NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

STEP-STRESS ACCELERATED DEGRADATION TESTING (SSADT)

FOR PHOTOVOLTAIC (PV) DEVICES AND CELLS

2010 Workshop on Accelerated Stress Testing & Reliability (ASTR)October 6-8, 2010

Denver, CO

Jinsuk Lee, Ryan Elmore, Changwon Suh and Wesley JonesComputational Science Center

National Renewable Energy LaboratoryNREL/PR-2C00-49487

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08GO28308 with the National Renewable Energy Laboratory.

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Introduction of SSADT What is SSADT? Why do we need SSADT? What can be estimated from SSADT?

Reliability testing for PV Current reliability testing How to apply SSADT to PV area (e.g,. CIGS)

Statistical process for SSADT Inference using the lifetime prediction model

Discussion

Outline

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Develop a step-stress degradation testing (SSADT) for PV reliability tests

Stage 1: construct a statistical model for SSADT - current Stage 2: apply to reliability testing for thin film PV

Develop a lifetime prediction model for PV products (cell level, but expandable to module level)

estimate lifetime characteristics (mean time, warranty time, failure rate) and activation energies

Explore the current performance tests for Cu(In,Ga)Se2, CIGS, device and cells; and provide physical and statistical models for their degradation

Objective

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

What is SSADT ?

stre

sstime

SSALTSSADTst

ress

time

ALTADT

Stress vs. Time plot

3 chambers 30 testing units

1 chamber 10 testing units

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

What is SSADT ?

Degradation vs. Time plot

degr

adat

ion

time

.7

.5

.3

τ1 τ2 τ3

w1 w1 + (τ2 - τ1)

w2 w2 + (τ3 – τ2)

L(t | s0 =45˚C)

L(t | s0 =65˚C)

L(t | s0 =85˚C)τ2 – τ1

Cumulative Exposure Model

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

ALT may offer little help for highly reliable products which are not likely to fail during a rather short period of time

ADT collects the degradation data at higher levels of stress and then uses these data to predict the product’s lifetime at a use-condition

Why do we need SSADT?

ALT ADT SSADT

ALT ADT SSADT

SSADT is an economical and flexible test plan- In particular, it is not easy to determine suitable test stress levels in ALT/ADT for new developing products where we don’t have knowledge of appropriate stress levels.

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Product lifetime parameters at various use-conditions- 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)

What can be estimated from SSADT ?

Prediction of Mean time to failure

& Failure rate

Prediction of Warranty time

22.31 yrs5.12E-6

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Performance Testing for CIGS (CIGS, NREL, leaded by John Pern)1. Damp Heat Test: 85°C/85%RH2. Dry Heat Test: 85°C/4-10%RH3. Pressure Cooker: 110°C/100%RH/~6psi4. SSADT

Measurement for Degradation (J-V measurement System) Open-circuit voltage (Voc) Short-circuit current (Isc) Fill factor (FF) Conversion efficiency of the device (η) Series resistance (Rs) Shunt resistance (Rsh)

Reliability Testing for Cu(In,Ga)Se2, CIGS-based Thin film PV

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Statistical Models

Expected degradation for SSADT (by using CEM)

L(t) =

L(t | s1) if 0 ≤ t < τ1

L(t + w1 −τ1 | s2) if τ1 ≤ t < τ 2

ML(t + wm−1 −τ m−1 | sm) if τ m−1 ≤ t < τ m

Degradation model over time

L(t | si ) = L(0) ⋅ exp[−β i tα ], i = 1,2,L ,m

Physical model for temperature and humidity (Generalized Eyring Model)

β i = a ⋅ exp −b

RH i

⋅ exp Ea

k ⋅ (273+Ti )

* Arrhenius Model for Temperature

β i = exp a −Ea

k ⋅ (273+Ti )

degr

adat

ion

time

1

0 τ1 τ2 τ3w1 w1 + (τ2 - τ1)

L(t | s1 )

L(t | s2)

L(t | s3 )

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Degradation of CIGS

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

2Damp heat: 85°C/85%RH(CIGS Modules)

Nor

mal

ized

Effi

cien

cy (%

)

Time (hr)

Increase Humidity

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.

65°C/85%RH

65°C/50%RH

85°C/50%RH

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Example of SSADT Data(LED lamps of fax machine (Tseng & Wen 2000))

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

s1 s3 s5s4s2

Degradation

Time

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Overall Process of Statistical Analysis

Statistical Model

Estimate α ; βi (a, b, Ea)

Estimate Product’s lifetime; Ea;

degradation rate

Detect Upper limit condition

Least square estimation by minimizing

SSE(α,a,b) = ln(−lnL0(t)) − ln(−lnH0(t)){ }2

t∑

Observed data

Given D= criteria for failure,

ˆ t f = − ln D / ˆ β 0( )1/ ˆ α

Least square estimation by minimizing

Estimate at each stress level

SSE(β0,α( j),ω1 ,L ,ω j−1) = ln(− ln H 0 (t)) − Α j −α( j) ln(ω j−1 + t −τ j−1)[ ]{ }2

t= tj−1

tj

∑

Detect the violation for the constant assumption with

ˆ α (i) − ˆ α ( j) < δ

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Example for detecting a upper limit of stress

ln(w j−1 + t −τ j−1)

ln(− ln H 0 (t))

85°C/85%RH

110°C/85%RH

65°C/65%RH

55°C/65%RH

45°C/40%RH

α5=0.931*

α4=0.817+

α3=0.794*

α2=0.781*

α1=0.788*

“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

SSE(β0,α( j),ω1 ,L ,ω j−1) = ln(− ln H 0 (t)) − Α j −α( j) ln(ω j−1 + t −τ j−1)[ ]{ }2

t= tj−1

tj

∑

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

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Develop statistical models for a cutting-edge life-testing technique, SSADT, with temperature-humidity condition for PV reliability testing- applicable to all PV reliability testing (including module levels and all PV technologies)

Discuss the benefits of SSADT

Consider other applicable degradation models (discussed by Nelson (1990)): e.g., some temperature-humidity models

Study two main areas for SSADT: Statistical inference and Optimal planning

Discuss about other statistical methods to build a SSADT model and analyze its data – e.g., LSE vs. MLE, Bayesian inference, generalized linear models, etc.

Discussion

NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

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

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.

W. Nelson, Accelerated Testing – Statistical Models, Test Plans, and Data Analysis, Wiley & Sons, New York, 1990.

J. Lee and R. Pan, “Bayesian inference model for step-stress accelerated life testing with type-II censoring, in Proc. The Annual Reliability and Maintainability Symposium, Las Vegas, NV, 2008.

J. Lee and R. Pan, “Analyzing Step-Stress accelerated Life Testing Data Using Generalized Linear Models,” IIE Transactions, 42, 2010, pp589-598.

Key Reference