In string photovoltaic (PV) systems, the power-voltage (P-V) characteristic under partial shading conditions (PSC) displays multiple peaks requiring global maximum power point (GMPP) tracking (GMPPT) algorithms to identify the PV array GMPP. Several GMPPT algorithms scan wide voltage tracks to detect the GMPP, even larger than a P-V curve full scan. Moreover, many algorithms have been tested only for simple PSC that lead to three well distinct peaks at most. This paper initially presents a trapezoidal area, called the maximum power trapezium (MPT), in the P-V plane that contains all possible GMPPs for any PSC. Using the MPT and information about the minimum voltage difference between adjacent local peaks, a GMPPT algorithm is proposed, which tracks the GMPP of a string PV array under any severe PSC reducing its voltage track and so its tracking time. Simulation and experimental results show the superior performance of the proposed algorithm, in comparison to the state-of-art algorithms, in terms of tracking time, energy loss, and total voltage track during the search for the GMPP.