1. Introduction

Hybrid thermal concentrating photovoltaics (CPV) [1–4] have been regularly proposed as an interesting way of mixing low-temperature residential heating with cell cooling. However, no suggested approach has actually reached commercial use. This is partially because of the low quality of heat at low temperatures and the extra cost.

Lighting of indoor spaces requires the emission of bodies at very high temperatures. On Earth, the free and natural source of light is the sun, the surface of which radiates at above 5778 K. Humans only use a small fraction of the spectrum for vision. The exclusive use of solar light inside buildings can be achieved by mixing solar-light-distributing devices that redirect solar light to all parts of the building during daylight hours with intelligent architecture (windows, fanlights, etc.).

In fact, the use of transparent optical guides for solar lighting of buildings is already a commercial technology [5,6], and different prototypes of this method have been proposed [7–11]. This involves coupling concentrated sunlight into fibers or other guides made of plastic or glass. However, a long payback time would be required to produce light for indoor illumination through purely optical mechanisms because a concentrating infrastructure and a tracker system are required for capturing the light injected into the optics fibers; needs can be covered by a conventional CPV system.

2. Basic concept and advantages with respect to conventional CPV

A simple model for a hybrid lighting-CPV module is shown in Fig. 1 . It consists of a bifocal Fresnel lens parquet where part of the overall collector area is used for directing sunlight towards the optical guide, while the remaining area focuses the incoming light onto a solar cell for electrical energy conversion, as in a conventional CPV system. The corners of the CPV Fresnel lens are the least efficient areas of the lens because they need to redirect incoming light over larger angles and have a lower acceptance angle. These areas can be better made the most if they are devoted to the illumination system by shaping a new lens that focuses the sunlight on the fiber and constitutes the primary optical stage of the lighting system.

 

Fig. 1 Artist’s impression of the use of optical fibers in a CPV bi-concentration parquet of lenses.

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In Fig. 2 , an ideal quantitative case example is presented, showing the predictable advantage of using the hybrid lighting-CPV system. On the left-hand side, 100 W of solar energy is needed to obtain 2190 lm for illumination, if a 30% efficient multi-junction CPV system for PV electrical generation and a LED lamp are used. On the right, we predict that the same 2190 lm can be achieved if we inject only 35% of the direct sunlight [12] into fibers that we assume are only 65% efficient, leaving 65 W of solar power that can be converted into 21 W for other electrical applications.

 

Fig. 2 Comparative schema: classic CPV and Hybrid Lighting-CPV.

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Assuming a small additional cost for the Hybrid Lighting-CPV system, we can see that the hybrid concept could obtain an obvious advantage over the conventional CPV.

3. Limits of the hybrid approach

First, we will focus on the practical design limits of the illumination system. The optical limitations of lenses and fibers, as well as the thermal and transmission properties of materials involved, will impose limits on the hybrid operation.

3.1 Maximum optical concentration

The optical design of the illumination system has an additional constraint compared to CPV optical systems: the limited numerical aperture imposed by the fibers [13]. The higher the concentration ratio desired, the wider the cone of rays entering the fiber. However, the fiber will only transmit the rays within its numerical aperture (NA), which is defined as:

The concentration ratio is defined as the ratio between the entrance aperture area of the primary lens and the entrance area of the fiber. The limited NA imposed by the fiber leads to a maximum concentration ratio. Matching the NA of the fibers (determined by θ_inc,max) to the NA of the concentrated beam (determined by the angle setting the exit cone from the concentrator θ_lens), the above-mentioned concentration limit can be deduced:

Low-cost fibers are made of highly transparent plastic, such as polymethyl methacrylate (PMMA). Considering a typical value of NA = 0.55 for PMMA fibers, Eq. (2) yields a C_max of 993×. However, this figure must be reduced for practical concentrators owing to the effects described below.

3.2 Limitations due to fiber transmission loses and concentrating optics

Here, we only consider multimode fibers that have sufficient thickness to be analyzed by geometric optics [14]. Although the NA of the fiber defines the maximum incidence angle, the bulk absorption at the core and light leakages caused by the absorption at the cladding at every total internal reflection (TIR) [15] reduce considerably the practical value of the NA of the concentrated light beam for reducing power losses. In order to minimize the impact of these two sources of losses, absorption and TIR, only a small portion of the NA of the fibers must be used.

