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Contract No. DE-AC36-08GO28308

Automated Data Collection 

for Determining Statistical 

Distributions of Module Power 

Undergoing Potential-Induced 

Degradation

Preprint

Peter Hacke

National Renewable Energy Laboratory

Sergiu Spataru

Aalborg University

Presented at the 24th Workshop on Crystalline Silicon Solar Cells & 

Modules: Materials and Processes

Breckenridge, Colorado

July 27–30, 2014

Conference Paper

NREL/CP-5J00-62468

August 2014
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Automated Data Collection for Determining Statistical Distributions of Module Power

Undergoing Potential-Induced Degradation

Peter Hacke1 and Sergiu Spataru2

1

National Renewable Energy Laboratory (NREL), Golden, CO, 80401, United States 2

Aalborg University, 9220 Aalborg East, Denmark

We propose a method for increasing the frequency of data collection and reducing the time and cost of 

accelerated lifetime testing of photovoltaic modules undergoing potential-induced degradation. This 

consists of in-situ measurements of dark current-voltage curves of the modules at elevated stress 

temperature, their use to determine the maximum power at 25°C standard test conditions, and distribution 

statistics for determining degradation rates as a function of stress level. The semicontinuous data obtained 

by this method clearly show degradation curves of the maximum power, including an incubation phase, 

rates and extent of degradation, precise time to failure, and partial recovery. Stress tests were performed on 

crystalline silicon modules at 85% relative humidity and 60°, 72°, and 85°C. Activation energy for the 

mean time to failure (1% relative) of 0.85 eV was determined and a mean time to failure of 8,000 h at 25°C 

and 85% relative humidity is predicted. No clear trend in maximum degradation as a function of stress 

temperature was observed.

Introduction

Photovoltaic (PV) module manufacturers, who are applying multi-decade warranties on their products,

and customers seeking to predict return on investment find it impractical to perform lifetime tests on 

modules at normal operating conditions because of the long times required. Acceleration is applied, for 

example, when a manufacturer would like to project the median time to failure in the field under a certain 

operating environment. This may be achieved by experimentally determining the activation energy for the 

time to failure for the degradation mode and PV module design of interest. The data can be used to estimate 

the mean time to failure of the PV module at some arbitrary operating condition or used in modeling the 

degradation in the climate of deployment. However, application of statistical methods to accelerated 

lifetime testing of PV modules has been impeded by the expense of cumbersome module transfers and by 

transients in stress levels from moving modules between the environmental chamber to the solar simulator 

or flash tester to quantify degradation. Non-contiguous points along the degradation curves also make it 

difficult to clarify the shape of the curve.

Potential-induced degradation (PID) is of recent interest because it has been discovered to be a source of 

relatively rapid and significant degradation in some PV modules in the field [1]. In conventional n+

/p frontjunction cells, PID has been associated with sodium migration toward the cell [2]—specifically, sodium at 

stacking faults [3].

We previously showed the utility of dark current-voltage (I-V) curves measured by intermittently 

lowering the module temperature from the elevated stress temperature to 25°C for determining the extent of 

module power loss by PID at standard test conditions (STC) or under low light conditions [4,5]. With these 

results, an Arrhenius plot was used to determine the activation energy of the mean time to failure for 

lifetime prediction at a use temperature [4]. We subsequently developed the methodology for calculating 

the STC power of the module undergoing PID using dark I-V curves measured at elevated stress 

temperatures and equipment to automate the data taking [6]. This eliminates the temperature and relative 

humidity (RH) transients associated with the return of the chamber to 25°C for dark I-V curve 

measurements and allows for significantly more frequent dark I-V curve measurements on a great number 

of modules.

We receive inspiration from the study of optoelectronic devices such as lasers and light-emitting diodes, 

whereby a photodetector is placed in front of the device for continuous monitoring of degradation as a

function of temperature and time [7] to move away from the labor-intensive procedures that give 

discontinuous data. In this paper, we first review the concept of superposition for accurate determination of 

the STC fraction power degraded using 25°C dark I-V curves and those measured at elevated stress 

temperature. With these methods, STC power is evaluated for replicas of a module type undergoing PID at 

several stress temperatures. STC power is monitored semicontinuously using dark I-V curves measured at 

the stress temperature. This permits us to precisely understand and determine the statistical distribution of 

the time to failure of the modules, without temperature transients and interruptions for 25°C measurements.
2

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An Arrhenius analysis is applied to fit the time-to-failure results as a function of temperature, and an 

activation energy is calculated. Finally, extrapolation of time to failure to a use condition is demonstrated.

