 195.7 195.7

199.72 199.72 199.72 199.72
3.3
3.3 195.7 195.7 195.7 195.7 93.695 93.695 93.7 93.7 195.7 195.7 195.7 195.7

The PR allows the comparison of partially shaded PV arrays of any size and under different irradiances. It can be seen that the HRPVA has increased the generated power by only 0.598% and FRPVA has increased the generated power by 8.49% when compared to TCT. Further, the performance ratio has also increased from 0.9 to 0.977 from TCT configuration to FRPVA configurations. These increments are because these configurations prevents bypass diodes from turning ON, which would short the 500-W/m2 modules. Also, the ON resistance of these diodes has a power loss of 3.3 W in TCT configuration but that's not the case with HRPVA and FRPVA. However, the powerevoltage characteristic curve is smoother than that of TCT, as shown in Fig. 8, which in turn reduce the probability of misleading the MPPT.

Array's PR Power MPP (W) (app II) change w.r.t. TCT (%)

199.72 3143.8 199.72 199.72 199.72
3.3
3.3 195.7 3847.3 195.7 92.05 92.05 189.27 189.27 93.7 3847.3 93.7 195.7 195.7 195.7 195.7

0.7765

e

0.9502

þ22.37

0.9502

þ22.37

Fig. 10. Application example 2: arrays' PeV characteristic curves.

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1000 1000 1000 500 500 500

1000 1000 1000 500 500 500

1000 1000 1000 1000 1000 1000

1000 1000 1000 1000 1000 1000

1000 500 1000 500 1000 500 500 1000 500 1000 500 1000

1000 1000 1000 1000 1000 1000

1000 1000 1000 1000 1000 1000

Fig. 11. a) Quarter-row shading irradiance levels b) Reported solution for HRPVA [56]. Table 7 Possible solutions for FRPVA in quarter-row shading.

Full reconfigurable photovoltaic array Reported Solution[56] 1000 1000 500 1000 1000 500 1000 1000 1000 1000 1000 500 500 1000 1000 1000 1000 1000 500 1000 1000 500 1000 1000

Some of the possible solutions 500 1000 1000 1000 1000 500 1000 1000 500 1000 1000 1000 1000 500 1000 1000 500 1000 1000 1000 1000 500 1000 1000 (a)

1000 500 1000 1000 500 1000 1000 1000 1000 500 1000 1000 500 1000 1000 1000 1000 500 1000 1000 500 1000 1000 1000 (b)

................and many more

6.2. Application example 2: double-row shading The PS situation together with the irradiance levels received by individual modules is as shown in Fig. 9, known as double erow shading is considered. Table 8 Application example 3: Array and modules' MPP powers. Individual module's MPP (W)

TCT

176.81 176.81 176.81 94.7 94.7 94.7 202.4 HRPVA 202.4 (for reported 202.4 solution [56]) 98.54 98.54 98.54 FRPVA 98.54 (for solution a) 202.44 98.54 202.44 98.54 202.44

176.81 176.81 176.81 94.7 94.7 94.7 98.54 98.54 98.54 202.4 202.4 202.4 98.54 98.54 202.44 98.54 202.44 98.54

176.81 176.81 176.81 191.43 191.43 191.43 202.4 202.4 202.4 202.4 202.4 202.4 202.44 202.44 202.44 202.44 202.44 202.44

6.2.1. Partial reconfigurable photovoltaic array The reported solution [56] is shown in Table 4 for HRPVA. By applying the above proposed connection laws, the other configurations are also possible in HRPVA, which yield same MPP power and are also shown. Thus there are thirteen possible solutions for HRPVA. In this PS situation, there are eight modules which are consecutively shaded, thus parallel connection of two pairs of shaded modules cannot be avoided.

Power Array's PR (app II) change MPP w.r.t. (W) TCT (%)

176.81 3837.3 0.9026 176.81 176.81 191.43 191.43 191.43 202.4 4234 0.9959 202.4 202.4 202.4 202.4 202.4 202.4 4234 0.9959 202.4 202.4 202.4 202.4 202.4

e

þ9.3

þ9.3

Fig. 12. Application example 3: arrays' PeV characteristic curves.

