Photovoltaic (PV) grid support functionality (frequency support) can be accomplished with the aid of flexible power point tracking (FPPT) technology. However, the convergence rate of FPPT algorithms needs to be fast, to provide grid support under transients. To fulfil this purpose, a Newton's method-based (NM-B) FPPT algorithm is proposed in this paper that offers quadratic convergence, which is a higher convergence rate compared to the existing methods. Moreover, the search algorithm requires only a single initialization point, thus eliminating the difficulty of setting up the search boundary as in the case of the binary search-based and secant method-based (SM-B) FPPT algorithms. Simulation validation is performed for the proposed NM-B FPPT algorithm and the results are compared with the SM-B FPPT algorithm.