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Contract No. DE-AC36-08GO28308

Evaluation of Photodiode-Based 

Pyranometers and Reference 

Solar Cells on a Two-Axis 

Tracking System 

Preprint

Frank Vignola, Josh Peterson, and Rich Kessler

University of Oregon

Mike Dooraghi and Manajit Sengupta

National Renewable Energy Laboratory 

Fotis Mavromatakis

Technological Educational Institute of Crete 

Presented at the 2018 World Conference on 

Photovoltaic Energy Conversion (WCPEC-7)

Waikoloa, Hawaii

June 10–15, 2018

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Conference Paper

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July 2018
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Evaluation of Photodiode-based Pyranometers and Reference 

Solar Cells on a Two-Axis Tracking System

Frank Vignola1, Josh Peterson1, Rich Kessler1, Mike Dooraghi2, Manajit Sengupta2, and 

Fotis, Mavromatakis3

1

University of Oregon, Eugene, Oregon, 97403, USA, 2National Renewable Energy Laboratory, 

Golden, Colorado, 80401, USA, 3Technological Educational Institute of Crete, Greece

Abstract — The performance of photodiode-based pyranometers 

and reference solar cells are examined on a two-axis tracker 

surface. This is the third in a series of papers examining the 

performance of photodiode-based pyranometers and reference 

solar cells on fixed and tracking surfaces. Because the instruments 

are oriented normally to the incident radiation, angle-of-incidence

effects are minimized. By removing the angle-of-incidence effects 

inherent in earlier studies, the change in the sensor’s clear sky 

responsivity can be more clearly identified. It was found that the 

photodiode-based pyranometers demonstrate a larger change in 

responsivity than the reference solar cells. Spectral measurements 

are recommended to verify the cause of this difference.

Index Terms — Pyranometer, reference cell, spectral radiation, 

two-axis tracking, temperature dependence, systematic bias

I. INTRODUCTION

Photodiode-based pyranometers and reference solar cells are 

often used to monitor the performance of photovoltaic (PV) 

systems. These instruments yield different results in the 

analysis of system performance and it is important to better 

characterize the strengths and weaknesses of these sensors in 

monitoring the performance of PV systems. In addition, these 

instruments are used to estimate the performance of PV systems 

and it is important to understand any bias introduced by these 

instruments and to evaluate if adjustments can be made to the 

data generated by these sensors to remove any biases 

introduced. This technique has been successfully applied to 

rotating shadowband radiometers (RSRs) also called rotating 

shadowband irradiometers (RSI).

In two earlier studies [1], [2] the behavior of photodiodebased pyranometers and reference solar cells was studied on 

horizontal, fixed-tilt, and one-axis tracking surfaces. The 

effects of temperature on the sensors was small compared to the 

effects of changing spectral distribution of the incident 

radiation and the angle-of-incidence of the irradiance on the 

sensors. Calibrations of the representative instruments

illustrating the magnitude of the various effects are shown in 

Fig. 1. Models exist for estimating the spectral effects and 

angle-of-incident effects [3], [4]. The model for the angle-ofincidence effect for the reference cell shown in Fig. 1 did not 

consider the spectral effects in its development. It is difficult to 

separate the two affects because they both change as the angleof-incidence varies.

With a two-axis tracking system, the sensors are normal to 

the direct irradiance form the sun (DNI), and under sunny skies, 

the angle-of-incident effects largely disappear. The total 

(global) irradiance on this two-axis tracking surface (GNI) 

consists of the DNI plus diffuse irradiance on the normal 

surface (DfNI) and ground-reflected irradiance on the normal 

surface (GRNI). DfNI and GRNI do generate angle-of-incident 

effects, but these effects are expected to be an order of 

magnitude smaller under clear skies.

