## 5 Conclusions  
In a conventional parabolic trough solar collector, the reflector is a complete parabolic trough mirror. This type of mirror tends to have significant fabrication errors, leading to larger focal spots and reduced optical efficiency. In this study, we proposed a novel cylindrical mirror-spliced trough solar system. Building on the previously developed parabolic trough system model, we introduced a new ray-tracing method to investigate the system's performance. This new spliced system consists of multiple strip-like cylindrical mirror reflectors, each aligned along a parabola line. The normal vector of each cylindrical mirror is consistent with the parabola normal vector at its installation point. The receiver is placed at the focal point formed by the centers of the cylindrical mirrors. Compared to trough mirrors, cylindrical mirrors are easier to manufacture and have lower surface slope errors under similar production conditions. Although cylindrical mirrors introduce some aberration in the reflected light, the efficiency loss is significantly outweighed by the benefits of reduced slope errors. Overall, the novel cylindrical mirror-spliced system outperforms conventional trough systems in terms of performance.  
We also introduced a new ray-tracing method and developed a MATLAB code based on the relevant equations. By comparing it with SolTrace software, we validated the accuracy of the method. Using the MATLAB program, we performed calculations and optimizations for the spliced cylindrical system with a cavity receiver, determining the optimal values of r/w and f/w for maximum net efficiency. We combined conventional trough mirrors and cylindrical mirrors with both tube and cavity receivers and evaluated the performance of three different systems by calculating their intercept factor, optical efficiency, and net efficiency. The conclusions of this study are as follows:  
1. A new ray-tracing method is proposed based on the transverse distribution of solar radiation. It has been validated with Soltrace, with the maximum intercept factor error in the calculations being less than 0.31%.
2. Under NS tracking modes, the optimal annual net efficiencies for the spliced cylindrical solar trough system with a cavity receiver is 65.5%. The optimal f/w ratio is 1.1, and the optimal r/w value is 0.017. This system has higher efficiency than conventional trough systems; this is because cylindrical mirrors can achieve lower slope errors and the impact of optical error is reduced.
* The trough system with a cavity receiver generally has lower intercept factors and optical efficiency compared to systems with tube receivers. However, due to reduced heat loss from the receiver and lower incident angle errors, the net efficiency achieved is higher. The annual net efficiency of the segmented cylindrical mirror system with a cavity receiver is 13.27% higher than that of a trough with a tube receiver, although the optical efficiency is 1.68% lower under the same design parameters.  
Conceptualization, B.L. and W.H.; methodology, B.L. and W.H.; software, B.L. and V.M.; validation, B.L. and V.M.; formal analysis, B.L. and V.M.; resources, W.H.; data curation, B.L. and V.M.; writing--original draft preparation, B.L. and V.M.; writing--review and editing, B.L. and V.M.; supervision, W.H.; project administration, W.H. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflicts of interest.