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1000 1000 1000 500 500 500

1000 1000 1000 1000 500 500

1000 1000 1000 1000 1000 500

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6.2.2. Full reconfigurable photovoltaic array The reported solution [56] is shown in Table 5 for FRPVA. By applying the above proposed rules, many other configurations are possible which yield same MPP power and some of them are shown due to limited space. The array and modules' MPP powers are as shown in Table 6. It can be seen that both HRPVA and FRPVA has increased the generated power by 22.37% when compared to TCT. The PR has also increased from 0.7765 to 0.9502. This increase comes from preventing bypass diodes from turning ON, which has a power loss of 3.3 W in TCT configuration and would short the 500 W/m2 modules. The powerevoltage characteristic curve is also smoother in both configurations as compared to TCT, as shown in Fig. 10, which reduces the probability of misleading the MPPT.

1000 1000 1000 1000 1000 1000

Fig. 13. Oblique shading irradiance levels.

Table 9 Possible solutions for HRPVA in oblique shading.

Half reconfigurable photovoltaic array Reported solution (m)[56] 1000 1000 1000 500 500 500

500 1000 500 1000 1000 1000

1000 1000 1000 1000 1000 500

1000 1000 1000 1000 1000 1000

Total solutions (m+n)

Proposed solutions (n) 1000 1000 1000 500 500 500

500 500 1000 1000 1000 1000

1000 1000 1000 1000 1000 500

1000 1000 1000 1000 1000 1000

3 (m=1;n=2)

(a)

1000 1000 1000 500 1000 500 500 1000 500 1000 500 1000

1000 1000 1000 1000 1000 500

1000 1000 1000 1000 1000 1000

(b)

Table 10 Possible solutions for FRPVA in oblique shading.

Full reconfigurable photovoltaic array Reported solution [56] 1000 1000 500 1000 500 1000 1000 1000 1000 500 1000 1000 1000 1000 500 1000 1000 500 1000 1000 1000 500 1000 1000

Some of the possible solutions 500 1000 1000 1000 1000 500 1000 1000 500 1000 1000 1000 500 1000 500 1000 1000 1000 1000 1000 1000 500 1000 1000 500 1000 1000 1000 1000 500 1000 1000 500 1000 1000 1000 1000 500 1000 1000 500 1000 1000 1000 1000 1000 500 1000 ................and many more

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Table 11 Application example 4: array and modules' MPP powers. Power Array's PR (app II) change MPP w.r.t. (W) TCT (%)

Individual module's MPP (W)

TCT

153.34 153.34 153.34 75.03 92.02 84.72 HRPVA (for 191.57 solution a) 191.57 172.1 88.71 88.71 98.699 FRPVA (for 98.539 solution a) 202.44 98.539 98.539 202.44 202.44

153.34 153.34 153.34 174.31 92.02 84.72 88.71 88.71 172.1 191.57 191.57 200.20 202.44 98.539 202.44 202.44 202.44 98.539

153.34 153.34 153.34 174.31 196.35 84.72 191.57 191.57 172.1 191.57 191.57 98.699 202.44 202.44 202.44 98.539 202.44 202.44

153.34 3434.1 153.34 153.34 174.31 196.35 170.61 191.57 3940.6 191.57 172.1 191.57 191.57 200.20 202.44 4234 202.44 202.44 202.44 202.44 202.44