II. THE DATA

The data come from instruments mounted on a two-axis 

tracker at the Solar Radiation Research Laboratory (SRRL) at 

the National Renewable Energy Laboratory (NREL). Until 

December 2017, the (GNI) was measured using a Kipp and 

Zonen (K&Z) CMP11 pyranometer (responsivity uncertainty 

of +1.9%/-2.75% (30°-60°). Starting in December 2017, a K&Z 

CMP22 pyranometer replaced the CMP11. The CMP22 is a 

secondary standard pyranometer and provides some of the best 

global and tilted measurements available (uncertainty in 

responsivity about 1.5% to 60°). Also on the two-axis tracker 

was a LI-COR LI-200 pyranometer and an IMT reference solar 

Fig. 1: Calibration of a K&Z CMP-22 (blue dashed line) and LI200 SA (green dotted line) pyranometer and an IMT reference 

solar cell (solid black line). The modeled estimate of the angle of 

incident effect [3] for the reference cell is the red dotted line.
2

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cell. The calibrations of all three instrument were determined 

by NREL. The reference solar cell was calibrated in the 

laboratory under a reference lamp and the pyranometers were 

calibrated under NREL’s Broadband Outdoor Radiometer 

Calibration procedures.

The data are averaged over 1 minute and made available on 

the NREL midc-srrl-bms website along with other 

measurements conducted at SRRL. The DNI contribution was 

measured with a K&Z CHP 1 pyrheliometer operated at SRRL. 

The accuracy of the DNI data is about 0.7% at the 95% 

confidence level [5].

The DNI spectral data were obtained from a Prede PGS-100 

direct normal spectroradiometer with traceability to National 

Institute of Standards Technology spectral irradiance lamp 

standards (through a LICOR LI-1800 spectroradiometer). The 

instrument has spectral bandwidth of 3.6nm and the detector is 

maintained at 35°C ± 2°C. The usable spectral range of the 

instrument is 350-1,050 nm. Measurements are made by a SiCCD with a 1° field of view. Data are taken at increments of 

approximately 0.7nm every 5 minutes.

III. EVALUATION OF THE DATA

Initial evaluations looked at the ratio of the LI-200A and IMT

measurements to the reference GNI measurements under clearsky conditions. One clear day was selected in summer and 

another day was selected in winter. It was expected that both 

would show a dependence on the time of day as the solar zenith 

angle increased. Models that examine the spectral distribution 

dependence of the photodiode pyranometers use air mass as a 

parameter because Rayleigh scattering is dependent on the 

amount of air the light passes through, preferentially scatters 

shorter wavelength radiation. Therefore, as the amount of air 

traversed by light increases, the more the spectral distribution 

shifts to longer wavelengths [6] (see Fig 2). Because the solar 

cell used in the LI-200 pyranometer and the IMT reference solar 

cell are more sensitive to the wavelengths around 900-1000 nm, 

the responsivity is expected to increase as air mass increases. 

This is what is seen with the instruments on a two-axis tracker,

as shown in Figs. 3 and 4.

As with the photodiode pyranometer on a one-axis tracker 

[2], the global normal photodiode pyranometer’s responsivity 

increase between 10% and 15% as the air mass increases in the 

early morning and late afternoon. The increases in responsivity 

of the reference solar cell is much less, only about 5%. Similar 

increases in responsivity of reference solar cells were observed 

for a one-axis tracking system. In the previous study [2], it was 

postulated that the smaller change in responsivity for a 

reference solar cell was associated with the spectral effects 

balancing the effects associated with the change in the angleof-incidence.

The advantage of the present study is that the instruments are 

normal to the incident radiation from the sun and only a small 

amount of the GNI comes from diffuse irradiance and ground 

reflected irradiance.

The total irradiance on a two-axis tracking surface, GNI, is 

related to the DNI and the diffuse and ground reflected 

irradiance by a simple equation.

GNI = DNI + DfNI + GRNI (1)

where DfNI is the diffuse irradiance on a surface normal to the 

sun and GRNI is ground-reflected irradiance incident on the 

two-axis tracking sensor. To get an idea of the percentage of 

Fig. 3: Plot of the ratio of the LI-200 and IMT reference cell 

measurements divided by the reference GNI values obtained with a 

CM11 pyranometer. The Li-200SA ratio data are plotted as blue Xs. 

The IMT ratio data are plotted as brown Os. Data were obtained on 

July 1, 2017 under clear-sky conditions. Some data in the morning 

and evening hours were eliminated because of the obstructions or 

mountains on the horizon. A few large outliers were eliminated during 

the day to more clearly show the trends. The 5% difference between 

the ratios of the two instruments is related to calibrations.

