# Performance Prediction and Optimization of Multi-Mirror Combined Solar Dish Collector
###### Abstract  
An analytical method to calculate and optimize the performance of a multi-mirror combined solar dish collector is proposed in this work. It is based on the method of directly calculating the optical efficiency of a reflecting point, which can consider the influence of many factors. The distribution of the reflected solar intensity is obtained by the convolution of the actual solar intensity distribution and Gaussian distribution of the optical error. Then, the optical efficiency for a single mirror is calculated through integration over the total area of the mirror, and the method is validated by the SoITrace code. It is a rather quick method that reduces the amount of calculation and keeps high accuracy. The heat loss per unit area for the cavity receiver is assumed to be constant at a definite operation temperature for performance analysis and optimization. Taking a 62.25 m\({}^{2}\) combined dish system with 249 square spherical mirrors as an example, the effects of system focal length, open radius of receiver, optical error, and focal length of the mirror on the system intercept factor and efficiency are studied. An optimization model is developed for maximizing the annual average net thermal efficiency. If the mirrors used have the same focal length for reducing the manufacture cost, when the optical error is 2 mrad, the net thermal efficiency and the intercept factor of the optimized system are 85.87% and 98.60%, respectively, while the concentration ratio is about 2000.  
solar dish collector; multi-mirror; spherical mirror; optical performance; optimization 2022122347 202212347 202212347 202212347 202212347 202212347 202212347 202212347 2022212  
with an output power of 90 kW and optical efficiency of about 88% [5]. The Australian National University (ANU) designed and produced a 400 m\({}^{2}\) combined dish system named 'SG3\({}^{\prime}\) in 2003 that consists of identical multi-triangle spherical mirror to reduce the cost of production [6]. A similar system was subsequently constructed at the Ben Gurion University in Israel [7]. Later, in 2011, ANU designed and built a 500 m\({}^{2}\) multi-mirror combined system [2]. It contained 380 identical 1.17 m \(\times\) 1.17 m spherical mirrors with a focal length of 13.4 m. In the same year, [PERSON] [8] proposed a multi-mirror combined technology that uses multiple flat mirrors to form a dish shape. In 2012, [PERSON] [9] designed an 8.15 kW combined dish system consisting of 164 flat mirrors, and analyzed the effects of the mirror size and position on optical performance. There are three types of method for the optical performance simulation of solar dish concentrators in the literature. The first method is the ray tracing method which is a microscopic method and can be applied in most cases, where it can provide an enormous amount of numerical information. It is easy to code and has been developed by many researchers [10; 11; 12], but it obscures functional relationships and is time-consuming, as pointed out by [PERSON] and [PERSON] [13]. The second method is to first calculate the solar energy flux at the receiver surface, and then the total intercepted energy is obtained through integration; many functions have been proposed to predict the flux at the receiver. The first function for calculating the radiation flux of the solar dish receiver was proposed by [PERSON] and [PERSON] [14], which is based on the assumption that the solar radiation source is a uniform disc. Later, some similar distribution equations were proposed by [PERSON] [15], [PERSON], and [PERSON] [16] with the same assumption. In fact, it is different from a real solar disc because of the effect of solar limb darkening [17]. [PERSON] [18] considered the brightness distribution of the solar disc, but ignored the solar halo and the optical error of the concentrator. [PERSON] and [PERSON] [19] considered the elliptical distribution of the optical error to propose a general function for a solar concentrator which was applied in the Helios program.