Technical Report

NREL/TP-520-45299

August 2009

Uncertainty Analysis of Certified 

Photovoltaic Measurements at 

the National Renewable Energy 

Laboratory 

K. Emery
National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393

303-275-3000 • www.nrel.gov 

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

Contract No. DE-AC36-08-GO28308

Technical Report

NREL/TP-520-45299

August 2009

Uncertainty Analysis of Certified 

Photovoltaic Measurements at 

the National Renewable Energy 

Laboratory 

K. Emery

Prepared under Task No. PVA93420
NOTICE

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iii

TABLE OF CONTENTS

 

Abstract ................................................................................................................................v 

1.0 Introduction ..........................................................................................................................1 

References ............................................................................................................................3 

2.0 Uncertainty of Primary Calibration of Photovoltaic Cells ...................................................4 

 1. References to Norms and Standards ..............................................................................4 

 2. Summary ........................................................................................................................4 

 3. Procedures ......................................................................................................................4 

 4. Test Bed Specific Equipment.........................................................................................5 

 5. Uncertainty in <CV> .....................................................................................................6 

 6. References to Section 2 ................................................................................................12 

3.0 Uncertainty of Photovoltaic Cell Spectral Responsivity ...................................................15 

 1. References to Norms and Standards ............................................................................15 

 2. Summary ......................................................................................................................15 

 3. Procedures ....................................................................................................................15 

 4. Test Bed Specific Equipment.......................................................................................16 

 5. Uncertainty in QE(λ) vs. λ ...........................................................................................16 

 6. References to Section 3 ................................................................................................21 

4.0 Uncertainty of Electrical Performance of Photovoltaic Cells ............................................22 

 1. References to Norms and Standards ............................................................................22 

 2. Summary ......................................................................................................................22 

 3. Procedures ....................................................................................................................22 

 4. Test Bed Specific Equipment.......................................................................................24 

 5. Uncertainty Analysis ....................................................................................................25 

 6. References to Section 4 ................................................................................................34 

5.0 Uncertainty of Electrical Performance of Photovoltaic Modules ......................................37 

 1. References to Norms and Standards ............................................................................37 

 2. Summary ......................................................................................................................37 

 3. Procedures ....................................................................................................................37 

 4. Test Bed Specific Equipment.......................................................................................40 

 5. Uncertainty Analysis ....................................................................................................41 

 6. References to Section 5 ................................................................................................51 

Glossary ......................................................................................................................................54 

Appendix 1 ..................................................................................................................................55 

Appendix 2 ..................................................................................................................................58 
iv

List of Figures

Figure 1. Irradiance traceability path for NREL’s PV Cell and Module Performance

Characterization Group ............................................................................................... 1 

Figure 2. Simplified block diagram of the primary calibration test station ............................... 6 

Figure 3. Typical annual primary reference cell calibration ...................................................... 7 

Figure 4. Quantum efficiency curve of WPVS Reference Cell 930216-1 ................................. 8 

Figure 5. Frequency of temperatures in the 2002 Primary Reference Cell calibration 

data set ...................................................................................................................... 10 

Figure 6. Calibration value measured at NREL compared with the WPVS average value 

of four international photovoltaic calibration laboratories including NREL ............ 11 

Figure 7. Nineteen years of primary reference cell calibrations on the same mono-Si cell ..... 11 

Figure 8. Seventeen years of primary reference cell calibrations on the same GaAs cell ....... 12 

Figure 9. Filter quantum-efficiency system. This equipment is used to measure the 

quantum efficiency (QE) of a PV cell....................................................................... 16 

Figure 10. QE curve of WPVS reference cell N45 showing the standard deviation and 

signal-to-noise ratio .................................................................................................. 17 

Figure 11. The Spectrolab X25 solar simulator and custom I-V measurement system ............. 24 

Figure 12. Simplified block diagram of current versus voltage test station ............................... 25 

Figure 13. Typical I-V curve for a reference cell ....................................................................... 27 

Figure 14. The Spectrolab LACSS solar simulator and custom I-V measurement system ........ 40 

Figure 15. Simplified block diagram of current versus voltage test station ............................... 40 

Figure 16. Typical I-V curve for a cell in module package test device ..................................... 43 

Figure 17. Typical I-V curve for a module test device .............................................................. 44 

Figure 18. Typical spatial nonuniformity of large-area continuous solar simulator 

showing ±1% for areas less than 30 cm by 30 cm; ................................................... 47 

Figure 19. Schematic diagram of bias box ................................................................................. 58 

List of Tables

Table 1. Summary of Standard Primary Reference Cell Uncertainty Components .................. 8 

Table 2. Error Sources for Measurement of the Photocurrent ................................................ 18 

Table 3. Error Sources for Measurement of the Light Power ................................................. 19 

Table 4. Error Sources Related to the Monochromatic Light ................................................. 19 

Table 5. Detector Measurement Services Uncertainties Relative Expanded 

Uncertainty (k = 2) .................................................................................................... 20 

Table 6. Major Errors Sources in Normalized Filter Quantum Efficiency Measurements ..... 21 

Table 7. Summary of Standard Secondary Reference Cell Uncertainty Components ............ 25 

Table 8. Summary of Standard Secondary Reference Module Uncertainty Components ...... 41 
v 

ABSTRACT

The measurement of the photovoltaic (PV) performance with respect to reference conditions 

requires measuring the current versus voltage with respect to a given tabular reference spectrum, 

junction temperature, and total irradiance. This report briefly discusses the procedures 

implemented by the PV Cell and Module Performance Characterization Group at the National 

Renewable Energy Laboratory (NREL) to achieve the lowest practical uncertainty. We present a

rigorous uncertainty analysis of these procedures following the International Organization for 

Standardization (ISO) “Guide to the Expression of Uncertainty in Measurement.” This 

uncertainty analysis is required for our team’s laboratory accreditation under ISO standard 

17025, “General Requirements for the Competence of Testing and Calibration Laboratories.” 

Our PV cell and module performance laboratory was certified by the American Association for 

Laboratory Accreditation (A2LA) to perform ISO 17025-accredited calibrations on 

September 14, 2004. (See Appendix 1 for copies of the certificates.) The two agencies authorized 

to grant ISO 17025 accreditation in the United States are A2LA and National Voluntary 

Laboratory Accreditation Program (NAVLAP). 
vi 

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1 

1.0 INTRODUCTION

The phrase “trust but verify” was popular during the Strategic Arms Limitation Talks in the 

1980s, where the United States and Soviet Union trusted each other but required continuous 

unattended monitoring for compliance with treaty obligations. In the scientific community, the 

peer review process is critical to verify the quality of a manuscript. Errata and letters to the editor 

allow results to be challenged and defended. All laboratories must trust some other laboratory for 

at least part of their calibration traceability path for instruments that report a result. The level of 

trust that one has in a calibration depends on the laboratory’s stature as a national calibration 

facility (e.g., AIST [National Institute of Advanced Industrial Science and Technology], NIST

(National Institute of Standards and Technology], or PTB [Physikalisch-Technische 

Bundesanstalt]), an ISO 17025-accredited calibration laboratory, the original equipment 

manufacturer, or a national laboratory such as the National Renewable Energy Laboratory 

(NREL) [1]. National standards laboratories such as NIST for the United States and ISO 17025-

accredited calibration laboratories have the highest stature because of the rigor in their 

procedures—a verified quality system. 

The same “trust but verify” axiom is applicable to the Photovoltaic Cell and Module 

Performance Characterization Group at NREL, where our primary function is verifying the 

performance of PV devices. ISO 17025 requires that these calibrations be performed by a 

national standards facility such as NIST or an ISO 17025-accredited laboratory. Figure 1 shows 

the team’s calibration traceability chain.

NIST

QE systems

Total Irradiance,

Cavity radiometer

Continuous solar

simulator - Modules

Pulsed Solar simulator -

Module

Natural sunlight

- Modules

Spectral

Irradiance

World Radiometric Reference for Total

Irradiance (SI traceable)

Pulsed Solar simulator -

Concentrator cells

Primary

Reference cell

NREL

Metrology

Secondary

Reference

cell

Figure 1. Irradiance traceability path for NREL’s PV Cell and Module Performance Characterization 

Group. Equipment to measure voltage, resistance, current, and temperature is calibrated by 

NREL’s Metrology Group. 
2 

A key requirement for certified calibration laboratories is that they must demonstrate their 

proficiency though formal uncertainty analysis and periodic intercomparisons. NREL has 

participated in numerous formal [2–8] and informal intercomparisons over the years. This is an 

ongoing process where, at any point, an intercomparison could reveal differences outside of 

estimated uncertainty limits. When this occurs, a detailed uncertainty analysis of both groups’ 

methods often reconciles differences.

To perform a rigorous uncertainty analysis, one must choose typical cases and make a variety of 

assumptions such as equipment in calibration, trained operators, and best practices followed as 

documented in the test-bed work instructions. The samples chosen in these uncertainty analyses 

were a typical 2-cm by 2-cm packaged silicon (Si) reference cell and an 18-W commercial Si 

module. The scope of the uncertainty analysis for cells was based on the American Society for 

Testing and Materials (ASTM) standard E1040 and International Electrotechnical Commission 

(IEC) standard 60904-2 requirements for packaged reference cells and was restricted to singlejunction technologies. Voltage and current limitations should not eliminate any cell technology 

that fits within the area limitation. The scope for the modules is restricted to single-junction 

technologies and by physical dimensions. The current and voltage limitations for the module 

measurements cover all known and planned cell and flat-module currents and voltages for 

samples that satisfy the size constraint.

Our requirements for an ISO 17025-certified calibration of a single-junction secondary reference 

cell or module are the following: 

• Permanent sample identification (ID) must be marked on the sample. 

• An attached temperature sensor is required for cell calibrations of type J, K, T 

thermocouple, a thermistor, or resistance temperature detector (RTD). The sensor type 

must be specified or obvious by the type of thermocouple connector. No attached 

temperature sensor is allowed for module calibrations. 

• Two voltage and two current wires are connected to the sample. 

• The cell must be mounted in a metal package for temperature control for cell calibration; 

it is otherwise eligible for module calibration. The package should be mechanically sound 

and protected from damage during shipment and handling. An air gap between the sensor 

and any window is allowed. 

• Any required mating connector should be supplied with the wires identified (+, -, current, 

voltage). 

• The spectral responsivity of the module must be determined via a cell that is 

representative of the module or wires connected to a single cell in the module being 

calibrated.

• There should be no inherent instabilities or metastable behavior such as in amorphous 

silicon. 

• The maximum Voc for cells is 40 V and for modules is 290 V. The minimum Voc for cells 

is 0.1 V and for modules is 0.5 V.

• The maximum Isc for cells is 15 A and for modules is 50 A. The minimum Isc for cells is 

1 mA and for modules is 100 mA.

• The area must be between 0.5 cm by 0.5 cm and 20 cm by 20 cm for cells. The area must 

be between 1 cm by 1 cm and 150 cm by 120 cm for modules. 
3 

References

1. K. Emery, A. Anderberg, J. Kiehl, C. Mack, T. Moriarty, L. Ottoson, and S. Rummel, “Trust 

But Verify: Procedures to Achieve Accurate Efficiency Measurements for All Photovoltaic 

Technologies,” Proc. 31st IEEE PVSC, Orlando FL, pp.1781–1784, Jan. 3–7, 2005. 

2. H. Ossenbrink, R. Van Steenwinkel, and K. Krebs, “The Results of the 1984/1985 RoundRobin Calibration of Reference Solar Cells for the Summit Working Group on Technology, 

Growth and Employment,” Joint Research Center, ISPRA Establishment, ISPRA Italy, Tech 

Rep. EUR 10613 EN (April 1986). 

3. K.A. Emery, C.R. Osterwald, L.L. Kazmerski, and R.E. Hart, “Calibration of Primary 

Terrestrial References Cells When Compared with Primary AM0 Reference Cells,” Proc. 8th

European Photovoltaic Solar Energy Conf., Florence, Italy, May 9–12, 1988, pp.64–68. 

4. J. Metzdorf, T. Wittchen, K. Heidler, K. Dehne, R. Shimokawa, F. Nagamine, H. 

Ossenbrink, L. Fornarini, C. Goodbody, M. Davies, K. Emery, and R. Deblasio, “Objectives 

and Results of the PEP '87 Round-Robin Calibration of Reference Cells and Modules,” Proc. 

21st IEEE Photovoltaic Specialists Conf., Orlando, FL, May 21–25, 1990, pp.952–959, IEEE, 

New York, 1990. (invited) 

5. J. Metzdorf, T. Wittchen, K. Heidler, K. Dehne, R. Shimokawa, F. Nagamine, H. 

Ossenbrink, L. Fornarini, C. Goodbody, M. Davies, K. Emery, and R. Deblasio, “The Results 

of the PEP '87 Round-Robin Calibration of Reference Cells and Modules,- Final Report,” 

PTB Technical Report PTB-Opt-31, Braunschweig, Germany, November 1990, ISBN 3-

89429-067-6. 

6. C.R. Osterwald, S. Anevsky, A.K. Barua, J. Dubard, K. Emery, D. King, J. Metzdorf, F. 

Nagamine, R. Shimokawa, N. Udayakumar, Y.X. Wang W. Zaaiman, A. Zastrow, and J. 

Zhang, “Results of the PEP ‘93 Intercomparison of Reference Cell Calibrations and Newer 

Technology Performance Measurements,” Proc. 25th IEEE Photovoltaic Specialists Conf., 

Washington D.C., May 13–17, 1996, pp.1263–1266, IEEE, New York, 1996. 

7. C.R. Osterwald, S. Anevsky, A.K. Barua, J. Dubard, K. Emery, D. King, J. Metzdorf, F. 

Nagamine, R. Shimokawa, N. Udayakumar, Y.X. Wang W. Zaaiman, A. Zastrow, and J. 

Zhang, “The Results of the PEP ‘93 Intercomparison of Reference Cell Calibrations and 

Newer Technology Performance Measurements: Final Report,” March 1998, NREL Tech. 

Rep. NREL/TP-520-23477. 

8. S. Rummel, A. Anderberg, K. Emery, D. King, G. TamizhMani, T. Arends, G. Atmaram, L. 

Demetrius, W. Zaaiman, N. Cereghetti, W. Herrmann, W. Warta, F. Neuberger, K. Morita, 

and Y. Hishikawa, “Results from the Second International Module Inter-comparison,” Proc. 

IEEE 4th World Conference on Photovoltaic Energy Conversion, pp.2034–2037, May 7–12, 

2006 Waikoloa, HI. 
4 

2.0 UNCERTAINTY OF PRIMARY CALIBRATION OF

PHOTOVOLTAIC CELLS

1. Reference to Norms and Standards

• ASTM E1125, “Standard Test Method for Calibration of Primary Non-Concentrator 

Terrestrial Photovoltaic Reference Cells Using a Tabular Spectrum”

• Procedure ISO GUM “International Organization for Standardization, Guide to the 

Expression of Uncertainty in Measurement. ISO: Geneva, 1995, ISBN 92-67-10188-9. 

• ISO-VIM “International Vocabulary of Basic and General Terms in Metrology,” 2nd

Edition 1993. 

• ASTM standard E 1328 Terminology Relating to Photovoltaic Solar Energy 

Conversion” 

2. Summary

This uncertainty analysis is for ASTM E1125, “Standard Test Method for Calibration of Primary 

Non-Concentrator Terrestrial Photovoltaic Reference Cells Using a Tabular Spectrum” [1]. The 

analysis is restricted to single-junction monocrystal or multicrystal Si, GaAs, GaInP, GaInAs, 

Ge, or InP cells that are packaged with connectors [2]. Other technologies or unpackaged 

samples have additional error sources related to contacting and a larger spectral-mismatch 

correction. This analysis is restricted to samples less than 4 cm2 in area. The calibration value of 

the PV reference cell is determined with respect to a reference temperature (typically 25°C) and 

reference irradiance (typically ASTM G159 global [3], 1000 W/m2). In September 2008, our 

group switched to the ASTM G173 [4] reference spectrum. This new spectrum is nearly identical 

to the old spectrum (currents were affected by less than 1% for most cases, and 2% for all typical 

PV technologies). The group has essentially been following these procedures since 1984 [5–18]. 

