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

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

Contract No. DE-AC36-08GO28308

Determining Outdoor CPV Cell 

Temperature

Preprint

Matthew Muller, Chris Deline, Bill Marion, 

Sarah Kurtz, and Nick Bosco 

Presented at the 7th International Conference on Concentrating 

Photovoltaic Systems (CPV-7) 

Las Vegas, Nevada

April 4-6, 2011

Conference Paper

NREL/CP-5200-51338

April 2011
NOTICE

The submitted manuscript has been offered by an employee of the Alliance for Sustainable Energy, LLC 

(Alliance), a contractor of the US Government under Contract No. DE-AC36-08GO28308. Accordingly, the US 

Government and Alliance retain a nonexclusive royalty-free license to publish or reproduce the published form of 

this contribution, or allow others to do so, for US Government purposes.

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, 

express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of 

any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately 

owned rights. Reference herein to any specific commercial product, process, or service by trade name, 

trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, 

or favoring by the United States government or any agency thereof. The views and opinions of authors 

expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.

Available electronically at http://www.osti.gov/bridge

Available for a processing fee to U.S. Department of Energy

and its contractors, in paper, from:

U.S. Department of Energy

Office of Scientific and Technical Information

P.O. Box 62

Oak Ridge, TN 37831-0062

phone: 865.576.8401

fax: 865.576.5728

email: mailto:reports@adonis.osti.gov

Available for sale to the public, in paper, from:

U.S. Department of Commerce

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

phone: 800.553.6847

fax: 703.605.6900

email: orders@ntis.fedworld.gov

online ordering: http://www.ntis.gov/help/ordermethods.aspx

Cover Photos: (left to right) PIX 16416, PIX 17423, PIX 16560, PIX 17613, PIX 17436, PIX 17721

Printed on paper containing at least 50% wastepaper, including 10% post consumer waste.
1 

Determining Outdoor CPV Cell Temperature

Matthew Muller, Chris Deline, Bill Marion, Sarah Kurtz, Nick Bosco

National Renewable Energy Laboratory (NREL), Golden, CO, 80401 USA (303)384-6164

Abstract. An accurate method is needed for determining cell temperature when measuring CPV modules outdoors. It 

has been suggested that cell temperature can be calculated through a procedure that shutters sunlight to the cells while 

measuring the transients in open-circuit voltage (Voc) and heat sink temperature. This paper documents application of 

this shutter procedure to multiple CPV modules at NREL. The challenges and limitations are presented along with an 

alternate approach to measuring CPV cell operating temperature.

Keywords: CPV, Cell, Temperature, Power, Ratings, IEC.

PACS: 85.30, 88.05, 88.40

INTRODUCTION

The CPV community has been working to 

standardize a procedure for rating module power. The

IEC TC82 WG7 recently agreed to define power 

ratings at concentrator standard test conditions (CSTC, 

25°C cell, 1000W/m2

) and concentrator standard 

operating conditions (CSOC, 20°C ambient, 

900W/m2

). Translation between CSOC and CSTC 

requires knowledge of the cell temperature for both 

conditions [1]. With CPV modules the heat sink

temperature can be measured, but the difference 

between the heat sink and the cell temperatures can 

easily be 10-30°C and is dependent on heat sink 

design, thermal attachment, measurement location,

irradiance, wind speed and other factors.

A procedure has been suggested that requires 

shuttering the module aperture while measuring 

meteorological conditions, module voltage and heat 

sink temperature. The data from this procedure, 

combined with the cell temperature coefficient of 

voltage, provide a means to determine the temperature 

difference between the cell and the measurement 

location on the heat sink. An assumption that this 

temperature difference is proportional to direct normal 

irradiance (DNI) allows a translation to cell 

temperature at CSOC.

This study applies the above shuttering procedure 

to multiple module designs that are on-sun at NREL. 

The challenges and limitations of the shutter procedure 

are discussed along with a cautionary note for indoor 

flash testing of CPV modules. Finally an alternate 

method is considered for calculating outdoor CPV cell 

temperature.

METHODS

The principle of shuttering a PV/CPV module 

while measuring voltage transients has been discussed 

for many years though there exists no formal 

procedure. A very basic approach is used in this study 

for both the shuttering and accompanied 

measurements. A piece of heavy black cloth is placed 

over the face of the module and then manually

snapped off the module to complete the shutter event. 