Fig. 2: Change in spectral distribution during the day. Because the 

sun is lower in the sky in the morning and afternoon compared to 

noon, the amount of air traversed by the sunlight increases. As the 

path length through the atmosphere increases, the larger percentage of 

blue (short wavelength) light is scattered from the DNI. Data at 9:00 

and 15:00 are almost identical (dotted red and blue lines. At noon, 

black line, show a higher percentage of short wavelength irradiance.
3

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irradiance from the DfNI and GRNI compared to the total GNI 

on a clear day, the DNI was subtracted from the measured GNI 

and the percentage DfNI + GRNI was plotted against time of 

day (Fig. 5). For the July 1, 2017 data, the percentage of DfNI 

+ GRNI varied between 10 and 17%. For January 2, 2018, the 

maximum DfNI + GRNI contribution was about 9.5%. This 

means that the DNI contributed 80% to 90% of the irradiance 

incident on the sensors and the angle of incident effects would 

be relevant only for the DfNI + GRNI irradiance, which only 

made up 10% to 17% of the total GNI. The portion of the DfNI 

that came from the sky exhibited only a little angle-of-incidence 

effect because the diffuse irradiance consists of irradiance from 

a wide variety of angles. The GRNI becomes more important 

as the pyranometer’s tilt is increased. During the middle of the 

day, especially in the summer the pyranometer see much less 

GRNI. The ground-reflected irradiance could have some angleof-incidence effects, but calibration studies show that angle-ofincident effects become significant only for angles-ofincidence greater than 55° (see Fig. 1).

Therefore, a clear majority of the change in ratios shown in 

Figs. 3 and 4 are the result of changes in the spectral irradiance, 

although changes in temperature might play a role. The spectral 

response of a LI-200SA pyranometer and the IMT reference 

solar cell is shown in Fig. 6. These responsivities are 

normalized to one at their peak responsivity. The cell used in 

the LI 200SA pyranometer has changed over time, and different 

pyranometers will exhibit different responsivities. The LI-200 

SA pyranometer is an older model whereas the IMT reference 

cell uses much newer technology, hence the slightly higher 

responsivity.

The spectral responsivity is important because the spectral 

distribution of incident radiation changes during the day (Fig. 

2). An estimate of the effect of changing spectral distribution 

during the day can be obtained by averaging the responsivity of 

the instrument times the spectral irradiance and dividing by the 

sum of the spectral irradiance during the day.

RR = ∑ IIλλ∙RRλλ λλ=4000 λλ=200

∑ IIλλ λλ=4000 λλ=200

(2)

where RR is the average responsivity, and Iλ is the intensity at 

wavelength λ, and Rλ is the responsivity at wavelength λ. This 

calculation was carried out using DNI spectral data from 

Golden, Colorado (shown for January 2, 2018 in Fig. 2) and the 

Fig. 5: Plot of the ratio of (GNI-DNI)/GNI on July 1, 2017 (orange 

circles) and January 2, 2018 (blue x’s). Clear sky data. The difference 

between the GNI and DNI is the DfNI + GRNI. During the day, the 

percentage of DfNI + GRNI on the two-axis tracking surface varied 

between 10% and 20%.

Fig. 6: Relative spectral responsivity of a LI-200SA pyranometer 

and an IMT reference cell are given in percent normalize to 100% 

at maximum. The relative spectral response of different 

pyranometers and reference cells will vary, but the general 

characteristics are similar. Responsivity data taken at NREL

Fig. 4: Plot of the ratio of the LI-200SA and IMT reference cell 

(brown circles) measurements divided by the reference GNI values 

obtained with a CM22 pyranometer. The LI-200SA pyranometer 

data are shown as blue Xs. The IMT reference solar cell data are 

shown as brown Os. Data were obtained on January 2, 2018, under 

clear-sky conditions. Data in the very early morning and late evening 

hours were eliminated because of the obstructions or mountains on 

the horizon. A few large outliers were eliminated during the day to 

more clearly show the trends. The 5% different between the LI2000SA ratios and the IMT reference cell ratios is related to 

calibrations.
4

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responsivities shown in Fig. 6 at 9:00 a.m., noon, and 3:00 p.m. 

