NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Outdoor PV Module Degradation 

of Current-Voltage Parameters

Preprint

Ryan M. Smith, Dirk C. Jordan,

and Sarah R. Kurtz

To be presented at the 2012 World Renewable Energy Forum

Denver, Colorado

May 13–17, 2012

Conference Paper

NREL/CP-5200-53713

April 2012
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1

OUTDOOR PV MODULE DEGRADATION OF CURRENT-VOLTAGE PARAMETERS

Ryan M. Smith

Dirk C. Jordan

Sarah R. Kurtz

National Renewable Energy Laboratory

1617 Cole Boulevard

Golden, CO 80401

email: ryan.smith@nrel.gov

ABSTRACT

Photovoltaic (PV) module degradation rate analysis 

quantifies the loss of PV power output over time and is 

useful for estimating the impact of degradation on the cost 

of energy. An understanding of the degradation of all 

current-voltage (I-V) parameters helps to determine the 

cause of the degradation and also gives useful information 

for the design of the system. This study reports on data 

collected from 12 distinct mono- and poly-crystalline 

modules deployed at the National Renewable Energy 

Laboratory (NREL) in Golden, Colorado. Most modules 

investigated showed < 0.5%/year decrease in maximum 

power due to short-circuit current decline.

1. INTRODUCTION

Long-term performance of photovoltaic (PV) systems is 

vital to their continuing success in the market place. The 

gradual energy output loss over long periods of time is a 

major concern to all renewable energy stakeholders. A wide 

variety of degradation rates has been reported in the 

literature with respect to technologies, age, manufacturers, 

and geographic locations, and has been recently 

summarized. [1] Significant variation in the data can be 

caused by different module types, age, construction

(encapsulation, front- and back-sheet), electrical set-up 

(open-circuit, short-circuit, load resistor, grid-tied), and

measurement uncertainty. [2] The literature contains an 

excellent review of long-term field testing based on discreet

I-V measurements [3], but fewer reports include more 

comprehensive I-V parameters investigation, including 

voltage and current at maximum power point. [4, 5, 6

2. EXPERIMENTAL DETAILS

] In 

this paper we present results of detailed I-V measurements 

on 12 crystalline silicon (Si) modules located at the National 

Renewable Energy Laboratory (NREL) in Golden, 

Colorado.

Over the past 17 years, 100 modules have been installed on 

the Performance and Energy Ratings Testbed (PERT) at 

NREL’s Outdoor Test Facility (OTF). Module installation 

dates vary greatly, with the earliest installation in 1993. 

There is an equally large variation in the monitoring times,

from merely a few months to more than 17 years of 

continuous data. The modules, mounted side-by-side at the 

latitude tilt of 40o (±1°) facing south (±2°), were held at 

maximum power with current-voltage curves taken typically 

every 15 minutes. Environmental parameters were recorded 

simultaneously and included plane-of-array (POA)

irradiance (W/m2

), wind speed (m/s), ambient temperature 

(°C), and back-of-module temperature (°C). To date over 

6.2 million I-V curves have been captured, with some of the 

earliest modules characterized by over 194,000 curves.

Further details are discussed elsewhere. [7]

Fig. 1: Performance and Energy Ratings Testbed (PERT) at 

NREL. Photo credit: Warren Gretz, NREL PIX 03877.
2

3. MODELING CRITICAL I-V PARAMETERS

Determining degradation rates accurately for individual I-V 

parameters, such as short-circuit current (Isc), open-circuit 

voltage (Voc), maximum power (Pmax), maximum current 

(Imax), maximum voltage (Vmax), and fill factor (FF),

required extraction of these parameters from each I-V curve. 

The manufacturer of the I-V curve tracer generates these 

values internal to the device, but the method is not robust 

for all data sets, so additional modeling was completed. 

Each I-V curve was composed of up to 300 discrete current 

and voltage pairs and due to incomplete scans or other 

anomalies, extraction of the six parameters varies with the 

extraction technique.