For comparison, a fast (~5 ms) mechanical aperture is 

similarly employed to shutter directly in front of a 

CPV cell under 1000x concentration. During 

shuttering, Keithley multimeters are used to measure 

module open-circuit voltage (Voc) and heat sink 

temperature using a fast response platinum resistance 

temperature detector (RTD). The module is covered 

for a significant period of time before all shuttering 

events in an attempt to equilibrate the cell and heat 

sink temperature within 1 degree Celsius.

Figure 1 provides an example of what is measured 

and what is calculated when using the shutter 

procedure.

Fig.1 Example Results from Shutter Procedure. 

Voc and heat sink temperature are measured while cell 

temperature is calculated using Eq. (1).

70

60

50

40

30

Open-circuit voltage ( V)

0 1 2 3 4 5 6 7

Time (sec)

44

42

40

38

36

Temperatur e (°C)

Aug 11, 9:01

901 W/m2

Wind 0.1 m/s

Tamb 27.8 C

Voc

Temp_heat sink

Tcell from Voc
2 

Tcell = Th,0 + (Vmax-Voc(t))/(Ns⋅βVocr) 

(1)

Ns = Number of cells in series in module

Tcell = Calculated cell temperature

Th,0 = Heat sink temperature at shutter initiation

Vmax = Maximum measured Voc for shutter event

Voc(t) = Measured Voc as a function of time

βVocr = Voc temperature coefficient, 

-0.0045 (V/°C/cell) 

Eq. (1) assumes the cell temperature is approximately 

equal to the heat sink temperature when Vmax is 

reached. Even if the light is shuttered instantaneously, 

the increase in V may be delayed if the photocarrier 

lifetime in the germanium junction is long or by 

capacitive effects.

ALTERNATIVE METHODS FOR 

DETERMINING CELL TEMPERATURE

Two primary alternative methods are currently in 

use for quantifying operating cell temperature for CPV 

modules.

1) The manufacturers may characterize the thermal 

resistance between the cell and a thermocouple on the 

heat sink by a range of methods that involve access to 

the inside of the module. 

2) The Voc of the on-sun module, corrected for 

irradiance, is used to calculate the temperature [2-3]. 

Method 1 can provide accurate measurements, but is 

not easily verified on a closed module. With Method 

2, the Voc can be corrected for variable irradiance 

using the measured irradiance as defined in IEC 

60904-5 [2] or the module’s own Isc as described by 

King as the “Voc,Isc Method” [3] and as in Eq. (2) [4].

Tc,Voc,Isc = [Voc -Vocr+βm⋅Tr]/[Ns⋅ (n⋅k/q)⋅ln(Isc/Iscr) +βm] 

(2)

Where:

Isc = Measured short-circuit current, (A)

Voc = Measured open-circuit voltage, (V)

Tc,Voc,Isc = Average module cell temperature (K)

Tr = 298.15 Kelvin Reference temperature

Iscr = Isc of module at reference conditions (A)

Vocr = Voc of module at reference conditions (V)

βm = Module Voc temperature coefficient (V/°C) at 

measured irradiance

n = Empirically determined dimensionless cell ‘diode 

factor’; for triple junction CPV cell, this will be ~3

k = Boltzmann’s constant, 1.38066E-23 (J/K)

q = Elementary charge, 1.60218E-19 (coulomb)

The values for Iscr, Vocr, βm, and n can be estimated 

using cell measurements in conjunction with the

number of cells wired in series and the number of 

parallel strings within the module.

RESULTS

The shutter procedures described above were 

applied to four modules of different designs and to a 

single cell behind a CPV lens. Initial voltage 

transients for all modules and the single cell are 

presented in Fig. 2. For comparative purposes, the 

module Voc was divided by the number of cells wired 

in series. The differences between measured heat sink 

temperatures (Th,sink) and calculated cell temperatures, 

based on the voltage transients in Fig. 2, are plotted in 

Fig. 3. All four modules were measured on the same 

day when the DNI was between 950-1000 W/m2 and 

the wind was approximately 4 m/s.

Fig. 2 Voltage Transients During and After Shuttering

Fig.3 Calculated Tcell-Th,sink following the shutter event.

The time to reach the maximum Voc varies from about 

0.005 to 0.15 seconds and is assumed to be the shutter 

time. The shortest shutter time was achieved using the 

mechanical aperture. The remaining variation in 

shutter time is due to inconsistency in manually 

pulling cloth off modules and from the range of 

module sizes tested. For modules about a meter wide, 

~0.1 seconds was the shortest shutter time that was

achieved. Summary information associated with Fig. 

