NREL/CP-5200-55487. Posted with permission.

Reprinted from: L. Dunn, M. Gostein, and K. Emery, “Comparison of Pyranometers vs. Reference Cells for Evaluation of PV Array Performance,” 

Proceedings of the 38th IEEE Photovoltaic Specialists Conference (PVSC), Austin, TX, June 3-8, 2012. © 2012 IEEE.

1 

Comparison of Pyranometers vs. PV Reference Cells 

for Evaluation of PV Array Performance 

Lawrence Dunn,

1 Michael Gostein,1

 and Keith Emery2

1

Atonometrics, Inc., Austin, TX 78757, USA, 2National Renewable Energy Laboratory, Golden, CO 

80401, USA 

Abstract — As the photovoltaics (PV) industry has grown, the 

need for accurately monitoring the solar resource of PV power 

plants has increased. Historically, the PV industry has relied on 

thermopile pyranometers for irradiance measurements, and a 

large body of historical irradiance data taken with pyranometers 

exists. However, interest in PV reference devices is increasing. In 

this paper, we discuss why PV reference devices are better suited 

for PV applications, and estimate the typical uncertainties in 

irradiance measurements made with both pyranometers and PV 

reference devices. We assert that the quantity of interest in 

monitoring a PV power plant is the equivalent irradiance under 

the IEC 60904-3 reference solar spectrum that would produce the 

same electrical response in the PV array as the incident solar 

radiation. For PV-plant monitoring applications, we find the 

uncertainties in irradiance measurements of this type to be on 

the order of ±5% for thermopile pyranometers and ±2.4% for 

PV reference devices.

Index Terms — energy resources, instrumentation and 

measurement, measurement uncertainty, photovoltaic cells, 

calibration.

I. INTRODUCTION

The two most popular tools used by the photovoltaics (PV) 

industry for measuring irradiance are thermopile pyranometers 

and calibrated PV Reference Devices (PVRDs). Currently, the 

PV community has a poor understanding of which device is 

better suited for PV applications. In this work, we explain 

why PVRDs are better suited for PV applications, and we 

calculate typical measurement uncertainties for measurements 

made with both PVRDs and pyranometers. 

Thermopile pyranometers (which we refer to in this work 

simply as “pyranometers”) are devices that have junctions of 

dissimilar metals in contact with a painted black surface that 

absorbs solar radiation (the “hot” junction) and a separate 

surface that does not absorb solar radiation (the “cold” 

junction). They measure irradiance indirectly by measuring 

the temperature difference between those two surfaces [1]. 

Pyranometers have an essentially flat spectral response from 

~400 to ~2700 nm, the transmittance of quartz. Because of 

this flat spectral response over a wide range of incident 

wavelengths, pyranometers are well suited to measure total

incident shortwave radiation, independent of the spectral 

composition of that radiation. Pyranometer uncertainties are 

usually quoted with respect to the measurement of total 

incident solar radiation.

Unlike pyranometers, PVRDs convert incident photons to 

electrons through the photovoltaic effect. The efficiency of 

this photon-to-electron conversion is a wavelength-dependent 

function that is specific to various PV device technologies, 

and to some extent, to individual PV devices.

The Spectral Responsivity (SR) of a PV device is defined as 

the number of amps of current produced at its short-circuit 

current (ISC) condition for a given number of watts of incident 

radiation at wavelength λ. The ISC of a PV device is therefore 

given by: 

( ) ( ) ∫ SC ⋅= dSREAI λλλ , (1)

where A is the area of the PV device in m2

, λ1 and λ2 are the 

upper and lower wavelength bounds of integration in nm 

(typically from ~300 to ~1200 nm for a silicon PV device), 

E(λ) is the spectral irradiance of the incident spectrum in 

Wm-2nm-1, and SR(λ) is the spectral response of the PV device 

in AW-1. 

For PVRD calibrations performed by NREL and other PV 

calibration labs, the calibrated ISC is reported using the IEC 

standard 60904-3 reference solar spectrum [2] for E(λ). 

