Polyharmonic splines for interpolation over sun path

Abstract

The optimization of solar tower power plants and other concentrating solar power (CSP) systems requires a customized approach for interpolation over the annual sun path. A good interpolation should predict accurately the efficiency of the system for different positions of the sun by using a small number of sampling points. This is very important to reduce the amount of simulations (e.g. ray tracing, cone optics, etc.), which are necessary to evaluate the annual performance for different CSP system configurations. From a mathematical point of view, the interpolation over sun path is an example of bivariate interpolation over a domain of irregular shape, and many methods are available to address it. In this paper, the advantages of meshless methods are investigated. The obtained results show that polyharmonic splines provide a good fit for the optical efficiency of the heliostat field of a solar tower system. The interpolated optical efficiency simplifies the calculation of annual energy reflected from the heliostat field to the receiver, and the result has an absolute error of 0.1% for less than 30 sampling points.