Electro-optical study of a ×1024 concentrator photovoltaic system


  • This article was published online on 27 August 2012. An error was subsequently identified where Equation (5) was shown as Equation (4). This notice is included in the online and print versions to indicate that both have been corrected 6 December 2014.


Concentrator photovoltaic (CPV) systems are one of the most promising technologies for future energy supply. Several studies reported the interest of using a Fresnel lens coupled with a secondary optical element in such a system. For high concentration factor, the optimization of the optical configuration plays a key role regarding electrical performances. On the other hand, the thermal management of the solar cell is also critical to ensure a better module efficiency. This paper presents a study of a ×1024 CPV system performances and a methodology for estimating the optical chain efficiency, the cell temperature impact and the alignment requirements. Module efficiencies were then measured as a function of the cell temperature and correlated to optical performances through current-tension characterizations under real solar illumination conditions and the estimation of the power density received by the solar cell. The system yield was up to 27% for a cell temperature around 30 °C, confirming that high concentration ratio should be of great interest in the near future. A 1D model was also developed in order to quantify the possible improvements of this CPV system. Using a solar cell with an efficiency of 36.7% at ×600, we then demonstrated that the ×1024 CPV system could reach up to 30% in standard test conditions. Copyright © 2012 John Wiley & Sons, Ltd.


Since the 1990s, concentrator photovoltaic (CPV) systems using Fresnel lenses have been considered as an attractive technique for the reduction of the photovoltaic electricity production cost. Recently, significant advances have been performed on ×300 up to ×600 modules [1-7]. The use of secondary optical element (SOE) was largely studied because it enables to improve the alignment and assembly requirements, minimizing this way the energy cost production (€/kWh). The acceptance angle of CPV systems is also increased by using SOEs. Reflective truncated pyramid with an on-axis optical efficiency around 89% was the first optical component studied [8]. In this case, for an off-axis angle around 1°, 80% of the on-axis power is guided to the cell. Refractive SOEs (truncated pyramidal waveguide and spherical dome) bring the homogenization of the flux density received by the cell, which reduces serial resistances usually generated by a nonuniform irradiation (Gaussian-shaped beam profile). Dielectric-filled truncated pyramid exhibited on-axis optical efficiency of 81.8% [9]. The Light Prescriptions Innovators developed Fresnel–Köhler optical components that gave on-axis efficiency around 85% for a ×625 concentrator module. For an off-axis angle around 1.4°, this concentrator guides 90% of the on-axis power to the cell [10, 11]. They showed that this concentrator technology enhances both acceptance angle and homogenization of the flux received by the cell compared with conventional reflexive and refractive SOEs.

The size reduction of expensive epitaxial semiconductors is one of the most promising ways to reduce the electricity cost production in CPV power plant. This is possible by increasing the concentration ratio and by using a standard cell area of 0.3 to 1 cm². For high concentration ratio (typically up to ×1000 on a 1 cm² cell area), the choice of the SOE is critical to ensure the best module efficiency. Indeed, the focal length of such a system is higher than for conventional concentration ratio, needing an accurate optical alignment. Furthermore, the power density to be dissipated by the cell is also greater for high concentration ratio. The energy production cost is directly impacted by the choice of the heat sink technology (active or passive).

In this way, this paper presents optical, electrical and thermal characterization of a ×1024 concentrator system based on a reflective truncated pyramid SOE and an active heat sink. A real solar illumination set-up was developed that comprises a solar tracker, a ×1024 CPV module, a CCD camera and a cooling and micrometric translating sample holder. The first objective was to understand the on-axis and off-axis optical chain performances, the thermal solicitation of the cell and its impact on module efficiency. The second one was to identify and quantify the efficiency improvement of the system on the basis of an electro-optical 1D modelling.


The ×1024 CPV module studied in this work is presented in Figure 1(a). It was composed of a 320 × 320 mm² silicone on glass (SOG) Fresnel lens and a 1 cm² Concentrating Triple-Junction (CTJ) EMCORE (Somerset, New Jersey, US) solar cell mounted on a copper/alumina receiver and encapsulated with a silicone-based material (Dow Corning Sylgard 184, Midland, Michigan, US). The SOE was an inverted pyramidal reflector fixed on the receiver with the encapsulating material. A cooled sample holder was used for the management of thermal dissipation, and micrometric moving plates were mounted for better optical alignment accuracy. The module was fixed on a specific real solar illumination set-up (Figure 1(b)), which is a two-axes rotation tracking system coupled with a pyrheliometer for direct normal irradiance (DNI) measurements.

Figure 1.

