Mathematical Analysis and Proof of Existence of The Photovoltaic Exponential Model

This paper derives the Photovoltaic Exponential Model (PVEM) from fundamental physical principles of solar cells and known boundary conditions, a numerically efficient model that approximates current-voltage (I-V) curves of photovoltaic (PV) modules using parameters readily available from the module’s manufacturer data sheet and standard test conditions. A demonstration of the PVEM’s utility is presented by obtaining an analytical approximation for the maximum power point (MPP) using the Lambert W function, which serves as a complement to traditional numerical methods. This solution is validated using 613 sets of I-V curves measured by Sandia National Laboratories as well as metadata from 20,000+ PV modules. Mean absolute V<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mp</inf> errors are less than 1% compared with experimental measurements.