# Assessment of the RACPC Performance under Diffuse Radiation for Use in BIPV System
## 2 Novel Rotationally Asymmetrical Compound Parabolic Concentrator (RACPC)  
A concentrator called rotationally asymmetrical compound parabolic concentrator (RACPC) was developed by [PERSON] et al. [32]. The design algorithm was implemented in software by using MATLAB(r). The design software requires the following input parameters: the index of refraction of the concentrator's material (n), the total height of the concentrator (H\({}_{\text{tot}}\)), the length of the PV cell (L\({}_{\text{PV}}\)), the half- acceptance angle (\(\theta_{\text{a}}\)), the width of the PV cell (W\({}_{\text{PV}}\)), the number of extreme rays (N); and the trial width of the entrance aperture (d\({}_{1}\)) [32].  
A 2D symmetrical design is first produced using the input parameters as is shown in Figure 2. The first 2D symmetrical design is created at position \"1\" by defining the coordinates of the side wall of the parabola and calculating the trial height taking into account that a number of extreme rays enter the concentrator at the critical angle. Second, the software compares the calculated entrance aperture with the trial entrance aperture; and using the different between the two apertures it adjusts the trial entrance aperture until after several iterations an acceptable error value is achieved [32]. Then, for the total height of the concentrator a similar process takes place, the difference between the calculated total height is compared with the desired total height and adjusted by varying the \"trial\" half-acceptance angle until an acceptable error value is reached. For the position \"2\" (Figure 2) the process is repeated [32].  
The new design is computed by incrementing the angle of rotation of the cross section by 1\({}^{\circ}\); and when an 180\({}^{\circ}\) rotation around the y-axis is completed, the process stops. Thus, the following three output parameters are obtained: the final width of the entrance, the final half-acceptance angle and the geometrical concentration gain of the concentrator [32].  
The advantages of the RACPC in comparison with a conventional CPC designs include [32]: (i) the flat entrance aperture of the RACPC helps to mould arrays of these concentrators, with a thin layer of the same material joining them together thus reducing the assembly cost of the system; (ii) the square exit aperture allows for the solar cell to be easily attached, and (iii) due to the concentration  
Figure 2: Demonstration of the angular rotation of the 2-D cross-sections to produce the rotationally asymmetrical compound parabolic concentrator (RACPC) [33].  
provided on both planes perpendicular to the propagation of light along the concentrator axis and a higher geometrical concentration gain, it can be considered as a 3D design.  
The detail design process, variation of RACPC designs, and extensive simulations to determine the optical concentration gain of each RACPC designs under direct irradiance has been explored in detail by [PERSON] et al. in [32]. They found that the RACPC can achieve the maximum optical concentration gain value of 6.2 for a 5 cm tall RACPC design. One specific design of RACPC-PV that has a total height of 3 cm was fabricated and tested indoor to verify its performance under direct irradiance [18]. A square PV cell of 1 cm sides was attached to the RACPC. The test which was carried out under standard test conditions (Irradiance of 1000 W/m\({}^{2}\), temperature of 25 \({}^{\circ}\)C and A.M. 1.5 G) demonstrated a greater maximum power output when compared with a similar size non-concentrating PV cell; achieving a gain of 3.33.  
However, diffuse solar irradiation also has an impact on the performance of the concentrator; particularly in countries at a higher latitude. So far, the performance of RACPC under diffuse radiation has never been investigated. The aim of this paper is to analyse and determine the concentrator's behavior under overcast day conditions. This will improve the overall understanding of overall the performance of this concentrator under direct and diffuse irradiance.