# Performance Prediction and Optimization of Multi-Mirror Combined Solar Dish Collector
## 4 Discussion  
In this work, a model for the direct calculation of optical efficiency for the optical performance of a combined dish concentrated solar system with a cavity receiver was first proposed and then validated with SolTrace. In this method, the optical efficiency of each reflection point on the mirror is first calculated, and then the total optical efficiency is obtained by integrating the whole mirror. Spherical mirrors, as well as flat mirrors or other curved mirrors, in a combined dish system can be analyzed using the proposed method, but the spherical mirror combined dish system was analyzed as an example in this work. Each mirror is regarded as a heliostat; therefore, the present method for the combined solar dish system is rather similar to that of the solar tower system, but the receiver is a cavity with a circular opening, unlike the rectangular opening of the solar tower system. This leads to more computation than the solar tower system because numerical integration is needed for integration to the azimuth angle, which is analytically solved in the heliostat of the solar tower system. However, it still needs only 3% of the time of the SolTrace code. The average and maximum relative difference between the present integration method and the SolTrace code is only 0.51% and 1.14%, respectively. The present results indicates that the present integration methods for calculating the optical performance of the combined solar dish system have good precision and higher computation speed than that of the SolTrace method. The optical performance of a combined solar dish system composed of 249 spherical mirrors was studied using this model. The effects of receiver radius, system focal length, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Optical Error** **(mrad)** & **Radius of Receiver (m)** & **Focal Length of System (m)** & **Optimal Net Thermal Efficiency** & **Intercept Factor** \\ \hline
1 & 0.09 & 7.5 & 0.8630 & 0.9892 \\
2 & 0.10 & 7 & 0.8605 & 0.9881 \\
3 & 0.11 & 6.5 & 0.8583 & 0.9898 \\
4 & 0.12 & 6 & 0.8526 & 0.9857 \\
5 & 0.14 & 6 & 0.8482 & 0.9861 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The optimal annual net thermal efficiency and optimized parameters of the multi-dish system for optical errors ranging from 1–5 mrad; each focus length of the mirror is equal to the distance from the receiver. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Optical Error** **(mrad)** & **Radius of Receiver (m)** & **Focal Length of Mirror (m)** & **Net Thermal Efficiency** & **Intercept Factor** \\ \hline
1 & 0.09 & 8.5 & 0.8620 & 0.9880 \\
2 & 0.10 & 8 & 0.8587 & 0.9860 \\
3 & 0.11 & 8 & 0.8570 & 0.9883 \\
4 & 0.12 & 7.5 & 0.8512 & 0.9841 \\
5 & 0.14 & 7.5 & 0.8479 & 0.9857 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The annual thermal efficiency under optimal design with the same focus length of the mirror. optical error, and mirror focal length on the optical performance of the combined disc system were analyzed. Previously, the flux distribution at the receiver surface was studied under different designs for the combined solar dish system using the solar trace method. [PERSON] et al. [6] studied the combined dish system with a triangle spherical mirror, whereas [PERSON] et al. [26] studied the combined dish system with a circular parabolic mirror. However, they gave little information on the intercept factor. The optical performance of a combined dish system is seldom studied. The present study provides rather complete information on the optical performance of a combined dish system. [PERSON] et al. [6] showed that the radius of the receiver for 90% interception of the solar power increases if the optical error of the mirror increases. The present paper indicates that the intercept factor of the system increases if the radius increases or if the optical error of the mirror decreases. Hence, the present results are rather consistent with those of the [PERSON], but give more complete information.