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

Minimizing Variation in Outdoor 

CPV Power Ratings

Preprint

Matthew Muller, Bill Marion, Jose Rodriguez, 

and Sarah Kurtz

Presented at the 7th International Conference on Concentrating 

Photovoltaic Systems (CPV-7)

Las Vegas, Nevada

April 4-6, 2011

Conference Paper

NREL/CP-5200-51339

July 2011
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1 

Minimizing Variation In Outdoor CPV Power Ratings

Matthew Muller, Bill Marion, Jose Rodriguez, Sarah Kurtz

NREL, Golden, CO, 80401 USA (303)384-6475, matthew.muller@nrel.gov

Abstract. The CPV community has agreed to have both indoor and outdoor module power ratings. The indoor rating 

provides a repeatable measurement off the factory line while the outdoor rating provides a measure of true on-sun 

performance. The challenge with an outdoor rating is that conditions that impact the measurement such as the spectrum, 

temperature, wind speed, etc are constantly in flux. This work examines methodologies for determining the outdoor 

power rating with the goal of minimizing variation even if data are collected under changing meteorological conditions.

Keywords: CPV, Power Rating, Spectrum, IEC standards

PACS: 80,88

INTRODUCTION

The CPV community has been working to 

standardize a procedure for rating module power. 

According to the most recent IEC TC82 WG7 

agreement, there will be an indoor power rating at 

concentrator standard test conditions (CSTC, 25C cell, 

1000W/m2

) and an outdoor power rating at 

concentrator standard operating conditions (CSOC, 

20C ambient, 900W/m2

). [1]. While the development 

of both these procedures present significant 

challenges, this paper focuses on the outdoor power 

rating.

NREL has been accumulating outdoor performance 

data on CPV modules from various manufacturers 

since early 2009. This paper examines this data set as 

a means to minimize variation of CPV module power 

ratings under CSOC. Specifically the following 

questions are addressed:

1) If a given module is measured over multiple 

months, with bounds placed on tracking accuracy, 

ambient temperature, wind conditions, 500 nm Aerosol 

Optical Depth (AOD), Precipitable Water Vapor

(PWV), and geometric AirMass (AM), how consistent 

will the power measurement be?

2) For a given module, How consistent of a power 

rating can be achieved when applying a statistical 

regression to monthly data sets?

3) Is there an alternative to statistical regression that 

results in monthly power ratings with less variation? 

OUTDOOR MEASUREMENT CHALLENGES

It is difficult to rate module power under outdoor 

conditions and achieve consistent results. Flat-plate

PV uses indoor simulators specifically to avoid this

problem but the unique designs of CPV present a need 

to use on-sun measurements. It is a useful starting 

point to understand how much power varies under 

clear-sky conditions for both tracked flat-plate and 

CPV. In efforts to restrict data to clear-sky CSOC 

conditions, a baseline filter has been applied to the 

data used throughout this work. Specifically, the 

following is accepted:

Direct Normal Irradiation (DNI) ≥750 W/m2

Diffuse Irradiation ≤140 W/m2

10C ≤Ambient Temperature ≤30C

5 minute DNI deviation ≤2%

Tracking Error ≤0.15 degrees

Instantaneous Wind Speed ≤5m/s

5 minute average Wind Speed ≤5m/s

The basis of the above filtering comes from ASTM E 

2527-06 [2] with the restrictions on diffuse radiation

and DNI deviation created to ensure no clouds or haze 

are within 10 degrees of the sun. Tracking error 

criteria were added as an extra precaution to reject data 

when the tracker is off-sun for any reason and to 

remove any relationship with tracking that might be 

seen for modules with tight acceptance angles.

Figure 1 shows July through December power data 

for both a tracked flat-plate module and a CPV 

module. The flat-plate data cover a greater irradiance 

range as they are measured against global normal 

irradiance (GNI) rather than DNI. Measured Power is 

divided by a rated power at 900 W/m2 so both modules 

can be easily compared on the same graph.

