## Improving performances of Fresnel CPV systems: Fresnel-RXI Köhler concentrator |

Optics Express, Vol. 22, Issue S2, pp. A205-A210 (2014)

http://dx.doi.org/10.1364/OE.22.00A205

Acrobat PDF (1397 KB)

### Abstract

The optical design presented here has been done in order to achieve superior optical performance in comparison with the state-of-the-art Fresnel CPV systems. The design consists of a Photovoltaic Concentrator (CPV) comprising a Fresnel lens (F) as a Primary Optical Element (POE) and a dielectric solid RXI as a Secondary Optical Element (SOE), both with free-form surfaces (i.e. neither rotational nor linearly symmetric). It is the first time the RXI-type geometry has been applied to a CPV secondary. This concentrator has ultra-high *CAP* value ready to accommodate more efficient cells eventually to be developed and used commercially in future.

© 2014 Optical Society of America

## 1. Introduction

*CAP*) [2] in CPV optical design. It is:where

*C*is the geometrical concentration defined as the ratio of the concentrator entry aperture area to the solar cell active area and the acceptance angle (

_{g}*α*) is defined as the incidence angle at which concentrator collects 90% of the on-axis power [1]. For a given concentrator architecture, the

*CAP*value is practically constant. The

*CAP*value has the theoretical upper limit derived from the conservation of étendue theorem [2]. Assuming that

*n*is the refractive index of the material surrounding solar cell, it is

3. E. A. Katz, J. M. Gordon, and D. Feuermann, “Effects of ultra-high flux and intensity distribution in multi-junction solar cells,” Prog. Photovolt. Res. Appl. **14**(4), 297–303 (2006). [CrossRef]

4. J. M. Gordon, E. A. Katz, W. Tassew, and D. Feuermann, “Photovoltaic hysteresis and its ramifications for concentrator solar cell design and diagnostics,” Appl. Phys. Lett. **86**(7), 073508 (2005). [CrossRef]

*FF*) loss is produced in MJ cells if different wavelengths have different irradiance distribution (known as chromatic aberration [7]) due to local current mismatch between top and middle cells.

8. P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. **43**(7), 1489–1502 (2004). [CrossRef]

*C*and high

_{g}*α*(i.e. high

*CAP*). Optical free-form surfaces can be manufactured with classical techniques: embossing, compression molding, etc. used for the POE, plastic injection and glass molding (widely known in automotive industry) for the SOE. The production cost is essentially the same as for non-free-form elements; with their superior optical performance.

## 2. Fresnel-RXI Köhler (FRXI) concentrator design

10. J. C. Miñano, J. C. Gonźlez, and P. Benítez, “A high-gain, compact, nonimaging concentrator: RXI,” Appl. Opt. **34**(34), 7850–7856 (1995). [CrossRef] [PubMed]

8. P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. **43**(7), 1489–1502 (2004). [CrossRef]

*WF1*and

_{i}/WF1_{o}*WF2*) are to be coupled in order to calculate two free-form surfaces where one of them passes through one prescribed curve and may be consistent with normal vectors of this curve. This curve may be obtained by the SMS 2D calculation using, for instance,

_{i}/WF2_{o}*WF1*, and a third pair of wavefronts,

_{i}/WF1_{o}*WF3*(see Fig. 2). In our design, normal vectors at the points of the SMS curve are close to the normal vectors of the SMS surface, so we are achieving a partially coupled third pair of wavefronts. As the starting point of the SMS 2D we use a point

_{i}/WF3_{o}*P*placed on the front RI surface whose normal (

**) is chosen. Let**

*n*_{P}*WF1*be the spherical output wavefront originated at one corner

_{o}*(-x*and

_{0}, y_{0}, 0)*WF3*its counterpart on the other corner of the cell

_{o}*(-x*.The rays of the input plane wavefronts

_{0}, -y_{0}, 0)*WF1*and

_{i}*WF3*make an angle

_{i}*-α/2*and

*α/2*in the

*yz*-plane, to the direction connecting the center of the cell and center of the POE Fresnel lens unit, respectively. The optical path length (

*OPL*) is constant. We are doing the SMS method sequence and calculating the “seed” curve as the profile of two-mirror (XX) system.

*WF1*and

_{i}/WF1_{o}*WF2*) in a direction perpendicular to the “seed” curve. The

_{i}/WF2_{o}*WF2*is defined as the spherical wavefront placed at

_{o}*(x*, and the

_{0}, y_{0}, 0)*WF2*is a plane wavefront whose rays make an angle

_{i}*–α/2*in the

*xz*-plane to the direction connecting the center of the receiver with the center of the Fresnel lens unit meanwhile the rays of the

*WF1*make an angle

_{i}*α/2*to the same direction (see Fig. 3). During the SMS 3D calculation, the RXI is considered as a three surface optical device. Input ray bundles are first refracted on the front surface (R), than reflected on the back surface (X) and reflected once more on the front surface (I), without considering the actual surface position (i.e. if rays intercept previously other surface, they are not deflected by it). The initial front refractive surface (R

