Uncertainty of PV Module Energy Rating in accordance with IEC 61853

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Werner Herrmann, TÜV Rheinland Solar GmbH


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).

IEC 61853-1: 2011 Photovoltaic (PV) module performance testing and energy rating - Part 1: Irradiance and temperature performance measurements and power rating
IEC 61853-2: 2016 Photovoltaic (PV) module performance testing and energy rating - Part 2: Spectral responsivity, incidence angle and module operating temperature measurements
IEC 61853-3: 2018 Photovoltaic (PV) module performance testing and energy rating - Part 3: Energy rating of PV modules
IEC 61853-4: 2018 Photovoltaic (PV) module performance testing and energy rating - Part 4: Standard reference climatic profiles

Table 1: IEC 61853 standard series

Figure 1 Uncertainty of PV Module Energy Rating.png

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 61853-4 (climate data) and IEC 60904-3 (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]

EMOD,Year is the calculated PV module annual energy yield (IEC 61853-3), HYear is the annual in-plane solar radiation of the selected reference climate (IEC 61853-4), PMAX,STC is the PV module nominal output power at STC and GREF,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 61853-4 defines 6 climates:

-     Tropical humid

-     Subtropical arid

-     Subtropical coastal

-     Temperate coastal

-     Temperate continental

-     High elevation


-     Ambient temperature

-     Wind speed at module height

-     Sun elevation

-     Sun incidence angle

-     Global horizontal irradiance

-     Direct horizontal irradiance

-     Global in-plane irradiance

-     Direct in-plane irradiance

-     Spectrally resolved global in-plane 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 60904-3) and relative spectral responsivity of the PV module with the same “Kato” wavelength basis.

(G-T) matrix of PMAX (G-T) measurement in accordance with IEC 61853-1:

PV module temperature: 15°C to 75°C

Irradiance: 100 W/m² to 1100 W/m²

Relative PMAX uncertainty [math]\displaystyle{ \frac {\Delta P_{MAX}} {P_{MAX}} }[/math] to be calculated for each (G-T) test condition of the (G-T) matrix.
ar parameter of angular response curve Angular response measurement in accordance with IEC 61853-2 The uncertainty of the incident angle modifier ΔIAM (θ) increases with the incident angle θ. Δar 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 60904-8 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 (u0 and u1) that are determined in accordance with IEC 61853-2. These parameters describe the impacts of irradiance (u0) and wind speed (u1). The u0 and u1 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(G-T): Uncertainty related to measurement uncertainty of the (G-T) power matrix
  • ΔCSERSMM: Uncertainty related to spectral mismatch uncertainty
  • ΔCSERAR: Uncertainty related to angular response uncertainty
  • ΔCSERTMOD: Uncertainty related to modelling of PV module operating temperature
  • ΔCSERDATA: 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].

CSER uncertainty related to interpolation and extrapolation methods

Interpolation and extrapolation of the (G-T) power matrix

The (G-T) power matrix, measured in accordance with IEC 61853-1, does not cover all operating conditions contained in the six reference climates of IEC 61853-4. Extrapolation and interpolation methods for the PMAX data table must be applied that will introduce uncertainties.

As interpolation and extrapolation methods are not clearly defined in the standard IEC 61853-1, harmonised calculation methods have been developed in the MetroPV project [1]. Figure 2 summarises the recommended procedures.

Figure 2 Uncertainty of PV Module Energy Rating.png

Figure 2: Interpolation and extrapolation methods of the G-T matrix for PMAX 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 high-resolution AM1.5 reference spectral irradiance (IEC 60904-3) 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 c-Si PV module (PMAX (G-T) 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: ΔCSERDATA uncertainty related to interpolation and transition to low resolution can be assumed lower than ±0.1 %

Figure 3 Uncertainty of PV Module Energy Rating.png

Figure 3: Translation of high-resolution AM1.5 spectral irradiance to low resolution AM1.5 Kato spectrum [2]

Figure 4 Uncertainty of PV Module Energy Rating.png

Figure 4: Translation of high-resolution spectral responsivity to low resolution Kato wavelength bands

CSER uncertainty related to G-T matrix uncertainty of PMAX

The term “power rating” describes the output power of PV modules under variable operating temperature and irradiance.  It is measured in accordance with IEC 61853-1 and reported in the form of a data table, commonly known as (G-T) matrix where the 22 data points are presented in matrix form (see Figure 1).  

