2.1.

Concentration and Acceptance Angle Product (CAP)

As CPV has the goal of minimizing energy cost, several aspects have to be taken into account. A key aspect is an efficient and low-cost optical design, which is best met when a minimum number of elements are used, combined with relaxed tolerances and high concentrations, which decrease the size of high-efficiency solar cells for the same energy production. It is a difficult task to reach high concentration and high tolerance at the same time, so we have to find a trade-off between these two parameters.

One of the merit functions in CPV, which is the basis for our previous statement, is commonly interpreted as the CAP, and it is given by

Assuming that $n$ is the refractive index of the material surrounding the solar cell, it should be noted that: $\mathrm{CAP}\le n$ . This provides the theoretical limit on the capabilities of a system to transfer the flux from a source to the target derived from the conservation of étendue theorem. ² Most concentrators fail to approach this limit. The surrounding medium is sometimes air ( $n\approx 1$ ), and sometimes a clear silicone ( $n\approx 1.4$ to 1.5). CAP is useful because for a given concentrator architecture (the same number and type of optical elements), its value is practically constant.

2.2.

Optical Efficiency

Optical efficiency of the concentrator is defined as the light power transmission efficiency through the concentrator of the light that illuminates the concentrator’s entire entry aperture and reaches the target (solar cell). This definition is a wavelength dependent. Usually weighted with the ASTM G173 AM1.5D spectral distribution, ¹⁰ it is used by optics manufacturers as it is cell independent.

2.3.

Spectral and Spatial Nonuniformity on Cell Illumination

Typically, solar concentrators provide nonuniform irradiance on the cell. The nonuniform patterns can create efficiency losses, especially considering that solar cell grids are typically designed for uniform irradiance conditions. This is not because uniform irradiance distribution is optimal in terms of efficiency, ¹³ but because it is simple and it adapts better to arbitrary irradiance distributions.

When a nonuniform irradiance distribution creates a local photocurrent exceeding the peak tunneling current density, efficiency drop may occur. ^{14 , 15} Apart from this situation, if the irradiance distributions corresponding to spectral bands of the different junctions are matched, it is not a severe problem, even if these distributions are not uniform.

A different situation happens when the spectral irradiances over the different junctions are not matched for all points of the cell. Internal currents spreading perpendicular to the main current appear to balance the local photocurrent mismatch between junctions caused by mismatch of irradiance in their bands. ^{16 , 17} The sensitivity of multijunction cells to spectral irradiance distribution is expected to increase in the future, for four- and five-junction cells.

4.1.

Free-Form Concentrators

Breaking the rotational symmetry allows for an optical performance difficult to obtain with classical approaches. One of the best examples of an extremely asymmetric concentrator is the XR free-form technology, developed by the company LPI using the simultaneous multiple surfaces three-dimensional (SMS 3-D) design method ³⁵ (see Fig. 3).

Fig. 3

XR free-form concentrator. (a) CAD design of the concentrator. (b) Free-form lens of the XR free-form concentrator. (c) SMS design method on XR free-form concentrator.

Two free-form surfaces are designed with the SMS 3-D method [SMS curves contained in these surfaces, called spines and ribs, are shown in Fig. 3(a)]. The SOE is a highly asymmetric free-form surface [see Fig. 3(b)], and the homogenization is performed by a very short TIR prism that protrudes from the lens back (its length is similar to the cell side) [Fig. 3(c)]. Simulation results for XR show the acceptance angle of $\alpha =\pm 1.85\mathrm{deg}$ at $C_{\mathrm{g}}=1000\times$ , which implies a CAP $\sim 1.0$ , the highest ever reported to the authors’ knowledge. ³⁶

4.2.