0.75

0.85

0.95

1.05

1.15

1.25

1.35

1.45

1.55

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

750 850 950 1050 1150

Power/RatedPower

Power/RatedPower

Available Irradiance (W/m2)

Flat Plate (left axis)

CPV (right axis)

Fig. 1 Power Variation for Flat-Plate and CPV
2 

The left and right axes have been intentionally shifted 

so the data do not fall on top of each other. While both 

modules show power variations of at least 10% at 

various irradiances, the flat-plate, in general, shows

slightly higher variation than the CPV.

Figure 2 presents the same data set as Fig. 1 but all 

data points have been corrected to a cell temperature 

that is representative of each module at CSOC.

0.75

0.85

0.95

1.05

1.15

1.25

1.35

1.45

1.55

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

750 850 950 1050 1150

Power/RatedPowerPower/RatedPower

Available Irradiance (W/m2)

Flat Plate (left axis)

CPV (right axis)

Fig.2 Temperature Corrected Flat-plate and CPV Data

It is clear that the temperature correction significantly

reduces variation for the flat-plate module but the 

changes are subtle for the CPV module. The CPV 

module shows an increase in data scatter at low DNI, a 

slight tightening at high DNI, and a bend that becomes 

more noticeable around 850 W/m2

. It is not that the 

temperature correction has failed for the CPV module, 

but rather significant variation remains due to spectral 

effects. Because of the 10% variation still seen after a 

temperature correction it is logical to consider filtering 

or putting bounds on various parameters that impact 

CPV performance. Figure 3 is the temperature 

corrected data with additional filtering such that PWV

is between 1-3 cm, and AOD is between 0.06 and 

0.135. Comparing Fig.2 to Fig.3, the variation in 

power for a given DNI is reduced by almost half.

0.75

0.85

0.95

1.05

1.15

1.25

1.35

1.45

1.55

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

750 850 950 1050 1150

Power/RatedPowerPower/RatedPower

Available Irradiance (W/m2)

Flat Plate (left axis)

CPV (right axis)

Fig.3 CPV Power Data with Spectral Filtering

The improvements seen in Fig.3 are primarily due to 

PWV filtering while AOD filtering added only slight 

benefits. Additional filtering was applied to limit AM

and the results were that high and low DNI data were

removed but that variation for mid-range DNI was 

unchanged. Removing data with AM greater than 2 

does prove useful to eliminate data with increased 

scatter at the lower irradiances. From the perspective 

of mathematical analysis, it is justified to eliminate 

data with AM > 2 because all CPV modules on-sun at 

NREL begin to have a negative relationship between 

power and AM in this range [3]. It is this negative 

relationship that is responsible for the bend in the CPV 

data shown in Figs 1-3. Ultimately, the compilation of 

information from Figs. 1-3 suggests that if data is 

temperature corrected and limits are placed on PWV 

and AOD it is possible to reduce the variation in a 

power rated at CSOC to about 5%. As power rating 

methods are considered hereafter, 5% represents a 

useful target for variation as applied to monthly data 

sets.

ASTM-2527 APPLIED TO MONTHLY DATA

In order to test a CPV module outdoors it first

needs to be mounted on a tracker and aligned with the 

sun. At an ideal test site this could be done in a midmorning hour and then I-V curves could be taken for 

the module in the midday hours to achieve a power 

rating. In reality the module might be mounted one 

day, aligned another, and then it be weeks before the 

needed data is acquired. With this in mind, it is a 

reasonable approach to autonomously gather data for 

multiple weeks and apply the statistical regression 

given in Eq.1 as specified in ASTM E 2527-06 [2]. 

Pmax=DNI(a1+a2DNI+a3Tambient+a4Wind) (1) 

Figure 5 presents the variation in the ASTM power 

rating over multiple months for two CPV modules and 

one flat-plate module.

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20

% change in power rating

Month 0=Jan2009

CPV1 CPV2 FlatPlate

Fig.5 ASTM Power Rating Applied Monthly

The left axis in fig.5 shows the percent change in the 

power rating from the month with the lowest rating. 