Measurement uncertainty for PMAX 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 (G-T) uncertainty table for PMAX.

  • Irradiance non-uniformity: The irradiance non-uniformity 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 PMAX 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 non-uniformity: Depending on the air circulation conditions in the temperature chamber uncertainty contributions can result from a higher temperature non-uniformity in the PV module area compared to STC measurements. Uncertainties related to temperature non-uniformity will also arise when heating is achieved by continuous light exposure (i.e. steady-state solar simulator).

As the temperature range of the (G-T) 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 (G-T)i an uncertainty ΔPMAX,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 PMAX related uncertainties to CSER uncertainty is to weight ΔPMAX,i values with the radiated solar energy in the associated (G-T)i bin. As an example, Table 4 shows the percentage contributions of (G-T)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_{G-T}=\pm \frac {\sum \Delta P_{MAX,i} \cdot E_{(G-T),i}} {E} }[/math]

where E(G-T),i is the percentage contribution of the (G-T)i range to annual solar radiation E.

Table 5 shows the values of ΔCSER(G-T) uncertainty calculated for the six reference climates on the basis of ΔPMAX,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: u0 = 35 W/(m² K)
  • Wind related coefficient: u1 = 5 J/(m3 K).
Result: ΔCSER(G-T) uncertainty related to the measurement uncertainty of the (G-T) power matrix lies in the range of ±2%. Differences between reference climates are less than 0.2%.

Table 3 Uncertainty of PV Module Energy Rating.png

Table 3: Assumed expanded measurement uncertainty ΔPMAX for different (G-T) bins

Table 4 Uncertainty of PV Module Energy Rating.png

Table 4: Percentage contributions of (G-T)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


Irradiance weighted operating temperature


ΔCSER(G-T) 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(G-T) uncertainty calculated for IEC 61853-4 reference climates.

CSER uncertainty related to spectral mismatch calculation

Impacts related to measurement uncertainty of spectral responsivity

The irradiance values in the reference climate data tables of IEC 61853-4 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 Monte-Carlo analysis.

A Monte-Carlo 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 ΔCSERSMM.

Monte-Carlo 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 c-Si 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 Uncertainty of PV Module Energy Rating.png

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 Monte-Carlo 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 Uncertainty of PV Module Energy Rating.png

Table 6: SMM uncertainty of summer days (temperate climate: Cologne, Germany)

Table 7 Uncertainty of PV Module Energy Rating.png

Table 7: SMM uncertainty of winter days (temperate climate: Cologne, Germany)

Result: For temperate climate, the daily spectral mismatch uncertainty ΔCSERSMM is less than 0.2% throughout the year. A conservative estimate for spectral mismatch related uncertainty ΔCSERSMM is ±0.2%. This value can be assumed for all reference climates.

Temperature related impact

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 irradiance-weighted spectral mismatch SMMG, which is calculated according to

[math]\displaystyle{ SMM_{G}= \frac { \sum_{i} SMM_{i} \cdot G_{i} } { \sum_{i} G_{i} } }[/math]

SMMi is the spectral mismatch calculated in accordance with IEC 60904-7 for data point (i).

Result: Differences in annual irradiance-weighted spectral mismatch ΔSMMG are less than ±0.05% if the temperature shift of PV module spectral responsivity is considered.

CSER uncertainty analysis related to ar uncertainty

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 61853-2. 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 c-Si 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 (ar), which is the input  parameter for CSER calculation.

