Modeling PV Module Power Degradation to Evaluate Performance Warranty Risks

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!


33

Outline

• Motivation

• Context

• Annual Degradation Rate: A Fresh Look

• Systematic Approaches:

Monte Carlo

Convolution

• Application

• Summary and Outlook


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


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


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)


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


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]


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


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%


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


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


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!

Engineering

Modeling PV Module Power Degradation to Evaluate Performance Warranty Risks