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Comparison of potential-induced degradation (PID) of n-type and p-type silicon solar cells
Energy 161 (2018) 266e276
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Comparison of potential-induced degradation (PID) of n-type and ptype silicon solar cells a, c Jan Slamberger , Michael Schwark a, Bas B. Van Aken b, Peter Virti c c, * a
AIT Austrian Institute of Technology GmbH, Donau-City-Strasse 1, A-1220 Vienna, Austria ECN Solar Energy, PO Box 1, 1755 ZG Petten, Netherlands c University of Maribor, Faculty of Energy Technology, Hocevarjev trg 1, SI-8270 Krsko, Slovenia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 March 2018 Received in revised form 14 July 2018 Accepted 18 July 2018 Available online 19 July 2018
Potential-induced degradation (PID) of photovoltaic (PV) modules is one of the most severe types of degradation, where power losses on system level may even exceed 30%. The PID process depends on the strength of the electric field, the temperature, the relative humidity, conductive soiling, time and the PV module materials. For p-type cells, it has been established that the decrease of the shunt resistance, due to migration of sodium ions across the n/p junction is the root cause of the degradation. On the other hand, it has recently been confirmed for n-type cells that the PID occurs due to an increase in recombination as charges are driven to the anti-reflection (AR) coating/emitter interface. In this paper, we present the comparison between PID of p-type and n-type crystalline silicon (c-Si) solar cells and their progression of PID. The time evolution of PID is studied by light and dark I-V curve measurements, electroluminescence images and progressions of the one- and two-diode equivalent model parameters, viz. photocurrent, 1st and 2nd diode reverse saturation currents, 1st and 2nd diode ideality factors, shunt resistance and series resistance. © 2018 Published by Elsevier Ltd.
Keywords: Photovoltaic (PV) systems Potential-induced degradation (PID) Crystalline silicon (c-si) solar cells n-type p-type
1. Introduction In PV power plants, PV modules are connected in series and therefore the system voltage can reach ±600 to ±1500 V. Common transformerless PV inverters do not allow grounding of the electronically active part and therefore one part of the string of modules has a positive and the other part a negative voltage compared to the grounded frames. PID is the power loss caused by an applied high voltage difference between the active solar cells and the frame of the PV modules. It has been reported in many studies [1e4], that p-type cells can be affected by PID at a negative voltage potential, while n-type cells can be affected with both positive and negative voltage, depending on topology [5,6]. Beside the system voltage, the PID is strongly dependent on the temperature and relative humidity. There is a variety of proposals for modelling the PID at ptype PV modules, which are mainly interpolations to polynomial or exponential functions [7e9]. However, the parameters of those models have to be adapted to every different PV modules and they are not universally applicable.
* Corresponding author. E-mail address: [email protected] (P. Virti c). https://doi.org/10.1016/j.energy.2018.07.118 0360-5442/© 2018 Published by Elsevier Ltd.
The main suspects for the PID mechanism of p-type solar cells are sodium ions (Naþ), which drift due to the negative electric field (electric field is oriented from the grounded frame of PV module to the PV cell electrical connection with negative potential according to the grounded frame) from the sodium-rich glass through antireflection (AR) coating and penetrate crystal defects crossing the p-n junction. This leads to the reduction of the shunt resistance Rsh in the diode model of the solar cell and the increase of reverse saturation current and the diode ideality factor due to the recombination in the space-charge region (non-conducting layer between p-doped and n-doped semiconductor). In the I-V characteristics, the significant drop of fill factor is seen. In n-type cells, it was shown in Ref. [5] that the drift of Naþ ions is not the reason for power loss under high system voltage. The presumed PID mechanism in n-type solar cells is the surface polarization, where there are either negative or positive charges (depending on topology) accumulated within the SiNx stack that act as passivation and anti-reflection (AR) coating. As described in Ref. [6], in the n-PERT (passivated emitter, rear totally diffused) c-Si solar cells, due to the negative electric field, the positive charges increase the recombination rate by forcing the emitter surface to go into depletion. This makes it harder for holes to reach the metallisation grid and as they spend more time/distance, the probability
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of recombining increases. The result is a significant drop in the short-circuit current and open circuit voltage, while the fill factor decreases only slightly. The dark I-V characterization was reported to be an appropriate method to monitor PID in situ during the stress test [10e12]. The main disadvantage of dark I-V characterization is that the serial resistance Rsh is slightly lower compared to light I-V characterization [11] and obviously, it is not possible to determine the photocurrent out of it. The other possibility is to measure light I-V characteristics. This has the disadvantage to stop the stress test, to decrease the temperature of the module to 25 C for measuring and start the stress test again at 60 C or 85 C. The adjustment of the temperature from PID-to IV-conditions is done either with or without stress voltage. This leads to either additional degradation or regeneration at the test temperature, where degradation process occurs when a stress voltage is applied and regeneration when there is no stress voltage. Even more, after achieving the test temperature and relative humidity of 85%, it is advisable to wait 12e24 h (stabilization phase) before turning on the stress voltage, otherwise, the PID will be much faster due to the formation of condensation on glass surface [4]. In the stabilization phase at test temperature, a PV module already affected by PID may regenerate for several percentages. The characteristics of the solar cells could be well described with single- or double-diode equivalent current models. The singlediode model is good for first approximations but for a detailed research, the models with two or more diodes are needed. The double-diode model has for the first time been described in the year 1963 [13], where the first diode represents diffusion current and the second diode the recombination current and has been well established in the past years [8,9,11,14]. Both models are nonlinear and therefore a numerical approach for the determination of the parameters (photocurrent, 1st and 2nd diode reverse saturation currents, 1st and 2nd diode ideality factors, shunt resistance and series resistance) is necessary. In the past, the fitting methods with least squares were mostly used for this determination. However, today some new approaches exist with an equation in explicit form of the double-diode model [15,16]. These new approaches include some simplifications or bring in additional parameters. As an alternative to already-published research, where only the changes of parameters of single- or double-diode model before and after PID stress test are presented [2], we present in this paper for the first time the progression of the PID effect during the stress test at different types of c-Si solar cells described with the parameters of the single- and double-diode model. The parameters of the equivalent circuit models were defined with the fitting to the measured dark curves data, using the nonlinear least-squares fitting method. Authors in Ref. [9] presented parameters changes of double-diode model during the stress test but only for one type of solar cells and with shorter time intervals of measurements. With high time resolution and longer period of measurements we have clearly shown parameters trends. Reference [4] also presents the progression of PID effect during the stress test but only for one shunt resistance of double-diode model at significantly shorter total testing time. Moreover, this paper shows for the first time side by side comparison between PID of p-type and n-type modules presented by light I-V curve and characteristics, electroluminescence images and progressions of parameters of single- and double-diode equivalent models.
