Development of a mathematical model for optimizing a heliostat field layout using differential evolution method

Abstract

Summary In this study, differential evolution was employed to perform optimization of a heliostat field. A complete mathematical code was developed for this purpose, which generates a heliostat field and calculates the optimum spacing between heliostats through differential evolution optimization technique. The optimization was executed for two sets of two cases and compared with an un‐optimized case. In the first case, only the optical performance was optimized, whereas in the second case, the normalized ratio of the optical performance to the land area covered by the heliostat field was maximized. In the first set of cases, the extra security distance between the heliostats was neglected, whereas in the second set of cases, the extra security distance was taken into account. To apply and examine the application of the optimization algorithm developed, 3 days of the year were selected: March 21, June 21, and December 21, considering Dhahran, Saudi Arabia as an illustrative example. For June 21, when the extra security distance between the heliostats is neglected, the optical efficiency of the un‐optimized case was 0.6026, while for the first optimized case, it was 0.6395, and for the second optimized case, it was 0.6033. However, when the extra security distance was considered, the optical efficiency of the un‐optimized case was 0.6167; while for the first optimized case, it was 0.6241, and for the second optimized case, it was 0.6167. Similar observations were realized for the other cases selected. Copyright © 2015 John Wiley & Sons, Ltd.

Investigation the Integration of Heliostat Solar Receiver to Gas and Combined Cycles by Energy, Exergy, and Economic Point of Views

“…Here, η re f denotes the efficiency of the mirror reflectivity rate that is assumed to be 95% in this study [41]. η s&b is the efficiency of shadowing and blocking, η at represents the efficiency of atmospheric attenuation, η spillage defines the efficiency of spillage, and η cos is the cosine efficiency.…”

“…The atmospheric attenuation efficiency depends on two parameters, weather conditions and distance of heliostat and the receiver. For a distance more than 1000 m following equation can be expressed [41]:…”

Multi‐objective optimization of solar‐aided coal‐fired power generation system under off‐design work conditions

“…η ref is the product of mirror nominal reflection efficiency and nominal cleanliness, and can be calculated by Equation (5). [29][30][31] η cos is caused by the included angle of incident ray and the vector normal to the heliostat surface, which is calculated by Equation (6). 25,30,31 η atm is directly related to the distance between the heliostat center and the receiver, and can be calculated by Equation (7).…”

“…[29][30][31] η cos is caused by the included angle of incident ray and the vector normal to the heliostat surface, which is calculated by Equation (6). 25,30,31 η atm is directly related to the distance between the heliostat center and the receiver, and can be calculated by Equation (7). 25,32 η int accounts for the fraction of the reflected rays that hit the target, and is calculated by the HFLCAL model 30 of Equation (8).…”

“…The detailed design parameters of the reference heliostat field are available in Ref. 31 The results showed that, the absolute value of the maximum relative error of the heliostat field efficiency was 0.526%. The receiver efficiency model used in this paper is verified by the final test and evaluation results from the Solar Two project 52 and the validation results are shown in Table 1.…”