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Influence of local shunting on the electrical performance in industrial Silicon solar cells
Solar Energy 139 (2016) 581–590
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Influence of local shunting on the electrical performance in industrial Silicon solar cells P. Somasundaran ⇑, R. Gupta Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
a r t i c l e
i n f o
Article history: Received 11 June 2016 Received in revised form 16 September 2016 Accepted 14 October 2016
Keywords: Shunts Spatial location Distributed diode model Performance degradation
a b s t r a c t The paper presents the results of investigation on the influence of an ohmic shunt located at various spatial positions on the solar cell performance by distributed diode model based simulations. By systematically varying the parameters such as shunt resistance, proximity to metallization, shunt area, and irradiance a deep insight about the shunt impact on the solar cell performance have been obtained. Further, effect of spatial positioning of shunts has been investigated by considering shunted region of same area and severity at various locations of the solar cell, via the simulation approach. The presented simulation approach has been experimentally validated. The influence of shunt on the relative power and relative open circuit voltage has been studied considering different irradiance levels. The study revealed new insights about significance of spatial positions of the shunts and the proximity of finger and busbar metallization. A dramatic improvement in the solar cell’s electrical performance can be gained by either preventing the occurrence of shunts at the identified critical locations or isolating them by laser or chemical technique or removing them. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Shunts present in various locations of the solar cell can be detrimental to its performance (Barbato et al., 2014; Botchak Mouafi et al., 2016; Chithambaranadhan et al., 2015; Compagnin et al., 2013; Dongaonkar et al., 2013; Fortes et al., 2014; Giaffreda et al., 2014; Guthrey et al., 2016; Phillips et al., 2015). It would be interesting to understand the possible improvement in the solar cell performance, with either removal of shunts (Hovestad et al., 2015; Zhang et al., 2010) or their isolation (Abbott et al., 2007; Chithambaranadhan et al., 2015; Hao et al., 2014) or preventing them from occurring at least in the most detrimental locations. The aim of the present work is to present a systematic study of influence of ohmic shunts at significant spatial locations in an industrial Silicon solar cell. Distributed diode model, (Foss et al., 2006; Galiana et al., 2005; Gupta et al., 2007a,b; Gupta et al., 2012; Somasundaran et al., 2012; Somasundaran and Gupta, in press; Zekry and Al-Mazroo, 1996), developed based on experimentally measured parameters, has been utilized for the study. Ohmic shunts have been simulated at various critical spatial locations in the solar cell.
⇑ Corresponding author. E-mail address: [email protected] (P. Somasundaran). http://dx.doi.org/10.1016/j.solener.2016.10.020 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.
Degradation in output power and open circuit voltage have been measured in terms of relative power and relative open circuit voltage which were calculated with respect to the values when the solar cell is not shunted. Important effect of irradiance on shunt related losses has been accounted for by performing simulations at two different irradiance levels. The study has provided further insight into the shunting phenomena. The influence of shunt on the relative power at each spatial position has been found by comparing the power at MPP for the following two distinct cases: (1) when the shunt is present in the solar cell and (2) when the shunt is not present in the solar cell (i.e., after replacing the shunted area by the shunt-free area). A comprehensive understanding of the influence of the critical shunt locations in the industrial Silicon solar cell can be useful to achieve a dramatic improvement in the electrical performance of the industrial Silicon solar cells by preventing the occurrence of shunts at the identified critical locations or by detecting and isolating the shunts at the identified critical locations or by removing them and replacing with shunt-free area. The localised shunts can be imaged and detected using an IR camera (Chithambaranadhan et al., 2015; Hao et al., 2014) or liquid crystal sheets (Hao et al., 2014). Lock-in Infrared Thermography can be exploited for the imaging and detection of strong shunts in a few seconds of measurement time (Gupta et al., 2007a,b). Based on the criticality, the localised shunts can then be isolated by a combination of laser scribing and chemical
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etching as proposed in Hao et al. (2014) gaining a far improved performance of the solar cell. Further, severe shunts under busbar or finger metallization in multi/mono-crystalline solar cells can be repaired in an effective manner by the chemical etching method proposed in Chithambaranadhan et al. (2015). 2. Model In distributed diode model, a solar cell is divided into smaller elementary areas wherein each elementary area is represented by the Shockley’s one diode equivalent circuit and the model has been utilized to study shunt related losses by comparing illuminated I-V characteristics for various cases of shunting. Since the shunting phenomena most of the time, manifest itself in very small regions in the solar cell, it is necessary to divide the given solar cell area into a large number of elementary areas, so as to represent each small region of the solar cell in the developed model. In the present work, to investigate the effect of shunts on the industrial Silicon solar cell having dimensions of 125 mm 125 mm, schematic of which is shown in Fig. 1(a) with position of ten shunts, the solar cell was divided into 375 375 equal elementary areas as shown in Fig. 1(b), considering the finger thickness into consideration. Effect of spatial positioning of shunts has been investigated by simulating the extended shunts of same magnitude at ten different locations considering the effect of metallization on shunting phenomenon. Degradation in performance caused by shunts depends not only on their spatial location in the solar cell but also their proximity to the busbar and finger metallization. Hence shunts have been classified into two major categories: (1) shunt not under metallization and (2) shunt under metallization. Shunt not under metallization includes: shunt between busbars not under finger, shunt in close proximity of busbar not under finger, shunt on the edge not under finger and shunt on corner not under finger and have been designated as a, b, c and d respectively in Fig. 1(a). Shunt under metallization includes shunt on corner under finger, shunt on edge under finger, shunt in close proximity of busbar under finger, shunt between busbars under finger, shunt under busbar and under finger, and shunt under busbar but not under finger and have been designated as e, f, g, h, i and j respectively in Fig. 1(a). Area of the extended shunt under consideration is important in quantifying the effect of shunts on the solar cell performance. Each elementary area has a dimension of 1/3 mm 1/3 mm, since the model was formed by dividing the industrial solar cells of dimensions 125 mm 125 mm into 375 375 equal elementary areas
for greater spatial resolution and better accuracy. The extended shunts have been simulated with 90 elementary areas in each spatial positions of shunting, thus yielding a total shunt area of 10 mm2. Each elementary area has been modelled by the solar cell equivalent circuit based on Shockley’s one diode model consisting of a diode, a shunt resistance and a current source in parallel as seen in Fig. 2. Current flow in the model can be described based on the Shockley’s diode equation:
I ¼ IL ðV þ IRs Þ=Rsh Io ½expfðq=nkTÞðV þ IRs Þg 1
ð1Þ
where IL is the photo-generated current (A) I, the net current flowing through the cell (A), Io, reverse saturation current (A), q, electronic charge (C), V, applied voltage across terminals of cell (V), n, ideality factor, k, Boltzmann’s constant (J/K), T, absolute temperature (K). Rs, the series resistance (X), Rsh, the shunt resistance (X). In the dark condition, the equation reduces to the following form:
I ¼ Io ½expðqV=nkTÞ 1
ð2Þ
Ideality factor n, and reverse saturation current Io for the solar cell under study has been calculated by the accurate analytical
Fig. 2. Distributed diode model of the solar cell showing only 3 3 elementary areas and wherein each elementary area is modelled by Shockley’s one diode model.
Fig. 1. (a) Schematic of the solar cell having shunt at ten different significant positions. (b) Meshing over the solar cell to divide it into small equal elementary areas.
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P. Somasundaran, R. Gupta / Solar Energy 139 (2016) 581–590 Table 1 Measured parameters of the solar cell on which the external shunt was introduced. Condition
Open circuit voltage Voc (V)
Short circuit current Isc (A)
Series resistance Rs (X)
Shunt resistance Rsh (X)
Voltage at MPP Vm (V)
Current at MPP Im (A)
Power at MPP Pm (W)
Before shunting After shunting
0.606 0.591
0.695 0.706
0.193 0.193
50 33.33
0.434 0.42
0.559 0.563
0.243 0.236
method proposed in Humada et al. (2016) and Phang et al. (1984), from the manufacturer’s data sheet and the experimental dark I-V curves.
0.0
n ¼ ½Vm þ Rso Im Voc =½Vth fln ðIsc Vm =Rsho Im Þ
Io ¼ ðIsc Voc =Rsh ÞexpðVoc =nVth Þ
ð3Þ ð4Þ
where Vm is the voltage at Maximum Power Point (V), Rso is the reciprocal of slope of I-V curve at open circuit point (X), Im is the current at Maximum Power Point (A), Voc is the open circuit voltage (V), Vth is thermal voltage = kT/q at 300 K (V), Isc is the short circuit current (A), Rsho is the reciprocal of slope of I-V curve at short circuit point (X), Isc is the short circuit current (A), and Rsh is the shunt resistance (X). 3. Experimental validation of the simulation approach
Current (A)
lnðIsc Voc =Rsh Þ þ Im =ðIsc fVoc =Rsho gÞg
3.5
0.8 3.5
3.0
3.0
2.5
2.5
Table 2 Parameters of the ohmic shunt externally introduced to the shunt free multicrystalline solar cell. Parameters
Value
Shunt resistance Shunt area Shunt location
10.2 X 5 mm 1 mm 12 mm away from busbar and 15 mm from edge and by width at exactly the middle of the cell
0.4
0.6
Simulated Experimental
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0 0.0
The simulation approach presented in Section 2 has been experimentally validated by introducing shunt resistance of known value externally to a shunt free Silicon solar cell, and whose dark I-V curve has been measured before and after introducing the external shunt. The shunt has been introduced at a defined location and a defined area. The measured parameters of the solar cell, before and after introducing the external shunt, have been summarized in Table 1. The parameters of the externally introduced shunt have been summarized in Table 2. Since the shunt parameters such as the shunt resistance, location of the shunt, area of the shunt and nature of the shunt are known, the simulation approach based on the distributed diode model has been exploited to estimate the shunt resistance of the shunted area by comparing the simulated dark I-V curve with the measured dark I-V curve. Actual value of shunt resistance and the estimated value of the shunt resistance have been separately simulated in the illuminated model of the solar cell yielding the efficiency and fill factor for the actual and estimated value of shunts. The error in estimation of efficiency by the simulation approach has been 7.33% and in Fill Factor has been 6.55%. Fig. 3 compares the experimental dark I-V curve obtained by the Solar Simulator in the laboratory and the simulated dark I-V curve obtained from the distributed diode model of a shunt free multicrystalline solar cell whose parameters are summarized in Table 3. It can be seen that there is a good degree of agreement between both the curves, which supports the validity of the developed model. The model has been verified with several shunt free and shunted industrial multi-crystalline and mono-crystalline Silicon solar cells. An illustration of the model verification can be seen in Fig. 4, wherein the experimental and simulated dark I-V curves
0.2
0.2
0.4
0.6
0.0 0.8
Voltage (V) Fig. 3. Comparison of experimental and simulated dark I-V curves for a typical shunt free multi-crystalline solar cell of 125 mm 125 mm dimension.