Fig. 2 shows modeled compared to measured values for FF, 

Imax, Isc, Pmax, Vmax, and Voc as a percentage of the maximum 

measured value. Significant discrepancies necessitated the 

modeling and may have a variety of causes. For instance, 

sometimes the I-V sweep was incomplete, leading to 

erroneous values. Another source of error was particularly 

on variable days when the POA irradiance changed 

significantly during the I-V sweep; many of these sweeps 

were excluded from analysis. Further examples are 

illustrated in Fig. 3 that show the measured curve and the 

modeled sections. Particularly the ends of the I-V curve 

were not always captured correctly, as is illustrated in inset 

(a). Inset (b) demonstrates a situation in which the modeled 

Pmax point falls between the discrete points. Modeling of 

these critical points required dividing the measurement 

points into smaller sets representing the conditions near Isc, 

Pmax, and Voc. The method used to isolate the measurement 

points for modeling was based on the ASTM standard 

E1036-08, sections 8.5 through 8.10. [8] Isc and Voc were 

obtained by extrapolating using linear fits. As an addition to 

E1036-08, a minimum of six unique current-voltage pairs 

were required. The points near the expected Pmax were 

modeled using a 4th order polynomial fit and the maximum 

point determined from the first derivative. [9

Subsequently, Imax and Vmax were obtained and the FF was 

calculated using the extrapolated values obtained for Voc

and Isc.

]

Fig. 2: Modeled versus measured I-V parameters as a 

percentage of the maximum measured value.

Fig. 3: Typical I-V curve showing measured and modeled 

parts of the curve. Insets (a) and (b) illustrate examples of 

issues that can lead to discrepancies between measured and 

modeled values.

4. DEGRADATION RATE DETERMINATION

Module temperature coefficients for Isc, Voc, and Pmax (α, β, 

and γ, respectively) were determined from the measured 

data by filtering to a specific set of environmental 

conditions with considerations made to the requirements of 

IEC 61215 edition 2, section 10.4 for the determination of 

temperature coefficients. First, a narrow band of 

measurements captured between 980 and 1020 W/m2 POA

irradiance were included. The ±20 W/m2 range around the 

standard test conditions (STC) [10] irradiance was chosen,

as it provided a reasonable compromise between stability in 

the calculated temperature coefficients, low calculated 

uncertainty in the derived temperature coefficients, and an 

acceptable number of points from which the coefficients 

were determined.
3 

When the filtering interval was further reduced, the 

uncertainty increased significantly due to the reduced 

number of data points and their disproportional influence. 

Second, the difference between pre- and post-trace POA

irradiance measurements was restricted to < 8 W/m2 in order 

to reduce the impact of irradiance changes on the shape of 

the captured I-V curve. This interval appeared to be a good 

compromise between a narrow filter and its dramatically 

reduced number of available curves and a wider filter with 

an increase in the number of distorted curves. Note that IEC 

61215 edition 2, section 10.4 requires that irradiance be 

limited to ±2% (±20 W/m2

) to eliminate variable conditions; 

this is more than double the range used in this study.

Finally, the ambient temperature and the difference between 

the ambient and module backsheet temperature were 

restricted to >10°C to eliminate traces when modules were 

fully or partially covered with snow. A linear fit of modeled 

Voc, modeled Isc, and modeled Pmax to module temperature 

provided an intercept and a slope for each parameter from 

which the relative thermal coefficients were calculated at a 

reference module temperature of 45oC, a realistic operating 

point for the climate. 

Figures 4 through 6 detail the empirically derived relative 

temperature coefficients for the modules covered in this 

study and compare them to temperature coefficients 

tabulated from over 280 manufacturer data sheets of these 

technologies. It was noted that the determination of β and γ 

from outdoor current-voltage data was more accurate than 

the determination of α due to the high degree of linearity of 

Voc and Pmax to module temperature. The temperature 

coefficients derived from outdoor data correspond well with 

those published by the manufacturers, who most likely state 

the values determined through IEC 61215 qualification 

testing for terrestrial crystalline silicon modules. 

Fig. 4: Relative temperature coefficients of current, α, by 

technology. Blue symbols represent the coefficients 

calculated from field data. Faded solid circles represent 

coefficient values from manufacturer data sheets. For better 

visibility, the data were jittered in the x-axis.

Fig. 5: Relative temperature coefficients of voltage, β, by 

technology. Blue symbols represent the coefficients 

calculated from field data. Faded solid circles represent 

coefficient values from manufacturer data sheets.
4 

Fig. 6: Relative temperature coefficients of maximum 

power, γ, by technology. Blue symbols represent the 

coefficients calculated from field data. Faded solid circles 

represent coefficient values from manufacturer data sheets.

