# A Concentrator Photovoltaic System Based on a Combination of Prism-Compound Parabolic Concentrators

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## Abstract

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## 1. Introduction

## 2. Proposed Sunlight Concentrator of CPV System

_{i}of the sunlight ray at the edge of the prism is equal to angle α of the prism (θ

_{i}= α). The refracted ray should be in the direction of the parabolic rim axis of the CPC (acceptance angle of CPC: θ

_{acc}). Based on Snell’s law, the relationship between θ

_{i}and θ

_{acc}is shown in Equation (1):

_{P}is the refractive index of the prism. Solving Equation (1), we can find the structure of the prism. For this CPV system, the effective sunlight collecting area is calculated by the product of CPC length and input size D (the input size D is indicated in Figure 3b). The output apertures are two edges of the slab waveguide whose area is the multiplication of the length of the CPC by thickness d (parameter d is also indicated in Figure 3b). Therefore, the geometric concentration ratio of the system, C

_{R}, is the input size D divided by two times the waveguide thickness, as shown in Equation (2).

## 3. Optical Analysis and Performance

_{PMMA}= 1.49, was selected for the prism, CPC, and slab waveguide. To evaluate the losses in the system, we inserted three luminous flux receivers in the simulation model, as shown in Figure 5.

#### 3.1. Optimization of the Shape of the CPC

_{CPC}. The C

_{CPC}is defined by the ratio between the input aperture size and the output aperture size of the CPC. The changing of the C

_{CPC}does not affect the geometric concentration ratio of the system, C

_{R}which was defined by Equation (2). We fixed the input aperture of the CPC (input size of system) to D = 200 mm. The thickness of the slab waveguide is d = 2 mm. Based on Equation (2), the concentration ratio of the system achieves C

_{R}= 50. Based on this, the geometry model of the sample CPC was created in LightTools™ for ray tracing analysis. The LightTools™ software was also used to study the behavior of rays within the P-CPC for different CPC structures. A total of 1000 rays were traced [4]. The ray-tracing analysis was conducted for a few different CPC structures. Figure 7 shows the variation of the P-CPC concentration system with different C

_{CPC}.

_{CPC}increases, the incident angle of sunlight at the surface of the prism decreases, so Fresnel loss also decreases. The leak at the parabolic rim and the slab waveguide also change with different C

_{CPC}s. In order to optimize the structure of P-CPC for maximum efficiency, we carried out a simulation with several different CPC concentration ratio C

_{CPC}ranging from 2 to 8 in 0.5 increments. Figure 8 shows the variation of optical efficiencies at different C

_{CPC}concentration ratios for the CPC. The simulation for optical efficiency of a sunlight concentrator based on a P-CPC was implemented. In the implementation we included material attenuation, Fresnel reflection losses, and geometrical losses (the leak at the parabolic wall of the CPC and the bottom surface of the slab waveguide). Figure 8 shows that C

_{CPC}= 3.5 is the optimal value for the CPC to obtain the highest efficiency of 89%.

#### 3.2. The Dependence of Efficiency on the System Concentration Ratio C_{R}

_{R}decreases from 100 to 50 in the step of 10. Figure 10a illustrates the P-CPC structures with some different slab waveguide thicknesses, d = 1 mm, 1.5 mm, and 2 mm, respectively. Figure 10b shows the simulated optical efficiency at different system concentration ratios. It can be seen that because of dispersion, system efficiency η decreases almost linearly with the increase of C

_{R}. The lower concentration ratio can provide higher optical efficiency, but it also increases the area requirement of solar cells.

#### 3.3. Tolerance of the System

#### 3.4. Irradiance Distribution on the Surface of the Solar Cell

^{2}, the minimum irradiation was 285 W/m

^{2}, and the average irradiance was 299 W/m

^{2}. A uniformity Equation (4) [26] was adopted to calculate the uniformity of P-CPC concentrator, which reached 92.5%. It is clear that the proposed P-CPC can provide excellent irradiance uniformity on the cell.

#### 3.5. Proposed Large-Scale System and Discussion

_{R}= 50 proposed in this study, III–V multi-junction solar cells are suggested. Multi-junction solar cells made of III–V compound semiconductors can have efficiencies of more than 40%. Although they are expensive, the smaller size solar cells for higher concentration ratios would make the system more cost-effective.

^{2}as shown in Figure 14. Figure 15 shows the power of sunlight at the collecting surface of CPV system and output power at different times. The total output energy per day can be calculated by integration of output power over time. Based on Figure 15, the total solar energy along a day at the output is 18 KWh. Using multi-junction solar cells made of III–V compound semiconductors which have efficiencies of more than 40%, the system can generate about 7.2 KWh of electricity per day.

## 4. Conclusions

_{geo}= 50 for the proposed concentrator system. In addition, the angular tolerance (acceptance angles) in the NS and the EW directions was also analyzed. By using a P-CPC, an acceptance angle of ±6° was achieved in the EW direction. This allows us to use a less accurate sun tracking system, such as a seasonal sun tracking system along the EW direction, as a cost-effective solution. This study is the first to use a combination of a prism and a CPC for a solar concentration system. The proposed system is very suitable for large-scale purposes. It shows great potential for commercial- and industrial-scale CPV applications. In the future, we will try to implement experimentation under real conditions to verify the accuracy of the simulation and the commercial viability of the system.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Conventional CPV systems using: (

**a**) a Fresnel lens; (

**b**) a CPC; (

**c**) Solar concentrator using a combination of prism-CPC.

**Figure 2.**(

**a**) A symmetrical CPC; and (

**b**) ray tracing of the sunlight beam that is parallel to the axis of the parabolic rim.

**Figure 7.**Schematic diagram of ray-tracing results for the P-CPC concentration system with different shapes of CPCs that have C

_{CPC}= 2.5; 3.5 and 4.5.

**Figure 10.**(

**a**) The variation of the P-CPC shape; and (

**b**) the variation of optical efficiency at different system concentration ratios (C

_{R}).

**Figure 12.**Variation of optical efficiency of the concentrator at different angular deviations along the (

**a**) EW direction; and (

**b**) NS direction.

**Figure 13.**(

**a**) A 2D irradiance distributions on the exit port of P-CPC; and (

**b**) a 3D irradiance distributions on the exit port of P-CPC.

**Figure 15.**Power of sunlight at the collecting surface (input power) and output power from solar concentration system at different times of the day.

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**MDPI and ACS Style**

Vu, N.H.; Shin, S. A Concentrator Photovoltaic System Based on a Combination of Prism-Compound Parabolic Concentrators. *Energies* **2016**, *9*, 645.
https://doi.org/10.3390/en9080645

**AMA Style**

Vu NH, Shin S. A Concentrator Photovoltaic System Based on a Combination of Prism-Compound Parabolic Concentrators. *Energies*. 2016; 9(8):645.
https://doi.org/10.3390/en9080645

**Chicago/Turabian Style**

Vu, Ngoc Hai, and Seoyong Shin. 2016. "A Concentrator Photovoltaic System Based on a Combination of Prism-Compound Parabolic Concentrators" *Energies* 9, no. 8: 645.
https://doi.org/10.3390/en9080645