3. Procedures

The procedure from E1125 follows: 

1. Mount the reference cell to be calibrated, collimator, absolute cavity radiometer, and 

spectral irradiance measurement equipment on the tracking platforms.

2. Measure the relative spectral irradiance of the sun, Es(λ), using the spectral irradiance 

measurement instrument and the procedure of Test Method E 1341 [20]. During the 

spectral irradiance measurement, perform steps 2.1 and 2.2 simultaneously. 

2.1. Measure the absolute cavity radiometer output, Et, and verify that the total 

irradiance is between 750 and 1100 Wm-2. 

2.2. Measure the reference cell short-circuit current, Isc. 

2.3. Calculate the calibration value

(1) 

2.4. Measure the reference cell temperature, Tm. 

CVIE U sc T = /
5 

2.5. Repeat 2.1 through 2.3 at least four times. These repetitions must be distributed in 

time during the spectral irradiance measurement.

2.6. Average the calibration values from 2.3.

3. Perform a minimum of five replications of step 2 on at least three separate days.

4. Extend the measured spectral irradiance to 300–4000 nm to encompass the limits of the 

reference spectrum given in Ref. 3 using the procedure described in [8,11,12]. 

5. Correct each measured CVu in step 2.6 for temperature to 25°C using 

(2) 

where Tcoef is the temperature coefficient of the short-circuit current in ppm / °C normalized 

to 25°C. 

(3) 

where:

 Sr(λ) Spectral responsivity of the reference cell (Test Method E1021[21]) 

 Eref(λ) Reference spectral irradiance

 Es(λ) Direct-beam solar spectral irradiance (Practice E1341[20])

 k Spectral correction factor

5.1. Calculate Eqs. 1 and 2 for all points on all days and compute the mean corrected 

calibration value, <CV>. 

5.2. Reject any points that meet the following criteria:

• CV more than 1.5% from the <CV>

• Isc range is greater than 1.5%

• CVu (Tm) standard deviation is greater than 1%. 

6. Verify that at least three days data with a minimum of five sets / day of valid data exist. If 

not, repeat steps 1–5 until all criteria are met.

7. Generate a test report / cover letter.

8. Have the data, record book, test report, and cover letter reviewed by someone familiar with 

the procedures, but who was not involved in the measurement. 

4. Test-Bed-Specific Equipment

 

Figure 2 is a simplified block diagram of the test bed. 

25 1

10 25 6

CV C CV

T CT

u u

coef m ( ) ( °= +

⋅ ⋅ °− − )

1 10 25 ( ) 6 − ⋅ ⋅ °−

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

= ⋅ − T CTCV M

coef m

u t

CV CV = ( u 25 300

4000

300

4000

° ⋅

( )⋅ ( )

( )

∫

∫

C

E S

E

ref r

ref

)

λ λλ

λ λ

d

d

⋅

( )

( )⋅ ( )

= ⋅ ⋅ ∫

∫

E

E S

IMk s

s r

sc T

λ λ

λ λλ

d

d

300

4000

300

4000 Et
6 

Figure 2. Simplified block diagram of the primary calibration test station. 

5. Uncertainty in <CV>

The uncertainty in the average temperature and spectrally corrected calibration value <CV> from 

Eq. 3 is determined using standard uncertainty analysis based on [2,23]. For convenience, the 

elemental Type A and Type B error sources will be expressed in terms of percentage of value. 

The analysis is based on the best measurement capability and represents the smallest uncertainty 

of nearly ideal PV reference cells. This means that the cells should be stable with no measurable 

degradation, packaged with wires and temperature sensors, and close to 2 cm by 2 cm in area. To 

simplify matters, the uncertainties of the input quantities are expressed in terms of percentage of 

value. Since all equations are or will be reduced to multiplications and divisions, the sensitivity 

coefficient reduces to unity. The uncertainty of the performance parameters will then be the same 

for similar cells. To express the uncertainty as a percentage, a typical case is used so that the 

voltmeter range and resolution can be converted to a percentage. The 2002 calibration of the 

World Photovoltaic Scale (WPVS) reference cell 930216-1 is used as a typical example of a Si 

reference cell (Fig. 3).

 
7 

Figure 3. Typical annual primary reference cell calibration.

The WPVS value for 930216-1 at standard reference conditions (25°C, 1000 Wm-2, global) is 

123.29 mA [15–18]. The spectral responsivity is given in Fig. 4. With the uncertainty 

components expressed as a percentage using Eqs. 1 through 3, the uncertainty in the mean 

calibration value <CV> can be written with a coverage factor of 2 for 95% confidence as 

(4) 

The type A error sources are from n’ readings of Isc and Et to obtain one CVu. Using Eq. 3, n data 

sets of CVare averaged to obtain <CV>. Table 1 lists the various uncertainty components and 

their values. 

U

U U

n

I CVC C U V

CV

sc U U 2

3

2

25

2

< > = ⎛

⎝

⎜

⎞

⎠

⎟ + ⎛

⎝

⎜

⎞

⎠

⎟ + ( ) °

′

⎛

⎝

⎜

⎞

⎠

⎟ + ⎛

⎝

⎜

⎞

⎠

⎟ + +⎛

⎝

⎜

⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

n

U U E M t T Uk

22 2 2

2 22 ⎣

⎢

⎢

⎤

⎦

⎥

⎥

0 5.
8 

Figure 4. Quantum efficiency curve of WPVS Reference Cell 930216-1.

Table 1. Summary of Standard Primary Reference Cell Uncertainty Components

Uncertainty

Component 

Source of Uncertainty Value of 

Uncertainty 

(%)

Coverage 

Factor

UIsc Measured Isc 0.029 Rectangular

UCVu(25°C) Corrected calibration value 0.27 n=35

UCVu Uncorrected calibration value 0.083 n’=85

UEt Measured total irradiance 0.34 Rectangular

UMT Temperature correction 0.14 Rectangular

Uk Spectral correction 0.80 Gaussian

Umeter Reference cell DMM (123 mA typical value)

From data sheet, confidence value not listed

0.021 Rectangular

1-year HP34401, 10 V, of reading 0.0035 Rectangular

1-year HP34401, 10 V, of range 0.0005 Rectangular

1-year HP34401, 10 V, 1 line cycle 0.001 Rectangular

HP34401, 10 V, temperature 23±10°C 0.005 Rectangular

Uresistor 1-year resistor calibration uncertainty 0.02 Gaussian

Ustabilityr Resistor 1-year stability (Julie CH-48T4 data sheet) 0.003 Rectangular

The measured Isc is the voltage measured across a 10-ohm resistor with an Agilent 34401A 

multimeter with a 10-power-line cycle integration period. The circuit used to bias the reference 

cell within 2 mV of 0 V is described in Appendix 2. From the typical case in Figs. 3 and 4, the 

measured voltage is taken to be 1.23 V. From the 1-year manufacturer’s specification, the 
9 

uncertainty on the 10-V range is 0.0040% of the reading plus 0.0007% of the range. The 

distribution is assumed to be rectangular because the data sheet does not specify the confidence 

value. The meter uncertainties supplied by the manufacturer are based on a 23±5°C operating 

temperature. Resistors and meters are in a temperature-controlled room at 23±5°C. The 

maximum expected resistor and meter temperature deviation is 23 ±10°C. The temperature 

coefficient of the meter outside of the 23 ±5°C is 0.0005%/°C of the reading and 0.0001%/°C for 

the 10-V range. The total error of the voltage reading across the 10-ohm current sense resistor is

Umeter = [% of range + temperature correction] + [% of reading + temperature correction] = 

100 • {[(0.0035 + 10 • 0.0005) • 0.01 • 1.23] + 

[(0.0005 + 10 • 0.0001) • 0.01 • 10]} / 1.23 = 0.021%. (5) 

The temperature coefficient for the 10-ohm resistor manufactured by Julie Research Laboratory 

(now manufactured by Ohm-Labs) is 5 ppm/°C or 0.0005 %/°C. The uncertainty of the 10-ohm 

resistor calibrated at NREL is 0.02% with 95% confidence level. The 1-year stability of the 

resistor is 0.003%/year from the data sheet. The power rating of the resistor is 6 W, and the 

power dissipated across the resistor of [10 ohm • (0.123 A)2 = 150 mW] is negligible. Hence, the 

uncertainty in Isc (Tm) is taken to be 

 = [(0.021)2 + (10 • 0.005)2

 + (0.02)2 + (0.003)2]

0.5

 = 0.029%. (6) 

The distribution is taken to be rectangular in the absence of further information. 

The total irradiance of the absolute cavity radiometer is a voltage measured with an Agilent 

34970A multimeter with 10-power-line cycle integration period. The absolute cavity radiometer 

is calibrated on an annual basis as a unit with the same cabling and electronics used in the 

calibration of reference cells. The uncertainty in Et is estimated to be 0.34% with a rectangular 

coverage factor [24,25]. 

The uncertainty in the spectral correction factor k, is a function of the magnitude of the 

correction factor [9,25]. A conservative estimate of the spectral correction factor uncertainty is 

20% of the value of [9,25]. Considering the restrictions on the cells and the clear-sky conditions 

under which primary calibrations take place, the spectral correction factor is typically less than 

2% for Si (0.98 to 1.02). For the 2002 data set for 930216-1, the spectral correction factor varied 

from 0.997 to 0.989. Experience with spectral corrections of outdoor primary calibration data of 

less than 2% indicate that the uncertainty Uk is 0.80%. The spectral correction factor is twice as 

large as simulator-based spectral corrections because of uncertainties in the spectral model 

extrapolation of the measured spectral irradiance from a 350–1000-nm wavelength range to a 

300–4000-nm wavelength range. The uncertainty in k is type B because there is only one spectral 

correction factor for each data point. The distribution is taken to be normal (Gaussian) based on 

Monte Carlo perturbation analysis [9,25]. 

The PV temperature is controlled to a nominal 25°C. The temperature is measured using the 

temperature sensor that is permanently attached to the reference cell. This means that, by 

definition, there is no error in the temperature sensor because all measurements of the PV 

reference cell are based on a 25°C cell temperature as measured by the attached sensor. Hence, 

= ( ) + ⋅

2

UI U TT meter resistor coefic sc ( ) ient resistor − + ( ) U U resistor + ( ) stability

⎡

⎣ ⎤ 2 2 2

⎦

0 5.
10 

the only error is in the correction of the data to the reference temperature. The entire 2002 

calibration set of 2233 data sets for 50 reference cells had a temperature range of 19.5° to 

31.5°C. Figure 5 shows the distribution of temperatures. 

Figure 5. Frequency of temperatures in the 2002 Primary Reference Cell calibration data set.

For convenience, the uncertainty in the correction will be based on a 2°C correction with a Isc

temperature coefficient of 456 ppm/°C = 0.0456%/°C. The uncertainty in the temperature 

coefficient can be estimated from the PEP intercomparison, where the WPVS temperature 

coefficient for 930216-1 was established [15,17,26]. The temperature coefficient for 930216-1 

measured independently at six laboratories varied from 250 to 600 ppm/°C [15]. Taking this 

range of temperature coefficient values for a ±4°C correction for temperature gives a temperature 

correction of 0.10% to 0.24%. The distribution is rectangular. Thus, UTcoef = 0.24 - 0.10 = 0.14%. 

Type A error sources arise from the calculation of CVu for a single data set and <CV> for all of 

the data sets. The standard deviation for CVu ranges from 0.054% to 0.125%, with an average 

standard deviation of 0.083%. The number of Isc (Tm) / Et readings during the spectral irradiance 

measurement equal to 85 are averaged to give CVu. The standard deviation for <CV> for the 

2002 calibration of 930216-1 was 0.27% based on 35 data sets. Figure 3 shows <CV>, CV, and 

CVu. 

Using Eq. 4, the expanded uncertainty with 95% confidence (coverage = 2) in the calibration 

value is 

 = 0.91% . (7) 

As a check on the uncertainty estimates, the calibration value for a specific reference cell as a 

function of time can be examined. The following figures list the calibration value as a function of 

time for several primary reference cells. Figure 6 shows the history of NREL’s two WPVS-

= ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠ < > ⎟ +

2 2

2 0 021

3

0 27

35

0 083

8

. .. U CV

5

0 34

3

0 14

3

0 80

2

222 ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ ... 2 0 5 ⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

.
11 

calibrated reference cells (15–17). The NREL primary calibration method was also performed 

near sea level in a different climate zone under less-than-ideal conditions in late March and early 

April of 2003 at the European Solar Test Installation (ESTI). Figures 7 and 8 show the 

calibration history of a mono-Si and GaAs cell, respectively. The letter “a” after the year in Figs. 

6–8 indicates a significant change in the software.

Figure 6. Calibration value measured at NREL compared with the WPVS average value of 

four international photovoltaic calibration laboratories including NREL.

Figure 7. Nineteen years of primary reference cell calibrations on the same mono-Si cell.
12 

Figure 8. Seventeen years of primary reference cell calibrations on the same GaAs cell.

 

6. References for Section 2 

1. ASTM Standard E1121, Standard Test Method for Calibration of Primary NonConcentrator Terrestrial Photovoltaic Reference Cells Using a Tabular Spectrum, Amer. 

Society for Testing Matls., West Conshocken PA, USA. 

2. ASTM Standard 1040, Specification for Physical Characteristics of Non-Concentrator 

Photovoltaic Reference Cells, Amer. Society for Testing Matls., West Conshocken PA, 

USA.

3. ASTM Standard G159, Standard Tables for Reference Solar Spectral Irradiances: Direct 

Normal and Hemispherical on 37° Tilted Surfaces, Amer. Society for Testing Matls., West 

Conshocken PA, USA. 

4. ASTM Standard G73, Standard Tables for Reference Solar Spectral Irradiances: Direct 

Normal and Hemispherical on 37° Tilted Surfaces, Amer. Society for Testing Matls., West 

Conshocken PA, USA. 

5. K.A. Emery, C.R. Osterwald, T.W. Cannon, D.R. Myers, J. Burdick, T. Glatfelter, W. 

Czubatyj, and J. Yang, “Methods for Measuring Solar Cell Efficiency Independent of 

Reference Cell or Light Source,” Proc. 18th IEEE Photovoltaic Spec. Conf., Las Vegas, 

NV, October 21–25, 1985, pp.623–628, IEEE, New York, 1985. 

6. C.R. Osterwald, (1986), Translation of Device Performance Measurements to Reference 

Conditions, Solar Cells 18, pp.269–279. 

7. C.R. Osterwald, K.A. Emery, D.R. Myers, and C.J. Riordan, “Extending the Spectral 

Range of Silicon-Based Direct-Beam Solar Spectral Radiometric Measurements,” Proc. 

20th IEEE Photovoltaic Specialists Conf., Las Vegas, NV, September 26–30, 1988, 

pp.1246–1250, IEEE, New York, 1989. 

8. C.R. Osterwald, K.A. Emery, D.R. Myers, and R.E. Hart, “Primary Reference Cell 

Calibrations at SERI: History and Methods,” Proc. 21st IEEE Photovoltaic Specialists 

Conf., Orlando, FL, May 21–25, 1990, pp.1062–1067, IEEE, New York, 1990. 
13 

9. K. A. Emery, C.R. Osterwald, S. Rummel, D.R. Myers, T.L. Stoffel, and D. Waddington, 

“A Comparison of Photovoltaic Calibration Methods,” Proc. 9th European Photovoltaic 

Solar Energy Conf., Freiburg, W. Germany, September 25–29, 1989, pp.648–651. 