Method

The principle of superposition [8] is used to transform the first-quadrant dark I-V curve to the fourth 

quadrant to obtain a quasi light I-V curve by subtracting the photocurrent of the module. To determine STC 

module power, we used the module short-circuit current Isc as the photocurrent. This has been observed to 

be relatively constant for modules undergoing PID [1]. The maximum power point (Pmax) is then evaluated 

on the translated I-V curve, as is conventionally done for curves obtained with solar simulators. This value 

determined from the dark I-V data can be compared to the measured power obtained with a solar simulator

at the end of the stress test, to show the success of the dark I-V analysis at determining Pmax. 

For simplicity of analyzing data, degradation of modules is expressed normalized to its initial power 

(Pmax/Pmax0). This ratio is abbreviated as R in the case when the measurements are performed at 25°C. 

Because we analyze the degradation in terms of the fraction Pmax/Pmax0, there is only mild sensitivity to the

Isc that is used to translate the dark I-V curves for both numerator and denominator in the analysis. The 

photocurrent parameter may be adjusted to have the Pmax results from the dark I-V curves match that of the 

solar simulator; however, the Isc-translated dark I-V curves generally yield accurate Pmax results for 

modules undergoing PID [4,6]. Solar simulator testing of the module is performed at the start and end of 

the stress test at 25°C, and dark I-V curves and R values derived thereof may be taken at 25°C during the 

course of PID testing to obtain a degradation curve [6]. In this case, the module temperature must be 

intermittently returned to 25°C when performing PID stress testing at elevated temperatures. This has the 

disadvantage of causing interruptions in the testing, stress-level transients that can degrade the integrity of 

the data, and as a result, fewer data points along the degradation curve are usually obtained. 

In the interest of maintaining the module under test at an elevated stress temperature without 

interruption, the relative degradation at the stress temperature T, PmaxT/PmaxT 0 (the ratio is abbreviated RT) 

can be similarly obtained from the Isc-translated dark I-V curves measured at temperature [6]. PmaxT 0 is 

taken from the initial Isc-translated curve at the first instant the module reaches the stress temperature. The

ratio RT is repeatedly calculated from the dark I-V curves using the superposition principle over the course 

of the degradation at temperature T to obtain a semicontinuous degradation curve. If R (degradation data

obtained at 25°C) is also measured, an offset is observed between the normalized module power at the 

stress temperature and that at 25°C (RT and R, respectively) and its change over time resulting from PID

can be seen [6]. To carry out stress at the constant elevated temperature, we seek to only use the initial and 

final 25°C dark I-V and/or solar simulator data to compute the STC degradation curve. The extent of the 

offset between RT and R was found to expand linearly as a function of the extent of degradation in the range 

of 0% to 32% relative [6]. Therefore, the entire STC degradation curve can be calculated from RT values 

obtained over the course of PID with measurement of the offset at the end of the stress test—RT F and RF are 

taken at the test temperature and 25°C, respectively. The linear scaling factor M represents the offset 

between R and RT, normalized to the fraction degraded, 1-RT, as determined at the end of the test (denoted 

by the subscript F), and it can be calculated as (RF-RT F)/(1-RT F). This results in a negative number in this

analysis. Then, the normalized 25°C (STC) power, R25, is recalculated for each RT measured as in Fig. 1 

according to R25 = RT-M(RT-1). 
3

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Fig. 1. Evolution of dark I-Vderived 25°C (STC) power 

(normalized to initial power) 

obtained from dark I-V curves 

taken at the 60°C stress 

temperature. Initial and final 25°C 

solar simulator results are also 

shown.

Finally, time-to-failure statistics are modeled using an Arrhenius relationship, tf = A·exp (Ea/kT), which 

is used to calculate a pre-exponential A and activation energy Ea, which can then be used to predict mean 

time to failure at some use temperature T.