Multifold Köhler Concentrators

Multifold Köhler systems, proprietary technology of LPI, ³⁷ represent a family of concentrators developed in recent years. Those concentrators work as the Köhler integration arrays produce a uniform irradiance on the solar cell. In CPV, Sandia Labs was the first company to use this concept in 1989. ³⁸ This photovoltaic concentrator has one Köhler integrating pair composed of a Fresnel lens as the POE and a single-surface imaging lens as the SOE, which encapsulates the cell. The secondary lens (single optical surface—SILO) is placed in the focal plane of the primary lens (Fresnel lens) and it images the Fresnel lens aperture onto the solar cell thus providing uniform irradiance distribution on the solar cell as the Fresnel lens aperture is uniformly illuminated by the sun. If the cell is squared, the primary can be a square trimmed without losing optical efficiency. The POE images the sun on the SOE aperture. Consequently, the SOE contour defines the acceptance angle. Concentrations higher than $300\times$ are not adequate because of the incapability of the SILO SOE to image the whole POE properly, whose angular size as seen from the SOE (the SOE “field-of-view” in imaging terminology) and the required magnification (POE to cell ratio) are too large for a single refractive surface to manage, especially for the wide spectrum required. In addition, the spectral uniformity between different junctions decreases with concentration. ³⁹

One proposed solution to this limitation is a new technology called multifold Köhler concentrators. ^{40 , 41} The main idea is to concentrate the sunlight through Köhler integrator pairs, divided into multiple channels, each one comprising two optical surfaces.

The most explored multifold Köhler concentrator is known as the FK4 concentrator ⁴⁰ that contains a Fresnel lens as the POE, and one free-form refractive surface as the SOE (see Fig. 4).

Fig. 4

The FK4 is an advanced fourfold Fresnel-Köhler concentrator. (a) The optical system is illustrated together with the edge-rays distribution. (b) Actual manufactured Fresnel lens POE and free-form SOE, both fourfold, are shown. (c and d) Actual CCD image of the cell plane under outdoor sun tracking. It is a white square illumination, indicating the excellent spatial and spectral uniformity provided.

The FK4 is fourfold symmetric. A standard version of this optics developed by companies Evonik and LPI, called Ventana™, in its first variant uses PMMA as POE material. It operates at $1024\times$ with an acceptance angle of $\pm 1.1\mathrm{deg}$ . ^{40 , 42} Outdoors electrical efficiency of 32.0% was measured with this Ventana™ when uses a 39.2% efficient Spectrolab C3MJ+ cell. ⁴³ The FK prototype with SOG Fresnel lens and Solar Junction A-SLAM™ cell using dilute-nitrides (cell efficiency approximately 42.0%), showed a single-cell concentrator maximum peak efficiency of 36.0% and regressed 35.6% efficiency, ⁴³ proximate to the current world record shown in Ref. 29.

Other types of multifold Köhler are designed for both refractive and reflective POEs. For instance, a fourfold Köhler approach to an asymmetric mirror was developed to address the reflective configuration ⁴⁴ [see Fig. 5(a)]. A fourfold Köhler FK4 configuration has a domed Fresnel lens ⁴⁵ in order to increase the acceptance angle of its flat Fresnel lens predecessor [see Fig. 5(b)]. Quite remarkable is Fresnel-RXI Köhler whose POE is a flat Fresnel lens and whose SOE is a fourfold free-form SMS 3-D RXI lens which contains two free-form surfaces [Fig. 5(c)]. It leads to a $\mathrm{CAP}=0.85$ , the highest reported for flat Fresnel POEs to the authors’ knowledge. ⁴⁶ Recently, a Fresnel-Köhler of ninefold was developed ⁴⁷ [shown in Fig. 5(d)]. This system was developed to pave the way for four-junction cell–based systems, and it keeps excellent spatial and spectral irradiance uniformity even for very high concentrations and very high temperatures, which affect the refractive index of the SOE.

Fig. 5

Different configurations of multifold Köhler family: (a) shadow-free mirror-based fourfold XR Köhler concentrator; (b) the domed-shaped fourfold Fresnel-Köhler; (c) Fresnel-RXI Köhler; and (d) ninefold Fresnel-Köhler.

High CAP value (shown in Fig. 6) may be used for maximizing other functions of merit in CPV not directly related with $C_{\mathrm{g}}$ and $\alpha$ (e.g., the electrical efficiency), described in Sec. 4.3.