10. K.A. Emery, C.R. Osterwald, and C.V. Wells, “Uncertainty Analysis of Photovoltaic 

Efficiency Measurements,” Proc. 19th IEEE Photovoltaic Specialists Conf., New Orleans, 

LA, May 4–8, pp.153–159, IEEE, New York, 1987. 

11. K.A. Emery, C.R. Osterwald, L.L. Kazmerski, and R.E. Hart, “Calibration of Primary 

Terrestrial References Cells When Compared with Primary AM0 Reference Cells,” Proc. 

8th European Photovoltaic Solar Energy Conf., Florence, Italy, May 9–12, 1988, pp.64–68. 

12. C. Osterwald and K. Emery, Spectroradiometric Sun Photometry,” Journal of Atmospheric 

and Oceanic Technology 17, pp.1171–1188, 2000. 

13. K.A. Emery, D. Waddington, S. Rummel, D.R. Myers, T.L. Stoffel, and C.R. Osterwald, 

SERI Results from the PEP 1987 Summit Round Robin and a Comparison of 

Photovoltaic Calibration Methods, SERI Tech. Rep. TR-213-3472, March 1989. 

14. J. Metzdorf, T. Wittchen, K. Heidler, K. Dehne, R. Shimokawa, F. Nagamine, H. 

Ossenbrink, L. Fornarini, C. Goodbody, M. Davies, K. Emery, and R. Deblasio, 

“Objectives and Results of the PEP '87 Round-Robin Calibration of Reference Cells and 

Modules,” Proc. 21st IEEE Photovoltaic Specialists Conf., Orlando, FL, May 21–25, 1990, 

pp.952–959, IEEE, New York, 1990. 

15. J. Metzdorf, T. Wittchen, K. Heidler, K. Dehne, R. Shimokawa, F. Nagamine, H. 

Ossenbrink, L. Fornarini, C. Goodbody, M. Davies, K. Emery, and R. Deblasio, “The 

Results of the PEP '87 Round-Robin Calibration of Reference Cells and Modules,- Final 

Report” PTB Technical Report PTB-Opt-31, Braunschweig, Germany, November 1990, 

ISBN 3-89429-067-6. 

16. C.R. Osterwald, S. Anevsky, A.K. Barua, J. Dubard, K. Emery, D. King, J. Metzdorf, F. 

Nagamine, R. Shimokawa, N. Udayakumar, Y.X. Wang, W. Zaaiman, A. Zastrow, and J. 

Zhang, “Results of the PEP ‘93 Intercomparison of Reference Cell Calibrations and Newer 

Technology Performance Measurements,” NREL Technical Report NREL/TP-520-23477, 

March 1998. Proc. 25th IEEE Photovoltaic Specialists Conf., Washington D.C., May 13–

17, 1996, pp.1263–1266, IEEE, New York, 1996. 

17. C.R. Osterwald, S. Anevsky, A.K. Barua, J. Dubard, K. Emery, D. King, J. Metzdorf, F. 

Nagamine, R. Shimokawa, N. Udayakumar, Y.X. Wang, T. Wittchen, W. Zaaiman, A. 

Zastrow, and J. Zhang, “Results of the PEP’93 Intercomparison of Reference Cell 

Calibrations and Newer Technology Performance Measurements,” Proc. 26th IEEE PVSC 

Conf., Anaheim, CA. Sept. 29–Oct. 2, 1997, pp.1209–1212, IEEE, New York, 1997. 

18. C.R. Osterwald, S. Anevsky, K. Bücher, A.K. Barua, P. Chaudhuri, J. Dubard, K. Emery, 

B. Hansen, D. King, J. Metzdorf, F. Nagamine, R. Shimokawa, Y.X. Wang, T. Witchen, 

W. Zaaiman, A. Zastrow, and J. Zhang, “The World Photovoltaic Scale: An International 

Reference Cell Calibration Program,” Progress in Photovoltaics Research and 

Applications 7, pp.287–297, 1999. 

19. K. Emery, “The Results of the First World Photovoltaic Scale Recalibration,” NREL Tech. 

Rep. NREL/TP-520-27942, (March 2000).

20. ASTM Standard E 1341, Practice for Obtaining Spectroradiometric Data from Radiant 

Sources, Amer. Society for Testing Matls., West Conshocken PA, USA. 

21. ASTM Standard E1021, Standard Test Methods for Measuring Spectral Response of 

Photovoltaic Cells, Amer. Society for Testing Matls., West Conshocken PA, USA. 

22. “The Expression of Uncertainty and Confidence in Measurement,” United Kingdom 

Accreditation Service, M3003, Middlesex, UK, December 1997. 
14 

23. International Organization for Standardization, Guide to the Expression of Uncertainty in 

Measurement. ISO: Geneva, 1995, ISBN 92-67-10188-9. 

24. I. Reda, “Calibration of a Solar Absolute Cavity radiometer with Traceability to the World 

radiometric Reference,” NREL Tech. Rep. NREL/TP-463-20619, January 1996.

25. I. Reda, 2002 NREL Pyrheliometer Comparisons (NPC-2002), Solar Radiation Research 

Laboratory, NREL.

26. H. Field and K. Emery, “An Uncertainty Analysis of the Spectral Correction Factor,” Proc. 

23rd IEEE Photovoltaic Specialists Conf., Louisville, KY, May 10–14, 1993, pp.1180–

1187, IEEE, New York, 1993. 

27. K. Emery, “The Results of the First World Photovoltaic Scale Recalibration,” NREL Tech. 

Rep. NREL/TP-520-27942, (March 2000).
15 

3.0 UNCERTAINTY OF PHOTOVOLTAIC CELL 

SPECTRAL RESPONSIVITY

1. Reference to Norms and Standards

• ASTM standard E1021, “Standard Test Methods for Measuring Spectral Response of 

Photovoltaic Cells”

• Procedure ISO GUM “International Organization for Standardization, Guide to the 

Expression of Uncertainty in Measurement. ISO: Geneva, 1995, ISBN 92-67-10188-9. 

• ISO-VIM “International Vocabulary of Basic and General Terms in Metrology,” 2nd

Edition 1993. 

• ASTM standard E 1328 Terminology Relating to Photovoltaic Solar Energy 

Conversion” 

2. Summary

This uncertainty analysis is for ASTM E1021, “Standard Test Methods for Measuring Spectral 

Response of Photovoltaic Cells” [1]. The analysis is restricted to single-junction monocrystal or 

multicrystal Si, GaAs, GaInP, GaInAs, Ge, or InP cells that are packaged with connectors [2]. 

Other technologies or unpackaged samples have additional error sources related to contacting, 

shading, and nonlinear behavior. This analysis is restricted to samples less than 4 cm2 in area. 

The calibration value of the PV reference cell is determined with respect to a reference 

temperature (typically 25°C) and reference irradiance (typically ASTM G159 global [3], 1000 

W/m2). The PV Cell and Module Performance Characterization group has essentially been 

following these procedures since 1984 [4–17]. 

3. Procedures

The procedure from ASTM standard E1021 follows: 

1. Calibrate the system by measuring the total power with a pyroelectric radiometer 

generating a file of power, P(λ) versus wavelength λ. 

2. Measure the responsivity of the reference detector.

3. Correct the calibration over the range of the reference detector, generating a corrected file 

of P(λ) vs. λ from the following equation: 

(1) 

where:

Sref(λ) Calibrated spectral responsivity of the reference detector in units of A/W 

I

R Measured current of the reference detector.

4. Verify that the calibration is valid by comparing the measured value of the reference 

detector with the calibrated value. Repeat steps 2 to 3 as needed.

5. Place the sample on the temperature control plate, which will maintain the temperature at 

25°C ± 2°C. 

6. Mount the sample with the connector into the input leads for the filter spectral response 

system.

P I

S

R

ref

( ) λ λ = ( )
16 

7. Select the wavelength range, measure the spectral responsivity, and save the normalized 

data QE(λ) versus λ from the following equation: 

(2) 

where: 

I

T Measured current of the device under test 

P(λ) From Eq. 1. 

4. Test Bed Specific Equipment

Figure 9 is a simplified block diagram of the test bed. 

5. Uncertainty in QE(λ) vs. λ

Figure 10 is a plot of the typical quantum efficiency for a Si WPVS cell used in this study [4,5]. 

The numerous sources of uncertainty in determining QE(λ) vs. λ are documented in Refs. 6 and 

7 and listed in Tables 2 to 4. Since the data are normalized, any wavelength-independent 

multiplicative errors drop out. For the filter QE system and the Si cell in Fig. 10 the dominant 

error sources are the lamp intensity fluctuations, reference detector calibration uncertainty, 

spatial uniformity of the monochromatic light, and blocking of the light outside of the filter’s 

pass band. The calibrated spectral responsivity Sref(λ) in Eq. 1 is obtained from NIST. Table 5 

lists the detector measurement uncertainties from the NIST Web site of calibration services 

(http://ts.nist.gov/).

 Figure 9. Filter quantum-efficiency system. This equipment is used to measure the 

quantum efficiency (QE) of a PV cell.

100 QE I

Max QE P

T

( ) () ()

λ λ λλ = [ ]
17 

The major error sources for the filter QE measurement system are listed in Table 6 as a 

percentage of the measured QE. The error from intensity fluctuations are both Type A and Type 

B. The reason is because the measurement is an average of ten readings, but since a stored 

calibration file is used, the intensity drift of the lamp with time during the generation of the 

calibration file and during the measurement is proportional to I

T . The reference detector 

uncertainty is a composite from Table 5. The spatial uniformity error exists because the spatial 

uniformity of the monochromatic beam is a function of wavelength and the reference detector 

and device under test are not exactly the same size. The filter blocking error can be estimated by 

assuming that the filters have no pinholes and that the 10-nm bandwidth filters meet their 

specified blocking of 10–4 and integrating the power in the light source outside of the pass band. 

The error sources are larger for wavelengths less than 400 nm and near the energy gap (where 

the infrared quantum efficiency goes to zero). Combining the uncertainties in Table 6 gives

(3) 

UQE = 4 % . (4) 

This value is consistent with the observed ~3% variation in the measured QE in Fig. 10, which 

should be a monotonically increasing then decreasing response. 

Figure 10. QE curve of WPVS reference cell N45 showing the standard deviation and 

signal-to-noise ratio. 

UQE = 2 0 5

10

2 0

3

0 5

2

2 0

3

2 2 2

⎛ . ...

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

2 2 0 5

2 0

3

. .
18 

Table 2. Error Sources for Measurement of the Photocurrent 

Electrical Instrumentation 

 Current-to-voltage (I-to-V) converter 

 Commercial current or custom amplifier

 Gain, linearity, noise, offset 

 Shunt resistor 

 Calibration, drift, thermovoltages

 Signal from I-to-V converter measured with

 Lock-in amplifier (typically < 1 mA)

 Calibration, resolution, accuracy 

 Waveform to sine wave correction factor 

 Overloading, noise, dynamic range 

 Time-constant 

 Procedures for using lock-in amplifier 

 An AC voltmeter

 Gain, offset from noise level

 Linearity, time-constant 

PV Cell or Module 

Temperature 

 Response time to periodic light 

 Linearity of PV device 

White-light bias spatial uniformity

Monochromatic light spatial uniformity

 Voltage bias of cell being measured

 Spectral content of bias light 

 Device sensitivity to polarization of light 

Mechanical 

 Mechanical movement of optics 

Mechanical vibration

Chopped stray monochromatic light
19 

Table 3. Error Sources for Measurement of the Light Power

Filament or Xe-Arc Light Source 

Intensity fluctuations

 Change in spectrum with age and current 

Stored Calibration File 

 Monochromatic source calibration drift with time

Stray Light 

Detector sees light that cell does not see

Area of detector different from device area

Different field of views

 Monochrometer 

 Incomplete attenuation of higher and 

 lower grating orders

Narrow-bandwidth filters

 Pinholes in the filter 

 Degradation of blocking filter 

 Insufficient blocking (~10-4) 

Detectors and Associated Electronics in General 

Calibration, resolution, accuracy

 Gain, phase, offset, linearity 

Spatial uniformity of detector element

Drift in temperature of room

 Change in the detector’s field of view 

 Degradation of detector 

Spectral response of detector 

Pyroelectric Detector 

Time constant of detector

 Microphonics, signal to noise 

Phase-angle adjustment

Waveform factor (square wave assumed)

Table 4. Error Sources Related to the Monochromatic Light

Bandwidth 

Filter Defects 

Polarization Variation with Wavelength 

Wavelength Offset, Error 

Wavelength Variation with Room Temperature 

Beam Wanders with Wavelength 

Beam Larger than the Test Device 

Detector area versus PV area

 Position of detector and PV different 

Spatial uniformity of beam

Beam Smaller than Detector and Device Area 

Partially shaded regions

Spatial variation in responsivity of PV
20 

Table 5. Detector Measurement Services Uncertainties Relative Expanded Uncertainty (k = 2) 

______________________________________________________________________________ 

Wavelength UV 100 (UV) S1337 (Visible) GE (NIR) InGaAs (NIR)

[nm] [%] [%] [%] [%]

200 3.8 3.8 

250 1.3 1.3 

300 1.3 1.3 

350 1.8 1.8 

400 1.5 1.5 

450 0.38 0.24 

500 0.38 0.22 

550 0.20 

600 0.20 

650 0.20 

700 0.20 0.46 0.38 

750 0.22 0.42 0.36 

800 0.22 0.68 0.54 

850 0.22 0.44 0.44 

900 0.22 0.50 0.40 

950 2.6 1.2 1.3 

1000 1.7 0.9 0.9 

1050 2.7 0.9 0.9 

1100 4.2 0.52 0.50 

1150 0.8 0.8 

1200 1.4 1.5 

1250 0.9 0.9 

1300 0.9 0.9 

1350 0.9 0.9 

1400 1.2 1.2 

1450 0.9 0.9 

1500 1.0 1.0 

1550 1.1 1.1 

1600 1.4 1.3 

1650 1.1 1.0 

1700 1.7 2.2 

1750 2.6 2.7 

1800 3.4 4.2 

______________________________________________________________________________ 
21 

Table 6. Major Errors Sources in Normalized Filter Quantum Efficiency Measurements

Source Type A Uncertainty Type B Uncertainty Coverage 

 % % # Readings 

Intensity fluctuations 0.5 2.0 10, Rectangular 

Reference detector – 0.5 Gaussian

Spatial uniformity – 2.0 Rectangular 

Filter blocking – 2.0 Rectangular 

______________________________________________________________________________ 

6. References for Section 3

1. ASTM Standard E1021, Standard test methods for measuring spectral response of 

photovoltaic cells, Amer. Society for Testing Matls., West Conshocken PA, USA. 

2. “The Expression of Uncertainty and Confidence in Measurement,” United Kingdom 

Accreditation Service, M3003, Middlesex, UK, December 1997. 

3. International Organization for Standardization, Guide to the Expression of Uncertainty in 

Measurement. ISO: Geneva, 1995, ISBN 92-67-10188-9. 

4. C.R. Osterwald, S. Anevsky, A.K. Barua, J. Dubard, K. Emery, D. King, J. Metzdorf, F. 

Nagamine, R. Shimokawa, N. Udayakumar, Y.X. Wang, W. Zaaiman, A. Zastrow, and J. 

Zhang, “Results of the PEP ‘93 Intercomparison of Reference Cell Calibrations and Newer 

Technology Performance Measurements,” NREL Technical Report NREL/TP-520-23477, 

March 1998. Proc. 25th IEEE Photovoltaic Specialists Conf., Washington D.C., May 13–

17, 1996, pp.1263–1266, IEEE, New York, 1996. 

5. C.R. Osterwald, S. Anevsky, A.K. Barua, J. Dubard, K. Emery, D. King, J. Metzdorf, F. 

Nagamine, R. Shimokawa, N. Udayakumar, Y.X. Wang, T. Wittchen, W. Zaaiman, A. 

