# Performance Prediction and Optimization of Multi-Mirror Combined Solar Dish Collector
###### Abstract
It was further developed in the CIRCE program [20] for performance analysis of various solar dish concentrating collectors. However, both of these functions for calculation of the radiation flux at the receiver surface are too complicated to integrate analytically; thus, a numerical method is often preferred. On the basis of the Gaussian brightness distribution approximation, [PERSON] and [PERSON] [13] presented an angular acceptance function for both flat and sphere receivers to calculate the optical efficiency. [PERSON] and [PERSON] [21] reported a different equation which was also based on the Gauss approximation. The third method is to directly calculate the optical efficiency of a paraboloid dish solar concentrator with a cavity [22] or sphere [23] receiver solar dish system, which is fast while ensuring accuracy. The optical performance of a solar dish system is affected by many factors, such as geometric concentration ratio, rim angle, focal length, and optical error of mirrors [22]. [PERSON] and [PERSON] [24] introduced that the optimization of system performance is closely related to the rim angle of the system, receiver size, and concentration ratio. There have been many studies on the performance analysis and optimization of solar parabolic dish concentrators for typical single-mirror systems, but there is little research on combined dish systems except for the solar trace. In the performance analysis of multi-mirror combined solar dish systems, [PERSON] et al. [25] applied a ray tracing method to predict the flux density distribution of a 400 m\({}^{2}\) solar combined dish system. Using this method, the optical performance of 54 triangular spherical mirrors in the system was further analyzed in 2003 [6]. [PERSON] et al. [2] applied the ray tracing method to evaluate the optical performance of a 500 m\({}^{2}\) square spherical multi-mirror combined dish concentrating system and preliminarily demonstrated that the optimized combined dish system can achieve a geometric concentration ratio of more than 2000. [PERSON] [26] developed a design and optimization analysis of a combined dish system containing 16 mirrors. They calculated the flux density distribution of the receiver under different optical errors and focal plane radii using the Monte Carlo ray tracing method. A similar analysis was also performed for this combined system [27]. [PERSON] et al. [28] conducted a study on a combined dish system consisting of 450 square mirrors of 0.1 m \(\times\) 0.1 m, and used TracePro software to analyze the flux density distribution of two concentrator surfaces. Currently, ray tracing is the main method to study the optical performance of a combined dish system. However, this method requires tracking a large number of rays to obtain high accuracy, which is very time-consuming and difficult to use for system optimization; accordingly, only some specific designs have been studied. In this work, using the previously developed method of directly calculating the optical efficiency of concentrators [29], a new model for the optical efficiency calculation of a combined dish system is first proposed, and the accuracy of this method is validated by the SolTrace code. Then, the optical performance of a combined solar dish system composed of 249 spherical mirrors is studied using the method. The effects of the receiver radius, system focal length, optical error, and mirror focal length on the optical performance of the combined disc system are analyzed. Lastly, in order to maximize the annual average net thermal efficiency, an optimization model is developed, and the optimal design parameters of the combined dish system are calculated.