Mathematical modeling of solar cells: novel approaches based on Special Trans Function Theory

In a mathematical sense, regardless of the equivalent circuit, solar cells are represented by nonlinear dependencies of current and voltage. First, this paper discusses novel mathematical formulations of the current–voltage dependencies of solar cells for single-diode, double-diode, and triple-diode models (SDM, DDM, and TDM, respectively). Second, for SDM, although the analytical solution expressed through Special Trans Function Theory (STFT) was known in the literature, in this paper, its applicability was checked for the first time, and a comparison was made with a literature approach. Third, for both DDM and TDM, novel original iterative procedures for current–voltage dependencies based on the application of the STFT have been proposed. Fourth, the accuracy and efficiency of all the proposed solutions were confirmed by observing two different, well-known solar cells. Furthermore, the applicability of the proposed solutions was confirmed by experimentally measuring the current‒voltage characteristics of solar cells under different climatic conditions. The proposed modeling approaches undoubtedly represent a new field for the application of STFTs.