Figure 3 shows the angular transmission function of a particular PMMA fiber with NA = 0.55. The theoretical basis and concrete details used to obtain the transmission function vs. incidence angle can be reviewed in the appendix. This example case shows that while the angle of incidence is kept below 15° (equivalent to NA = 0.26), the transmission function is very flat and close to the maximum, but beyond that angle, the power losses become very significant. This means that although the NA of the fiber is 0.55, the NA of the concentrated beam should be limited to 0.26 for a good power transmission.

 

Fig. 3 Angular transmission function for a fiber 2 m long and 3 mm in diameter (α_core = 3.5 × 10⁻⁵ m⁻¹ and k_cladding = 1 × 10⁻⁵).

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The angular transmission function represents the power loss in the fiber for a single ray, and must be integrated to compute the total losses for all of the rays in a light cone produced by a lens with a given f-number (f#). Since the rays entering the lens are nearly perpendicular, we can assume that the rays inside the cone generated by the lens are all meridian rays. The fiber transmission as a function of the f-number (T_{fiber_cone}) of the primary lens is given then by Eq. (4), where the f-number corresponds to a particular incidence angle of the light cone (Eq. (3)):

The resulting fiber transmittance versus f-number is shown in Fig. 4 for the fiber with NA = 0.55. Before any further analysis, we can conclude that the higher the f-number is, the lower the power transmission losses are in the fiber.

 

Fig. 4 Transmission function vs. f-number for a fiber of NA = 0.5 (α_core = 3.5 × 10⁻⁵ m⁻¹ and k_cladding = 1 × 10⁻⁵).

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On the other hand, another source of losses to be considered is chromatic aberration caused by the primary lens. The larger the focal distance is, the higher the spatial effect of chromatic aberration at the focus is, which reduces the effective concentration and acceptance angle as detailed below. However, it should be desirable as a compact receptor in order to take advantage of its small size. Even more important, due to geometric and manufacturing constraints (as it is used a bifocal lens parquet), the f-number of the lighting part (f_lighting) cannot be larger than the f-number of the CPV part (f_CPV), but is, at most, equal, which imposes the following limit:

That means that considering typical CPV f-numbers in the range 1.3–2 and a collecting area percentage of 35% for the illumination part, a maximum f-number ranging between 2.2 and 3.4 is obtained for the lens of the illumination system.

3.3 Combined optical efficiency of the lighting concentrator system

An increase in the f-number causes the chromatic aberration associated with the lens to increase the spot size and then decrease the effective concentration ratio and acceptance angle. For a given concentration ratio, this effect leads to a decrease of the optical efficiency of the lighting lens for longer focal distance because some rays do not enter the fiber.

Assuming an optical design with an acceptance angle of 1°, and taking into account the refractive index variation between 400 nm and 750 nm (visible spectrum) of the primary PMMA lenses, we have analyzed the optical efficiency as a function of the f-number, calculated with a ray-tracing simulation using a Monte Carlo approach. The results of this simulation are shown in Fig. 5 with the curve labeled “Lens efficiency.”

 

Fig. 5 Global transmission efficiency, obtained as a product of the fiber and optical efficiencies, versus f-number for a fiber of NA = 0.55 (PMMA fiber of length 2 m and diameter 3 mm, α_core = 3.5 × 10⁻⁵ m⁻¹, and k_cladding = 1 × 10⁻⁵).

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If we combine these effects on the total optical efficiency of the system due to the fibers and the lenses we can obtain the global performance of the lighting concentrator part as a function of the f-number. This is shown as the red curve in Fig. 5.

Therefore, for the example case of fibers of NA = 0.55 and PMMA acrylic lenses, the optimum f-number for lengths between 2 and 15 meters ranges between 2 and 4. These values are practicable for adapting the lighting optics in a CPV module.

3.4 Limits of concentration level imposed by the fiber and primary lens material

Lens transmittance is relevant not only in the visible range, which affects the luminous flux of the illumination system, but also in the ultraviolet and infrared regions because these ranges are significantly absorbed by the PMMA fiber, contributing to temperature increases. Therefore, the maximum concentration achievable is also limited by the amount of non-lighting radiation entering the fiber. Additionally, UV affects the reliability of the fiber, especially that of the cladding [16].

Another point to be considered is that PMMA primary lenses can potentially filter more UV and IR than a Silicon On Glass (SOG) parquet of lenses. However, a reduction of UV and IR radiation decreases the efficiency of the CPV part, and this effect is even greater if multijunction cells are used. For that reason, an ideal hybrid system should filter the UV and IR only on the part of the parquet that focuses into the optical fiber.