The number of manufacturers expressing uncertainties in the 

temperature coefficients was limited. Of over 280 data

sheets tabulated for comparison, only 10 stated uncertainties 

in their temperature coefficients. Of interest to our work is 

the observation that the manufacturer-stated uncertainties of 

α, β, and γ are, on average, 26%, 8.5%, and 9.6% of the 

coefficient magnitude, respectively. The calculated 

uncertainties for the coefficients derived from field data are 

9.6%, 1.1%, and 1.3%, respectively. 

Fig. 7: Uncertainty of manufacturer's’ temperature 

coefficients (faded solid circles) and calculated module 

temperature coefficients (blue symbols). 

Fig. 8: Uncorrected (left) and irradiance- and temperaturecorrected values (right) for Pmax, Isc, Voc, and FF, 

respectively.

Degradation rates were calculated from a reduced data set 

established using parameter filters: 800 to 1100 W/m2 POA 

irradiance and < 8W/m2 pre- to post-trace POA irradiance 

delta. Correction of each critical I-V curve parameter was 

performed using well-established methods and reproduced 

in equations (1) through (6). [11, 12

Corrected conditions consist of POA of 1000 W/m2 and a 

more normal operating condition of 45oC, rather than the 

STC condition of 25oC, and are indicated by the zero 

subscripts. 

] The open-circuit 

voltage calculation was simplified to exclude δ(T), the Voc

correction for irradiance as a function of temperature. This

simplification has a small effect on the absolute values that 

are reported, but a negligible effect on the measured 

degradation rates. In these equations, G is the POA

irradiance (W/m2

) and T is the module temperature (oC). 

Uncorrected Corrected 
5 

TABLE 1: DEGRADATION RATE SUMMARY ܫௌ஼బ ൌ ቀீబ

ீ ቁ ቂ ூೄ಴ଵାఈሺ்ି்బሻ

ቃ (1) 

ܸை஼బ ൌ ቂ ௏ೀ಴

ଵାఉሺ்ି்బሻ

ቃ (2) 

ܲ௠௔௫బ ൌ ቀீబ

ீ ቁ ቂ ௉೘ೌೣଵାఊሺ்ି்బሻ

ቃ (3) 

ܫ௔௠௫బ ൌ ூ೘ೌೣቀ

ಸబ

ಸ ቁ

൫ଵାఈሺ்ି்బሻ൯

 = ܫ௔௠௫ ቀ

ூೄ಴బ

ூೄ಴

ቁ (4) 

ܸ௠௔௫బ ൌ ௏೘ೌೣ

ଵାఉሺ்ି்బሻ ൌ ܸ௠௔௫ ቀ

௏ೀ಴బ

௏ೀ಴

ቁ (5) 

ܨܨ ଴ൌ ൤ ௉೘ೌೣబ

ூೄ಴బ ௏ೀ಴బ

൨ (6) 

In the first step, the filtered data were grouped into blocks 

representing one week of measurements, and the mean value 

for each parameter block was calculated. Second, the 

weekly averaged data are graphed as a time series and 

degradation rates are determined from a linear least-squares 

fit. Fig. 8 shows uncorrected (left) and irradiance- and 

temperature-corrected values (right) for Pmax, Isc, Voc, and 

FF, respectively. The statistical uncertainty for the 

degradation rate is a Type A uncertainty according to the 

ISO Guide to the Expression of Uncertainty and can be 

calculated directly from the standard errors of the regression 

and using error propagation. [13] This process was repeated 

for the 12 modules in this study, the results of which are 

summarized in Figures 9 and 10 and Table 1. All 

degradation rates in Table 1 are in (%/year). 

Fig. 9: Degradation rates for individual I-V parameters. 

Each module is represented by a different symbol. Mono-Si 

are in red while poly-Si modules are in blue. A negative 

value implies decreased performance with time. 

