Modified Newton-Raphson Method to Achieve Variable Step Hill-Climbing Algorithm for Maximum Power Point Tracking

This work presents a derivation of the Newton-Raphson method, treated here as the Quasi-Newtonian (QN) algorithm. The QN has the same proprieties as the traditional Newton-Raphson method for extreme seeking, but due to a different manipulation of the Taylor series expansion, the method becomes a second-order method instead of a first-order method. Hence acquiring a fast convergence. That characteristic is explored in the performance of the Perturb and Observe algorithm for maximum power point tracking of photovoltaic systems. At this work, the QN is used not only to analyze the slope of the PxV curve of the photovoltaic system in order to choose the perturbation direction inserted by the Perturb and Observe algorithm (P&O) but to calculate the value of the perturbation as well. The simulation results have shown a fast-tracking of the maximum power point (MPP) and a small steady-state error when compared to the classical P&O algorithm.