Table 3 Fixed simulation parameters. Parameters
Value
Number of busbars Number of fingers Cell length Cell breadth Sheet resistance Saturation current density Jo Ideality factor n Temperature T Busbar resistivity Finger resistivity Busbar breadth Busbar thickness Finger cross sectional area
2 52 125 mm 125 mm 40 X/sq. 6.39 109 A/cm2 1.5 300 K 6 106 X cm Giaffreda et al. (2014) 6 106 X cm Giaffreda et al. (2014) 2 mm Giaffreda et al. (2014) 23 lm Giaffreda et al. (2014) 1425 lm2 Giaffreda et al. (2014)
for both a shunt free monocrystalline industrial solar cell and a shunted multi-crystalline industrial solar cell of 125 mm 125 mm dimensions have been compared. Fig. 5 presents the comparison of simulated illuminated I-V curves with the actual value of shunt resistance introduced externally and the shunt resistance value estimated by the simulation approach for a shunt free single busbar multi-crystalline Silicon solar cell whose parameters are summarized in Table 4. The maximum deviation between the two curves is 4.54%. The reason for the deviation could be due to the fact that in the experiment the shunt has been externally introduced to the cell by means of an ohmic contact whereas in the model the shunt is internally connected. 4. Simulation The influence of the shunts on the electrical performance of the solar cell will depend on the shunt resistance, the location of the
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0.0
0.1
0.2
0.3
0.4
0.5
0.6
1 Experimental -Shunt free Cell Simulated -Shunt free Cell Expermental - Shunted Cell Simulated -Shunted Cell
0
0
-1
-1
ln[I] (A)
0.7 1
-2
-2
-3
-3
-4 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Cell Current (A)
0.4
0.6
0.8
0.8
0.6
0.6
0.4
0.4 Actual value of shunt resistance Estimated value of shunt resistance
0.2
0.0
0.0 0.2
Load resistance Area normalised shunt resistance = Rsh Ash Irradiance
106 10 X 106 103 X cm2 Fecher et al. (2014)
Shunt position: (a) Under metallization (six positions)
(b) Not under metallization (four positions)
0.4
1–1000 W/m2 1. Busbar shunt under finger 2. 3. 4. 5. 6. 1.
Busbar shunt not under finger Shunt near busbar under finger Middle shunt under finger Edge shunt under finger Corner shunt under finger Shunt near busbar not under finger
2. Middle shunt not under finger 3. Edge shunt not under finger 4. Corner shunt not under finger 103 cm2 Fecher et al. (2014) 102 cm2
investigation. The degradation in performance has been measured in terms of relative power (Power of the shunted solar cell at MPP/ Power of the solar cell having no shunts at MPP). The simulation parameters have been determined in part from the test cells and in part from the literature and are summarized in Table 3. The simulation parameters which are varied have been summarized in Table 5. For each parameter combination in Table 5, the illuminated I-V curves have been simulated by varying the load resistance RL from 1 lX to 10 X. From this set of illuminated I-V curves, the cell’s maximum power Pm and its open circuit voltage Voc, have been determined. 5. Results and discussion
0.2
0.0
Value
Shunt area, Ash:
Fig. 4. Comparisons of experimental and simulated dark I-V curves for a typical shunt free mono-crystalline and a shunted multi-crystalline Silicon solar cell of 125 mm 125 mm dimensions.
0.2
Parameter
-4 0.7
Cell Voltage (V)
0.0
Table 5 Varied simulation parameters.
0.6
Cell Voltage (V) Fig. 5. Comparison of the simulated illuminated I-V curves with the actual (externally introduced shunt resistance) and estimated value (by simulation approach) of shunt resistance for the shunt free multi-crystalline Silicon solar cell whose parameters are described in Table 4.
Table 4 Parameters of the shunt free multi-crystalline solar cell. Parameters
Value
Number of busbars Number of fingers Cell length Cell breadth Saturation current density Jo Ideality factor n Temperature T
1 14 63 mm 38 mm 9.47 E-8 A/cm2 1.98 300 K
shunt, proximity to the metallization, irradiance under which the solar cell is operating, area of the shunt and the operating point of the module in which the solar cell is connected. The most critical factors are the shunt resistance and spatial location of the shunt in the cell and have been considered in the following. Two different irradiance levels have been considered in each of the cases under
5.1. Influence of shunt resistance and shunt location on the solar cell performance The influence of shunt resistance has been investigated by varying its value from a range of 0.001 X which has been reported in the literature (Fecher et al., 2014) to a high value of 10 X considering each significant spatial locations of shunts, at two different irradiance levels of 100 W/m2 and 1000 W/m2. At each significant spatial location of shunt described in Section 2, the relative power has been determined by the model. 5.1.1. Influence on relative power Fig. 6 illustrates the variation of relative power with shunt resistance at 100 W/m2 irradiance considering shunts under metallization. All the six significant different shunt positions have been included in this plot. Fig. 6 reveals that at very low shunt values the relative power reduces to almost zero for all six shunt positions under metallization. At high shunt values near 10 X, the relative power increases to 90%, for all six shunt positions under metallization. In the intermediate region, the relative power increases in an exponential manner with the increase in shunt resistance. At very low values and at very high values of shunt resistance, spatial variation appears to vanish, however there is actually a significant difference in the initial region, which has been brought out by the inset, which have been plotted considering the shunt resistance in the range of 0.001 X and 0.01 X, shown in Fig. 6. At very low values of shunt, the solar cell is severely affected by the shunt and thus power will be reduced dramatically, however the difference in the power produced between different shunt positions still
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Relative Power
0.8
0.01
0.1
1
10 1.0
Busbar Shunt under finger Busbar Shunt not under finger Edge Shunt under finger Corner Shunt under finger Middle Shunt under finger Shunt near busbar under finger
0.6
0.4
0.4
0.002
0.02
0.2
0.004
0.006
0.008 0.01 0.02
0.01
0.00
0.01
0.1
0.0020.002
1
0.0 10 0.00
0.004 0.01 0.0040.0060.008 0.006 0.008 0.01
holds significance. This is a novel finding, since it is generally expected that spatial variation vanishes at very low shunt values (Fecher et al., 2014). Busbar shunt under finger and busbar shunt not under finger causes the greatest degradation in relative power as revealed by Fig. 6. At very high values of shunt resistance, the solar cell is delivering very much close to its full power and in this region; difference due to spatial location vanishes. For the values of shunt resistances which lie between the above mentioned extremes, spatial dependence of shunt losses becomes more obvious as revealed by Fig. 6. A maximum difference of 30% can be detected from the curves, which is close with the findings for the thin film module for different spatial positions of shunts (Fecher et al., 2014). Fig. 7 depicts the variation of relative power with shunt resistance for the shunts under metallization for 1000 W/m2 irradiance. At higher irradiance levels, it is expected that there is reduction in degradation due to shunting, since there is more lateral current flow, and the influence of the shunt diminishes comparatively. Even at very low shunt resistances values, it can be seen that, for all the shunt positions, the cell has a slightly better performance
Relative Power
0.8
1
10 1.0
Busbar Shunt under finger Busbar Shunt not under finger Edge Shunt under finger Corner Shunt under finger Middle Shunt under finger Shunt near busbar under finger
0.8
0.6
0.6
0.4
0.4
0.14 0.12
0.2
0.2
0.10 0.08 0.06 0.04 0.02
0.0 1E-3
0.00
0.01
0.1
10 1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2 1E-3
0.01
0.1
1
0.2 10
Shunt Resistance (Ohm)
Fig. 6. Variation of relative power with shunt resistance under 100 W/m irradiance for six cases of shunts under metallization.
0.1
1
0.01
2
0.01
0.1
0.2
Shunt Resistance (Ohm)
1E-3 1.0
0.01
Edge Shunt not under finger Corner Shunt not under finger Shunt near busbar not under finger Middle Shunt not under finger
0.8
0.6
0.0 1E-3
1E-3 1.0
Relative Power
1E-3 1.0
1
0.002
0.0 10
0.004 0.0060.008 0.01
Shunt Resistance (Ohm) Fig. 7. Variation of relative power with shunt resistance under 1000 W/m2 irradiance for six cases of shunts under metallization.
