Uncertainty of PV Module Energy Rating in accordance with IEC 61853
Werner Herrmann, TÜV Rheinland Solar GmbH
Introduction
The energy rating of PV modules is related to its energy yield performance in a specific climate. In contrast to the nominal output power, which is only related to the performance at a single operating point (Standard test Conditions, STC), the energy rating considers the interaction of the PV module characteristics with the climatic conditions at the operating site. With neglect of shading and soiling, the following PV module parameters affect the amount of produced energy: (a) temperature behaviour, (b) low irradiance behaviour, (c) spectral responsivity and (d) angular responsivity.
To be able to compare the energy yield performance of PV modules, the IEC 61853 standard series (Table 1) defines a specific metric, which describes the energy yield performance of PV modules by a single parameter, the Climate Specific Energy Rating (CSER).
Title  

IEC 618531: 2011  Photovoltaic (PV) module performance testing and energy rating  Part 1: Irradiance and temperature performance measurements and power rating 
IEC 618532: 2016  Photovoltaic (PV) module performance testing and energy rating  Part 2: Spectral responsivity, incidence angle and module operating temperature measurements 
IEC 618533: 2018  Photovoltaic (PV) module performance testing and energy rating  Part 3: Energy rating of PV modules 
IEC 618534: 2018  Photovoltaic (PV) module performance testing and energy rating  Part 4: Standard reference climatic profiles 
Table 1: IEC 61853 standard series
Figure 1: Methodology of IEC 61853 series for climate specific energy rating
As shown in Figure 1, the calculation of the Climate Specific Energy Rating (CSER) of PV modules requires the input of various PV module performance parameters (blue boxes) and tabulated reference data (grey boxes) that are documented in IEC 618534 (climate data) and IEC 609043 (AM1.5 spectral irradiance distribution). The yellow boxes represent data processing steps.
The CSER value is calculated according to the following equation
[math]\displaystyle{ CSER= \frac {E_{MOD,Year}/H_{Year}} {P_{MAX,STC}/G_{REF,STC}} }[/math]
E_{MOD,Year} is the calculated PV module annual energy yield (IEC 618533), H_{Year} is the annual inplane solar radiation of the selected reference climate (IEC 618534), P_{MAX,STC} is the PV module nominal output power at STC and G_{REF,STC} is the STC reference irradiance, which is set to 1000 W/m². The CSER parameter can be interpreted as the DC performance ratio of the PV module. CSER=1 means that the annual average operational efficiency corresponds to the STC efficiency of the PV module. In practice, CSER values differ from 1 and the deviation from 1 indicates annual yield losses or gains. Table 1 gives an overview of all input quantities for CSER calculation with remarks on uncertainty aspects.
Input quantity  Information source  Uncertainty aspects 
Reference climates  IEC 618534 defines 6 climates:
 Tropical humid  Subtropical arid  Subtropical coastal  Temperate coastal  Temperate continental  High elevation Parameters:  Ambient temperature  Wind speed at module height  Sun elevation  Sun incidence angle  Global horizontal irradiance  Direct horizontal irradiance  Global inplane irradiance  Direct inplane irradiance  Spectrally resolved global inplane irradiance 
For all parameters an annual time series of hourly averages is given.
Spectral irradiance data are presented in a low resolution for 32 discrete wavelength bands (Kato bands [2]) Spectral mismatch calculation requires the calculation of the low resolution AM1.5 spectral irradiance (IEC 609043) and relative spectral responsivity of the PV module with the same “Kato” wavelength basis. 
(GT) matrix of P_{MAX}  (GT) measurement in accordance with IEC 618531:
PV module temperature: 15°C to 75°C Irradiance: 100 W/m² to 1100 W/m² 
Relative P_{MAX} uncertainty [math]\displaystyle{ \frac {\Delta P_{MAX}} {P_{MAX}} }[/math] to be calculated for each (GT) test condition of the (GT) matrix. 
a_{r} parameter of angular response curve  Angular response measurement in accordance with IEC 618532  The uncertainty of the incident angle modifier ΔIAM (θ) increases with the incident angle θ. Δa_{r} uncertainty results from the procedure defined in section 5. 
Relative spectral responsivity (SR) curve of the PV module  SR measurement is performed in accordance with IEC 609048 and related to 25°C device temperature  SR uncertainty is wavelength dependent and follows a bathtub curve. Temperature related shifts of the SR curve are not considered. 
