## 3 Results
### Optimization of the Cylindrical Mirror-Spliced Trough  
The biggest challenge when using spliced cylindrical mirrors instead of parabolic trough mirrors as reflectors is the significant aberration present in cylindrical mirrors. It is necessary to control the width of the cylindrical mirror to reduce the effects of spherical aberrations. The requirements for optical imaging are that the ratio of mirror aperture to focal length should be less than 1/10.8, and the requirements for solar collectors are more moderate. In this study, the width of the cylindrical mirror should not exceed 1/5 of the trough width. When using tube receivers and cavity receivers, this value corresponds to a mirror width to focal length ratio of 1/2.5 and 1/6, respectively, which is well below the requirements for optical imaging. The mylindrical mirrors' slope error is lower than trough mirrors, which is approximated to be 1-2 mrad while the slope error of parabolic trough mirrors is about 3-4 mrad. Therefore, using cylindrical mirrors instead of convectional parabolic trough mirrors as reflectors can effectively reduce manufacturing complexity and lower slope errors, making the performance almost indistinguishable from that of conventional trough solar collector systems with similar slope errors. In Figure 3, we calculated the intercept factor of the cylindrical mirror-spliced solar collector system with a cavity receiver as the incident angle changes under different mirror slope errors. When the incident angle is 0.2 rad and the slope error is 1 mrad, the system intercept factor is 88.6%. When it reached 3 mrad, the intercept factor decreased to 65.2% with a reduction of 26.4%. When the mirror slope error increases from 1 mrad to 3 mrad, the intercept factor will be significantly affected, coinciding with the slope error difference between spliced cylindrical mirrors and trough mirrors. Therefore, spliced cylindrical mirrors, instead of trough mirrors, can dramatically improve solar trough performance. Figure 2: Trough system intercept factor calculated using the ray-tracing method, cone optics method and SolTrace software at different receiver half-widths. For conventional trough solar collector systems, the ratio of focal length to trough width (f/w) and the ratio of the receiver to focal length (r/f) are critical parameters in the numerical design and optimization of the solar collector systems. In Figures 4 and 5, we calculated the net efficiency of the cylindrical mirror-spliced solar collector system with different f/w and r/f parameters as the incident angle changes. The solar collector's system net efficiency will change significantly at various incident angles due to the f/w and r/f impact. For example, when f/w was 0.78, the solar collector system efficiency was low when the incident angle was still low. After the incident angle was increased, the solar collector system efficiency began to be higher than the other types. When the incident angle is less than 0.9 rad, the solar trough collector system efficiency with an f/w of 0.87 performs best. After exceeding 0.9 rad, the solar trough collector efficiency with an f/w of approximately 0.78 is the highest. The net efficiency of the trough increases with r/f. When the r/f value is higher than a certain level, the benefits brought by the increase in concentration ratio are no longer advantageous over higher heat losses, and the net efficiency of the solar trough collector begins to decline. In Figure 6, the solar trough collector is optimized and the changes in the annual average net efficiency of the cylindrical mirror-spliced trough using a cavity receiver under different focal length ratios to half trough width (f/w) and half-width of receiver ratios to half trough width (r/w) parameters in the NS and EW tracking modes are calculated. In the NS and EW tracking modes, the optimal net efficiency of the cylindrical spliced mirror trough is 65.8% and 60.3%, respectively.