Fig. 8. Variation of relative power with shunt resistance under 100 W/m2 irradiance for four cases of shunts not under metallization.
at this higher irradiance. For example, in the case of corner shunt under finger, the relative power improves by 20% for very low shunt values due to higher irradiance. At higher shunt values, the relative power reaches almost 100% for all shunt positions under metallization, which means an improvement by almost 10% when compared to the case under 100 W/m2 irradiance. Variation of relative power considering shunts not under metallization is presented in Fig. 8. The plots have been obtained under 100 W/m2 irradiance. It can be seen that, when the shunts are not under metallization, there is much improvement in performance of the solar cell. For the corner shunt there is the greatest improvement in relative power, which is found to be 80% for even very low shunt resistance of 0.001 X. Further, it is revealed by Fig. 8 that even shunts of very low resistances becomes almost harmless when they are located at certain shunt positions such as at the corner of the cell. When shunts are located away from the metallization fingers and busbars, they will be screened by the surrounding sheet resistance and the influence of the shunt decreases. The higher the sheet resistance, the greater will be the shunt screening by the sheet resistance. Considering the shunts not under metallization, shunt near busbar not under finger causes the greatest degradation in relative power as seen in Fig. 8. The inference which can be drawn from the above result is that even proximity of a shunt to the busbar will have a dramatic impact on the influence of the shunt on the electrical performance of solar cell, even if it is not located directly under finger or busbar metallization. The explanation for this impact can be related to the fact that the busbars carries far greater current, being the least resistive path for the current in the solar cell. Hence when a shunt occurs in the close proximity of busbar, the probability of greater current sinking through the shunt increases. Fig. 9 summarises the variation of relative power considering shunts not under metallization under 1000 W/m2 irradiance. In the higher irradiance conditions, there ensues a greater improvement in relative power for all shunt positions. Comparing with shunts under metallization there is an improvement of 90–95% in relative power for the most of the shunts not under metallization, for the lowest values of shunt resistance considered in the present study. Under high irradiances, there is much higher lateral current flow and the presence of busbars and fingers ensures that current through the shunt not under or in proximity of metallization remains low. Loss in relative power reduces dramatically and is in the range of 3–11%.
P. Somasundaran, R. Gupta / Solar Energy 139 (2016) 581–590
Relative Power
1E-3 1.00
0.01
0.1
1
10 1.00
0.96
0.96
0.92
0.92
0.88
0.88
0.84
0.80 1E-3
Edge Shunt not under finger Corner Shunt not under finger Shunt near busbar not under finger Middle Shunt not under finger
0.01
0.1
0.84
1
0.80 10
Shunt Resistance (Ohm) Fig. 9. Variation of relative power with shunt resistance under 1000 W/m2 irradiance for four cases of shunts not under metallization.
Spatial variation between different shunt positions arises due to the difference in the possibility in collection of current at different locations, since the shunt acts as a potential sink for the current. For a shunt at the corner, it has a limited possibility to sink the current since it can collect current only from a 90° collection angle due to its location. For a shunt at the edge, there is an increased possibility to collect the current, since it can have 180° collection angle. For shunts at all the other spatial locations, there is a still higher possibility to collect the current from the surrounding current generation areas since all the other shunt positions such as middle shunt, busbar shunt and shunt near busbar have the maximum possible current collection angle of 360° (Fecher et al., 2014). However, the presence of metallization fingers and busbars in close proximity of the shunt at any shunt positions changes the scenario dramatically. In this case, since the fingers and busbars are collectors of current from the nearby current generation areas, there is current crowding in the metallization areas, which is more pronounced in the busbar areas. Hence, naturally, a shunt in the metallization areas can sink considerable quantity of current resulting in a critical influence on the solar cell performance. Naturally, a shunt even at the corner or the edge of the solar cell under the finger metallization will critically influence the performance leading to considerable degradation in power as demonstrated in Section 5.2, wherein a difference of 80% in relative power between the corner shunt under and not under finger has been observed. A comprehensive understanding of the influence of the critical shunt locations in the industrial Silicon solar cell has been gained by the study. A dramatic improvement in the electrical performance of the industrial Silicon solar cells can be achieved by preventing the occurrence of shunts at the identified critical locations or by isolating them by laser or chemical technique or by removing them.
5.2. Influence of proximity to the metallization on the solar cell performance Influence of metallization has been analysed for two types of common shunts: the edge shunt and the corner shunt. Variation of relative power with shunt resistance is presented in Fig. 10 for the edge shunt under and not under finger metallization. Fig. 11 presents the variation of relative power for the corner shunt under and not under finger metallization. The effect of metallization is really significant at the lowest shunt values for both cases of shunts.
1E-3 1.0
0.8
Relative Power
586
0.01
0.1
1
Edge Shunt under finger Edge Shunt not under finger
10 1.0
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0 1E-3
0.01
0.1
1
0.0 10
Shunt Resistance (Ohm) Fig. 10. Variation of relative power with shunt resistance for the edge shunt under and not under finger.
In the case of edge shunt, a difference of 40% in relative power has been observed, whereas in the case of corner shunt the difference between the two shunts due to presence of finger metallization can rise to 80%, for critically low values of shunt resistance. The influence of proximity to metallization fingers assumes a dramatic role in the context of the above finding. The results obtained leads to the inference that even shunt located at the corner or edge of the solar cell can critically degrade the performance of the solar cell when they are located under finger metallization. 5.3. Influence of irradiance on the solar cell performance It has been evident from the investigation conducted in the present study that the shunt losses depend critically on the shunt resistance, and location of the shunt as well as proximity to the busbar and finger metallization. However, since the current generation in a solar cell depends principally on the illumination intensity, it is expected that the current drawn by the shunt will depend drastically on the irradiance falling on the solar cell. Hence it would be interesting to investigate how the severity of shunt losses will be influenced by the varying levels of irradiance for various positions of shunting. It has been understood from the foregoing study that the local positions of shunts and their proximity to the metallization holds a critical influence on the shunted cell performance. Due to the above reason, it would be interesting to study the effect of change in irradiance on the shunt losses with shunts at various local positions described in detail in Section 2. The local shunt positions considered in the present study are representative regions having equal areas and wherein ohmic shunts of equal shunt resistance have been simulated for different irradiances. Irradiance has been varied from a lower value of 1 W/m2 to the higher value of 1000 W/m2 representing 1 Sun irradiance in series of logical steps. The temperature rise arising due to the higher irradiances has been neglected in the present study. Based on the described model, the shunts have been simulated taking one case at a time for varying irradiances, but keeping the shunt area and the shunt resistance same in each case. In order to keep the total shunt resistance of the shunted area same in each local position of shunting, a shunt resistance of 1 X has been assumed in all the ten cases of shunting considered in the present work. Output power and open circuit voltage has been estimated for varying illumination intensities and compared with the output
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0.01
0.1
1
10 1.0
Relative Power
Corner Shunt under finger Corner Shunt not under finger
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
1E-3
0.01
0.1
1
0.0 10
Shunt Resistance (Ohm) Fig. 11. Variation of relative power with shunt resistance for the corner shunt under and not under finger.
power and open circuit voltage for the cell having no shunts. For the purpose of comparison, a relative output power ([Output power of the shunted solar cell/Output power of shunt free solar cell at the same irradiance]) and a relative open circuit voltage ([Open circuit voltage of the shunted solar cell/Open circuit voltage of the shunt free solar cell at the same irradiance]) have been defined. Fig. 12 illustrates the variation of relative open circuit voltage for four cases of local positions of shunts considered in the present study. Based on the results, it is apparent that the spatial positions of shunts are very much significant while considering the shunt related losses, particularly at low irradiance levels. Variation in relative open circuit voltage from 35% and up to a maximum of even 55% between different shunt positions for the same shunt resistance and shunt area have been observed from the simulation results which reveals the critical importance of shunt positions. The trend also reveals that at high irradiance levels near to 1 Sun (1000 W/m2), the difference in shunt losses gradually reduces to a minimum, since the impact of shunt itself would reduce in comparison to the low irradiance case. At very low irradiance levels, that is say less than 10 W/m2, also there is a saturation
1
10
100
Relative Open Circuit Voltage
1.0
1000 1.0
0.8
0.8
0.6
0.6
0.4
0.4 Corner Shunt not under finger Edge Shunt not under finger Middle Shunt not under finger
0.2
0.0 1
10
100
region, since the open circuit voltage reduces to very low levels. However, there is actually a difference in performance between different shunt positions even at these low irradiance levels though they do not appear so pronounced, since the photovoltaic generation itself is very low due to very low irradiance. For example, for a shunt at corner not under finger, the relative open circuit voltage is almost five times that of the busbar shunt under the finger at 1 W/m2 irradiance. At this point, in order to understand the significance of the combined impact of proximity to metallization and shunt positions, shunts under metallization and not under metallization have been considered separately in the following. Fig. 13 visualizes the variation of relative open circuit voltage with varying irradiance levels for the four cases of shunts under metallization. From Fig. 13, the real significance of the spatial dependence of shunts which are all located under metallization can be understood. At an irradiance level between 10 W/m2 and 100 W/m2, there is an almost 35% difference between two cases of shunts under metallization, which can be significant. For the shunts not under metallization, as shown in Fig. 12, the difference in relative open circuit voltage between the different shunt positions are more accentuated and apparent. Fig. 14 illustrates the variation of relative power at MPP for three cases of shunts not under metallization for low irradiance levels. It reveals that there can be a difference of more than 40% between different positions of shunts located not under metallization for the shunt resistance considered in the present study. This is an appreciably large value since, since an increase in output power in this range can be of considerable significance. Further since, the actual shunt value may reach even value in the range of 0.001 X in some cases, the effect may be accentuated to critical levels. Considering the shunt positions under and not under metallization, the maximum difference which has been observed is 70% in relative open circuit voltage at low irradiances. Fig. 15 visualizes the variation of relative power at MPP for the four cases of shunts under metallization for low irradiance levels. It reveals that there can be a difference of more than 25–30% between different cases of shunts located under metallization for the shunt resistance considered in the present study. At very low and high irradiance levels, a saturation region has been observed for both cases of shunting when considered separately. Of course, the difference in power loss between the shunts under metallization and those not under metallization still holds well, though to a lesser degree. A maximum difference of 60% in
0.2
0.0 1000
Irradiance (W/sq.m.) Fig. 12. Variation of relative open circuit voltage with irradiance for three local positions of shunting not under metallization.