Fig. 6

Concentration and acceptance angle product values of different Fresnel-based systems with rather good to excellent irradiance uniformity.

4.3.

Advanced Designs

Two main sources of conversion losses in present HCPV three-junction (3J) cells are: (1) still inefficient utilization of the solar spectrum and (2) the reflection losses of concentrator cells, mainly due to the grid line shading factor.

An external confinement cavity can recover the light reflected from 3J cells. By adding the external confinement cavity, the light reflected by both 3J cell metallic grid-lines and semiconductor surface is recovered. In this way, the concentration is reduced, the acceptance angle is maintained, and relative electrical efficiency is boosted. The proof-of-concept concentrator CFK was developed, ⁴⁸ and a relative efficiency increase of about 6.0% was measured at $18.45\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ with C3MJ+ solar cells ⁴³ (see Fig. 7). With higher concentrations and optimized grid-lines shading factor ( $fs$ ), we may reach an important relative electrical efficiency boost. For instance, if we use the FRXI architecture with external cavity, for irradiance level of $130\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ on the solar cell with the semiconductor reflectivity set to 3%, ⁴⁹ grid-lines and mirror reflectivity of 90% and $fs=11.45\%$ , we model a relative electrical efficiency gain of 11.4%. ⁵⁰

Fig. 7

(a) CFK in operation. The POE is placed in upper part. Some simulated rays impinging on the solar cell are reflected onto its surface and recovered by the cavity. (b) Measured IV-curves for CFK (higher current level, red curve) and FK (lower current level, blue curve), both corrected for the CSTC standard conditions: $\mathrm{DNI}=1000\mathrm{W}/{\mathrm{m}}^2$ and $T_{\text{cell}}=25\mathrm{deg}$ . The CFK shows $I_{\mathrm{sc}}=0.839$ A and a module electrical efficiency $\eta =32.5\%$ , while FK presents $I_{\mathrm{sc}}=0.791$ A and $\eta =30.8\%$ .

Spectrum splitting (SS) features address more efficient spectrum partition. An advanced SS concentrator was developed with a flat filter that works at 40 to $50\times$ (in order to be cost-effective), and the use of two coplanar commercial 3J and silicon cells that can share the same heat spreader, simplifying the heat management and wiring (see Fig. 8). ⁵⁰ Other benefits provided by this concept are: (1) use of an external confinement cavity that recovers light reflected by 3J cell; (2) SOE working with two cells, filter and cells, forms a single piece of dielectric, which simplifies its mounting; (3) this advanced Köhler concentrator addresses tight tolerances (at high concentration); and (4) cells work at high geometrical concentration ( $500\times$ ) and in this way contribute to the cost-effectiveness of this SS concept.

Fig. 8

(a) Asymmetric twofold Köhler-Fresnel lens illuminating the corresponding twofold RXI-RR SOE. (b) Onefold SOE RXI-RR with dichroic filter and external cavity.

Last few years many different approaches with the dichroic beam-splitting system were proposed. The Very High Efficiency Solar Cell program (VHESC, funded by DARPA) developed different cell designs for four-, five-, and six-junction systems, for a nontracking system (i.e., low concentration) (see Fig. 9). The five-junction system composed of a two-terminal/two-junction (GaInP/GaAs) cell, a silicon cell, and a three-terminal/two-junction (GaInAsP/GaInAs) cell led to 42.7% computed efficiency at $20\times$ for the two-junction cells and $8.7\times$ for the silicon cell. ⁵¹

Fig. 9

A 37.5% efficient, $40\times$ concentrator unit developed in the VHESC program.

Within the same VHESC program, another simpler four-junction system concentrator unit module was developed. It consists of a single-sided convex lens working at approximately $20\times$ and a dichroic filter to split the concentrated light between a two-junction/three-terminal (GaInP/GaAs) cell and another two-junction/three-terminal (GaInAsP/GaInAs) cell. It has the current world record for this type of a submodule (shown in Fig. 9) with an efficiency of 38.5% $\pm 1.9\%$ under the ASTM G173. ⁵² The VHESC module architecture is a good illustration of the beam division systems’ wiring and assembly complexity. The placement of the GaInP/GaAs cell in an oblique downward position well inside the module makes the heat sink design challenging.