Despite the calibration being reported for a single incident 

spectral distribution, PVRDs that are calibrated under the IEC 

60904-3 reference spectrum can be used to measure irradiance 

under varying incident spectra. When a calibrated PVRD is 

illuminated by a different spectrum, the irradiance indicated 

by the calibrated PVRD is the irradiance as if the PVRD were

illuminated by the reference spectrum. In exactly the same 

way, the power generated by a PV array will depend on the 

E(λ) of the incident radiation and the SR(λ) of the PV modules

comprising the array.

We therefore assert that the specific irradiance quantity that 

best correlates to PV plant power output is the equivalent 

irradiance under the IEC 60904-3 reference solar spectrum 

that would produce the same electrical response in the PV 

array as the incident solar radiation. We refer to this measure 

of irradiance, distinct from the total solar irradiance which is

independent of the spectrum of the incident light, as 

IrradiancePV. 

Because we assume that the quantity of most interest to a 

PV power-plant operator is the power generated by the PV 

array, it follows that the best and easiest way to measure 

IrradiancePV is with a calibrated PVRD with a spectral 
2 

response that matches the spectral response of the modules 

comprising the PV array.

In this work, we quantify the uncertainty in representative 

measurements of IrradiancePV made with both pyranometers 

and PV reference devices.

For this analysis, we follow the conventions for estimating 

uncertainty outlined in the International Guidelines of 

Uncertainty in Measurement GUM (JCGM 100:2008) [3]. A 

detailed introduction to measurement uncertainty is beyond 

the scope of this paper, but we recommend Refs. [4–6] for an 

introduction to the GUM framework of estimating 

uncertainties in measurement. 

As Reda [7] summarized, the GUM method of calculating 

measurement uncertainty can be expressed in four steps, 

shown in Table I.

II. THERMOPILE PYRANOMETERS

Detailed pyranometer uncertainty analyses of calibrations 

and Global Horizontal Irradiance (GHI) measurements made 

with respect to total incident solar radiation have been 

thoroughly documented in the literature, primarily by the 

National Renewable Energy Laboratory (NREL) [7–9]. Reda 

recently published a method for calculating uncertainties in 

measuring shortwave solar irradiance with a thermopile 

pyranometer [7]. In that work, Reda assumed the availability 

of net-longwave radiation measurements from a pyrgeometer 

co-located with the thermopile pyranometer, allowing for the 

correction of thermal offsets effects. Here, we perform an 

uncertainty analysis following Reda’s example, but 

corresponding to the irradiance defined earlier as

IrradiancePV, rather than to the total broadband irradiance, and 

assuming pyrgeometer data are not available, which we 

believe more accurately represents the typical pyranometer 

use case.

In the absence of pyrgeometer data, the measurement 

equation for IrradiancePV measured with a thermopile 

pyranometer is: 

R

V IrradiancePYR

PV = (2) 

where the “PYR” superscript indicates measurement by a 

pyranometer, V is the pyranometer’s output voltage (usually in 

μV), and R is the responsivity of the pyranometer from its 

calibration in μV/Wm-2. Note GHI is measured if the 

pyranometer is mounted perpendicular to the zenith, whereas

Plane-of-Array (POA) irradiance is measured with the 

pyranometer co-planar with the sample in question (e.g., PV 

modules, building facade). We assume that for POA 

measurements, the pyranometer cable is facing away from the 

sun (e.g., north in the northern hemisphere).

A. Voltage Measurement Uncertainty

We first estimate a representative voltage measurement 

expanded uncertainty, expressed with a 95% confidence level.

Following Reda [7], we use a representative instrument and 

corresponding instrument characteristics and uncertainty: a 

datalogger, with a listed type B expanded uncertainty of 

0.07% of the reading + the offset, where the offset is 4.01 μV 

(equal to 3x the resolution of 0.67 μV + 2 μV). The output 

voltage is assumed to have a rectangular probability 

distribution and an infinite number of degrees of freedom, 

with a corresponding coverage factor of √3 [7]. 

