Accurate altitude–azimuth tracking angle formulas for a heliostat with mirror–pivot offset and other fixed geometrical errors

Abstract

High precision tracking formulas were developed for a receiver-oriented toroidal heliostat with the standard spinning-elevation tracking geometry in a previous paper. The spinning-elevation tracking geometry included some mirror–pivot offset, orthogonal intersecting rotational axes and the elevation axis being parallel to the mirror surface plane. This paper analyzes the tracking accuracy of these standard spinning elevation tracking formulas to show that they are accurate with negligible tracking error. Hence, the mirror-surface-center normal obtained from these formulas is accurate for any dual-axis tracking heliostat. Then, the accurate mirror-surface-center normal information is used to determine general altitude–azimuth tracking angles for a heliostat with a mirror–pivot offset and other geometrical errors. The main geometrical errors in a typical altitude–azimuth tracking geometry are the azimuth axis tilt from the vertical, the non-orthogonality between the two heliostat rotational axes, the non-parallel degree between the mirror surface plane and the altitude axis, and the encoder reference errors. An actual heliostat in a solar field is used as an example to demonstrate use of the general altitude–azimuth tracking formulas, with the tracking angles for this heliostat on typical days graphically illustrated. The altitude–azimuth tracking angle formulas are further verified by an indoor laser-beam tracking test on a specially designed heliostat model.