IEC 61853-2
Uncertainly analysis for angular response measurement in accordance with IEC 61853-2
Table 9: Calculation spreadsheet for angular response uncertainty. As several uncertainty sources are dependent on the rotation angle setting of the test apparatus, MU tables have to be provided for each setting. The given values are example data for 40° rotation angle.
Table 9 shows the listing of uncertainty sources for angular response measurement of a solar cell and a PV module in accordance with IEC 61853-2 [1]. For modules, the standard defines various measurement methods with simulated sunlight, all of which have in common that the IAM measurement relates to a single cell in the connection circuit.
The values given in the yellow fields for uncertainty sources are example data. It is the task of the test laboratory to calculate these values from measurement series or to give estimates based on best practice. The review of the uncertainty analysis by technical auditors is part of laboratory accreditation in accordance with ISO/IEC 17025.
Remarks:
| 1) | Perform repetitive measurements for each angle and determine the standard uncertainty. |
| 2) | Sources for the measurement uncertainties 𝑢_R (𝜃) could be Temperature coefficients of R, calibration of R, Unknown calibration values of R (AutoRange). |
| 3) | Sources for the measurement uncertainties 𝑢_(R,NL) (𝜃) are non-linearities of the measurement electronics. For AOI measurements the current output of the DUT changes by a factor of 10 (Cos(85°)≈0.09). If the measurement electronics such as amplifier and multimeters show a non-linearity in the measurement range of interest, these deviations must be considered as measurement uncertainty. |
| 4) | The centre of the DUT must be placed exactly in the centre of rotation, if divergent light sources are used. In case of a misalignment, systematic measurement deviations dependent on 𝜃 can occur. Consequently, the alignment accuracy must be considered as measurement uncertainty. The measurement uncertainty can be derived from a sensitivity analysis, i.e. by measurements with well-defined misalignments and evaluation of the systematic measurement deviation. |
| 5) | The surface, i.e. the reference plane of the DUT must be placed exactly in the centre of rotation, if divergent light sources are used. In case of a misalignment, systematic measurement deviations dependent on 𝜃 can occur. Consequently, the alignment accuracy must be considered as measurement uncertainty. The measurement uncertainty can be derived from a sensitivity analysis, i.e. by measurements with well-defined misalignments and evaluation of the systematic measurement deviation." |
| 6) | Partly polarized light leads to measurement deviations relative to the unpolarised reference conditions. The uncertainty should be proportional to the overall magnitude of the polarization effect, i.e. the uncertainty should become negligible, if the DUT does not show any polarization effect. The estimated magnitude of the polarization effect should be treated as uncertainty, if no correction is applied. |
| 7) | An extended light source with an aperture A, leads to an angular distribution of the incoming light between 𝜃−∆𝜃 and 𝜃+∆𝜃 on the extended DUT with a dimension L at a distance z. Additionally, there is an alignment uncertainty resulting in an angle offset 𝜃_0. Consequently, this leads to a measurement deviation, that can be derived from a measured AOI dependence. This should be treated as measurement uncertainty. |
| 8) | The DUT could be non-linear with respect to irradiance. This linearity can be of different magnitude dependent on irradiance level. If the AOI testing conditions (i.e. low irradiance) differ significantly in irradiance from the target conditions of the DUT (i.e. STC), the effect on non-linearity should be treated as measurement uncertainty." |
| 9) | There are different uncertainty sources for the temperature measurement: Accuracy of temperature sensor, Calibration of temperature sensor, Possible temperature offsets (i.e. due to thermal gradient between temperature Sensor and pn-junction), Temperature non-uniformity of DUT. |
| 10) | Dependent on the measurement facility there could be inter-reflections leading to a falsification of the measurement signal. The effect can be dependent on the angle 𝜃. The magnitude of this effect and hence the estimated measurement uncertainty can be derived from: Measurements, Estimations from reflectivity coefficients of facility components, Ray tracing simulation- |
| 11) | The relative light transmission of a PV device can generally be assumed to be wavelength dependent, since absorption and reflectivity coefficients are generally wavelength dependent. If the light spectral irradiance differs significantly from the reference spectrum (i.e. halogen lamp vs AM1.5), the spectral relative light transmission is weighted differently leading to different measurement results. In this case an appropriate measurement uncertainty must be considered. |
| 12) | The reproducibility is an estimated uncertainty that covers possible unknown systematic effects/deviations. If a measurement is repeated several times under identical conditions and if the deviation between these measurements extend the deviations that can be expected from the measurement noise or other quantified uncertainties, then these deviations should be quantified and treated as an additional measurement uncertainty. The kind of distribution for that uncertainty should be chosen according to the observed distribution of that reproducibility. The reproducibility could be angle dependent and/or angle independent. Instability of monitor principle is a source of this uncertainty |
| 13) | Contributions to the measurement signal that do not originate from the direct illumination |
| 14) | Non-uniformity of irradiance changes within rotation volume of PV device. This effect is generally not measured (high effort). It can be modelled, and the estimated impact should be treated as measurement uncertainty. |
Since the relative light transmission is a current measurement normalized to normal incidence, correlations of the measurement uncertainties between 𝐼sc (𝜃) and 𝐼sc (0°) must be taken into account. Systematic effects could cancel out i.e. could be enhanced.
The highest contribution is given by the uncertainty related to incident angle ΔΘ. For assumed ΔΘ=0.5° the related uncertainty at Θ=80° is
[math]\displaystyle{ \Delta IAM = \left [ \left ( \frac { cos (80.5^\circ) } { cos (80^\circ) } -1 \right ) , \left ( \frac { cos (79.5^\circ) } { cos (80^\circ) } -1 \right ) \right ] = [-4.44,+4.19] }[/math]
As previously mentioned, the IAM uncertainty is dependent on the incident angle Θ. Therefore, the calculation spreadsheet must be filled for all Θ settings: 0°, 10°, 20°, 30°, 40°, 50°, 60°, 65°, 70°, 75° and 80°. As an example, Figure 2 shows the IAM (Θ) curve with associated measurement uncertainties ΔIAM (Θ).
Figure 2: Incident Angle Modifier curve IAM (Θ) and associated measurement uncertainties
Based on the IAM measurements, the angular response curve of a PV module is described by a single parameter (ar) which is derived from the IAM model defined in IEC 61853-2 [4]. With reference to Figure 2 the uncertainty of the ar parameter will result from the upper and lower IAM range limits. In this example the evaluation yields ar = 0.168 ±0.008.
References
[1] IEC 61853-2:2016 “Photovoltaic (PV) module performance testing and energy rating - Part 2: Spectral responsivity, incidence angle and module operating temperature measurements”