Operating temperature  The operating temperature is modelled with two parameters (u_{0} and u_{1}) that are determined in accordance with IEC 618532. These parameters describe the impacts of irradiance (u_{0}) and wind speed (u_{1}).  The u_{0} and u_{1} parameters are subject to uncertainty, which is mainly determined by the number of useful data with thermal equilibrium in the monitoring period and the resulting wind speed range [6]. 
Table 2: Overview of CSER uncertainty sources
With this background, the CSER uncertainty is composed of the following components:
 ΔCSER_{(GT)}: Uncertainty related to measurement uncertainty of the (GT) power matrix
 ΔCSER_{SMM}: Uncertainty related to spectral mismatch uncertainty
 ΔCSER_{AR}: Uncertainty related to angular response uncertainty
 ΔCSER_{TMOD}: Uncertainty related to modelling of PV module operating temperature
 ΔCSER_{DATA}: Uncertainty related to data processing
In the following sections of this paper, the contributions to CSER uncertainty are individually analysed. All CSER calculations were performed with an Excel software developed by TÜV Rheinland. The tool has been validated against others from European research institutes under the work presented in [1].
Interpolation and extrapolation of the (GT) power matrix
The (GT) power matrix, measured in accordance with IEC 618531, does not cover all operating conditions contained in the six reference climates of IEC 618534. Extrapolation and interpolation methods for the P_{MAX} data table must be applied that will introduce uncertainties.
As interpolation and extrapolation methods are not clearly defined in the standard IEC 618531, harmonised calculation methods have been developed in the MetroPV project [1]. Figure 2 summarises the recommended procedures.
Figure 2: Interpolation and extrapolation methods of the GT matrix for P_{MAX} as defined in [1]. Eqn 14 and Eqn 14b refer to the definitions in [1].
Translation of spectrally resolved data to Kato bands
For all reference climates, tabulated spectral irradiances are based on 32 wavelength intervals, which commonly known as Kato bands [2]. Spectral mismatch calculation therefore requires the translation of highresolution AM1.5 reference spectral irradiance (IEC 609043) and PV module spectral responsivity to these intervals (Figures 3 and 4). With regard to minimized uncertainties introduced by the translation, averaging and interpolation methods have been presented in [1].
The robustness of best practice methods has been validated with CSER intercomparison studies, in which European research institutes have processed a given data set of a cSi PV module (P_{MAX} (GT) matrix, angular response, spectral responsivity). Results were published in [1] and have shown that the proposed methods reduce differences DCSER to 0.1 % (rel.).
Result: ΔCSER_{DATA} uncertainty related to interpolation and transition to low resolution can be assumed lower than ±0.1 % 
Figure 3: Translation of highresolution AM1.5 spectral irradiance to low resolution AM1.5 Kato spectrum [2]
Figure 4: Translation of highresolution spectral responsivity to low resolution Kato wavelength bands
The term “power rating” describes the output power of PV modules under variable operating temperature and irradiance. It is measured in accordance with IEC 618531 and reported in the form of a data table, commonly known as (GT) matrix where the 22 data points are presented in matrix form (see Figure 1).
Measurement uncertainty for P_{MAX} data points is not constant, but dependent on several factors. It is the task of the test laboratory to consider these impacts in the uncertainty analysis and present an (GT) uncertainty table for P_{MAX}.
 Irradiance nonuniformity: The irradiance nonuniformity in the test area of a solar simulator usually changes with the lamp power or by using attenuator masks. A contribution to measurement uncertainty arises from the fact that the average irradiance in the module area may deviate from the irradiance measured at the location of the reference cell. Compensation may be required by adjusting the scaling factor of the reference cell.
 Uncertainty related to irradiance setting: High precision WPVS reference cells are not designed for operation in high ambient temperature environment. To avoid degradation, the reference cell preferably shall be placed outside the temperature chamber, in which the test module is installed. An uncertainty contribution arises from the transfer of calibration to the new position outside the test chamber.
 Spectral mismatch uncertainty: Spectral responsivity of the PV module under test changes with operating temperature. Furthermore, the spectral transmittance of the glass cover at the light entrance side of the temperature chamber will have an impact on the spectral irradiance reaching the PV module. Both effects are combined with spectral mismatch uncertainty.
 Temperature measurement uncertainty: Infrared temperature sensors, which are typically used for P_{MAX} measurement under STC, may not be suitable for operation in a high temperature environment. A uncertainty contribution results from the use of contact sensors such as Pt100 or thermocouples.
