## Abstract

This paper proposes a fast method to characterize the two-dimensional angular transmission function of a concentrator photovoltaic (CPV) system. The so-called inverse method, which has been used in the past for the characterization of small optical components, has been adapted to large-area CPV modules. In the inverse method, the receiver cell is forward biased to produce a Lambertian light emission, which reveals the reverse optical path of the optics. Using a large-area collimator mirror, the light beam exiting the optics is projected on a Lambertian screen to create a spatially resolved image of the angular transmission function. An image is then obtained using a CCD camera. To validate this method, the angular transmission functions of a real CPV module have been measured by both direct illumination (flash CPV simulator and sunlight) and the inverse method, and the comparison shows good agreement.

© 2010 OSA

## 1. Introduction

With the growing use of CPV technology for high-efficiency solar cells and new optical system designs, new tools for CPV characterization must be developed to improve the technology and reduce its cost. In this paper, we introduce a method to measure the angular transmission function of a CPV module, using a static optical setup based on CCD photography.

The angular transmission function T(α) is defined here as the ratio of the light power reaching the cell when the module has a deviation angle α relative to the best alignment, as determined by transmitted light power [1]. This number ranges from zero to one, which means that absolute optical losses are not included. The direction defined by the angle α is related to a given light source path contained in a plane; more specifically, this plane is usually a meridian plane of the optical system (see Fig. 1
). The angular transmission function can also be expressed as a function of the azimuthal angle *ϕ*, and the one-dimensional curve for a given meridian plane of azimuthal angle *ϕ _{1}* can be expressed as

The angular transmission function depends on the distribution of light arriving at the CPV panel, and the angular transmission function *T(ϕ,θ)* for a given light source can be theoretically expressed as the convolution of the light source angular distribution *S(ϕ,θ)* and the impulse-response angular transmission function *H(ϕ,θ)* [2].

*H(ϕ,θ)*is defined as the angular transmission function of a CPV system when a set of parallel beams with the same intensity and direction (i.e., zero angular spread as given by a delta (δ) function) covers the whole CPV aperture area. In practice, measuring the theoretical function

*H(ϕ,θ)*by direct illumination would require a light source with nearly unachievable collimation constraints (i.e.,

*S(α) = δ(*α

*)*), which is impractical.

When characterizing CPV systems, a realistic angular transmission function gives information about the CPV system performance under real conditions and corresponds to a setup using the Sun as the light source. That is, a realistic angular transmission function is the convolution of the impulse-response angular transmission function *H(ϕ,θ)* with the solar disc angular distribution *S*(*ϕ,θ*)_{Sun}_{.}

*T(*α

*)*, the CPV module must be placed in a sun-tracker structure, and the output maximum power (P

_{Sun}_{mp}) values should be recorded as a function of the sun misalignment

*α*along a meridian plane of azimuthal angle

*ϕ*. The resulting transmission function depends on the apparent angular size and spectrum of the Sun, which varies with atmospheric conditions and effective air mass (which affect the optical path length through the Earth's atmosphere); as a result, each measurement is not easily reproducible. Moreover, due to variable weather and long acquisition times, measurements using the Sun are impractical on a production line.

_{1}Therefore, the angular characterization of a CPV module would preferably be performed using a solar simulator that produces a light beam similar to direct sunlight over the input aperture of the module. The resultant measured angular transmission function, *T(*α*) _{Simulator}*, can be derived from the convolution of the light source distribution

*S(ϕ,θ)*and the impulse-response angular transmission function

_{Simulator}*H(ϕ,θ).*

The angular transmission function *T(*α*)* and its derived acceptance angle are measured for a CPV module under the flash solar simulator by varying the misalignment angle of the receiver with the light beam, as shown in Fig. 2
. If a motor structure is available, the angular transmission curve can be measured in a few minutes. However, the transmission function is obtained only along one axis, i.e., for a given *ϕ* value, and may require impractically long acquisition times for use on a production line, depending on the angular resolution required.

If the impulse-response angular transmission function *H(ϕ,θ)* is known, then the angular transmission for any light source distribution or illumination condition can be calculated, provided that the angular distribution is known. Moreover, a two-dimensional angular distribution function that is independent of the misalignment axis is desirable. In this paper, we present an alternative method to evaluate the angular transmission of a CPV module. This method is based on using the cell itself under forward bias to produce a Lambertian light emission at the receiver. Using a CCD camera, the emitted light is recorded after being projected on a screen by a large-area collimator mirror. The acquired image is a two-dimensional representation of the CPV impulse-response angular transmission function *H(*ϕ,θ*)*.

