Exact Solution to the Mean Value Theorem Applied to the Maximum Power Point Estimation

In this work, the exact solution to the mean value theorem problem applied to the maximum power point (MPP) calculation is presented; besides, an improvement to this solution is developed based on an expression of the MPP that depends on the optimal load and the characteristic parameters of the photovoltaic module. Both approximations depend only on the natural logarithm, avoiding the evaluation of the Lambert-W function. The validation of the approximations is performed by comparing them with real measurements and the numerical solution of the five-parameter single-diode model using the dataset from 11 commercial modules and six different technologies, as well as by comparing them with existing approximations in the literature.