Angular responsivity measurements

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Husyira Al Husna Binti Mohd Nasim1, Tom R. Betts1, George Koutsourakis2

1Centre for Renewable Energy Systems Technology (CREST), Loughborough University, Loughborough, LE11 3GR, United Kingdom

2National Physical Laboratory (NPL), Hampton Road, Teddington, Middlesex, TW11 0LW, United Kingdom


The proportions of direct and diffuse contributions to solar global (horizontal) irradiance are governed by the solar elevation angle (the sun vertical position above the horizon) and the weather. PV modules operating outdoors are fixed optimal tilted angle, to maximise incident irradiation on the modules over the full year. This is typically 10-20° lower than the site latitude, depending on climate. Since the diffuse component is much weaker than the direct, the impact of the view-factor reduction in incident diffuse radiation on the module plane due to this orientation is not significant. Tilting the module from the horizontal does however introduce a third influence on the direct/diffuse ratio – the angle of incidence of the sun to the module.

Figure 1: Schematic of optimal orientation angle of a PV module operating outdoors and seasonal sun path geometry with respect to a point on earth at a latitude of about 50° N [1]

The optimal orientation of a PV module is generally when the surface of the modules is perpendicular to the direction of the direct beam (irradiance incident at 0). Careful calculation of the optimal angle, incorporating sun path information and typical weather patterns, maximises the overall annual in-plane irradiation. However, the apparent sun position varies continuously and as the angle of incidence (AoI) increases, the efficiency of a PV module decreases due to the increased reflection. The impact of angular losses in PV module performance over a long period of time, i.e. energy yield, can be significant [2], therefore the incorporation of this effect in the performance calculation is crucial and it is also included in the IEC 61853-2 standard [3]. Outdoor angular response measurement methods is more advanced than that of indoor methods due to the limitations of simulated light sources (particularly collimation for large areas). The application of the ideal natural sunlight allows for the measurement of angular response characteristic of large area PV devices without the concern of reduction in irradiance uniformity even in tilted orientations. A typical indoor measurement method employs a light source that is far from ideal regarding the angular distribution of the light beams, which results in high volume non-uniformity in the setup.

Main considerations in angular response measurements

The angular response of an ideal optical device is described by a cosine response; its response is proportional to the cosine of the angle of incidence [4]. The angle of incidence dependency of PV module performance is influenced by the combination of cosine effect and additional optical losses due to the orientation of the modules with respect to the light source, predominantly angle dependent reflectance. The angular response characterisation of a PV device measures its current response at various angles, which is dictated largely by the optical properties of the outer glass used in the device, but may also be affected by internal layers in front of the PV active components. This is calculated by normalising the measurement of short-circuit current at different AoI (𝐼𝑠𝑐 (𝜃)) to that when the AoI is 0° (𝐼𝑠𝑐 (0°)). The cosine effect in the measurement is removed by dividing the normalised short-circuit current measurement by the cosine of AoI (cos 𝜃)(1): [math]\displaystyle{ \tau\left(\theta\right)=\frac{I_{SC}(\theta)}{I_{SC}\left(0^o\right)\ cos\theta} }[/math]

The measurement of the angular response can be performed using both natural and artificial light. The main requirements for angular response measurement are visualised in Figure 2.

Figure 2: Ideal measurement setup for the angular response characterisation of PV modules [1]
Reduced background light

To measure the true response of a PV module in respect to AoI from the light source, care must be taken in the measurement setup to ensure that any irradiance other than the intended light source is minimised or eliminated. Means to prevent reflection from surfaces around the surface of the PV module such as the ceiling, floor, and nearby objects has to be incorporated in the measurement setup. If the measurement takes place outdoors, there may be reflected light from neighbouring buildings and trees and also the ground.

Minimal divergence of light source

A perfectly collimated light is ideal in the application to angular response characterisation to eliminate the error in the measurement due to light divergence. In the application to PV measurements, this effect will cause variations in the AoI across the DUT even in “normal” position. Further to this, as the device is rotated the intensity of light will also vary between the parts of the device closer to the light source and those further away. In practice, having a perfectly collimated light source is not possible for a full-sized module area measurement setup employing a solar simulator, therefore the magnitude of the uncertainty contributed by this effect has to be incorporated in the measurement.

For outdoor measurements, it is necessary that the measurement takes place when the sky is clear to ensure so far as possible that only the direct normal irradiance (DNI) is used in the measurement. The solar DNI is the closest to a perfectly collimated light, considering the very large distance to the light source, approximately 149 million km away.

High irradiance volume uniformity

This requirement especially applies to the indoor measurement setup due to the variation of divergent light source. While the non-uniformity of the projected illumination in 𝑥𝑦 dimension can be quite high for the standard solar simulator, irradiance measured at different distance from the light source (𝑧 direction) vary. This volume non-uniformity is what caused the “simulator effect” in the angular dependence measurement of series connected PV modules [5]. The non-uniformity effects will result in a systematic error in the measurement, though this can be corrected for using details of 3-dimensional irradiance uniformity of the measurement area.

