Analytical Derivation of the Closed-Form Power Law $J$ –$V$ Model of an Illuminated Solar Cell From the Physics Based Implicit Model

Recently, we introduced a simple power law model (PLM) to represent the J-V characteristics of an illuminated solar cell with parasitic resistances. The model is useful for design, characterization, and parameter extraction of solar cells and modules. The form of this model was arrived at by intuition, and its applicability to a few moderate-quality cells with bias-independent photocurrent was demonstrated by curve fitting to theoretical and measured J-V data. In this paper, we present an analytical derivation of the closed-form PLM from a physics-based implicit J-V equation having a bias-dependent photocurrent and an exponential term. Apart from providing a theoretical basis for the hitherto empirical PLM, the derivation expands the scope of this model significantly to cover poor- to high-quality cells with different physical phenomena and provide new insights.