For example, the flat-plate module shows its lowest 
3 

power rating in month 19 (hence 0% change) while in 

month 20 the rating is about 2% higher than month 19.

Fig. 5 shows that using ASTM-2527 can result in 

power ratings that vary by 10% for CPV and 5% for 

flat-plate. Although applying Eq. 1 is simple, the 

coefficients a1, a2, a3, and a4 fail to accurately measure 

actual relationship between power and meteorological 

conditions. For example, the flat-plate module shows 

increased performance in moving from hot summer 

months to cold winter months. Although power 

should increase as temperature decreases, the 

coefficients related to ambient temperature and wind 

speed fail to capture this known relationship, as 

evidenced by greater than a 130% variation in both 

coefficients over 6 months. The variation in 

regression coefficients can be more extreme with CPV 

modules. For example, the coefficient related to 

ambient temperature is positive in some months but 

negative in other months.

Fig. 5 also shows that both CPV modules have 

their lowest power ratings in the winter months. In 

these months, it is typically drier, the AM is higher 

than 1.5 (At NREL, December, January minimum AM 

is > 2, November, February minimum AM is > 1.7), 

and low ambient temperatures bring some CPV lenses 

out of optimum focus. It is worth noting, that some 

CPV modules show a lens related performance drop 

when the ambient temperature is less than 15C. 

Overall, the ASTM rating shows high variability in the 

winter months because the regression has no terms to 

account for changing spectral conditions or 

temperature dependent lens performance. Consider 

that if November through February were dropped from

Fig. 5, CPV1 would have a variation of 7.6% and 

CPV2 would have a variation of 6.8%.

Although it would be ideal to complete a power 

rating on any sunny day and make corrections for 

temperature and spectral conditions it is probably 

necessary to avoid some extreme conditions. From 

this research and from past work [3], it is 

recommended that any data with an AM greater than 2 

or PWV below 0.5 cm should be rejected. In general it 

is suggested that data for a CPV power rating should 

include measurements where AM 1.5 is realized in 

order to avoid extrapolation.

ALTERNATIVE APPROACHES TO ASTM-2527

Although a month-to-month variation of 7-10% is 

too high for an acceptable power rating procedure,

analysis above suggested that filtering or applying

corrections to the data could reduce variation. 

Filtering based on AM inadvertently removes the 

highly variable winter months and therefore makes it 

difficult to compare a corrective method to one that 

relies on heavy filtering. In order to do a meaningful 

comparison, data from November through February 

and all AM > 2 is excluded from all comparisons that 

follow. 

In attempts to reduce variation in the monthly 

power rating many alternate equations and filtering 

requirements were considered. The key findings from 

these attempts are conveyed by examining the results 

from the following methods: 

ASTM1: added filtering 1.3≤AM≤1.7

ASTM2: using Eq.1 with a5AM term added

Regression1: PT=a1DNI+a2DNI2

+a3AM

Regression2: PT,AM,PWV= a1DNI+a2DNI2

ISFOC: Power translation used by ISFOC [4], [5]

ISFOC1: translation with added filtering 1.3≤AM≤1.7

ISFOC2: translation with correction for AM and PWV

PT in “Regression1” represents the peak power point 

translated from the calculated cell temperature to a cell 

temperature that is representative of CSOC. Cell 

temperature is calculated using open circuit voltage 

(Voc), short circuit current (Isc), and cell 

specifications as by the “Voc,Isc Method” in use by

Sandia National Laboratories [6]. With the cell 

temperature, the CSOC temperature, and temperature 

coefficient for III-V cells, the current and voltage are 

translated to CSOC to get PT. PT,AM,PWV represents the 

peak power translation to a CSOC cell temperature 

plus additional corrections to AM of 1.5, and a PWV 

of 1.4 cm, as calculated by Equation 2. 