4. Experimental results

This section describes the experiments carried out to determine the operating limits and transmission efficiency of plastic fibers. In accordance with the theoretical studies and simulations described above, the experiments have been conducted with several PMMA fibers of 2 and 3 mm diameter and high NA. The main characteristics of the measured fibers are n_core = 1.49 and n_cladding = 1.39, so the NA is 0.575.

In order to characterize the fiber absorption, it is necessary to measure the core and cladding absorption parameters. All the measurements have been completed with collimated light and a photopic sensor that provides a response equivalent to that of the human eye to the light coming from the optical fiber to be measured. The sensor consists of a solar cell with a photopic filter that integrates the luminous efficacy function (see Fig. 6 ).

 

Fig. 6 Sensor based on a solar cell to measure light transmission of optical fibers, including a photopic filter.

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To determine the absorption of the core, the spectral transmittance has been measured for fibers of two different lengths and of the same diameter. By using differential measurements, both spectral and absolute transmission values can be determined. Figure 7 shows an almost constant transmission value in the visible region of 96% per meter. Some other PMMA fibers with less luminosity have shown 80%/m transmission. Then the core absorption coefficient is deduced to be α_core = -ln(0.96) = 0.0408 m⁻¹.

 

Fig. 7 Spectral transmittance of 1 meter of a PMMA fiber and the luminous efficacy function.

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The angular transmission function of the fiber compared to the theoretical one is shown in Fig. 8 . From these results, the cladding losses and consequently the effective extinction coefficient of the cladding can be deduced by fitting experimental measurements with the theoretical curve. The values of k_cladding obtained from the measured optical fibers are around 1 × 10⁻⁴: the best value is 0.9 × 10⁻⁴, and the worst is 3 × 10⁻⁴.

 

Fig. 8 Angular transmission function experimentally obtained for a plastic fiber of NA = 0.55 (α_core = 3 × 10⁻² m⁻¹ and k_cladding = 1 × 10⁻⁴).

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4.1 Transmission losses vs. f-number

Using the solar-cell-based sensor, we measured the overall power transmission of the lighting system (including both the optics and the fiber) in real sunlight, with several lenses having the same diameter but different f-numbers.

The results of this experiment are shown in Fig. 9 . The measured values show good agreement with the shape of the theoretical curve. As discussed earlier, for low f-numbers, the efficiency decreases seen are due to the fiber losses and Fresnel losses in the lens, while for high f-numbers, the decrease is caused by the optical characteristics of the lens, specifically, because the chromatic aberration enlarges the spot size.

 

Fig. 9 Theoretical and measured efficiency of the lighting subsystem (PMMA fiber of length 2 m and diameter 3 mm).

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Longer fibers will slightly shift the maximum peak to higher f-numbers due to the longer optical path of light inside the fiber and the higher number of reflections (see the appendix for details of the transmission of a light ray inside an optical fiber).

4.2 Maximum concentration vs. fiber temperature

The temperature reached by the fiber is affected by the absorption of concentrated light by the core and cladding. Since PMMA softens at 85°C, in order to be conservative, we impose a maximum operational temperature of 65°C in exceptionally high ambient temperature and solar irradiation conditions.

The temperature increase at the entrance of the fiber, which is the hottest and most critical point, has been experimentally measured as a function of the concentration level by means of 1) an SOG Fresnel lens capable of concentrating up to 200 suns at the entrance of the fiber and 2) a diaphragm to vary the aperture area of the lens. A thermographic camera, the emissivity of which has been trimmed experimentally, was used to determine the temperature at the entrance of the fiber. Figure 10 shows the results of this experiment.

 

Fig. 10 Measured fiber temperature as a function of the concentration ratio.

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With the temperature limit of 65°C, the maximum concentration attainable on the fiber without any spectral filtering is 100× . Filtering the IR with a hot mirror, the maximum value increases to 150× , which is still attainable without any secondary optical element for the lighting system. It should be noted that, in the hybrid system, the concentration ratio of the electricity-generating part of the system would be much higher.

5. Conclusions

We have proposed a hybrid CPV module that simultaneously produces electricity and injects concentrated light into optical guides for lighting. It has been verified that the CPV module and the fiber optics for collection and distribution of visible light are compatible

The transmission efficiency versus the incidence angle has been studied as a function of the absorption coefficient of the core and the extinction coefficient of the cladding in order to understand the losses in fibers for concentrated light. It can be concluded that the higher the f-number of the light cone feeding the fiber is, the lower the losses are. However, this value is also limited by the optical efficiency of the lens versus the f-number and the compactness of the receptor. The optimal f-number ranges between 2 and 4.

