Quaternion-based irradiance calculation method applicable to solar power plants energy production

Precise forecasting of renewable energy production is crucial for ensuring the reliable operation of the electricity grid. Developing more accurate predictive models and computational methodologies can enhance energy production and improve overall system stability. This paper introduces a novel computational approach utilizing quaternions to calculate expected solar irradiance on a given surface. The proposed method incorporates quaternion rotations and translation vectors to model the motion of astronomical objects, both independently and in relation to each other, a factor critical for accurate irradiance estimation. This approach has the potential to replace the commonly used equatorial coordinate system-based computations, offering significant improvements in adaptability, efficiency, and accuracy. The quaternion-based method provides a 9.9% improvement in average angle deviation and a 25.46% improvement in maximum angle deviation from the ground truth of the Sun’s angle of incidence, compared to the equatorial coordinate system-based model. This improvement translates to a 6.5905 kWh/m 2 discrepancy in clear sky annual irradiation between the two models, which is highly significant for solar power plants. Additionally, the proposed quaternion-based calculation is adaptable for estimating irradiation on any surface following an orbital trajectory, as well as on other planets. Moreover, the model is easily extendable to include other motions, thanks to the composition property of quaternions. The article presents the calculation methodologies of both models, performs a comparative analysis of the computational results, and presents the differences in computational efficiency between the two approaches. • Correction Factors Not Required : No correction factors needed for each GPS coordinate. • Applicability to Various Orbital Trajectories : Works with any orbital path, unlike equatorial-based method. • Extensibility for Additional Motions : Extends to handle additional motions like obliquity, nutation, and precession. • Reduced Computational Complexity : Fewer trigonometric functions mean faster, more stable calculations. • Improved Accuracy : Provides more accurate solar irradiation estimates than equatorial-based method.