_{0}) is chosen as a surface obtained by extruding the “seed” curve in the

*xz*-direction. Normal congruences

*WF1*and

_{i}*WF2*are refracted on the R

_{i}_{0}surface, perfectly coupled with normal congruences

*WF1*and

_{o}*WF2*, respectively, and new surfaces X and I are recalculated while maintaining the

_{o}*OPL*constant. The calculated I surface is considered as a new R surface (R

_{1}) and the described process is repeated

*N*times until the sequence of surfaces R

_{N}converges towards the final design. Calculated SMS points may be organized in chains perpendicular to the “seed” curve. Once the surfaces are calculated, the resulting chains are interpolated by means of Non-Uniform Rational B-Spline (

*NURBS*) surfaces that can be analyzed through ray tracing.

## 3. Simulation results for Köhler RXI concentrators

*f*-number of

*f*/1.4 (where

*f*-number is the ratio of the distance between the cell and Fresnel lens to the Fresnel lens diagonal, i.e. a purely geometrical definition, without the usual optical interpretation). The SOE area is below 4% of the Fresnel lens. SOE size is reduced for smaller

*f*-numbers. RXI without frontal metallization is done in order to make the design cheaper and easier to manufacture.

12. G. Butel, B. Coughenour, H. Macleod, C. Kennedy, B. Olbert, and J. R. Angel, “Second-surface silvered glass solar mirrors of very high reflectance,” Proc. SPIE **8108**, 81080L (2011). [CrossRef]

### 3.1. Concentration-acceptance angle product (CAP)

*CAP*values of our designs. A merit function called effective

*CAP*(

*CAP**) is defined by substituting in Eq. (1) angle

*α*by the angle

*α**that is the minimum sun’s tilting angle from the on-axis position at which the cell photocurrent reduces to 90% of its on-axis value. The value of

*CAP**can be experimentally measured [13

13. P. Benítez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express **18**(S1), A25–A40 (2010). [CrossRef]

*f*-number the XRXI design is obtained. The angular acceptance increased from ± 1.02° to ± 1.24° (see Table 1). This design has strong theoretical importance with the

*CAP*value as one of two highest ever obtained in a CPV, and among Köhler designs being the highest [14].

### 3.2. Optical efficiency

*AM1.5d ASTM G173*spectrum. Table 2 contains the effective optical efficiency calculated by weighting the polychromatic optical efficiency by the EQEs of a “standard” 3J solar cell receiver [13

13. P. Benítez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express **18**(S1), A25–A40 (2010). [CrossRef]

### 3.3. Irradiance and intensity on the cell

*AM1.5d ASTM G173*spectrum so that the integral value for each subrange equals unity.

## 4. Comparison

13. P. Benítez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express **18**(S1), A25–A40 (2010). [CrossRef]

15. J. C. Miñano, P. Benítez, P. Zamora, M. Buljan, R. Mohedano, and A. Santamaría, “Free-form optics for Fresnel-lens-based photovoltaic concentrators,” Opt. Express **21**(S3), A494–A502 (2013). [CrossRef] [PubMed]

*f*-number) is listed together with the

*C*of different configurations (Table 3). This table corrects for some mistakes found in Fig. 8 of Ref [15

_{g}15. J. C. Miñano, P. Benítez, P. Zamora, M. Buljan, R. Mohedano, and A. Santamaría, “Free-form optics for Fresnel-lens-based photovoltaic concentrators,” Opt. Express **21**(S3), A494–A502 (2013). [CrossRef] [PubMed]

*CAP*value in comparison with other concentrators (Fig. 5 (Right)).

## 5. Conclusions

*CAP*value outperforms the conventional Fresnel-based HCPV concentrators. Good irradiance uniformity and chromatic balance with a high tolerance angle at high concentration values is obtained and that leads to the advanced features of these systems.

## Acknowledgments

## References and links

1. | A. Luque, |

2. | P. Benítez and J. C. Miñano, “Concentrator optics for the next generation photovoltaics,” in |

3. | E. A. Katz, J. M. Gordon, and D. Feuermann, “Effects of ultra-high flux and intensity distribution in multi-junction solar cells,” Prog. Photovolt. Res. Appl. |

4. | J. M. Gordon, E. A. Katz, W. Tassew, and D. Feuermann, “Photovoltaic hysteresis and its ramifications for concentrator solar cell design and diagnostics,” Appl. Phys. Lett. |

5. | A. Braun, B. Hirsch, E. A. Katz, J. M. Gordon, W. Guter, and A. W. Bett, “Localized radiation effects on tunnel diode transitions in multi-junction concentrator solar cells,” Sol. Energy Mater. Sol. Cells |

6. | J. M. Olson, “Simulation of nonuniform irradiance in multijunction III-V solar cells,” in |

7. | S. Kurtz and M. J. O’Neill, “Estimating and controlling chromatic aberration losses for two-junction, two terminal devices in refractive concentrator systems,” in |

