A Novel Quaternion-based Method to Calculate Solar Irradiation on a Surface

The calculation of the solar irradiance is crucial in evaluating the performance of solar power plants and can ground their malfunction-analysis. In this paper, a new solar irradiance calculation method is presented to support these aims. The proposed method uses quaternions to describe the interaction between the Earth and the Sun regarding their motion to determine the angle of incidence of solar radiation on a given surface. The angular values obtained can be used to determine the estimated solar irradiance for a given surface using an arbitrary meteorological model. The method is highly scalable, thus the orientation and tilt of the surface can be varied by adding additional quaternion rotations. By changing the parameters and the meteorological model, it can be used to calculate the irradiance of a given surface of any object or device in the solar system. To show the accuracy of the proposed model, the generated data using the proposed method was compared with measured data from a meteorological station. The Pearson correlation coefficient showed a strong correlation (r=0.9613) between the measured and calculated data, confirming the proposed method's usefulness.