2.6

2.7

2.8

2.9

3

3.1

3.2

0 0.5 1 1.5

Volts/Cell

Time (s)

M1

M2

M3

M4

Single Cell

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2 2.5 3

Cell Temp minus Heat Sink Temp (C)

Time (s)

M1 M2

M3 M4
3 

2 and Fig. 3 is presented in Table 1 along with the 

number of rows built into the module, the 

manufacturer-suggested Tcell-Th,sink for 1-sun 

conditions, and Tcell-Th,sink calculated using Eq. (2) on

long term data taken at NREL for the same modules. 

TABLE 1. Summary Data for Modules and Single Cell

Shutter

Time

(s)

V/Cell

Decline 

Rate 

Maximum 

Measured

(V/(s*cell))

TcellTh,sink 

Shutter

Method

(°C) 

TcellTh,sink

1-sun

Suggested 

Value

(°C)

TcellTh,sink

1-sun

Voc,Isc

Method

(°C) 

Single

Cell

0.005 -.60 16 N/A N/A

M1

1 row

0.13 -0.46 19 18 33-43

M2

4 rows

0.15 -0.14 2 27 15-22

M3

>10 rows

0.083 -0.09 <1 15 5-12

M4

>10 rows

0.14 -0.05 4 24 4-14

ANALYSIS

In Table 1, for M2-M4 Tcell-Th,sink is significantly 

lower using the shutter method as compared to 

manufacturer suggestions or using Voc, Isc, and 

reference conditions at 25°C. Temperatures suggested 

by the manufacturers have not been verified but the 

shutter-method results for M2 and M3 appear to be too 

low to be credible. 

The maximum measured voltage decline rates 

show that the cell temperature is increasing much 

faster in the single cell and M1 as compared to the 

other modules. It is expected that the rate of decline in 

Voc is related to cell design and design for thermal 

management but the specifics of these designs are 

unknown. Interestingly, with the given data set, as the 

number of rows in the module increases the maximum 

voltage decline rate decreases. If the number of rows 

in a module impacts the measured voltage decline rate 

this will introduce systematic error to the shutter 

procedure, causing an underestimation of the 

temperature difference. To this end, a simple model 

was constructed to simulate the effect of a finite 

shuttering speed on the maximum measureable cell 

temperature. Voltage measurements of the single cell 

shuttered with the mechanical aperture (5 ms) and by

hand (70 ms) were first converted to cell temperature 

using the Eq. (1), see Fig. 4. The temperature rise of 

the cell was then fit with a double exponential function 

for each shuttering event. Each fit yields two time 

constants and temperature off-sets, the faster of which 

is taken as the temperature increase of the cell over the 

heatsink. The voltage response according to this 

exponential fit is then summed for a number of rows, 

which are simulated to start heating according to the 

shuttering speed of 70 ms.

Fig. 4 Calculated Tcell for two shutter times

The summed voltage response is then divided by the 

number of rows considered and converted to 

temperature with Eq. (1). The modeled shutter 

procedure results for a module with 1-10 rows are

presented in Fig. 5 along with the temperature offset 

calculated with the fast 5 ms mechanical aperture. The 

results suggest a 25 % error due to the shuttering speed 

on only 1 row of cells, while increasing the number of 

rows further increases the error to over 70 % with a 10 

row module.

Fig. 5 Modeling the effect of a finite shutter speed on the 

calculation of Tcell-Theat,sink for a module with 1-10 rows

The data shown in the rightmost column of Table 1

are presented as a range because accurate module or 

cell data, as required by Eq. (2), were not readily 

available. Consider Tc,Voc,Isc-Theat,sink for M4, which is 

plotted against Isc in Fig. 6 for a clear-sky monthly 

data set. M4 was shipped to NREL with indoor I-V 

data but no information on βm and n. For this reason, 

two different parameter sets have been applied in Eq. 