PMMA optical fibers have been chosen for the first tests, which have been characterized experimentally. It has been concluded that the maximum concentration level is limited by the PMMA softening temperature to 100×, although higher concentrations are possible with UV and IR filtering. The f-number and concentration ratio allow us making progress on the design and fabrication of the optical part of the hybrid module. This continuing work will allow us to quantify the added benefit that light generation provides to CPV modules and systems for building integrated applications.

Appendix A

The light entering into a fiber is refracted according to Snell’s law. The angle of incidence (θ_inc) of the most tilted ray of light that can enter an optical fiber is limited by the NA according to Eq. (1); therefore, the angle of the ray of light inside the core of the fiber (θ_core) is given by

(A1)$${\theta }_{\text{core}}={\sin }^{-1}\left(\frac{n_{\text{air}}}{n_{\text{core}}}\sin {\theta }_{\text{inc}}\right).$$

For a fiber of length (L) and core diameter (d), as described in Fig. 11 , the number of reflections (N_ref) depends on the angle of the light ray in the core as shown in Eq. (A2):

 

Fig. 11 Schematic showing the parameters of the optical fiber and the lens.

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(A2)$$N_{\text{ref}}\left({\theta }_{\text{core}}\right)=\frac{L}{d}\tan {\theta }_{\text{core}}.$$

The total path (L_opt) covered by this ray is given by Eq. (A3):

(A3)$$L_{\text{opt}}\left({\theta }_{\text{core}}\right)=\frac{L}{\cos {\theta }_{\text{core}}}.$$

The losses at the core-cladding interface can be calculated by applying the Fresnel equations and using the complex refractive index of the cladding (ñ_cladding = n + jk), the imaginary part of which accounts for absorption losses. The extinction coefficient (k) represents the damping factor of the electromagnetic wave, so it is related to the absorption coefficient of the cladding (α_cladding) as shown in Eq. (A4):

(A4)$$k_{\text{cladding}}={\alpha }_{\text{cladding}}\frac{\lambda }{4\pi }.$$

η_TIR is defined as the effective reflectivity of the total internal reflection (TIR) at the core-cladding interface [17] for each ray angle inside the fiber. For n and k, we are assuming a constant value in the visible range, which is realistic for this approach:

(A5)$$R_{\perp }={\left[\frac{\cos {\theta }_{\text{reb}}-\sqrt{n_{\text{rel}}{}^2-{\sin }^2{\theta }_{\text{reb}}}}{\cos {\theta }_{\text{reb}}+\sqrt{n_{\text{rel}}{}^2-{\sin }^2{\theta }_{\text{reb}}}}\right]}^2,$$

(A6)$$R_{\perp }={\left[\frac{\cos {\theta }_{\text{reb}}-\sqrt{n_{\text{rel}}{}^2-{\sin }^2{\theta }_{\text{reb}}}}{\cos {\theta }_{\text{reb}}+\sqrt{n_{\text{rel}}{}^2-{\sin }^2{\theta }_{\text{reb}}}}\right]}^2,$$

(A7)$${\eta }_{TIR}\left({\theta }_{reb}\right)=\frac{\left|R_{\perp }\right|+\left|R_{\parallel }\right|}{2},$$

where $n_{rel}=\frac{{ñ}_{\text{cladding}}}{n_{\text{core}}}\text{ and }{\theta }_{\text{reb}}=90°-{\theta }_{\text{core}}.$

So, finally, the transmittance for a given incidence angle of a ray entering the fiber is expressed as

(A8)$${\mathcal{T}}_{\text{fiber}}\left({\theta }_{\text{core}}\right)=e^{-{\alpha }_{\text{core}}\cdot L_{\text{opt}}}\cdot {\eta }_{\text{TIR}}{}^{N_{\text{ref}}},$$

where α_core is the absorption coefficient of the core per unit of fiber length (it can be considered constant in the visible range with an error less than 2% for PMMA fibers with lengths up to 10 meters). We note that there are two clear components of the transmission expression: the first accounts for the losses in the core, and the second accounts for the losses in the cladding.

Acknowledgments

The authors would like to thank to Steve Askins, César Domínguez and Guillermo García for the help in the development of the experiments and to Marta Victoria for her useful comments. This work has been partially supported by the Spanish Ministry of Science and Innovation under the LUZ-CPV Project and the Comunidad de Madrid under the NUMANCIA-2 Project (Reference: S2009/ENE-1477). Rubén Núñez is thankful to the Spanish Ministerio de Economía y Competitividad for his FPI grant.

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