A Maximum Power Point Tracking (MPPT) algorithm is proposed based on the assumption that a simplified three-parameter photodiode-based model can provide an excellent approximation of a PV module i - v curve around its maximum power point (MPP). Procedures to obtain the MPP coordinates and the three parameters of the approximated i - v curve from experimental online measurements, analytical and Newton-Raphson iterative calculations are thoroughly described. Initializing the model as well as optimizing it to operate faster by identifying only subsets of the model parameters provides excellent MPPT efficiency in both static and dynamical MPPT situations. The performance of the proposed algorithm has been verified in comparison with other well-known MPPT methods using the software-in-the-loop approach. Next, its performance has been evaluated by using the MATLAB-based hardware-in-the loop experimental setup that provides the required reproducibility of the different synthetic and real irradiance and temperature profiles considered.