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Modeling the Ranges of Stresses for 

Different Climates/Applications

International PV Module 

QA Forum

Michael Kempe, Sarah 

Kurtz, John Wohlgemuth, 

David Miller, Matthew 

Reese, Arrelaine 

Dameron

July 15, 2011

NREL/PR-5200-52312
NATIONAL RENEWABLE ENERGY LABORATORY

Introduction

2

Photovoltaic modules must be designed to be installed in a wide 

variety of environments with variable types of mounting 

configurations. 

The environment influences the amount of UV radiation, the 

exposure to humidity, and the range of ambient temperatures 

that will be seen. 

Additionally, the mounting configuration influences convective 

heat transfer creating the potential for significant variability in 

thermal stresses at the same geographic location.

All these environmental, site specific, attributes must be 

considered when evaluating the durability of photovoltaic 

modules. 
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Outline

3

Activation Energy

Effect of Environment

Effect of Mounting Configuration

Moisture ingress

Edge Seal Modeling

Generic Corrosion Models

Conclusions
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Degradation Processes Are Thermally Activated

4





 



 −

∝ kT

Ea

Rate e

• Photovoltaic modules will degrade because of many different 

environmental stress factors:

I. Temperature

II. Humidity

III. UV light

IV. Thermal cycling

V. Dynamic loading

VI. Static loading

• Here, we will discuss simple degradation processes dominated by 

temperature and/or moisture effects

The Arrhenius equation is one of the most commonly reported models for the 

temperature dependence of degradation processes.
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Definition of Equivalent Temperature

5

[ ]

e dt

t t

e

kT t

Ea

eq kT

Ea

t

t

( ) 2

1 2 1

1

−

−

∫ − =



 

Teq gives a characteristic temperature for an environment that is related to 

the expected degradation kinetics. However, the Choice of the activation 

energy is vital.





















∫ −

−





 



=

 −

e dt

t t

k

E

eq

kT t

Ea

t

t

a T

2 ( )

2 1 1

1 ln

Rate at Constant Temperature = Time Average Degradation Rate
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Typical Thermal Degradation Activation Energies

6

R. R. Dixon, "Thermal Aging Predictions from an Arrhenius Plot with Only One Data Point," Electrical Insulation, IEEE 

Transactions on, vol. EI-15, pp. 331-334, 1980
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Modeling Parameters

7

•Used TMY-3 data from several representative climates.*

•Module temperature approximated according to King et al.**

* http://apps1.eere.energy.gov/buildings/energyplus/, as described in: S. Wilcox and W. Marion, "Users Manual for TMY3 Data Sets" Technical Report NREL/TP-581-

43156, revised May, 2008.

** D.L. King, W.E. Boyson, and J.A. Kratochvil, "Photovoltaic Array Performance Model," Sandia National Laboratories, SAND2004-3535, (2004).

Tm = Tamb + Irradiance ×exp[−a − b ×WS]+ ∆T × Irradiance/1000

Module type Mount a b ∆T (°C)

Glass/cell/glass Open rack -3.47 -0.0594 3

Glass/cell/glass Close roof -2.98 -0.0471 1

Glass/cell/polymer sheet Open rack -3.56 -0.0750 3

Glass/cell/polymer sheet Insulated back -2.81 -0.0455 0

Polymer/thin-film/steel Open rack -3.58 -0.113 3

22X Linear concentrator Tracker -3.23 -0.130 13
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Teq Varies by Location and Mounting Configuration

8

70

60

50

40

30

20

Equivalent temperature (°C)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Activation energy (eV)

Insulated Back

Close Roof

Tracker

Open Rack B

Open Rack A

Open Rack C

Riyadh

(a)

70

60

50

40

30

20

Equivalent temperature (°C)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Activation energy (eV)

Insulated Back

Close Roof

Tracker

Open Rack B

Open Rack A

Open Rack C

Miami

(c)

70

60

50

40

30

20

Equivalent temperature (°C)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Activation energy (eV)

Insulated Back

Close Roof

Tracker

Open Rack B

Open Rack A

Open Rack C

Munich (d)

S. Kurtz, K. Whitfield, G. TamizhMani, M. Koehl, D. Miller, J. Joyce, J. Wohlgemuth, N. Bosco, M. Kempe, and T. Zgonena, "Evaluation of 

high-temperature exposure of photovoltaic modules," Progress in Photovoltaics: Research and Applications, DOI: 10.1002.