Experiment

This experiment is carried out with an apparatus previously described [4,6]. It consists of an 

environmental chamber at 85% RH run sequentially with five modules each at 60°, 72°, and 85°C. A highvoltage power supply applied -1,000 V system voltage to the shorted module leads after the modules 

reached temperature and humidity equilibrium. The module frames were grounded. Modules were 

maintained to tolerance limits of ±2°C and ±5% RH over the course of the stress test. A 10 A power supply 

was used to drive forward-bias current through the modules to measure dark I-V curves; a switching 

network was used to switch modules intermittently from high-voltage bias for the dark I-V curve trace in 4 

h intervals, and a computer controlled the sequencing of the measurements and conditions.

Conventional 60-cell multicrystalline front-junction n+/p cells were used. They were commercial 

modules from the same production lot with near-sequential serial numbers.

Results and discussion

The relative degradation in STC power is shown in Fig. 2 as a function of time for three temperatures 

with five replicas tested at each temperature using the method described above. No special outliers or early 

failures were detected; however, effects of an interruption of the data recording due to equipment problems 

can be seen in the 60°C data, the longest of the tests. Mean scaling factors M (with standard deviations) 

were -0.22 (0.13), -0.52 (0.09), and -0.56 (0.24) for the 60°, 72°, and 85°C conditions, respectively.

Several phases of the degradation curve can be seen most clearly in the 60°C condition: a period of 

relative stability or incubation, followed by degradation in power, a point of maximum power loss, and then 

a period of recovery. Interestingly, the higher stress temperatures do not show differing maximum

degradation compared to the lowest. The maximum degree of degradation appears to be independent of the 

test temperature, so the higher temperature (85°C), with its benefit of greater acceleration, is equally 

suitable for revealing the maximum amount of degradation in these PV modules. Some variation in the 

degradation between modules stress tested at each temperature is seen, which may result from distribution 

in sensitivity of the cells within the modules.
4

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Fig. 2. Normalized STC 

power of PV modules 

undergoing PID at 85% 

RH, -1000 V bias, and 

at three temperatures 

indicated on the plot. 

The data were obtained 

semicontinuously at the 

stress temperature.

A 1% relative degradation level is chosen to determine the time to failure in each sample without 

censoring. Some samples do not degrade much more than this level, so failures would not be measured in 

some samples if the failure level were greater. The data with degradation up to this level and several data 

points beyond are taken to determine the points of failure (Fig. 3). Only the degradation segments of the 

curves were analyzed. Additional models will be required to model the incubation and recovery stages. A 

linear fit to the subset of data is achieved if the data are scaled to the power of two, as previously shown for 

other PID data [4]. The intersection of the degradation curve as a function of time with the failure level,

0.99 fraction power remaining, can easily be seen. 

Fig. 3. Subset of the normalized STC power of PV modules undergoing PID at 85% RH, -1000 V bias, and 

at three temperatures indicated on the plot. The data are successfully fit linearly with the time (h) scaled to 

the power of two, and the intersection in time of the curves at the failure criterion of 0.99 relative power 

remaining can be seen. 

The time-to-failure data were plotted on a lognormal cumulative failure probability plot as shown in 

Fig. 4. The data are reasonably well fit; however, the differing slopes based on the extent of data we have

(five data points per temperature) suggest differing shape factors to the distribution as a function of stress 

level when viewed in this lognormal plot.
5

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Fig. 4. Cumulative failure probability 

vs. time for three temperatures as 

shown on a lognormal plot. 

The time to failure for each sample in each temperature category is plotted on an Arrhenius scale to 

determine the activation energy corresponding to the time to failure (Fig. 5). The points in each temperature 

category are shown with the computed lognormal distribution using the distribution shown in Fig. 4. The 

Arrhenius fitting curve and 95% confidence intervals are shown to either side of it. The curve is extended 

to 25°C, along with a computed lognormal distribution, to estimate the time to failure at that temperature. 

The data set shows an activation energy of 0.85 eV. This result may be influenced by factors such as 

module materials and design and the failure criterion chosen. A previous, more limited study yielded Ea = 

0.726 eV. The study had a different failure criterion on differing modules performed by reducing chamber 

temperature from the stress temperature to 25°C to obtain the STC power degradation curves. The 

approximately 8,000 h mean time to failure shown for the 25°C, 85%RH, and -1,000 V case must be 

considered with the understanding that the actual use conditions are not constant. These accelerated tests 

were performed in the dark. Illumination, especially the ultraviolet (UV) component, is found to mitigate 

PID to an extent [9]. If the humidity factor is removed (such as on a sunny day with low humidity), a stress 

factor is removed—specifically, the leakage current from the module face to ground is significantly 

interrupted, in which case modules have been shown to recover to an extent by thermal activation [1]. On 

the other hand, for some periods, relative humidity can be higher than 85%. 