compare the progression of the PID and characteristics of the cells. The first two types of cells were the commercial p-type based multicrystalline Si solar cells, where the cells of the first type were cut from the edge or corner of the silicon block and the cells of the second type were cut from the centre of the block. The cells cut from the edge or corner have compared to the cells cut from the centre a higher rate of impurity and therefore they were suspected to present a higher rate of degradation. The third and fourth types of the cells were n-type based front junction single crystalline Si solar cells - n-PERT. The fourth type had additionally a modified boron emitter and dielectric layer as published in Ref. [6]. All test cells have been laminated into single-cell mini-modules using a commercial glass, EVA encapsulant and back sheet. Aluminium profiles were pressed to the glass on two sides to simulate the real frames (Fig. 1). 2.2. PID stress test and measurement setup The high voltage stress test with 1000 V between the module contacts and the frame (Fig. 2) has been processed in a climatic chamber at 85% relative humidity at two different temperatures (60 C and 85 C). 60 C is proposed by the standard IEC 62804 as a minimal stress temperature, whereby many research institutes use also 85 C, where the degradation speeds up. Before and after each test, the I-V characteristics have been measured with a Pasan flash tester, class AAA (Spectral match to AM1.5 is between 0.75 and 1.25, non-uniformity of irradiance is lower than 2%, short-term instability of irradiance is lower than 0.5% and long-term instability of irradiance is lower than 2%) at standard test conditions (STC) and at low irradiance. The PID degradation at low irradiance is normally 2 to 5 times higher due to the same impact of shunt resistance at lower photocurrent. The measurement at low irradiance is an appropriate method to detect the PID already in the early stage. Additionally, the electroluminescence images have been captured at 9 A (~Isc) and 1 A (~0.1 Isc). Moreover, the in situ dark I-V characteristics measurements with the frequency of 10 min have been performed to monitor the progression of the degradation. Fig. 3 shows the in situ measurement setup and climate chamber with 4 test samples. The samples have been connected to separate high voltage channels. 2.3. Analysis In the post-processing phase, the analysis of the progression of I-V characteristics has been made. Additionally, the single-diode (Fig. 4) and double-diode (Fig. 5) models with concentrated parameters have been fitted to the measured dark I-V characteristics. The single-diode and double-diode models for solar cell are described with (1) and (2) [13], where Iph is the photocurrent (electric current produced by a photoelectric effect - ideal current source); ID, ID1 and ID2 the currents flowing through the diodes D, D1
2. Methods 2.1. Fabrication of test samples For this study, four different types of cells have been used to
267
Fig. 1. Test sample front view (left), and back view (right).
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and D2; Io, Io1 and Io2 the reverse saturation currents of diodes D, D1 and D2; n, n1, n2, the ideality factors of diodes D, D1 and D2; Rs the series resistance; Rsh the shunt resistance; I the output current; V the output voltage; T the temperature in Kelvin; q the electron charge ð1:60217646$1019 CÞ and k the Boltzmann's constant ð1:3806503$1023 J=KÞ.
qðVþIRs Þ V þ IR s I ¼ Iph ID IRsh ¼ Iph Io eð nkT Þ 1 Rsh I ¼ Iph ID1 ID2 IRsh ¼ Iph Io1 e
qðVþIRs Þ n1 kT
1
!
Io2 e
qðVþIRs Þ n2 kT
! 1
(1)
V þ IRs Rsh (2)
Fig. 2. Connection of PV module to high voltage source.
For the determination of the parameters of nonlinear models, the Matlab's function lsqnonlin, which is a part of the Optimization Toolbox™, has been used. This function is able to solve nonlinear least-squares problems with searching of the minimum of the sum of square residuals of the nonlinear fitting problems, defined with (3), where r is residual, xk independent variable, yk function of xk and a0, …an fit parameters. As a result, it returns the vector of parameters values and additionally squared norm of the residual (SNR), which we used to compare the quality of fit.
r¼
X ðyk f ða0 ; …an ; xk ÞÞ2
(3)
k
As presented in Ref. [8], the Rs does not change with PID, therefore, it has been set as a constant. Moreover, in p-type cells, the changes of Io1 and n1 comparing to Io2 and n2 during the PID progress are negligible and therefore they have been also set as constants. Similarly, in n-type cells, the Rsh and n2 have been set as constants. 3. Results and discussion Fig. 3. Climate chamber and measurement setup.
Fig. 4. Single-diode model of solar cell.
3.1. I-V characteristics Figs. 6e9 show the I-V curves of the different cell types before (blue line) and after (red line) PID stress tests performed at 60 C (a) and 85 C (b), whereby the Tables 1e4 present the value of I-V characteristics at standard test conditions (STC) and at low irradiance (185 W/m2, 25 C, 1,5AM). There is no pass/fail criteria in the current version of standard (IEC 62804) for testing the PID, but anyway, a lot of researchers and manufacturers use the term “PID free” if the power loss at STC is less than 5%. At the same time the power loss at low irradiance could be up to 4 times higher. In this study, the PID effect could be seen by all tested samples, whereby the degradation was low for cell types II and III (<%5 @ STC). But even those cells show more than 10% power loss at low irradiances. For cell type IV, a significant drop in short-circuit current could be detected, whereby only a small change of fill factor appeared, compared to the cell type I after the PID stress test at 85 C, where the main change is the decrease of shunt resistance and a corresponding significant drop in fill factor. 3.2. Electroluminescence
Fig. 5. Double-diode model of solar cell.
The PID losses could be well seen from electroluminescence (EL) images by comparing the images before and after PID stress test under the same conditions. Figs. 10e13 show side by side comparison of EL images before and after PID with the two different
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(a)
269
(b)
Fig. 6. (a) I-V curves of cell type I at STC before and after PID stress test (60 C, 85% RH, 1000 V and 148 h). (b) I-V curves of cell type I at STC before and after PID stress test (85 C, 85% RH, 1000 V and 60 h).
(a)
(b)
Fig. 7. (a) I-V curves of cell type II at STC before and after PID stress test (60 C, 85% RH, 1000 V and 148 h). (b) I-V curves of cell type II at STC before and after PID stress test (85 C, 85% RH, 1000 V and 60 h).
(a)
(b)
Fig. 8. (a) I-V curves of cell type III at STC before and after PID stress test (60 C, 85% RH, 1000 V and 80 h). (b) I-V curves of cell type III at STC before and after PID stress test (85 C, 85% RH, 1000 V and 60 h).
currents. Firstly, the current of 9 A (roughly of Isc @STC) and secondly the lower current of 1 A (roughly of 10% of Isc @ STC) have been sent through the module. The dark parts present lower local efficiency of the cell. The analysis of EL images at 9 A before and after the PID stress test at 60 C shows almost no changes in efficiency for cell types I, II and III, with homogeneous loss of efficiency by cell type IV, which is also comparable to the results of I-V characteristics. Meanwhile, from the EL images taken at 1 A before and after the PID stress at
60 C, in addition to cell type IV, homogeneous loss of efficiency by cell types I and II has been detected. Furthermore, the analysis of EL images at 9 A before and after the PID stress test at 85 C shows the local efficiency losses by cell types I and III and again homogeneous losses by cell type IV. EL images of cell type II show no changes in efficiency. Additionally, the EL image of cell type I taken after the PID test at 85 C at 1 A shows significant loss of efficiency, where no signal could be detected at the same exposure time as by image taken before PID stress test.