(a) Scheme of the ×1024 concentrator photovoltaic (CPV) module and (b) real solar illumination set-up.

Current-tension and current-power behaviours of the solar cell were first characterized with a flash tester under various incident power densities at 25 °C by the Instituto of Energia Solar (IES) (Figure 2(a)). From these measurements, the solar cell efficiency of 36.7% was found for a ×600 concentration ratio. In order to understand the thermal solicitation of the cell and its impact on the module efficiency, we also determined the open-circuit voltage (Voc) variations as a function of the power density (dP) received by the cell. Figure 2(b) presents these results compared with EMCORE datasheets (Table 1) [12]. As already established in the state of the art [13], the open-circuit voltage (Voc) follows a logarithmic behaviour with the incident power density (dP ≥ 1). In our case, we found Equation (1).

display math(1)
Figure 2.

(a) Current-tension/current-power curves and (b) power density dependence on the Voc variation for the EMCORE concentrator triple-junction solar cell studied.

Table 1. Temperature dependence of the current density, the open circuit voltage and the efficiency of the concentrator triple-junction EMCORE solar cell [12].
ΔJsc+7.2 mA/m²/°C
ΔVoc−4 mV/°C
Δη6 × 10−2%/°C


The use of SOG Fresnel lens induces optical losses because of glass and silicone absorption, reflexion at interfaces and nonideal Fresnel grating. Spectrophotometric analysis, concentration efficiency measurement and imaging analysis of the spectral and geometrical energy distribution at the focal point were performed. The imaging analysis is based on a Lambertian diffusive screen placed at different distances from the Fresnel lens. An energy mapping of the light spot imaged on the screen was then acquired with a CCD camera. A spectral cartography of the light spot was recorded by placing an optical filter centred at 532 nm between the lens and the Lambertian screen. A picture was then taken for several screen positions allowing this way a whole description of the spectral and spatial distribution of the light around the focal point of the lens. Figure 3(a) presents the spot light sizes measured at 532 nm for different lens to screen distances. The spot light was considered as Gaussian-shaped beam, and its size was measured at 90% of the total energy (Figure 3(b)). For AM1.5D solar spectrum, the limiting junction of GaInP/GaAS/Ge solar cells in terms of current density is the top one (i.e. GaInP) [14]. Considering chromatic aberrations of the Fresnel lens, the energy spatial distribution in the 400–600 nm range has to match the solar cell size. In other words, the optical system (Fresnel lens coupled with SOE) has to be designed in such a way that the spectrum of light transmitted to the cell closely matches the spectrum for which this cell exhibits its highest efficiency. We found that for a distance of around 505 mm, 90% of the incident energy density at 532 nm is intercepted by the solar cell (Figure 3(a and b)). This position is considered as the best one to transmit the maximum light to the limiting junction with an illumination area close to the solar cell size (i.e. 1 cm²).

Figure 3.

(a) Spatial energy distribution measured on the screen at 532 nm for different lens to screen distances and (b) energy profile at 532 nm for a lens to Lambertian screen of 505 mm.

Spectrophotometric measurements were performed on a glass sample with a 200 µm-thick silicone layer in order to estimate the spectral response of the Fresnel lens. The transmission of this test sample balanced by the AM1.5 solar spectrum gives a 300–1700 nm integrated value of 89.5%. In order to determine the concentration efficiency of the lens, the grating geometrical defects such as tip rounding and a slightly different slope of the pitch have to be taken into account [15]. For a DNI of 650 W/m², we estimated the power transmitted through the Fresnel lens around 54 W. Considering a lens area of 0.1024 m², the lens efficiency is then 82%.

The SOE was a reflector with dimensions optimized through ray-tracing simulations. Its reflexion properties are plotted in Figure 4(a) as a function of the irradiation incidence angle. The SOE transfer function was calculated through its reflexion coefficient (average values of the curves in Figure 4(a)) and the energy profile at 532 nm for a lens to cell distance of 505 mm (Figure 3(b)). At these wavelength and position, only 10% of the incident flux is intercepted by the SOE, and 90% of the light coming from the Fresnel lens is directly collected by the solar cell. Furthermore, this element was bonded to the receiver with a 300 µm-thick silicone encapsulate that induced optical losses because of reflexion at the encapsulate/air interface (Figure 4(a)). The power density recovered by the SOE and the total power density received by the cell are plotted in Figure 4(b). We finally found a theoretical efficiency of the optical chain around ηOpt = 77% for a DNI of 650 W/m². The power density recovered by the SOE was around ηSOE = 7% of the incident power density, and losses due to the encapsulating material were estimated around 3%.