0.8078

e

0.9269

þ14.75

0.9959

þ23.3

6.3. Application example 3: quarter-row shading The PS situation as shown in Fig. 11(a) is applied to TCT connected PV array, HRPVA and FRPVA. The reported solution [56] is shown in Fig. 11(b) for HRPVA. By applying the above proposed rules, the other HRPVA configurations are not possible and the reported solution [56] is the only solution for this shading scenario. This is because altering the location of modules will put two shaded modules in parallel and which should be avoided for enhance power generation. However some of the FRPVA configurations are shown in Table 7 together with the reported solution [56]. As shown in Table 8, the HRPVA and FRPVA both has increased the generated power from 3837.3 W to 4234 W and percentage increase in power is 9.3% when compared to TCT. The 1000 W/m2 module is now able to produce 202.4 W instead of 176.81 W and the 500-W/m module is able to produce 98.54 W instead of 94.7 W as compared to TCT configuration. This increase is because the configuration prevents bypass diodes from turning ON, which otherwise would short the 500 W/m2 modules. The reconfigurable PV arrays have approximately unity performance ratio and the PV characteristics of both reconfigurable arrays are smoother as compared to TCT configuration as shown in Fig. 12, thus simplifying the task of MPPT algorithm. 6.4. Application example 3: oblique shading The PS situation as shown in Fig. 13, known as oblique shading is imposed on the three arrays i.e. TCT configuration, HRPVA and FRPVA.

Fig. 14. Application example 4: arrays' PeV characteristic curves.

6.4.1. Partial reconfigurable photovoltaic array The reported solution [56] is shown in Table 9 for HRPVA. The above proposed rules yields other possible HRPVA configurations, which are also shown. Thus, there are three possible solutions for HRPVA. 6.4.2. Full reconfigurable photovoltaic array The reported solution [56] is shown in Table 10 for FRPVA. By applying the above proposed rules, some of the other possible configurations are also shown, which yield same MPP power. As shown in Table 11, the HRPVA and FRPVA has increased the coherence between the modules' MPPs and also the array's MPP. The generated power has also increased by 14.75% in HRPVA with 0.93 performance ratio and FRPVA has also increased the generated power by 23.3% and approximately unity PR. The 1000 W/m2 module is now able to produce 202.44 W in FRPVA instead of 196.35 W in TCT configuration. The powerevoltage characteristic curve of HRPVA and FRPVA is much smoother than that of TCT, as shown in Fig. 14, which reduces the probability of misleading the MPPT. Thus it can be seen that the proposed rules can result in multiple solutions (if it is possible to connect shaded modules diagonally instead of parallel connection) for each shading patterns in both the categories i.e. half reconfiguration and full reconfiguration in comparison to only one solution reported [56] for same shading scenarios. Thus the proposed rules is capable to provide a complete base for the connection of modules in large photovoltaic fields without any tedious mathematical formu lations. 7. Conclusion In this paper, certain rules for the connection of shaded and non-shaded modules is proposed for TCT (total-cross-tied) interconnected photovoltaic arrays. These rules can be used for a fully reconfigurable or a partially reconfigurable array. As confirmed by a number of application case studies a) by connecting the modules according to these rules can significantly reduce partial shading losses when compared to TCT interconnections; b) offers multiple solution to reconfigure PV arrays as compared to only one solution reported in literature; c) the powerevoltage characteristic curve is also much smoother than that of TCT and thus ease the work of MPP techniques; d) can easily be implemented for the design of large photovoltaic structures without tedious mathematical formulation. Appendix I. Parameters of the KC 200 GT 200 W PV module.

Parameters

Values

Ipv,n Voc,n MPP Power Gn Rp Rs Kv KI Ns a

8.21 A 32.9 V 200 W 1000 W/m2 415.405 Ohm 0.221 Ohm 0.1230 V/K 0.0032 A/K 54 1.3

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Appendix II. Performance ratio calculation [21]

[22] Application example

Calculation

1 1 1 2 2 2 3 3 3 4 4 4

(4013.4*1000)/(916.67*24*202.44) (4037.4*1000)/(916.67*24*202.44) (4354.3*1000)/(916.67*24*202.44) (3143.8*1000)/(833.33*24*202.44) (3847.3*1000)/(833.33*24*202.44) (3847.3*1000)/(833.33*24*202.44) (3837.3*1000)/(875*24*202.44) (4234*1000)/(875*24*202.44) (4234*1000)/(875*24*202.44) (3434.1*1000)/(875*24*202.44) (3940.6*1000)/(875*24*202.44) (4234*1000)/(875*24*202.44)

TCT HRPVA FRPVA TCT HRPVA FRPVA TCT HRPVA FRPVA TCT HRPVA FRPVA

[23]

[24]

[25] [26]

[27]

[28]

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