The technique shown here can be used to evaluate the activation energy for time to failure of various 

module types on a relative basis; but additional real-world factors may be introduced, such as illumination 

and PID degradation inclusive of recovery phenomena. This technique may also be extended in the future 

to analyze mean time to failure for other degradation modes. 

Fig. 5. Three-point Arrhenius 

fit to the lifetime data with 

activation energy 0.85 eV. 95% 

confidence intervals are shown 

to either side of the Arrhenius 

fit. Lognormal distributions are 

shown around the data points 

and the analysis is extended to a 

hypothetical 25°C use condition 

as an example. 

Summary and conclusions 

We demonstrated the application of failure distribution statistics to PV modules undergoing PID in an 

environmental chamber, facilitated by the development of an automated in-situ monitoring technique 
6

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

consisting of analysis of the dark I-V curves taken at the stress temperature. Semicontinuous degradation 

curves were obtained and lognormal statistics were applied to draw cumulative failure probability and 

activation energy plots. Activation energy for time to failure was determined to be 0.85 eV. We found that 

the maximum amount of degradation was independent of the stress temperature applied.

The authors would like to thank Garry Babbitt, Greg Perrin, and Kent Terwilliger for their help in 

setting up and performing the experiments and Sarah Kurtz, John Wohlgemuth, and Bill Marion for 

reviewing this manuscript. This work was supported by the U.S. Department of Energy under Contract No. 

DE-AC36-08-GO28308 with the National Renewable Energy Laboratory.

References

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pp. 2817–2822.

[2] P. Hacke et al., “Characterization of multicrystalline silicon modules with system bias voltage applied in damp 

heat,” 25th European Photovoltaic Solar Energy Conference and Exhibition/5th World Conference on Photovoltaic 

Energy Conversion, 6–10 September 2010, Valencia, Spain, pp. 3760–3765.

[3] V. Naumann, et al., “The role of stacking faults for the formation of shunts during potential-induced degradation 

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10.1002/ pssr.201307090.

[4] P. Hacke et al., “Testing and analysis for lifetime prediction of crystalline silicon PV modules undergoing 

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[5] P. Hacke et al. “In-situ measurement of crystalline silicon modules undergoing potential-induced degradation in 

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Crystalline Silicon Solar Cells & Modules: Materials and Processes Breckenridge, Colorado, July 28–31, 2013, 

http://www.nrel.gov/docs/fy13osti/60044.pdf, accessed July 16, 2014.

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crystalline silicon modules undergoing potential-induced degradation stress testing,” Progress in Photovoltaics, 

2014, in print. Correspondences of the simplified terms given in this paper to those in [6] are as follows:

R = Pdeg(tk) = Pmax(tk)/Pmax(t0)

RT = Pdeg(tk, T) = Pmax(tk, T)/Pmax(t0, T)

R25 = Pdeg(tk, 25°C) = Pdeg(tk, T)- M*[ Pdeg(tk, T)-1]

RF = Pdeg(tn, 25°C)

RT F = Pdeg(tn, T)

M =[Pdeg(tn, 25°C)- Pdeg(tn, T)]/(1- Pdeg(tn, T)]

[7] P. Gale, “Estimating Laser Diode Lifetimes and Activation Energy,” Application Note #33, IXL Lightwave, 

Corporation, 2008; http://assets.newport.com/webDocumentsN/images/AN33_Laser_Diode_Activation_IX.pdf, 

accessed July 3, 2014.

[8] F. A. Lindholm, et al., “Application of the superposition principle to solar-cell analysis,” IEEE Transactions on 

Electron Devices 26(3) pp. 165–171 (1979)

[9] P. Hacke, “Testing modules for potential-induced degradation – a status update of IEC 62804,” Proceedings of the 

2014 NREL PV Module Reliability Workshop, Golden, CO, Feb. 25–26, 2014.