B. Responsivity Measurement Uncertainty

Our calculation of the expanded uncertainty in R is listed in 

Table II. Note that of the sources of uncertainty in Table II, 

only one of them (the calibration uncertainty) would be listed 

in the calibration certificate of the pyranometer. Other sources 

of error would be specific to the measurement conditions,

particular instrument used in the measurement, etc., and may 

be gleaned from experience or instrument manufacturer’s 

specifications. Here, we use Reda’s work in Ref. [7] as a 

guide for creating a representative list of the known sources 

and magnitudes of uncertainty of POA measurements made 

with a thermopile pyranometer, but include two additional 

sources of uncertainty: a “Spectral Mismatch with Respect to

PV” error term, and a “Thermal Offset” term. The first term 

originates from the fact that pyranometers measure total 

broadband irradiance, largely independently of wavelength. 

We have also eliminated an “aging per year” term, with a 

0.2% contribution (assuming that the pyranometer is 

calibrated at least annually). Note that we do not include a 

response time error, although pyranometer response times are 

typically on the timescale of seconds, whereas PV response 

times are on the order of ms or less. 

The “Spectral Mismatch with Respect to PV” term arises 

due to the mismatch between the spectral response of 

pyranometers and PV devices, as discussed in the 

introduction. In recent work, we have quantified this effect to 

TABLE I

GUM METHOD OF ESTIMATING UNCERTAINTIES

1 Determine the measurement equation, in the form Y = 

f(X1,X2,...,XN).

2 

List or estimate the standard uncertainties, ui, defined as 

standard deviations of each input quantity, Xi, and of each 

component that might introduce additional uncertainty, such 

as interpolation, fit error, environmental conditions, etc.

3 

Calculate the combined standard uncertainty using sensitivity 

coefficients and the root-sum-of-squares (RSS) method. 

Combine “Type A” (i.e., statistical), and “Type B” (i.e., nonstatistical) standard uncertainties using a RSS method. 

4 

Calculate the expanded uncertainty, U, and therefore the 

confidence interval about the estimate of the output value, Y, 

using the expression U=k∙u, where k is coverage factor, and 

is calculated from known or assumed probability distributions 

and associated degrees of freedom.
3 

be as high as ~3% for monthly periods, and ~1.5% for annual 

periods [10]. We use the 3% figure in Table II as a 

conservative estimate.

The “Thermal Offset” error term refers to a now wellknown negative-bias error in thermopile-based pyranometer 

irradiance measurements [1,11]. This error is largest in 

pyranometers with all-black receivers. Due to the typical lack 

of thermal equilibrium, net energy flows exist among the sky, 

absorbing sensor, and pyranometer dome. This effect has been 

quantified as ~2% at 1-sun for all-black pyranometers, and 

~0.2% at 1-sun for pyranometers with black and white 

absorbing sensors. Alternatively, the error can be minimized 

by subtracting the infrared (IR) radiative loss (i.e., thermal 

offset) term by measuring the long-wavelength radiation using 

a pyrgeometer co-located with the pyranometer [12]. 

The angular alignment errors are due to the uncertainties in 

aligning the pyranometer with the sample in the azimuthal and 

zenith angular directions. We assume these are limited by 

appropriate physical mounting mechanisms. An additional 

angular response error for Angles of Incidence (AOI) less 

than 30° and higher than 60° has also been included [7]

because of the non-ideal angular response of pyranometers, in 

part due to the air gap between the sensor and dome. 

C. Details of PYR

PV Irradiance Uncertainty Calculation

Although more complicated approaches that reduce 

calibration uncertainty by taking R to be a function of the 

zenith angle have been demonstrated [13], we assume R to be 

a constant, which we believe to be more representative of a

typical pyranometer use case.