Module 

Manufacturer Technology Rd PmaxRd IscRd VocRd FF Rd ImaxRd VmaxYears 

1 A mono -0.29 -0.19 -0.02 -0.08 -0.20 -0.11 9.3

2 A mono -0.33 -0.27 -0.01 -0.06 -0.30 -0.08 8.1

3 A mono -0.21 -0.21 -0.03 0.03 -0.16 -0.07 9.3

4 A mono -0.25 -0.10 -0.02 -0.14 -0.25 -0.02 9.4

5 B poly -0.04 -0.14 -0.02 0.13 -0.04 0.03 10.4

6 B poly -0.07 -0.15 0.01 0.07 -0.16 0.12 10.4

7 C mono -0.39 -0.30 -0.01 -0.09 -0.30 -0.06 17.2

8 D poly 0.29 0.24 0.05 0.00 0.25 0.08 6.4

9 D poly -0.07 0.16 0.02 -0.24 -0.10 0.10 6.4

10 D poly -0.85 -0.23 -0.07 -0.58 -0.65 0.02 3.8

11 E poly -1.14 -0.24 0.00 -0.96 -0.46 -0.76 11.6

12 E poly -0.61 -0.26 -0.06 -0.33 -0.30 -0.30 12.7

Median -0.27 -0.20 -0.01 -0.08 -0.23 -0.04 9.4

St Dev 0.38 0.17 0.03 0.31 0.22 0.24 3.4
6

Fig. 10: Type A uncertainty for calculated degradation rates. 

Each module is represented by a different symbol. Mono-Si

data are in red while poly-Si modules are in blue.

Poly-Si modules show a broader distribution of degradation 

rates than mono-Si modules, which could be an artifact due 

to most mono-Si modules coming from one manufacturer.

The group of modules can be generally divided into two 

different categories: one is characterized by relatively 

modest decline in Pmax of less than 0.5%/year (Modules 1-

9), whereas the second group is characterized by Pmax

degradation significantly higher than 0.5%/year (Modules 

10-12). The group with modest Pmax degradation is 

characterized by large contributions due to Isc degradation, 

which can more typically be attributed to delamination, 

discoloration, and cracked individual cells, while a smaller 

percentage can be attributed to light-induced degradation 

and soiling. [14, 15] The optical image of Fig. 11 shows 

two of these typical attributes: discoloration and soiling. 

The infrared (IR) image shows relatively uniform heating of 

the module and the absence of any hot-spot heating.

Fig. 11: Optical (left) and infrared (right) image of Module 

7. Photo credit: Dirk Jordan, NREL PIX 20326.

In contrast, the group with the larger Pmax degradation is 

characterized by large contributions due to FF degradation,

indicating that series resistance may have increased or shunt 

resistance decreased. Voc degradation is very low for both 

groups. Fig. 12 shows an overlay of temperature- and 

irradiance-corrected I-V curves from the beginning and end 

of life of Module 11, which display typical behavior of an 

increased series resistance during field exposure. The cause 

for Module 10 and 12 is not as clear and could be a 

combination of lowered shunt resistance, increased series 

resistance, or increased cell mismatch.

Fig. 12: Temperature- and irradiance-corrected I-V curves 

from the beginning of life (solid blue) and end of life 

(dashed red) of Module 11.

Lastly, an important question regarding inverter sizing is 

whether the Pmax degradation is primarily due to current 

degradation or voltage degradation. In this study, 10 out of 

12 modules showed < 0.2%/year degradation in Vmax.

5. CONCLUSION

Twelve modules on the PERT at NREL were investigated 

for their long-term degradation in I-V parameters. For more 

accurate degradation rate determination, individual I-V 

curves were modeled, filtered, and then irradiance- and 

temperature-corrected. The majority of the modules showed 

< 0.5%/year degradation, with this degradation mostly 

linked to decreases in short-circuit current. Of the three 

modules that showed -0.6% to 1.1 %/year degradation, one 

showed clear evidence of increased series resistance with 

some degradation in current, while the other two showed a 

combination of causes.

0.0

0.5

1.0

1.5

2.0

2.5

0 10 20

Current (A)

Voltage (V)

10/18/2000 - 12 pm

10/15/2010 - 12 pm
7

6. ACKNOWLEDGMENTS

The authors would like to thank Joseph del Cueto for 

discussions about the PERT systems and Jose Rodriguez, 

Ed Gelak, and Carl Osterwald for PERT development and 

operations.

This work was supported by the U.S. Department of Energy 

under Contract No. DE-AC36-08-GO28308 with the 

National Renewable Energy Laboratory.

 

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