for January 2, 2018. A similar analysis was done for 6:00 a.m., 

noon and 6:00 p.m. for July 1, 2017. The results are shown in 

Table 1 for the LI-200SA pyranometer and Table 2 for the IMT 

reference cell

The difference between the modeled and measured ratios for 

the LI-200 SA pyranometer is from 0.3% to 2.5% and for the 

IMT reference cell from -1.6% to -0.2%. With the uncertainties 

in the instrument responsivities and irradiance measurements,

the spectral dependence of the change is very well established.

Two factors have been neglected. The first is the DfNI and 

GRNI irradiance that changes during the day, and the second is 

the effect of temperature. The reference cell does take 

temperature into account, and the data are adjusted to account 

for the temperature. At this point, no effects of temperature on 

the LI-200 SA pyranometer were considered.

If the change in responsivity was totally related to the change 

in spectral distribution and the assumed spectral responsivity of 

the instruments were accurate, then one would assume that the 

change observed in the ratio to the reference instrument shown 

in Figs. 2 and 3 would be approximately the same as that shown

in Tables 1 and 2. The ratios as determined from the data shown 

in Figs. 2 and 3 are given in Table 3.

The temperature effect is also spectrally sensitive and the 

effect increases as the energy of the light (longer wavelengths) 

approaches the energy needed to jump the band-gap for the 

solar cell (Fig. 7). Often the effects of temperature on the 

measurements from photodiode pyranometers and reference 

cells are recorded as average effects over the total 

measurement. This result fails to consider the change in spectral 

distribution during the day that would make temperature related 

effects more prominent in the morning and afternoon as the 

average spectral distribution shifts to longer wavelengths.

If the spectral dependent temperature effect on the LI-200SA 

pyranometer were included, the increase responsivity compared 

to noon would decrease from 1.035 to 1.030 in the morning and 

increase slightly to 1.036 in the afternoon for the Jan. 2, 2018 

comparison and decrease from 1.052 to 1.045 in the morning 

and increase from 1.058 to 1.059 in the afternoon on July 1, 

2017. The effects of temperature in these examples is small in 

this comparison, but it is likely that there would be a 2% 

difference in the ratios if one compared the July and January 

data. For short-circuit current, the output increases with an 

increase in temperature. This shows up in decrease in 

responsivity in the morning and the increase in responsivity in 

the afternoon because the noon time temperature is typically 

higher than the morning temperature and slightly less than the 

afternoon temperature.

Models exist that consider the effect of changing spectral 

distribution during the day. One such model is the King air mass 

correction formula [King, 1998]. Instead of using the King air 

mass correction formula, we use the formula:

Table 1: Calculated change in responsivity for a LI-200 SA 

pyranometer

Date Time Average R Increase in R 

from Noon

SZA

Jan. 2, 2018 9:00 am 0.4917 1.035 75.96

Noon 0.4752 ---- 62.59

3:00 pm 0.4918 1.035 74.68

July 1, 2017 6:00 am 0.4964 1.052 76.28

Noon 0.4750 ---- 16.72

6:00 pm 0.5028 1.058 74.60

Table 2: Calculated change in responsivity for an IMT 

reference cell Table 3: Measured ratio of tested instruments 

Date Time Average R Increase in R 

from Noon

SZA

Jan. 2, 2018 9:00 am 0.5781 1.0234 75.96

Noon 0.5649 ---- 62.59

3:00 pm 0.5789 1.0248 74.68

July 1, 2017 6:00 am 0.5856 1.0298 76.28

Noon 0.5687 ---- 16.72

6:00 pm 0.5904 1.0383 74.60

Fig. 7. Typical temperature dependence of a silicon photodiode as a 

function of wavelength. Data from QE tests taken at NREL at different 

temperatures.

