Theoretical derivation of super-ellipse model as approximation of physics-based implicit model for solar PV

Recently, it has been shown that the super-ellipse model can be used to represent the voltage-current characteristics of illuminated solar PV modules. Since the model is claimed to be empirical in nature, this paper demonstrates that the super-ellipse model can be derived as a theoretical approximation of the physics-based implicit model of solar PV. Further, the model parameters used in the super-ellipse model can be approximated to the physical parameters of the implicit model of solar PV. Here, it is also shown how the model parameters of the super-ellipse model vary with the ambient temperature and solar irradiance. The super-ellipse model is compared with other explicit models for different solar modules and shows satisfactory results in representing the voltage-current (current-density) curve of the solar PV module.