Zastrow, and J. Zhang, “Results of the PEP’93 Intercomparison of Reference Cell 

Calibrations and Newer Technology Performance Measurements,” Proc. 26th IEEE PVSC 

Conf., Anaheim, CA. Sept. 29–Oct. 2, 1997, pp.1209–1212, IEEE, New York, 1997. 

6. K.A. Emery, “Measurement and Characterization of Solar cells and Modules,” Handbook 

of Photovoltaic Science and Engineering, Chap. 16, pp.701–747, A. Luque and S. Hegedus 

editors, John Wiley & Sons, W. Sussex, U.K., ISBN 0-471-49196-9, 2003. 

7. K. Emery, D. Dunlavy, H. Field, and T. Moriarty “Photovoltaic Spectral Responsivity 

Measurements,” Proc. 2nd World Conference and Exhibition on Photovoltaic Solar Energy 

Conversion, Vienna Austria July 6–10, 1998, Joint Research Center report EUR 18656, 

pp.2298–2301. 

8. K.A. Emery, C.R. Osterwald, and C.V. Wells, “Uncertainty Analysis of Photovoltaic 

Efficiency Measurements,” Proc. 19th IEEE Photovoltaic Specialists Conf., New Orleans, 

LA, May 4–8, pp.153–159, IEEE, New York, 1987. 

9. H. Field and K. Emery, “An Uncertainty Analysis of the Spectral Correction Factor,” Proc. 

23rd IEEE Photovoltaic Specialists Conf., Louisville, KY, May 10–14, 1993, pp.1180–

1187, IEEE, New York, 1993. 
22 

4.0 UNCERTAINTY OF ELECTRICAL PERFORMANCE

OF PHOTOVOLTAIC CELLS

 

1. Reference to Norms and Standards

• ASTM E948, “Standard Test Method for Electrical Performance of Photovoltaic Cells 

Using Reference Cells Under Simulated Sunlight.” This procedure meets or exceeds the 

requirements in IEC standard 60904-1, “Photovoltaic Devices – Measurement of 

Photovoltaic Current-Voltage Characteristics.” 

• Procedure ISO GUM “International Organization for Standardization, Guide to the 

Expression of Uncertainty in Measurement. ISO: Geneva, 1995, ISBN 92-67-10188-9. 

• ISO-VIM “International Vocabulary of Basic and General Terms in Metrology,” 2nd

Edition 1993. 

• ASTM standard E 1328 Terminology Relating to Photovoltaic Solar Energy 

Conversion” 

2. Summary

This uncertainty analysis is for ASTM E948, “Standard Test Method for Electrical Performance 

of Photovoltaic Cells Using Reference Cells Under Simulated Sunlight” [1]. The analysis is 

restricted to single-junction monocrystal or multicrystal Si, GaAs, GaInP, GaInAs, Ge, or InP 

cells that are packaged with connectors [2]. Other technologies or unpackaged samples have 

additional error sources related to contacting and a larger spectral mismatch correction. This 

analysis is restricted to samples less than 100 cm2 in area. The current versus voltage (I-V) 

characteristics are measured within 2°C of the reference temperature (typically 25°C) and within 

2% of the reference irradiance (typically ASTM G159 global [3], 1000 W/m2). Using ASTM 

G173 global [4] gives essentially the same uncertainty because the spectra are nearly identical 

affecting the Isc for Si cells less than 1%. The international equivalent of these spectra are IEC 

standard 60904-3 editions 1 and 2. Our group has essentially been following these procedures 

since 1984 [9–14]. To simplify matters, the uncertainties of the input quantities are expressed in 

terms of percentage of value. Since all equations are or will be reduced to multiplications and 

divisions, the sensitivity coefficient reduces to unity. The uncertainty of the performance 

parameters will then be same for similar cells.

3. Procedures

The procedure from E948 follows: 

1. Measure the cell area, A, using the definition in Terminology E 1328 [5]. 

2. Measure the relative spectral responsivity of the PV cell to be calibrated using Test Method 

E1021 [6]. 

3. Choose a primary reference cell.

4. Determine the spectral mismatch parameter, M, using Test Method E 973 [7,9,10]. 
23 

 , (1) 

where:

St(λ) Measured spectral responsivity of the test cell (Test Method E1021 [8])

Sr(λ) Measured spectral responsivity of the reference cell (Test Method

 E1021 [8]) 

Eref(λ) Reference spectral irradiance

Es(λ) Measured spectral irradiance of the light source (Test method E973 [7])

λ1, λ2, λ3, λ4 Wavelength limits of integration. 

5. Mount the reference cell in the center of the test plane and verify that the plate temperature 

or reference cell temperature are within ±2°C of the temperature corresponding to the 

reference cell short-circuit current calibration value, IRR. 

6. Adjust the simulator so that the measured reference cell short-circuit current IRM is within 

2% of the spectrally corrected calibration value or

 (2) 

7. Transfer this value to an intensity monitor giving a calibration value for the intensity 

monitor by recording the average of at least ten measurements of the following equation: 

, (3) 

where:

IMR Calibrated short-circuit current of the intensity monitor located near the

 edge of the test plane. 

IMM Measured short-circuit current of the intensity monitor located near the

 edge of the test plane. 

8. Mount the cell to be tested on the temperature-controlled plate in the same position as the 

reference cell and adjust the plate temperature so the cell is within 2°C of the reference 

temperature. 

9. Measure the open-circuit voltage, Voc, with the load disconnected. 

10. Measure the current versus voltage (ITM, V) characteristic of the cell under test by changing 

the operating point with the variable load so that the curve is swept through 0 V and 0 A. 

At each operating point on the (ITM, V) characteristic, measure the cell voltage, V, cell 

current, ITM, and IMM. Correct the measured current, ITM, for intensity fluctuations, giving 

1

2

3

4

M

E

s

S

t

E

s

S

r

Eref S

r

=

∫ () ()

∫ () ()

λ λλ ( )

λ

λ

λ λλ

λ

λ

d λ λ

d

∫ ( )

∫ () ()

d

d

λ

λ

λ

λ λλ

λ

λ

3

4

1

2

Eref S

t

≤ ( ) 0 98 ≤ 1 I

M I RR

RM . .02

I I I MI MR MM RR RM = ( )( )
24 

the calibrated current of the test cell under the reference spectrum at the reference 

irradiance and temperature, ITR, using 

. (4) 

11. Measure the open-circuit voltage, Voc, with the load disconnected. 

12. Determine the calibrated Isc by performing a linear-regression fit to all ITR- V points that 

satisfy the constraint that all currents are within 4% of the current at 0 V and of all voltages 

within 0.20 times the voltage at 0 A. 

13. Determine the maximum power, Pmax, by performing a polynomial fit to all ITR- V points 

that satisfy the constraints that the measured power is within 85% of the largest measured 

power and the voltage is within 80% of the voltage at the largest measured power as 

recommended by E948. The polynomial that gives the best fit to the data up to a fifth order 

is used. The voltage at maximum power, Vmax, is the real root of the derivative of the fit of 

the power versus voltage polynomial set to 0. This voltage is then substituted into the 

power vs. voltage polynomial to obtain the Pmax. The current at maximum power, Imax, is 

calculated from Pmax / Vmax. 

14. The current vs. voltage data points, (ITR, V), along with a variety of information including 

Voc, Isc, Pmax, temperature, time, cell ID, cell type, manufacturer, reference cell, and its 

calibration, the record book number and page, change in Voc before and after the 

measurement, are saved.

 

4. Test-Bed-Specific Equipment

 

Figure 11 is a photograph of the test bed. 

Figure 11. The Spectrolab X25 solar simulator and custom I-V measurement system.

I II I TR TM MR MM =
25 

Figure 12 is a simplified block diagram of the test bed. 

Figure 12. Simplified block diagram of current versus voltage test station. 

5. Uncertainty Analysis

 

Table 7 summarizes the standard uncertainty components. All uncertainty components are given 

in percentage with a typical 2-cm by 2-cm Si cell as the reference case.

Table 7. Summary of Standard Secondary Reference Cell Uncertainty Components

Uncertainty

Component 

Source of Uncertainty Value of 

Uncertaint

y (%)

Coverage 

Factor

UM-DMM Intensity Monitor meter (25 mV typical value) 0.013 Rectangular

1-year HP34401, 1 V, of reading 0.004 Rectangular

1-year HP34401, 1 V, of range 0.0007 Rectangular

1-year HP34401, 1 V, 1 line cycle 0.001 Rectangular

HP34401, 1 V, temperature 23±15 °C 0.0075 Rectangular

UMM, UMM’ Measured Monitor current 0.025 Gaussian

1-year resistor stability (Julie CH-48T4 data 

sheet)

0.003 Gaussian

1-year resistor calibration uncertainty 0.02 Gaussian

Resistor temperature 0.0005%/°C • 15°C 0.075 Gaussian

UR-DMM Reference cell DMM (130 mA typical value, 10 Ω 

current sense)

0.016 

1-year HP34401, 10 V, of reading 0.005 Rectangular

1-year HP34401, 10 V, of range 0.0007 Rectangular
26 

Uncertainty

Component 

Source of Uncertainty Value of 

Uncertaint

y (%)

Coverage 

Factor

1-year HP34401, 10 V, 1 line cycle 0.001 Rectangular

HP34401, 10 V, temperature 23±15°C 0.0075 Rectangular

URM Measured reference cell current 0.027 Gaussian

1-year resistor stability (Julie CH-48T4 data sheet) 0.003 Gaussian

1-year calibration uncertainty 0.02 Gaussian

Resistor temperature 0.0005%/°C 0.0225 Gaussian

UI-DMM Test device current DMM (130 mA typical value) 0.021 Gaussian

1-year HP34401, 1 V, of reading 0.004 Gaussian

1-year HP34401, 1 V, of range 0.0007 Gaussian

1-year HP34401, 1 V, 1 line cycle 0.001 Gaussian

HP34401, 100 mV, temperature 23±15°C 0.0075 Gaussian

UTM Measured test cell current (Riedon PF1121 <5A,

Riedon PF1328 >5A) 

0.038 

0.11 

Gaussian

1-year resistor stability Riedon PF1121

 Riedon PF1328

0.01

0.1

Gaussian

1-year resistor calibration uncertainty 0.02 Gaussian

Resistor temperature 0.0015%/°C 0.0225 Gaussian

UTT Test cell current for ±1°C 0.05 Rectangular

UTR Reference cell current for ±1°C 0.05 Rectangular

URR Primary reference cell Calibration value 0.91 Rectangular

RC Least-squares fit standard deviation for ITR (Isc of 

test cell)

0.03 N=15

RT Reference cell Isc to monitor Isc transfer standard 

deviation

0.02 N=125

US Error from spatial nonuniformity 0.5 Rectangular

UM Error in the spectral correction factor M 0.4 Gaussian

UIsc Uncertainty in test cell Isc 1.27 coverage=2

UP-fit Error in Pmax from the fit 0.06 Gaussian

UTV Test cell voltage for ±1°C 0.5 Rectangular

UV Measured test cell voltage 0.006 Rectangular

UVmax Maximum power voltage 0.7 coverage=2

UImax Maximum power current 1.4 coverage=2

UPmax Maximum power 1.40 coverage=2

UVoc Open-circuit voltage 0.58 coverage=2

UA Area 1.20 coverage=2

Uη Efficiency 1.84 coverage=2

UFF Fill factor (from UVoc, UIsc, UPmax) 1.97 coverage=2

UFF Fill factor - more rigorous neglecting intensity 

errors 

0.58 coverage=2
27 

5.1 Uncertainty in Isc

The uncertainty in the short-circuit current of the reference cell, ITR from Eq. 4, is determined 

using standard uncertainty analysis based on [22,23]. For convenience, the elemental Type A and 

Type B error sources will be expressed in terms of percentage of value. The analysis is based on 

the best measurement capability and represents the smallest uncertainty of nearly ideal PV 

reference cells. This means that the cells should be stable with no measurable degradation, 

packaged with wires and temperature sensors, and close to 2 cm by 2 cm in area. Combining 

Eqs. 3 and 4 yields 

(5) 

To express the uncertainty as a percentage, a typical I-V case is used so that the voltmeter range 

and resolution can be converted to a percentage. Figure 13 is the I-V curve for the typical case.

Figure 13. Typical I-V curve for a reference cell.

The measured monitor value IMM, or IMM’ is the voltage measured across a 10-ohm resistor with 

an Agilent 34401A multimeter with 1-power-line cycle integration period. The measured 

monitor voltage is typically 250 mV. An op-amp circuit is used to bias the monitor cell within 

2 mV of zero volts and monitor the current with a 10-ohm 4-terminal resistor (Appendix 2). 

From the 1-year manufacturer’s specification, the uncertainty on the Agilent 34401A voltmeter 

I II TR TM M = ( )( ) M RR RM MM ′I MI I
28 

1-V range is 0.0040% of the reading plus 0.0007% of the range plus 0.001% of range because 

the power line cycle was not longer than 1. The distribution is assumed to be rectangular because 

the data sheet does not specify the confidence value. The meter uncertainties supplied by the 

manufacturer are based on a 23±5°C operating temperature. Since the resistors and meters are in 

a temperature-controlled room at 23±15°C, the maximum expected resistor and meter 

temperature deviation is 23 ±15°C. The temperature coefficient of the meter outside of the 

23 ±15°C is 0.0005%/°C of the reading and 0.0001%/°C of the range for the 1-V range. The total 

error of the voltage reading across the 1-ohm current sense resistor UM–DMM is

UM-DMM = [% of reading + temperature correction] + [% of range + temperature correction] = 

100 • {[(0.0007 + 15 • 0.0005) • 0.01 • 0.25] + 

[(0.0040 + 15 • 0.0001 + 0.001) • 0.01 • 1]} / 0.25 V = 0.013%. (6) 

The temperature coefficient of the 10-ohm resistor manufactured by Julie Research Laboratory 

model CH-48T4 (now manufactured by Ohm-Labs) is 5 ppm/°C or 0.0005 %/°C. The 

uncertainty of the 10-ohm resistor calibration at NREL is 0.02%. The 1-year stability of the 

resistor is taken as 0.003 %/year from the data sheet. The power rating of the resistor is 6 W and 

the power dissipated across the resistor is (10 ohm • 0.0252 A2 = 6 mW), so resistor heating is 

negligible. Hence, UMM and UMM’ the uncertainties in IMM and IMM’ respectively taken to be 

 = [(0.013%)2 + (15 • 0.005 )2 + (0.02)2 + (0.003)2]

0.5 

 = 0.025%. (7) 

The distribution is taken to be rectangular in the absence of further information.

The primary reference cell measured short-circuit current IRM is the voltage measured across a 

10-ohm resistor with an Agilent 34401A multimeter with 1-power-line cycle integration period. 

The circuit used to bias the reference cell within 2 mV of 0 V is described in Appendix 2. The 

reference cell current at standard reporting conditions (SRC) is typically 130 mA. From the 1-

year manufacturer’s specification, the uncertainty on the 10-V range is 0.0035% of the reading 

plus 0.0005% of the range plus 0.001% of the range because the power-line cycle was not longer 

than 1. The meter uncertainties are based on a 23±15°C operating temperature. The total error of 

the reference cell voltage reading UR-DMM is 

UR-DMM = [% of reading + temperature correction] + [% of range + temperature correction] = 

100 • {[(0.0035 + 15 • 0.0005) • 0.01 • 1.30] + 

[0.0005 + (15 • 0.0001 + 0.001) • 0.01 • 10]} / 1.30 

 = 0.008%. (8) 

The uncertainty of the 10-ohm resistor calibrated at NREL is 0.02% with 95% confidence level. 