 Temperature nonuniformity: Depending on the air circulation conditions in the temperature chamber uncertainty contributions can result from a higher temperature nonuniformity in the PV module area compared to STC measurements. Uncertainties related to temperature nonuniformity will also arise when heating is achieved by continuous light exposure (i.e. steadystate solar simulator).
As the temperature range of the (GT) matrix does not fully cover the operating conditions of the 6 reference climates, it is necessary to define the temperature range 10°C to 15°C. This leads to the temperature and irradiance binning shown in Table 3. For each bin (GT)_{i} an uncertainty ΔP_{MAX,i} is assigned according to the results of the uncertainty analysis of the test laboratory. The example data given in Table 3 are conservative estimates by the author.
With temperature and irradiance binning, a practical approach to estimate the contribution of P_{MAX} related uncertainties to CSER uncertainty is to weight ΔP_{MAX,i} values with the radiated solar energy in the associated (GT)_{i} bin. As an example, Table 4 shows the percentage contributions of (GT)_{i} bins to annual solar radiation E, calculated for the “Temperate coastal” reference climate.
Based on Tables 3 and 4, the CSER uncertainty is calculated according to the following equation
[math]\displaystyle{ \Delta CSER_{GT}=\pm \frac {\sum \Delta P_{MAX,i} \cdot E_{(GT),i}} {E} }[/math]
where E_{(GT),i} is the percentage contribution of the (GT)_{i} range to annual solar radiation E.
Table 5 shows the values of ΔCSER_{(GT)} uncertainty calculated for the six reference climates on the basis of ΔP_{MAX,i} uncertainties given in Table 3. The modelling of PV module temperature (see section 6) has been performed with the default parameters for glass/backsheet construction of PV modules.
 Irradiance related coefficient: u_{0} = 35 W/(m² K)
 Wind related coefficient: u_{1} = 5 J/(m^{3} K).
Result: ΔCSER_{(GT)} uncertainty related to the measurement uncertainty of the (GT) power matrix lies in the range of ±2%. Differences between reference climates are less than 0.2%. 
Table 3: Assumed expanded measurement uncertainty ΔP_{MAX} for different (GT) bins
Table 4: Percentage contributions of (GT)_{i} bins to annual solar radiation E, calculated for the “Temperate coastal” reference climate.
Reference climate  Annual solar radiation (E) [kWh/m²]  Average daytime solar irradiance
[W/m²] 
Irradiance weighted operating temperature
[°C] 
ΔCSER_{(GT)} uncertainty 
Tropical humid  1677.7  400.7  43.6  ±2.06% 
Subtropical arid  2295.5  531.8  42.3  ±2.01% 
Subtropical coastal  1496.6  341.8  33.5  ±1.96% 
Temperate coastal  972.8  233.3  21.8  ±1.92% 
Temperate continental  1266.0  304.9  24.2  ±1.92% 
High elevation  2139.1  494.6  15.1  ±1.88% 
Table 5: Relative ΔCSER_{(GT)} uncertainty calculated for IEC 618534 reference climates.
The irradiance values in the reference climate data tables of IEC 618534 refer to irradiance measurement of with a pyranometer. Accordingly, a spectral mismatch correction of the irradiance values is required, which requires the spectral response curve of the PV module as input.
The spectral curve of PV modules is affected by wavelength dependent measurement uncertainty. This uncertainty source will propagate to spectral mismatch (SMM) uncertainty and thus to CSER uncertainty. The evaluation of spectral responsivity (SR) related CSER uncertainty can be performed by MonteCarlo analysis.
A MonteCarlo analysis tool is not yet available for CSER calculation. Therefore, an existing tool developed by TÜV Rheinland for calculation of SMM uncertainty has been used, which refers to specific SMM inputs. Data analysis has been performed for outdoor data sets of 4 example days in a temperate climate (Cologne, Germany). The results can be used as indication for SMM related ΔCSER_{SMM}.
MonteCarlo analysis of spectral mismatch uncertainty was based on the following inputs:
 Spectral irradiance: High resolution spectral irradiance (300 nm to 1600 nm), measured at the full hour, 4 reference days from Cologne site
 Irradiance sensor: Pyranometer
 Spectral responsivity (SR): SR of cSi PV module measured at 25°C (Figure 5)
 SR Measurement uncertainty: Wavelength dependent UC of DSR test apparatus (Figure 5)
 Uncertainty distribution: Gaussian for each SR data point
 Simulation runs: 2000
Figure 5: Spectral responsivity and associated expanded measurement uncertainty
To just separate the contribution of spectral responsivity related uncertainty, the measurement uncertainties of irradiance and spectral irradiance were set to zero in the total wavelength range.