Figure 4.

(a) Reflectivity of the secondary optical element (SOE) as a function of the incident angle and of the silicone encapsulate/air interface and (b) decomposition of the power density in the optical chain.

The optical chain efficiency also depends on the operating temperature. It is well known that the thermo-mechanical deformation of the grating and the refraction index variation of the silicone with temperature have a significant impact on the concentration performances of the Fresnel lens. They tend indeed to shift the lens focus and increase the spot size [16-19]. As shown in Figure 5(a and b), the efficiency and the temperature of the lens were simultaneously measured as a function of DNI. One can notice that DNI strongly impacts the lens temperature. The efficiency of the optical chain was then modelled through the dependence of the Fresnel lens performances on the DNI and on the basis of the optical chain efficiency previously calculated for 650 W/m² (ηOpt = 77% for lens efficiency of 82%). As for the Fresnel lens, we assume that the yield of the optical chain follows a linear behaviour with DNI (Figure 5(b)).

Figure 5.

(a) Temperature variations of the Fresnel lens as a function of the direct normal irradiance (DNI) and (b) Fresnel lens and optical chain efficiencies as a function of the DNI.


Because the cell temperature assessment strongly depends on knowing Voc at 25 °C and at a given power density, we used Equation (2) to determine the temperature during irradiation, where T0 is the room temperature, inline image is the open-circuit voltage measured at T0 for a given power density, inline image is the measured open-circuit voltage and σ the temperature dependence coefficient of the open-circuit voltage (Table 1) [12].

display math(2)

With the cell receiver clamped on the cooled sample holder, we performed efficiency measurements of the ×1024 CPV system. A pyrheliometer is used to record the DNI, allowing this way an accurate measurement of the efficiency. The system efficiency was calculated by using Equation (3), where SLens is the lens area and PMax the maximum output power of the system:

display math(3)

The lens–cell distance was optimized using micrometric moving plates through the maximum short-circuit current (Icc) output. A distance of 500 ± 5 mm was found, which is in a good agreement with the results obtained with the imaging analysis (Figure 3(a)). The fill factor (FF) was quasi-constant for a lens to cell distance from 495 to 510 mm (around 81%). As reported in Figure 6(a), the efficiency varied from 25% up to 27% in the 30–70 °C range. The temperature dependence coefficient was Δη = −5 × 10−2%/°C, which is in good agreement with the EMCORE datasheet (Table 1: 6 × 10−2%/°C for a CTJ cell at 80 W/cm²) [12].

Figure 6.

(a) System efficiency measurements as a function of the cell temperature and (b) short-circuit current variations as a function of the direct normal irradiance (DNI).

For a cell temperature (Tcell) around 75 °C, we found that the system efficiency varied from 23.4% to 24.5% depending on the DNI. The best efficiency was obtained for DNI = 800 W/m². These measurements underline that the performances of a CPV system obviously depend on the DNI, which impacts not only simultaneously the cell efficiency and the cell temperature but also the lens efficiency. Indeed, the performances of SOG Fresnel lenses are known to be sensitive to temperature, so indirectly to DNI. The lens used was optimized by the manufacturer for a working room temperature. This failure was characterized by means of short-circuit current measurements as a function of the DNI (Figure 6(b)). One can notice a break slope in the Icc variations for DNI > 800 W/m².

In the same graphic, we plotted IES and EMCORE measurements that take into account the optical efficiency of the system (ηOpt = 77%). The discrepancy between this curve and experimental dots obtained for DNI < 950 W/m² can be explained by the impact of the lens temperature on its optical performances and by the decrease of the cell efficiency in the case of high power density. This will be discussed in more details in the modelling section.

Furthermore, measurements of the optical alignment tolerances of the system were carried out using the micrometric moving plates for x, y and z displacements of the solar cell. The data are plotted in Figures 7(a and b) compared with ray-tracing simulations results. Considering that 95% of the optimal efficiency (on-axis system) should be preserved in case of misalignments, the combination of the SOE with the Fresnel lens leads to ±3 mm for x displacement, ±13 mm for z displacement and ±0.3° for the off-axis angle. These results were in good agreement with the ray-tracing simulations, even if only the photons flux was taken into account in the modelling. This method is then well adapted and might be sufficient for the characterization of on-axis and off-axis CPV system performances.

Figure 7.

Measurements and ray-tracing simulations of (a) the optical alignment tolerances (Δx and Δz) and (b) the off-axis tolerances of the system.