The Julie resistor temperature coefficient is negligible at 5 ppm/°C = 0.0005%/°C. The 1-year 

stability of the resistor is taken as 20 ppm/year because the resistors have been in use for more 

than 10 years. The power rating of the resistor is 6 W and the power dissipated across the resistor 

is (10 ohm • 0.132 A2

 = 174 mW), so resistor heating is negligible. Hence, the uncertainty URM in 

IRM is taken to be 

UMM MM UU T ′ = ( ) M DMM res − +

2

 , istor coeficient resistor T UU resistor st ( ) ⋅ − + ( ) +

2 2

( ) ability

⎡

⎣ ⎤⎦

2 0 5.
29 

 = [(0.008)2 + (15 • 0.0005 )2 + (0.02)2 + (0.003)2]

0.5 

 = 0.022%. (9) 

The distribution is taken to be rectangular in the absence of further information.

The measured current of the cell under test ITM is the voltage measured across a current sense 

resistor with an Agilent 34401A multimeter with 1-power-line cycle integration period, as shown 

in Fig. 12. Depending on the current range and current limit, a particular Riedon resistor is 

selected to maintain between 30 and 300 mV across the resistor. The precision 4-terminal lowtemperature coefficient Riedon resistors are nominally 0.01, 0.1, 1.0, 10, and 100 ohms. A 

typical short-circuit current for a test cell is 130 mA. So, the software would select the 1-V range 

and a 1-ohm current sense resistor. This is near the worst-case scenario, being at the low end of

the meter 1-V range. From the 1-year 34401A manufacturer’s specification, the uncertainty on 

the 1-V range is 0.0040% of the reading plus 0.0007% of the range plus 0.001% of range 

because the power-line cycle was not longer than 1. The meter uncertainties are based on a 

23±15°C operating temperature (0.005%/°C). The total error UI-DMM of the voltage reading is 

UI-DMM = [% of reading + temperature correction] + [% of range + temperature correction] =

100 • {[(0.0040 + 15 • 0.0005) • 0.01 • 0.130] + 

 [(0.0007 + 15 • 0.0001 + 0.001) • 0.01 • 1.0]} / 0.130 = 0.021%. (10) 

The uncertainty of the Riedon Corporation model PF1121 1-ohm resistor calibration is 0.02%. 

The resistor temperature coefficient is negligible at 5 ppm/°C = 0.0005%/°C. The 1-year stability 

of the resistor is specified as 0.01%/ year. For currents above 5 A, the 1-year stability is 

0.1%/year. The power rating of the Riedon resistor is 30 W and the power dissipated across the 

resistor is [1 ohm • (0.130 A)2 = 17 mW], so resistor heating is negligible. Hence, UTM, the 

uncertainty in ITM, is taken to be 

= [(0.021)2 + (15 • 0.0015)2 + (0.02)2 + (0.01)2]

0.5 = 0. 038% . (11) 

The distribution is taken to be rectangular. For currents > 5 A, the UTM = 0.11%. 

The uncertainty in the reference cell, IRR, has been determined elsewhere and confirmed by 

international intercomparisons to be less than 1% [11–21]. From the uncertainty analysis for a 

typical Si primary reference cell calibrated at NREL, the uncertainty in IRR is 0.91% with a 

coverage of 2 or 95% confidence. 

There is an uncertainty in IRM and ITM because of temperature. The temperature is controlled with 

a thermoelectrically controlled plate capable of maintaining a temperature to within 0.1°C. The 

important parameter is how close the measured temperature of the reference cell and test cell are 

to the reference temperature. The reference temperature is typically 25°C and the temperature is 

controlled to within ±1°C. Assuming a typical short-circuit temperature coefficient of 0.05% / °C 

gives 0.05% for the temperature uncertainty of the test cell UTT and reference cell UTR. 

URM R DMM resistor = ( ) U TT + ⋅ −

2

( ) coeficient resistor − + ( ) U U resistor + stability

2 2

( )2

= ( ) + ⋅ − −

2

UTM I DMM resistor coeficient re U TT ( ) esistor + ( ) U U resistor + ( ) stability

⎡

⎣ ⎤⎦

2 2 2 0 5.
30 

There is an additional uncertainty in ITM, US, because the light in the test plane is not spatially 

uniform. This error is a function of the size of the reference cell compared with the test cell and 

how close the monitor is to the cell under test. The spatial uniformity also changes with intensity 

fluctuations. This error source varies from set-up to set-up. But only one measurement of transfer 

calibration and one set-up is performed to obtain IMR, so this error is a Type B error source with a 

rectangular distribution. The uncertainty in US is estimated to be 0.5%.

Type A error sources arise from the calibration of the intensity monitor IMR and a least-squares fit 

to the restricted I-V data set to obtain ITR. The standard deviation RT for IMR is typically 0.02%, 

with the number of readings averaged equal to 125. The standard deviation for ITR (Isc) in Fig. 13 

is RC = 0.03% for a fit to 16 I-V points. This is the standard deviation of the intercept [25]. The 

uncertainty in the voltage in the linear regression is taken to be 0 because the intercept is the 

parameter of interest and the voltage is measured at the same time (group trigger) with the same 

model of meter (34401A) and has an estimated uncertainty of less than 1 mV or 0.02%. All other 

error sources are Type B because they do not involve averages of repeated measurements.

The uncertainty in the spectral correction factor M is a function of the magnitude of M [13,22]. A 

conservative estimate of the uncertainty in M is 20% of the value of M [13,22]. Since the 

restrictions on the cells make M less than 2% (0.98 to 1.02), then the uncertainty in M is taken to 

be UM = 0.40%. This is less than the uncertainty for the outdoor calibrations because the spectral 

irradiance over the entire range of the cavity radiometer is less well known. For simulator 

measurements, the spectral irradiance is measured over the entire response range of the PV test 

and reference cell. The distribution is taken to be normal (Gaussian) based on Monte Carlo 

perturbation analysis [11,20]. 

The expanded uncertainty with 95% confidence (coverage = 2) in the short-circuit current is

 

U Isc = 1.27% . (12) 

For currents above 5 A, UIsc= 1.36%. 

U

UU U

Isc

TM MM MM

2 33 3

2 2

=

⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

′

22 2

2

3 3

125 16

+ ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

+⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜

U U

R R

RR RM

T C ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜

2 2 22

3 33 2

U U UU TT TR S M ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

2

0 5.

=

⎛

⎝

⎜ ⎞

⎠

⎟

2

0 038

3

.

UIsc

2 2 22 0 025

3

0 025

3

0 91

3

0 0

+ ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + . . .. 27

3

0 02

125

0 03

16

0 05

3

2

2 2

⎛

⎝

⎜ ⎞

⎠

⎟

+⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + . .. ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

2 22 2 0 05

3

0 5

3

0 4

2

. ..

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

0 5.
31 

5.2 Uncertainty in Pmax

The maximum power, Pmax, is defined as the maximum of the product of the current and voltage 

under standard reporting conditions. The maximum power is a function of contacting because of 

the distributed resistance nature of photovoltaics. The uncertainty from this error source is zero 

because the analysis assumes that separate voltage and current wires are attached to the cell. The 

current at Pmax is defined as Imax, while the voltage at Pmax is Vmax. The largest measured power 

may not be the maximum power because of noise on the measured current versus voltage. For 

this reason, the maximum power is obtained by a polynomial curve fit to a restricted set of data 

points. The fitting constraints on the restricted (V, ITR) data are based on the largest measured 

power Pm and the voltage Vm at Pm. 

0.85 • Pm ≤ P ≤ 1.15 • Pm (13) 

and 

0.8 • Vm ≤ V≤ 1.2 • Vm , (14) 

where P is the product of the measured voltage and corrected current ITR. This procedure reduces 

the uncertainty in the “true” maximum power by allowing least-squares polynomial curve-fitting 

to “average” over multiple data points. The uncertainty UP-fit in the fit of the restricted current 

versus voltage data UPmax was determined to be less than 0.06 % by modeling the I-V data of the 

test case using the standard diode equation with series and shunt resistance and a similar number 

of points in the fit and introducing a random error in the current until the mean square error of 

the fit was within 1% of the actual measured data and modeled data. The temperature coefficient 

of the voltage was assumed to be 0.5%/°C giving UTV. Since the data are not corrected for 

temperature, the error in the power is a function of the deviation from the reference temperature. 

In this analysis, the deviation of “true” cell temperature from the reference temperature is 

assumed to be ±1°C. The error in the voltage meter UV-DMM is based on a single voltage reading 

at 10-line-cycles integration period and a voltage of 0.4488 V (from Fig. 12).

 UV-DMM = [% of reading + temperature correction] + [% of range + temperature correction] =

100 • {[(0.0007 + 15 • 0.0005) • 0.01 • 0.449] + 

[(0.0040 + 15 • 0.0001) • 0.01 • 1]} / 0.449 = 0.0095. (15) 

The expanded uncertainty with 95% confidence (coverage = 2) in the maximum power is 

 

UPmax = 1.40% . (16) 

=

⎛

⎝

⎜ ⎞

2

3

U max

U

P

TM

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ′ ⎛ 2 2 22

3 3 33

U U UU MM MM RR RM

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

+⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ +

2 2

2 2

125

3 3

R

UUU

T

TT TR S

3 2 2 3

2 2 2 2

⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜

⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ UM UP fit − UTV + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

UV

3

2

0 5.

UP = 2

0 03

max

. 8

3

0 025

3

0 025

3

0 91

3

222 ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ... ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

+⎛

⎝

⎜ ⎞

⎠

⎟

2 22

2

0 027

3

0 02

125

0 05

3

. .

. + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ 0 05

3

0 5

3

0 4

2

0 06

2

2 2 2 . ... ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

2 2 2 0 5

3

0 009

2

. .
32 

The uncertainty in Vmax and Imax can be conservatively estimated to be less than the uncertainty in 

Pmax and greater than the uncertainty in Isc. A more accurate estimate is difficult because of the 

sample-specific nonanalytic nonlinear relationship between the uncertainty Pmax, Imax, and Vmax. 

The uncertainty in Vmax is greater than the uncertainty in Voc because of additional resistancerelated error sources. Hence,

U I max = 1.4% (17) 

and 

UVmax = 0.7% . (18) 

5.3 Uncertainty in Voc

The open-circuit voltage is measured with the cell open-circuited with a single 10-line-cycle 

integration period reading (0.580 V from Fig. 12). The dominant error is from a ±1°C uncertainty 

in temperature, resulting in an uncertainty in the voltage UTV. The Voc error from an error in the 

irradiance is assumed to be zero because the irradiance is constrained to be within ±2% of 

standard reference conditions by procedures. This error is a function of the cell and is 

logarithmic in nature. 

UV = [% of reading + temperature correction] + [% of range + temperature correction] =

100 • {[(0.004 + 15 • 0.0005) • 0.01 • 0.580] + 

[(0.0035 + 15 • 0.0005) • 0.01 •1]} / 0.580 = 0.006%. (19) 

 

UVoc = 0.58 . (20) 

5.4 Uncertainty in Area 

Two components of the uncertainty in the area are related to the subjective interpretation of the 

edge of the cell and the ability to measure the distance between edges. We consider the typical 

reference cell nominal dimensions area of 2 cm by 2 cm. The x-y coordinates of the four corners 

are recorded, and the area is calculated from the following formula for a general quadrilateral: 

A= absolute value {[(x4-x1) (y1-y2) - (x1-x2) (y4-y1)] + [(x1-x2) (y2-y3) - (x2-x3) (y1-y2)] +

[(x2-x3) (y3-y4) - (x3-x4) (y2-y3)] + [(x3-x4) (y4-y1) - (x4-x1) (y3-y4)]} / 4 . (21) 

However, if the sides are all the same length and at right angles and are aligned with the x-axis, 

then 

2

3 2

2 2

U U U

V

TV V

oc = ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

0 5.

= ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

2 2

2 0 5

3

0 006

3

. . UVoc

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

0 5.
33 

x4 - x1 = x2 - x3 = 0 (22) 

x = x1 - x2 = x3 - x4 (23) 

y3 - y4 = y1 - y2 = 0 (24) 

y = y4 - y1 = y2 - y3 . (25) 

Hence, the uncertainty in the area can be determined from the average of eight distance 

measurements. The values are measured with a resolution of 2-μm uncertainty in the distance. 

The microscope can resolve features below 1 μm in size. For a typical 2-cm by 2-cm cell under 

glass, using the microscope with optimum magnification, it is estimated that the subjective edge 

resolution is 20 μm. Hence, the uncertainty in the distance measurement is 100 • 0.0022 / 2 = 

0.11%. In the absence of further information, we use a rectangular distribution in the uncertainty 

in measuring the four corner x-y coordinates (eight distance measurements). Intercomparison 

among trained operators in the testing group indicates that a subjective error arising from the 

operator’s judgment of where the sample edge is located introduces a 0.7% random error. 

 = 1.20% . (26) 

The assumption of a square aligned with the stage’s x-axis in determining the uncertainty is 

justified because there is no loss in uncertainty if the sample is misaligned with respect to the 

stage or if the sides are not equal length.

5.5 Uncertainty in Efficiency

The efficiency with respect to standard reference conditions defined by a temperature, spectral, 

and total irradiance can be written as

(27) 

The uncertainty in η can be written as

(28) 

5.6 Uncertainty in Fill Factor

The fill factor, FF, is defined as 

(29) 

2 0 7

3

8 0 11

2

2

. . UA = ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

2 0 5 ⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

.

⋅

= 100 max η

P

E A ref

2

2

3 = ⎛

⎝

⎜ ⎞

⎠ Uη ⎟ +

U U A Pmax

.

. .

3

2 1 20

2

1 40

2

2 0 5 2 ⎛

⎝

⎜

⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ = ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ =

2 0 5

1 84

.

. %

≡ 100 max FF

P

V I oc sc
34 

The uncertainty UFF in FF can be written as 

, (30) 

assuming that Voc, Isc, and Pmax are not correlated. In fact, to a first order, increasing Isc by a 

given percentage will increase Pmax by the same percentage. Furthermore, the constraints on the 

measurement require that the fill factor be measured within 2% of the correct irradiance. For 

devices that are not series resistance-limited, a 2% variation in intensity will have a negligible 

effect on the fill factor. A more realistic estimate of the uncertainty in FF would be to remove all 

terms related to the uncertainty in the irradiance. This leaves errors related to temperature, 

current measurement meter, voltage measurement meter, and curve fits. 

 

UFF = 0.58 . (31) 

 

6. References for Section 4 

1. ASTM Standard E948, Standard Test Methods for Electrical Performance of NonConcentrator Photovoltaic Cells Using Reference Cells, Amer. Society for Testing Matls., 

West Conshocken PA, USA. 

2. ASTM Standard 1036, Specification for Physical Characteristics of Non-Concentrator 

Photovoltaic Reference Cells, Amer. Society for Testing Matls., West Conshocken PA, 

USA.

3. ASTM Standard G159, Standard Tables for Reference Solar Spectral Irradiances: Direct 

Normal and Hemispherical on 37° Tilted Surfaces, Amer. Society for Testing Matls., West 

Conshocken PA, USA. 

4. ASTM Standard G173, Standard Tables for Reference Solar Spectral Irradiances: Direct 

Normal and Hemispherical on 37° Tilted Surfaces, Amer. Society for Testing Matls., West 

Conshocken PA, USA. 

5. ASTM Standard E1328, Standard Terminology Relating to Photovoltaic Solar Energy 

Conversions, Amer. Society for Testing Matls., West Conshocken PA, USA. 

6. ASTM Standard E1021, Standard Test Methods for Measuring Spectral Response of 

Photovoltaic Cells, Amer. Society for Testing Matls., West Conshocken PA, USA. 

7. ASTM Standard E973, Standard Test Method for Determination of the Spectral Mismatch 

Parameter Between a Photovoltaic Device and a Photovoltaic Reference Cells, Amer. 

Society for Testing Matls., West Conshocken PA, USA. 

8. ASTM Standard E1021, Standard Test Methods for Measuring Spectral Response of 

Photovoltaic Cells, Amer. Society for Testing Matls., West Conshocken PA, USA. 

UFF = 2

U UU P VI max oc sc

3 33

2 22 ⎛

⎝

⎜

⎞

⎠

⎟ + ⎛

⎝

⎜

⎞

⎠

⎟ + ⎛

⎝

⎜

⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ = ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

0 5 2 22

2 1 40

3

0 58

3

1 27

3

.

