An Explicit PV String Model Based on the Lambert $W$ Function and Simplified MPP Expressions for Operation Under Partial Shading

In this paper, a reformulation of the widely used one-diode model of the photovoltaic (PV) cell is introduced, employing the Lambert W function. This leads to an efficient PV string model, where the terminal voltage is expressed as an explicit function of the current, resulting in significantly reduced calculation times and improved robustness of simulation. The model is experimentally validated and then used for studying the operation of PV strings under partial shading conditions. Various shading patterns are investigated to outline the effect on the string I-V and P-V characteristics. Simplified formulae are then derived to calculate the maximum power points of a PV string operating under any number of irradiance levels, without resorting to detailed modeling and simulation. Both the explicit model and the simplified expressions are intended for application in shading loss and energy yield calculations.