## 2. The luminescence inverse method

The measurement technique introduced here is an adaptation of the so-called inverse method, which was proposed to evaluate the optical efficiency of CPC concentrators [5] and has also been applied to other small single-stage concentrators [6]. The inverse method involves a Lambertian emission of light at the receiver plane, which is transmitted back through the optical system on a reverse optical path. The radiant flux of the backward-traveling beam exiting the optical element from the input aperture contains information about the angular transmission function of the concentrator. The intensity of the flux exiting the optic in any given direction is proportional to the transmission function for that direction (defined by a pair of angular coordinates (*ϕ,θ*)). In the classical method, backward light is focused and projected on a white screen, and the image is captured by a CCD camera [1].

There are several technical issues related to CPV technology that must be considered in order to adapt the inverse method to real CPV module measurements. The CPV system must be studied not only as isolated optics but also as a real system including all of the defects resulting from coupling to the cell and assembly of the module. We apply a forward bias to the solar cell to produce the Lambertian light beams by electro-luminescence [7]; therefore, the performance of the actual manufactured concentrator can be studied. Likewise, a method for capturing the emitted light is needed because concentrator lenses are typically larger than the optical aperture of a camera. One possibility to capture the emitted light is to use another set of optics focused at infinity that has a larger area than the CPV aperture area. Taking advantage of the 2 m diameter collimator mirror of the Helios 3198 simulator, we can focus the backward emission of the concentrator onto a white screen at the focal length of the mirror. The diagram of the proposed method is presented in Fig. 3 .

If the cell emits in all possible ray directions with the same intensity, then the light rays exiting the module in a given direction *(ϕ,θ)* will have an intensity that is proportional to the direct angular transmission for that direction when the concentrator is illuminated by uniform, collimated radiation, i.e., the impulse response angular transmission function *H(*ϕ,θ*)*. In reality, the obtained angular transmission function is modified by the slightly-scattered reflection of the collimating optics *H _{Mirror}(ϕ,θ)* because the light is recorded after the parabolic mirror. The mirror scattering has the uniform effect of widening the angular spread of the emitted light, which can be calculated through convolution.

*H*has been characterized, the real

_{Mirror}(ϕ,θ)*H(*ϕ,θ

*)*can be computed using deconvolution techniques. Nevertheless, the angular size of the CPV angular transmission functions is much greater than the effect of mirror scattering (in the range of 0.1°); therefore, this scattering effect can be neglected in most cases.

#### 2.1 Solar cell as a Lambertian emitter

When excess carriers are injected into a solar cell by forward biasing, they preferentially recombine at the lowest energy gap between the valence band and the conduction band. If this minimum gap is direct, then the photon energies of the emitted radiation are narrowly distributed around the energy of that bandgap. The materials for top and middle junctions of the typical 3-junction solar cells (GaInP/GaInAs/Ge), used as receivers in high concentration PV systems, have direct gaps and therefore their emissions are measurable.

An optical characterization of the cell under forward bias has been performed to evaluate if the light emission is Lambertian and uniform in the whole cell area, which is a necessary condition for the described inverse method. We have analyzed the radiant intensity curve of the cell’s emission at different incident angles using a CCD camera. The spectral response of the Si CCD sensor is sensitive to photons up to 1100 nm in wavelength, and thus the two emission peaks at 680 nm and 890 nm from the top and middle junctions, respectively, can be recorded. Using cold and hot mirrors (i.e., long-pass and short-pass filters), both emission bands were isolated and measured individually. The light emission was measured to be Lambertian and uniform across the whole cell area.

The study of electroluminescence in solar cells is a well known technique that has been used to characterize electrical cell anomalies, internal shunts and mechanical defects [8]. The direct current values recommended for the luminescence method correspond to 10% of the value of the working photocurrent at which the CPV module is designed to perform best [7]. Under this direct current, spreading series resistance should not yet be manifest, and relatively bright luminescence indicates a high quality cell. In a defect-free forward-biased cell, the current density can be assumed to be constant over the entire cell area, and thus, a spatially uniform cell emission can be assumed. Although a high level of injected current could represent a risk to the solar cell, choosing a value lower than the solar cell current under normal operating conditions should not be dangerous. Indeed this current value (0.1 times the nominal short-circuit current) is 12.5 times less than the required by the currently approved IEC 62108 standard [8]. Therefore, the direct current value used on this method is far from inducing damage on the cell.