Unlike the probability distribution of V, we assume the 

probability distribution of R to be normal with ~500 degrees 

of freedom [7], with a coverage factor corresponding to a 95% 

confidence interval of 1.96 [14]. With this assumption, we can 

calculate representative standard uncertainties for the 

pyranometer POA irradiance measurements made throughout 

the course of a representative day. For a representative 

pyranometer, we take the responsivity, R (19 μV/Wm-2), and 

global horizontal irradiance values from a compilation of 

pyranometer calibration results compiled by NREL [15]. The 

pyranometer is assumed to be mounted co-planar with a PV 

array, and IrradiancePOA values were calculated from the GHI 

values collected at NREL and given in Ref. [15], using the 

following expression [16]: 

( )

( ) Zenith

AOI IrradiancePOA GHI

θ

θ

cos

cos = , (3)

where θZENITH is the angle between the sun and the zenith, and 

θAOI is the angle of incidence (i.e., the angle between the 

vector normal to the POA and the vector from the POA to the 

sun), which depends on θZenith, the angle between the plane of 

array and the plane perpendicular to the zenith (i.e., the tilt 

angle, which we take to be equal to the latitude of the PV 

installation), the azimuthal angle of the sun, and the azimuthal 

angle of the PV array [17]. In this case, the GHI data were 

collected in Golden, Colorado, at a latitude of 39.742°.

The pyranometer’s output voltage values, V, used in 

uncertainty calculations were calculated by multiplying the 

calculated values of IrradiancePOA by the measured zenithangle-dependent values of R throughout the course of the day, 

as provided in Ref. [15]. 

Fig. 1. Calculated POA irradiance for the pyranometer, along with 

accompanying expanded uncertainty error bars (left axis), and 

relative contributions to total uncertainty from the inputs to Eq. (2), 

V and R (right axis).

The expanded uncertainty in PYR

PV Irradiance throughout the 

day was calculated by multiplying the standard uncertainty 

throughout the day by a coverage factor of 1.96, obtained by 

assuming a Student’s t-distribution with an infinite number of 

degrees of freedom and a 95% confidence interval [14]. 

Figure 1 shows the calculated values of PYR

PV Irradiance

along with accompanying expanded uncertainty (shown as

error bars), and the relative contributions to the total expanded 

uncertainty from the input quantities to the measurement 

equation. The relative contributions were calculated by 

dividing the absolute value of each (ci∙ui) by the sum of the 

absolute values of all the (ci∙ui), where the ci are the sensitivity 

coefficients and the ui are the standard uncertainties.

III. PV REFERENCE DEVICES

Within the normal range of light intensities of interest 

incident on a PV power plant, the ISC of a PV device is 

essentially linearly proportional to incident light intensity 

TABLE II

THERMOPILE PYRANOMETER RESPONSIVITY 

EXPANDED UNCERTAINTY

Calibration 3.0%

Spectral Mismatch with Respect to PV 3.0%

Angular Response for AOI <30° and >60° 2.0%

Thermal Offset 2.0%

Angular Alignment Error 0.5%

Nonlinearity 0.5%

Temperature Response 1.0%

Total (Root Sum of Squares) 5.24%
4 

[18,19]. (We account for slight nonlinearities in our 

uncertainty budget below.) Therefore, with a properly 

calibrated PV device, light intensity may be measured by 

measuring the ISC of the device.

We define PVRD

PV Irradiance to be IrradiancePV measured 

with a calibrated PVRD. Following the steps listed in Table I 

to calculate the expanded uncertainty in PVRD

PV Irradiance , we 

start by first writing the measurement equation. Note that in 

the calculations shown below we assume that the spectral 

response of the PVRD matches the spectral response of the 

power-generating PV devices, so that no spectral correction is 

needed [20]. In this case, the measurement equation is given 

by:

( ) sc ref

ref

Isc Cell ref

PVRD sc M

PV I

G

TT

I

Irradiance

,

,

1 −+ = α

, (4) 

where Isc,M is the measured short-circuit current of the

calibrated PV device in amps, αISC is the temperature 

coefficient of Isc,M in %/°C, TCell is the cell temperature of the 

PV device in °C, Tref is the reference calibration temperature 

of the PV device (typically 25°C), Gref is the reference 

calibration irradiance of the PV device (typically 1000 W/m2

), 

and Isc,ref is the reference short-circuit current of the PV 

device, in amps, at the reference temperature and reference 

irradiance.