(2) as shown in Fig. 6. Data from Kinsey et al [5] 

indicate, for triple junction Spectrolab cells, βm can 

range from 4-6 mV/°C per cell at varying 

concentration levels and that n ranges from 3-4 

depending on cell properties. Taking this data into 

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10

Cell Temp minus Heat Sink Temp (C)

Number of Rows

ΔT from 5ms shutter
4 

account, for parameter set 1, Vocr is taken from the 

indoor I-V data, βm=0.0045* Ns, and n=3. In parameter 

set 2, Vocr has been increased by 1.4%, βm is varied 

with irradiance as documented by Kinsey, et al [5], 

and n=3.9. For both parameter sets, Tc,Voc,Isc -Theat,sink is 

approximately linear with Isc and extrapolates to zero 

when Isc is near zero. Although both calculations 

present plausible results, they range from 4-14°C at the 

maximum Isc, demonstrating a potential error of 10°C

associated with Eq. (2).

Fig. 4 Tc,Voc,Isc- Theat,sink against Isc for M4

While it is ideal to have all parameters clearly 

specified for Eq. (2), βm and n are most critical as they 

establish the slope of the linear relationship. Iscr from 

indoor flash testing or estimates from on-sun testing 

are adequate as a 10% error results in only a 1°C

change in the calculated cell temperature. If βm and n

are known it is possible to adjust Vocr to reflect zero 

temperature difference for zero irradiance, minimizing 

potential errors associated with deviation of the Vocr

from the nameplate Vocr. 

IMPLICATIONS FOR FLASH TESTING

The voltage transients presented in Table 1 and in 

Fig. 2 show that rapid cell heating introduces 

significant error to the shutter procedure. This raises 

questions about the possibility of significant heating 

while flash testing modules indoors. The voltage of 

the single cell presented in Fig. 2. rises from 2.15 to 

3.15 volts in 5ms and then declines to 3.12 volts after 

60 ms. This indicates that the cell temperature has 

risen ~6.5°C in just 60 ms. It should be noted that this 

particular cell was under ~1000X geometric

concentration and was packaged by a CPV 

manufacturer. Although the voltage transient can vary 

from manufacturer to manufacturer, such rapid heating

suggests that flash tests need to be conducted in less 

than 20-30 ms and that I-V sweeps should be run in 

both directions to confirm that heating is insignificant 

during the sweeps.

CONCLUSIONS

Shuttering CPV modules has been investigated as a 

method for calculating on-sun cell temperature. The

shuttering procedure can be useful for small modules 

or when a fast shutter is available, but this study 

suggests that heating of the initially exposed cells 

during the shuttering process may underestimate the 

cell temperature by as much as 5-10°C. Temperatures 

calculated using the shuttering procedure are up to 

25°C lower than temperatures measured by the module 

manufacturers, implying that the error can be even 

greater in some cases.

Single-cell data show that in just 60 ms it is 

possible for cell temperature to rise ~ 6.5°C. This 

rapid heating suggests that indoor flash tests need to be 

completed in 20-30 ms in order to avoid significant 

rise in cell temperature. It is suggested that I-V 

sweeps be performed in both directions to validate that 

cell temperature is maintained during the I-V sweeps.

Alternative methods for calculating on-sun cell 

temperature are discussed. Specifically, with 

correction for irradiance variations, the Voc is only an 

accurate indicator of cell temperature if accurate data 

is available for βm and n. Adjustment of the Vocr to 

reflect zero temperature difference for zero irradiance 

can minimize potential errors associated with deviation 

of the Vocr from the nameplate Vocr. 

ACKNOWLEDGMENTS 

This work was completed under contract # DEAC36-08GO28308. The authors would like to 

acknowledge Keith Emery’s help in acquiring data 

using a mechanically controlled aperture.

REFERENCES

1. IEC 62670-1, “Concentrator photovoltaic (CPV) module 

and assembly performance testing and energy rating – 

Performance measurement and power rating,” Draft 

Standard. 

2. IEC 60904-5, “Photovoltaic Devices – Part 5: 

Determination of the equivalent cell temperature (ECT) 

of photovoltaic (PV) devices by the open-circuit voltage 

method.” 

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

Performance Model,” Sandia National Laboratories 

Report, SAND2004-3535, August 2004. 

(www.sandia.gov/pv) 

4. D. King, private communication, Nov 2009. 

5. G. S. Kinsey, et al., “Concentrator Multijunction Solar 

Cell Characteristics Under Variable Intensity and 

Temperature,” Prog. Photovolt: Res. Appl. 2008; 16:503-

508.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10 12 14 16

Isc

Tcell Voc,Isc Minus Measured Heat Sink Temp 

Parameter set 1

Parameter set 2