1
10
100
1.0
Relative Open Circuit Voltage
1E-3 1.0
Corner Shunt under finger Busbar Shunt under finger Busbar Shunt not under finger Near Busbar Shunt nder finger
0.8
1000 1.0
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0 1
10
100
0.0 1000
Irradiance (W/sq.m.) Fig. 13. Variation of relative open circuit voltage with irradiance for four cases shunts under metallization.
P. Somasundaran, R. Gupta / Solar Energy 139 (2016) 581–590
1
10
100
1.0 Corner Shunt not under finger Edge Shunt not under finger Middle Shunt not under finger
0.8
Relative Power
1000 1.0
0 1.0
100 200 300 400 500 600 700 800 900 1000 1100 1.0 Higher Shunt area 0.1 sq. cm Lower Shunt area 0.01 sq.cm
0.8
0.6
0.6
0.4
0.4
Relative Power
588
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.2
0.2
0.0 1
10
100
0.0 1000
0.0 0
Irradiance (W/sq.m.)
0.0 100 200 300 400 500 600 700 800 900 1000 1100
Irradiance (W/sq.m)
relative power has been observed between the corner shunt not under finger and the busbar shunt under finger at low irradiance condition. The study reveals that the irradiance level at which the solar cell operates holds a key and critical role in determining the shunt losses along with the spatial locations of shunts. 5.4. Influence of area of the shunt on the solar cell performance The influence of shunt area has been investigated by keeping the absolute shunt resistance constant in all cases of shunting considered, while varying the shunt area and area normalised shunt resistance. Fig. 16 illustrates the variation of relative power with irradiance for two different shunt areas, however having the same absolute shunt resistance. Clearly, the greater area of the shunt results in more loss for the same absolute shunt resistance. The main reason for this effect can be traced to the fact that increased shunt area brings the edge of the shunt area near to metallization fingers compared to a smaller shunt area. A second reason is that most of the current in the shunt flows through the edges and not through the centre (Fecher et al., 2014). A greater perimeter results in a larger area of influence.
1
10
100
1.0 Corner Shunt under finger Busbar Shunt under finger Busbar Shunt not under finger Near Busbar Shunt nder finger
Relative Power
0.8
1000 1.0
Fig. 16. Variation of relative power with irradiance for two different shunt areas and having the same absolute shunt resistance.
0 1.0
100 200 300 400 500 600 700 800 900 1000 1100 1.0 Higher Shunt area 0.1 sq. cm Smaller Shunt Area 0.01 sq.cm
Relative Open Circuit Voltage
Fig. 14. Variation of relative power at MPP with illumination for three cases of shunts not under metallization.
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0 0
0.0 100 200 300 400 500 600 700 800 900 1000 1100
Irradiance (W/sq.m) Fig. 17. Variation of relative open circuit voltage with irradiance for two different shunt areas and having the same absolute shunt resistance.
Fig. 17 summarises the variation of relative open circuit voltage with irradiance for two different shunt areas. In this case also, the greater shunt area results in greater loss in open circuit voltage.
0.8
5.5. Influence of sheet resistivity on the shunted cell performance 0.6
0.6
0.4
0.4
0.2
0.2
0.0 1
10
100
0.0 1000
Irradiance (W/sq.m.) Fig. 15. Variation of relative power at MPP with irradiance for the four cases of shunts under metallization.
When shunts are not under metallization, it is expected that there will be considerable influence due to sheet resistivity on the shunting effect. It would be interesting to quantify the influence of sheet resistivity on the performance of a cell in the presence of shunts. A simple method of doing it is by the calculation of the cell shunt resistance while sheet resistivity is varied over a practical range of values. The said calculation has been done and result obtained which reveals an interesting trend. Fig. 18 presents the variation of cell shunt resistance with the sheet resistivity for (a) edge shunt not under finger, (b) middle shunt not under finger, (c) corner shunt not under finger, and (d) shunt in close proximity of busbar not under finger. The result reveals that sheet resistivity influences the cell shunt resistance to a considerable extent when
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0
10
20
30
40
50
60
70
80
90
40 Corner Shunt not under finger Edge Shunt not under finger Middle Shunt not under finger Shunt near busbar not under finger
Cell Shunt Resistance(Ohm)
35 30
100 110 40 35 30
589
increased influence region with increased area of shunt which brings the region close to more fingers. A comprehensive understanding of the criticality of significant shunt locations in the industrial solar cell has been gained by the study. A dramatic improvement in the electrical performance of the industrial solar cells can be achieved by preventing the occurrence of shunts at the identified critical locations or by isolating them by laser or chemical technique or by removing them.
25
25
20
20
15
15
Conflict of interest
10
10
5
5
The authors declare that there is no conflict of financial/personal interest or belief that could affect the objectivity of the research work presented in the submitted paper and there is no conflict of interest regarding the publication of this paper.
0 0
10
20
30
40
50
60
70
80
90
0 100 110
Sheet Resistivity (Ohm/sq.) Fig. 18. Variation of cell shunt resistance with the sheet resistivity of the solar cell for shunts not under metallization: (a) corner shunt not under finger, (b) edge shunt not under finger, (c) middle shunt not under finger, and (d) shunt near busbar not under finger.
shunts are not under metallization. Thus the increased sheet resistance would lead to increased shunt screening leading to an improved cell performance in the presence of shunts. 6. Conclusions The paper presented a simple distributed diode model to simulate the electrical behaviour of an industrial Silicon solar cell having an ohmic shunt. The chosen solar cell has the dimensions of 125 mm2. Parameters of the chosen solar cell represent typical values for test cells. The simulation approach has been experimentally validated by connecting an external shunt of known parameters and comparing the degradation in efficiency and fill factor for actual value of the shunt resistance and estimated value of shunt resistance. The shunt resistance, irradiance, shunt location and shunt size have been systematically varied and impact on the solar cell performance has been evaluated. Important finding is that, the performance depends critically on the shunt position and proximity to the metallization to the extent that the difference in loss in the relative power can be 80% between different shunt positions at 100 W/m2 irradiance. Comparing with shunts under metallization, there is an improvement of more than 90% in relative power for the most of the shunts not under metallization, for the lowest values of shunt resistance considered in the present work. In general, it was found that the proximity to the busbar and finger metallization and the shunt position holds the key to the impact the shunt will have on the solar cell performance in addition to the resistance of shunt itself. The underlying mechanism could be the reduced current screening due to the enhanced current flow when the shunt is under the busbar or finger metallization. The irradiance has been varied over a wide range, that is from 1 to 1000 W/m2, and variation in relative power and relative open circuit voltage have been analysed considering all the significant shunt positions. A maximum difference of 60% in relative power and 70% in relative open circuit voltage has been found between the corner shunt not under finger and the busbar shunt under finger at low irradiance condition. A deeper understanding of the irradiance dependence of shunt losses has been gained by the study. Study of area dependence revealed that increase in shunt area for the same absolute shunt resistance results in greater loss in power and open circuit voltage. The underlying reason could be the
References Abbott, M.D., Trupke, T., Hartmann, H.P., Gupta, R., Breitenstein, O., 2007. Laser isolation of shunted regions in industrial solar cells. Prog. Photovoltaics Res. Appl. 15, 613–620. Barbato, M., Meneghini, M., Cester, A., Mura, G., Zanoni, E., Meneghesso, G., 2014. Influence of shunt resistance on the performance of an illuminated string of solar cells: theory, simulation, and experimental analysis. IEEE Trans. Dev. Mater Reliab. 14 (4), 942–950. Botchak Mouafi, Y.P., Zuschlag, A.S., Pichon, P.-Y., Fritz, J.M., Schonecker, A., Hahn, G., 2016. Novel RGS materials with high fill factors and no material-induced shunts with record solar cell efficiencies exceeding 16%. Sol. Energy Mater. Sol. Cells 146, 25–34. Chithambaranadhan, D., Veeramuthu, V., Nguyen, Q., Lommasson, T.C., Goldberg, R., Boström, T., 2015. Efficiency improvement in nonprime crystalline silicon solar cells by chemical isolation of shunts under front metallization. IEEE J. Photovoltaics 5 (1), 206–211. Compagnin, A., Meneghini, M., Barbato, M., Giliberto, V., Cester, A., Vanzi, M., Mura, G., Zanoni, E., Meneghesso, G., 2013. Thermal and electrical investigation of the reverse bias degradation of silicon solar cells. Microelectron. Reliab. 53, 1809– 1813. Dongaonkar, S., Loser, S., Sheets, E.J., Zaunbrecher, K., Agrawal, R., Marks, T.J., Alam, M.A., 2013. Universal statistics of parasitic shunt formation in solar cells, and its implications for cell to module efficiency gap. Energy Environ. Sci. 6, 782–787. Fecher, F.W., Romero, A.P., Brabec, C.J., Buerhop-Lutz, C., 2014. Influence of shunt on the electrical behavior in thin film photovoltaic modules – A 2D finite element simulation study. Sol. Energy. 105, 494–504. Fortes, M., Comesana, E., Rodriguez, J.A., Otero, P., Garcia-Loureiro, A.J., 2014. Impact of series and shunt resistances in amorphous silicon thin film solar cells. Sol. Energy 100, 114–123. Foss, S.E., Olaisen, B.R., Marstein, E.S., Holt, A., 2006. A new 2.5D distributed SPICE model of solar cells. In: Proceedings of 21st European Photovoltaic Solar Energy Conference and Exhibition, pp. 430–434. Galiana, B., Algora, C., Rey-Stolle, I., Vara, I.G., 2005. A 3-D Model for concentrator solar cells based on distributed circuit units. IEEE Trans. Electronic Dev. 52 (12), 2552–2558. Giaffreda, D., Magnone, P., Meneghini, M., Barbato, M., Meneghesso, G., Zanoni, E., Sangiorgi, E., Fiegna, C., 2014. Local shunting in multicrystalline silicon solar cells: distributed electrical simulations and experiments. IEEE J. Photovoltaics 4 (1), 40–47. Gupta, R., Breitenstein, O., Schneider, J., 2007a. Characterization of crystalline silicon on glass (CSG) modules by surface potential mapping. In: Proceedings of 22nd European Photovoltaic Solar Energy Conference and Exhibition, pp. 1434–1437. Gupta, R., Breitenstein, O., Zettner, J., Karg, D., 2007b. In-line shunt detection in solar cells by fast lock-in infrared thermography. In: Proceedings of 22nd European Photovoltaic Solar Energy Conference and Exhibition, pp. 1975–1978. Gupta, R., Somasundaran, P., Nandi, D.K., 2012. Electrical simulation and characterization of shunts in solar cells. J. Appl. Mech. Mater. 110–116, 2453– 2457. Guthrey, H., Johnston, S., Weiss, D.N., Grover, S., Jones, K., Blosse, A., Al-Jassim, M., 2016. Three-dimensional minority-carrier collection channels at shunt locations in silicon solar cells. Sol. Energy 135, 163–168. Hao, H.L., Zhong, S.H., Zhang, X., Shen, W.Z., 2014. Optimization of shunt isolation processing for silicon solar cells via laser and chemical etching. Appl. Surf. Sci. 311, 870–875. Hovestad, A., Bressers, P.M.M.C., Meertens, R.M., Frijters, C.H., Voorthuijzen, W.P., 2015. Electrochemical etching of molybdenum for shunt removal in thin film solar cells. J. Appl. Electrochem. 45, 745–753. Humada, A.M., Hojabri, M., Mekhilef, S., Hamada, H.M., 2016. Solar cell parameters extraction based on single and double-diode models: a review. Renew. Sustain. Energy Rev. 56, 494–509. Phang, J., Chan, D., Phillips, J., 1984. Accurate analytical method for the extraction of solar cell model parameters. Electron. Lett. 20, 406–408.
