## 1 Introduction  
A concentrated photovoltaic (CPV) unit is generally composed of a primary optical element (POE), a secondary optical element (SOE) and a solar cell. The function of the POE is to concentrate a large-area solar energy into a small III-V solar cell. Furthermore, the SOE is applied to redirect the sun light into the solar cell and to distribute the energy uniformly on the solar cell [1; 2; 3]. The most common type of refractive POE is a flat Fresnel lens. In addition, there are two major materials for Fresnel lens, _i.e._, PMMA and Silicone-on-Glass, and the latter is believed to have a better outdoor life and reliability under solar radiation and humidity [4; 5; 6; 7]. If only a POE is applied in a photovoltaic system, nonuniformity of the concentrated distribution on the solar cell surface is observed, resulting in localized hot spot or even damage of the solar cell [1; 8]. Localized hot spots and poor uniformity will reduce efficiency of the photovoltaic system and service life of the solar cell. Keeping the power production of a photovoltaic system in real operation conditions under influences of wind and vibration is important. Therefore, precise orientation to the sun of the photovoltaic system is required. One of the ways for lowering the effect of the inaccurate orientation on the concentrator system power efficiency and for improving the irradiation uniformity on the solar cell surface is the application of the SOE located before the solar cell [8; 9]. Secondary optical elements are specular or refracting optical elements of various forms. The parameters of SOE used in a CPV unit are usually tailored according to the design parameters of the POE, performance requirements and the size of the solar cell [8]. Using a SOE with a Fresnel lens in a CPV unit will achieve high optical efficiency, lower the sensitivity to the sun tracking error, and improve the uniformity of irradiance distribution on a solar cell [8; 9; 10]. The three major factors used in evaluating a CPV system include the optical efficiency, the acceptance angle and the uniformity of irradiance distribution on the solar cell. The optical efficiency of a photovoltaic system is defined as the ratio of the radiant flux on the solar cell and the POE surface. The acceptance angle \(\theta_{90\%}\) is commonly defined as the incidence angle corresponding to 90% of the maximum optical efficiency at normal incidence. In other words, the optical characteristic of a CPV unit is highly affected by the design of the SOE. Therefore, an optimum SOE tailored for a specific CPV unit is essential to achieve the highest optical performance. [PERSON] _et al._ proposed optimization of SOE for CPV unit with a flat Fresnel lens [8]. Recently, [PERSON] and [PERSON] applied simplex algorithm to attain optimum prism displacements of a Fresnel lens, leading to a uniformity irradiance on the solar cell with broad solar spectrum [11]. [PERSON] _et al._ achieved high uniformity and chromatic balance for CPV system by using a dielectric solid RXI-type SOE in a CPV system comprising a flat Fresnel lens [12]. [PERSON] _et al._ analyzed the performance of a CPV module considering the temperature-dependent model of the optical elements and the solar cell. [13]. In this study, the size of the square Fresnel lens is 40 mm \(\times\) 40 mm, the size the solar cell is 1.25 mm \(\times\) 1.25 mm, and the theoretical geometric concentration ratio is 1024. The square solar cell is placed on the focal plane of the POE, of which the focal length is 130.1 mm. The Fresnel lens is made by silicone-on-glass with urethane prism grooves of pitch 0.2 mm on a 2 mm thick flat BK7 glass, and the internal transmittance of BK7 is assumed as 0.99 in the simulation [12]. The commercial package, ASAP (Breault Research Organization, Inc., Tucson, AZ, USA), was applied to perform the optical simulations in this research. In addition, light source with a divergence angle of 0.265 degrees and AM1.5D were assumed in the simulation.