Using the previous cell characterization and the estimation of the optical chain performances, we developed a 1D model on the basis of the external quantum efficiency (EQE) of the CTJ EMCORE solar cell measured with a Spequest instrument (LOT ORIEL, Massy, France) (Figure 8). The current densities of the top, middle and bottom junctions were respectively calculated from AM1.5D solar spectrum using Equation (4), where SI(λ) is the solar irradiance, q is the electronic charge, h is the Planck constant and c the light velocity.

display math(4)
Figure 8.

External quantum efficiency (EQE) of the concentrator triple-junction EMCORE solar cell—current densities of the top, middle and bottom junctions calculated from the AM1.5 solar spectrum.

The output power is the product of the lower current density of the three junctions by the open-circuit tension (Voc) and the FF. The Voc depends both on the cell temperature and on the power density received by the solar cell. We used the temperature dependence coefficient from the EMCORE datasheet (Table 1) and the logarithm law measured on the flash tester for the power density dependence (1). The temperature dependence of the current density was also taken into account from the EMCORE datasheet (Table 1) [12].

The optical chain efficiency estimated in the optical characterization chapter was used to calculate the power density received by the solar cell: ηOpt = −0.0214 × DNI + 90.702. From these results, the system efficiency can be expressed as Equation (5). In this equation, the FF is equal to 81%. The variation of this parameter with the DNI is estimated to be ±1%.

display math(5)

In Figure 9(a), measured and calculated short-circuit current (Isc) variations as a function of the DNI are plotted. One can observe a good agreement between modelling and experimental results, which indicates that the DNI dependence of the optical chain efficiency was well modelled. In the same graphic, the results of the modelling without this DNI dependence are also plotted giving this way the theoretical short-circuit current that could be achieved in the case of a constant optical chain efficiency (ηOpt = 77% = constant). In Figure 9(b), the measured and modelled system efficiencies are represented as a function of the estimated cell temperature. As for short-circuit current modelling, we calculated the theoretical system efficiency achieved without the DNI dependence of the optical chain yield. The efficiency of the CPV module could then rise up to 28.5% for Tcell = 30 °C. We believe that the optical design (e.g. Fresnel lens grating design) and the manufacturing process have to be optimized to guarantee stable performances and then an optimal yield in the 25 to 50 °C range.

Figure 9.

Comparison between experimental data and modelling: (a) short-circuit current as a function of direct normal irradiance (DNI) and (b) system efficiency as a function of estimated cell temperature.

An antireflective coating on the entrance side of the Fresnel lens can also significantly enhance the short-circuit current and then the ×1024 system efficiency. First measurements were performed and showed an increase of the short-circuit current and consequently of the system efficiency (Figures 10(a and b)). For an estimated cell around 30 °C, the system efficiency was increased up to 27.7%. The optimal lens to cell distance was found to be around 497 ± 5 mm instead of 505 ± 5 mm without antireflective coating. Alignment tolerances measurements will be performed and presented in a future study.

Figure 10.

Enhancement of the performances using a Fresnel lens with antireflective coating: (a) short-circuit measurements and (b) system efficiency measurements.


In this paper, an electro-optical study of a ×1024 CPV system was presented. The cell temperature impact and the alignment requirements were analysed in particular. The module efficiency was measured as a function of cell temperature and correlated to optical performances through current-tension characterizations under real solar illumination conditions. The efficiency was found to vary from 27% to 25% for Tcell ranging from 30 °C to 70 °C with an optical yield around ηOpt = 77% at 650 W/m². Almost 95% of this on-axis efficiency is preserved within alignment tolerances of ±3 mm in x, ±13 mm in z and off-axis angle of ±0.3°.

Finally, a 1D model that takes into account the EQE of the solar cell and the dependence of the lens efficiency on lens temperature was developed. We showed that by using a thermally stable lens, an improvement of the short-circuit current (+1 A) could be achieved for high DNI. The efficiency of the CPV module could then rise up to 28.5% for Tcell = 30 °C.

The future work concerns the development of a low-cost cooling system (active or passive) to ensure a cell temperature around 40 °C in operational conditions and then system efficiency around 27% for high direct solar irradiance. The use of the next generation of III–V solar cell could significantly increase the electrical performances. Indeed, we can expect cell efficiency around 39% for ×1024 concentration ratio inducing an STC yield around 30%. Regarding the dependence of the optical efficiency on lens temperature, future works have to be carried out to ensure an optimal yield in the temperature range of interest (typically from 25 to 50 °C).


This work has been financially supported by HELIOTROP SAS. The authors would like to acknowledge Mr Jean-Luc Martin, Mr Frédéric Mezzasalma, Mr Colasson Stéphane and the IES team for their support and for their significant contribution.