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Presented at the European Photovoltaic Solar Energy Conference in September 2012.
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Modeling of PV Module Power
Degradation to Evaluate
Performance Warranty Risks
Thomas Roessler1 and Kenneth J. Sauer2
1Yingli Green Energy Europe GmbH2Yingli Green Energy Americas, Inc.
27th EUPVSEC, Frankfurt, September 24-28, 2012
4DO5.5 Roessler and Sauer
22
Motivation
• Module manufacturers provide performance warranties
• Goal: Quantify associated financial risk
• Illustration: Data from SUPSI – ISAAC PV system built 1982
Warranty Limit
Warranty Risk
Model for time evolution of module power
distributions is needed!
4DO5.5 Roessler and Sauer
33
Outline
• Motivation
• Context
• Annual Degradation Rate: A Fresh Look
• Systematic Approaches:
Monte Carlo
Convolution
• Application
• Summary and Outlook
4DO5.5 Roessler and Sauer
44
Context: Vázquez and Rey-Stolle
• Time evolution of a Gaussian distribution of module powers
2
0
0
0
)(
2
1exp
)(2
1),(
Bt
AtPP
BttPp
M. Vázquez and
I. Rey-Stolle,
Prog. Photovolt.:
Res. Appl.
16 (2008) p. 419.
Extend to arbitrary, realistic module power distributions
Relate broadening to degradation rate distributions
4DO5.5 Roessler and Sauer
55
Context: Jordan and Kurtz
• Encompassing compilation of published measured annual
degradation rates rD for PV modules
• Example result: Distribution q(rD) for crystalline Si modules
D.C. Jordan and
S.R. Kurtz,
Prog. Photovolt.:
Res. Appl. (2011).
Reasonably good fit with gamma distribution
4DO5.5 Roessler and Sauer
66
Annual Degradation Rate: A Fresh Look
• Determined from power P measured at time t and t+Dt
• Repeating this for module population yields distribution q(rD)
• Two interpretations of q(rD):
0 2 4
Fre
qu
ency
Degradation Rate [%/y]
250 255 260
Fre
qu
ency
Module Power [W]
t
ttPtPrD
D
D
)]()([
Probability that the
power of a given module
will degrade by some
amount DP after one
year ( Monte Carlo)
Result of evolution of an
initial Dirac delta function
distribution of module
powers after one year
( Convolution)
(with Dt in years)
4DO5.5 Roessler and Sauer
77
Systematic Approaches: Introduction
• Monte Carlo simulation (evolution from year n to year n+1
by sampling module power & degradation rate distributions):
• Convolution approach [used, e.g., to solve heat or diffusion
equation, kernel is “fundamental solution” for d(P-P0)]:
• Main new aspects:
Applicable to arbitrary initial module power distributions
Explicitly consider distributions of degradation rates q(rD)
')'(~)'()(1 dPPPqPpPp nn
)(~)()(1 PqPpPp ss
n
s
n D
Kernel
4DO5.5 Roessler and Sauer
88
Systematic Approaches: Choice of Parameters
• Realistic initial module
power distribution:
Truncated Gaussian
Representing one
power class for given
module construction
• Degradation rate distribution:
Gamma distribution fit to data
for mono c-Si by Jordan & Kurtz
Maximum at 0.42%, median of 0.59%
230 240 250 260 270 280 290
Fre
qu
ency
Module Power [W]
All 60 Cell Modules
260W Power Class
0 2 4F
req
uen
cyDegradation Rate [%/y]
4DO5.5 Roessler and Sauer
99
0.7 0.8 0.9 1 1.1
Fre
qu
ency
P/P0
Initial
5y
10y
15y20y
25y
Systematic Approaches: Central Result
• Time evolution:
Warranty Limit,
e.g. 80%
Warranty Risk
4DO5.5 Roessler and Sauer
1010
Application: Performance Warranties
• Three different examples:
75
80
85
90
95
100
105
0 5 10 15 20 25
Wa
rra
nty
Lim
it [
%]
Module Age [years]
Stepwise Performance Warranty
Linear Performance Warranty
Agressive Linear Performance Warranty
Linear decrease:
0.71%
0.5%
4DO5.5 Roessler and Sauer
1111
Application: Incremental Warranty Risk
• “Incremental warranty risk” = percentage of modules
underperforming for the first time at a given module age
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 5 10 15 20 25
Ag
gre
ssiv
e L
inea
r [%
]
Incr
emen
tal W
arr
an
ty R
isk
Ste
pw
ise
an
d L
inea
r [%
]
Module Age [years]
Stepwise
Linear
Aggressive Linear
Total warranty
risk:
3.6%
3.6%
74%!!!
Higher cost of
replacement, tighter
control over system
performance
4DO5.5 Roessler and Sauer
1212
Application: Influence of Light-Induced Degradation
• LID: Gaussian with average 1.3%, std. deviation 0.24%
Total warranty
risk:
3.6%
10%
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 5 10 15 20 25
Incr
emen
tal W
arr
an
ty R
isk
[%
]
Module Age [years]
Linear, no LID
Linear, with LID
4DO5.5 Roessler and Sauer
1313
Summary and Outlook
• Summary:
Two systematic and general approaches for time evolution of
module power distributions presented
Simple application to comparison of incremental warranty risk
for different warranty terms demonstrates basic utility
Effects of LID easily incorporated
• Outlook:
Use actual distributions for module power & degradation rates
Consider module volume from different production years
Consider time dependence of cost of module replacement
Time dependence of degradation rate distributions?
Thanks for your attention!
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