## 3 Results
### Performance Comparison of Three Trough Systems  
In this paper, we considered three trough solar collector systems using tube receivers and cavity receivers, respectively. The cavity receiver radius is set to match that of the tube receiver. We combined different receivers and mirror types to calculate three different trough collector systems. The manufacturing of conventional trough solar collectors with mirrors is more challenging than that of cylindrical mirror-spliced solar collectors. Under the same manufacturing conditions, the slope error of a trough mirror can be three times greater than that of a cylindrical mirror. Given that the slope error of cylindrical mirrors is lower than that of trough mirrors under the same conditions, we set the cylindrical mirror-spliced slope error to 1 mrad and the conventional trough mirror slope error to 3 mrad, with other system parameters as shown in Table 1.  
Table 3 shows the daily average and annual average of the intercept factor, the optical efficiency, and the net efficiency of the three trough solar collector systems during the spring equinox day, summer solstice day, and winter solstice day in the north-south tracking mode. We observed that reducing the mirror slope error brought significant performance improvements with all other parameters unchanged. The trough solar collector systems using trough mirrors performed significantly worse than those using segmented cylindrical mirrors, with a system performance reduction of 28.00%. Therefore, using spliced cylindrical mirrors can significantly improve system performance. The trough solar collector system with cavity receivers has a lower intercept rate than that of a trough collector with a tube receiver of the same aperture width and vacuum tube diameter. On the spring equinox day, the intercept factor of the trough system with the tube receiver was 92.04%, and when we switched it to a cavity receiver, the intercept factor \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Spring Equinox**} & \multicolumn{1}{c}{**Summer**} & \multicolumn{1}{c}{**Winter Solstice**} & \multicolumn{1}{c}{**Annual Average**} \\ \hline Net efficiency & 67.26\% & 68.17\% & 58.53\% & 65.52\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Under the NS tracking mode, the daily average net efficiency of a cylindrical mirror-spliced trough system with a cavity receiver at different times in the 2020 calendar year with optimized parameters: focal length = 4.5 m, half-width of trough = 4 m, half-width of receiver = 0.07 m.  
Figure 7: Under north–south tracking mode, the annual average net efficiency of a cylindrical mirror-spliced trough system with a cavity receiver at optimized parameters: focal length = 4.5 m, half-width of trough = 4 m, half-width of receiver = 0.07 m.  
dropped to 61.05%, resulting in a reduction of 33.67%, and when the trough mirror system was replaced with a cylindrical mirror-spliced system, the intercept dropped to 88.34%, resulting in a reduction of 4.00%. However, considering that cavity receivers have lower heat loss and do not require accounting for the receiver's absorptivity, systems with cavity receivers typically have better net efficiency. In NS tracking systems, among the three combinations, the trough solar collector system with cylindrical mirrors spliced with cavity receivers showed the best net efficiency. On the spring equinox day, its net efficiency was as high as 63.00%. When switched to a trough mirror with tube receivers, the net efficiency dropped to 48.89%, with a reduction of 22.39%, and when switched to trough mirrors with cavity receivers, the net efficiency dropped to 42.37%, with a reduction of 41.52%. The trough solar collector systems with tube receivers require a larger rim angle, which makes them more affected by the incident angle effect, leading to lower system mirror reflectivity and thus lower performance.