#### 2.2 CCD image: Impulse-response angular transmission function

The image created on the Lambertian surface is a spatially resolved representation of the angular distribution of the emitted light beams, i.e., the two-dimensional impulse-response angular transmission curve *H(ϕ,θ)* of the CPV optical system. In the CCD image, each pixel is related to a bundle of rays of light coming from the CPV system in the same direction and arriving on the target at the same point because of the collimation of the parabolic mirror. When the CCD camera is not far enough from the screen or is not normal to it, perspective errors may appear. By using a reference frame image, these perspective effects can be corrected.

Once the impulse-response angular transmission function *H(ϕ,θ)* is known, the angular transmission function *T(ϕ,θ)* under different illumination conditions can be calculated as the convolution of the impulse-response *H(ϕ,θ)* and a given light source distribution *S(ϕ,θ)*. Any light source distribution *S(ϕ,θ)* can be measured with a simple, direct photograph with the CCD camera. Thus, a two-dimensional convolution can be performed to obtain the transmission function of a CPV module relative to different light source distributions (see Fig. 4
).

Transmission curves provided by direct methods are one-dimensional functions obtained by moving the source on a path that is commonly contained within a meridian plane of the optical system, although other paths are also possible. In Fig. 4, the dashed red line is related to the transmission function of the CPV module along the path that corresponds to the best alignment with the light source. For a meridian plane of given azimuthal angle *ϕ _{1}*, the intersection can be expressed using Eq. (1).

## 3. Results and discussion

To validate the luminescence inverse method, several CPV system technologies were measured by direct methods (flash solar simulator and in-Sun measurements) and by the luminescence inverse method.

To perform this comparison, some spectral issues associated with the receiver cells used in the CPV have to be considered. As mentioned previously, appropriate filters are added to the CCD camera when measuring the angular transmission curve to record emissions related to each subcell separately. When comparing the results for the angular transmission function from the direct and luminescence inverse methods, one must consider the effect of using monochromatic light in the inverse method instead of having full spectrum light, as in the direct method. The question is important due to potential chromatic aberration effects in refractive optical systems. Because the refractive index varies with wavelength, the light distribution at the receiver plane could be different depending on which wavelength is considered. The optical design of a CPV system is often optimized for a given wavelength, such as 550 nm, which means that for 550 nm monochromatic light, the measured acceptance angle would likely be enhanced compared to the measurement at another wavelength. However, the effect on the angular transmission curve when using monochromatic light will be different depending on the optical system design of the CPV, and this can be estimated by ray tracing simulations.

Figure 5 shows the angular transmission curves obtained using a flash solar simulator and the luminescence inverse method for a given CPV module with a single lens-cell unit. The angular transmission curve for 680 nm is slightly wider than the curves for 890 nm and white light. Although this difference is due to the effects of chromatic aberration, the results are consistent with those from the direct method. This similarity in results applies not only to the flash simulator measurements but also to outdoor measurements, as shown in the angular transmission curves in Fig. 6 .

## 4. Conclusions

In order to recognize and resolve typical defects in a CPV module, such as narrowing of the acceptance angle, misalignments between units and local problems in the optical performance of a lens, a new measurement method based on a CCD camera is proposed.

Taking advantage of simple image photography, the two-dimensional angular transmission curve of a CPV system, independent of any light source distribution, is obtained in a cost-effective way. Once this impulse-response angular transmission function is known, we can predict the performance of the CPV system under different illumination conditions. To validate this method, several measurements have been performed with real CPV system technologies by direct methods and the luminescence inverse method. These results have been compared and show good agreement.

## Acknowledgments

This work has been partially supported by the Spanish Ministry MCEI under Consolider Ingenio 2010 Program, Project GENESIS-FV (CSD20006-0004), which also directly supports R. Herrero’s work through a FPI grant, and the European Commission within the project NACIR (226409-2) under the VII Framework Program.

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