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

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, 3days 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.