Method to determine the tracking angles of heliostats

The heliostats with two tracking axes are considered, and the method is presented to find the tracking angles for reflection of sun light to a given target. An important advantage of the method is that the tracking axes are not required to be orthogonal like in azimuth-elevation, tilt-roll or target-aligned heliostats. All of these configurations are covered in a unified way, and the presented solution is valid even for arbitrary orientation of tracking axes. The ability to have such a general solution is very valuable, because the orthogonality condition may not hold precisely for manufacturing reasons or due to degradation of heliostats. These deviations need to be corrected properly to achieve a high concentration of sun light. The offsets between tracking axes are also taken into account. However, the targeting problem for heliostats in this case becomes considerably different from the inverse kinematic problems for robotic arm manipulators. It is shown that the tracking angles can be found iteratively, and the convergence of results is very fast for a typical set of parameters used in solar thermal plants. To simplify the use of the method, a Python-library HelioK was developed, and it is demonstrated how to work with it in a Jupyter-notebook. To explain the kinematics of heliostats better, a 3D model of heliostat is provided, which was made and animated in an open-source 3D editor Blender. The main highlights of the method: • The tracking axes and the facet of heliostat can have an arbitrary orientation, and there can be offsets between them. • The tracking problem is solved both for targets attached to heliostat (local aiming) and for separated targets (global aiming). • The single-axis trackers are included as a limiting case.