A. Isc Measurement Uncertainty

Our calculation of the expanded uncertainty of Isc,M is 

shown in Table III. The uncertainty due to the measurement

electronics was calculated assuming an uncertainty of 0.2% of 

the reading + 0.06% of the measurement scale, with the 

measurement scale taken to be 2X the value of Isc,ref. In 

Table III, we have listed an uncertainty for the measurement 

of an Isc reading corresponding to 0.8 suns. 

We assume that the measurement electronics hold the PV 

device at V = 0 (i.e., short circuit) to within ~2% of the value 

of open-circuit voltage (Voc). From experience, we list an 

additional uncertainty of 0.1% in Isc,M due to this deviation 

from V = 0. We also list the uncertainty due to the 

nonlinearity of the PV device with light intensity, from 

experience, to be 0.3%, and the uncertainty due to any angular 

alignment error to be 0.5%. 

We assume a rectangular probability distribution in Isc,M

with an infinite number of degrees of freedom and a 95% 

confidence interval, resulting in a coverage factor of √3.

B. Expanded Uncertainty in αIsc

As a means of estimating the uncertainty in αIsc, we note 

that the European Joint Research Center European Solar Test 

Installation is accredited to measure temperature coefficients 

of PV module currents with a total expanded uncertainty of 

±0.016%/°C [21]. A typical value of the Isc temperature 

coefficient of a crystalline silicon (c-Si) PV device is 

0.05%/°C [22]. Using this value as a typical Isc temperature 

coefficient, the total expanded measurement uncertainty listed 

by ESTI is ±32%.

As a separate means of estimating this uncertainty, we note 

that the temperature coefficient of a single PV reference cell 

measured independently at six internationally recognized 

laboratories as part of the PEP 1987 reference cell and module 

international inter-comparison varied from 0.025 to 

0.06 %/°C, implying an uncertainty of at least ±41% from the 

midpoint αIsc value of 0.0425 %/°C [19]. 

Based on these data, we use as a conservative estimate an 

expanded uncertainty of ±0.025 %/°C in the value of αIsc, 

which results in an uncertainty of ±50% of the typical c-Si Isc

temperature coefficient of 0.05 %/°C. Nothing is known about 

the probability distribution of this input parameter, so we 

assume a rectangular probability distribution with an infinite 

number of degrees of freedom, and a 95% confidence interval, 

resulting in a coverage factor of √3.

C. Expanded Uncertainty in TCell

We next turn to the expanded uncertainty estimate in the 

cell temperature of the PVRD. As an example, we assume 

temperature measurements are carried out on the back surface 

of the PVRD with a Resistive Temperature Detector (RTD), 

with an associated expanded measurement uncertainty of

±0.3°C at 0°C and ±0.8°C at 100°C [23]. We also assume the 

use of an RTD temperature transmitter with an associated 

measurement uncertainty of ±0.1% of full scale [24]. Finally, 

we note that King et al. have found the cell temperature of a 

packaged PV device to be higher than the back-surface 

temperature of the package by n∙3°C [25] to n∙8°C, where n is 

the number of suns. Assuming the typical temperature offset is 

approximately known for the PVRD, we assign an additional 

temperature uncertainty of 3°C for this effect. Combining 

these three components using a root-sum-of-squares 

calculation results in an upper limit of the total expanded 

temperature measurement uncertainty of ±3.11°C. We assume 

a rectangular probability distribution and infinite number of 

degrees of freedom, with a corresponding coverage factor of 

√3.

D. Expanded Uncertainty in Isc,ref 

To estimate the uncertainty in the reference short-circuit 

current, IRef, we note that NREL’s expanded uncertainty with a 

95% confidence interval for certified measurements of a 

suitable PV cell Isc at 1000 W/m2

, 25°C, and under the 

reference spectrum is ±1.27% [22]. 

TABLE III

PV DEVICE ISC,M EXPANDED UNCERTAINTY

Measurement Electronics (at 0.8 suns) 0.35%

Nonlinearity with Light Intensity 0.30%

Deviation of ~2% of Voc from V = 0 0.1%

Angular Alignment Error 0.5%

Total (Root Sum of Squares) 0.63%
5 

A complete uncertainty analysis of the outdoor calibration 

of a secondary PV device using a calibrated PV cell from 

NREL results in a total expanded uncertainty in ISC,Ref of 

±2.05% to ±2.17%, for calibrations performed at POA 

irradiances above ~300 W/m2 [26]. We assume a constant 

expanded uncertainty in Isc,ref of ±2.17% with a student’s tprobability distribution and infinite number of degrees of 

freedom, with a corresponding coverage factor of 1.96. 