Another approach ⁵³ is a system using a two-terminal/two-junction (GaInP/GaAs) cell and a GaSb infrared (IR) solar cell within a Cassegrain-type concentrator (see Fig. 10). The SS is done on the curved surface of the secondary mirror. The GaSb IR cell is placed after the secondary mirror. The GaInP/GaAs is set close to the apex of the primary. Independent heat sinks and wiring for the module are used (so the whole set is four-terminal). However, the difficulty of manufacturing and the cost of the multilayer dichroic filter needed on the curved surface (the one of the secondary mirror) represent drawbacks regarding this module.

Fig. 10

Dual-focus Cassegrain module concept. ⁵³

There are many different proposed SS solutions that represent different challenges: heat management for noncoplanar cells arrangement, assembling complexity, correspondence between experimental and simulated performance, cost-effectiveness (use of dichroic filters), etc. High concentration of sunlight allows the use of complex filters and multiple PV materials. In order to guarantee cost-effectiveness, the filter can be deposited directly on top of the PV cell, but due to thin film stress (possible cracking or flaking) this option requires careful attention to material mismatch and to the influence of temperature and flux gradients across the device.

SS systems of potentially higher practical efficiency than MJ cells are of special interest, due to the limits to the number of PV cells that in practice may be stacked on top of each other, as well as due to electrical, cooling, and material constraints.

Several photovoltaics SS systems for terrestrial applications have been prototyped, but in most cases, measurement results have not demonstrated the predicted efficiencies. There is also a lack of practical systems to demonstrate the feasibility of this technology and to bring the cost down. Practical experience leading to more efficient solutions and a larger production volume is necessary. This is true for all CPV systems.

For SS systems, it is especially hard to compete with tandem or MJ cells since large research efforts have recently been put in constant improvement of electrical conversion efficiency for those devices. Due to demonstrated high efficiency and simplicity of the tandem cell, this approach has a benefit on the market in comparison with the SS systems. The SS systems have added requirements to optics and do not have the same history of long-term operation.

4.4.

Other Concepts

Several other interesting optical designs address parameters such as the efficiency, CAP, etc. Weight and volume are the major concerns in order to decrease the transportation and tracking costs.

Several research groups and start-up companies are focused on planar CPV technologies. There is no commercial product on the market yet. Morgan Solar developed a light guide solar optic, which concentrates the light in planar direction, and has announced the same thickness and weight as a flat PV panel (see Fig. 11). The design eliminates the focal distance between optics and solar cell. With an ultrathin optical structure of acrylic and glass, this system traps the light inside the optics and redirects it onto the MJ cell placed at the optic’s center, ⁵⁴ reducing both depth and weight. This is a monolithic module with the glass SOE embedded in the center of the concentrator physically attached to the MJ cell. Concentrations of 1000 suns and acceptance angle of $\pm 0.9\mathrm{deg}$ are claimed. ⁵⁵

Fig. 11

Light-guide solar optic from Morgan Solar. ⁵⁴ The light is trapped and redirected to the multijunction cell in the center of the optics, reducing the depth requirements.

Vasylyev et al. presented a ring array concentrator (see Fig. 12), a point-focus design based on the concept of a reflective lens, which can be considered as a mirrored Fresnel lens. ⁵⁶ It combines an optical efficiency over a broad extension of the spectrum by using mirrors (thus avoiding the double refraction of lens) with the design flexibility and rear-focus operation of lenses. This system was designed to operate in a range of $C_{\mathrm{g}}\sim 400\times$ to $1100\times$ . Each ring that forms a quasi-Gaussian flux distribution is designed to illuminate a specific part of the receiver area. Hence, when the individual focal spots overlap, the resulting illumination pattern becomes rather uniform across the entire active area of the receiver.

Fig. 12

Ring array concentrator. ⁵⁶