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Using Uncertainty Analysis 

to Guide the development 

of Accelerated Stress Tests

NREL Photovoltaic Module Reliability 

Workshop (PVMRW)

Michael Kempe

Golden, Colorado

Tuesday, February 25, 2014

NREL/PR-5200-61539
2

Introduction

• PV modules degrade in response to 

environmental stresses such as heat, humidity, 

UV irradiation, CTE mismatch, high voltage, and 

etc..

• Many degradation processes are driven by 

complex combinations of these stress factors. 

• For generalized accelerated stress tests, a 

significant amount of uncertainty is inherent.

• A better understanding of the uncertainty in 

the relevant stress factors will aid in the 

development of accelerated stress tests.
3

Outline

• Look at the hydrolysis of a typical back-sheet 

made of PET as a case study for a material with 

an unusually high level of understanding of 

degradation. 

• Apply kinetic models of paints and coatings 

degradation to backsheets.

• Discuss concerns with developing a single test 

for all degradation modes.
4

PET Hydrolysis Modeling

• PET is commonly used in back-sheet materials:

o Low cost

o Good electrical insulator

o Long term track record

• Hydrolysis results in embrittlement of PET which can 

lead to cracking and back-sheet failure.

• However, hydrolysis is only one potentially relevant 

failure mechanism, but it is extremely well 

understood.

O

O O

O

PolyEthylene Terepthalate (PET)

n
5

PET Hydrolysis Kinetics

O

O O

O

PolyEthylene Terepthalate (PET)

n

H H

+ O O

O O

O H

n-x

HO O

O O

O

x

+

tffff =

e

Ea

RR

A RR 2

Ea=129±3.4 kJ/mol

A=1.2·1017±1.3·1017h 

Pickett et. al**

RH expressed as a percentage. 

*PET becomes brittle (1/3 initial tensile strength) and “failed” when about 0.55% hydrolysis 

of ester bonds. 

*W. McMahon, H. A. Birdsall, G. R. Johnson, and C. T. Camilli, "Degradation Studies of Polyethylene Terephthalate," Journal of Chemical & Engineering Data, vol. 4, pp. 57-79, 1959.

**J. E. Pickett and D. J. Coyle, "Hydrolysis Kinetics of Condensation Polymers Under Humidity Aging Conditions," Polymer Degradation and Stability, vol. 98, pp. 1311-1320, 2013.
6

Hydrolysis Mechanism is Well Understood

O

O

R

H O H

H

O

H

O

O

R

H O

H

H

O

H

O

O

R

H

O H

H

O

H

O

O

R

H

O H

H

O

H

O

O

R

H

O

H

H

O

H Scheme 4*

Scheme 6*

• Picket et. al* proposed these mechanisms and reaction intermediates as 

possible hydrolysis pathways.

*J. E. Pickett and D. J. Coyle, "Hydrolysis Kinetics of Condensation Polymers Under Humidity Aging Conditions," Polymer 

Degradation and Stability, vol. 98, pp. 1311-1320, 2013. **Shi Z, Hsieh Y-H, Weinberg N, Wolfe S. The neutral hydrolysis of methyl acetate—Part 2. Is there a tetrahedral intermediate? Can J Chem 2009: 87; 544-555.

Euranto EK, Cleve NJ. Kinetics of the neutral hydrolysis of chloromethyl chloroacetate. Acta Chemica Scand. 1963: 17; 1584-1594.
7

Site Specific Equivalent T and RH

RRww wwwww a a = RRWW =

∑ RRne −E

k

∑ e −E

k

1

n

RHWA is an average effective relative humidity weighted towards higher 

temperatures where most of the damage occurs.

The equivalent temperature (Teq) gives the temperature at RHWA for which constant 

conditions will produce a degradation rate equivalent to the yearly average. 

T e = − EE

kkk ∑ e −E

k

N

tffff =

e

Ea

RR

A RR 2
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Uncertainty Propagation

σf

2 ≈

∂∂

∂

2

σ 2 + ∂∂

∂∂

2

σb

2 + 2

∂∂

∂

∂∂

∂∂ CCC ...

