Simulations of reflected sun beam traces over a target plane for an azimuth–elevation tracking heliostat with fixed geometric error sources

• The general tracking formula for an azimuth–elevation heliostat is re-rewritten.
• The mechanism of heliostat tracking error in the reflection direction is described.
• The simulation model for the heliostat tracking error trace over a day is given.
• This simulation model is powerful with many typical geometrical error parameters.
• Typical simulated error results are shown for typical heliostat tracking errors.

For a heliostat with geometric errors, the reflected central solar ray from the mirror surface center forms a curved error trace on the target plane during the day rather than staying fixed on one target point. A general azimuth–elevation tracking angle formula has been developed for a heliostat with a mirror-pivot offset and other typical geometric errors. This tracking angle formula is re-rewritten here as a series of easily solved expressions. This azimuth–elevation tracking angle formula is then used in a new complete geometric model of the sun-beam tracking errors for an azimuth–elevation tracking heliostat to simulate the sun beam tracking error trace on the target plane for a heliostat with fixed geometric errors. Here, the analysis is for a point sun and a point heliostat (or the heliostat considered as a small optical flat). The mirror surface center is defined as the orthogonal projection of the heliostat pivot on the mirror surface plane. The reflected sun-beam centre in the target plane is defined as the intersection of the mirror-surface-centre reflected central solar ray with the target plane. Due to a position tracking error in the target plane depending on the position and the orientation of the specific target plane, the position tracking error is further converted to the angular tracking error in the reflection direction to facilitate evaluation of the heliostat tracking performance. Simulations for the artificial #78 heliostat in the Beijing solar tower system on June 21st are shown to illustrate this heliostat tracking error model. This heliostat tracking error model can be used to reveal the effect of various geometrical errors in pedestal tilt etc. on the location of the beam at the target, and thus is useful in setting limits on the various geometrical errors. Essentially this paper allows one to estimate the offset of the reflected solar beam centre due to specific geometrical tracking errors, once the beam centre is computed by some other means. It also allows one to determine a limit on each error or set of errors which are allowable for a given purpose.