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(a)
(b)
Fig. 9. (a) I-V curves of cell type IV at STC before and after PID stress test (60 C, 85% RH, 1000 V and 2.5 h). (b) I-V curves of cell type IV at STC before and after PID stress test (85 C, 85% RH, 1000 V and 90 h).
Table 1 The parameters of I-V characteristics of cell type I at STC and low irradiance (185 W/m2) before and after PID stress test at 60 C (148 h) and 85 C (60 h).
1000 W/m
2
185 W/m2
Initial After PID Initial After PID Initial After PID Initial After PID
@ 60 C
@ 85 C @ 60 C @ 85 C
Pmax [W]
Isc [A]
Uoc [V]
Imp [A]
Ump [V]
FF [%]
3.86 3.70 3.84 2.28 0.72 0.64 0.71 0.15
8.69 8.68 8.67 8.40 1.64 1.61 1.64 1.58
0.617 0.613 0.616 0.590 0.574 0.568 0.567 0.309
8.04 7.77 8.00 5.32 1.51 1.46 1.51 0.87
0.481 0.477 0.480 0.429 0.473 0.435 0.471 0.168
72.1 69.6 71.9 46.0 76.9 69.3 76.4 29.9
DPmax [%] 4.1 40.6 12.3 78.9
Table 2 The parameters of I-V characteristics of cell type II at STC and low irradiance (185 W/m2) before and after PID stress test at 60 C (148 h) and 85 C (60 h).
1000 W/m
2
185 W/m2
Initial After PID Initial After PID Initial After PID Initial After PID
@ 60 C @ 85 C @ 60 C @ 85 C
Pmax [W]
Isc [A]
Uoc [V]
Imp [A]
Ump [V]
FF [%]
3.96 3.85 3.96 3.91 0.73 0.62 0.74 0.70
8.80 8.78 8.79 8.78 1.66 1.63 1.66 1.66
0.622 0.619 0.621 0.621 0.574 0.574 0.574 0.573
8.14 7.98 8.14 8.03 1.52 1.41 1.54 1.48
0.486 0.483 0.487 0.486 0.478 0.442 0.478 0.475
72.4 70.9 72.6 71.7 76.5 66.3 77.0 73.2
DPmax [%] 2.8 1.3 15.1 5.4
Table 3 The parameters of I-V characteristics of cell type III at STC and low irradiance (185 W/m2) before and after PID stress test at 60 C (80 h) and 85 C (60 h).
1000 W/m2
185 W/m2
Initial After PID Initial After PID Initial After PID Initial After PID
@ 60 C @ 85 C @ 60 C
@ 85 C
Pmax [W]
Isc [A]
Uoc [V]
Imp [A]
Ump [V]
FF [%]
4.47 4.44 4.39 4.22 0.84 0.82 0.80 0.71
9.33 9.35 9.30 9.17 1.76 1.76 1.75 1.71
0.649 0.647 0.645 0.636 0.603 0.603 0.598 0.580
8.66 8.64 8.76 8.43 1.66 1.62 1.61 1.57
0.516 0.510 0.512 0.501 0.506 0.503 0.499 0.452
73.8 73.4 73.1 72.4 79.1 76.6 76.8 71.6
The comparison of EL images of p-type and n-type cells shows the different degradation effects due to the PID. In the case of ptype cells, where the main degradation mechanism is the penetration of Naþ ions and consequently a reduction of shunt resistance, the local defects at high-current can be clearly seen. Furthermore, out of low-current EL images, the PID effects could already be detected in early stage. On the other hand, in the case of n-type cells, where the main degradation mechanism is the surface
DPmax [%] 0.7 3.9 2.4 11.3
polarization and therefore reduction of Isc and Uoc, the homogenous loss over the whole cell can be seen. 3.3. Single-diode parameters The progressions of the single-diode model's parameters during the PID stress tests are presented in Figs. 14e17. For all cell types, the series resistance was set to be a constant, determined from dark
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Table 4 The parameters of I-V characteristics of cell type IV at STC and low irradiance (185 W/m2) before and after PID stress test at 60 C (2.5 h) and 85 C (90 h).
1000 W/m2
185 W/m2
Initial After PID Initial After PID Initial After PID Initial After PID
@ 60 C @ 85 C
@ 60 C @ 85 C
Pmax [W]
Isc [A]
Uoc [V]
Imp [A]
Ump [V]
FF [%]
4.59 3.82 4.59 3.87 0.85 0.66 0.84 0.65
9.22 8.42 9.20 8.47 1.75 1.65 1.74 1.67
0.649 0.609 0.648 0.612 0.606 0.563 0.603 0.564
8.67 7.75 8.66 7.81 1.65 1.41 1.65 1.41
0.529 0.492 0.529 0.495 0.513 0.462 0.511 0.464
76.6 74.4 76.9 74.6 80.0 70.8 80.2 69.1
EL @ 9 A 60 s After PID
16.8 15.7 23.4 22.6
EL @ 1 A 240 s Before PID
After PID
PID @ 85 °C, 60 h
PID @ 60 °C, 148 h
Before PID
DPmax [%]
Fig. 10. Electroluminescence images of the cell type I.
EL @ 9 A 60 s After PID
EL @ 1 A 240 s Before PID
After PID
PID @ 85 °C , 60 h
PID @ 60 °C , 148 h
Before PID
Fig. 11. Electroluminescence images of the cell type II.
I-V curves taken before the start of PID stress test. For all cell types, the diode reverse saturation current and diode ideality factor are increasing and the shunt resistance is decreasing, whereby the changes of cell types I and II have significantly slower progress as the changes of cell types III and IV. Moreover, for cell type IV, the degradation has reached the final stage after a couple of hours, while cell types I, II and III did not reach the final stage after more than a dozen hours and will continue with the time.
3.4. Double-diode parameters The double-diode equivalent current circuit model, compared to single-diode model, describes better the physics [13] of the real solar cell, where the first diode represents diffusion current and the second diode the recombination current. At p-type cells, the progression of parameters Io1, n1 and Rs has shown no significant changes, which could be related to PID. Similarly, in n-type cells, the
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EL @ 9 A 15 s
EL @ 1 A 60 s
After PID
Before PID
After PID
PID @ 85 °C , 60 h
PID @ 60 °C , 80 h
Before PID
Fig. 12. Electroluminescence images of the cell type III.
EL @ 9 A 15 s After PID
Before PID
After PID
PID @ 85 °C , 90 h
PID @ 60 °C , 2.5 h
Before PID
EL @ 1 A 60 s
Fig. 13. Electroluminescence images of the cell type IV.
n
Rsh [ ]
PID @ 85 °C
PID @ 60 °C
Io [A]
Fig. 14. Progression of single-diode parameters during the PID stress test - type I.