Mounting Configuration: ±10oC

Location: ±15oC 

Activation Energy: ±10oC 

Total Range: ±30oC 
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Thermal Acceleration Depends on Mounting 

and Environment

9

S. Kurtz, K. Whitfield, G. TamizhMani, M. Koehl, D. Miller, J. Joyce, J. Wohlgemuth, N. Bosco, M. Kempe, and T. Zgonena, "Evaluation of 

high-temperature exposure of photovoltaic modules," Progress in Photovoltaics: Research and Applications, DOI: 10.1002.

0.1

1

10

100

1000

Time at 85°C for one year of aging (h)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Activation energy (eV)

Riyadh

Insulated Back

Close Roof

Tracker

Open rack

(a)

0.1

1

10

100

1000

Time at 85°C for one year of aging (h)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Activation energy (eV)

Miami

Insulated Back

Close Roof

Tracker

Open rack

(c)

0.1

1

10

100

1000

Time at 85°C for one year of aging (h)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Activation energy (eV)

Munich

Insulated Back

Close Roof

Tracker

Open rack

(d)

•Environment : 10X to 100X

•Mounting: 10X to 100X

•Activation Energy: 10 X to 1000X

•Overall there is a 10,000X 

variability in degradation rates.
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Do all Processes Have the Same Activation?

10

0.1

1

10

100

1000

1E-08

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1

Permeability (g mm/m

2/day)

Diffusivity and Solubility (cm

2/s, g/cm

3)

Activation Energy (eV)

Diffusivity 

Solubility Permeability 

100

10-1

10-2

10-3

10-4

10-5

10-6

10-7

10-8

Data obtained from Fickian fit to transient water vapor permeation through films of a variety of PV polymeric materials. Calculated at 850C.

Mass Transport Phenomena Have Low Activation Energies.

H20 Transport Properties at 85oC
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Edge Seal Modeling

The use of fillers, pigments, and desiccants makes the 

determination of modeling parameters much more difficult.

11

100%

RH% S S e kT

Ea

m o

s 



 





−

=





 



 −

=

kT

Ea

eff o

D

D D e

Mobile phase water absorption is split between the 

polymer matrix and the mineral components.

Assume linearity with relative humidity.

Mobile phase water diffusivity is an effective 

diffusivity. This accounts for a rapid equilibration 

between adsorbed and dissolved water.

A non-reversible reaction with water. RH2O
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0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 5 10 15 20 25 30

Ingress Depth (cm)

Time (years)

Insulated Back, Glass/Polymer

Close Roof, Glass/Glass

Open Rack, glass/glass

Open Rack, Glass/Polymer

Mounting Configuration Is Not a Large Factor

12

Denver Colorado

Used TMY3 Data and Temperature estimates similar to King et al, and Kurtz et al.

X = K t
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Preliminary Results for Different Climates

13

A sensitivity analysis gave about ±15% on K and Width, and ±30% on 20 yr equivalent time.

9.22

56

7.77

16

0.0327

 

Open Rack, glass/glass

Close Roof, Glass/Glass

Open Rack, Glass/Polymer

Insulated Back, Glass/Polymer

Do (cm2/s)=

EaD (kJ/mol)=

So (g/cm3

)=

EaS (kJ/mol)=

Reactive Ca absorption (g/cm3)=

Open Rack, Glass/Polymer

Insulated Back, Glass/Polymer

Open Rack, glass/glass

Close Roof, Glass/Glass

Open Rack, Glass/Polymer

Insulated Back, Glass/Polymer

Open Rack, glass/glass

Close Roof, Glass/Glass

Open Rack, Glass/Polymer

Insulated Back, Glass/Polymer

Open Rack, glass/glass

Close Roof, Glass/Glass

MUNICH

PHOENIX SKY HARBOR 

INTL AP

MIAMI INTL AP

DENVER/CENTENNIAL 

[GOLDEN - NREL]

Open Rack, glass/glass

Close Roof, Glass/Glass

Open Rack, Glass/Polymer

Insulated Back, Glass/Polymer

Open Rack, glass/glass

Close Roof, Glass/Glass

RIYADH

BANGKOK

Open Rack, Glass/Polymer

Insulated Back, Glass/Polymer

 