PT,AM,PWV = PT – 0.01(AM-1.5)DNI∙A

– 0.006(PWV-1.4)DNI∙A (2)

In Eq.2, “A” is the module aperture area, DNI is 

measured, AM is calculated, and PWV is calculated 

from the dew point temperature. Eq.2 assumes that 

module efficiency increases 1% per AM unit and 0.6% 

per PWV unit. Although this assumption is not true 

for the entire range of AM and PWV it is approximate 

for the data under consideration [3]. The AM and 

PWV translation mentioned in method “ISFOC2”, is 

achieved via Eq.2 by substituting the ISFOC power 

translation for PT. 

The results from applying alternatives “ASTM1” 

through “ISFOC2” to CPV1 and CPV2 are presented 

in Table 1 in comparison to ASTM-2527. 

Table 1 Comparison of Power Rating Methods 

Maximum Monthly Variation in Power Rating

Method CPV1 CPV2

ASTM-2527 7.6% 6.8%

“ASTM1” 8.7% 8.1%

“ASTM2” 8.0% 7.3%

“Regression1” 5.4% 6.7%

“Regression2” 4.2% 5.7%

“ISFOC” 6.9% 6.2%

“ISFOC1” 6.2% 6.1%

“ISFOC2” 2.9% 5.5%
4 

DISCUSSION

Examining the results in Table 1, it is clear that 

attempts to adapt the ASTM method using additional 

filtering or by adding an AM term actually increased 

variation. Although not shown here, the same is true

for filtering or adding terms to ASTM-2527, involving 

global normal irradiance (GNI), AOD, or PWV.

“Regression 1” represents the results of an effort to 

build a new CPV power rating regression from scratch. 

This was done by taking a year of CPV data from 

NREL and looking for the “best fit” as judged by 

lowest standard error and the Tstat on the included 

variables. Regressions were considered for both the 

measured power and PT (the power translated to CSOC 

temperature) against linear and nonlinear terms using 

DNI, GNI, diffuse irradiance, wind speed, ambient 

temperature, heat sink temperature, AM, PWV, and 

AOD. PT=a1DNI+a2DNI2

+a3AM+a4PWV was found 

to be the “best fit” regression with a standard error of 

1.8%, while PWV had the lowest Tstat of 7.7 and all 

other variables had Tstats in the range of 15 to 25. 

This “best fit” regression was applied to monthly data 

sets and it was quickly found that PWV was not 

relevant on a monthly basis, hence why “Regression1” 

in Table 1 does not include PWV. In comparison to 

ASTM, “Regression1” reduces variation for CPV1 but 

does little for CPV2. “Regression1” is ultimately 

given a failing mark because of the marginal 

improvement for CPV2 and observations that the AM 

coefficient is positive in some months while negative 

in others.

“Regression2” is more a corrective or translation 

approach to computing a power rating. Eq. 2 shows 

that corrections have been made for cell temperature, 

AM, and PWV while a regression is only used to find 

the relationship between corrected power and DNI. 

The results of 4.2% variation for CPV1 and 5.7% for 

CPV2 suggest that more translation/correction is 

beneficial compared to regression. 

With evidence supporting a translation approach, it 

is valuable to consider the full translation to CSOC 

that ISFOC has been using on a system level for 

several years [4]. In the ISFOC method, a measured 

power is translated to CSOC using I-V measurements, 

cell specifications, and cell temperature via a heat sink 

temperature measurement (assuming knowledge of the 

thermal resistance between the cell and heat sink). 

The translation is typically done for an entire I-V 

curve and then the new peak power point is found. 

The ISFOC approach has been applied to NREL data 

both translating the entire I-V curve and translating 

just the original peak power point. It was found that 

the uncertainty associated with translating only the 

peak power point is at least an order of magnitude less 

than the uncertainty of the monthly power ratings 

being examined. To simplify data processing, this 

method is used in some cases. It also must be stated 

that NREL does not have knowledge of the thermal 

resistance between the heat sink and the cell for all 

CPV modules under test. For those modules with a 

known thermal resistance, a comparison was done 

between the cell temperature calculated via the 

“Voc,Isc Method” and that using the heat sink 

measurement. On average there is less than a 2C 

difference between each approach. To be consistent,

the “Voc,Isc Method” is used to calculate cell 

temperature for all modules under examination. The 

monthly power rating is computed by translating all 

acceptable I-V curves for the given month and then 

averaging the results.