SNR
J. Slamberger et al. / Energy 161 (2018) 266e276
n
Rsh [ ]
SNR
PID @ 85 °C
PID @ 60 °C
Io [A]
273
Fig. 15. Progression of single-diode parameters during the PID stress test - type II.
n
Rsh [ ]
SNR
PID @ 85 °C
PID @ 60 °C
Io [A]
Fig. 16. Progression of single-diode parameters during the PID stress test - type III.
n
Rsh [ ]
SNR
PID @ 85 °C
PID @ 60 °C
Io [A]
Fig. 17. Progression of single-diode parameters during the PID stress test - type IV.
progression of parameters Io2, Rsh and Rs has shown no significant correlation with PID related changes. Those parameters were set as constants, to minimise the noise in the progression of the PID related parameters. Those constants were determined from the
dark I-V curves taken before the start of PID stress test. The progressions of the variable double-diode model's parameters during the PID stress tests are presented in Figs. 18e21. Also, like the single-diode model, in the double-diode model, the diode reverse saturation current and diode ideality factor are increasing and the shunt resistance is decreasing for cell types I and II. In this case, the parameters of the second diode are changing and parameters of the first diode are set to constants. Furthermore, compared to the single-diode model, the quality of the doublediode fits at strongly PID effected p-type cells is almost constant and much better. For cell types III and IV, the changes of reverse saturation current and ideality factor of the first diode of the double-diode model are comparable to those of single-diode model. Additionally, the shunt resistance of double-diode model was set to constant and the reverse saturation current of the second diode is time-dependent. Comparable to the reverse saturation current of the first diode, the reverse saturation current of the second diode has much higher values and moreover, the progression is much slower and the degradation by cell type IV does not end after a couple of hours.
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n2
Rsh [ ]
SNR
PID @ 85 °C
PID @ 60 °C
Io2 [A]
Fig. 18. Progression of double-diode parameters during the PID stress test - type I.
n2
Rsh [ ]
SNR
PID @ 85 °C
PID @ 60 °C
Io2 [A]
Fig. 19. Progression of double-diode parameters during the PID stress test - type II.
n1
Io2 [A]
SNR
PID @ 85 °C
PID @ 60 °C
Io1 [A]
Fig. 20. Progression of double-diode parameters during the PID stress test - type III.
Furthermore, an extra stress test with four modules of cell type IV was performed to investigate the progression of the photocurrent during the PID test. The modules were connected to the high
voltage source with the different time delays and disconnected at the same time. Before and after this test, the light I-V characteristics were measured and the parameters for the double-diode model
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n1
Io2 [A]
SNR
PID @ 85 °C
PID @ 60 °C
Io1 [A]
275
Fig. 21. Progression of double-diode parameters during the PID stress test - type IV.
were determined. Fig. 22 presents the progression of normalized photocurrent during the PID stress test, described with (4), where Iph;n is normalized photocurrent, Iph;min minimal photocurrent and Iph;max maximal (initial) photocurrent.
I ph;n ¼
I ph I ph;min I ph;max I ph;min
(4)
The progression of the photocurrent could be well described with an Arrhenius-like fit equation (5), where t is time and b, t fit parameters. The values of the fit parameters for cell type IV are b ¼ 2.144 and t ¼ 0.8147 h. t b
Iph;n ¼ eðtÞ
(5)
The form of the progression seems to be similar to reverse saturation current of the first diode with the opposite sign. Compared to cell type IV, there is no significant change of the Isc (Tables 1e3) at cell types I, II and III, where the Iph could be set as a constant.
4. Conclusion This work presents a comparison between the PID mechanisms of p-type and n-type c-Si solar cells. The reasons for PID effect by p-
type cells is the local shunting, caused by penetration of Naþ ions in p-n junction of the cells, whereby the reason for PID effect by ntype cells is the surface polarization on the surface of AR coating, where positive/negative charges recombine with the electrons and holes instead of being collected by cell's p-n junction. The degradation can reach several dozen percents for both cell types, while in the case of n-type cells, the degradation reaches a stable state very fast. In the case of p-type cells, the degradation proceeds further because of a continuous increase of the amount of Naþ in the wafer and can reach >90% losses on the module level. Because of different phenomena appearing in p- and n-cells, also the first indicators showing on PID are different. The form of I-V curves by p-type cells shows a reduction in shunt resistance and fill factor, whereas the main indicators for n-type cells are significant reduction of shortcircuit current and open circuit voltage. The comparison of EL images at current near to Isc at STC shows local efficiency losses by ptype cells and homogeneous efficiency losses by n-type cells. Furthermore, the comparison of progression of double diode parameters shows that the main degradation indicators by p-type cells are the decrease of the shunt resistance and the increase of the reverse saturation current and the ideality factor of the second diode. In the case of the n-type cells, the main degradation indicators are the increase of the reverse saturation current and the ideality factor of the first diode, the increase of the reverse saturation current of the second diode and the significant reduction of photocurrent. The photocurrent could not be determined in situ by dark I-V measurement, but has to be determined out of the light I-V curves. Acknowledgements This work was performed as part of the INFINITY project. A project of the Austrian “Energy Research Program” funded by the Austrian Climate and Energy Fund and the Austrian Research Promotion Agency (FFG). Both are gratefully acknowledged. The authors would like to thank Carinthian Tech Research (CTR) for donating the p-type cells and the colleagues at ECN e Solar Energy and the Photovoltaic Systems team at AIT for their support and making this study possible. References
Fig. 22. Progression of photocurrent (normalized) during the PID stress test at 60 C Type IV.
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J. Slamberger et al. / Energy 161 (2018) 266e276 incomplete recovery of shunt resistance and quantum efficiency losses. IEEE J Photovoltaics 2015;5(6):1540e8. Lausch D, et al. Potential-induced degradation (PID): introduction of a novel test approach and explanation of increased depletion region recombination. IEEE J Photovoltaics 2014;4(3):834e40. Koentopp MB, Krober M, Taubitz C. Toward a PID test standard: understanding and modeling of laboratory tests and field progression. IEEE J Photovoltaics 2016;6(1):252e7. Hara K, Jonai S, Masuda A. Potential-induced degradation in photovoltaic modules based on n-type single crystalline Si solar cells. Sol Energy Mater Sol Cells 2015;140:361e5. Stodolny MK, et al. PID- and UVID-free n-type solar cells and modules. Energy Procedia 2016;92:609e16. Taubitz C, Schütze M, Koentopp MB. Towards a kinetic model of potentialinduced shunting. In: Proc. 27th European photovoltaic solar Energy conference and exhibition; 2012. p. 3172e6. Hacke P, et al. Testing and analysis for lifetime prediction of crystalline silicon PV modules undergoing degradation by system voltage stress. IEEE J Photovoltaics 2013;3(1):246e53. Spataru S, Hacke P, Sera D, Packard C, Kerekes T, Teodorescu R. Temperaturedependency analysis and correction methods of in situ power-loss estimation for crystalline silicon modules undergoing potential-induced degradation stress testing. Prog Photovoltaics Res Appl 2015;23:1536e49. no. January
2015. [10] Luo W, et al. In-situ characterization of potential-induced degradation in crystalline silicon photovoltaic modules through dark I-V measurements. IEEE J Photovoltaics 2017;7(1):104e9. [11] King DL, Hansen BR, Kratochvil J a, Quintana M a. Dark current-voltage measurements on photovoltaic modules as a diagnostic or manufacturing tool. In: Conf. Rec. 26 IEEE photovolt. Spec. Conf; 1997. p. 1125e8. no. September. [12] Hacke P, et al. System voltage potential-induced degradation mechanisms in PV modules and methods for test. In: 37th IEEE photovoltaic specialists conference (PVSC); 2011. p. 814e20. [13] Wolf M, Rauschenbach H. Series resistance effects measurements. Adv Energy Convers 1963;3(2):455e79. [14] Wolf M, Noel GT, Stirn RJ. “Investigation of the double exponential in the current-voltage characteristics of silicon solar cells. IEEE Trans Electron Dev 1977;24(4):419e28. [15] xian Lun S, Wang S, hong Yang G, ting Guo T. A new explicit double-diode modeling method based on Lambert W-function for photovoltaic arrays. Sol Energy 2015;116:69e82. [16] Dehghanzadeh A, Farahani G, Maboodi M. A novel approximate explicit double-diode model of solar cells for use in simulation studies. Renew Energy 2017;103:468e77.