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Phillips, A.B., Khanal, R.R., Song, Z., Watthage, S.C., Kormanyos, K.R., Heben, M.J., 2015. Simultaneous shunt protection and back contact formation for CdTe solar cells with single wall carbon nanotube layers. Appl. Phys. Lett. 107, 253901. http://dx.doi.org/10.1063/1.4938130 (1-4). Somasundaran, P., Sinha, A., Gupta, R., 2012. Simulation and characterization of spatial variation of shunts in industrial solar cells by PSpice and dark lock-in infrared thermography. In: Proceedings of 27th European Photovoltaic Solar Energy Conference and Exhibition, pp. 744–748.
Somasundaran, P., Gupta, R., 2016. Evaluation of shunt losses in industrial Silicon solar cells. Int. J. Photoenergy. (in press). Zekry, A., Al-Mazroo, A.Y., 1996. A distributed SPICE-model of a solar cell. IEEE Trans. Electronic Dev. 43 (5), 691–700. Zhang, L., Shen, H., Yang, Z., Jin, J., 2010. Shunt removal and patching for crystalline silicon solar cells using infrared imaging and laser cutting. Prog. Photovoltaics Res. Appl. 18 (1), 54–60.
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Solar Energy journal homepage: www.elsevier.com/locate/solener
Influence of local shunting on the electrical performance in industrial Silicon solar cells P. Somasundaran ⇑, R. Gupta Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
a r t i c l e
i n f o
Article history: Received 11 June 2016 Received in revised form 16 September 2016 Accepted 14 October 2016
Keywords: Shunts Spatial location Distributed diode model Performance degradation
a b s t r a c t The paper presents the results of investigation on the influence of an ohmic shunt located at various spatial positions on the solar cell performance by distributed diode model based simulations. By systematically varying the parameters such as shunt resistance, proximity to metallization, shunt area, and irradiance a deep insight about the shunt impact on the solar cell performance have been obtained. Further, effect of spatial positioning of shunts has been investigated by considering shunted region of same area and severity at various locations of the solar cell, via the simulation approach. The presented simulation approach has been experimentally validated. The influence of shunt on the relative power and relative open circuit voltage has been studied considering different irradiance levels. The study revealed new insights about significance of spatial positions of the shunts and the proximity of finger and busbar metallization. A dramatic improvement in the solar cell’s electrical performance can be gained by either preventing the occurrence of shunts at the identified critical locations or isolating them by laser or chemical technique or removing them. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Shunts present in various locations of the solar cell can be detrimental to its performance (Barbato et al., 2014; Botchak Mouafi et al., 2016; Chithambaranadhan et al., 2015; Compagnin et al., 2013; Dongaonkar et al., 2013; Fortes et al., 2014; Giaffreda et al., 2014; Guthrey et al., 2016; Phillips et al., 2015). It would be interesting to understand the possible improvement in the solar cell performance, with either removal of shunts (Hovestad et al., 2015; Zhang et al., 2010) or their isolation (Abbott et al., 2007; Chithambaranadhan et al., 2015; Hao et al., 2014) or preventing them from occurring at least in the most detrimental locations. The aim of the present work is to present a systematic study of influence of ohmic shunts at significant spatial locations in an industrial Silicon solar cell. Distributed diode model, (Foss et al., 2006; Galiana et al., 2005; Gupta et al., 2007a,b; Gupta et al., 2012; Somasundaran et al., 2012; Somasundaran and Gupta, in press; Zekry and Al-Mazroo, 1996), developed based on experimentally measured parameters, has been utilized for the study. Ohmic shunts have been simulated at various critical spatial locations in the solar cell.
⇑ Corresponding author. E-mail address: [email protected] (P. Somasundaran). http://dx.doi.org/10.1016/j.solener.2016.10.020 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.
Degradation in output power and open circuit voltage have been measured in terms of relative power and relative open circuit voltage which were calculated with respect to the values when the solar cell is not shunted. Important effect of irradiance on shunt related losses has been accounted for by performing simulations at two different irradiance levels. The study has provided further insight into the shunting phenomena. The influence of shunt on the relative power at each spatial position has been found by comparing the power at MPP for the following two distinct cases: (1) when the shunt is present in the solar cell and (2) when the shunt is not present in the solar cell (i.e., after replacing the shunted area by the shunt-free area). A comprehensive understanding of the influence of the critical shunt locations in the industrial Silicon solar cell can be useful to achieve a dramatic improvement in the electrical performance of the industrial Silicon solar cells by preventing the occurrence of shunts at the identified critical locations or by detecting and isolating the shunts at the identified critical locations or by removing them and replacing with shunt-free area. The localised shunts can be imaged and detected using an IR camera (Chithambaranadhan et al., 2015; Hao et al., 2014) or liquid crystal sheets (Hao et al., 2014). Lock-in Infrared Thermography can be exploited for the imaging and detection of strong shunts in a few seconds of measurement time (Gupta et al., 2007a,b). Based on the criticality, the localised shunts can then be isolated by a combination of laser scribing and chemical
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etching as proposed in Hao et al. (2014) gaining a far improved performance of the solar cell. Further, severe shunts under busbar or finger metallization in multi/mono-crystalline solar cells can be repaired in an effective manner by the chemical etching method proposed in Chithambaranadhan et al. (2015). 2. Model In distributed diode model, a solar cell is divided into smaller elementary areas wherein each elementary area is represented by the Shockley’s one diode equivalent circuit and the model has been utilized to study shunt related losses by comparing illuminated I-V characteristics for various cases of shunting. Since the shunting phenomena most of the time, manifest itself in very small regions in the solar cell, it is necessary to divide the given solar cell area into a large number of elementary areas, so as to represent each small region of the solar cell in the developed model. In the present work, to investigate the effect of shunts on the industrial Silicon solar cell having dimensions of 125 mm 125 mm, schematic of which is shown in Fig. 1(a) with position of ten shunts, the solar cell was divided into 375 375 equal elementary areas as shown in Fig. 1(b), considering the finger thickness into consideration. Effect of spatial positioning of shunts has been investigated by simulating the extended shunts of same magnitude at ten different locations considering the effect of metallization on shunting phenomenon. Degradation in performance caused by shunts depends not only on their spatial location in the solar cell but also their proximity to the busbar and finger metallization. Hence shunts have been classified into two major categories: (1) shunt not under metallization and (2) shunt under metallization. Shunt not under metallization includes: shunt between busbars not under finger, shunt in close proximity of busbar not under finger, shunt on the edge not under finger and shunt on corner not under finger and have been designated as a, b, c and d respectively in Fig. 1(a). Shunt under metallization includes shunt on corner under finger, shunt on edge under finger, shunt in close proximity of busbar under finger, shunt between busbars under finger, shunt under busbar and under finger, and shunt under busbar but not under finger and have been designated as e, f, g, h, i and j respectively in Fig. 1(a). Area of the extended shunt under consideration is important in quantifying the effect of shunts on the solar cell performance. Each elementary area has a dimension of 1/3 mm 1/3 mm, since the model was formed by dividing the industrial solar cells of dimensions 125 mm 125 mm into 375 375 equal elementary areas
for greater spatial resolution and better accuracy. The extended shunts have been simulated with 90 elementary areas in each spatial positions of shunting, thus yielding a total shunt area of 10 mm2. Each elementary area has been modelled by the solar cell equivalent circuit based on Shockley’s one diode model consisting of a diode, a shunt resistance and a current source in parallel as seen in Fig. 2. Current flow in the model can be described based on the Shockley’s diode equation:
I ¼ IL ðV þ IRs Þ=Rsh Io ½expfðq=nkTÞðV þ IRs Þg 1
ð1Þ
where IL is the photo-generated current (A) I, the net current flowing through the cell (A), Io, reverse saturation current (A), q, electronic charge (C), V, applied voltage across terminals of cell (V), n, ideality factor, k, Boltzmann’s constant (J/K), T, absolute temperature (K). Rs, the series resistance (X), Rsh, the shunt resistance (X). In the dark condition, the equation reduces to the following form:
I ¼ Io ½expðqV=nkTÞ 1
ð2Þ
Ideality factor n, and reverse saturation current Io for the solar cell under study has been calculated by the accurate analytical
Fig. 2. Distributed diode model of the solar cell showing only 3 3 elementary areas and wherein each elementary area is modelled by Shockley’s one diode model.
