As the most abundant renewable energy on earth, solar energy has the advantages of cleanliness, sustainability, and wide distribution. It can effectively alleviate the energy and environmental crises caused by fossil energy, and is widely used in various fields of production and life. This energy source can be effectively utilized by a solar concentrating power system, which concentrates light and creates a high density of radiant energy flow. The compound parabolic concentrator (CPC) is a typical non-imaging concentrator, which is widely used in many fields such as photoelectric conversion, photothermal conversion, and photochemistry due to its advantages in light concentration performance and collection of solar radiation. Conventional CPC with circular absorbers, where the energy is concentrated in the top area can generate overheating, thus affecting the operation of the system. Based on the principle of non-imaging optics and the theory of differential geometric curves, an arc absorber solar compound parabolic concentrator (A-CPC) is constructed. Then its optical performances and solar radiation collection characteristics are also explored.

The areas of S-CPC that need to be improved are identified, and the mathematical model of A-CPC is established using the differential geometry method based on the non-imaging edge-ray principle. Then the geometric model was fabricated using 3D printing technology and the reliability of the model is verified by laser optical experiments. Meanwhile, optical simulation software is used for ray tracing simulation to determine the theoretical value of the position on the absorber, and the experimental and theoretical values are compared and analyzed. Following this, the concentrating characteristics of A-CPC are calculated and analyzed by using geometrical optics and solar radiation theory. It is analyzed in comparison with S-CPC mainly in terms of optical efficiency, energy flux density ,and radiation collection.

With the A-CPC model constructed by the theory, the width of the optical aperture and the height of the model is reduced by 15.6% and 30.3% respectively compared with S-CPC, which effectively reduces the manufacturing cost (Table 1). In the laser experiments, the maximum absolute errors between the experimental and theoretical values are 0.23 mm and 0.39 mm, and the average absolute errors are 0.18 mm and 0.15 mm (Fig. 7). The reliability of the constructed model is proved experimentally by taking into account the various influencing factors, within the allowable range of error. The A-CPC has an increased range of receivable angles and a 5% increase in average optical efficiency compared to the S-CPC, which enhances the ability to collect solar radiation (Fig. 8). The working time for beam radiation increased by an average of 31.38% per month, favoring the collection of more radiation. The enhancement ratio of working time matched the heat demand, with the greatest enhancement ratio during the winter months (Fig. 9). A-CPC can effectively improve the energy flow density on the top surface of the absorber when collecting solar radiation, realizing that the energy flow density on the top surface of the absorber is limited to a low level when the model is in operation, which is consistent with the theoretical model (Fig. 10). In addition, the annual radiation collection of A-CPC is 2267.51 MJ/m², which is 25.69% more than that of S-CPC (Fig. 12). At the same time, its energy consumption ratio is higher, which provides better economy.

Based on the edge-ray principle of non-imaging, a CPC with a curved absorber is constructed by using differential geometry. The optical performance and concentration characteristics are also explored using solar geometrical optics and radiation theory. It is shown that the A-CPC has an increased range of receivable angles and a 5 percentage points increase in average optical efficiency compared to the S-CPC. At the same time, the working time of direct radiation of A-CPC is increased by 1.2 h per month on average, which is 31% higher than that of S-CPC, and it has better weather adaptability. A-CPC improves the energy flow density distribution on the absorber surface and can effectively reduce the energy flow density in the top region of the absorber. The average energy flow density in the top region at an incidence angle of 30° decreased by 4.65 kW/m². A-CPC collects significantly more radiation throughout the year than S-CPC, with an increase of 234.3 MJ/m² for direct radiation and 229.1 MJ/m² for diffuse radiation. Meanwhile, it is smaller in size and requires less material to manufacture than S-CPC, which provides a better economy. The improvement of optical performance makes A-CPC potentially valuable for engineering applications.