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Energy journal homepage: www.elsevier.com/locate/energy
Comparison of potential-induced degradation (PID) of n-type and ptype silicon solar cells a, c Jan Slamberger , Michael Schwark a, Bas B. Van Aken b, Peter Virti c c, * a
AIT Austrian Institute of Technology GmbH, Donau-City-Strasse 1, A-1220 Vienna, Austria ECN Solar Energy, PO Box 1, 1755 ZG Petten, Netherlands c University of Maribor, Faculty of Energy Technology, Hocevarjev trg 1, SI-8270 Krsko, Slovenia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 March 2018 Received in revised form 14 July 2018 Accepted 18 July 2018 Available online 19 July 2018
Potential-induced degradation (PID) of photovoltaic (PV) modules is one of the most severe types of degradation, where power losses on system level may even exceed 30%. The PID process depends on the strength of the electric field, the temperature, the relative humidity, conductive soiling, time and the PV module materials. For p-type cells, it has been established that the decrease of the shunt resistance, due to migration of sodium ions across the n/p junction is the root cause of the degradation. On the other hand, it has recently been confirmed for n-type cells that the PID occurs due to an increase in recombination as charges are driven to the anti-reflection (AR) coating/emitter interface. In this paper, we present the comparison between PID of p-type and n-type crystalline silicon (c-Si) solar cells and their progression of PID. The time evolution of PID is studied by light and dark I-V curve measurements, electroluminescence images and progressions of the one- and two-diode equivalent model parameters, viz. photocurrent, 1st and 2nd diode reverse saturation currents, 1st and 2nd diode ideality factors, shunt resistance and series resistance. © 2018 Published by Elsevier Ltd.
Keywords: Photovoltaic (PV) systems Potential-induced degradation (PID) Crystalline silicon (c-si) solar cells n-type p-type
1. Introduction In PV power plants, PV modules are connected in series and therefore the system voltage can reach ±600 to ±1500 V. Common transformerless PV inverters do not allow grounding of the electronically active part and therefore one part of the string of modules has a positive and the other part a negative voltage compared to the grounded frames. PID is the power loss caused by an applied high voltage difference between the active solar cells and the frame of the PV modules. It has been reported in many studies [1e4], that p-type cells can be affected by PID at a negative voltage potential, while n-type cells can be affected with both positive and negative voltage, depending on topology [5,6]. Beside the system voltage, the PID is strongly dependent on the temperature and relative humidity. There is a variety of proposals for modelling the PID at ptype PV modules, which are mainly interpolations to polynomial or exponential functions [7e9]. However, the parameters of those models have to be adapted to every different PV modules and they are not universally applicable.
* Corresponding author. E-mail address: [email protected] (P. Virti c). https://doi.org/10.1016/j.energy.2018.07.118 0360-5442/© 2018 Published by Elsevier Ltd.
The main suspects for the PID mechanism of p-type solar cells are sodium ions (Naþ), which drift due to the negative electric field (electric field is oriented from the grounded frame of PV module to the PV cell electrical connection with negative potential according to the grounded frame) from the sodium-rich glass through antireflection (AR) coating and penetrate crystal defects crossing the p-n junction. This leads to the reduction of the shunt resistance Rsh in the diode model of the solar cell and the increase of reverse saturation current and the diode ideality factor due to the recombination in the space-charge region (non-conducting layer between p-doped and n-doped semiconductor). In the I-V characteristics, the significant drop of fill factor is seen. In n-type cells, it was shown in Ref. [5] that the drift of Naþ ions is not the reason for power loss under high system voltage. The presumed PID mechanism in n-type solar cells is the surface polarization, where there are either negative or positive charges (depending on topology) accumulated within the SiNx stack that act as passivation and anti-reflection (AR) coating. As described in Ref. [6], in the n-PERT (passivated emitter, rear totally diffused) c-Si solar cells, due to the negative electric field, the positive charges increase the recombination rate by forcing the emitter surface to go into depletion. This makes it harder for holes to reach the metallisation grid and as they spend more time/distance, the probability
J. Slamberger et al. / Energy 161 (2018) 266e276
of recombining increases. The result is a significant drop in the short-circuit current and open circuit voltage, while the fill factor decreases only slightly. The dark I-V characterization was reported to be an appropriate method to monitor PID in situ during the stress test [10e12]. The main disadvantage of dark I-V characterization is that the serial resistance Rsh is slightly lower compared to light I-V characterization [11] and obviously, it is not possible to determine the photocurrent out of it. The other possibility is to measure light I-V characteristics. This has the disadvantage to stop the stress test, to decrease the temperature of the module to 25 C for measuring and start the stress test again at 60 C or 85 C. The adjustment of the temperature from PID-to IV-conditions is done either with or without stress voltage. This leads to either additional degradation or regeneration at the test temperature, where degradation process occurs when a stress voltage is applied and regeneration when there is no stress voltage. Even more, after achieving the test temperature and relative humidity of 85%, it is advisable to wait 12e24 h (stabilization phase) before turning on the stress voltage, otherwise, the PID will be much faster due to the formation of condensation on glass surface [4]. In the stabilization phase at test temperature, a PV module already affected by PID may regenerate for several percentages. The characteristics of the solar cells could be well described with single- or double-diode equivalent current models. The singlediode model is good for first approximations but for a detailed research, the models with two or more diodes are needed. The double-diode model has for the first time been described in the year 1963 [13], where the first diode represents diffusion current and the second diode the recombination current and has been well established in the past years [8,9,11,14]. Both models are nonlinear and therefore a numerical approach for the determination of the parameters (photocurrent, 1st and 2nd diode reverse saturation currents, 1st and 2nd diode ideality factors, shunt resistance and series resistance) is necessary. In the past, the fitting methods with least squares were mostly used for this determination. However, today some new approaches exist with an equation in explicit form of the double-diode model [15,16]. These new approaches include some simplifications or bring in additional parameters. As an alternative to already-published research, where only the changes of parameters of single- or double-diode model before and after PID stress test are presented [2], we present in this paper for the first time the progression of the PID effect during the stress test at different types of c-Si solar cells described with the parameters of the single- and double-diode model. The parameters of the equivalent circuit models were defined with the fitting to the measured dark curves data, using the nonlinear least-squares fitting method. Authors in Ref. [9] presented parameters changes of double-diode model during the stress test but only for one type of solar cells and with shorter time intervals of measurements. With high time resolution and longer period of measurements we have clearly shown parameters trends. Reference [4] also presents the progression of PID effect during the stress test but only for one shunt resistance of double-diode model at significantly shorter total testing time. Moreover, this paper shows for the first time side by side comparison between PID of p-type and n-type modules presented by light I-V curve and characteristics, electroluminescence images and progressions of parameters of single- and double-diode equivalent models.
