This research proposes a new method based on quaternion rotations to calculate the expected irradiance from the Sun to a given surface. The method uses quaternion rotations and translation vectors to model the motions of objects, both proper and relative to each other, that are relevant for irradiance. Using quaternion rotations, objects can be rotated along arbitrary axes in their coordinate system while preserving the orientation of the base coordinate system, and the origin of the base coordinate systems can be rotated relative to each other so that the transition between them can be solved by simple translation vectors.
An additional goal of the method is to be able to replace the equatorial coordinate system, which is currently widely used, and provide easy scalability to add additional quaternion rotation. The generated irradiance values were compared with data measured by a meteorological station during the validation process. In the case of clear skies, the comparison resulted in a high degree of correlation, which shows usually above 0.95 correlation factor, between the data. Based on the correlation, the generated expected irradiance data can be used as a reference for teaching neural networks that can discriminate weather-induced variations in the data measured by solar power inverters. As a result, it can increase the efficiency of fault detection algorithms that enable more stable energy production and indirectly reduce the necessity of fossil fuel use.