E. Details of PVRD

PV Irradiance Uncertainty Calculation

Sensitivity coefficients were calculated by taking the first 

derivative of Eq. (4) with respect to each input parameter [5]. 

The standard uncertainties corresponding to each input 

parameter were calculated by dividing the listed expanded 

uncertainties by their corresponding coverage factors.

The same GHI data used for pyranometer uncertainty 

calculations were used in the calculations of the input 

parameters in Eq. (4) as a function of time of day. TCell was 

estimated using the following expression from Ref. [25]: 

( ( ))





 



 +

+= ⋅+

2 W/m1000

3

exp

POA

Cell Amb POA

Irradiance

TT Irradiance ba WS

, (5)

where TAmb is the ambient temperature, a and b are 

phenomenological constants that depend on the type of PV 

device mounting (e.g., building-integrated PV or rackmounted), and PV device fabrication (e.g., glass/cell/glass or 

glass/cell/polymer) [16], and WS is wind speed. TAmb and WS

were taken from the TMY3 database [27] for the times of day, 

date, and location corresponding to the GHI data collected by 

NREL and provided in Ref. [15]. 

ISC,M was calculated as a function of time of day using 

IrradiancePOA assuming a short-circuit current temperature 

coefficient of 0.05%/°C, a value of ISC,Ref of 2.0 amps, and a 

value of GRef of 1000 W/m2

. 

For each irradiance data point throughout the day, the total 

standard uncertainty was calculated with reference to Eq. (4), 

where the input variables are ISC,M, ISC,ref,, TM, and αIsc. 

Assuming a t-distribution with infinite degrees of freedom, we 

used a coverage factor of k = 1.96 (corresponding to a 

confidence level of 95%) to calculate the total expanded 

uncertainty in IrradiancePV throughout the day.

Fig. 2. Calculated POA irradiance for PV reference device, along 

with accompanying expanded uncertainty error bars (left axis), and 

relative contributions to total uncertainty from the inputs to Eq. (4).

Figure 2 shows the calculated values of PVRD

PV Irradiance

along with accompanying expanded uncertainty (shown as 

error bars), and the relative contributions to the total expanded 

uncertainty from the input quantities to the measurement 

equation. The relative contributions were calculated by 

dividing the absolute value of each (ci∙ui) by the sum of the 

absolute values of all the (ci∙ui). 

IV. RESULTS AND DISCUSSION

Figure 3 shows the total expanded uncertainties in the 

measurements of the IrradiancePV made in the plane of array 

throughout the course of a representative day with a 

thermopile pyranometer and a PV reference device.

Uncertainties are expressed in absolute terms (W/m2

) on the 

left y-axis and as a percentage of IrradiancePOA on the right 

y-axis. Figures 1 and 2 show that for pyranometers, the bulk 

of the measurement uncertainty is due to the uncertainty in the 

device’s responsivity, R, whereas for PVRDs, the bulk of the 

measurement uncertainty is due to uncertainty in the reference 

short-circuit current value of the device, Isc,ref. 

Fig. 3. Expanded uncertainties in POA irradiance measurements 

made with a thermopile pyranometer and PV reference device.

The PVRD achieves an expanded uncertainty that is a factor 

of ~2 lower than the thermopile pyranometer. During the 

majority of the day uncertainties are on the order of +/-5% for 

a pyranometer, and +/-2.4% for a PVRD, both stated with 

95% confidence intervals. We therefore conclude that 
6 

PVRDs provide superior irradiance measurements for PV 

power plant monitoring applications. 

ACKNOWLEDGEMENTS

The NREL portion of this work was supported by the U.S. 

Department of Energy under Contract No. DE-AC36-08-

GO28308 with the National Renewable Energy Laboratory.

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