compare the progression of the PID and characteristics of the cells. The first two types of cells were the commercial p-type based multicrystalline Si solar cells, where the cells of the first type were cut from the edge or corner of the silicon block and the cells of the second type were cut from the centre of the block. The cells cut from the edge or corner have compared to the cells cut from the centre a higher rate of impurity and therefore they were suspected to present a higher rate of degradation. The third and fourth types of the cells were n-type based front junction single crystalline Si solar cells - n-PERT. The fourth type had additionally a modified boron emitter and dielectric layer as published in Ref. [6]. All test cells have been laminated into single-cell mini-modules using a commercial glass, EVA encapsulant and back sheet. Aluminium profiles were pressed to the glass on two sides to simulate the real frames (Fig. 1). 2.2. PID stress test and measurement setup The high voltage stress test with 1000 V between the module contacts and the frame (Fig. 2) has been processed in a climatic chamber at 85% relative humidity at two different temperatures (60 C and 85 C). 60 C is proposed by the standard IEC 62804 as a minimal stress temperature, whereby many research institutes use also 85 C, where the degradation speeds up. Before and after each test, the I-V characteristics have been measured with a Pasan flash tester, class AAA (Spectral match to AM1.5 is between 0.75 and 1.25, non-uniformity of irradiance is lower than 2%, short-term instability of irradiance is lower than 0.5% and long-term instability of irradiance is lower than 2%) at standard test conditions (STC) and at low irradiance. The PID degradation at low irradiance is normally 2 to 5 times higher due to the same impact of shunt resistance at lower photocurrent. The measurement at low irradiance is an appropriate method to detect the PID already in the early stage. Additionally, the electroluminescence images have been captured at 9 A (~Isc) and 1 A (~0.1 Isc). Moreover, the in situ dark I-V characteristics measurements with the frequency of 10 min have been performed to monitor the progression of the degradation. Fig. 3 shows the in situ measurement setup and climate chamber with 4 test samples. The samples have been connected to separate high voltage channels. 2.3. Analysis In the post-processing phase, the analysis of the progression of I-V characteristics has been made. Additionally, the single-diode (Fig. 4) and double-diode (Fig. 5) models with concentrated parameters have been fitted to the measured dark I-V characteristics. The single-diode and double-diode models for solar cell are described with (1) and (2) [13], where Iph is the photocurrent (electric current produced by a photoelectric effect - ideal current source); ID, ID1 and ID2 the currents flowing through the diodes D, D1
2. Methods 2.1. Fabrication of test samples For this study, four different types of cells have been used to
267
Fig. 1. Test sample front view (left), and back view (right).
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and D2; Io, Io1 and Io2 the reverse saturation currents of diodes D, D1 and D2; n, n1, n2, the ideality factors of diodes D, D1 and D2; Rs the series resistance; Rsh the shunt resistance; I the output current; V the output voltage; T the temperature in Kelvin; q the electron charge ð1:60217646$1019 CÞ and k the Boltzmann's constant ð1:3806503$1023 J=KÞ.
qðVþIRs Þ V þ IR s I ¼ Iph ID IRsh ¼ Iph Io eð nkT Þ 1 Rsh I ¼ Iph ID1 ID2 IRsh ¼ Iph Io1 e
qðVþIRs Þ n1 kT
1
!
Io2 e
qðVþIRs Þ n2 kT
! 1
(1)
V þ IRs Rsh (2)
Fig. 2. Connection of PV module to high voltage source.
For the determination of the parameters of nonlinear models, the Matlab's function lsqnonlin, which is a part of the Optimization Toolbox™, has been used. This function is able to solve nonlinear least-squares problems with searching of the minimum of the sum of square residuals of the nonlinear fitting problems, defined with (3), where r is residual, xk independent variable, yk function of xk and a0, …an fit parameters. As a result, it returns the vector of parameters values and additionally squared norm of the residual (SNR), which we used to compare the quality of fit.
r¼
X ðyk f ða0 ; …an ; xk ÞÞ2
(3)
k
As presented in Ref. [8], the Rs does not change with PID, therefore, it has been set as a constant. Moreover, in p-type cells, the changes of Io1 and n1 comparing to Io2 and n2 during the PID progress are negligible and therefore they have been also set as constants. Similarly, in n-type cells, the Rsh and n2 have been set as constants. 3. Results and discussion Fig. 3. Climate chamber and measurement setup.
Fig. 4. Single-diode model of solar cell.
3.1. I-V characteristics Figs. 6e9 show the I-V curves of the different cell types before (blue line) and after (red line) PID stress tests performed at 60 C (a) and 85 C (b), whereby the Tables 1e4 present the value of I-V characteristics at standard test conditions (STC) and at low irradiance (185 W/m2, 25 C, 1,5AM). There is no pass/fail criteria in the current version of standard (IEC 62804) for testing the PID, but anyway, a lot of researchers and manufacturers use the term “PID free” if the power loss at STC is less than 5%. At the same time the power loss at low irradiance could be up to 4 times higher. In this study, the PID effect could be seen by all tested samples, whereby the degradation was low for cell types II and III (<%5 @ STC). But even those cells show more than 10% power loss at low irradiances. For cell type IV, a significant drop in short-circuit current could be detected, whereby only a small change of fill factor appeared, compared to the cell type I after the PID stress test at 85 C, where the main change is the decrease of shunt resistance and a corresponding significant drop in fill factor. 3.2. Electroluminescence
Fig. 5. Double-diode model of solar cell.
The PID losses could be well seen from electroluminescence (EL) images by comparing the images before and after PID stress test under the same conditions. Figs. 10e13 show side by side comparison of EL images before and after PID with the two different
J. Slamberger et al. / Energy 161 (2018) 266e276
(a)
269
(b)
Fig. 6. (a) I-V curves of cell type I at STC before and after PID stress test (60 C, 85% RH, 1000 V and 148 h). (b) I-V curves of cell type I at STC before and after PID stress test (85 C, 85% RH, 1000 V and 60 h).