... ⎢

⎢

⎤

⎦

⎥

⎥ =

0 5

1 98

.

. %

= ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞ 2

2

3 3

U U U

FF

TV V

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

−− −

2 22

33 3

UUU R DMM I DMM M DMM ⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜

⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤ −

22 2 2

3 15 2

U R TT C UP fit

⎦

⎥

⎥

0 5.

= ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ +

2 2

2 0 5

3

0 006

3

.. . 0 UFF

016

3

0 021

3

0 013

3

0 05

3

222 ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ... ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

2 2 2 0 5

0 03

15

0 06

2

. . .
35 

9. K.A. Emery, C.R. Osterwald, T.W. Cannon, D.R. Myers, J. Burdick, T. Glatfelter, W. 

Czubatyj, and J. Yang, “Methods for Measuring Solar Cell Efficiency Independent of 

Reference Cell or Light Source,” Proc. 18th IEEE Photovoltaic Spec. Conf., Las Vegas, 

NV, October 21–25, 1985, pp.623–628, IEEE, New York, 1985. 

10. C.R. Osterwald, (1986), Translation of Device Performance Measurements to Reference 

Conditions, Solar Cells, 18, pp.269–279. 

11. C.R. Osterwald, K.A. Emery, D.R. Myers, and C.J. Riordan, “Extending the Spectral 

Range of Silicon-Based Direct-Beam Solar Spectral Radiometric Measurements,” Proc. 

20th IEEE Photovoltaic Specialists Conf., Las Vegas, NV, September 26–30, 1988, 

pp.1246–1250, IEEE, New York, 1989. 

12. C.R. Osterwald, K.A. Emery, D.R. Myers, and R.E. Hart, “Primary Reference Cell 

Calibrations at SERI: History and Methods,” Proc. 21st IEEE Photovoltaic Specialists 

Conf., Orlando, FL, May 21–25, 1990, pp.1062–1067, IEEE, New York, 1990. 

13. K. A. Emery, C.R. Osterwald, S. Rummel, D.R. Myers, T.L. Stoffel, and D. Waddington, 

“A Comparison of Photovoltaic Calibration Methods,” Proc. 9th European Photovoltaic 

Solar Energy Conf., Freiburg, W. Germany, September 25–29, 1989, pp.648–651. 

14. K.A. Emery, C.R. Osterwald, and C.V. Wells, “Uncertainty Analysis of Photovoltaic 

Efficiency Measurements,” Proc. 19th IEEE Photovoltaic Specialists Conf., New Orleans, 

LA, May 4–8, pp.153–159, IEEE, New York, 1987. 

15. H. Ossenbrink, R. Van Steenwinkel, and K. Krebs, ”The Results of the 1984/1985 RoundRobin Calibration of Reference Solar Cells for the Summit Working Group on Technology, 

Growth and Employment,” Joint Research Center, ISPRA Establishment, ISPRA Italy, 

Tech Rep. EUR 10613 EN (April 1986). 

16. K.A. Emery, C.R. Osterwald, L.L. Kazmerski, and R.E. Hart, “Calibration of Primary 

Terrestrial References Cells When Compared with Primary AM0 Reference Cells,” Proc. 

8

th European Photovoltaic Solar Energy Conf., Florence, Italy, May 9–12, 1988, pp.64–68. 

17. K.A. Emery, D. Waddington, S. Rummel, D.R. Myers, T.L. Stoffel, and C.R. Osterwald, 

“SERI Results from the PEP 1987 Summit Round Robin and a Comparison of Photovoltaic 

Calibration Methods,” SERI Tech. Rep. TR-213-3472, March 1989. 

18. J. Metzdorf, T. Wittchen, K. Heidler, K. Dehne, R. Shimokawa, F. Nagamine, H. 

Ossenbrink, L. Fornarini, C. Goodbody, M. Davies, K. Emery, and R. Deblasio, 

“Objectives and Results of the PEP '87 Round-Robin Calibration of Reference Cells and 

Modules,” Proc. 21st IEEE Photovoltaic Specialists Conf., Orlando, FL, May 21–25, 1990, 

pp.952–959, IEEE, New York, 1990. 

19. J. Metzdorf, T. Wittchen, K. Heidler, K. Dehne, R. Shimokawa, F. Nagamine, H. 

Ossenbrink, L. Fornarini, C. Goodbody, M. Davies, K. Emery, and R. Deblasio, “The 

Results of the PEP '87 Round-Robin Calibration of Reference Cells and Modules,- Final 

Report” PTB Technical Report PTB-Opt-31, Braunschweig, Germany, November 1990, 

ISBN 3-89429-067-6. 

20. C.R. Osterwald, S. Anevsky, A.K. Barua, J. Dubard, K. Emery, D. King, J. Metzdorf, F. 

Nagamine, R. Shimokawa, N. Udayakumar, Y.X. Wang, W. Zaaiman, A. Zastrow, and J. 

Zhang, “Results of the PEP ‘93 Intercomparison of Reference Cell Calibrations and Newer 

Technology Performance Measurements,” Proc. 25th IEEE Photovoltaic Specialists Conf.,

Washington D.C., May 13–17, 1996, pp.1263–1266, IEEE, New York, 1996. 

21. C.R. Osterwald, S. Anevsky, A.K. Barua, J. Dubard, K. Emery, D. King, J. Metzdorf, F. 

Nagamine, R. Shimokawa, N. Udayakumar, Y.X. Wang, T. Wittchen, W. Zaaiman, A. 

Zastrow, and J. Zhang, “Results of the PEP’93 Intercomparison of Reference Cell 

Calibrations and Newer Technology Performance Measurements,” Proc. 26th IEEE PVSC 

Conf., Anaheim, CA. Sept. 29–Oct. 2, 1997, pp.1209–1212, IEEE, New York, 1997. 
36 

22. Keith Emery, “The Results of the First World Photovoltaic Scale Recalibration,” NREL 

Tech. Rep. NREL/TP-520-27942, (March 2000). 

23. H. Field and K. Emery, “An Uncertainty Analysis of the Spectral Correction Factor,” Proc. 

23rd IEEE Photovoltaic Specialists Conf., Louisville, KY, May 10–14, 1993, pp.1180–

1187, IEEE, New York, 1993. 

24. “The Expression of Uncertainty and Confidence in Measurement,” United Kingdom 

Accreditation Service, M3003, Middlesex, UK, December 1997. 

25. International Organization for Standardization, Guide to the Expression of Uncertainty in 

Measurement. ISO: Geneva, 1995, ISBN 92-67-10188-9. 

26. M.G. Natrella, "Experimental Statistics," National Bureau of Standards Handbook 91, p.5–

34. August 1, 1993, reprinted October 1966. 
37 

5.0 UNCERTAINTY OF ELECTRICAL PERFORMANCE OF

PHOTOVOLTAIC MODULES

 

1. Reference to Norms and Standards

• ASTM E1036 “Standard Test Methods for Electrical Performance of Nonconcentrator 

Terrestrial Photovoltaic Modules and Arrays Using Reference Cells. “This procedure 

meets or exceeds the requirements in IEC standard 60904-1, “Photovoltaic Devices – 

Measurement of Photovoltaic Current-Voltage Characteristics.” 

• Procedure ISO GUM “International Organization for Standardization, Guide to the 

Expression of Uncertainty in Measurement. ISO: Geneva, 1995, ISBN 92-67-10188-9. 

• ISO-VIM “International Vocabulary of Basic and General Terms in Metrology,” 2nd

Edition 1993. 

• 1.4.ASTM standard E 1328 Terminology Relating to Photovoltaic Solar Energy 

Conversion” 

2. Summary

This uncertainty analysis is for ASTM E1036, “Standard Test Methods for Electrical 

Performance of Nonconcentrator Terrestrial Photovoltaic Modules and Arrays Using Reference 

Cells” [1]. The analysis is restricted to stable, single-junction modules or cells that are packaged 

with connectors [2]. This analysis is restricted to samples less than 150 cm by 120 cm in area. 

The analysis is also restricted to samples with Voc in the range of 0.5 to 290 V and Isc in the range 

of 0.1 to 50A. The current vs. voltage characteristics are measured within 2°C of the reference 

temperature (typically 25°C) and within 2% of the reference irradiance (typically ASTM G173 

global or equivalently IEC 60904-3 [3,4], 1000 W/m2). Our group has essentially been following 

these procedures on this test bed since its inception in 1985 [5–7]. To simplify matters, the 

uncertainties of the input quantities are expressed in terms of percentage of value. Since all 

equations are or will be reduced to multiplications and divisions, the sensitivity coefficient 

reduces to unity. The uncertainty of the performance parameters will then be the same for similar 

devices.

3. Procedures

The procedure from E1036 follows: 

1. Measure the module or cell in module package aperture area, A, using the definition in 

Terminology E 1328 [8]. This is the total area minus the frame area. This may give 

unrealistically small current densities or low efficiencies for packages that have inactive 

large borders around the active cell(s).

2. Measure the relative spectral responsivity of the PV device to be calibrated using Test 

Method E1021 [9]. In many cases, the uncertainty and difficulties in measuring a module 

spectral responsivity may be prohibitive. For these cases, a cell representative of the typical 

responsivity of the module is acceptable.

3. Choose a primary reference cell.
38 

4. Determine the spectral-mismatch parameter, M, using Test Method E 973 [10]: 

 , (1) 

where:

St(λ) Measured spectral responsivity of the test device (Test Method E1021 [9])

Sr(λ) Measured spectral responsivity of the reference cell (Test Method

 E1021 [9]) 

Eref(λ) Reference spectral irradiance

Es(λ) Measured spectral irradiance of the light source (Test method E973 [10])

λ1, λ2, λ3, λ4 Wavelength limits of integration.

5. The following procedures follow E1036 for module I-V measurements [1]. These 

procedures are equivalent to IEC standard 60904-1.

5.1. Mount the reference cell in the center of the test plane and verify that the plate 

temperature or reference cell temperature are within ±2°C of the temperature 

corresponding to the reference cell short-circuit current calibration value, IRR.

5.2. Adjust the simulator so that the measured reference cell short-circuit current IRM is 

within 2% of the spectrally corrected calibration value or

 (2)

5.3. Transfer this value to an intensity monitor giving a calibration value for the 

intensity monitor by recording the average of at least ten measurements of the 

following equation:

, (3)

where:

IMR Calibrated short-circuit current of the intensity monitor located near the edge 

of the test plane

IMM Measured short-circuit current of the intensity monitor located near the edge 

of the test plane.

5.4. Mount the device to be tested on the temperature-controlled plate in the same 

position as the reference cell. Keep the module within 5° of the reference 

temperature.

5.5. Measure the open-circuit voltage, Voc, with the load disconnected.

1

2

3

4

M

E

s

S

t

E

s

S

r

Eref S

r

=

∫ ( ) ( )

∫ ( ) ( )

λ λ λ ( )

λ

λ

λ λ λ

λ

λ

d λ λ

d

∫ ( )

∫ ( ) ( )

d

d

λ

λ

λ

λ λ λ

λ

λ

3

4

1

2

Eref S

t

≤ ( ) 0 98 ≤ 1 I

M I RR

RM . .02

I I I MI MR MM RR RM = ( ) ( )

 . 
39 

5.6. Measure the current versus voltage (ITM, V) characteristic of the device under test 

by changing the operating point with the variable load so that the curve is swept 

through 0 V and 0 A. At each operating point on the (ITM, V) characteristic, 

measure the device voltage, V, device current, ITM, and IMM. Correct the measured 

current, ITM, for intensity fluctuations giving the calibrated current of the test 

device under the reference spectrum at the reference irradiance and temperature ITR

using

 . (4) 

5.7. Measure the open-circuit voltage, Voc, with the load disconnected.

5.8. Determine the calibrated Isc by performing a linear-regression fit to all ITR- V points 

that satisfy the constraint that all currents are within 4% of the current at 0 V and 

all voltages are within 0.20 times the voltage at 0 A.

5.9. Determine the maximum power, Pmax, by performing a polynomial fit on all ITRV points that satisfy the constraints that the measured power is within 85% of the 

largest measured power and the voltage is within 80% of the voltage at the largest 

measured power as recommended by E1036. The polynomial that gives the best 

fit to the data up to a fifth order is used. The voltage at maximum power, Vm, is 

the real root of the derivative of the fit of the power versus voltage polynomial set 

equal to 0. This voltage is then substituted into the power versus voltage 

polynomial to obtain the Pmax. The current at maximum power, Imax, is calculated 

from the Pmax / Vmax.

5.10. The current vs. voltage data points, (ITR, V), along with a variety of information 

including Voc, Isc, Pmax, temperature, time, device ID, device type, manufacturer, 

reference cell, and its calibration, the record book number and page, and change in 

Voc before and after the measurement, are saved.

 

I I I I TR TM MR MM =
40 

4. Test-Bed-Specific Equipment

 

Figure 14 is a photograph of the test bed, and Figure 15 shows a simplified block diagram of the 

test bed.

Uncertainty Analysis

 

Figure 14. The Spectrolab LACSS solar simulator and custom I-V measurement system.

Temperature meters

Voltage, current, intensity

Kepco PSP

Mac & PC

Monitor cell

Module patch panel

Primary 

reference 

cell holder

Resistor box

Figure 15. Simplified block diagram of current versus voltage test station. 
41 

5. Uncertainty Analysis

Table 8 summarizes the standard uncertainty components. All uncertainty components are given 

in percentage with a 55-cm by 32-cm Si module as the reference case. All uncertainties are based 

on a 1-year calibration interval.

Table 8. Summary of Standard Secondary Reference Module Uncertainty Components 

Uncertainty

Component 

Source of Uncertainty Value of

Uncertainty 

(%)

Coverage 

Factor 

UM-DMM Intensity Monitor meter (94 mV typical value) 0.018 Rectangular

1-year HP34401, 100 mV, of reading 0.005 Rectangular

1-year HP34401, 100 mV, of range 0.0035 Rectangular

1-year HP34401, 100 mV, 1 line cycle 0.001 Rectangular

HP34401, 100 mV, meter temperature 23±15°C 0.0075 Rectangular

UMM, UMM’ Measured Monitor current 0.029 Rectangular

1-year resistor stability (Julie CH-48T4 data sheet) 0.003 Rectangular

1-year resistor calibration uncertainty 0.02 Rectangular

Resistor temperature 0.0005%/°C 0.0075 Rectangular

UR-DMM Reference cell DMM (101 mA typical value) 0.017 Rectangular

1-year HP34401, 100 mV, of reading 0.005 Rectangular

1-year HP34401, 100 mV, of range 0.0035 Rectangular

HP34401, 100 mV, meter temperature 23±15°C 0.0075 Rectangular

URM Measured reference cell current 0.028 Rectangular

1-year resistor stability (Julie CH-48T4 data sheet) 0.003 Rectangular

1-year calibration uncertainty 0.02 Rectangular

Resistor temperature 0.0015%/°C 0.0225 Rectangular

UI-DMM Test device current DMM (1.41 A typical value) 0.055 Rectangular

1-year HP34401, 100 mV, of reading 0.005 Rectangular

1-year HP34401, 100 mV, of range 0.0035 Rectangular

1-year HP34401, 100 mV, 1 line cycle 0.001 Rectangular

HP34401, 100 mV, meter temperature 23±15°C 0.0075 Rectangular

UTM Measured test device current 0.120 Rectangular

1-year resistor stability 0.1 Rectangular

1-year resistor calibration uncertainty 0.02 Rectangular

Resistor temperature 0.002%/°C 0.03 Rectangular

UTT Test device current for ±2°C 0.10 Rectangular

UTR Reference cell current for ±5°C 0.25 Rectangular

URR Primary reference cell calibration value 0.91 Rectangular

RC Least-squares fit standard deviation for ITR (Isc of 

test device)

0.42 N=9

RT Reference cell Isc to monitor Isc transfer standard 

deviation

0.02 N=30

US Error from spatial nonuniformity

< 30-cm x 30-cm area

> 3-cm x 30-cm area

1.0 

3.0 

Rectangular

UM Error in the spectral correction factor M 0.4 Gaussian

UIsc Uncertainty in test device Isc coverage=2
42 

Uncertainty

Component 

Source of Uncertainty Value of

Uncertainty 

(%)

Coverage 

Factor 

< 30 cm x 30 cm area

> 30-cm x 30-cm area

1.67

3.67 

UP-fit Error in Pmax from the fit 0.06 Gaussian

UTV Test device voltage for ±2°C 1.00 Rectangular

UV Measured test device voltage 0.008 Rectangular

UVmax Maximum power voltage 1.6 coverage=2

UImax Maximum power current

< 30-cm x 30-cm area

> 30-cm x 30-cm area

1.4 

3.5

coverage=2

UPmax Maximum power

< 30-cm x 30-cm area

> 30-cm x 30-cm area

2.03 

3.85

coverage=2

UVoc Open-circuit voltage 1.16 coverage=2

UA Area 0.63 coverage=2

Uη Efficiency

< 30-cm x 30-cm area

> 30-cm x 30-cm area

2.13 

3.90

coverage=2

UFF Fill factor 1.19 coverage=2

5.1 Uncertainty in Isc

The uncertainty in the short-circuit current of the reference cell, ITR from Eq. 4, is determined 

using standard uncertainty analysis based on [11–13]. For convenience, the elemental Type A 

and Type B error sources will be expressed in terms of percentage of value. The analysis is based 

on the best measurement capability and represents the smallest uncertainty of nearly ideal PV 

reference devices. This means that the devices should be stable with no measurable degradation, 

packaged with wires and temperature sensors, and close to 10 cm by 10 cm. For samples with 

one side larger than 30 cm, an additional spatial nonuniformity error must be considered. 