Fig. 1. (a) Schematic of the solar cell having shunt at ten different significant positions. (b) Meshing over the solar cell to divide it into small equal elementary areas.
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P. Somasundaran, R. Gupta / Solar Energy 139 (2016) 581–590 Table 1 Measured parameters of the solar cell on which the external shunt was introduced. Condition
Open circuit voltage Voc (V)
Short circuit current Isc (A)
Series resistance Rs (X)
Shunt resistance Rsh (X)
Voltage at MPP Vm (V)
Current at MPP Im (A)
Power at MPP Pm (W)
Before shunting After shunting
0.606 0.591
0.695 0.706
0.193 0.193
50 33.33
0.434 0.42
0.559 0.563
0.243 0.236
method proposed in Humada et al. (2016) and Phang et al. (1984), from the manufacturer’s data sheet and the experimental dark I-V curves.
0.0
n ¼ ½Vm þ Rso Im Voc =½Vth fln ðIsc Vm =Rsho Im Þ
Io ¼ ðIsc Voc =Rsh ÞexpðVoc =nVth Þ
ð3Þ ð4Þ
where Vm is the voltage at Maximum Power Point (V), Rso is the reciprocal of slope of I-V curve at open circuit point (X), Im is the current at Maximum Power Point (A), Voc is the open circuit voltage (V), Vth is thermal voltage = kT/q at 300 K (V), Isc is the short circuit current (A), Rsho is the reciprocal of slope of I-V curve at short circuit point (X), Isc is the short circuit current (A), and Rsh is the shunt resistance (X). 3. Experimental validation of the simulation approach
Current (A)
lnðIsc Voc =Rsh Þ þ Im =ðIsc fVoc =Rsho gÞg
3.5
0.8 3.5
3.0
3.0
2.5
2.5
Table 2 Parameters of the ohmic shunt externally introduced to the shunt free multicrystalline solar cell. Parameters
Value
Shunt resistance Shunt area Shunt location
10.2 X 5 mm 1 mm 12 mm away from busbar and 15 mm from edge and by width at exactly the middle of the cell
0.4
0.6
Simulated Experimental
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0 0.0
The simulation approach presented in Section 2 has been experimentally validated by introducing shunt resistance of known value externally to a shunt free Silicon solar cell, and whose dark I-V curve has been measured before and after introducing the external shunt. The shunt has been introduced at a defined location and a defined area. The measured parameters of the solar cell, before and after introducing the external shunt, have been summarized in Table 1. The parameters of the externally introduced shunt have been summarized in Table 2. Since the shunt parameters such as the shunt resistance, location of the shunt, area of the shunt and nature of the shunt are known, the simulation approach based on the distributed diode model has been exploited to estimate the shunt resistance of the shunted area by comparing the simulated dark I-V curve with the measured dark I-V curve. Actual value of shunt resistance and the estimated value of the shunt resistance have been separately simulated in the illuminated model of the solar cell yielding the efficiency and fill factor for the actual and estimated value of shunts. The error in estimation of efficiency by the simulation approach has been 7.33% and in Fill Factor has been 6.55%. Fig. 3 compares the experimental dark I-V curve obtained by the Solar Simulator in the laboratory and the simulated dark I-V curve obtained from the distributed diode model of a shunt free multicrystalline solar cell whose parameters are summarized in Table 3. It can be seen that there is a good degree of agreement between both the curves, which supports the validity of the developed model. The model has been verified with several shunt free and shunted industrial multi-crystalline and mono-crystalline Silicon solar cells. An illustration of the model verification can be seen in Fig. 4, wherein the experimental and simulated dark I-V curves
0.2
0.2
0.4
0.6
0.0 0.8
Voltage (V) Fig. 3. Comparison of experimental and simulated dark I-V curves for a typical shunt free multi-crystalline solar cell of 125 mm 125 mm dimension.
Table 3 Fixed simulation parameters. Parameters
Value
Number of busbars Number of fingers Cell length Cell breadth Sheet resistance Saturation current density Jo Ideality factor n Temperature T Busbar resistivity Finger resistivity Busbar breadth Busbar thickness Finger cross sectional area
2 52 125 mm 125 mm 40 X/sq. 6.39 109 A/cm2 1.5 300 K 6 106 X cm Giaffreda et al. (2014) 6 106 X cm Giaffreda et al. (2014) 2 mm Giaffreda et al. (2014) 23 lm Giaffreda et al. (2014) 1425 lm2 Giaffreda et al. (2014)
for both a shunt free monocrystalline industrial solar cell and a shunted multi-crystalline industrial solar cell of 125 mm 125 mm dimensions have been compared. Fig. 5 presents the comparison of simulated illuminated I-V curves with the actual value of shunt resistance introduced externally and the shunt resistance value estimated by the simulation approach for a shunt free single busbar multi-crystalline Silicon solar cell whose parameters are summarized in Table 4. The maximum deviation between the two curves is 4.54%. The reason for the deviation could be due to the fact that in the experiment the shunt has been externally introduced to the cell by means of an ohmic contact whereas in the model the shunt is internally connected. 4. Simulation The influence of the shunts on the electrical performance of the solar cell will depend on the shunt resistance, the location of the
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0.0
0.1
0.2
0.3
0.4
0.5
0.6
1 Experimental -Shunt free Cell Simulated -Shunt free Cell Expermental - Shunted Cell Simulated -Shunted Cell
0
0
-1
-1
ln[I] (A)
0.7 1
-2
-2
-3
-3
-4 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Cell Current (A)
0.4
0.6
0.8
0.8
0.6
0.6
0.4
0.4 Actual value of shunt resistance Estimated value of shunt resistance
0.2
0.0
0.0 0.2
Load resistance Area normalised shunt resistance = Rsh Ash Irradiance
106 10 X 106 103 X cm2 Fecher et al. (2014)
Shunt position: (a) Under metallization (six positions)
(b) Not under metallization (four positions)
0.4
1–1000 W/m2 1. Busbar shunt under finger 2. 3. 4. 5. 6. 1.
Busbar shunt not under finger Shunt near busbar under finger Middle shunt under finger Edge shunt under finger Corner shunt under finger Shunt near busbar not under finger
2. Middle shunt not under finger 3. Edge shunt not under finger 4. Corner shunt not under finger 103 cm2 Fecher et al. (2014) 102 cm2
investigation. The degradation in performance has been measured in terms of relative power (Power of the shunted solar cell at MPP/ Power of the solar cell having no shunts at MPP). The simulation parameters have been determined in part from the test cells and in part from the literature and are summarized in Table 3. The simulation parameters which are varied have been summarized in Table 5. For each parameter combination in Table 5, the illuminated I-V curves have been simulated by varying the load resistance RL from 1 lX to 10 X. From this set of illuminated I-V curves, the cell’s maximum power Pm and its open circuit voltage Voc, have been determined. 5. Results and discussion
0.2
0.0
Value
Shunt area, Ash:
Fig. 4. Comparisons of experimental and simulated dark I-V curves for a typical shunt free mono-crystalline and a shunted multi-crystalline Silicon solar cell of 125 mm 125 mm dimensions.
0.2
Parameter
-4 0.7
Cell Voltage (V)
0.0
Table 5 Varied simulation parameters.
0.6
Cell Voltage (V) Fig. 5. Comparison of the simulated illuminated I-V curves with the actual (externally introduced shunt resistance) and estimated value (by simulation approach) of shunt resistance for the shunt free multi-crystalline Silicon solar cell whose parameters are described in Table 4.