Assumes f(a,b,...) has normally distributed uncertainties and ignores higher order terms.

σ

ee

= − 1

kkk ∑ e −E

K

N

− EE

k2

∑ e −E

K

T

∑ e −E

K

σE

T e = − EE

kkk ∑ e −E

k

N
9

Pet Hydrolysis Uncertainty

• The uncertainty in the service life 

was a function of the uncertainty 

in the prefactor A and Ea, with a 

significant correlation between 

the two.

• The uncertainty in all other terms 

is dependent only on σEa. 

• The uncertainty in the order 

parameter n was assume to be 

zero.

• The uncertainty in the weather, 

materials, microclimate, and etc

was ignored. 

• Thus this represents a minimal 

estimate of uncertainty.
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Pet Hydrolysis Uncertainty

• A 1000 h 25 y 

equivalent test 

can be designed 

by using only 

thermal 

acceleration.

• Alternatively, 

the acceleration 

can be split 

between higher 

temperature 

and higher 

humidity.
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Pet Hydrolysis Uncertainty

• A 1000 h test is suitable for screening tests or qualification tests.

• A 6 month test provides more flexibility in a reasonable amount of 

time.

• A 2.5 y test is an acceleration factor of 10× which is generally 

believed to provide reasonable accelerations for unknown processes.
12

Reduced Uncertainty for Longer Test Times

• This represents the smallest amount of uncertainty possible. It ignores 

variability from exposure, construction and other test specific sources, 

and assumes the failure mode is directly related to PET hydrolysis.
13

Kinetics of Paints and Coatings Degradation

• 50 coatings with respect to color shift, 

cracking, gloss loss, fluorescence loss, 

retroreflectance loss, adhesive transfer, and 

shrinkage.

RD~Ix ∙ + m ∙ T T ∙ Tf

− o

10

*R. M. Fischer and W. D. Ketola, "Error Analyses and Associated Risk for Accelerated Weathering Results," Third International Service Life 

Symposium, Sedona, AZ February 2004, 2004.

*Fischer et. al

Tf=1.41±0.23 Acceleration per 100C increase.

X=0.64±0.2 Irradiance acceleration exponent.

m=-0.0015±0.12 Time of Wetness (TOW) factor.

b=1.071±0.0026
14

Modeling Assumptions for a PV Backsheet

• Assume UV on back of rack mounted system 

is 0.5% of global horizontal irradiance.

• Ignore TOW 

o Very high uncertainty with a low mean value 

indicating a very small effect.

o Condensation is predominantly on the front 

making application of this effect dubious on the 

back. 
15

Location Specific Effective Conditions

ASTM G173 has 35.6 W/m2 between 295 and 385 nm

To =

10

f

∑ f

T

10

N IWW =

∑ IxTf

− o

10

N

1

x
16

Much Greater Uncertainty in 25 y Tests

• Temperature and irradiance optimized to 

minimize the uncertainty in a 25 y equivalent 

stress test.
17

Optimal Exposure Conditions

• ASTM G173 using 0.5018 W/m2/nm @340 nm

o 1000 h test - 5 to 10 UV suns

o 6 month test - 1 to 2 UV suns

o 2.5 y test - 0.17 to 0.33 UV suns
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Conclusion

• With an extremely good understanding of the 

degradation kinetics, one can design a 25 y equivalent 

test to within ~±1 y. Unfortunately, this is an unusual 

occurrence and produces results with a very narrow 

scope.

• For backsheet materials, a generic and long, ~2.5 y, test 

may yield reasonable uncertainties of ~± 8 y.

• Accelerated stress tests must be very targeted at specific 

materials and failure modes, or be of a very long 

duration.

• Estimates for irradiance for a 25 y backsheet test:

– 1000 h test - 5 to 10 UV suns

– 6 month test - 1 to 2 UV suns

– 2.5 y test - 0.17 to 0.33 UV suns
19

Acknowledgements

Sarah Kurtz

John Wholgemuth

David Miller

Peter Hacke

This work was supported by the U.S. 

Department of Energy under Contract No. 

DE-AC36-08-GO28308 with the National 

Renewable Energy Laboratory.