Combining Eqs. 3 and 4 yields 

. (5) 

To express the uncertainty as a percentage, a typical I-V case is used so the voltmeter range and 

resolution can be converted to a percentage. The I-V curves are shown for the typical small-area 

case (Fig. 16) and medium-area case (Fig. 17). The analysis will be based on the larger module 

sample, with the exception of an area-dependent spatial nonuniformity term. 

I II TR TM M = ( )( ) M RR RM MM ′I MI I
43 

The measured monitor value IMM, or IMM’ is the voltage measured across a 0.1-ohm resistor with 

an Agilent 34401A multimeter. The integration period for step 5.3 is 10 line cycle and 

contributes no additional error, while the integration period in step 5.7 is at 1 line cycle and 

introduces an additional 0.001% error of range. The measured monitor voltage is typically 94 

mV. An op-amp circuit is used to bias the monitor cell within 2 mV of 0 V and monitor the 

current with a 1-ohm 4-terminal resistor (Appendix 2). From the 1-year manufacturer’s 

specification, the uncertainty on the Agilent 34401A voltmeter 100-mV range is 0.0050% of the 

reading plus 0.0035% of the range plus 0.001% of range because the power-line cycle was not

longer than 1. The meter uncertainties supplied by the manufacturer are based on a 23±5°C 

operating temperature. Since the resistors and meters are in a temperature-controlled room at

Figure 16. Typical I-V curve for a cell in module package test device.
44 

23±15°C, the maximum expected resistor and meter temperature deviation is 23 ±15°C. The 

temperature coefficient of the meter outside of the 23 ±15°C is 0.0005%/°C of reading and 

0.0001%/°C of range for 1-V range. The total error of the voltage reading across the 1-ohm 

current sense resistor UM–DMM is

UM-DMM = [% of reading + temperature correction] + [% of range + temperature correction] 

= 100 • {[(0.005 + 15 • 0.005) • 0.01 • 0.094] + 

 [(0.0035 + 0.001+15 • 0.005) • 0.01 • 0.1]} / 0.094 = 0.018%. (6) 

UM-DMM = 0.019 % for 1-line cycle in step 5.7

Figure 17. Typical I-V curve for a module test device.
45 

The temperature coefficient of the 1-ohm resistor manufactured by Electro Scientific Industries 

Corporation (ESI) is 15 ppm/°C or 0.0015 %/°C. The uncertainty of the 1-ohm ESI resistor 

calibration is 0.02%. The 1-year stability of the resistor is taken as 20 ppm/year because the 

resistors have been in use for more than 10 years. The power rating of the resistor is 6 W and the 

power dissipated across the resistor is (1 ohm • 0.0252 A2 = 0.6 mW), so resistor heating is 

negligible. Hence, UMM and UMM, the uncertainties in IMM and IMM, respectively, are taken to be 

UMM’ = 0.029% = [0.0182 + (0.0015 • 15 )2 + 0.022 + 0.022]

0.5 

UMM = 0.028% = [0.0192 + (0.0015 • 15 )2 + 0.022 + 0.022]

0.5 (7) 

The distribution is taken to be rectangular in the absence of further information. 

The primary reference cell measured short-circuit current IRM in step 5.3 is the voltage measured 

across a 1-ohm resistor with an Agilent 34401A multimeter with 10-power-line cycle integration 

period. The circuit used to bias the reference cell within 2 mV of 0 V is described in Appendix 2. 

The reference cell current at standard reporting conditions is typically 101 mA. From the 1-year 

manufacturer’s specification, the uncertainty on the 100-mV range is 0.0050% of the reading 

plus 0.0035% of the range. The meter uncertainties are based on a 23±15°C operating 

temperature. The total error of the voltage reading UR-DMM is

UR-DMM = [% of reading + temperature correction] + [% of range + temperature correction] 

 = 100 • {[(0.0050 + 15 • 0.005) • 0.01 • 0.101] + 

[0.0035 + (15 • 0.005) • 0.01 • 0.1]} / 0.101 

 = 0.017%. (8) 

The uncertainty of the 1-ohm resistor calibration is 0.02%. The resistor temperature coefficient is 

negligible at 15 ppm/°C = 0.0015%/°C. The 1-year stability of the resistor is taken as 20 

ppm/year because the resistors have been in use for more than 10 years. The power rating of the 

resistor is 6 W and the power dissipated across the resistor is (1 ohm • 0.132 A2 = 17 mW), so 

resistor heating is negligible. Hence, the uncertainty URM in IRM is taken to be 

 = [0.0172 • (0.0015 • 15)2

 + 0.0022 + 0.022]

0.5 

 = 0.028% . (9) 

The distribution is taken to be rectangular in the absence of further information. 

The measured current of the device under test ITM is the voltage measured across a current sense 

resistor with an Agilent 34401A multimeter with 1-power-line cycle integration period, as shown 

in Fig. 15. Depending on the current range and current limit, a particular resistor is selected to 

maintain between 10 and 100 mV across the resistor. The precision 4-terminal low-temperaturecoefficient Riedon resistors are nominally 0.001, 0.01, 0.1, 1.0, and 10 ohms. A typical shortcircuit current for a test device is 1.41 A. So, the software would select the 100-mV range and a 

0.01-ohm current sense resistor. This is near the worst-case scenario, being at the low end of the 

meter 100-mV range. From the 1-year 34401A manufacturer’s specification, the uncertainty on 

the 1-V range is 0.0050% of the reading plus 0.0035% of the range plus 0.001% of range 

UMM MM UU T ′ = ( ) M DMM res − +

2

 , istor coeficient resistor T UU resistor st ( ) ⋅ − + ( ) +

2 2

( ) ability

⎡

⎣ ⎤⎦

2 0 5.

URM R DMM resistor = ( ) U TT + ⋅ −

2

( ) coeficient resistor − + ( ) U U resistor + stability

2 2

( )2
46 

because the power-line cycle was not longer than 1. The meter uncertainties are based on a 

23±15°C operating temperature (0.005%/°C). The total error UI-DMM of the voltage reading is 

UI-DMM = [% of reading + temperature correction] + [% of range + temperature correction] 

= 100 • {[(0.0050 + 15 • 0.005) • 0.01 • 0.0141] + 

[(0.0035 + 0.001 + 0.0075) • 0.01 • 0.1]} / 0.0141 = 0.055%. (10) 

The uncertainty of the Riedon Corporation model PF1238 0.01 ohm resistor calibration is 0.02%. 

The resistor temperature coefficient is negligible at 20 ppm/°C = 0.0020%/°C. The 1-year 

stability of the resistor is specified as 0.1 %/ year. The power rating of the Riedon resistor is 60 

W and the power dissipated across the resistor is [0.01 ohm • (1.412 A)2 = 20 mW], so resistor 

heating is negligible. Hence, UTM, the uncertainty in ITM, is taken to be 

 = [0.0552 + (0.0020 • 15)2 + (0.022 + 0.102)]0.5 = 0.120% . (11) 

The distribution is taken to be rectangular in the absence of further information. 

The uncertainty in the reference cell, IRR, has been determined elsewhere and confirmed by 

international intercomparisons to be less than 1% with 0.91% estimated as U95 from uncertainty 

analysis [14–24]. 

There is an uncertainty in IRM and ITM because of temperature. The important parameter is how 

close the measured temperature of the reference cell and test device is to the reference 

temperature. The reference temperature is typically 25°C and the temperature is within ±5°C. 

Assuming a typical short-circuit temperature coefficient of 0.05%/°C gives 0.25% for the 

temperature uncertainty of the test device UTT and reference cell UTR. 

There is an additional uncertainty in ITM, US, because the light in the test plane is not spatially 

uniform. This error is a function of the size of the reference cell compared with the test device 

and how close the monitor is to the device under test. The spatial uniformity also changes with 

intensity fluctuations. This error source varies from set-up to set-up. But only one measurement 

of transfer calibration and one set-up is performed to obtain IMR, so this error is a Type B error 

source with a rectangular distribution. Figure 18 shows a typical spatial nonuniformity map of 

the large-area continuous solar simulator (LACSS). For the 55-cm by 32-cm approximate area 

for the example, the uncertainty in US is estimated to be 3%.

= ( ) + ⋅ − −

2

UTM I DMM resistor coeficient re U TT ( ) esistor + ( ) U U resistor + ( ) stability

⎡

⎣ ⎤⎦

2 2 2 0 5.
47 

Type A error sources arise from the calibration of the intensity monitor IMR and a least-squares fit 

to the restricted I-V data set to obtain ITR. The standard deviation RT for IMR, is typically 0.02% 

with the number of readings averaged equal to 30. The standard deviation for ITR (Isc) in Fig. 16 

is RC = 0.042% for a fit to nine I-V points. This is the standard deviation of the intercept [12]. 

The uncertainty in the voltage in the linear regression is taken to be zero because the intercept is 

the parameter of interest and the voltage is measured at the same time (group trigger) with the 

same model of meter (34401A) and has an estimated uncertainty of less than 1 mV or 0.006%. 

All other error sources are Type B because they do not involve averages of repeated 

measurements. 

The uncertainty in the spectral correction factor M is a function of the magnitude of M [13,22]. A 

conservative estimate of the uncertainty in M is 20% of the value of M [16,25]. Since the 

restrictions on the devices make M less than 2% (0.98 to 1.02), then the uncertainty in M is taken 

to be UM = 0.40%. This is less than the uncertainty for the outdoor calibrations because the 

spectral irradiance over the entire range of the cavity radiometer is less well known. For 

simulator measurements, the spectral irradiance is measured over the entire response range of the 

PV test device and reference cell. The distribution is taken to be normal (Gaussian) based on 

Monte Carlo perturbation analysis [16,25]. 

Figure 18. Typical spatial nonuniformity of large-area continuous solar simulator showing 

±1% for areas less than 30 cm by 30 cm; if a 10-cm by 10-cm cell is used, then the 

nonuniformity is ±0.5%. For larger modules, the spatial nonuniformity is typically ±3%. 
48 

The expanded uncertainty with 95% confidence (coverage = 2) in the short-circuit current is

UIsc = 3.67% for spatial nonuniformity of ±3% 

UIsc = 1.67% for spatial nonuniformity of ±1%. (12) 

5.2 Uncertainty in Pmax

The maximum power, Pmax, is defined as the maximum of the product of the current and voltage 

under standard reporting conditions. The maximum power is a function of contacting because of 

the distributed resistance nature of photovoltaics. The uncertainty from this error source is zero 

because the analysis assumes that separate voltage and current wires are attached to the device. 

The current at Pmax is defined as Imax, while the voltage at Pmax is Vmax. The largest measured 

power may not be the maximum power because of noise on the measured current versus voltage. 

For this reason, the maximum power is obtained by a polynomial curve fit to a restricted set of 

data points. The fitting constraints on the restricted (V, ITR) data are based on the largest 

measured power Pm and the voltage Vm at Pm. 

0.85 • Pm ≤ P ≤ 1.15 • Pm (13) 

and 

0.8 • Vm ≤ V≤ 1.2 • Vm , (14) 

where P is the product of the measured voltage and corrected current ITR. This procedure reduces 

the uncertainty in the “true” maximum power by allowing least-squares polynomial curve-fitting 

to “average” over multiple data points. The uncertainty UP-fit in the fit of the restricted current 

versus voltage data UPmax was determined to be less than 0.06 % by modeling the I-V data of the 

test case using the standard diode equation with series and shunt resistance and a similar number 

of points in the fit and introducing a random error in the current until the mean square error of 

the fit was within 1% of the actual measured data and modeled data. The temperature coefficient 

of the voltage was assumed to be 0.5%/°C giving UTV. Since the data are not corrected for 

temperature, the error in the power is a function of the deviation from the reference temperature. 

In this analysis, the deviation of “true” device temperature from the reference temperature is

U

UU U

Isc

TM MM MM

2 33 3

2 2

=

⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

′

22 2

2

3 3

30 9

+ ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

+⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

U U

R R

RR RM

T C ⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

2 2 22

3 33 2

U U UU TT TR S M

⎟

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

2

0 5.

=

⎛

⎝

⎜ ⎞

⎠

⎟ +

2

2

0 120

3

.

UIsc

0 029

3

0 028

3

0 91

3

0 028 2 22 ⎛ . . ..

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ +

3

0 02

30

0 042

9

0 25

3

2

2 2

⎛

⎝

⎜ ⎞

⎠

⎟

+⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ .. . ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎢

⎢

2 22 2 0 25

3

3 0

3

0 4

2

. ..

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

0 5.
49 

assumed to be ±2°C. The error in the voltage meter UV is based on the average of two voltage 

readings at 1-line-cycle integration period and a voltage of 17.48 V (from Fig. 16).

UV = [% of reading + temperature correction] + [% of range + temperature correction] 

= 100 • {[(0.0045 + 0.0075) • 0.01 • 17.48] + 

 [(0.0006 + 0.001 + 0.0075) • 0.01 • 100]} / 17.48 = 0.024%. (15) 

The expanded uncertainty with 95% confidence (coverage = 2) in the maximum power is 

UPmax = 3.85% for spatial nonuniformity of ±3% 

UPmax = 2.03% for spatial nonuniformity of ±1% . (16) 

The uncertainty in Vmax and Imax can be conservatively estimated to be less than the uncertainty in 

Pmax and greater than the uncertainty in Isc. A more accurate estimate is difficult because of the 

sample-specific nonanalytic nonlinear relationship between the uncertainty Pmax, Imax, and Vmax. 

The uncertainty in Vmax is greater than the uncertainty in Voc because of additional resistancerelated error sources. Hence,

UImax = 3.5% for spatial nonuniformity of ±3% 

UImax = 1.4% for spatial nonuniformity of ±1% (17) 

and 

UVmax =1.6% . (18) 

5.3 Uncertainty in Voc

The open-circuit voltage is measured with the device open-circuited with a single 10-line-cycle 

integration period reading (17.48 V from Fig. 16). The dominant error is from a ±2°C uncertainty 

in temperature resulting in an uncertainty in the voltage UTV. The Voc error from an error in the 

irradiance is assumed to be zero because the irradiance is constrained to be within ±2% of 

standard reference conditions by procedures. This error is a function of the device and is 

logarithmic in nature.