Table 3: Measured ratio of tested instruments

Date Time LI200SAIMT Increase 

from Noon 

LI-200SA

Increase 

from

Noon IMT

Jan. 2, 2018 9:00 am 1.050 0.977 1.050 1.025

Noon 1.000 0.953 ---- ----

3:00 pm 1.054 0.981 1.054 1.029

July 1, 2017 6:00 am 1.090 0.997 1.097 1.042

Noon 0.993 0.956 ---- ----

6:00 pm 1.100 1.009 1.108 1.055
5

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FA =0.0609 * e (Air mass) +0.9753 (3)

from [Vignola, 2017]. The two formulas are almost identical 

from air masses from 1 to 6, but the results from Eq. 3 do not 

increase as rapidly at higher air masses as the King model

results.

The change in the spectral distribution during the day is 

mainly responsible for the shape of the plots in Fig. 8. The 

difference between the LI-200SA pyranometer and the IMT 

reference cell is related to the difference in their spectral 

distributions. This is similar to the results obtained by King in 

1997. At solar zenith angles around 75o, the IMT reference cell 

ratios start to decrease. At present, the cause for this decrease is 

under investigation.

The behavior of the instruments should also be compared 

from summer to winter. This is shown in Fig. 9, which plots 

similar data but against the solar zenith angle. The data in Fig. 

8 are not normalized. Three differences are exhibited here. The 

ratio of the LI-200 SA to CM11 in summer does not pass 

through one at 45o. The ratio looks like it could pass through 

one at 45o with the ratio of the LI-200 SA to CMP22 in January, 

however, the effect of the temperature difference between July 

and January would increase the January ratios by about 2%. 

With the uncertainty in the responsivities determined for the 

instruments the clear-sky results for the LI-200SA ratios can be 

considered consistent. More detailed studies are needed to 

reduce the uncertainties. Similar behavior is found between the 

IMT reference cell ratios in July and January. The reference 

cells do take some of the temperature effects into account, but 

there could be some residual temperature effects that could 

account for this difference. Alternatively, the difference could 

be related to the calibration differences between the CMP11 

and CMP22 pyranometers.

The reference cells were calibrated in the laboratory under an 

artificial lamp. The LI-200SA calibration was determined at 

45o, as were the K&Z pyranometers. Calibration of the 

reference cell under standard outdoor pyranometer calibration 

procedure might reduce this difference. Because PV modules 

are also calibrated under a standard lamp, this difference might 

be worth a more thorough examination. 

One aspect that is unexplained is the drop of the reference 

cell ratios at solar zenith angles greater that 75o. One would 

expect that the ratios would continue to increase similar to the 

LI-200SA pyranometers. The possibilities for this decrease is 

possible differential shading of the reference cells or a 

difference in the ground-reflected irradiance seen by the 

instruments. 

IV. SUMMARY AND FUTURE EFFORTS

This is the third in a series of studies comparing photodiodebased pyranometers and reference cells against thermopilebased pyranometers [1, 2]. This was done for horizontal, fixed 

tilt, one-axis tracking, and two-axis tracking surfaces. As 

expected the differences under clear skies are related to the 

angle-of-incidence effects, changing spectral distributions 

during the day, and some temperature dependence. As the 

instrument is moved from horizontal to fixed-tilt to one-axis 

tracking to two-axis tracking, the effect of the spectral change 

during the day become more pronounced. This results from the 

instruments being pointed more directly at the sun in the early 

morning and later afternoon hours and at these times when the 

spectral distribution varies most from the noon-time 

distribution. Having the instruments pointed more directly at 

the sun as the orientation is changed from horizontal to fixed, 

to one-axis and then to two-axis tracking surfaces decreases the 

angle of incident effects. Therefore, tests at different 

Fig. 8: Ratio of LI-200SA pyranometer (blue line) and IMT reference 

cell (red dots) to the reference CM 11 pyranometer on a two-axis 

tracking surface. Modeled spectral adjustment factor is plotted as 

black dashes. Curves are normalized to 1 at 45o.

0.90

0.95

1.00

1.05

1.10

1.15

1.20

15o 20o 25o 30o 35o 40o 45o 50o 55o 60o 65o 70o 75o 80o 85o 90o

Ratio To Reference

Solar Zenith Angle (Degrees)

Comparison to Reference on a Two-Axis Tracking Surface

Golden, Colorado - July 1, 2017

LI/CM11-45 IMT/CM11-45 Air Mass Adjustment Factor

Fig. 9: Comparisons of the ratio of a LI-200SA pyranometer to a CM11 

(black Xs) in July or a CM22 in January (blue circles) and an IMT

reference cell to a CM11 (green triangles) in July or a CM22 in January 

(brown Os).