The results of MonteCarlo simulation for the four example days are shown in tables 6 and 7. It appears that spectral responsivity uncertainty has a minor impact on CSER uncertainty.
Table 6: SMM uncertainty of summer days (temperate climate: Cologne, Germany)
Table 7: SMM uncertainty of winter days (temperate climate: Cologne, Germany)
Result: For temperate climate, the daily spectral mismatch uncertainty ΔCSER_{SMM} is less than 0.2% throughout the year. A conservative estimate for spectral mismatch related uncertainty ΔCSER_{SMM} is ±0.2%. This value can be assumed for all reference climates. 
The spectral responsivity of PV modules is temperature dependent in the region >900 nm. Uncertainties are introduced to CSER calculation because temperature effects are not considered in the CSER procedure.
Spectral related uncertainty of CSER has been studied in [3] based on the annual irradianceweighted spectral mismatch SMM_{G}, which is calculated according to
[math]\displaystyle{ SMM_{G}= \frac { \sum_{i} SMM_{i} \cdot G_{i} } { \sum_{i} G_{i} } }[/math]
SMM_{i} is the spectral mismatch calculated in accordance with IEC 609047 for data point (i).
Result: Differences in annual irradianceweighted spectral mismatch ΔSMM_{G} are less than ±0.05% if the temperature shift of PV module spectral responsivity is considered. 
The angular responsivity of a PV module is measured in the incident angle range 0° (normal incident) to 80° in accordance with the test procedure defined in IEC 618532. The resulting IAM (Incident Angle Modifier) curve, which is a direct measure for incident angular losses. As an example, Figure 6 shows the IAM curve of a cSi PV module. The angular loss for a specific incident angle can be directly read from the difference of the IAM curve to the line of optimal cosine behaviour IAM (q) = 1. In a second step the IAM values are approximated by the equation shown below [4]. Curve fitting results in a single parameter (a_{r}), which is the input parameter for CSER calculation.
[math]\displaystyle{ IAM( \theta )= \frac { 1exp(cos \theta / a_{r}) } { 1exp(1 / a_{r}) } }[/math]
Figure 6 shows the measured 11 IAM data points with associated uncertainty bars (red lines). The blue curve is the fitted IAM (q) curve that has been determined by applying the least mean square method, resulting in a_{r} =0.168. The uncertainty of the a_{r} parameter derives from the uncertainty of the IAM measurement and the uncertainty of the fitting. As shown in Figure 6, a_{r} uncertainty can be approximated by fitting the data points at the upper and lower IAM uncertainty bars. In this example the evaluation yields a_{r} = 0.168 ±0.008.
Figure 6: Incident Angle Modifier curve IAM (q) and associated expanded measurement uncertainties
The impact of a_{r} uncertainty on the CSER value can be analysed with CSER calculations covering the complete a_{r}uncertainty range, which is 0.160 to 1.76. Table 8 shows the results of CSER calculation for the reference climate data sets of IEC 618534.
Table 8: CSER uncertainty related to angular response uncertainty
Result: For all reference climates, the angular response related ΔCSER_{AR} remains below ±0.5%, so that this value can be regarded as good estimate for an upper uncertainty limit. 
IEC 618533 uses the temperature model of [5] to calculate the PV module operating temperature for given environmental conditions. For constant environmental conditions, the equilibrium temperature of the PV module () is primarily a function of the ambient temperature (), the wind speed () and the global solar irradiance (G) incident on the active surface of the module.
[math]\displaystyle{ T_{M}T_{AMB}= \frac { G } { u_{o}+ u_{1} \cdot v_{w} } }[/math]
The coefficient describes the influence of the irradiance and the impact of wind speed. The unit of is W / (m² K); the unit for is J / (m^{3} K).
The procedure for determining the modelling parameters is defined in the standard IEC 618532. Because the test method has deficiencies it is currently under revision in the IEC working group IEC TC82 WG2: The data filter is too strict and results in a low number of useful data points. As u_{0} and u_{1} are determined by linear regression, both parameters are affected by high uncertainty. Therefore, a more accurate method [6] is referenced to estimate the CSER uncertainty related to the modelling of PV module operating temperature.
Uncertainties related to determination of u_{0} and u_{1} parameters are caused by factors such as mounting configuration, sky temperature, wind conditions directions, seasonal variation and site geography. The values determined are highly site specific.