Accurate angle adjustment

An accurate adjustment of tilt angle is crucial. A goniometric stage is usually employed in the angular response measurement setup to introduce controlled variation of AoI for both indoor and outdoor measurements. In the case of indoor measurement, the DUT is typically fixed to the centre of the stage, aligned to the centre of light source so that the AoI shift will be symmetrical in both directions (normal to +90°/normal to -90°). The thickness of the DUT also has to be taken into account while making this adjustment, to make the axis of rotation pass through the front surface.

Stable temperature

Electrical parameters of PV devices are temperature dependent and angular response measurement can be time consuming. Performing such a measurement in a controlled temperature environment is ideal, otherwise temperature monitoring and temperature corrections should be applied. The IEC 61853-2 standard includes a correction procedure to be applied for the outdoor measurement method.

Indoor measurements

The standard indoor measurement procedure outlined in the IEC 61853-2 is rather simple. It requires the ISC measurement of the DUT to be taken at two orthogonal angular directions relative to the normal of the DUT for cases where rotationally asymmetric behaviour of the module is observed. For this, the application of a high precision rotation stage with symmetrical rotation is crucial.

The AoI is varied in 10° steps between -60° to +60° while 5° step increment is recommended outside this range due to the higher rate of optical loss experienced by the DUT at high AoI. Variation in the temperature of the DUT is monitored for stability throughout the measurement to remove the need for temperature correction. The angular transmission of the DUT at each AoI is calculated using (1).

Figure 3: Schematic of the experimental layout for angular response measurements of small samples

Indoor measurement layouts can suffer from high irradiance volume nonuniformity when measuring PV modules, as a result of employing a non-perfectly collimated light source. Irradiance non-uniformity especially in the z-axis (optical axis from light source to module) is significant at high AoI when the horizontal edges of the DUT are moved closer to/further from the light source relative to its centre point. The influence of non-uniform irradiance is prominent in the case of electrical measurements of large area PV modules. For modules of series connected cells with bypass diodes, the I-V characteristic is affected by the least performing cell within each bypass-protected block. Figure 3 shows an exaggerated schematic of the angular response measurement of a typical commercial c-Si PV module with 3 strings (3 bypass diodes) using an extended light source. At higher tilt angles (e.g. 60°), the bottom half of the module is moved closer to the source with respect to the rotation point in comparison to the top half. This results in 3 steps observed in the I-V characteristic measurement which correspond to the distance of the string to the light source and the resulting differences in photocurrent generation.

Figure 4: Schematic of setup configuration for angular response measurement of a tilted PV module with 3 bypass diodes (left) and the resulting measured I-V characteristic (right).

The non-uniformity effect in the z-axis can be reduced by restricting the electrical measurement to an individual cell within the module instead of the entire module. This can be achieve by the following methods:

  1. Production of a mini module with identical optical configuration to the full-size module: This method benefits from the reduced total active area so that the non-uniformity effect in the angular response measurement can be reduced. A single cell to test is manufactured with dummy (not electrically connected) cells surrounding the active one to recreate the neighbouring cell effects as would be experienced by a cell in a full module. The drawback of this method is that it requires the manufacturer to produce bespoke samples for testing, which will be made outside of the main production lines and may not be representative, besides being impractical in terms of effort.
  2. Individual cell contact through the back sheet of the module: Electrical measurement probes are attached directly to the back of a cell in the module under scrutiny. This method allows the electrical measurement of a single cell without altering the optical configuration but it is a destructive method which makes the module unusable after testing.
  3. Non-destructive method – based on partial-illumination [6]: In this method, the target cell within the module is partially masked to reduce the effective incident irradiance on the cell. This forces the target to be the current-limiting cell in the corresponding string. As a result, the specific cell’s short-circuit current can be detected, since the lowest plateau in the I-V measurement will always show the electrical performance of the target cell.
Figure 5: Experimental results of angular response measurements, on the left for various PV cells and on the right for two different PV modules [1]