Table 4 Parameters of the shunt free multi-crystalline solar cell. Parameters
Value
Number of busbars Number of fingers Cell length Cell breadth Saturation current density Jo Ideality factor n Temperature T
1 14 63 mm 38 mm 9.47 E-8 A/cm2 1.98 300 K
shunt, proximity to the metallization, irradiance under which the solar cell is operating, area of the shunt and the operating point of the module in which the solar cell is connected. The most critical factors are the shunt resistance and spatial location of the shunt in the cell and have been considered in the following. Two different irradiance levels have been considered in each of the cases under
5.1. Influence of shunt resistance and shunt location on the solar cell performance The influence of shunt resistance has been investigated by varying its value from a range of 0.001 X which has been reported in the literature (Fecher et al., 2014) to a high value of 10 X considering each significant spatial locations of shunts, at two different irradiance levels of 100 W/m2 and 1000 W/m2. At each significant spatial location of shunt described in Section 2, the relative power has been determined by the model. 5.1.1. Influence on relative power Fig. 6 illustrates the variation of relative power with shunt resistance at 100 W/m2 irradiance considering shunts under metallization. All the six significant different shunt positions have been included in this plot. Fig. 6 reveals that at very low shunt values the relative power reduces to almost zero for all six shunt positions under metallization. At high shunt values near 10 X, the relative power increases to 90%, for all six shunt positions under metallization. In the intermediate region, the relative power increases in an exponential manner with the increase in shunt resistance. At very low values and at very high values of shunt resistance, spatial variation appears to vanish, however there is actually a significant difference in the initial region, which has been brought out by the inset, which have been plotted considering the shunt resistance in the range of 0.001 X and 0.01 X, shown in Fig. 6. At very low values of shunt, the solar cell is severely affected by the shunt and thus power will be reduced dramatically, however the difference in the power produced between different shunt positions still
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Relative Power
0.8
0.01
0.1
1
10 1.0
Busbar Shunt under finger Busbar Shunt not under finger Edge Shunt under finger Corner Shunt under finger Middle Shunt under finger Shunt near busbar under finger
0.6
0.4
0.4
0.002
0.02
0.2
0.004
0.006
0.008 0.01 0.02
0.01
0.00
0.01
0.1
0.0020.002
1
0.0 10 0.00
0.004 0.01 0.0040.0060.008 0.006 0.008 0.01
holds significance. This is a novel finding, since it is generally expected that spatial variation vanishes at very low shunt values (Fecher et al., 2014). Busbar shunt under finger and busbar shunt not under finger causes the greatest degradation in relative power as revealed by Fig. 6. At very high values of shunt resistance, the solar cell is delivering very much close to its full power and in this region; difference due to spatial location vanishes. For the values of shunt resistances which lie between the above mentioned extremes, spatial dependence of shunt losses becomes more obvious as revealed by Fig. 6. A maximum difference of 30% can be detected from the curves, which is close with the findings for the thin film module for different spatial positions of shunts (Fecher et al., 2014). Fig. 7 depicts the variation of relative power with shunt resistance for the shunts under metallization for 1000 W/m2 irradiance. At higher irradiance levels, it is expected that there is reduction in degradation due to shunting, since there is more lateral current flow, and the influence of the shunt diminishes comparatively. Even at very low shunt resistances values, it can be seen that, for all the shunt positions, the cell has a slightly better performance
Relative Power
0.8
1
10 1.0
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0.8
0.6
0.6
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0.14 0.12
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0.10 0.08 0.06 0.04 0.02
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1
0.2 10
Shunt Resistance (Ohm)
Fig. 6. Variation of relative power with shunt resistance under 100 W/m irradiance for six cases of shunts under metallization.
0.1
1
0.01
2
0.01
0.1
0.2
Shunt Resistance (Ohm)
1E-3 1.0
0.01
Edge Shunt not under finger Corner Shunt not under finger Shunt near busbar not under finger Middle Shunt not under finger
0.8
0.6
0.0 1E-3
1E-3 1.0
Relative Power
1E-3 1.0
1
0.002
0.0 10
0.004 0.0060.008 0.01
Shunt Resistance (Ohm) Fig. 7. Variation of relative power with shunt resistance under 1000 W/m2 irradiance for six cases of shunts under metallization.
Fig. 8. Variation of relative power with shunt resistance under 100 W/m2 irradiance for four cases of shunts not under metallization.
at this higher irradiance. For example, in the case of corner shunt under finger, the relative power improves by 20% for very low shunt values due to higher irradiance. At higher shunt values, the relative power reaches almost 100% for all shunt positions under metallization, which means an improvement by almost 10% when compared to the case under 100 W/m2 irradiance. Variation of relative power considering shunts not under metallization is presented in Fig. 8. The plots have been obtained under 100 W/m2 irradiance. It can be seen that, when the shunts are not under metallization, there is much improvement in performance of the solar cell. For the corner shunt there is the greatest improvement in relative power, which is found to be 80% for even very low shunt resistance of 0.001 X. Further, it is revealed by Fig. 8 that even shunts of very low resistances becomes almost harmless when they are located at certain shunt positions such as at the corner of the cell. When shunts are located away from the metallization fingers and busbars, they will be screened by the surrounding sheet resistance and the influence of the shunt decreases. The higher the sheet resistance, the greater will be the shunt screening by the sheet resistance. Considering the shunts not under metallization, shunt near busbar not under finger causes the greatest degradation in relative power as seen in Fig. 8. The inference which can be drawn from the above result is that even proximity of a shunt to the busbar will have a dramatic impact on the influence of the shunt on the electrical performance of solar cell, even if it is not located directly under finger or busbar metallization. The explanation for this impact can be related to the fact that the busbars carries far greater current, being the least resistive path for the current in the solar cell. Hence when a shunt occurs in the close proximity of busbar, the probability of greater current sinking through the shunt increases. Fig. 9 summarises the variation of relative power considering shunts not under metallization under 1000 W/m2 irradiance. In the higher irradiance conditions, there ensues a greater improvement in relative power for all shunt positions. Comparing with shunts under metallization there is an improvement of 90–95% in relative power for the most of the shunts not under metallization, for the lowest values of shunt resistance considered in the present study. Under high irradiances, there is much higher lateral current flow and the presence of busbars and fingers ensures that current through the shunt not under or in proximity of metallization remains low. Loss in relative power reduces dramatically and is in the range of 3–11%.
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Relative Power
1E-3 1.00
0.01
0.1
1
10 1.00
0.96
0.96
0.92
0.92
0.88
0.88
0.84
0.80 1E-3
Edge Shunt not under finger Corner Shunt not under finger Shunt near busbar not under finger Middle Shunt not under finger
0.01
0.1
0.84
1
0.80 10
Shunt Resistance (Ohm) Fig. 9. Variation of relative power with shunt resistance under 1000 W/m2 irradiance for four cases of shunts not under metallization.
Spatial variation between different shunt positions arises due to the difference in the possibility in collection of current at different locations, since the shunt acts as a potential sink for the current. For a shunt at the corner, it has a limited possibility to sink the current since it can collect current only from a 90° collection angle due to its location. For a shunt at the edge, there is an increased possibility to collect the current, since it can have 180° collection angle. For shunts at all the other spatial locations, there is a still higher possibility to collect the current from the surrounding current generation areas since all the other shunt positions such as middle shunt, busbar shunt and shunt near busbar have the maximum possible current collection angle of 360° (Fecher et al., 2014). However, the presence of metallization fingers and busbars in close proximity of the shunt at any shunt positions changes the scenario dramatically. In this case, since the fingers and busbars are collectors of current from the nearby current generation areas, there is current crowding in the metallization areas, which is more pronounced in the busbar areas. Hence, naturally, a shunt in the metallization areas can sink considerable quantity of current resulting in a critical influence on the solar cell performance. Naturally, a shunt even at the corner or the edge of the solar cell under the finger metallization will critically influence the performance leading to considerable degradation in power as demonstrated in Section 5.2, wherein a difference of 80% in relative power between the corner shunt under and not under finger has been observed. A comprehensive understanding of the influence of the critical shunt locations in the industrial Silicon solar cell has been gained by the study. A dramatic improvement in the electrical performance of the industrial Silicon solar cells can be achieved by preventing the occurrence of shunts at the identified critical locations or by isolating them by laser or chemical technique or by removing them.
5.2. Influence of proximity to the metallization on the solar cell performance Influence of metallization has been analysed for two types of common shunts: the edge shunt and the corner shunt. Variation of relative power with shunt resistance is presented in Fig. 10 for the edge shunt under and not under finger metallization. Fig. 11 presents the variation of relative power for the corner shunt under and not under finger metallization. The effect of metallization is really significant at the lowest shunt values for both cases of shunts.
1E-3 1.0
0.8
Relative Power
586
0.01
0.1
1
Edge Shunt under finger Edge Shunt not under finger
10 1.0
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0 1E-3
0.01
0.1
1
0.0 10
Shunt Resistance (Ohm) Fig. 10. Variation of relative power with shunt resistance for the edge shunt under and not under finger.
In the case of edge shunt, a difference of 40% in relative power has been observed, whereas in the case of corner shunt the difference between the two shunts due to presence of finger metallization can rise to 80%, for critically low values of shunt resistance. The influence of proximity to metallization fingers assumes a dramatic role in the context of the above finding. The results obtained leads to the inference that even shunt located at the corner or edge of the solar cell can critically degrade the performance of the solar cell when they are located under finger metallization. 5.3. Influence of irradiance on the solar cell performance It has been evident from the investigation conducted in the present study that the shunt losses depend critically on the shunt resistance, and location of the shunt as well as proximity to the busbar and finger metallization. However, since the current generation in a solar cell depends principally on the illumination intensity, it is expected that the current drawn by the shunt will depend drastically on the irradiance falling on the solar cell. Hence it would be interesting to investigate how the severity of shunt losses will be influenced by the varying levels of irradiance for various positions of shunting. It has been understood from the foregoing study that the local positions of shunts and their proximity to the metallization holds a critical influence on the shunted cell performance. Due to the above reason, it would be interesting to study the effect of change in irradiance on the shunt losses with shunts at various local positions described in detail in Section 2. The local shunt positions considered in the present study are representative regions having equal areas and wherein ohmic shunts of equal shunt resistance have been simulated for different irradiances. Irradiance has been varied from a lower value of 1 W/m2 to the higher value of 1000 W/m2 representing 1 Sun irradiance in series of logical steps. The temperature rise arising due to the higher irradiances has been neglected in the present study. Based on the described model, the shunts have been simulated taking one case at a time for varying irradiances, but keeping the shunt area and the shunt resistance same in each case. In order to keep the total shunt resistance of the shunted area same in each local position of shunting, a shunt resistance of 1 X has been assumed in all the ten cases of shunting considered in the present work. Output power and open circuit voltage has been estimated for varying illumination intensities and compared with the output
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0.01
0.1
1
10 1.0
Relative Power
Corner Shunt under finger Corner Shunt not under finger
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
1E-3
0.01
0.1
1
0.0 10
Shunt Resistance (Ohm) Fig. 11. Variation of relative power with shunt resistance for the corner shunt under and not under finger.
