DEVELOPMENT OF A COMPLEX MATHEMATICAL MODEL OF THE SOLAR TRACKER SPATIAL POSITIONING SYSTEM AS A PARALLEL STRUCTURE MECHANISM

Abstract

The paper presents the results of a study aimed at improving the accuracy and efficiency of solar tracking systems through the development of a complex mathematical model of a solar tracker mechanism as a spatial positioning system with two degrees of freedom. The relevance of this work is determined by the increasing requirements for the efficiency of photovoltaic installations, where even minor orientation errors cause significant energy losses. Unlike traditional simplified approaches, the proposed model considers the real kinematic behavior of the mechanism, including the displacement of rotation axes, backlash in joints, distances between rotation centers, elastic deformations of structural elements, and asymmetry of the panel mass. Based on analytical equations of direct and inverse kinematics, a mathematical model has been developed that describes the relationship between the control angles of the actuators and the spatial orientation of the panel. To compensate for geometric and structural errors, a correction module has been designed implementing a two-level approach: geometric compensation (considering the displacement of the axes) and functional adaptation (adjusting parameters based on experimental calibration). The model has been implemented as a computational algorithm capable of real-time correction using the Newton–Raphson method for inverse kinematics. Simulation results confirmed that the proposed approach provides a stable orientation accuracy of up to ±0.2°, improving energy collection efficiency by 3–5% compared to standard systems without compensation. The developed method demonstrates adaptability to mechanical deviations and environmental variations, ensuring long-term precision tracking. The obtained results can be used to design hybrid tracking systems that combine analytical modeling and sensor feedback, as well as to create intelligent next-generation solar trackers capable of self-calibration and real-time correction of mechanical and operational deviations. The proposed mathematical and algorithmic framework forms a foundation for developing highly efficient, adaptive, and reliable solar tracking mechanisms for autonomous photovoltaic systems.