Statistical Modeling of Photovoltaic Reliability Using Accelerated Degradation Techniques

Jinsuk Lee, Ryan Elmore, and Wesley JonesComputational Science Center, National Renewable Energy Laboratory, Golden, CO, USA

Presented at the 2011 PV Module Reliability Workshop, 16‐17 February 2011,  Golden, Colorado

Introduction & Objective

 Introduce cutting‐edge life‐testing technique, accelerated degradationtesting (ADT), for PV reliability testing

 Apply two common types of ADT for life‐time prediction of PV modules:multiple constant‐stress ADT (MCSADT) and step‐stress ADT (SSADT)

 Develop statistical models for use of SSADT with the thermal‐humiditystress condition through the cumulative damage model (CDM)

 Provide quantitative models for prediction of PV module life‐timeincluding mean‐time‐to‐failure (MTTF), warranty time andfailure/degradation rates

 Estimate accelerated testing parameters, such as activation energy,

Statistical Models for SSADT

T (°C) T (°C)

T (°C)

75°C

65°C

55% 70% 85%RH(%)

85°C

T (°C)

T (°C)

75°C

65°C

55% 70% 85%RH(%)

85°C

T (°C)

75°C

65°C

55% 70% 85%RH(%)

85°C

Matrix 1 Matrix 2 Matrix 3

Matrix 4 Matrix 5 Matrix 6

Test Matrix Test Design

T (°C)

85°C

RH (%)

85%

75°C

Accelerated Testing

acceleration factors, upper limit condition of stress via statistical inferenceprocedure

(Constant) Accelerated Testing(Constant) Accelerated TestingDegradation(ADT)

Failure(ALT)

Thermal‐Cycling(TCT)

( )

75°C

65°C

55% 70% 85%RH(%)

85°C

( )

75°C

65°C

55% 70% 85%RH(%)

85°C

75°C

65°C

55% 70% 85%RH(%)

85°C

Matrix 4 Matrix 5

 The thermal‐humidity condition Temperature (T): 3 levels (65°C, 75°C, 85°C) Relative Humidity (RH): 3 levels (55%, 70%, 85%) No interaction between T and RH

 6 possible test matrices can be considered for the SSADT plan

65°C 55%

85%

2mo Time (month)

4mo 6mo

70%

8mo 10mo

 This plot depicts a test design based on “Test Matrix 5” which has five stress levels

 Level 1 (s1): 65°C & 55%RH Level 2 (s2): 65°C & 70%RH Level 3 (s3): 75°C & 70%RH Level 4 (s4): 75°C & 85%RH Level 5 (s5): 85°C & 85%RH

Degradation Model

SSADT Model

(Time‐varying) Accelerated Testing(Time‐varying) Accelerated Testing

Progressive Step-stress Testing

Regressive Step-stress Testing

Profile Step-stress Testing

use-level

stress-level

deg

rad

atio

n

time

use-level

stress-level

stre

ss

time

tem

per

atu

re Coffin-Manson ModelNorris-Landzberg Model

time

time

stre

ss

X    X

X    X

Model

 Linear: Exponential: Power: Logarithmic: And some used:

 Linear: Exponential: Power: Logarithmic: And some used:

Stage 1: Defining a degradation pattern

L(t) a  t  b(s)

L(t) b(s)  exp[a  t]

L(t) b(s)  ta

L(t) a  ln t  b(s)

 Temp:

 Temp & RH:

 Other two stresses

 Three stresses

 Temp:

 Temp & RH:

 Other two stresses

 Three stresses

Stage 2: Defining a physical model for stress

L(t) exp[b(s)ta ]

L(t) 1 b(s)  ta 1(Tseng and Wen, 2000)

(Mitsuo, 1991)

b(s;  T ) exp c Ea

k  (273T )









b(s; T, RH ) c exp  d

RH



exp

Ea

k  (273T )







 

b(s; T, RH ) c exp d RH  expEa

k  (273T )







 

deg

rad

atio

n

L(t | s1 =65 ̊C & 55%)

L(t)

L(t | s1) if  0  t  1

L(t w1 1 | s2 ) if  1  t   2

L(t w2  2 | s3) if   2  t   3        

L(t w3  3 | s4 ) if   3  t   4

L(t w4  4 | s5) if   4  t   5











 Expected degradation for SSADT

Cumulative Damage Model (CDM)

St ti ti l P f

Multiple Constant‐Stress ADT (MCSADT)

 The accelerated life testing (ALT) technique may offer little help for highreliable products which are not likely to fail during a rather short periodtime

 ADT collects the degradation data instead of failure data when it is moredifficult to obtain sufficient failure data for ALT

 Single constant‐stress testing (e.g, Damp‐Heat Test) can be used forqualification testing with a specific durability criteria

 MSCADT can be used for life‐time prediction of products

n

timeτ1 τ2 τ3

L(t | s3 =75 ̊C & 75%)

L(t | s4 =75 ̊C & 85%)

L(t | s5 =85 ̊C & 85%)

τ5τ4

w1 w1 + (τ2 - τ1)

L(t | s2 =65 ̊C & 75%)

deg

rad

atio

n

L(t | s3 =75 ̊C & 75%)

L(t | s2 =65 ̊C & 75%)

L(t | s1 =65 ̊C & 55%)

by Horizontal Shift

(τ2 - τ1)

(τ2 - τ1)

Statistical Model

Estimate α ; βi (a, b, Ea)