power and open circuit voltage for the cell having no shunts. For the purpose of comparison, a relative output power ([Output power of the shunted solar cell/Output power of shunt free solar cell at the same irradiance]) and a relative open circuit voltage ([Open circuit voltage of the shunted solar cell/Open circuit voltage of the shunt free solar cell at the same irradiance]) have been defined. Fig. 12 illustrates the variation of relative open circuit voltage for four cases of local positions of shunts considered in the present study. Based on the results, it is apparent that the spatial positions of shunts are very much significant while considering the shunt related losses, particularly at low irradiance levels. Variation in relative open circuit voltage from 35% and up to a maximum of even 55% between different shunt positions for the same shunt resistance and shunt area have been observed from the simulation results which reveals the critical importance of shunt positions. The trend also reveals that at high irradiance levels near to 1 Sun (1000 W/m2), the difference in shunt losses gradually reduces to a minimum, since the impact of shunt itself would reduce in comparison to the low irradiance case. At very low irradiance levels, that is say less than 10 W/m2, also there is a saturation
1
10
100
Relative Open Circuit Voltage
1.0
1000 1.0
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0.4 Corner Shunt not under finger Edge Shunt not under finger Middle Shunt not under finger
0.2
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100
region, since the open circuit voltage reduces to very low levels. However, there is actually a difference in performance between different shunt positions even at these low irradiance levels though they do not appear so pronounced, since the photovoltaic generation itself is very low due to very low irradiance. For example, for a shunt at corner not under finger, the relative open circuit voltage is almost five times that of the busbar shunt under the finger at 1 W/m2 irradiance. At this point, in order to understand the significance of the combined impact of proximity to metallization and shunt positions, shunts under metallization and not under metallization have been considered separately in the following. Fig. 13 visualizes the variation of relative open circuit voltage with varying irradiance levels for the four cases of shunts under metallization. From Fig. 13, the real significance of the spatial dependence of shunts which are all located under metallization can be understood. At an irradiance level between 10 W/m2 and 100 W/m2, there is an almost 35% difference between two cases of shunts under metallization, which can be significant. For the shunts not under metallization, as shown in Fig. 12, the difference in relative open circuit voltage between the different shunt positions are more accentuated and apparent. Fig. 14 illustrates the variation of relative power at MPP for three cases of shunts not under metallization for low irradiance levels. It reveals that there can be a difference of more than 40% between different positions of shunts located not under metallization for the shunt resistance considered in the present study. This is an appreciably large value since, since an increase in output power in this range can be of considerable significance. Further since, the actual shunt value may reach even value in the range of 0.001 X in some cases, the effect may be accentuated to critical levels. Considering the shunt positions under and not under metallization, the maximum difference which has been observed is 70% in relative open circuit voltage at low irradiances. Fig. 15 visualizes the variation of relative power at MPP for the four cases of shunts under metallization for low irradiance levels. It reveals that there can be a difference of more than 25–30% between different cases of shunts located under metallization for the shunt resistance considered in the present study. At very low and high irradiance levels, a saturation region has been observed for both cases of shunting when considered separately. Of course, the difference in power loss between the shunts under metallization and those not under metallization still holds well, though to a lesser degree. A maximum difference of 60% in
0.2
0.0 1000
Irradiance (W/sq.m.) Fig. 12. Variation of relative open circuit voltage with irradiance for three local positions of shunting not under metallization.
1
10
100
1.0
Relative Open Circuit Voltage
1E-3 1.0
Corner Shunt under finger Busbar Shunt under finger Busbar Shunt not under finger Near Busbar Shunt nder finger
0.8
1000 1.0
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Irradiance (W/sq.m.) Fig. 13. Variation of relative open circuit voltage with irradiance for four cases shunts under metallization.
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1.0 Corner Shunt not under finger Edge Shunt not under finger Middle Shunt not under finger
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100 200 300 400 500 600 700 800 900 1000 1100 1.0 Higher Shunt area 0.1 sq. cm Lower Shunt area 0.01 sq.cm
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Irradiance (W/sq.m)
relative power has been observed between the corner shunt not under finger and the busbar shunt under finger at low irradiance condition. The study reveals that the irradiance level at which the solar cell operates holds a key and critical role in determining the shunt losses along with the spatial locations of shunts. 5.4. Influence of area of the shunt on the solar cell performance The influence of shunt area has been investigated by keeping the absolute shunt resistance constant in all cases of shunting considered, while varying the shunt area and area normalised shunt resistance. Fig. 16 illustrates the variation of relative power with irradiance for two different shunt areas, however having the same absolute shunt resistance. Clearly, the greater area of the shunt results in more loss for the same absolute shunt resistance. The main reason for this effect can be traced to the fact that increased shunt area brings the edge of the shunt area near to metallization fingers compared to a smaller shunt area. A second reason is that most of the current in the shunt flows through the edges and not through the centre (Fecher et al., 2014). A greater perimeter results in a larger area of influence.
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10
100
1.0 Corner Shunt under finger Busbar Shunt under finger Busbar Shunt not under finger Near Busbar Shunt nder finger
Relative Power
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1000 1.0
Fig. 16. Variation of relative power with irradiance for two different shunt areas and having the same absolute shunt resistance.
0 1.0
100 200 300 400 500 600 700 800 900 1000 1100 1.0 Higher Shunt area 0.1 sq. cm Smaller Shunt Area 0.01 sq.cm
Relative Open Circuit Voltage
Fig. 14. Variation of relative power at MPP with illumination for three cases of shunts not under metallization.
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Irradiance (W/sq.m) Fig. 17. Variation of relative open circuit voltage with irradiance for two different shunt areas and having the same absolute shunt resistance.
Fig. 17 summarises the variation of relative open circuit voltage with irradiance for two different shunt areas. In this case also, the greater shunt area results in greater loss in open circuit voltage.
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5.5. Influence of sheet resistivity on the shunted cell performance 0.6
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Irradiance (W/sq.m.) Fig. 15. Variation of relative power at MPP with irradiance for the four cases of shunts under metallization.
When shunts are not under metallization, it is expected that there will be considerable influence due to sheet resistivity on the shunting effect. It would be interesting to quantify the influence of sheet resistivity on the performance of a cell in the presence of shunts. A simple method of doing it is by the calculation of the cell shunt resistance while sheet resistivity is varied over a practical range of values. The said calculation has been done and result obtained which reveals an interesting trend. Fig. 18 presents the variation of cell shunt resistance with the sheet resistivity for (a) edge shunt not under finger, (b) middle shunt not under finger, (c) corner shunt not under finger, and (d) shunt in close proximity of busbar not under finger. The result reveals that sheet resistivity influences the cell shunt resistance to a considerable extent when
P. Somasundaran, R. Gupta / Solar Energy 139 (2016) 581–590
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40 Corner Shunt not under finger Edge Shunt not under finger Middle Shunt not under finger Shunt near busbar not under finger
Cell Shunt Resistance(Ohm)
35 30
100 110 40 35 30
589
increased influence region with increased area of shunt which brings the region close to more fingers. A comprehensive understanding of the criticality of significant shunt locations in the industrial solar cell has been gained by the study. A dramatic improvement in the electrical performance of the industrial solar cells can be achieved by preventing the occurrence of shunts at the identified critical locations or by isolating them by laser or chemical technique or by removing them.
25
25
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20
15
15
Conflict of interest
10
10
5
5
The authors declare that there is no conflict of financial/personal interest or belief that could affect the objectivity of the research work presented in the submitted paper and there is no conflict of interest regarding the publication of this paper.
0 0
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0 100 110
Sheet Resistivity (Ohm/sq.) Fig. 18. Variation of cell shunt resistance with the sheet resistivity of the solar cell for shunts not under metallization: (a) corner shunt not under finger, (b) edge shunt not under finger, (c) middle shunt not under finger, and (d) shunt near busbar not under finger.
shunts are not under metallization. Thus the increased sheet resistance would lead to increased shunt screening leading to an improved cell performance in the presence of shunts. 6. Conclusions The paper presented a simple distributed diode model to simulate the electrical behaviour of an industrial Silicon solar cell having an ohmic shunt. The chosen solar cell has the dimensions of 125 mm2. Parameters of the chosen solar cell represent typical values for test cells. The simulation approach has been experimentally validated by connecting an external shunt of known parameters and comparing the degradation in efficiency and fill factor for actual value of the shunt resistance and estimated value of shunt resistance. The shunt resistance, irradiance, shunt location and shunt size have been systematically varied and impact on the solar cell performance has been evaluated. Important finding is that, the performance depends critically on the shunt position and proximity to the metallization to the extent that the difference in loss in the relative power can be 80% between different shunt positions at 100 W/m2 irradiance. Comparing with shunts under metallization, there is an improvement of more than 90% in relative power for the most of the shunts not under metallization, for the lowest values of shunt resistance considered in the present work. In general, it was found that the proximity to the busbar and finger metallization and the shunt position holds the key to the impact the shunt will have on the solar cell performance in addition to the resistance of shunt itself. The underlying mechanism could be the reduced current screening due to the enhanced current flow when the shunt is under the busbar or finger metallization. The irradiance has been varied over a wide range, that is from 1 to 1000 W/m2, and variation in relative power and relative open circuit voltage have been analysed considering all the significant shunt positions. A maximum difference of 60% in relative power and 70% in relative open circuit voltage has been found between the corner shunt not under finger and the busbar shunt under finger at low irradiance condition. A deeper understanding of the irradiance dependence of shunt losses has been gained by the study. Study of area dependence revealed that increase in shunt area for the same absolute shunt resistance results in greater loss in power and open circuit voltage. The underlying reason could be the
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