The uncertainty of u_{0} and u_{1} parameters has been studied in [6] for a glassbacksheet PV module monitored in Braunschweig, Germany in the period May to September 2020. The analysis of monthly data sets resulted in the following seasonal variation of modelling parameters.
 u_{0}: 34  37 W / (m² K)
 u_{1}: 4.5  5.5 J / (m^{3} K)
Besides the seasonal variations, the results of additional studies with test samples of the same PV module type exposed in temperate climate (Cologne, Germany) and subtropical arid climate (Tempe, Arizona) are used to address site geography and climate in the following ranges [Table 10].
Temperate climate  Subtropical arid climate 
Location: Cologne, Germany  Location: Tempe, Arizona, USA 
Monitoring period: March – August 2016  Monitoring period: January – December 2016 


Table 10: Seasonal variation of modelling parameters u_{0} and u_{1} observed at test locations in temperate and subtropical arid climate
Based on these results the following uncertainties for the temperature modelling parameters of a glassbacksheet module design can be assumed:
 u_{0}: 35 ± 1.5 W / (m² K)
 u_{1}: 4 ± 1.5 J / (m^{3} K)
These uncertainties have been used to calculate the CSER spread for the six reference climates. The results are shown in Table 11 and reveal that CSER uncertainty ranges from 0.38% for high elevation climate and 0.78% for subtropical arid climate.
Table 11: CSER variation related to the uncertainty of temperature modelling parameters u_{0} and u_{1}. Percentage uncertainties in the bottom row are related to u_{0}=35 W/(m² K) and u_{1}=4 J/(m³ K).
Result: For all reference climates of IEC 618534, it can be assumed that the uncertainty of the CSER in relation to the temperature modelling is less than ±1%. 
Combined CSER uncertainty
The combined CSER uncertainty is calculated according to the following equation.
[math]\displaystyle{ \Delta CSER = \pm \sqrt{ ( \Delta CSER_{DATA} ) ^{2} + ( \Delta CSER_{GT} ) ^{2} + ( \Delta CSER_{SMM} ) ^{2} + ( \Delta CSER_{AR} ) ^{2} + ( \Delta CSER_{TMOD} ) ^{2} } }[/math]
Based on the results and assumptions of the previous sections (see Table 12), the combined CSER uncertainty is ±2.3%. It is dominated by ΔCSER_{(GT)} with a contribution of approx. 75%, followed by ΔCSER_{TMOD} with approx. 20% contribution. The other uncertainty sources contribute approx. 5%.
Description  Estimated uncertainty  Contribution to combined uncertainty  
ΔCSER_{DATA}:  CSER uncertainty related to data processing https://zenodo.org/record/5750185  < ±0.1%  0,2% 
ΔCSER_{(GT)}:  CSER uncertainty related to measurement uncertainty of the (GT) power matrix  ±2%  75,4% 
ΔCSER_{SMM}:  CSER uncertainty related to spectral mismatch uncertainty caused by spectral responsivity uncertainty  ±0.2%  0,8% 
ΔCSER_{AR}:  CSER uncertainty related to angular response uncertainty  < ±0.5%  4,7% 
ΔCSER_{TMOD}:  CSER uncertainty related to PV module temperature modelling  < ±1%  18,9% 
Table 12: Listing of CSER uncertainty sources with associated uncertainty contributions
References
[1] M. R. Vogt et al., PV module energy rating standard IEC 618533 – Intercomparison and best practice guidelines for implementation and validation, https://zenodo.org/record/5750185
[2] S. Kato, T. Ackerman, J. Mather, E. Clothiaux: The kdistribution method and correlatedk approximation for shortwave radiative transfer model, J. Quant Spectroscopy Radiative Transfer 62, 109–121, 1999, DOI: 10.1016/S00224073(98)000752
[3] W. Herrmann, I. Nixdorf, J. Bonilla Castro, Uncertainty of PV module energy rating caused by spectral effects, EUPVSEC 2020
[4] N. Martin. J.M. Ruiz: Calculation of the PV modules angular losses under field conditions by means of an analytical model, Solar Energy Materials & Solar Cells 70, pp 2538, 2001
[5] D. Faiman: Assessing the outdoor operating temperature of photovoltaic modules, Progress in Photovoltaics: Research and Applications, vol. 16, no. 4, pp. 307–315, 2008.
[6] W. Herrmann, C. Monokroussos, K. Lee: Comparison of different approaches to determine the Nominal PV Module Operating Temperature (NMOT), EUPVSEC 2021