=

⎛

⎝

⎜ ⎞

⎠

⎟

2

2

3

U max

U

P

TM + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ U U UU MM MM ′ RR RM ⎞

3 3 33

2 22

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

+⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜

2 22

2

30 9

3 3

R R

U U

T C

TT TR ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜

⎞

⎠

⎟ + −

2 2 2 2

3 2 2 3

U U S M UP fit UTV ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

2 2

0 5

3

U

U

V

P

.

max

...

=

⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ +

2

0 120

3

0 029

3

0 028

3

0 222

. . . . 91

3

0 028

3

0 020

30

0 042 222 ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ +

9

0 50

3

0 50

3

3

3

0

2

2 22

⎛

⎝

⎜ ⎞

⎠

⎟

+⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + . . . . . . 4

2

0 060

2

0 5

3

0 024

3

2 2 2

⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

2

0 5.
50 

UV = [% of reading + temperature correction] + [% of range + temperature correction] 

= 100 • {[(0.0045% + 0.0075) • 0.01 • 17.48] + 

 [(0.006 + 0.001 + 0.0075) • 0.01 • 100]} / 17.48 = 0.030%. (19) 

UVoc = 1.16% . (20) 

5.4 Uncertainty in Area

Two components of the uncertainty in the area are related to the subjective interpretation of the 

edge of the device and the ability to measure the distance between edges. We consider the 

rectangular module used in this analysis with dimensions area of 55 cm by 32 cm. 

Hence, the uncertainty in the area can be determined from the average of eight distance 

measurements. The values are measured with a resolution of 1-mm uncertainty in the distance. 

Hence, the uncertainty in the distance measurement is 

UA = 2{[100 • 0.1 / (55 • 30.5)]2 + [100 • 0.1 / (32 • 30.5)]2 }0.5 = 0.41%. (21) 

It is estimated that there is an additional 1-mm uncertainty due to operator judgment, which gives 

an additional 0.41% uncertainty. The resulting uncertainty in the area is 0.63%. 

5.5 Uncertainty in Efficiency

The efficiency with respect to standard reference conditions defined by a temperature, spectral, 

and total irradiance can be written as

. (22) 

The uncertainty in η can be written as

 for spatial nonuniformity of ±3% 

for spatial nonuniformity of ±1% . (23) 

U = 2 U

V

T

oc

V V

V

U

U oc

3 2

2 1

2 2 0 5 ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

=

.

.0

3

0 030

3

2 2 0 5 ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

. .

100 Pmax

E A ref

η =

2

3

2

ma U U U A P

η = ⎛

⎝

⎜ ⎞

⎠

⎟ + x

.

.

.

3

2 0 63

1 73

2 0 5

2

⎛

⎝

⎜

⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

= ⎛

⎝

⎜ ⎞

⎠ Uη ⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ =

=

3 85

1 73

3 90

2 0

2 0 5

.

. . %

.

.

Uη

63

1 73

2 03

1 73

2 13

2 2 0 5

.

.

. . %

.

⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ =
51 

5.6 Uncertainty in Fill Factor

The fill factor, FF, is defined as 

(24) 

The uncertainty UFF in FF can be written as 

, (25) 

assuming that Voc, Isc, and Pmax are not correlated. In fact, to a first order, increasing Isc by a 

given percentage due to spatial nonuniformity, reference cell uncertainty or other factors will 

increase Pmax by the same percentage. Furthermore, the constraints on the measurement require 

that the fill factor be measured within 2% of the correct irradiance. For devices that are not series 

resistance-limited, a 2% variation in intensity will have a negligible effect on the fill factor. A 

more realistic estimate of the uncertainty in FF would be to remove all terms related to the 

uncertainty in the irradiance. The sign on the voltage temperature coefficient of FF is in the same 

direction and similar magnitude for Voc and Pmax, effectively counting the temperaturedependence twice. This leaves errors related to temperature, current measurement meter, voltage 

measurement meter, and curve fits.

UFF = 1.19% . (26) 

 

6. References for Section 5 

1. ASTM Standard E1036, Standard Test Methods for Electrical Performance of 

Nonconcentrator Terrestrial Photovoltaic Modules and Arrays Using Reference Cells, 

Amer. Society for Testing Matls., West Conshocken PA, USA. 

2. ASTM Standard 1040, Specification for Physical Characteristics of Non-Concentrator 

Photovoltaic Reference Cells, Amer. Society for Testing Matls., West Conshocken PA, 

USA.

3. ASTM Standard G159, Standard Tables for Reference Solar Spectral Irradiances: Direct 

Normal and Hemispherical on 37° Tilted Surfaces, Amer. Society for Testing Matls., West 

Conshocken PA, USA.

4. IEC Standard 60904-3, Measurement Principles for Terrestrial Photovoltaic (PV) Solar 

Devices with Reference Spectral Irradiance Data, International Electrotechnical 

Commission, Geneva, Switzerland. 

FF 100 P

V I oc sc

≡ max

2

2 2

2

U

U U

FF

P Voc = ⎛

⎝

⎜

⎞

⎠

⎟ + ⎛

⎝

max ⎜

⎞

⎠

⎟ + ⎛

⎝

⎜

⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ = ⎛

⎝

⎜ ⎞

⎠

⎟ +

2 2 0 5 2

2

2 3 85

2

UI 1 sc

.

. .16

2

3 67

2

5 44

2 2 0 5 ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ = . . %

.

2

33 3

22 2

U U UU U

FF

TVVV DMM I = ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + − − − ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ DMM U UR M DMM TT C

3 3 39

2 22 ⎞

⎠

⎟ + ⎛

⎝

⎜

⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

=

−

2 2 0 5

2

2 1 00

U

U

P fit

FF

.

.

3

0 030

3

0 017

3

0 055

3

222 ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ... ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ + ⎛

⎝

⎜ ⎞

⎠

⎟ +

2 22 2 0 018

3

0 10

3

0 030

9

. .. 0 06

2

2 0 5

. .

⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥
52 

5. K. Emery, D. Dunlavy, H. Field, , T. Moriarty, L. Ottoson, and S. Rummel, “PV Cell and 

Module Characterization Capabilities at NREL,” Proc. 14th NREL/SNL Photovoltaics 

Program Review, Nov. 18–22, 1996, Lakewood, CO. 

6. S. Rummel, K. Emery, H. Field, T. Moriarty, A. Anderberg, D. Dunlavy, and L. Ottoson, 

“PV Cell and Module Performance Measurement Capabilities at NREL,” Proc. 15th NCPV 

Program Review Meeting, Denver, CO, September 8–11, 1998, AIP Proceedings CP-462, 

pp.553–558, 1998. 

7. K.A. Emery, C.R. Osterwald, T.W. Cannon, D.R. Myers, J. Burdick, T. Glatfelter, W. 

Czubatyj, and J. Yang, “Methods for Measuring Solar Cell Efficiency Independent of 

Reference Cell or Light Source,” Proc. 18th IEEE Photovoltaic Spec. Conf., Las Vegas, 

NV, October 21–25, 1985, pp.623–628, IEEE, New York, 1985. 

8. ASTM Standard E1328, Standard Terminology Relating to Photovoltaic Solar Energy 

Conversions, Amer. Society for Testing Matls., West Conshocken PA, USA. 

9. ASTM Standard E1021, Standard Test Methods for Measuring Spectral Response of 

Photovoltaic Cells, Amer. Society for Testing Matls., West Conshocken PA, USA. 

10. ASTM Standard E973, Standard Test Method for Determination of the Spectral Mismatch 

Parameter Between a Photovoltaic Device and a Photovoltaic Reference Cells, Amer. 

Society for Testing Matls., West Conshocken PA, USA. 

11. International Organization for Standardization, Guide to the Expression of Uncertainty in 

Measurement. ISO: Geneva, 1995, ISBN 92-67-10188-9. 

12. M.G. Natrella, "Experimental Statistics,, National Bureau of Standards Handbook 91, p.5–

34. August 1, 1993, reprinted October 1966. 

13. “The Expression of Uncertainty and Confidence in Measurement,” United Kingdom 

Accreditation Service, M3003, Middlesex, UK, December 1997. 

14. C.R. Osterwald, K.A. Emery, D.R. Myers, and R.E. Hart, “Primary Reference Cell 

Calibrations at SERI: History and Methods,” Proc. 21st IEEE Photovoltaic Specialists 

Conf., Orlando, FL, May 21–25, 1990, pp.1062–1067, IEEE, New York, 1990. 

15. K. A. Emery, C.R. Osterwald, S. Rummel, D.R. Myers, T.L. Stoffel, and D. Waddington, 

“A Comparison of Photovoltaic Calibration Methods,” Proc. 9th European Photovoltaic 

Solar Energy Conf., Freiburg, W. Germany, September 25–29, 1989, pp.648–651. 

16. K.A. Emery, C.R. Osterwald, and C.V. Wells, “Uncertainty Analysis of Photovoltaic 

Efficiency Measurements,” Proc. 19th IEEE Photovoltaic Specialists Conf., New Orleans, 

LA, May 4–8, pp.153–159, IEEE, New York, 1987. 

17. H. Ossenbrink, R. Van Steenwinkel, and K. Krebs, ”The Results of the 1984/1985 RoundRobin Calibration of Reference Solar Cells for the Summit Working Group on Technology, 

Growth and Employment,” Joint Research Center, ISPRA Establishment, ISPRA Italy, 

Tech Rep. EUR 10613 EN (April 1986). 

18. K.A. Emery, C.R. Osterwald, L.L. Kazmerski, and R.E. Hart, “Calibration of Primary 

Terrestrial References Cells When Compared with Primary AM0 Reference Cells,” Proc. 

8

th European Photovoltaic Solar Energy Conf., Florence, Italy, May 9–12, 1988, pp.64–68. 

19. K.A. Emery, D. Waddington, S. Rummel, D.R. Myers, T.L. Stoffel, and C.R. Osterwald, 

“SERI Results from the PEP 1987 Summit Round Robin and a Comparison of Photovoltaic 

Calibration Methods,” SERI Tech. Rep. TR-213–3472, March 1989. 

20. J. Metzdorf, T. Wittchen, K. Heidler, K. Dehne, R. Shimokawa, F. Nagamine, H. 

Ossenbrink, L. Fornarini, C. Goodbody, M. Davies, K. Emery, and R. Deblasio, 

“Objectives and Results of the PEP '87 Round-Robin Calibration of Reference Cells and 

Modules,” Proc. 21st IEEE Photovoltaic Specialists Conf., Orlando, FL, May 21–25, 1990, 

pp.952–959, IEEE, New York, 1990. 
53 

21. J. Metzdorf, T. Wittchen, K. Heidler, K. Dehne, R. Shimokawa, F. Nagamine, H. 

Ossenbrink, L. Fornarini, C. Goodbody, M. Davies, K. Emery, and R. Deblasio, “The 

Results of the PEP '87 Round-Robin Calibration of Reference Cells and Modules,- Final 

Report,” PTB Technical Report PTB-Opt-31, Braunschweig, Germany, November 1990, 

ISBN 3-89429-067-6. 

22. C.R. Osterwald, S. Anevsky, A.K. Barua, J. Dubard, K. Emery, D. King, J. Metzdorf, F. 

Nagamine, R. Shimokawa, N. Udayakumar, Y.X. Wang, W. Zaaiman, A. Zastrow, and J. 

Zhang, “Results of the PEP ‘93 Intercomparison of Reference Cell Calibrations and Newer 

Technology Performance Measurements,” Proc. 25th IEEE Photovoltaic Specialists Conf.,

Washington D.C., May 13–17, 1996, pp.1263–1266, IEEE, New York, 1996. 

23. C.R. Osterwald, S. Anevsky, A.K. Barua, J. Dubard, K. Emery, D. King, J. Metzdorf, F. 

Nagamine, R. Shimokawa, N. Udayakumar, Y.X. Wang, T. Wittchen, W. Zaaiman, A. 

Zastrow, and J. Zhang, “Results of the PEP’93 Intercomparison of Reference Cell 

Calibrations and Newer Technology Performance Measurements,” Proc. 26th IEEE PVSC 

Conf., Anaheim, CA. Sept. 29–Oct. 2, 1997, pp.1209–1212, IEEE, New York, 1997. 

24. K. Emery, “The Results of the First World Photovoltaic Scale Recalibration,” NREL Tech. 

Rep. NREL/TP-520-27942, (March 2000).

25. H. Field and K. Emery, “An Uncertainty Analysis of the Spectral Correction Factor,” Proc. 

23rd IEEE Photovoltaic Specialists Conf., Louisville, KY, May 10–14, 1993, pp.1180–

1187, IEEE, New York, 1993. 
54 

GLOSSARY

η Efficiency with respect to reference conditions

λ Wavelength

A Test cell area 

Eref(λ) Reference spectral irradiance

Es(λ) Measured spectral irradiance of the light source

Et Total irradiance

FF Fill factor

Imax current at Pmax 

IMM, IMM’ Measured the monitor current 

IMR Intensity monitor current under reference spectrum and irradiance 

IRM Measured reference cell current 

IRR Calibrated current of the reference cell under the reference conditions 

ITM Measured test cell current 

ITR Calibrated current of the test cell under the reference conditions 

I-V Current versus voltage 

k Spectral correction factor, inverse of M 

M Spectral mismatch parameter

Pmax Test maximum power under reference conditions

RT Standard deviation for IMR

R C Standard deviation for fit to obtain ITR 

St(λ) Measured spectral responsivity of the test cell 

Sr(λ) Measured spectral responsivity of the reference cell 

UIsc Combined uncertainty in the short-circuit current of the test cell with respect to 

reference conditions 

Uη Uncertainty in efficiency

UA Uncertainty in area

UFF Uncertainty in the fill factor

UM Uncertainty in M

UMM, UMM’ Uncertainty in the short-circuit current of the monitor cell

UPmax Uncertainty in the fit of the restricted current versus voltage data 

URM Uncertainty in measured reference current

URR Uncertainty in reference current under reference temperature, spectrum, and 

irradiance

US Uncertainty in current related to spatial nonuniformity

UTR Uncertainty in the short-circuit current of the reference cell

UTT Uncertainty in the short-circuit current of the test cell 

URR Uncertainty of the reference cell.

UV Uncertainty in measured voltage 

UTV Uncertainty in voltage related to temperature

UVoc Uncertainty in Voc

V Measured test cell voltage

Vmax Test cell voltage at Pmax

Voc Test cell open-circuit voltage 
55 

APPENDIX 1 

 
56 
57 
58 

APPENDIX 2 

 

Figure 19 below describes the operational amplifier circuit used to maintain the reference cell 

within 1 mV of 0 V. The bias box senses the voltage Vin remotely and measures the current Iin

across a precision 10-ohm shunt resistor (0.02%). 

Figure 19. Schematic diagram of bias box.
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Uncertainty Analysis of Certified Photovoltaic Measurements at the 

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The measurement of the photovoltaic (PV) performance with respect to reference conditions requires measuring the 

current versus voltage with respect to a given tabular reference spectrum, junction temperature, and total irradiance. 

This report briefly discusses the procedures implemented by the PV Cell and Module Performance Characterization 

Group at the National Renewable Energy Laboratory (NREL) to achieve the lowest practical uncertainty. We present 

a rigorous uncertainty analysis of these procedures following the International Organization for Standardization (ISO) 

“Guide to the Expression of Uncertainty in Measurement.” This uncertainty analysis is required for our team’s 

laboratory accreditation under ISO standard 17025, “General Requirements for the Competence of Testing and 

Calibration Laboratories.” Our PV cell and module performance laboratory was certified by the American Association 

for Laboratory Accreditation (A2LA) to perform ISO 17025-accredited calibrations on September 14, 2004.

15. SUBJECT TERMS

PV; performance; measurement; module; uncertainty analysis; ISO standard 17025; 

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