Table 1 shows that ISFOC translation results in a 

6.9% variation for CPV1 and 6.2% variation for 

CPV2. As these results are less than a percent better 

than the basic ASTM method, this suggests that 

filtering and additional corrections are worth 

considering. “ISFOC1”, which only accepts I-V 

curves with AM between 1.3 and 1.7, resulted in a 

slight improvement over ISFOC’s specified filtering. 

Finally, “ISFOC2” applies corrections for AM and

PWV based on Eq.2. Ultimately the “ISFOC2” 

method resulted in the lowest variation for a monthly 

power rating for both CPV1 and CPV2.

CONCLUSIONS

2009/2010 data, filtered to meet ASTM-2527 

conditions, have been examined for multiple CPV 

modules on-sun at NREL. A July to December data 

set shows CPV measured power can vary by as much 

as 10% at a given DNI. For the same data set, 

applying a temperature correction, limiting PWV to 1-

3 cm, and limiting AOD to 0.06-0.135 reduces 

variation to 5%.

With the larger data set providing perspective, 

attempts were made to calculate a monthly outdoor 

CPV power rating that would vary by less than 5%. 

ASTM-2527 was used as a baseline, while additional 

filtering, alternate regressions, and translations were 

considered in efforts to minimize month-to-month 

variation. 

Pure Regression-based approaches performed 

poorly while approaches that included correction for

temperature, AM and PWV provided the best results. 

“Regression2”, which corrected for all but DNI, had a 

variation of 4.2-5.7%. “ISFOC2”, which combined 

the ISFOC power translation with corrections for AM 

and PWV, had a variation of 2.9-5.5%.

The overall investigation led to several key 

suggestions/recommendations:

1) Exclude AM >2, PWV <0.5 from power rating data.

2) Exclude months that AM 1.5 does not occur. 
5 

3) PWV and AM should not be ignored.

4) Default to translation over regression approach.

5) Do not ignore temperature effects on lenses.

Future work should apply translation-based 

approaches to more modules and over longer time 

periods in order to confirm the results presented here. 

Efforts should be made to refine corrections for AM 

and PWV or to apply alternate corrections as data 

become available that improve ability to characterize 

the spectral conditions. Finally, corrections for 

variations in lens performance should be considered.

ACKNOWLEDGMENTS

This work was completed under contract # DE-AC36-

08GO28308.

REFERENCES

1. IEC 62670 Draft Standard

2. E-2527-06, “Standard Test Method for Rating Electrical 

Performance of Concentrator Terrestrial Photovoltaic 

Modules and Systems Under Natural Sunlight”, ASTM 

Int., West Conshohocken, PA (2006)

3. M. Muller, B Marion, S. Kurtz, J. Rodriguez, “An 

Investigation into Spectral Parameters as they Impact 

CPV Module Performance”, CPV6, AIP Conference 

Proceedings 1277, American Institute of Physics, 

Melville, NY, 2010, pp. 307-311.

4. M. Martinez, D. Sanchez, F. Rubio, J. Pachon, P. Banda, 

“CPV Systems Rating, Results and Lessons Learned at 

ISFOC”, CPV5, Palm Desert, Nov 2008

5. ISFOC “Specifications of general conditions for the call 

for tenders for concentration photovoltaic solar plants for 

the Institute of Concentration PhotovoltaicSystems 

(ISFOC)”2007 

6. D. King, W. Boyson, J. Kratochvil, “Photovoltaic Array 

Performance Model,” Sandia National Laboratories 

Report, SAND2004-3535, August 2004. 

(www.sandia.gov/pv)