Development of an analytical method and its quick algorithm to calculate the solar energy collected by a heliostat field in a year

In this paper, we firstly propose an analytical equation to calculate the energy collected by the heliostat field. A ray tracing method is developed based on the analytical equation. Then we introduce three approximations to reduce computation spending, and estimate the errors caused by these approximations. A fast and accurate algorithm is developed with the three approximations to calculate the energy collected by the heliostat field over a year. It was compared with the ray tracing results, which shows good consistency with them. With the method, the energy collected and efficiency of each heliostat in a year can be computed exactly and rapidly, the difference between the method and ray tracing method is less than 0.1% for the energy collected by a heliostat over a day. It needs only about 0.1% computation time used by ray tracing method to calculate the intercept factor of a heliostat at a moment, and 2.67 h to compute the annual collected energy of PS10 heliostat field by using one CPU of i3 processor when the time span for integration is 5 min and each heliostat is calculated.