General Best Practice Guidelines

Angular Characterisation of Small Cells
  • Light source:
    • The collimation of the light source dictates the uniformity in the DUT rotation volume and will likely be the limiting factor in a well-configured characterisation setup
    • Outdoor characterisation under natural sunlight should be considered for small area devices, where a sun tracker capable of supporting a baffle tube and dark enclosure (containing the rotation stage) is available. The beneficial qualities of the source are balanced by the drawbacks of weather dependence and reduced convenience, but it may be a suitable option for some institutes
    • Indoors, the volume uniformity can be improved through the use of beam-shaping optics and larger distance between source and DUT, but will be limited by the optical efficiency and the required irradiance-on-target
    • The area of illumination should exceed the area of the DUT by a small margin, so that the geometrical cosine loss is in effect throughout the range of motion of the DUT. If under-illumination must be used, effects due to parts of the front contact moving into and out of the illuminated area must be considered, as must the AoI beyond which the presented aspect of the DUT active area becomes smaller than the illuminated area (where the cosine effect ‘switches on’)
    • The quantity of ambient light falling on the DUT should be minimised. This includes stray light in the laboratory/enclosure and particularly reflections. Thus the area of illumination should not be grossly excessively, as this introduces unnecessary additional light into the test area. Multiple baffles should be employed around the beam from the source and the damping of light reflected from the DUT as it is rotated should be considered in the sizing and shaping of any housing enclosure used, or in room dressing where no enclosure is used. Outdoor characterisation should restrict the DUT field of view to the beam irradiance component only if at all possible (a shade/unshade method to infer the beam contribution is plausible, but direct use of the beam is preferred)
    • The capability to polarise the light source in different planes would enable full description of the DUT reflection characteristics. However, although polarisation of the diffuse component of natural sunlight is known to vary with location on the skydome, solar elevation angle and wavelength, it is not clear from literature what the impact of neglecting the polarisation is. There is insufficient information available to make a strong recommendation for this guide (except to conduct the required research)
    • For spectrally-resolved AoI characterisation requiring the use of bias lighting, these lights should rotate with the DUT to maintain a consistent operating point
  • Rotation stage:
    • The mounting for the DUT should contain at least one axis of rotation, perpendicular to the optical axis. Additional degrees of movement are convenient for acquiring the AoI characteristic about a second, orthogonal axis or full polar-hemisphere, else the DUT is remounted to achieve the same
    • The range of motion should be 0-90 degrees AoI minimum. A symmetrical range saves having to re-mount the DUT to conduct device symmetry validation. A range extending beyond 90 degrees may be useful for checking ambient stray light levels, but is not strictly required
    • The angular resolution must be specified for the requirements of the work: for characterisation of devices with highly specialised physical textures or periodic multilayer coating systems, resolution better than 1 degree may be required. The finest in the literature covered was 0.25 degree for sensor calibration, but 5 degrees is typical and showed no disjointed characteristic curves
    • The rotational positioning accuracy and repeatability should be within 10% of the resolution at worst, although most optics laboratory manual or motorised stages will far exceed this
  • DUT mounting/positioning
    • In the X-Y plane (perpendicular to the optical axis), the DUT active area centre should coincide with the optical axis. The Z positioning should set the axis of rotation at the front of the active cell (not the cover glass, nor back of device)
    • Frame edge effects such as shadowing and reflection are important for most encapsulated small-area cells and will negatively affect the quality of measurements taken at high AoI. Little can be done to mitigate this – it must be considered during the analysis
    • Deeply-textured cover glass on small cells may give false high readings at high AoI as light may be diverted from outside the active area of the cell. This would require verification with purely optical measurements
  • Electrical measurements
    • Measurement of full I-V curves in-situ is preferred. Where only ISC data can be acquired, a separate verification of the PMAX dependence on ISC would be required (for the energy metric work)
    • Other aspects of the device measurements should follow the existing IEC standards (specifically the 60904 series)
Angular Characterisation of Larger Devices

Most of the above considerations apply also to larger devices, with the following additional notes:

  • Light source
    • The source collimation requirements for uniformity in the larger volumes cannot be met indoors at present, leaving the choice between outdoor characterisation of the full module or characterisation on a smaller sub-part
    • Outdoor characterisation under natural sunlight is one of the proposed options in the IEC energy rating draft [3].
    • An indoor method is generally found to be more convenient and the recommendation is to follow the method presented by TÜV Rheinland [19], forcing a target cell into limiting condition
    • With large devices, there is likely to be more unwanted light in the test area (because of the large cover glass reflections). This should be minimised by covering non-essential parts of the device and/or ensuring the room is appropriately sized and dressed to damp reflected light
  • DUT mounting/positioning
    • Edge effects are less likely to affect characterisation on full modules, but where a masked sub-part is the target, care must be taken that the edge of the mask does not affect the results
    • The used part of the module should be representative, for example containing the same ratio of exposed cell to busbar


[1] H. B. M. N. Al Husna, “Characterisation of Spectral and Angular Effects on Photovoltaic Modules for Energy Rating,” Loughborough University, 2018.

[2] N. Martin and J. M. Ruiz, “Calculation of the PV modules angular losses under field conditions by means of an analytical model,” Sol. Energy Mater. Sol. Cells, vol. 70, no. 1, pp. 25–38, Dec. 2001.

[3] International Electrotechnical Commission, “IEC 61853-2 Photovoltaic (PV) module performance testing and energy rating Part 2: Spectral response, incidence angle and module operating temperature measurements,” IEC, 2016.

[4] J. J. Michalsky, L. C. Harrison, and W. E. Berkheiser, “Cosine response characteristics of some radiometric and photometric sensors,” Sol. Energy, vol. 54, no. 6, pp. 397–402, Jun. 1995.

[5] M. Bui, C. Voelker, B. Li, and D. M. J. Doble, “Oblique Angle of Incidence Measurement of PV Modules on a Solar Simulator,” in 26th European Photovoltaic Solar Energy Conference and Exhibition, 2011, pp. 4497–4499.

[6] W. Herrmann, M. Schweiger, and L. Rimmelspacher, “Solar Simulator Measurement Procedures for Determination of the Angular Characteristic of PV Modules,” in 29th European Photovoltaic Solar Energy Conference (29th EU PVSEC), 2014, pp. 2403–2406.