## 3 Results
### Performance Comparison of Three Trough Systems
We evaluated the optical efficiency performance of the three solar collector systems on the spring equinox day and found that the optical efficiency of the cylindrical mirror-spliced system was reduced by 1.88% in comparison with the trough mirror system with tube receivers and 24.05% reduction when we switched to a trough mirror with cavity receivers. Clearly, when considering factors like reflectivity and transmittance, trough collector systems with cavity receivers are less affected. In Figure 8, we calculated the average annual net efficiency of these three trough solar collector systems using data from the 2020 calendar year under the north-south horizontal axis tracking mode. Due to the lower mirror slope error of the spliced cylindrical mirror system, spherical and coma aberrations were reduced to negligible levels through system adjustments, resulting in a higher intercept factor compared to conventional trough systems. The combination of cylindrical mirrors spliced with cavity receivers had the highest annual average net efficiency of about 59.24%, followed by the combination of troughs with tube receivers, with an annual average net efficiency of about 45.97%. From the calculation data, it is evident that the combination of trough mirrors and cavity receivers performed poorly in all cases, indicating that this is not a suitable combination. In our calculations, the cylindrical mirror-spliced trough solar system with cavity receivers showed excellent net efficiency due to lower mirror slope errors, lower incident angle error, and lower heat loss. However, in practical applications, compared to trough systems, cylindrical mirror-spliced systems require rotation and pointing toward the center, resulting in a lower intercept area for spliced cylindrical mirrors of the same width. For a solar system with 16 cylindrical mirrors, when using tube receivers, the actual intercept area is 96.97% due to the larger maximum rim angle. Therefore, in practical use, the impact on intercept area must be considered when using tube receivers. Meanwhile, the intercept area when using cavity receivers is about 99.33% of that of a trough solar system, with the impact being almost negligible. \begin{table}
\begin{tabular}{c l c c c c} \hline  & & **Spring** & **Summer** & **Winter** & **Annual** \\  & & **Equinox** & **Solstice** & **Solstice** & **Average** \\ \hline Cylindrical spliced & Intercept factor & 85.34\% & 88.31\% & 70.31\% & 82.57\% \\ + & Optical efficiency & 72.46\% & 75.05\% & 59.53\% & 70.09\% \\ Cavity receiver & Net efficiency & 63.00\% & 64.86\% & 47.27\% & 59.24\% \\ \hline Trough & Intercept factor & 61.05\% & 64.72\% & 46.16\% & 58.46\% \\ + & Optical efficiency & 51.92\% & 55.11\% & 39.13\% & 49.7\% \\ cavity receiver & Net efficiency & 42.37\% & 45.96\% & 27.91\% & 39.87\% \\ \hline Trough & Intercept factor & 92.04\% & 94.12\% & 79.21\% & 89.61\% \\ + & Optical efficiency & 73.85\% & 75.81\% & 62.7\% & 71.77\% \\ pipe receiver & Net efficiency & 48.89\% & 51.4\% & 33.87\% & 45.97\% \\ \hline \end{tabular}
\end{table} 
Table 3: Daily average intercept factor, optical efficiency and net efficiency of four parabolic rough solar systems at different times in 2020 under the north–south horizontal axis tracking mode, with slope error \(\theta_{slope}\) = 1 mrad (cylindrical mirror)/3 mrad (trough mirror).