Estimate 

Least square estimation by minimizing

SSE(,a,b)  ln(lnL0(t)) ln(lnH0(t)) 2

t

Observed data

Given D= criteria for failure,

ˆ t f   ln D / ˆ 0 1/ ˆ 

Statistical Process for Lifetime Prediction

Expected value

stre

ss

time time

deg

rad

atio

n

45°C

65°C

85°C

85°C

65°C

45°C

 3 chambers 30 testing units

Step‐Stress ADT (SSADT)

 Step‐stress testing is one of the most basic time‐varying stress tests. In

timeτ1 τ2 τ3

L(t | s4 =75 ̊C & 85%)

L(t | s5 =85 ̊C & 85%)

τ5τ4

Product’s lifetime;  Ea; degradation rate

Detect Upper limit condition

Least square estimation by minimizing

Estimate at each stress levelSSE(0,( j),1 ,, j1)  ln( ln H 0 (t))   j ( j) ln( j1  t  j1)  

2

t t j1

t j



Detect the violation for the constant assumption with

ˆ (i) ˆ ( j) 

References:[1] J. Lee and R. Pan, “Analyzing Step-Stress accelerated Life Testing Data Using Generalized Linear Models,” IIE Transactions, 42, 2010, pp589-598.[2] S.-T. Tseng and Z.-C. Wen, “Step-Stress Accelerated Degradation Analysis For Highly Reliable Products, Journal of Quality Technology, 32, 2000, pp209-216.[3] W. Nelson, Accelerated Testing – Statistical Models, Test Plans, and Data Analysis, Wiley & Sons, New York, 1990.

Measurement for Degradation of PV Modules

Outputs from SSADT

 J‐V measurement System  Product lifetime parameters at various use‐conditions Prediction of 

a step‐stress test, multiple samples in one or more sets are exposed toseveral stress conditions over time.

 Step‐stress testing is an advanced reliability testing technique for highreliability products

 Economical: suitable for limited test facility and condition

 Flexible: useful for new developing products where there is notenough knowledge for test conditions

 SSADT can be constructed based on the cumulative damage model(CDM), which assumes that the remaining test units are failed accordingto the cumulative density function of current stress level regardless ofthe history on previous stress levels.

stre

ss

dat

ion

°

 1 chamber 10 testing units

 Open‐circuit voltage (Voc)

 Short‐circuit current (Isc)

 Fill factor (FF)

 Conversion efficiency of the device (η) Series resistance (Rs)

 Shunt resistance (Rsh)

0.7

0.8

0.9

1.0

1Dry heat: low‐pressure air at 85°C(encapsulated CIGS Modules)

2Damp heat: 85°C/85%RH(CIGSM d l )

Norm

alized

 Efficiency (%

)

Increase Humidity

65°C/85%RH

65°C/50%RH

85°C/50%RH

Degradation for Efficiency of CIGS Modules

p

‐Mean time to failure‐ Reliability (Warranty) time

‐ Failure rate Degradation rate at various use‐conditions Activation Energy (Ea)

 Upper limit level of stress (tolerable stress level)

ln( ln H 0 (t))

85°C/85%RH

100°C/85%RH

75°C/85%RH

75°C/75%RH

65°C/75%RH

α5=0.931*

α4=0.817+

α3=0.794*

α2=0.799*

α1=0.772*

SSE( 0,( j),1 ,, j1)  ln( ln H 0 (t))   j ( j) ln( j1  t  j1 )  2

t tj1

tj



R(t)=0.5 at 45°C

Warranty Time

R(t)=0.5 at 45°C

Detection of Upper Limit Level of Stress Prediction of MTTF 

and Failure Rate

slope

The Alliance for Sustainable Energy, LLC (Alliance), is the Manager and Operator of the National Renewable Energy Laboratory. Employees of the Alliance for Sustainable Energy,LLC, under Contract No. DE‐AC36‐08GO28308 with the U. S. Dept. of Energy have authored this work. The United States Government retains and the publisher, by accepting thearticle for publication, acknowledges that the United States Government retains a non‐exclusive, paid‐up, irrevocable, worldwide license to publish or reproduce the publishedform of this work, or allow others to do so, for United States Government purposes. NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiencyand Renewable Energy, operated by the Alliance for Sustainable Energy, LLC. NREL/PO‐2C00‐50738 • February 2011

time time

deg

rad

45°C

65°C

85°C

85°C

65°C

45°C

0 200 400 600 800 1000

0.6

(CIGS Modules)

Time (hr)

Decrease Temp.

1Data source: J. Wennerberg, “Design and Stability of Cu(In,Ga)Se2‐Based Solar Cell Modules,” Dissertation, ACTA Universitatis Upsaliensis, 2002.2 Data source: J. Wennerberg et al., “Cu(In,Ga)Se2‐Based thin‐film photovoltaic modules optimized for long‐term performance,” Solar Energy Materials & Solar Cells, 75, 2003, pp47‐55.

ln(w j1  t  j1)

 “α is independent of stress” is only valid for temperature less than or equal 85°C       ‐ The issue of “over‐stress” can lead to misleading results

Note, + : estimated value from Wennerberg et al. (2003) * : assumed value

22.31 yrs5.12E‐6

References:[2] S.-T. Tseng and Z.-C. Wen, “Step-Stress Accelerated Degradation Analysis For Highly Reliable Products, Journal of Quality Technology, 32, 2000, pp209-216.

- Slide Number 1