(a)
(b)
Fig. 7. (a) I-V curves of cell type II at STC before and after PID stress test (60 C, 85% RH, 1000 V and 148 h). (b) I-V curves of cell type II at STC before and after PID stress test (85 C, 85% RH, 1000 V and 60 h).
(a)
(b)
Fig. 8. (a) I-V curves of cell type III at STC before and after PID stress test (60 C, 85% RH, 1000 V and 80 h). (b) I-V curves of cell type III at STC before and after PID stress test (85 C, 85% RH, 1000 V and 60 h).
currents. Firstly, the current of 9 A (roughly of Isc @STC) and secondly the lower current of 1 A (roughly of 10% of Isc @ STC) have been sent through the module. The dark parts present lower local efficiency of the cell. The analysis of EL images at 9 A before and after the PID stress test at 60 C shows almost no changes in efficiency for cell types I, II and III, with homogeneous loss of efficiency by cell type IV, which is also comparable to the results of I-V characteristics. Meanwhile, from the EL images taken at 1 A before and after the PID stress at
60 C, in addition to cell type IV, homogeneous loss of efficiency by cell types I and II has been detected. Furthermore, the analysis of EL images at 9 A before and after the PID stress test at 85 C shows the local efficiency losses by cell types I and III and again homogeneous losses by cell type IV. EL images of cell type II show no changes in efficiency. Additionally, the EL image of cell type I taken after the PID test at 85 C at 1 A shows significant loss of efficiency, where no signal could be detected at the same exposure time as by image taken before PID stress test.
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(a)
(b)
Fig. 9. (a) I-V curves of cell type IV at STC before and after PID stress test (60 C, 85% RH, 1000 V and 2.5 h). (b) I-V curves of cell type IV at STC before and after PID stress test (85 C, 85% RH, 1000 V and 90 h).
Table 1 The parameters of I-V characteristics of cell type I at STC and low irradiance (185 W/m2) before and after PID stress test at 60 C (148 h) and 85 C (60 h).
1000 W/m
2
185 W/m2
Initial After PID Initial After PID Initial After PID Initial After PID
@ 60 C
@ 85 C @ 60 C @ 85 C
Pmax [W]
Isc [A]
Uoc [V]
Imp [A]
Ump [V]
FF [%]
3.86 3.70 3.84 2.28 0.72 0.64 0.71 0.15
8.69 8.68 8.67 8.40 1.64 1.61 1.64 1.58
0.617 0.613 0.616 0.590 0.574 0.568 0.567 0.309
8.04 7.77 8.00 5.32 1.51 1.46 1.51 0.87
0.481 0.477 0.480 0.429 0.473 0.435 0.471 0.168
72.1 69.6 71.9 46.0 76.9 69.3 76.4 29.9
DPmax [%] 4.1 40.6 12.3 78.9
Table 2 The parameters of I-V characteristics of cell type II at STC and low irradiance (185 W/m2) before and after PID stress test at 60 C (148 h) and 85 C (60 h).
1000 W/m
2
185 W/m2
Initial After PID Initial After PID Initial After PID Initial After PID
@ 60 C @ 85 C @ 60 C @ 85 C
Pmax [W]
Isc [A]
Uoc [V]
Imp [A]
Ump [V]
FF [%]
3.96 3.85 3.96 3.91 0.73 0.62 0.74 0.70
8.80 8.78 8.79 8.78 1.66 1.63 1.66 1.66
0.622 0.619 0.621 0.621 0.574 0.574 0.574 0.573
8.14 7.98 8.14 8.03 1.52 1.41 1.54 1.48
0.486 0.483 0.487 0.486 0.478 0.442 0.478 0.475
72.4 70.9 72.6 71.7 76.5 66.3 77.0 73.2
DPmax [%] 2.8 1.3 15.1 5.4
Table 3 The parameters of I-V characteristics of cell type III at STC and low irradiance (185 W/m2) before and after PID stress test at 60 C (80 h) and 85 C (60 h).
1000 W/m2
185 W/m2
Initial After PID Initial After PID Initial After PID Initial After PID
@ 60 C @ 85 C @ 60 C
@ 85 C
Pmax [W]
Isc [A]
Uoc [V]
Imp [A]
Ump [V]
FF [%]
4.47 4.44 4.39 4.22 0.84 0.82 0.80 0.71
9.33 9.35 9.30 9.17 1.76 1.76 1.75 1.71
0.649 0.647 0.645 0.636 0.603 0.603 0.598 0.580
8.66 8.64 8.76 8.43 1.66 1.62 1.61 1.57
0.516 0.510 0.512 0.501 0.506 0.503 0.499 0.452
73.8 73.4 73.1 72.4 79.1 76.6 76.8 71.6
The comparison of EL images of p-type and n-type cells shows the different degradation effects due to the PID. In the case of ptype cells, where the main degradation mechanism is the penetration of Naþ ions and consequently a reduction of shunt resistance, the local defects at high-current can be clearly seen. Furthermore, out of low-current EL images, the PID effects could already be detected in early stage. On the other hand, in the case of n-type cells, where the main degradation mechanism is the surface
DPmax [%] 0.7 3.9 2.4 11.3
polarization and therefore reduction of Isc and Uoc, the homogenous loss over the whole cell can be seen. 3.3. Single-diode parameters The progressions of the single-diode model's parameters during the PID stress tests are presented in Figs. 14e17. For all cell types, the series resistance was set to be a constant, determined from dark
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Table 4 The parameters of I-V characteristics of cell type IV at STC and low irradiance (185 W/m2) before and after PID stress test at 60 C (2.5 h) and 85 C (90 h).
1000 W/m2
185 W/m2
Initial After PID Initial After PID Initial After PID Initial After PID
@ 60 C @ 85 C
@ 60 C @ 85 C
Pmax [W]
Isc [A]
Uoc [V]
Imp [A]
Ump [V]
FF [%]
4.59 3.82 4.59 3.87 0.85 0.66 0.84 0.65
9.22 8.42 9.20 8.47 1.75 1.65 1.74 1.67
0.649 0.609 0.648 0.612 0.606 0.563 0.603 0.564
8.67 7.75 8.66 7.81 1.65 1.41 1.65 1.41
0.529 0.492 0.529 0.495 0.513 0.462 0.511 0.464
76.6 74.4 76.9 74.6 80.0 70.8 80.2 69.1
EL @ 9 A 60 s After PID
16.8 15.7 23.4 22.6
EL @ 1 A 240 s Before PID
After PID
PID @ 85 °C, 60 h
PID @ 60 °C, 148 h
Before PID
DPmax [%]
Fig. 10. Electroluminescence images of the cell type I.