0.32 316

0.33 330

0.36 408

0.38 454

0.34 353

0.34 364

0.37 432

0.39 471

0.41 525

0.42 551

0.48 705

0.51 795

0.50 767

0.51 805

0.58 1,029

0.61 1,161

0.70 1,520

0.72 1,580

0.78 1,889

0.82 2,062

0.83 2,115

0.84 2,192

0.92 2,625

0.96 2,867

20 yr equivalent 

at 850C/85% RH

 

(cm) (h)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20 y required 

width
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Absolute Humidity Correlates to Water Ingress

14

Average RH 

at Module 

Temperature 

(%)

Ambient 

Average RH 

(%)

0.6 Ev 

Module 

Equivalent 

Temperature 

(°C)

Average 

Module 

Temperature 

(°C)

Ambient 

Average 

Temperature 

(°C)

Average 

Ambient 

Water Vapor 

Pressure 

(kPa)

0.05 0.10 0.17

0.46

0.60

0.92

Linear Regression Correlation Coefficient 

for Edge Seal Moisture Ingress Distance R2
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Life Prediction Must Account For Sample Geometry

15

Seal Encapsulant

Glass

Glass

H2O

w

Glass

EVA

PVF

PET

PVF

Cells

Framed Silicon Wafer Module

Al Frame

Glass

EVA

Glass

Cells

Silicon Wafer Module

Backside of cells 

equilibrates in days. 

Front Side of cells 

exposed to moisture 

within weeks.

It may take several 

years for most of the 

module to be 

exposed to moisture.

Active materials may 

not be exposed to 

any moisture for 

decades.
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Typical Microelectronics Degradation Models

16

*D. J. Klinger, "Humidity acceleration factor for plastic packaged electronic devices," Quality and Reliability Engineering International, vol. 7, pp. 365-370, 1991.

**D. J. Coyle, H. A. Blaydes, J. E. Pickett, R. S. Northey, and J. O. Gardner, "Degradation kinetics of CIGS solar cells," Proceedings of the 2009 34th IEEE 

Photovoltaic Specialists Conference (PVSC 2009), pp. 001943-7, 2009.

α

ε 



 





− +

=





 



 −

RH

RH R k e RT

Ea

D o 1

e.g. CIGS Degradation Model by Coyle et al. Ea=0.38 eV, α=1.**

Typically, the effects of temperature and humidity are convoluted making the 

application of appropriate accelerated stress tests extremely difficult even if all the 

degradation kinetics were known. *
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Conclusions

17

1. The amount of thermal degradation is dependent on 

both the geographic location and on the mounting 

configuration.

2. Qualification testing (1000 h 850C/85%RH) may be 

either over- or under-stressing a module relative to its 

expected lifetime. (over-stressing for cold environment 

and high activation energy, under-stressing for hot and 

low activation energy).

3. For packaging that limits moisture ingress, the mounting 

configuration is less important and the average 

environmental absolute humidity correlates to the 

severity of moisture in the climate. 

4. Many degradation mechanisms are accelerated by both 

moisture and temperature making proper design of 

generically applicable accelerated stress tests difficult.
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Acknowledgements

18

This work was supported by the U.S. Department of Energy 

under Contract No. DE-AC36-08-GO28308 with the 

National Renewable Energy Laboratory.
NATIONAL RENEWABLE ENERGY LABORATORY 19
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Ingress Estimated Using Finite Element Analysis

20

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12

Ingress Depth (cm)

Time (month)

Insulated Back, Glass/Polymer

Close Roof, Glass/Glass

Open Rack, glass/glass

Open Rack, Glass/Polymer

Denver Colorado

Used TMY3 Data and Temperature estimates similar to King et al, and Kurtz et al.

X = K t
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Absolute Humidity Correlates to Water Ingress

21

R2 = 0.0529

R2 = 0.4577

R2 = 0.0978

R2 = 0.5963

R2 = 0.1674

R2 = 0.9201

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

0.0 0.2 0.4 0.6 0.8 1.0

Average Ambient Water Partial Pressure (kPa)

Temperature (0C) or RH (%)

20 yr Edge Seal Width (cm)

Factors Affecting Edge Seal Performance

Average RH at Module Temperature (%) Average Module Temperature (0C) Ambient Average RH (%)

Ambient Average Temperature (0C) 0.6 eV Module Equivalent Temperature (0C) Average Ambient Water Vapor Pressure (kPa)