[math]\displaystyle{ IAM( \theta )= \frac { 1-exp(-cos \theta / a_{r}) } { 1-exp(-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 ar =0.168. The uncertainty of the ar parameter derives from the uncertainty of the IAM measurement and the uncertainty of the fitting. As shown in Figure 6, ar uncertainty can be approximated by fitting the data points at the upper and lower IAM uncertainty bars. In this example the evaluation yields ar = 0.168 ±0.008.

Figure 6 Uncertainty of PV Module Energy Rating.png

Figure 6: Incident Angle Modifier curve IAM (q) and associated expanded measurement uncertainties

The impact of ar uncertainty on the CSER value can be analysed with CSER calculations covering the complete aruncertainty range, which is 0.160 to 1.76. Table 8 shows the results of CSER calculation for the reference climate data sets of IEC 61853-4.

Table 8 Uncertainty of PV Module Energy Rating.png

Table 8: CSER uncertainty related to angular response uncertainty

Result: For all reference climates, the angular response related ΔCSERAR remains below ±0.5%, so that this value can be regarded as good estimate for an upper uncertainty limit.

CSER uncertainty related to modelling of PV module operating temperature

IEC 61853-3 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 / (m3 K).

The procedure for determining the modelling parameters is defined in the standard IEC 61853-2. 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 u0 and u1 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 u0 and u1 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 u0 and u1 parameters has been studied in [6] for a glass-backsheet 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.

  • u0: 34 - 37 W / (m² K)
  • u1: 4.5 - 5.5 J / (m3 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
  • u0: 34 - 35 W / (m² K)
  • u1: 4 - 5.5 J / (m3 K)
  • u0: 33 - 36 W / (m² K)
  • u1: 2 - 4.5 J / (m3 K)

Table 10: Seasonal variation of modelling parameters u0 and u1 observed at test locations in temperate and subtropical arid climate

Based on these results the following uncertainties for the temperature modelling parameters of a glass-backsheet module design can be assumed:

  • u0: 35 ± 1.5 W / (m² K)
  • u1: 4 ± 1.5 J / (m3 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 Uncertainty of PV Module Energy Rating.png

Table 11: CSER variation related to the uncertainty of temperature modelling parameters u0 and u1. Percentage uncertainties in the bottom row are related to u0=35 W/(m² K)  and u1=4 J/(m³ K).

Result: For all reference climates of IEC 61853-4, 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_{G-T} ) ^{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(G-T) with a contribution of approx. 75%, followed by ΔCSERTMOD with approx. 20% contribution. The other uncertainty sources contribute approx. 5%.

Description Estimated uncertainty Contribution to combined uncertainty
ΔCSERDATA: CSER uncertainty related to data processing https://zenodo.org/record/5750185 < ±0.1% 0,2%
ΔCSER(G-T): CSER uncertainty related to measurement uncertainty of the (G-T) power matrix ±2% 75,4%
ΔCSERSMM: CSER uncertainty related to spectral mismatch uncertainty caused by spectral responsivity uncertainty ±0.2% 0,8%
ΔCSERAR: CSER uncertainty related to angular response uncertainty < ±0.5% 4,7%
ΔCSERTMOD: CSER uncertainty related to PV module temperature modelling < ±1% 18,9%

Table 12: Listing of CSER uncertainty sources with associated uncertainty contributions


[1] M. R. Vogt et al., PV module energy rating standard IEC 61853-3 –  Intercomparison and best practice guidelines for implementation and validation, https://zenodo.org/record/5750185

[2] S. Kato, T. Ackerman, J. Mather, E. Clothiaux: The k-distribution method and correlated-k approximation for shortwave radiative transfer model, J. Quant Spectroscopy Radiative Transfer 62, 109–121, 1999, DOI: 10.1016/S0022-4073(98)00075-2

[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 25-38, 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