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

15° 20° 25° 30° 35° 40° 45° 50° 55° 60° 65° 70° 75° 80° 85° 90°

Ratio to Reference

Solar Zenith Angle (Degree)

Ratio of a LI-200 SA Pyranometer and a IMT Reference Cell to 

a CM 11 or a CM 22 Pyranometer on a Two-Axis Tracker 

Golden Colorado, July 1, 2017 and January 2, 2018

January LI 200SA/Ref January IMT/Ref July LI 200SA/Ref July IMT/Ref
6

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orientations can help distinguish between angle-of-incidence

and spectral effects.

Models exist to account for the angle-of-incidence effects 

and the effects of changing spectral distribution. These models 

can be used to remove systematic biases from the 

measurements on various surfaces, however, the applicability 

of these models to different locations and the accuracy of these 

models need further testing. For example, for the two-axis 

tracking results incorporate the DfNI and GRNI as well as the 

DNI irradiance. An idea of the magnitude of the influence from 

effects caused by spectral changes in the DfNI and GRNI can

be estimated from Figs. 4 and 5. Because the total contribution 

of DfNI and GRNI to the GNI compared to the DNI 

contribution is only about 10% to 15%, it is not expected to 

significantly affect the results of this study. A 10% change in 

the DfNI and GRNI would result in only a 1% to 1.5% change 

in the overall responsivity. That said, it would be interesting to 

measure the spectral distribution on a one- and two-axis 

tracking surface to more precisely evaluate the effects of 

changing spectral distribution. This is also true when studying 

the spectral effects under cloudy or partially cloudy skies.

The ratio of the GNI from the LI-200SA pyranometer and the 

IMT reference cell to the reference GNI from the thermopilebased pyranometer could also be improved by using data only 

from a secondary standard pyranometer such as the CMP22. 

Data with the improved GNI reference instrument are now 

being gathered.

V. CONCLUSIONS

Both the photodiode-based pyranometer and reference solar 

cell used in this study exhibit an enhancement in responsivity 

as the amount of air mass though which light travels increases. 

The enhancement of the photodiode-based pyranometer is 

about three times that of the reference solar cell. Do PV

modules on two-axis trackers behave like reference solar cells? 

If so, the photodiode-based pyranometers are likely to 

overestimate the predicted performance of the modules and 

underestimate the efficiency of the PV system performance in

the morning and evening hours.

PV performance models often have elements that account for 

the spectral shift over the day. However, the estimates typically 

depend on accurate irradiance data. Data from instruments that 

also exhibit a spectral dependence over the day present a 

possibility of double counting this spectral affect. The 

temperature adjustment of the model also has a spectral 

component that should be considered. Therefore, it is important 

to understand the biases in the input data and how the model 

handles spectral characteristics of incident radiation and PV 

model spectral responsivity to accurately assess the model 

predictions and biases.

One can speculate on the reasons for these differences, but 

what is really needed is a set of spectral measurements for both 

irradiance and the responsivity of the photodiode-based 

pyranometer and the reference solar cell. With that information 

a more precise evaluation of the effects of spectral distribution 

can be undertaken. A spectral radiometer is already set up and 

running at SRRL to evaluate the one-axis tracker and a second 

system will be installed in Eugene, Oregon to validate the 

findings at two sites with diverse climates. Additionally, a 

spectral radiometer will soon be set up in the global normal

position at SRRL.

ACKNOWLEDGMENTS

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

under Contract No. DE-AC36-08GO28308 with Alliance for 

Sustainable Energy, LLC, the Manager and Operator of the 

National Renewable Energy Laboratory. Funding provided by 

U.S. Department of Energy Office of Energy Efficiency and 

Renewable Energy Solar Energy Technologies Office. We also 

thank the other sponsors of the UO Solar Radiation Monitoring 

Laboratory, the Bonneville Power Administration, and the 

Energy Trust of Oregon.

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