Analytical derivation of equivalent functional form of explicit J–V model of an illuminated solar cell from physics based implicit model

Recently a simple explicit model was introduced to represent theJ–Vcharacteristics of an illuminated solar cell with parasitic resistances and bias dependent photocurrent asj=(1−vm)/(1+αv), here the normalized voltage,vand normalized current densityjcan be represented asv=V/Vocandj=J/Jscrespectively, whereVocis the open circuit voltage andJscis the short circuit current density. The model is an equivalent rational function form and useful for design, characterization and calculation of maximum power point voltage. The model is intuitive and lacks the analytical support. In this paper an analytical derivation of the model is presented using the physics based implicitJ–Vequation.