Polynomial Approximation of Celestial Coordinates to Find the Kinematic Properties of Electrotechnical Complexes Equipped with Sun Tracking Systems
DOI:
https://doi.org/10.14529/power190308Keywords:
two-dimensional surface, azimuth, zenith, zenith velocity, azimuth velocity, azimuth acceleration, zenith acceleration, azimuth jerk, zenith jerk, high order polynomials, SPAAbstract
The synthesis and study of any solar plants is associated with the need to identify regular features of the effector movement, the angular position of which is controlled in Euclidean space. This information can be
obtained by processing data on the angular position of the Sun in predetermined geographical coordinates. However, any algorithm for calculating the solar position is time-localized, which means it cannot be used to uniformly analyze the annual and daily cycle of the Sun. To solve this problem, this research applies a new principle of processing calculation results, which is staged as follows. Using NREL SPA the astronomical algorithm, which is based on non-linear trigonometric equations, construct two-dimensional surfaces of azimuths of zenith angles. By approximating these surfaces with high-order polynomials and differentiating these polynomials in time, find azimuthal surfaces from zenith angular velocities, accelerations, and jerks. The calculated coefficients of the polynomials are tabulated for future use in evaluative calculations for structural and parametric synthesis of electrical systems for tracking the Sun in a given geographical location. To test the agreement with available local-time online algorithms, this research uses the MIDC SPA Calculator. Comparing the results of polynomial approximation with the output of this online calculator shows a good coincidence of the results and a low level of errors.
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