EL @ 9 A 60 s After PID
EL @ 1 A 240 s Before PID
After PID
PID @ 85 °C , 60 h
PID @ 60 °C , 148 h
Before PID
Fig. 11. Electroluminescence images of the cell type II.
I-V curves taken before the start of PID stress test. For all cell types, the diode reverse saturation current and diode ideality factor are increasing and the shunt resistance is decreasing, whereby the changes of cell types I and II have significantly slower progress as the changes of cell types III and IV. Moreover, for cell type IV, the degradation has reached the final stage after a couple of hours, while cell types I, II and III did not reach the final stage after more than a dozen hours and will continue with the time.
3.4. Double-diode parameters The double-diode equivalent current circuit model, compared to single-diode model, describes better the physics [13] of the real solar cell, where the first diode represents diffusion current and the second diode the recombination current. At p-type cells, the progression of parameters Io1, n1 and Rs has shown no significant changes, which could be related to PID. Similarly, in n-type cells, the
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272
EL @ 9 A 15 s
EL @ 1 A 60 s
After PID
Before PID
After PID
PID @ 85 °C , 60 h
PID @ 60 °C , 80 h
Before PID
Fig. 12. Electroluminescence images of the cell type III.
EL @ 9 A 15 s After PID
Before PID
After PID
PID @ 85 °C , 90 h
PID @ 60 °C , 2.5 h
Before PID
EL @ 1 A 60 s
Fig. 13. Electroluminescence images of the cell type IV.
n
Rsh [ ]
PID @ 85 °C
PID @ 60 °C
Io [A]
Fig. 14. Progression of single-diode parameters during the PID stress test - type I.
SNR
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n
Rsh [ ]
SNR
PID @ 85 °C
PID @ 60 °C
Io [A]
273
Fig. 15. Progression of single-diode parameters during the PID stress test - type II.
n
Rsh [ ]
SNR
PID @ 85 °C
PID @ 60 °C
Io [A]
Fig. 16. Progression of single-diode parameters during the PID stress test - type III.
n
Rsh [ ]
SNR
PID @ 85 °C
PID @ 60 °C
Io [A]
Fig. 17. Progression of single-diode parameters during the PID stress test - type IV.
progression of parameters Io2, Rsh and Rs has shown no significant correlation with PID related changes. Those parameters were set as constants, to minimise the noise in the progression of the PID related parameters. Those constants were determined from the
dark I-V curves taken before the start of PID stress test. The progressions of the variable double-diode model's parameters during the PID stress tests are presented in Figs. 18e21. Also, like the single-diode model, in the double-diode model, the diode reverse saturation current and diode ideality factor are increasing and the shunt resistance is decreasing for cell types I and II. In this case, the parameters of the second diode are changing and parameters of the first diode are set to constants. Furthermore, compared to the single-diode model, the quality of the doublediode fits at strongly PID effected p-type cells is almost constant and much better. For cell types III and IV, the changes of reverse saturation current and ideality factor of the first diode of the double-diode model are comparable to those of single-diode model. Additionally, the shunt resistance of double-diode model was set to constant and the reverse saturation current of the second diode is time-dependent. Comparable to the reverse saturation current of the first diode, the reverse saturation current of the second diode has much higher values and moreover, the progression is much slower and the degradation by cell type IV does not end after a couple of hours.
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n2
Rsh [ ]
SNR
PID @ 85 °C
PID @ 60 °C
Io2 [A]
Fig. 18. Progression of double-diode parameters during the PID stress test - type I.
n2
Rsh [ ]
SNR
PID @ 85 °C
PID @ 60 °C
Io2 [A]
Fig. 19. Progression of double-diode parameters during the PID stress test - type II.
n1
Io2 [A]
SNR
PID @ 85 °C
PID @ 60 °C
Io1 [A]
Fig. 20. Progression of double-diode parameters during the PID stress test - type III.
Furthermore, an extra stress test with four modules of cell type IV was performed to investigate the progression of the photocurrent during the PID test. The modules were connected to the high
voltage source with the different time delays and disconnected at the same time. Before and after this test, the light I-V characteristics were measured and the parameters for the double-diode model
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n1
Io2 [A]
SNR
PID @ 85 °C
PID @ 60 °C
Io1 [A]
275
Fig. 21. Progression of double-diode parameters during the PID stress test - type IV.
were determined. Fig. 22 presents the progression of normalized photocurrent during the PID stress test, described with (4), where Iph;n is normalized photocurrent, Iph;min minimal photocurrent and Iph;max maximal (initial) photocurrent.
I ph;n ¼
I ph I ph;min I ph;max I ph;min
(4)
The progression of the photocurrent could be well described with an Arrhenius-like fit equation (5), where t is time and b, t fit parameters. The values of the fit parameters for cell type IV are b ¼ 2.144 and t ¼ 0.8147 h. t b
Iph;n ¼ eðtÞ
(5)
The form of the progression seems to be similar to reverse saturation current of the first diode with the opposite sign. Compared to cell type IV, there is no significant change of the Isc (Tables 1e3) at cell types I, II and III, where the Iph could be set as a constant.
4. Conclusion This work presents a comparison between the PID mechanisms of p-type and n-type c-Si solar cells. The reasons for PID effect by p-
type cells is the local shunting, caused by penetration of Naþ ions in p-n junction of the cells, whereby the reason for PID effect by ntype cells is the surface polarization on the surface of AR coating, where positive/negative charges recombine with the electrons and holes instead of being collected by cell's p-n junction. The degradation can reach several dozen percents for both cell types, while in the case of n-type cells, the degradation reaches a stable state very fast. In the case of p-type cells, the degradation proceeds further because of a continuous increase of the amount of Naþ in the wafer and can reach >90% losses on the module level. Because of different phenomena appearing in p- and n-cells, also the first indicators showing on PID are different. The form of I-V curves by p-type cells shows a reduction in shunt resistance and fill factor, whereas the main indicators for n-type cells are significant reduction of shortcircuit current and open circuit voltage. The comparison of EL images at current near to Isc at STC shows local efficiency losses by ptype cells and homogeneous efficiency losses by n-type cells. Furthermore, the comparison of progression of double diode parameters shows that the main degradation indicators by p-type cells are the decrease of the shunt resistance and the increase of the reverse saturation current and the ideality factor of the second diode. In the case of the n-type cells, the main degradation indicators are the increase of the reverse saturation current and the ideality factor of the first diode, the increase of the reverse saturation current of the second diode and the significant reduction of photocurrent. The photocurrent could not be determined in situ by dark I-V measurement, but has to be determined out of the light I-V curves. Acknowledgements This work was performed as part of the INFINITY project. A project of the Austrian “Energy Research Program” funded by the Austrian Climate and Energy Fund and the Austrian Research Promotion Agency (FFG). Both are gratefully acknowledged. The authors would like to thank Carinthian Tech Research (CTR) for donating the p-type cells and the colleagues at ECN e Solar Energy and the Photovoltaic Systems team at AIT for their support and making this study possible. References
Fig. 22. Progression of photocurrent (normalized) during the PID stress test at 60 C Type IV.
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