8. | P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. |

9. | R. Winston, J. C. Miñano, and P. Benítez, |

10. | J. C. Miñano, J. C. Gonźlez, and P. Benítez, “A high-gain, compact, nonimaging concentrator: RXI,” Appl. Opt. |

11. | J. C. Miñano, M. Hernandez, P. Benítez, J. Blen, O. Dross, R. Mohedano, and A. Santamaría, “Free-form integrator array optics,” Proc. SPIE |

12. | G. Butel, B. Coughenour, H. Macleod, C. Kennedy, B. Olbert, and J. R. Angel, “Second-surface silvered glass solar mirrors of very high reflectance,” Proc. SPIE |

13. | P. Benítez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express |

14. | M. Buljan, P. Benítez, R. Mohedano, and J. C. Miñano, “Improving performances of Fresnel CPV systems: Fresnel RXI Köhler concentrator,” in |

15. | J. C. Miñano, P. Benítez, P. Zamora, M. Buljan, R. Mohedano, and A. Santamaría, “Free-form optics for Fresnel-lens-based photovoltaic concentrators,” Opt. Express |

**OCIS Codes**

(080.2740) Geometric optics : Geometric optical design

(220.1770) Optical design and fabrication : Concentrators

(350.6050) Other areas of optics : Solar energy

(220.4298) Optical design and fabrication : Nonimaging optics

**ToC Category:**

Solar Concentrators

**History**

Original Manuscript: November 4, 2013

Revised Manuscript: December 22, 2013

Manuscript Accepted: December 23, 2013

Published: January 16, 2014

**Citation**

Marina Buljan, Juan C. Miñano, Pablo Benítez, Rubén Mohedano, and Julio Chaves, "Improving performances of Fresnel CPV systems: Fresnel-RXI Köhler concentrator," Opt. Express **22**, A205-A210 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-S2-A205

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### References

- A. Luque, Solar Cells and Optics for Photovoltaic Concentration (Adam Hilger, 1989), pp. 205–238.
- P. Benítez and J. C. Miñano, “Concentrator optics for the next generation photovoltaics,” in Next Generation Photovoltaics: High Efficiency through Full Spectrum Utilization, A. Marti and A. Luque, eds. (Taylor and Francis, 2004), Chap. 13, pp. 285–325.
- E. A. Katz, J. M. Gordon, and D. Feuermann, “Effects of ultra-high flux and intensity distribution in multi-junction solar cells,” Prog. Photovolt. Res. Appl.14(4), 297–303 (2006). [CrossRef]
- J. M. Gordon, E. A. Katz, W. Tassew, and D. Feuermann, “Photovoltaic hysteresis and its ramifications for concentrator solar cell design and diagnostics,” Appl. Phys. Lett.86(7), 073508 (2005). [CrossRef]
- A. Braun, B. Hirsch, E. A. Katz, J. M. Gordon, W. Guter, and A. W. Bett, “Localized radiation effects on tunnel diode transitions in multi-junction concentrator solar cells,” Sol. Energy Mater. Sol. Cells93(9), 1692–1695 (2009). [CrossRef]
- J. M. Olson, “Simulation of nonuniform irradiance in multijunction III-V solar cells,” in 35th IEEE Photovoltaic Specialists Conference (PVSC) (2010), pp. 201–204.
- S. Kurtz and M. J. O’Neill, “Estimating and controlling chromatic aberration losses for two-junction, two terminal devices in refractive concentrator systems,” in Proceedings of 25th Photovoltaic Specialists Conference (Washington, DC, 1996), pp. 361–367.
- P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004). [CrossRef]
- R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics, 181–281(Elsevier-Academic Press, New York, 2005).
- J. C. Miñano, J. C. Gonźlez, and P. Benítez, “A high-gain, compact, nonimaging concentrator: RXI,” Appl. Opt.34(34), 7850–7856 (1995). [CrossRef] [PubMed]
- J. C. Miñano, M. Hernandez, P. Benítez, J. Blen, O. Dross, R. Mohedano, and A. Santamaría, “Free-form integrator array optics,” Proc. SPIE5942, 59420C (2005).
- G. Butel, B. Coughenour, H. Macleod, C. Kennedy, B. Olbert, and J. R. Angel, “Second-surface silvered glass solar mirrors of very high reflectance,” Proc. SPIE8108, 81080L (2011). [CrossRef]
- P. Benítez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express18(S1), A25–A40 (2010). [CrossRef]
- M. Buljan, P. Benítez, R. Mohedano, and J. C. Miñano, “Improving performances of Fresnel CPV systems: Fresnel RXI Köhler concentrator,” in Proceedings of 25th EU PVSEC, 5th World Conference on Photovoltaic Energy Conversion (Valencia, 2010), pp. 930–936.
- J. C. Miñano, P. Benítez, P. Zamora, M. Buljan, R. Mohedano, and A. Santamaría, “Free-form optics for Fresnel-lens-based photovoltaic concentrators,” Opt. Express21(S3), A494–A502 (2013). [CrossRef] [PubMed]

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