Statistical Modeling of Photovoltaic Reliability Using Accelerated Degradation Techniques Jinsuk Lee, Ryan Elmore, and Wesley Jones Computational 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 degradation testing (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‐humidity stress condition through the cumulative damage model (CDM)  Provide quantitative models for prediction of PV module life‐time including mean‐time‐to‐failure (MTTF), warranty time and failure/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 inference procedure (Constant) Accelerated Testing (Constant) Accelerated Testing Degradation (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 (s 1 ): 65°C & 55%RH  Level 2 (s 2 ): 65°C & 70%RH  Level 3 (s 3 ): 75°C & 70%RH  Level 4 (s 4 ): 75°C & 85%RH  Level 5 (s 5 ): 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 degradation time use-level stress-level stress time temperature Coffin-Manson Model Norris-Landzberg Model time time stress 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)  t a L(t)  a  lnt  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)t a ] L(t )  1 b(s)  t a   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    exp Ea k  (273T)       degradation L(t | s1 =65˚C & 55%) L(t )  L(t | s 1 ) if 0  t   1 L(t  w 1   1 | s 2 ) if  1  t   2 L(t  w 2  2 | s 3 ) if  2  t   3 L(t  w 3   3 | s 4 ) if  3  t   4 L(t  w 4   4 | s 5 ) if  4  t   5           Expected degradation for SSADT Cumulative Damage Model (CDM) St ti ti lP f Multiple Constant‐Stress ADT (MCSADT)  The accelerated life testing (ALT) technique may offer little help for high reliable products which are not likely to fail during a rather short period time  ADT collects the degradation data instead of failure data when it is more difficult to obtain sufficient failure data for ALT  Single constant‐stress testing (e.g, Damp‐Heat Test) can be used for qualification testing with a specific durability criteria  MSCADT can be used for life‐time prediction of products n time τ 1 τ 2 τ 3 L(t | s3 =75˚C & 75%) L(t | s4 =75˚C & 85%) L(t | s5 =85˚C & 85%) τ 5 τ 4 w1 w1 + (τ2 - τ1) L(t | s2 =65˚C & 75%) degradation 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 ; β i (a, b, E a ) Estimate Least square estimation by minimizing SSE(, a,b)  ln(lnL 0 (t))  ln(lnH 0 (t))   2 t  Observed data Given D= criteria for failure, ˆ t f  ln D/ ˆ  0   1/ ˆ  StatisticalProcess for Lifetime Prediction Expected value stress time time degradation 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 time τ1 τ2 τ3 L(t | s4 =75˚C & 85%) L(t | s5 =85˚C & 85%) τ5 τ4 Product’s lifetime; E a ; degradation rate Detect Upper limit condition Least square estimation by minimizing Estimate at each stress level SSE( 0 ,( j), 1 ,, j1 )  ln( ln H 0 (t))  j ( j) ln( j1  t  j1 )     2 ttj1 tj  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 to several stress conditions over time.  Step‐stress testing is an advanced reliability testing technique for high reliability products  Economical: suitable for limited test facility and condition  Flexible: useful for new developing products where there is not enough knowledge for test conditions  SSADT can be constructed based on the cumulative damage model (CDM), which assumes that the remaining test units are failed according to the cumulative density function of current stress level regardless of the history on previous stress levels. stress dation °  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 (encapsulatedCIGS Modules) 2Damp heat: 85°C/85%RH (CIGSM d l ) Normalized Efficiency (%) Increase Humidity 65°C/85%RH 65°C/50%RH 85°C/50%RH Degradation for Efficiency of CIGS Modules ‐ Mean time to failure ‐ Reliability (Warranty) time ‐ Failure rate  Degradation rate at various use‐conditions  Activation Energy (E a )  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(lnH0(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 the article for publication, acknowledges that the United States Government retains a non‐exclusive, paid‐up, irrevocable, worldwide license to publish or reproduce the published form 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 Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC. NREL/PO‐2C00‐50738  February 2011 time time degrad 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. 2Data 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(wj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 yrs 5.12E‐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.